text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
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{"url":"https:\/\/codegolf.meta.stackexchange.com\/questions\/8030\/hey-stack-exchange-how-are-we-doing","text":"# Hey Stack Exchange, how are we doing?\n\nThe last time we heard from a Stack Exchange community manager was in March of 2014, when Grace Note came to talk to us about the progress we've made as a site. That was back when was a thing, and the community's response to the news wasn't particularly positive given how code trolling had affected the site's overall quality.\n\nNow here we are, almost 2 years after Grace Note gave us that update. is off topic, dead, and buried. Our site stats, regardless of how much they actually matter, are excellent (as FlagAsSpam so nicely laid out for us here), save for the average number of questions we get per day. Our rate falls short of the expected 10, but sites have graduated with less.\n\nWhether or not we expect or even want to graduate, it would be nice to have some feedback from the folks at Stack Exchange on our progress and their take on us as part of the greater SE ecosystem.\n\nSo hey, SE, how are we doing? Notice us, senpai.\n\nUpdate: Here we are, over a month later, and we've been averaging over 10 questions per day for a while now! As of this writing, we're at 10.8 Q\/day.\n\n\u2022 Thankyou for posting this. I have been wondering the same thing. +1, and eagerly awaiting an answer. \u2013\u00a0DJMcMayhem Jan 10 '16 at 2:34\n\u2022 Wow, you read my mind! I was wondering the same thing too. But... how will we get Stack Exchange to notice our request, though? Grace Note last came here 3 months ago! \u2013\u00a0Hipe99 Jan 11 '16 at 5:20\n\u2022 @Hipe99 The community managers at Stack Exchange peruse the various site metas. Grace Note or another community manager should see this... eventually. \u2013\u00a0Alex A. Jan 11 '16 at 5:23\n\u2022 @AlexA. They'll see it soon\u2122 \u2013\u00a0Mego Jan 11 '16 at 7:43\n\u2022 @AlexA. Would it be inappropriate to post this to the main meta? \u2013\u00a0DJMcMayhem Jan 11 '16 at 13:49\n\u2022 @DJMcMayhem Yep. This is definitely a question for our meta since it's specific to this site. \u2013\u00a0Alex A. Jan 11 '16 at 15:09\n\u2022 ... crickets ... tumbleweed ... \u2013\u00a0Digital Trauma Jan 14 '16 at 17:17\n\u2022 Maybe we should poke it...? \u2013\u00a0ETHproductions Jan 14 '16 at 20:55\n\u2022 Admin is typing... \u2013\u00a0flawr Jan 14 '16 at 21:23\n\u2022 7.9 questions a day means you all are getting close. I'm guessing (at this rate) you'll get an election later in the year and a design sometime later. Not much else to say, really. \u2013\u00a0Jon Ericson Jan 15 '16 at 4:11\n\u2022 @JonEricson I'm an outsider to PPCG, so I don't have a substantial investment, but it seems to me that the 10 Q\/d threshold that's set for the more SE-traditional Q&A sites is inappropriately high for PPCG. I'm most active to date on Chem.SE; people go there because they don't know things, and there are a lot of things that a lot of people don't know. Here, though, people only post \"questions\" when they've actively thought up something (hopefully) clever. 10 coding challenges per day is a much higher bar than 10 questions per day. Graduate them, already! \u2013\u00a0hBy2Py Jan 28 '16 at 3:48\n\u2022 @JonEricson Hey, guess what! We're above 10 Q\/day and holding steady! :D \u2013\u00a0Alex A. Feb 21 '16 at 20:26\n\n## 1 Answer\n\nSo I guess senpai noticed us. See below for a special note from Grace Note.\n\n# Congratulations, you're graduating!\n\n\u2022 I'll accept my own answer because \u00af\\_(\u30c4)_\/\u00af \u2013\u00a0Alex A. Feb 23 '16 at 18:51","date":"2019-10-24 02:16:37","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.25250160694122314, \"perplexity\": 2606.772222466647}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570987838289.72\/warc\/CC-MAIN-20191024012613-20191024040113-00197.warc.gz\"}"} | null | null |
--[[
FILE THEME SONG:
use this model: models/spacebuild/nova/dronegun1.mdl
--todo:
check manhack sounds. those are good zaps
--scanner and roller mine too
]]
AddCSLuaFile()
SWEP.PrintName = "3p9: Nightfire-Samurai"
SWEP.Author = "Sky"
SWEP.Purpose = "Directed Energy Beam Weapon" --
SWEP.Instructions = "Primary Fire to shoot laser! Secondary Fire for a charging shot!"
SWEP.Category = "3P8"
SWEP.Spawnable = true
SWEP.AdminSpawnable = true
SWEP.Weight = 10 --
SWEP.Primary.ClipSize = 10
SWEP.Primary.DefaultClip = 1
SWEP.Primary.Automatic = false
SWEP.Primary.Ammo = "GaussEnergy"
SWEP.Primary.Delay = 1
SWEP.Primary.Recoil = 7
SWEP.Primary.TakeAmmo = 1
SWEP.Primary.Spread = 0.00
SWEP.Secondary.ClipSize = -1
SWEP.Secondary.DefaultClip = -1
SWEP.Secondary.Automatic = false
SWEP.Secondary.Ammo = "none"
SWEP.HoldType = "shotgun"
SWEP.ViewModelFOV = 70
SWEP.ViewModelFlip = false
SWEP.UseHands = true
SWEP.ViewModel = "models/weapons/c_smg1.mdl"
SWEP.WorldModel = "models/weapons/ar2_grenade.mdl"
SWEP.ShowViewModel = true
SWEP.ShowWorldModel = true
SWEP.ViewModelBoneMods = {
["ValveBiped.base"] = { scale = Vector(0.009, 0.009, 0.009), pos = Vector(0, 0, 0), angle = Angle(0, 0, 0) }
}
SWEP.VElements = {
["trigger"] = { type = "Model", model = "models/props_combine/combinecamera001.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(-0.5, 2, -0.5), angle = Angle(26.882, -1.17, 0), size = Vector(0.5, 0.5, 0.5), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["guard+"] = { type = "Model", model = "models/props_combine/railing_128.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(7, 2.5, -4.676), angle = Angle(0, -10.52, 180), size = Vector(0.075, 0.075, 0.075), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["top+"] = { type = "Model", model = "models/props_combine/combine_fence01b.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(-0.519, 1.557, -6), angle = Angle(3.055, 80.649, 90), size = Vector(0.1, 0.1, 0.1), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["stock"] = { type = "Model", model = "models/props_combine/combine_train02a.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(-3.636, 1.169, -3.636), angle = Angle(176.494, 81, 1), size = Vector(0.017, 0.017, 0.017), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["guard"] = { type = "Model", model = "models/props_combine/railing_128.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(7, 3.5, -4.676), angle = Angle(180, -10.52, 0), size = Vector(0.075, 0.075, 0.075), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["top"] = { type = "Model", model = "models/props_combine/combine_fence01a.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(-1.558, 1.557, -2.597), angle = Angle(3.506, 80.649, 90), size = Vector(0.1, 0.1, 0.1), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} }
}
SWEP.WElements = {
["trigger"] = { type = "Model", model = "models/props_combine/combinecamera001.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(-2.597, 1.299, -0.519), angle = Angle(17, 0, 0), size = Vector(0.5, 0.5, 0.5), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["guard+"] = { type = "Model", model = "models/props_combine/railing_128.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(15, 1.7, -6.5), angle = Angle(176.5, 0, 0), size = Vector(0.1, 0.1, 0.1), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["top+"] = { type = "Model", model = "models/props_combine/combine_fence01b.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(9.77, 1, -8), angle = Angle(0, 90, 93), size = Vector(0.1, 0.1, 0.1), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["stock"] = { type = "Model", model = "models/props_combine/combine_train02a.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(4, 1, -5.5), angle = Angle(180, 90, -3), size = Vector(0.018, 0.018, 0.018), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["guard"] = { type = "Model", model = "models/props_combine/railing_128.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(15, 0.6, -6.5), angle = Angle(-3.5, 0, 180), size = Vector(0.1, 0.1, 0.1), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} },
["top"] = { type = "Model", model = "models/props_combine/combine_fence01a.mdl", bone = "ValveBiped.Bip01_R_Hand", rel = "", pos = Vector(10, 1, -3.5), angle = Angle(0, 90, 95), size = Vector(0.1, 0.1, 0.1), color = Color(255, 255, 255, 255), surpresslightning = false, material = "", skin = 0, bodygroup = {} }
}
function SWEP:PrimaryAttack()
if (!self:CanPrimaryAttack()) then return end
local bullet = {}
bullet.Num = 1
bullet.Src = self.Owner:GetShootPos() + (self.Owner:GetAimVector())
bullet.Dir = self.Owner:GetAimVector()
bullet.Spread = Vector( self.Primary.Spread, self.Primary.Spread, self.Primary.Spread)
bullet.Tracer = 1
--laser beam effect here
bullet.TracerName = "ToolTracer" --cball_explode for when it hits, or HelicopterMegaBomb. could place with PhyscannonImpact for orange laser
bullet.Force = 100
bullet.Damage = 100
bullet.AmmoType = self.Primary.Ammo
local rnda = self.Primary.Recoil * -1
local rndb = self.Primary.Recoil * math.random(-1, 1)
self:ShootEffects()
self.Owner:FireBullets( bullet )
self.Owner:ViewPunch( Angle( rnda,rndb,rnda ) )
--subtract 1 hp
self.Owner:SetHealth(self.Owner:Health()+1)
--take 1 ammo
self:TakePrimaryAmmo(self.Primary.TakeAmmo)
self.Owner:SetAnimation(PLAYER_ATTACK1)
--delay
self:SetNextPrimaryFire(CurTime() + self.Primary.Delay)
--local gunSounds = {"ambient/levels/citadel/weapon_disintegrate2.wav"} --"ambient/levels/labs/electric_explosion1.wav", "ambient/levels/citadel/weapon_disintegrate3.wav"
--self.Weapon:EmitSound(gunSounds[math.random(#gunSounds)])
self.Weapon:EmitSound("ambient/levels/citadel/weapon_disintegrate2.wav")
--hit effects
local ply = self.Owner
local shootpos = ply:GetShootPos()
local endshootpos = shootpos + ply:GetAimVector() * 10000
local tmin = Vector(1,1,1)*-10
local tmax = Vector(1,1,1)*10
local tr = util.TraceHull( {
start = shootpos,
endpos = endshootpos,
filter = ply,
mins = tmin,
maxs = tmax,
mask = MASK_SHOT_HULL
} )
if not IsValid(tr.Entity) then
tr = util.TraceLine({
start = shootpos,
endpos = endshootpos,
filter = ply,
mask = MASK_SHOT_HULL
})
end
local vPoint = tr.HitPos
local effectdata = EffectData()
effectdata:SetOrigin( vPoint )
util.Effect( "cball_explode", effectdata )
end
function SWEP:SecondaryAttack()
--charged attack
--charging sound
--items/suitcharge1.wav
--fire sound
--ambient/levels/labs/electric_explosion3.wav
--ambient/levels/labs/electric_explosion4.wav
end
--saved as rifle in SCK :\ it's accurate
--[[/********************************************************
SWEP Construction Kit base code
Created by Clavus
Available for public use, thread at:
facepunch.com/threads/1032378
DESCRIPTION:
This script is meant for experienced scripters
that KNOW WHAT THEY ARE DOING. Don't come to me
with basic Lua questions.
Just copy into your SWEP or SWEP base of choice
and merge with your own code.
The SWEP.VElements, SWEP.WElements and
SWEP.ViewModelBoneMods tables are all optional
and only have to be visible to the client.
********************************************************/--]]
function SWEP:Initialize()
-- other initialize code goes here
self:SetWeaponHoldType(self.HoldType)
if SERVER then
local timer_name = "samurai_regen_"..self:EntIndex()
timer.Create(timer_name,10,0, function()
if IsValid(self) then
if self:Clip1()<self.Primary.ClipSize then
self:SetClip1(self:Clip1()+1)
end
else
timer.Destroy(timer_name)
end
end)
end
if CLIENT then
-- Create a new table for every weapon instance
self.VElements = table.FullCopy( self.VElements )
self.WElements = table.FullCopy( self.WElements )
self.ViewModelBoneMods = table.FullCopy( self.ViewModelBoneMods )
self:CreateModels(self.VElements) -- create viewmodels
self:CreateModels(self.WElements) -- create worldmodels
-- init view model bone build function
if IsValid(self.Owner) then
local vm = self.Owner:GetViewModel()
if IsValid(vm) then
self:ResetBonePositions(vm)
-- Init viewmodel visibility
if (self.ShowViewModel == nil or self.ShowViewModel) then
vm:SetColor(Color(255,255,255,255))
else
-- we set the alpha to 1 instead of 0 because else ViewModelDrawn stops being called
vm:SetColor(Color(255,255,255,1))
-- ^ stopped working in GMod 13 because you have to do Entity:SetRenderMode(1) for translucency to kick in
-- however for some reason the view model resets to render mode 0 every frame so we just apply a debug material to prevent it from drawing
vm:SetMaterial("Debug/hsv")
end
end
end
end
end
function SWEP:Holster()
if CLIENT and IsValid(self.Owner) then
local vm = self.Owner:GetViewModel()
if IsValid(vm) then
self:ResetBonePositions(vm)
end
end
return true
end
function SWEP:OnRemove()
self:Holster()
end
if CLIENT then
SWEP.vRenderOrder = nil
function SWEP:ViewModelDrawn()
local vm = self.Owner:GetViewModel()
if !IsValid(vm) then return end
if (!self.VElements) then return end
self:UpdateBonePositions(vm)
if (!self.vRenderOrder) then
-- we build a render order because sprites need to be drawn after models
self.vRenderOrder = {}
for k, v in pairs( self.VElements ) do
if (v.type == "Model") then
table.insert(self.vRenderOrder, 1, k)
elseif (v.type == "Sprite" or v.type == "Quad") then
table.insert(self.vRenderOrder, k)
end
end
end
for k, name in ipairs( self.vRenderOrder ) do
local v = self.VElements[name]
if (!v) then self.vRenderOrder = nil break end
if (v.hide) then continue end
local model = v.modelEnt
local sprite = v.spriteMaterial
if (!v.bone) then continue end
local pos, ang = self:GetBoneOrientation( self.VElements, v, vm )
if (!pos) then continue end
if (v.type == "Model" and IsValid(model)) then
model:SetPos(pos + ang:Forward() * v.pos.x + ang:Right() * v.pos.y + ang:Up() * v.pos.z )
ang:RotateAroundAxis(ang:Up(), v.angle.y)
ang:RotateAroundAxis(ang:Right(), v.angle.p)
ang:RotateAroundAxis(ang:Forward(), v.angle.r)
model:SetAngles(ang)
--model:SetModelScale(v.size)
local matrix = Matrix()
matrix:Scale(v.size)
model:EnableMatrix( "RenderMultiply", matrix )
if (v.material == "") then
model:SetMaterial("")
elseif (model:GetMaterial() != v.material) then
model:SetMaterial( v.material )
end
if (v.skin and v.skin != model:GetSkin()) then
model:SetSkin(v.skin)
end
if (v.bodygroup) then
for k, v in pairs( v.bodygroup ) do
if (model:GetBodygroup(k) != v) then
model:SetBodygroup(k, v)
end
end
end
if (v.surpresslightning) then
render.SuppressEngineLighting(true)
end
render.SetColorModulation(v.color.r/255, v.color.g/255, v.color.b/255)
render.SetBlend(v.color.a/255)
model:DrawModel()
render.SetBlend(1)
render.SetColorModulation(1, 1, 1)
if (v.surpresslightning) then
render.SuppressEngineLighting(false)
end
elseif (v.type == "Sprite" and sprite) then
local drawpos = pos + ang:Forward() * v.pos.x + ang:Right() * v.pos.y + ang:Up() * v.pos.z
render.SetMaterial(sprite)
render.DrawSprite(drawpos, v.size.x, v.size.y, v.color)
elseif (v.type == "Quad" and v.draw_func) then
local drawpos = pos + ang:Forward() * v.pos.x + ang:Right() * v.pos.y + ang:Up() * v.pos.z
ang:RotateAroundAxis(ang:Up(), v.angle.y)
ang:RotateAroundAxis(ang:Right(), v.angle.p)
ang:RotateAroundAxis(ang:Forward(), v.angle.r)
cam.Start3D2D(drawpos, ang, v.size)
v.draw_func( self )
cam.End3D2D()
end
end
end
SWEP.wRenderOrder = nil
function SWEP:DrawWorldModel()
if (self.ShowWorldModel == nil or self.ShowWorldModel) then
self:DrawModel()
end
if (!self.WElements) then return end
if (!self.wRenderOrder) then
self.wRenderOrder = {}
for k, v in pairs( self.WElements ) do
if (v.type == "Model") then
table.insert(self.wRenderOrder, 1, k)
elseif (v.type == "Sprite" or v.type == "Quad") then
table.insert(self.wRenderOrder, k)
end
end
end
if (IsValid(self.Owner)) then
bone_ent = self.Owner
else
-- when the weapon is dropped
bone_ent = self
end
for k, name in pairs( self.wRenderOrder ) do
local v = self.WElements[name]
if (!v) then self.wRenderOrder = nil break end
if (v.hide) then continue end
local pos, ang
if (v.bone) then
pos, ang = self:GetBoneOrientation( self.WElements, v, bone_ent )
else
pos, ang = self:GetBoneOrientation( self.WElements, v, bone_ent, "ValveBiped.Bip01_R_Hand")
end
if (!pos) then continue end
local model = v.modelEnt
local sprite = v.spriteMaterial
if (v.type == "Model" and IsValid(model)) then
model:SetPos(pos + ang:Forward() * v.pos.x + ang:Right() * v.pos.y + ang:Up() * v.pos.z )
ang:RotateAroundAxis(ang:Up(), v.angle.y)
ang:RotateAroundAxis(ang:Right(), v.angle.p)
ang:RotateAroundAxis(ang:Forward(), v.angle.r)
model:SetAngles(ang)
--model:SetModelScale(v.size)
local matrix = Matrix()
matrix:Scale(v.size)
model:EnableMatrix( "RenderMultiply", matrix )
if (v.material == "") then
model:SetMaterial("")
elseif (model:GetMaterial() != v.material) then
model:SetMaterial( v.material )
end
if (v.skin and v.skin != model:GetSkin()) then
model:SetSkin(v.skin)
end
if (v.bodygroup) then
for k, v in pairs( v.bodygroup ) do
if (model:GetBodygroup(k) != v) then
model:SetBodygroup(k, v)
end
end
end
if (v.surpresslightning) then
render.SuppressEngineLighting(true)
end
render.SetColorModulation(v.color.r/255, v.color.g/255, v.color.b/255)
render.SetBlend(v.color.a/255)
model:DrawModel()
render.SetBlend(1)
render.SetColorModulation(1, 1, 1)
if (v.surpresslightning) then
render.SuppressEngineLighting(false)
end
elseif (v.type == "Sprite" and sprite) then
local drawpos = pos + ang:Forward() * v.pos.x + ang:Right() * v.pos.y + ang:Up() * v.pos.z
render.SetMaterial(sprite)
render.DrawSprite(drawpos, v.size.x, v.size.y, v.color)
elseif (v.type == "Quad" and v.draw_func) then
local drawpos = pos + ang:Forward() * v.pos.x + ang:Right() * v.pos.y + ang:Up() * v.pos.z
ang:RotateAroundAxis(ang:Up(), v.angle.y)
ang:RotateAroundAxis(ang:Right(), v.angle.p)
ang:RotateAroundAxis(ang:Forward(), v.angle.r)
cam.Start3D2D(drawpos, ang, v.size)
v.draw_func( self )
cam.End3D2D()
end
end
end
function SWEP:GetBoneOrientation( basetab, tab, ent, bone_override )
local bone, pos, ang
if (tab.rel and tab.rel != "") then
local v = basetab[tab.rel]
if (!v) then return end
-- Technically, if there exists an element with the same name as a bone
-- you can get in an infinite loop. Let's just hope nobody's that stupid.
pos, ang = self:GetBoneOrientation( basetab, v, ent )
if (!pos) then return end
pos = pos + ang:Forward() * v.pos.x + ang:Right() * v.pos.y + ang:Up() * v.pos.z
ang:RotateAroundAxis(ang:Up(), v.angle.y)
ang:RotateAroundAxis(ang:Right(), v.angle.p)
ang:RotateAroundAxis(ang:Forward(), v.angle.r)
else
bone = ent:LookupBone(bone_override or tab.bone)
if (!bone) then return end
pos, ang = Vector(0,0,0), Angle(0,0,0)
local m = ent:GetBoneMatrix(bone)
if (m) then
pos, ang = m:GetTranslation(), m:GetAngles()
end
if (IsValid(self.Owner) and self.Owner:IsPlayer() and
ent == self.Owner:GetViewModel() and self.ViewModelFlip) then
ang.r = -ang.r -- Fixes mirrored models
end
end
return pos, ang
end
function SWEP:CreateModels( tab )
if (!tab) then return end
-- Create the clientside models here because Garry says we can't do it in the render hook
for k, v in pairs( tab ) do
if (v.type == "Model" and v.model and v.model != "" and (!IsValid(v.modelEnt) or v.createdModel != v.model) and
string.find(v.model, ".mdl") and file.Exists (v.model, "GAME") ) then
v.modelEnt = ClientsideModel(v.model, RENDER_GROUP_VIEW_MODEL_OPAQUE)
if (IsValid(v.modelEnt)) then
v.modelEnt:SetPos(self:GetPos())
v.modelEnt:SetAngles(self:GetAngles())
v.modelEnt:SetParent(self)
v.modelEnt:SetNoDraw(true)
v.createdModel = v.model
else
v.modelEnt = nil
end
elseif (v.type == "Sprite" and v.sprite and v.sprite != "" and (!v.spriteMaterial or v.createdSprite != v.sprite)
and file.Exists ("materials/"..v.sprite..".vmt", "GAME")) then
local name = v.sprite.."-"
local params = { ["$basetexture"] = v.sprite }
-- make sure we create a unique name based on the selected options
local tocheck = { "nocull", "additive", "vertexalpha", "vertexcolor", "ignorez" }
for i, j in pairs( tocheck ) do
if (v[j]) then
params["$"..j] = 1
name = name.."1"
else
name = name.."0"
end
end
v.createdSprite = v.sprite
v.spriteMaterial = CreateMaterial(name,"UnlitGeneric",params)
end
end
end
local allbones
local hasGarryFixedBoneScalingYet = false
function SWEP:UpdateBonePositions(vm)
if self.ViewModelBoneMods then
if (!vm:GetBoneCount()) then return end
-- !! WORKAROUND !! --
-- We need to check all model names :/
local loopthrough = self.ViewModelBoneMods
if (!hasGarryFixedBoneScalingYet) then
allbones = {}
for i=0, vm:GetBoneCount() do
local bonename = vm:GetBoneName(i)
if (self.ViewModelBoneMods[bonename]) then
allbones[bonename] = self.ViewModelBoneMods[bonename]
else
allbones[bonename] = {
scale = Vector(1,1,1),
pos = Vector(0,0,0),
angle = Angle(0,0,0)
}
end
end
loopthrough = allbones
end
-- !! ----------- !! --
for k, v in pairs( loopthrough ) do
local bone = vm:LookupBone(k)
if (!bone) then continue end
-- !! WORKAROUND !! --
local s = Vector(v.scale.x,v.scale.y,v.scale.z)
local p = Vector(v.pos.x,v.pos.y,v.pos.z)
local ms = Vector(1,1,1)
if (!hasGarryFixedBoneScalingYet) then
local cur = vm:GetBoneParent(bone)
while(cur >= 0) do
local pscale = loopthrough[vm:GetBoneName(cur)].scale
ms = ms * pscale
cur = vm:GetBoneParent(cur)
end
end
s = s * ms
-- !! ----------- !! --
if vm:GetManipulateBoneScale(bone) != s then
vm:ManipulateBoneScale( bone, s )
end
if vm:GetManipulateBoneAngles(bone) != v.angle then
vm:ManipulateBoneAngles( bone, v.angle )
end
if vm:GetManipulateBonePosition(bone) != p then
vm:ManipulateBonePosition( bone, p )
end
end
else
self:ResetBonePositions(vm)
end
end
function SWEP:ResetBonePositions(vm)
if (!vm:GetBoneCount()) then return end
for i=0, vm:GetBoneCount() do
vm:ManipulateBoneScale( i, Vector(1, 1, 1) )
vm:ManipulateBoneAngles( i, Angle(0, 0, 0) )
vm:ManipulateBonePosition( i, Vector(0, 0, 0) )
end
end
--[[**************************
Global utility code
**************************--]]
-- Fully copies the table, meaning all tables inside this table are copied too and so on (normal table.Copy copies only their reference).
-- Does not copy entities of course, only copies their reference.
-- WARNING: do not use on tables that contain themselves somewhere down the line or you'll get an infinite loop
function table.FullCopy( tab )
if (!tab) then return nil end
local res = {}
for k, v in pairs( tab ) do
if (type(v) == "table") then
res[k] = table.FullCopy(v) -- recursion ho!
elseif (type(v) == "Vector") then
res[k] = Vector(v.x, v.y, v.z)
elseif (type(v) == "Angle") then
res[k] = Angle(v.p, v.y, v.r)
else
res[k] = v
end
end
return res
end
end | {
"redpajama_set_name": "RedPajamaGithub"
} | 4,067 |
Q: Get top level parents ID inherit to all children in SQL I've a table like this
ID Name Parent Code
----------------------------------
1 Item1 NULL K123
2 Item2 NULL K324
3 Item3 1 NULL
4 Item4 2 NULL
5 Item5 3 NULL
6 Item6 5 NULL
7 Item7 4 NULL
8 Item8 NULL K567
9 Item9 8 NULL
10 Item10 NULL NULL
---------------------------------
I need to inherit the code to all children from its parent like this
ID Name Parent Code
----------------------------------
1 Item1 NULL K123
2 Item2 NULL K324
3 Item3 1 K123
4 Item4 2 K324
5 Item5 3 K123
6 Item6 5 K123
7 Item7 4 K324
8 Item8 NULL K567
9 Item9 8 K567
10 Item10 NULL NULL
---------------------------------
I tried the CTE below
;with CTE(ID,Name,Parent,Code,[Level]) as
(
select ID,Name,Parent,Code,0 as [Level] from tbl_mytable
union all
select T.ID,T.Name,T.Parent,T.Code,C.[Level]+1 from tbl_mytable T
inner join CTE C on C.Parent=T.ID
)
select * from CTE C
Which doesnt help me to achieve what I am trying. I'm just a beginner with CTE with which I dont think it can fix.
A: You were on the right track to use a recursive CTE, but your logic is a bit off. Consider this working version:
WITH cte AS (
SELECT * FROM tbl_mytable WHERE Parent IS NULL
UNION ALL
SELECT t1.ID, t1.Name, t1.Parent, COALESCE(t1.Code, t2.Code)
FROM tbl_mytable t1
INNER JOIN cte t2
ON t1.Parent = t2.ID
)
SELECT *
FROM cte
ORDER BY ID;
Demo
The base case component of the recursive CTE (i.e. what comes before the union) should be those records having no parents. This is how we know they are the highest parent level. Then, we join the CTE recursively by matching a given level to the parent immediately above it. Then, we use a trick to bring down the codes from the top level:
COALESCE(t1.Code, t2.Code)
This will start with one of the parent's codes, and then will propagate downwards to the various levels of children.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,604 |
<?php
namespace Xgettext\Parser;
use Xgettext\Poedit\PoeditString,
Xgettext\Poedit\PoeditPluralString;
abstract class AbstractRegexParser
{
protected $file;
protected $keywords;
protected $strings;
public function __construct($file, array $keywords = array('_'))
{
$this->file = $file;
$this->strings = array();
$this->keywords = $this->handleKeywords($keywords);
}
// make keword list and argument positions
private function handleKeywords($keywords)
{
$kwds = array();
foreach ($keywords as $keyword) {
if (false !== ($pos = strpos($keyword, ':'))) {
preg_match_all('`([\d]+)`', $keyword, $matches);
$kwds[substr($keyword, 0, $pos)] = $matches[0];
continue;
}
$kwds[$keyword] = array(1);
}
return $kwds;
}
public function extractCalls($line)
{
return array();
}
public function extractArguments($arguments)
{
return array();
}
public function parse($string = null)
{
$line_count = 0;
$handle = fopen($this->file, "r");
// foreach file line by line
while ($handle && !feof($handle)) {
$line = fgets($handle);
$comment = $this->file . ':' . ++$line_count;
$calls = $this->extractCalls($line);
// nothing found in the parsed line
if (empty($calls)) {
continue;
}
// foreach every call match to analyze arguments, they must be strings
foreach ($calls as $call) {
$arguments = $this->extractArguments($call['arguments']);
// false positive, no matching arguments inside
if (empty($arguments)) {
continue;
}
// first argument is msgid
$msgid = str_replace('\\' . $arguments[0]['delimiter'], $arguments[0]['delimiter'], $arguments[0]['arguments']);
// if we did not have found already this string, create it
if (!in_array($msgid, array_keys($this->strings))) {
// we have a plural form case
if (2 === count($this->keywords[$call['keyword']])) {
// we asked for a plural keyword above, but only one argument were found. Abort silently
if (!isset($arguments[1])) {
continue;
}
$msgid_plural = str_replace('\\' . $arguments[1]['delimiter'], $arguments[1]['delimiter'], $arguments[$this->keywords[$call['keyword']][1] - 1]['arguments']);
$this->strings[$msgid] = new PoeditPluralString($msgid, $msgid_plural);
} else {
$this->strings[$msgid] = new PoeditString($msgid);
}
}
// add line reference to newly created or already existing string
$this->strings[$msgid]->addReference($comment);
}
}
fclose($handle);
return $this->strings;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,872 |
Modern-minimalist design invites tonal warmth for a fresh pairing of tailored style and lush comfort. A slim gunmetal-toned iron base supports an intriguing blend of Polyester & Acrylic upholstery in a light grey finish. Oversize plush arms add further contrast to low-profile shape.
Dimensions: D:59" x W:111" x H:27" | {
"redpajama_set_name": "RedPajamaC4"
} | 8,260 |
Q: MSSQL Server 10 runaway log growth, 100GB/week I have started as an IT Manager and my remit covers MSSQL server. A database that I have inherited uses around 100GB of HD in the space of a week, in the LDF file. This in turn uses all available disk space on drive C: and the server falls over.
Can I therefore use the Restricted File Growth option on the LDF file to stop it using the entire drive? If so, what happens when this file is full?
Also, what would be causing this type of activity? Would this be due to a poorly written SQL query?
A: Check whether the DBs are in Full Recovery mode. If they are, have you got jobs running to actually back up the transaction logs running on a frequent enough schedule to keep them to a manageable size?
Edit:
When the file is full due to restricted growth your DB will stop processing transactions as it has nowhere to log them. You need to sort out the reason for the file growing so much rather than restricting the file.
A: If it is an extremely busy (and extremely huge) database, 100GB of logs per week may not be outrageous. Without more information on database size, transaction volume, record sizes, etc., that is difficult for us to judge.
The more important question is: if this database is being backed up each night, why aren't the logs getting pruned? Normally, one doesn't need to worry about transaction log volume per week.
Background information:
*
*On a properly configured MSSQL server, the transaction logs are physically separated from the data: they reside not only on a separate volume, but on a completely separate RAID array.
*If the database (or the physical volume that stores the database) is lost, you can restore from the most recent backup and then replay the transaction logs to recover data until the moment that the failure occurred.
*Any transaction log entries created before your most recent backup can be pruned from the LDF file. Usually, the logs themselves get backed up before they get pruned; this maintains the possibility of recovering to arbitrary points in time that may be prior to the most recent backup, if older backups are retained.
So, here's the bigger question: how is this SQL server being backed up, and are the transaction logs being pruned at the time of each backup? Was there a nightly backup process that suddenly stopped working?
If the previous administrator was too lazy to use proper service accounts -- and this is not uncommon -- lots of things, including backups, might have stopped working when his/her account was disabled and the built-in domain administrator account password was changed.
A: In addition - data and logs have no business on the c drive. Sploitting IO on a busy database is the key to performance.
A: Like Chris said, when your DB is set to full recovery mode, (which it almost definitely is) you must run some sort of backup in order to truncate the transaction log. If not you will see it continually grow. If you don't have care about the recovery window of that DB then you can just set the recovery mode back to Basic.
A: Also, move them out of the C drive. Running out of on that drive will let the DB crash and might cause corruption
A: I would change to the recovery model on the model database from FULL to SIMPLE.
In our organization a FULL recovery model is a deliberate decision for which we plan. Setting SIMPLE on the model database eliminates the possibility of a log file filling up a drive because it hasn't had regular backups.
A: Which version of MSSQL? SQL Server 2008 has removed the ability to truncate log files (and they have very good, valid reasons for doing so), so if your log file is out of control you need to start it again and get proper maintenance plans in place to ensure that it doesn't happen again.
That said, if you are not using:
*
*Mirroring
*Transaction log shipping
Then there's no real reason for you to be in Full recovery mode. If you switch it to Simple it will keep the log file from growing any further.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,696 |
\section{Introduction}
One of the most important undecided problems in theoretical physics is a description of mass spectrum of elementary particles (it is one from 30 problems in Ginzburg's list \cite{Ginz}). It is well known that a quark model, based on the flavor $\SU(3)$ group, does not explain the mass spectrum of elementary particles. The Gell-Mann--Okubo mass formula explains only a mass splitting within supermultiplets of $\SU(3)$-theory, namely, a hypercharge mass splitting within supermultiplets and a charge splitting within isotopic multiplets belonging to a given supermultiplet. An action of the group $\SU(3)$ is analogous to Zeeman effect in atomic spectra, that is, this action leads to different mass levels within charge multiplets via $\SU(3)/\SU(2)$-reduction. Masses of particles, belonging to a given supermultiplet of $\SU(3)$ in $\SU(3)/\SU(2)$-reduction, are defined by the Gell-Mann--Okubo mass formula \cite{Gel61,OR64} (quadratic case)
\begin{equation}\label{GMOQ}
m^2=m^2_0+\alpha+\beta Y+\gamma\left[I(I+1)-\frac{1}{4}Y^2\right]
+\alpha^\prime-\beta^\prime
Q+\gamma^\prime\left[U(U+1)-\frac{1}{4}Q^2\right],
\end{equation}
where $Q$ and $Y$ are charge and hypercharge of the particle, $I$ and $U$ are isotopic spins. The coefficients $\alpha$, $\alpha^\prime$, $\beta$, $\beta^\prime$, $\gamma$, $\gamma^\prime$ are satisfy the relation
\[
\frac{\alpha^\prime}{\alpha}=\frac{\beta^\prime}{\beta}=\frac{\gamma^\prime}{\gamma}=\theta,\quad
|\theta|\ll 1.
\]
In the case when the condition $\delta m^2/m^2_0\ll 1$ is fulfilled, the
quadratic mass formula (\ref{GMOQ}) can be replaced by the linear
mass formula
\begin{equation}\label{GMOL}
m=m_0+\alpha+\beta Y+\gamma\left[I(I+1)-\frac{1}{4}Y^2\right]
+\alpha^\prime-\beta^\prime
Q+\gamma^\prime\left[U(U+1)-\frac{1}{4}Q^2\right].
\end{equation}
In the case of flavor-spin $\SU(6)$-theory we have the following B\'{e}g-Singh mass formula \cite{BS,RF70}:
\begin{multline}\label{BS}
m^2=m^2_0+\mu_1C_2(3)+\mu_2\cdot 2J(J+1)+\mu_3Y+
\mu_4\left[2S(s+1)+\frac{1}{4}Y^2-C_2(4)\right]+\\
+\mu_5\left[-\frac{1}{2}Y^2+2T(T+1)\right]+
\mu_6\left[2N(N+1)-2S(S+1)\right],
\end{multline}
where $C_2(3)$ and $C_2(4)$ are Casimir operators of $\SU(6)$, $Y$ is a hypercharge, $J$ and $T$ are spin and isospin operators, $S$ and $N$ are so-called strange and non-strange spins. As in the case of $\SU(3)$-theory, a group action of $\SU(6)$ is analogous to Zeeman effect, that is, this action leads to a mass splitting of states within hypermultiplets of $\SU(6)$ (56-plet of baryons and 35-plet of mesons) via $\SU(6)/\SU(3)$- and $\SU(6)/\SU(4)$-reductions.
In the Gell-Mann--Okubo formulas (\ref{GMOQ})-(\ref{GMOL}) and B\'{e}g-Singh formula (\ref{BS}) $m_0$ depends on the chosen supermultiplet of $\SU(3)$ (hypermultiplet in the case of $\SU(6)$) and the concrete value of $m_0$ is not predicted by the $\SU(3)$- and $\SU(6)$-theories. Moreover, in Nature we see a wide variety of baryon octets (see, for example, Particle Data Group: pdg.lbl.gov), where mass distances between these octets are not explained by the $\SU(3)$- and $\SU(6)$-mass formulas. As a rule, all the predicted masses in $\SU(3)$- and $\SU(6)$-theories have a low accuracy (on an average 4\%--6\%).
It is well-known that in the standard model (SM) the number of basic parameters is 18, including the three gauge coupling constants \cite{Fri02}:
\[
m_e,\;m_u,\;m_d;\quad m_\mu,\;m_s,\;m_c;\quad m_\tau,\;m_b,\;m_t;
\]
\[
\theta_u,\;\theta_d,\;\theta,\;\delta;
\]
\[
M_w,\;M_h;
\]
\[
\alpha,\;\alpha_s,\alpha_W.
\]
Thirteen of these constants are directly related to the fermion masses, namely, lepton masses $(m_e,m_\mu,m_\tau)$, quark masses $(m_u,m_d,m_s,m_c,m_b,m_t)$ and mixing angles $(\theta_u,\theta_d,\theta,\delta)$. All these mass parameters have to be adjusted according to experimental measurements and cannot be predicted within the theory (SM). SM considers these mass parameters as ``fundamental constants''. For this reason the standard model must be regarded as a first step towards a more complete theoretical framework. As a consequence of this situation, we see in SM three types of so-called ``fundamental particles'' (quarks, leptons and gauge bosons).
On the other hand, in 1952, Numbu \cite{Num52} gave attention to an existence of empirical (``balmer-like'') relations in the mass spectrum of elementary particles:
\begin{equation}\label{Numbu}
m_N=\left(N/2\right)137\cdot m_e,
\end{equation}
where $N$ is a positive integer number, $m_e$ is the rest mass of electron. Further, in 1979, Barut \cite{Bar79} proposed a mass formula for the leptons:
\begin{equation}\label{Barut}
m(N)=m_e\left(1+\frac{3}{2}\alpha^{-1}\sum^{n=N}_{n=0}n^4\right),
\end{equation}
where $\alpha\approx 1/137$ is a fine structure constant. According to (\ref{Barut}), masses of electron, muon and $\tau$-lepton are defined at $N=0,1$ and 2, respectively. Later on, empirical relations of the form (\ref{Numbu}) were studied by many authors (see \cite{MG70,MG07,Pal07,SM08,MS08,Gro,Chiatti}). The Numbu formula (\ref{Numbu}) can be written also via the fine structure constant:
\begin{equation}\label{Alpha}
m=\frac{N}{2\alpha}m_e.
\end{equation}
This formula leads to a so-called $\alpha$-quantization of the elementary particle masses (see \cite{MG07,Gro}).
In 2003, Sidharth \cite{Sid1,Sid2} proposed the following empirical formula:
\begin{equation}\label{Sidharth}
\text{mass}=137\cdot m\left(n+\frac{1}{2}\right),
\end{equation}
where $m$ and $n$ are positive integer numbers. The Sidharth formula (\ref{Sidharth}) describes the all mass spectrum of elementary particles (known up to 2003) with an accuracy of $3\%$. Sidharth \cite{Sid2} attempted to relate the numbers $m$ and $n$ with the quantum numbers of harmonic oscillator. However, theoretical sense of these numbers, as the number $N$ in other ``balmer-like'' formulas ((\ref{Numbu})--(\ref{Alpha})), remains unclear.
In the present paper we study mass spectrum of ``elementary particles'', that is, a mass spectrum of actualized (localized) states of non-local quantum system (quantum domain). A spectrum of these states form a Hesenberg-like matter spectrum. According to Heisenberg \cite{Heisen1,Heisen}, in the ground of the all wide variety of elementary particles we have \textit{substrate of energy}, the mathematical (group-theoretical) form of which (obtained via the fundamental symmetries) is a \textbf{\textit{matter spectrum}}. The each level (\textit{state}) of matter spectrum is defined by a representation of a group of fundamental symmetry. The each elementary particle presents itself a some energy level of this spectrum. An essential distinctive feature of such description is an absence of fundamental particles. Heisenberg claimed that a notion ``consists of'' does not work in particle physics. Applying this notion, we obtain that the each particle consists of the all known particles. For that reason among the all elementary particles we cannot to separate one as a fundamental particle \cite{Heisen}. In Heisenberg's approach we have \textit{fundamental symmetries} instead fundamental particles. In Heisenberg's opinion, all known symmetries in particle physics are divided on the two categories: \textit{fundamental (primary) symmetries} (such as the Lorentz group, discrete symmetries, conformal group) and \textit{dynamical (secondary) symmetries} (such as $\SU(3)$, $\SU(6)$ and so on). A quantum microobject is non-local and there exists as a superposition of state vectors of nonseparable Hilbert space outside the Minkowski space-time\footnote{It is interesting to note that in the well-known Penrose program \cite{Pen77,PM72} a twistor structure is understood as the underlying (more fundamental) structure with respect to Minkowski space-time. In other words, space-time continuum is not fundamental substance in the twistor approach, this is a fully derivative entity generated by the underlying twistor structure. In parallel with the twistor approach, decoherence theory \cite{JZKGKS} claims that in the background of reality we have a \textit{non-local quantum substrate} (quantum domain), and all visible world (classical domain$\equiv$space-time continuum) arises from quantum domain in the result of decoherence process \cite{Zur03,Zur03b}.}. A structure of the matter spectrum is organized within a Gelfand-Neumark-Segal construction \cite{GN43,Seg47}, where cyclic representations of the operator algebra (energy operator) are defined by fundamental symmetry (Lorentz group). Within the given realization of operator algebra\footnote{It is obvious that at the other realization of operator algebra (for example, via the conformal group as a fundamental symmetry) we obtain the other structure of matter spectrum.} we introduce a mass formula defining an energetic weight of the each level of matter spectrum. The obtained spectrum leads to a \textit{linearly} increasing mass spectrum of the states (``elementary particles''). Thus, all the states of matter spectrum are described as a \textbf{\textit{single quantum system}}\footnote{The linear character of mass spectrum (observed in Nature more than 60 years ago \cite{Num52}) is a direct consequence of the united quantum system.}. In the sections 3--6 we show that state masses of lepton and hadron sectors of matter spectrum are proportional to the rest mass of electron with an accuracy of $0,41\%$, that leads to a \textit{mass quantization}. This situation looks like a charge quantization (all charged states, observed in Nature, have a charge which is an integral multiple of the electron charge).
\section{Lorentz group and mass formula}
As is known, a universal covering of the proper orthochronous Lorentz group $\SO_0(1,3)$
(rotation group of the Minkowski space-time $\R^{1,3}$)
is the spinor group
\[\ar
\spin_+(1,3)\simeq\left\{\begin{pmatrix} \alpha & \beta \\ \gamma &
\delta
\end{pmatrix}\in\C_2:\;\;\det\begin{pmatrix}\alpha & \beta \\ \gamma & \delta
\end{pmatrix}=1\right\}=\SL(2,\C).
\]
Let $\fg\rightarrow T_{\fg}$ be an arbitrary linear
representation of the proper orthochronous Lorentz group
$\SO_0(1,3)$ and let $\sA_i(t)=T_{a_i(t)}$ be an infinitesimal
operator corresponding to the rotation $a_i(t)\in\SO_0(1,3)$.
Analogously, let $\sB_i(t)=T_{b_i(t)}$, where $b_i(t)\in\SO_0(1,3)$ is
the hyperbolic rotation. The elements $\sA_i$ and $\sB_i$ form a basis of the group algebra
$\mathfrak{sl}(2,\C)$ and satisfy the relations
\begin{equation}\label{Com1}
\left.\begin{array}{lll} \ld\sA_1,\sA_2\rd=\sA_3, &
\ld\sA_2,\sA_3\rd=\sA_1, &
\ld\sA_3,\sA_1\rd=\sA_2,\\[0.1cm]
\ld\sB_1,\sB_2\rd=-\sA_3, & \ld\sB_2,\sB_3\rd=-\sA_1, &
\ld\sB_3,\sB_1\rd=-\sA_2,\\[0.1cm]
\ld\sA_1,\sB_1\rd=0, & \ld\sA_2,\sB_2\rd=0, &
\ld\sA_3,\sB_3\rd=0,\\[0.1cm]
\ld\sA_1,\sB_2\rd=\sB_3, & \ld\sA_1,\sB_3\rd=-\sB_2, & \\[0.1cm]
\ld\sA_2,\sB_3\rd=\sB_1, & \ld\sA_2,\sB_1\rd=-\sB_3, & \\[0.1cm]
\ld\sA_3,\sB_1\rd=\sB_2, & \ld\sA_3,\sB_2\rd=-\sB_1. &
\end{array}\right\}
\end{equation}
Defining the operators
\begin{gather}
\sX_l=\frac{1}{2}i(\sA_l+i\sB_l),\quad\sY_l=\frac{1}{2}i(\sA_l-i\sB_l),
\label{SL25}\\
(l=1,2,3),\nonumber
\end{gather}
we come to a \textit{complex envelope} of the group algebra $\mathfrak{sl}(2,\C)$.
Using the relations (\ref{Com1}), we find
\begin{equation}\label{Com2}
\ld\sX_k,\sX_l\rd=i\varepsilon_{klm}\sX_m,\quad
\ld\sY_l,\sY_m\rd=i\varepsilon_{lmn}\sY_n,\quad \ld\sX_l,\sY_m\rd=0.
\end{equation}
From the relations (\ref{Com2}) it follows that each of the sets of
infinitesimal operators $\sX$ and $\sY$ generates the group $\SU(2)$
and these two groups commute with each other. Thus, from the
relations (\ref{Com2}) it follows that the group algebra
$\mathfrak{sl}(2,\C)$ (within the complex envelope) is algebraically isomorphic to the direct sum $\mathfrak{su}(2)\oplus\mathfrak{su}(2)$\footnote{In a sense, it allows one to represent the group
$\SL(2,\C)$ by a product $\SU(2)\otimes\SU(2)$ as it done by Ryder in his
textbook \cite{Ryd85}. Moreover, in the works \cite{AE93,Dvo96} the
Lorentz group is represented by a product $\SU_R(2)\otimes\SU_L(2)$,
where the spinors $\psi(p^\mu)=\begin{pmatrix}\phi_R(p^\mu)\\
\phi_L(p^\mu)\end{pmatrix}$ ($\phi_R(p^\mu)$ and $\phi_L(p^\mu)$ are
the right- and left-handed spinors) are transformed within
$(j,0)\oplus(0,j)$ representation space, in our case $j=l=\dot{l}$.
However, the isomorphism $\SL(2,C)\simeq\SU(2)\otimes\SU(2)$ is not correct from group-theoretical viewpoint. Indeed, the groups $\SO_0(1,3)$ and $\SO(4)$ are real forms of the complex 6-dimensional Lie group $\SO(4,\C)$ with complex Lie algebra $D_2=A_1+A_1$. Real Lie algebras are compact iff the Killing form is negative definite \cite{Knapp}. That is the case for Lie algebra of $\SO(4)$, not for $\SO_0(1,3)$.}.
Further, introducing operators of the form (`rising' and `lowering' operators of the group $\SL(2,\C)$)
\begin{equation}\label{SL26}
\left.\begin{array}{cc}
\sX_+=\sX_1+i\sX_2, & \sX_-=\sX_1-i\sX_2,\\[0.1cm]
\sY_+=\sY_1+i\sY_2, & \sY_-=\sY_1-i\sY_2,
\end{array}\right\}
\end{equation}
we see that
\[
\ld\sX_3,\sX_+\rd=\sX_+,\quad\ld\sX_3,\sX_-\rd=-\sX_-,\quad\ld\sX_+,\sX_-\rd=2\sX_3,
\]
\[
\ld\sY_3,\sY_+\rd=\sY_+,\quad\ld\sY_3,\sY_-\rd=-\sY_-,\quad\ld\sY_+,\sY_-\rd=2\sY_3.
\]
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\end{picture}
\end{center}
\vspace{0.3cm}
\begin{center}\begin{minipage}{32pc}{\small {\bf Fig.\,1:} The system of interlocking (cyclic) representations $(l,\dot{l})$ of the Lorentz group.}\end{minipage}\end{center}
In virtue of commutativity of the relations (\ref{Com2}) a space of an irreducible finite-dimensional representation of the group $\SL(2,\C)$ can be spanned on the totality of
$(2l+1)(2\dot{l}+1)$ basis ket-vectors $|l,m;\dot{l},\dot{m}\rangle$ and basis bra-vectors
$\langle l,m;\dot{l},\dot{m}|$, where $l,m,\dot{l},\dot{m}$ are integer
or half-integer numbers, $-l\leq m\leq l$, $-\dot{l}\leq
\dot{m}\leq \dot{l}$. Therefore,
\begin{eqnarray}
&&\sX_-|l,m;\dot{l},\dot{m}\rangle= \sqrt{(l+m)(l-m+1)}|l,m-1;\dot{l},\dot{m}\rangle
\;\;(m>-l),\nonumber\\
&&\sX_+|l,m;\dot{l},\dot{m}\rangle= \sqrt{(l-m)(l+m+1)}|l,m+1;\dot{l},\dot{m}\rangle
\;\;(m<l),\nonumber\\
&&\sX_3|l,m;\dot{l},\dot{m}\rangle=
m|l,m;\dot{l},\dot{m}\rangle,\nonumber\\
&&\langle l,m;\dot{l},\dot{m}|\sY_-=
\langle l,m;\dot{l},\dot{m}-1|\sqrt{(\dot{l}+\dot{m})(\dot{l}-\dot{m}+1)}\;\;(\dot{m}>-\dot{l}),\nonumber\\
&&\langle l,m;\dot{l},\dot{m}|\sY_+=
\langle l,m;\dot{l},\dot{m}+1|\sqrt{(\dot{l}-\dot{m})(\dot{l}+\dot{m}+1)}\;\;(\dot{m}<\dot{l}),\nonumber\\
&&\langle l,m;\dot{l},\dot{m}|\sY_3= \langle l,m;\dot{l},\dot{m}|\dot{m}.\label{Waerden}
\end{eqnarray}
In contrast to the
Gelfand-Naimark representation
for the Lorentz group \cite{GMS,Nai58},
which does not find a wide application in physics,
a representation (\ref{Waerden}) is a most useful in theoretical physics
(see, for example, \cite{AB,Sch61,RF,Ryd85}). This representation for the
Lorentz group was first given by van der Waerden in his brilliant book
\cite{Wa32}.
It should be noted here that the representation basis, defined by the
formulae (\ref{SL25})--(\ref{Waerden}), has an evident physical meaning.
For example, in the case of $(1,0)\oplus(0,1)$-representation space
there is an analogy with the photon spin states. Namely, the operators
$\sX$ and $\sY$ correspond to the right and left polarization states of the
photon. For that reason we will call the canonical basis consisting of the
vectors $\mid lm;\dot{l}\dot{m}\rangle$ as
{\it a helicity basis}.
Thus, a complex envelope of the group algebra $\mathfrak{sl}(2,\C)$, generating complex momentum, leads to a \textit{duality} which is mirrored in the appearance of the two spaces: a space of ket-vectors $|l,m;\dot{l},\dot{m}\rangle$ and a dual space of bra-vectors $\langle l,m;\dot{l},\dot{m}|$.
Further, equations for arbitrary spin chains (spin multiplets)
\[
\boldsymbol{\tau}_{l\dot{l}},\;\boldsymbol{\tau}_{l+\frac{1}{2},\dot{l}-\frac{1}{2}},\;
\boldsymbol{\tau}_{l+1,\dot{l}-1},\;\boldsymbol{\tau}_{l+\frac{3}{2},\dot{l}-\frac{3}{2}},\;\ldots,\;
\boldsymbol{\tau}_{\dot{l}l},
\]
(horizontal lines of the representation cone on the Fig.\,1) in the bivector space $\R^6$ have the form \cite{Var03,Var07}
\[
\sum^3_{j=1}\Lambda^{l\dot{l}}_j\frac{\partial\psi}{\partial a_j}-
i\sum^3_{j=1}\Lambda^{l\dot{l}}_j\frac{\partial\psi}{\partial a^\ast_j}+m^{(s)}\dot{\psi}=0,
\]
\[
\sum^3_{j=1}\Lambda^{l+\frac{1}{2},\dot{l}-\frac{1}{2}}_j\frac{\partial\psi}{\partial a_j}-
i\sum^3_{j=1}\Lambda^{l+\frac{1}{2}\dot{l}-\frac{1}{2}}_j\frac{\partial\psi}{\partial a^\ast_j}+m^{(s)}\dot{\psi}=0,
\]
\[
\sum^3_{j=1}\Lambda^{l+1,\dot{l}-1}_j\frac{\partial\psi}{\partial a_j}-
i\sum^3_{j=1}\Lambda^{l+1\dot{l}-1}_j\frac{\partial\psi}{\partial a^\ast_j}+m^{(s)}\dot{\psi}=0,
\]
\[
\sum^3_{j=1}\Lambda^{l+\frac{3}{2},\dot{l}-\frac{3}{2}}_j\frac{\partial\psi}{\partial a_j}-
i\sum^3_{j=1}\Lambda^{l+\frac{3}{2}\dot{l}-\frac{3}{2}}_j\frac{\partial\psi}{\partial a^\ast_j}+m^{(s)}\dot{\psi}=0,
\]
\[
\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots
\]
\begin{equation}\label{BS2}
\sum^3_{j=1}\Lambda^{\dot{l}l}_j\frac{\partial\dot{\psi}}{\partial a_j}+
i\sum^3_{j=1}\Lambda^{\dot{l}l}_j\frac{\partial\dot{\psi}}{\partial a^\ast_j}+m^{(s)}\psi=0,
\end{equation}
where the spin\footnote{According to Weinberg theorem \cite{Wein}, a helicity
$\lambda$ of the particle, described by the representation
$\boldsymbol{\tau}_{l\dot{l}}$, is defined by an expression
$l-\dot{l}=\lambda$.} $s=l-\dot{l}$ changes as follows:
\[
l-\dot{l},\;l-\dot{l}+1,\;l-\dot{l}+2,\;l-\dot{l}+3,\,\ldots,\;\dot{l}-l.
\]
The system (\ref{BS2}) describes particle states with different masses and spins in $\R^6$. The state mass $m^{(s)}$, corresponding to the energy level $\sH_E\simeq\Sym_{(k,r)}$, is defined by the formula
\begin{equation}\label{MGY}
m^{(s)}=m_e\left(l+\frac{1}{2}\right)\left(\dot{l}+\frac{1}{2}\right),
\end{equation}
where $s=|l-\dot{l}|$. Mass spectrum and its dependence of the Lorentz group representations, characterizing by the pair $(l,\dot{l})$\footnote{Finite-dimensional representations $\boldsymbol{\tau}_{l\dot{l}}$ of the Lorentz group (usually denoted as $\fD^{(j/2,r/2)}$, here $j/2=l$, $r/2=\dot{l}$) play an important role in the axiomatic quantum field theory \cite{SW64,BLOT}. For more details about interlocking representations $\boldsymbol{\tau}_{l\dot{l}}$ see \cite{GY48,AD72,PS83}.}, was given in \cite{Var15}. Usually one consider the mass spectrum dependence of spin $s$ only (Lorentz group representation is fixed). As it is known, in this case non-physical mass spectrum arises, $m_i\sim 1/s_i$, that is, for very large $s_i$, masses are very small (the first mass formula of this type was given by Majorana \cite{Maj32} and similar mass formulas were considered by Gelfand and Yaglom \cite{GY48}, see also \cite{Esp12,Ulr13}). In the paper \cite{Var15} it has been shown that for representations $(l,\dot{l})$ of the Lorentz group the mass is proportional to $(l+1/2)(\dot{l}+1/2)$. Hence it immediately follows that particles (more precisely, particle states) with the \textit{same} spin but \textit{distinct} masses are described by \textit{different} representations of Lorentz group.
The operators $\boldsymbol{\Lambda}=(\Lambda^{l\dot{l}}_1,\Lambda^{l\dot{l}}_2,\Lambda^{l\dot{l}}_3)$ and $\overset{\ast}{\boldsymbol{\Lambda}}=(\Lambda^{\dot{l}l}_1,\Lambda^{\dot{l}l}_2,\Lambda^{\dot{l}l}_3)$ in (\ref{BS2}) have a common system of eigenfunctions with the energy operator $H$ (and operators $\sX_l$, $\sY_l$ of the complex momentum) for the each spin value $s=l-\dot{l}$. Hence it follows that $\boldsymbol{\Lambda}$ and $\overset{\ast}{\boldsymbol{\Lambda}}$ are Hermitian operators. It has been shown \cite{Var16} that a structure $\boldsymbol{\Lambda}$, $\overset{\ast}{\boldsymbol{\Lambda}}$ depends on the structure of elementary divisors.
In the case of $(l,0)\oplus(0,\dot{l})$ all elementary divisors of the operators $\boldsymbol{\Lambda}$ and $\overset{\ast}{\boldsymbol{\Lambda}}$ are simple, and Jordan form of the matrices of $\boldsymbol{\Lambda}$ and $\overset{\ast}{\boldsymbol{\Lambda}}$ is a diagonal matrix
\begin{equation}\label{SimpleJ}
\bJ(\Lambda)=-\bJ(\overset{\ast}{\Lambda})=\text{{\rm diag}}\left(\lambda_1,\lambda_2,\ldots,\lambda_{2l+1}\right),
\end{equation}
where $\lambda_1,\lambda_2,\ldots,\lambda_{2l+1}$ are eigenvalues of the operators $\boldsymbol{\Lambda}$ and $\overset{\ast}{\boldsymbol{\Lambda}}$.
In the case of $(l,\dot{l})\oplus(\dot{l},l)$ the operators $\boldsymbol{\Lambda}$ and $\overset{\ast}{\boldsymbol{\Lambda}}$ have elementary divisors with multiple roots, and Jordan form of the matrices of $\boldsymbol{\Lambda}$ and $\overset{\ast}{\boldsymbol{\Lambda}}$ is a block-diagonal matrix. For example, characteristic polynomial of $\Lambda^{s\frac{k}{2}}_3$ is
\begin{multline}
\boldsymbol{\Delta}(\Lambda^{s\frac{k}{2}}_3)=(\lambda-sk/2)^{m_1}(\lambda-(1-s)k/2)^{m_2}(\lambda-(2-s)k/2)^{m_3}
\ldots(\lambda-1/2)^{m_p}\lambda^{2s}\times\\
\times(\lambda+sk/2)^{m_{-1}}(\lambda+(1-s)k/2)^{m_{-2}}(\lambda+(2-s)k/2)^{m_{-3}}\ldots(\lambda+1/2)^{m_{-p}},
\nonumber
\end{multline}
where
\[
2\leq m_1\leq m^1_{\text{{\rm max}}},
\]
\[
2\leq m_2\leq m^2_{\text{{\rm max}}},
\]
\[
\ldots\ldots\ldots\ldots\ldots
\]
\[
2\leq m_{-p}\leq m^{-p}_{\text{{\rm max}}},
\]
here $m^1_{\text{max}}$ is a number of products among $(2s+1)(k+1)$ products of the $sk$-basis, which equal to eigenvalue $sk/2$; $m^2_{\text{max}}$ is a number of products among $(2s+1)(k+1)$ products of the $sk$-basis, which equal to eigenvalue $(1-s)k/2$ and so on.
The Jordan form of $\Lambda^{s\frac{k}{2}}_3$ is
\[
\bJ(\Lambda^{s\frac{k}{2}}_3)=\text{{\rm diag}}\left(\bJ({}_{s\frac{k}{2}}\Lambda^{s\frac{k}{2}}_3), \bJ({}_{\frac{(1-s)k}{2}}\Lambda^{s\frac{k}{2}}_3),\ldots,\bJ({}_{\frac{1}{2}}\Lambda^{s\frac{k}{2}}_3),
\bJ({}_{0}\Lambda^{s\frac{k}{2}}_3),\bJ({}_{-\frac{1}{2}}\Lambda^{s\frac{k}{2}}_3),\ldots,
\bJ({}_{-\frac{sk}{2}}\Lambda^{s\frac{k}{2}}_3)\right),
\]
where
\[
\bJ({}_{\frac{sk}{2}}\Lambda^{s\frac{k}{2}}_3)=\begin{Vmatrix}
\frac{sk}{2} & 1 & 0 & \dots & 0\\
0 & \frac{sk}{2} & 1 & \dots & 0\\
.&&\hdotsfor[3]{3}\\
.&&&\hdotsfor[3]{2}\\
.&&&.&1\\
0 & 0 & 0 & \dots & \frac{sk}{2}
\end{Vmatrix}
\]
is a Jordan cell corresponding to elementary divisor $(\lambda-sk/2)^{m_1}$ and so on. Thus, the states (cyclic representations) of the form $(l,0)\oplus(0,\dot{l})$ have a trivial Jordan structure that corresponds to a spectrum of ``point-like'' (structureless) particle. Whereas the states of the form $(l,\dot{l})\oplus(\dot{l},l)$ have non-trivial Jordan structure, and corresponding cyclic representations contain invariant subspaces (there are elementary divisors of higher order). In this case we come to a spectrum of inhomogeneous (``composite'') particle which endowed by a grain (parton) structure.
\subsection{Matter spectrum and Gelfand-Neumark-Segal construction}
It is well-known that a ground of algebraic formulation of quantum theory is the Gelfand-Neumark-Segal construction (GNS), defined by a canonical correspondence $\omega\leftrightarrow\pi_\omega$ between states and cyclic representations of $C^\ast$-algebra \cite{Emh,BLOT,Hor86}. One of the most important aspects in theory of $C^\ast$-algebras is a duality between states and representations. A relation between states and irreducible representations of operator algebras was first formulated by Segal \cite{Se47}. Let $\pi$ be a some representation of the algebra $\fA$ in the Hilbert space $\sH_\infty$, then for any non-null vector $\left|\Phi\right\rangle\in\sH_\infty$ the expression
\begin{equation}\label{VectState}
\omega_\Phi(A)=\frac{\langle\Phi\mid\pi(A)\Phi\rangle}{\langle\Phi\mid\Phi\rangle}
\end{equation}
defines a state $\omega_\Phi(A)$ of the algebra $\fA$. $\omega_\Phi(A)$ is called a \textit{vector state} associated with the representation $\pi$ ($\omega_\Phi(A)$ corresponds to the vector $\left|\Phi\right\rangle$). Let $S_\pi$ be a set of all states associated with the representation $\pi$. Two representations $\pi_1$ and $\pi_2$ with one and the same set of associated states (that is, $S_{\pi_1}=S_{\pi_2}$) are called phenomenologically equivalent sets (it corresponds to unitary equivalent representations). Moreover, the set $PS(\fA)$ of the all pure states of $C^\ast$-algebra $\fA$ coincides with the set of all vector states associated with the all \textit{irreducible representations} of the algebra $\fA$.
Further, let $\pi$ be a representation of $C^\ast$-algebra $\fA$ in $\sH_\infty$ and let $\left|\Phi\right\rangle$ be a \textit{cyclic vector}\footnote{Vector $\left|\Phi\right\rangle\in\sH_\infty$ is called a \textit{cyclic vector} for the representation $\pi$, if the all vectors $\left|\pi(A)\Phi\right\rangle$ (where $A\in\fA$) form a total set in $\sH_\infty$, that is, such a set, for which a closing of linear envelope is dense everywhere in $\sH_\infty$. $\pi$ with the cyclic vector is called a \textit{cyclic representation}.} of the representation $\pi$ defining the state $\omega_\Phi$. In accordance with Gelfand-Neumark-Segal construction (see \cite{BLOT}) the each state defines a some representation of the algebra $\fA$. At this point, resulting representation is irreducible exactly when the state is pure. Close relationship between states and representations of $C^\ast$-algebra, based on the GNS construction, allows us to consider representations of the algebra as an effective tool for organization of states. This fact becomes more evident at the concrete realization $\pi(\fA)$.
Let us consider a concrete realization of the operator algebra $\fA$. A transition $\fA\Rightarrow\pi(\fA)$ from $\fA$ to a concrete algebra $\pi(\fA)$ is called sometimes as `clothing'. So, the basic observable is an \textit{energy} which represented by a Hermitian operator $H$. Let $G=\SO_0(1,3)\simeq\SL(2,\C)/\dZ_2$ be the group of fundamental symmetry, where $\SO_0(1,3)$ is the Lorentz group. Let $\widetilde{G}\simeq\SL(2,\C)$ be the \textit{universal covering} of $\SO_0(1,3)$. Let $H$ be the energy operator defined on the separable Hilbert space $\sH_\infty$. Then all the possible values of energy (states) are eigenvalues of the operator $H$. At this point, if $E_1\neq E_2$ are eigenvalues of $H$, and $\left|\Phi_1\right\rangle$ and $\left|\Phi_2\right\rangle$ are corresponding eigenvectors in the space $\sH_\infty$, then $\langle\Phi_1\mid\Phi_2\rangle=0$. All the eigenvectors, belonging to a given eigenvalue $E$, form (together with the null vector) an \textit{eigenvector subspace} $\sH_E$ of the Hilbert space $\sH_\infty$. All the eigenvector subspaces $\sH_E\in\sH_\infty$ are finite-dimensional. A dimensionality $r$ of $\sH_E$ is called a \textit{multiplicity} of the eigenvalue $E$. When $r>1$ the eigenvalue $E$ is \textit{$r$-fold degenerate}. Further, let $\sX_l$, $\sY_l$ be infinitesimal operators of the complex envelope of the group algebra $\mathfrak{sl}(2,\C)$ for the universal covering $\widetilde{G}$, $l=1,2,3$. As is known \cite{BHJ26}, the energy operator $H$ commutes with the all operators in $\sH_\infty$, which represent a Lie algebra of the group $\widetilde{G}$. Let us consider an arbitrary eigenvector subspace $\sH_E$ of the energy operator $H$. Since the operators $\sX_l$, $\sY_l$ and $H$ commute with the each other, then, as is known \cite{Dir}, for these operators we can build a common system of eigenfunctions. It means that the subspace $\sH_E$ is invariant with respect to operators $\sX_l$, $\sY_l$ (moreover, the operators $\sX_l$, $\sY_l$ can be considered \textit{only on} $\sH_E$). Further, we suppose that there is a some \textit{local representation} of the group $\widetilde{G}$ defined by the operators acting in the space $\sH_\infty$. At this point, we assume that all the representing operators commute with $H$. Then the each eigenvector subspace $\sH_E$ of the energy operator is invariant with respect to operators of complex momentum $\sX_l$, $\sY_l$. It allows us to identify subspaces $\sH_E$ with symmetrical spaces $\Sym_{(k,r)}$ of interlocking representations $\boldsymbol{\tau}_{k/2,r/2}$ of the Lorentz group. Thus, we obtain a concrete realization (`clothing') of the operator algebra $\pi(\fA)\rightarrow\pi(H)$, where $\pi\equiv\boldsymbol{\tau}_{k/2,r/2}$. The system of interlocking representations of the Lorentz group is shown on the Fig.\,1 (for more details see \cite{Var03,Var07}). Hence it follows that the each possible value of energy (energy level) is a vector state of the form (\ref{VectState}):
\begin{equation}\label{VectState2}
\omega_\Phi(H)=\frac{\langle\Phi\mid\pi(H)\Phi\rangle}{\langle\Phi\mid\Phi\rangle}=
\frac{\langle\Phi\mid\boldsymbol{\tau}_{k/2,r/2}(H)\Phi\rangle}{\langle\Phi\mid\Phi\rangle},
\end{equation}
The state $\omega_\Phi(H)$ is associated with the representation $\pi\equiv\boldsymbol{\tau}_{k/2,r/2}$ and the each $\omega_\Phi(H)$ corresponds to a non-null (cyclic) vector $\left|\Phi\right\rangle\in\sH_\infty$.
Further, in virtue of the isomorphism $\SL(2,\C)\simeq\spin_+(1,3)$ we will consider the universal covering $\widetilde{G}$ as a \textit{spinor group}. It allows us to associate in addition a \textit{spinor structure} with the each cyclic vector $\left|\Phi\right\rangle\in\sH_\infty$ (in some sense, it be a second layer in `clothing' of the operator algebra). Spintensor representations of the group $\widetilde{G}\simeq\spin_+(1,3)$ form a \textit{substrate} of interlocking representations $\boldsymbol{\tau}_{k/2,r/2}$ of the Lorentz group realized in the spaces $\Sym_{(k,r)}\subset\dS_{2^{k+r}}$, where $\dS_{2^{k+r}}$ is a spinspace. In its turn, as it is known \cite{Lou91}, a spinspace is a minimal left ideal of the Clifford algebra $\cl_{p,q}$, that is, there exists an isomorphism $\dS_{2^m}(\K)\simeq I_{p,q}=\cl_{p,q}f$, where $f$ is a primitive idempotent of $\cl_{p,q}$, and $\K=f\cl_{p,q}f$ is a division ring of the algebra $\cl_{p,q}$, $m=(p+q)/2$. The complex spinspace $\dS_{2^m}(\C)$ is a complexification $\C\otimes I_{p,q}$ of the minimal left ideal $I_{p,q}$ of the real subalgebra $\cl_{p,q}$. So, $\dS_{2^{k+r}}(\C)$ is the minimal left ideal of the complex algebra $\C_{2k}\otimes\overset{\ast}{\C}_{2r}\simeq\C_{2(k+r)}$ (for more details see \cite{Var15,Var16}). Let us define a system of \textit{basic cyclic vectors} endowed with the complex spinor structure (these vectors correspond to the system of interlocking representations of the Lorentz group):
\begin{eqnarray}
&&\mid\C_0,\boldsymbol{\tau}_{0,0}(H)\Phi\rangle;\nonumber\\
&&\mid\C_2,\boldsymbol{\tau}_{1/2,0}(H)\Phi\rangle,\quad\mid\overset{\ast}{\C}_2,\boldsymbol{\tau}_{0,1/2}(H)\Phi\rangle;
\nonumber\\
&&\mid\C_2\otimes\C_2,\boldsymbol{\tau}_{1,0}(H)\Phi\rangle,\quad
\mid\C_2\otimes\overset{\ast}{\C}_2,\boldsymbol{\tau}_{1/2,1/2}(H)\Phi\rangle,\quad
\mid\overset{\ast}{\C}_2\otimes\overset{\ast}{\C}_2,\boldsymbol{\tau}_{0,1}(H)\Phi\rangle;\nonumber\\
&&\mid\C_2\otimes\C_2\otimes\C_2,\boldsymbol{\tau}_{3/2,0}(H)\Phi\rangle,\quad
\mid\C_2\otimes\C_2\otimes\overset{\ast}{\C}_2,\boldsymbol{\tau}_{1,1/2}(H)\Phi\rangle,\quad
\mid\C_2\otimes\overset{\ast}{\C}_2\otimes\overset{\ast}{\C}_2,\boldsymbol{\tau}_{1/2,1}(H)\Phi\rangle,\nonumber\\
&&\mid\overset{\ast}{\C}_2\otimes\overset{\ast}{\C}_2\otimes\overset{\ast}{\C}_2,\boldsymbol{\tau}_{0,3/2}(H)\Phi\rangle;
\nonumber\\
&&\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots
\nonumber
\end{eqnarray}
Therefore, in accordance with GNS construction we have complex vector states of the form
\begin{equation}\label{VectState3}
\omega^c_\Phi(H)=
\frac{\langle\Phi\mid\C_{2(k+r)},\boldsymbol{\tau}_{k/2,r/2}(H)\Phi\rangle}{\langle\Phi\mid\Phi\rangle},
\end{equation}
The states $\omega^c_\Phi(H)$ are associated with the complex representations $\boldsymbol{\tau}_{k/2,r/2}(H)$ and cyclic vectors $\left|\Phi\right\rangle\in\sH_\infty$.
As is known, in the Lagrangian formalism of the standard (local) quantum field theory \textit{charged particles} are described by \textit{complex fields}. In our case, pure states of the form (\ref{VectState3}) correspond to \textit{charged states}. At this point, the sign of charge is changed under action of the pseudoautomorphism $\cA\rightarrow\overline{\cA}$ of the complex spinor structure (for more details see \cite{Var01a,Var04,Var14}). Following to analogy with the Lagrangian formalism, where \textit{neutral particles} are described by \textit{real fields}, we introduce vector states of the form
\begin{equation}\label{VectState4}
\omega^r_\Phi(H)=
\frac{\langle\Phi\mid\cl_{p,q},\boldsymbol{\tau}_{k/2,r/2}(H)\Phi\rangle}{\langle\Phi\mid\Phi\rangle}.
\end{equation}
The states (\ref{VectState4}) are associated with the real representations $\boldsymbol{\tau}_{k/2,r/2}(H)$, that is, these representations are endowed with a \textit{real spinor structure}, where $\cl_{p,q}$ is a real subalgebra of $\C_{2(k+r)}$. States of the form (\ref{VectState4}) correspond to \textit{neutral states}. Since the real spinor structure is appeared in the result of reduction $\C_{2(k+r)}\rightarrow\cl_{p,q}$, then (as a consequence) a \textit{charge conjugation} $C$ (pseudoautomorphism $\cA\rightarrow\overline{\cA}$) for the algebras $\cl_{p,q}$ over the real number field $\F=\R$ and quaternionic division ring $\K\simeq\BH$ (the types $p-q\equiv 4,6\pmod{8}$) is reduced to \textit{particle-antiparticle interchange} $C^\prime$ (see \cite{Var01a,Var04,Var14}). As is known, there exist two classes of neutral particles: 1) particles which have antiparticles, such as neutrons, neutrino\footnote{However, it should be noted that the question whether neutrinos are Dirac or Majorana particles (truly neutral fermions) is still open (the last hypothesis being preferred by particle physicists).} and so on; 2) particles which coincide with their antiparticles (for example, photons, $\pi^0$-mesons and so on), that is, so-called \textit{truly neutral particles}. The first class is described by neutral states $\omega^r_\Phi(H)$ with the algebras $\cl_{p,q}$ over the field $\F=\R$ with the rings $\K\simeq\BH$ and $\K\simeq\BH\oplus\BH$ (types $p-q\equiv 4,6\pmod{8}$ and $p-q\equiv 5\pmod{8}$). With the aim to describe the second class of neutral particles we introduce \textit{truly neutral states} $\omega^{r_0}_\Phi(H)$ with the algebras $\cl_{p,q}$ over the number field $\F=\R$ and real division rings $\K\simeq\R$ and $\K\simeq\R\oplus\R$ (types $p-q\equiv 0,2\pmod{8}$ and $p-q\equiv 1\pmod{8}$). In the case of states $\omega^{r_0}_\Phi(H)$ pseudoautomorphism $\cA\rightarrow\overline{\cA}$ is reduced to identical transformation (particle coincides with its antiparticle).
In \cite{Var16b} it has been shown that basic energetic levels (states) of matter spectrum are constructed in terms of cyclic representations within GNS construction. A concrete realization of the operator algebra (energy operator) is defined via the spinor structure (SS). SS-morphisms define charge and discrete symmetries (charge conjugation $C$, parity transformation $P$, time reversal $T$ and their combinations) \cite{Var99,Var01a,Var01,Var05,Var05a,Var11,Var14}, associated with the each cyclic representation.
\subsection{Physical Hilbert space}
A set of pure states $\omega_\Phi(H)$, defined according to GNS construction by the equality (\ref{VectState2}), at the execution of condition $\omega_\Phi(H)\geq 0$ forms a \textit{physical Hilbert space}
\[
\bsH_{\rm phys}=\bsH^S\otimes\bsH^Q\otimes\bsH_\infty.
\]
It is easy to verify that axioms of addition, multiplication and scalar (inner) product are fulfilled for the vectors $\omega_\Phi(H)\rightarrow\left|\Psi\right\rangle\in\bsH_{\rm phys}$. We assume that a so-defined Hilbert space is \textit{nonseparable}, that is, in general case the axiom of separability is not executed in $\bsH_{\rm phys}$.
The space $\bsH_{\rm phys}$ is a second member of the pair $(\sH_\infty,\bsH_{\rm phys})$\footnote{In accordance with Heisenberg-Fock conception \cite{Heisen,Fock}, reality has a two-level structure: \textit{potential reality} and \textit{actual reality}. Heisenberg claimed that any quantum object (for example, elementary particle) belongs to both sides of reality: at first, to potential reality as a superposition, and to actual reality after reduction of superposition (for more details see \cite{Heisen,Fock,Var15b}).}, which defines two-level structure of the Hilbert space of single quantum system (quantum domain). Therefore, $\bsH_{\rm phys}$ describes spin and charge degrees of freedom of the particle state. In accordance with the charge degrees of freedom we separate three \textit{basic subspaces} in $\bsH_{\rm phys}$.\\
1) \textit{Subspace of charged states} $\bsH^\pm_{\rm phys}=\bsH^S\otimes\bsH^\pm\otimes\bsH_\infty$.\\
2) \textit{Subspace of neutral states} $\bsH^0_{\rm phys}=\bsH^S\otimes\bsH^0\otimes\bsH_\infty$.\\
3) \textit{Subspace of truly neutral states} $\bsH^{\overline{0}}_{\rm phys}=\bsH^S\otimes\bsH^{\overline{0}}\otimes\bsH_\infty$.\\
Basis vectors $\left|\Psi\right\rangle\in\bsH^\pm_{\rm phys}$ are formed by the states $\omega^c_\Phi(H)$ (see (\ref{VectState3})). Correspondingly, $\left|\Psi\right\rangle\in\bsH^0_{\rm phys}$ and $\left|\Psi\right\rangle\in\bsH^{\overline{0}}_{\rm phys}$ are formed by the states $\omega^{r}_\rho(H)$ and $\omega^{r_0}_\rho(H)$.
Pure states (cyclic representations) are divided with respect to a charge (an action of SS-pseudoautomorphism) on the subsets of charged, neutral and truly neutral states. The structure of matter spectrum is defined by a partition of a physical Hilbert space (state space) on the coherent subspaces \cite{Var16b}
\begin{equation}\label{Decomp3}
\bsH_{\rm phys}=\bigoplus_{b,\ell\in\dZ}\left[\bsH^\pm_{\rm phys}(b,\ell)\bigoplus\bsH^0_{\rm phys}(b,\ell)\bigoplus
\bsH^{\overline{0}}_{\rm phys}(b,\ell)\right],
\end{equation}
where
\[
\bsH^Q_{\rm phys}(b,\ell)=\bigoplus^{|l-\dot{l}|}_{s=-|l-\dot{l}|}\bsH^{2|s|+1}\otimes\bsH^Q(b,\ell)\otimes\bsH_\infty,\quad
Q=\{\pm,0,\overline{0}\}.
\]
Here $b$ and $\ell$ are eigenvalues of baryon $B$ and lepton $L$ charges. At the values of electric charge $Q=\{\pm,0,\overline{0}\}$ we have three basic subspaces: subspace of charged states $\bsH^\pm_{\rm phys}(b,\ell)$, subspace of neutral states $\bsH^0_{\rm phys}(b,\ell)$ and subspace of truly neutral states $\bsH^{\overline{0}}_{\rm phys}(b,\ell)$.
\section{Lepton sector}
The lepton sector contains states belonging to coherent subspaces $\bsH^\pm_{\rm phys}(0,\ell)$ and $\bsH^0_{\rm phys}(0,\ell)$\footnote{Or $\bsH^{\overline{0}}_{\rm phys}(0,\ell)$ in case of Majorana neutrinos (truly neutral fermions).}, where the lepton number (flavor) $\ell$ takes three values: $\ell_\alpha=\{\ell_e,\ell_\mu,\ell_\tau\}$. All the states (particles) of the lepton sector are fermions of the spin 1/2, therefore, according to GNS construction, they are described by cyclic representations belonging to spin lines 1/2 and -1/2 (see Fig.\,1). For the charged leptons we have the following coherent subspaces:
\begin{equation}\label{ChargeLep-}
\bsH^\pm_{\rm phys}(0,\ell_\alpha)=\bsH^2\otimes\bsH^\pm(0,\ell_\alpha)\otimes\bsH_\infty,
\end{equation}
\begin{equation}\label{ChargeLep+}
\overset{\ast}{\bsH}{}^\mp_{\rm phys}(0,\ell_\alpha)=\bsH^2\otimes\bsH^\mp(0,\ell_\alpha)\otimes\bsH_\infty,
\end{equation}
Charged leptons $e^-$, $\mu^-$, $\tau^-$ and their antiparticles ($e^+$, $\mu^+$, $\tau^+$) form qubit-like nonseparable states in the spaces (\ref{ChargeLep-}) and (\ref{ChargeLep+}), respectively.
Using the formula (\ref{MGY}), we define now masses of the charged leptons. The least rest mass corresponds to electron:
\[
m_e=0,511\;\;\text{MeV}.
\]
This experimental value of electron mass is a fundamental constant in the formula (\ref{MGY}). In other words, $m_e$ is an original point in the mass frame of reference, and theoretical masses of all other states (``elementary particles'') are calculated from which. The following (on the mass scale) lepton is a muon $\mu^-$ with experimental mass value
\begin{equation}\label{Mexp}
m_\mu=105,66\;\;\text{MeV}.
\end{equation}
The muon mass is approximately 207 times (206,77) as much the electron mass. This mass value corresponds to cyclic representation $(l,\dot{l})$ on the spin-1/2 line at $l=14$ and $\dot{l}=27/2$:
\begin{equation}\label{Mtheor}
m^{\frac{1}{2}}_\mu=m_e\left(l+\frac{1}{2}\right)\left(\dot{l}+\frac{1}{2}\right)=103,73.
\end{equation}
The absolute error between experimental (\ref{Mexp}) and calculated (\ref{Mtheor}) values is equal to $-1,93$; the relative error is $-1,98\%$.
Analogously, for the $\tau$-lepton with experimental mass value
\begin{equation}\label{Texp}
m_\tau=1776,84\;\;\text{MeV}
\end{equation}
we have a cyclic representation $(l,\dot{l})$ on the spin-1/2 line at $l=117/2$, $\dot{l}=58$ with the mass
\begin{equation}\label{Ttheor}
m^{\frac{1}{2}}_\tau=m_e\left(l+\frac{1}{2}\right)\left(\dot{l}+\frac{1}{2}\right)=1763,72.
\end{equation}
The absolute error between (\ref{Texp}) and (\ref{Ttheor}) is $-13,12$; the relative error is $-0,74\%$\footnote{In relation with the masses of charged leptons to be of interest to recall a further empirical mass formula. In 1983, Koide \cite{Koi83} proposed the following formula:
\[
m_e+m_\mu+m_\tau=\frac{2}{3}\left(\sqrt{m_e}+\sqrt{m_\mu}+\sqrt{m_\tau}\right)^2,
\]
which relates the masses of charged leptons. It should be noted that Koide predicted (on the ground of this formula) the mass $\tau$-lepton (1777 MeV) which coincides very exactly with the modern mass value of this particle (see (\ref{Texp})), whereas in 1983 this value had 1784 Mev. About Koide's formula and its interpretations and applications see \cite{Gsp05,Foot,Esp}.}.
Neutrino states of matter spectrum are described within coherent subspaces $\bsH^0_{\rm phys}(0,\ell)$ (Dirac neutrinos) or $\bsH^{\overline{0}}_{\rm phys}(0,\ell)$ (Majorana neutrinos). All neutrino states are neutral (or truly neutral) fermions of the spin 1/2. According to GNS construction, these states define cyclic representations of the spin lines 1/2 and -1/2. For the Dirac neutrinos we have two copies of coherent subspaces
\begin{equation}\label{Neutrino1}
\bsH^0_{\rm phys}(0,\nu_\alpha)=\bsH^2\otimes\bsH^0(0,\nu_\alpha)\otimes\bsH_\infty,
\end{equation}
\begin{equation}\label{Neutrino2}
\overline{\bsH}^0_{\rm phys}(0,\nu_\alpha)=\bsH^2\otimes\overline{\bsH}^0(0,\nu_\alpha)\otimes\bsH_\infty.
\end{equation}
These subspaces are transformed into each other under action of the SS-pseudoautomorphism. In case of Majorana neutrinos, for the each neutrino flavor ($\nu_\alpha=\{\nu_e,\nu_\mu,\nu_\tau\}$) we have the only one copy of coherent subspace
\begin{equation}\label{Neutrino3}
\bsH^{\overline{0}}_{\rm phys}(0,\nu_\alpha)=\bsH^2\otimes\bsH^{\overline{0}}(0,\nu_\alpha)\otimes\bsH_\infty.
\end{equation}
In this case SS-pseodoautomorphism is reduced to an identical transformation.
Further, for any kind of neutrino (Dirac or Majorana) all the neutrino states are defined by quantum superpositions
\begin{equation}\label{Neutrino}
\nu_\alpha=\sum_iU_{\alpha i}\nu_i,
\end{equation}
where $\nu_i$ are neutrino mass states, $U_{\alpha i}$ are elements of the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix (PMNS)
\begin{multline}
U=\begin{pmatrix} 1 & 0 & 0\\
0 & \cos\theta_{23} & \sin\theta_{23}\\
0 & -\sin\theta_{23} & \cos\theta_{23}
\end{pmatrix}\times\\
\times\begin{pmatrix} \cos\theta_{13} & 0 & \sin\theta_{13}\exp(-i\delta)\\
0 & 1 & 0\\
-\sin\theta_{13}\exp(-i\delta) & 0 & \cos\theta_{13}
\end{pmatrix}\times\\
\times\begin{pmatrix} \cos\theta_{12} & \sin\theta_{12} & 0\\
-\sin\theta_{12} & \cos\theta_{12} & 0\\
0 & 0 & 1
\end{pmatrix}.\nonumber
\end{multline}
Here the mixing angle $\theta_{12}$ describes ``solar'' and ``reactor'' oscillations, and $\theta_{23}$ serves for description of ``atmospheric'' and ``acceleration'' oscillations \cite{Olsh}. Thus, all neutrinos form superpositions of the type (\ref{Neutrino}) in the coherent subspaces (\ref{Neutrino1})--(\ref{Neutrino2}) or (\ref{Neutrino3}).
Neutrino oscillations show that lepton number (flavor) is not conserved for the neutrino, that is, neutrino with a definite flavor cannot be considered as a particle with a definite mass, therefore, it presents by itself a quantum superposition of massive neutrino states\footnote{It should be noted that mixing matrix $U$ is attributed to neutrino only for convenience. In fact, $U$ is a general lepton mixing matrix \cite{Bed}. Can we expect that instead charged lepton with a definite flavor there exists a quantum superposition $\ell_i=\sum_\alpha U_{\alpha i}\ell_\alpha$ and, as a consequence, there are oscillations of charged leptons \cite{Bed}? It is natural to assume that the superposition structure (\ref{Neutrino}), which is characteristic of neutrino, is also a general feature of the all objects of microworld. To all appearances, an absence of experimental evidences in favour of existence of oscillations of charged leptons consists in the fact that for majority of practical cases the mass square difference of charged leptons is too much for a creation of charged leptons in a coherent quantum superposition.}.
\section{Meson sector}
A meson sector of the matter spectrum is formed by the states belonging to coherent subspaces $\bsH^\pm_{\rm phys}(0,0)$ and $\bsH^0_{\rm phys}(0,0)$ (or $\bsH^{\overline{0}}_{\rm phys}(0,0)$), where the lepton $\ell$ and baryon $b$ numbers are equal to zero. All mesons are states with integer spin. Therefore, in accordance with GNS construction all meson states are described by cyclic representations belonging to spin lines of integer spin with the non-null mass. Below we give tables for the lines of spin $0$, $1$, $\ldots$, $4$, including all known at the present time (according to Particle Data Group \cite{PDG}\footnote{In the tables we include only states with a three-star status (at the minimum).}) mesons of these spin lines. In the first column of the each table we give a standard designation of the state and its mass in MeV. The second column of the table contains a calculated (according to (\ref{MGY})) mass value of the corresponding state. The third column contains a relative error between experimental and calculated values. In the fourth column we give parameters $l$ and $\dot{l}$ of the corresponding cyclic representation.
\begin{center}
{\textbf{Table\,I.} Mesons: spin-0 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $\pi$ -- $139,57$ & $139,12$ & $-0,32$ & $(16,16)$\\
2. & $K$ -- $493,67$ & $491,07$ & $-0,52$ & $(61/2,61/2)$\\
3. & $f_0(500)$ & $507,03$ & $+1,40$ & $(31,31)$\\
4. & $\eta$ -- $547,86$ & $539,74$ & $-1,46$ & $(32,32)$\\
5. & $\eta^\prime(958)$ -- $957,78$ & $966,94$ & $+0,95$ & $(43,43)$\\
6. & $a_0(980)$ & $989,29$ & $+0,94$ & $(87/2,87/2)$\\
7. & $f_0(980)$ -- $990$ & $989,29$ & $-0,07$ & $(87/2,87/2)$\\
8. & $\eta(1295)$ & $1277,50$ & $-1,35$ & $(99/2,99/2)$\\
9. & $\pi(1300)$ & $1303,18$ & $+0,24$ & $(50,50)$\\
10. & $f_0(1370)$ & $1381,74$ & $+0,85$ & $(103/2,103/2)$\\
11. & $\eta(1405)$ -- $1408,8$ & $1408,44$ & $-0,02$ & $(52,52)$\\
12. & $K^\ast_0(1430)$ & $1435,39$ & $+0,37$ & $(105/2,105/2)$\\
13. & $a_0(1450)$ & $1435,39$ & $-1,00$ & $(105/2,105/2)$\\
14. & $\eta(1475)$ & $1462,61$ & $-0,84$ & $(53,53)$\\
15. & $f_0(1500)$ & $1490,08$ & $-0,66$ & $(107/2,107/2)$\\
16. & $f_0(1710)$ -- $1723\pm{}^{6}_{5}$ & $1719$ & $-0,23$ & $(115/2,115/2)$\\
17. & $\pi(1800)$ -- $1812\pm 12$ & $1809,07$ & $-0,16$ & $(59,59)$\\
18. & $D$ -- $1869,62$ & $1870,39$ & $+0,04$ & $(60,60)$\\
19. & $D^\pm_s$ -- $1968,30$ & $1964,28$ & $-0,21$ & $(123/2,123/2)$\\
20. & $D^\ast_{s0}(2317)^\pm$ -- $2317,7\pm 0,6$ & $2328,24$ & $+0,48$ & $(67,67)$\\
21. & $\eta_c(1S)$ -- $2983,6\pm 0,61$ & $2990,50$ & $+0,23$ & $(76,76)$\\
22. & $\chi_{c0}(1P)$ -- $3414,75$ & $3394,19$ & $-0,60$ & $(81,81)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\renewcommand{\arraystretch}{1.0}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
23. & $\eta_c(2S)$ -- $3639,2\pm 1,2$ & $3648,67$ & $+0,26$ & $(84,84)$\\
24. & $\chi_{c0}(3915)$ -- $3918,4\pm 1,9$ & $3912,34$ & $-0,15$ & $(87,87)$\\
25. & $B$ -- $5279,29$ & $5264,45$ & $-0,28$ & $(101,101)$\\
26. & $B^0_s$ -- $5366,79$ & $5368,69$ & $+0,04$ & $(102,102)$\\
27. & $B^\pm_c$ -- $6275\pm 1$ & $6296,03$ & $+0,32$ & $(221/2,221/2)$\\
28. & $\chi_{b0}(1P)$ -- $9859,44$ & $9873,03$ & $+0,14$ & $(277/2,277/2)$\\
29. & $\chi_{b0}(2P)$ -- $10232,5$ & $10231,37$ & $-0,006$ & $(141,141)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\textbf{Table\,II.} Mesons: spin-1 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $\rho(770)$ -- $775,26$ & $777,1$ & $+0,24$ & $(39,38)$\\
2. & $\omega(782)$ -- $782,65$ & $797,16$ & $+1,93$ & $(79/2,77/2)$\\
3. & $K^\ast(892)$ & $901,28$ & $+1,04$ & $(42,41)$\\
4. & $\phi(1020)$ -- $1019,46$ & $1011,78$ & $-0,76$ & $(89/2,89/2)$\\
5. & $h_1(1170)$ & $1177,22$ & $+0,61$ & $(48,47)$\\
6. & $b_1(1235)$ -- $1229,5$ & $1226,78$ & $-0,22$ & $(49,48)$\\
7. & $a_1(1260)$ & $1251,95$ & $-0,63$ & $(99/2,97/2)$\\
8. & $K_1(1270)$ -- $1272\pm 7$ & $1277,37$ & $+0,42$ & $(50,49)$\\
9. & $f_1(1285)$ -- $1281,9$ & $1277,37$ & $-0,35$ & $(50,49)$\\
10. & $\pi_1(1400)$ & $1408,32$ & $+0,59$ & $(105/2,103/2)$\\
11. & $K_1(1400)$ -- $1403\pm 7$ & $1408,32$ & $+0,38$ & $(105/2,103/2)$\\
12. & $K^\ast_1(1410)$ -- $1414\pm 15$ & $1408,32$ & $-0,40$ & $(105/2,103/2)$\\
13. & $f_1(1420)$ -- $1426,4$ & $1435,27$ & $+0,62$ & $(53,52)$\\
14. & $\omega(1420)$ & $1435,27$ & $+0,62$ & $(53,52)$\\
15. & $\rho(1450)$ & $1462,48$ & $+0,86$ & $(107/2,105/2)$\\
16. & $\pi_1(1600)$ & $1602,37$ & $+0,15$ & $(56,55)$\\
17. & $\omega(1650)$ & $1660,11$ & $+0,61$ & $(57,56)$\\
18. & $\phi(1680)$ & $1689,37$ & $+0,56$ & $(115/2,113/2)$\\
19. & $K^\ast(1680)$ & $1689,37$ & $+0,56$ & $(115/2,113/2)$\\
20. & $\rho(1700)$ & $1689,37$ & $-0,62$ & $(115/2,113/2)$\\
21. & $D^\ast(2007)^0$ -- $2006,97$ & $1995,97$ & $-0,55$ & $(125/2,123/2)$\\
22. & $D^\ast(2010)^\pm$ & $1995,97$ & $-0,69$ & $(125/2,123/2)$\\
23. & $\phi(2170)$ -- $2175,97\pm 15$ & $2192,19$ & $+0,79$ & $(131/2,129/2)$\\
24. & $D_1(2420)^0$ & $2432,74$ & $+0,53$ & $(69,68)$\\
25. & $D_{s1}(2460)^\pm$ & $2468,13$ & $+0,33$ & $(139/2,137/2)$\\
26. & $D_{s1}(2536)^\pm$ & $2539,67$ & $+0,14$ & $(141/2,139/2)$\\
27. & $D^\ast_{s1}(2700)^\pm$ -- $2709\pm 4$ & $2722,99$ & $+0,52$ & $(73,72)$\\
28. & $J/\psi(1S)$ -- $3096,916$ & $3108,79$ & $+0,38$ & $(78,77)$\\
29. & $\chi_{c1}(1P)$ -- $3510,66$ & $3520,15$ & $+0,27$ & $(83,82)$\\
30. & $\chi_{c}(1P)$ -- $3525,38$ & $3520,15$ & $-0,16$ & $(83,82)$\\
31. & $\psi(2S)$ -- $3686,09$ & $3691,85$ & $+0,16$ & $(85,84)$\\
32. & $\psi(3770)$ -- $3773,15\pm 0,33$ & $3779,23$ & $+0,16$ & $(86,85)$\\
33. & $\chi(3872)$ -- $3871,69\pm 0,17$ & $3867,63$ & $-0,10$ & $(87,86)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\renewcommand{\arraystretch}{1.0}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
34. & $\chi(3900)$ -- $3888,7\pm 3,4$ & $3912,22$ & $+0,60$ & $(175/2,173/2)$\\
35. & $\psi(4040)$ -- $4039\pm 1$ & $4047,50$ & $+0,18$ & $(89,88)$\\
36. & $\psi(4160)$ -- $4191\pm 5$ & $4185,09$ & $-0,14$ & $(181/2,179/2)$\\
37. & $\chi(4260)$ -- $4251\pm 9$ & $4278,08$ & $+0,64$ & $(183/2,181/2)$\\
38. & $\chi(4360)$ -- $4354\pm 10$ & $4372,12$ & $+0,42$ & $(185/2,183/2)$\\
39. & $\psi(4415)$ -- $4421\pm 4$ & $4419,51$ & $-0,03$ & $(93,92)$\\
40. & $\chi(4430)$ -- $4478\pm{}^{15}_{18}$ & $4467,12$ & $-0,24$ & $(187/2,185/2)$\\
41. & $\chi(4660)$ -- $4665\pm 10$ & $4660,32$ & $-0,10$ & $(191/2,189/2)$\\
42. & $B^\ast$ -- $5325,1$ & $5316,32$ & $-0,16$ & $(102,101)$\\
43. & $B^\ast_s$ -- $5415,4\pm{}^{1,8}_{1,5}$ & $5421,07$ & $+0,10$ & $(103,102)$\\
44. & $B_1(5721)^0$ & $5741,47$ & $+0,36$ & $(106,105)$\\
45. & $B_{s1}(5830)^0$ -- $5828,4$ & $5850,31$ & $+0,37$ & $(107,106)$\\
46. & $\Upsilon(1S)$ -- $9460,30\pm 0,26$ & $9451,33$ & $-0,09$ & $(136,135)$\\
47. & $\chi_{b1}(1P)$ -- $9892,78$ & $9872,90$ & $-0,20$ & $(139,138)$\\
48. & $\Upsilon(2S)$ -- $10023,26$ & $10015,47$ & $-0,08$ & $(140,139)$\\
49. & $\chi_{b1}(2P)$ -- $10255,46$ & $10231,24$ & $-0,24$ & $(283/2,281/2)$\\
50. & $\Upsilon(3S)$ -- $10355,2$ & $10376,37$ & $+0,20$ & $(285/2,283/2)$\\
51. & $\chi_{b1}(3P)$ -- $10512,1\pm 2,3$ & $10522,51$ & $+0,09$ & $(287/2,285/2)$\\
52. & $\Upsilon(4S)$ -- $10579,4$ & $10595,97$ & $+0,16$ & $(144,143)$\\
53. & $\Upsilon(10860)$ -- $10876\pm 11$ & $10892,35$ & $+0,15$ & $(146,145)$\\
53. & $\Upsilon(11020)$ -- $11019\pm 8$ & $11042,07$ & $+0,21$ & $(147,146)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\textbf{Table\,III.} Mesons: spin-2 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $f_2(1270)$ -- $1275,5$ & $1276,99$ & $+0,12$ & $(101/2,97/2)$\\
2. & $a_2(1320)$ -- $1318,3$ & $1328,60$ & $+0,78$ & $(103/2,99/2)$\\
3. & $K^\ast_2(1430)$ & $1434,89$ & $+0,34$ & $(107/2,103/2)$\\
4. & $f^\prime_2(1525)$ & $1517,87$ & $-0,50$ & $(55,53)$\\
5. & $\eta_2(1645)$ -- $1617\pm 5$ & $1630,73$ & $+0,85$ & $(57,55)$\\
6. & $\pi_2(1670)$ -- $1672\pm 3$ & $1659,73$ & $-0,73$ & $(115/2,111/2)$\\
7. & $K_2(1770)$ -- $1773\pm 8$ & $1778,28$ & $+0,29$ & $(119/2,115/2)$\\
8. & $K_2(1820)$ -- $1816\pm 13$ & $1808,56$ & $-0,40$ & $(60,58)$\\
9. & $\pi_2(1880)$ & $1869,88$ & $-0,54$ & $(61,59)$\\
10. & $f_2(1950)$ & $1963,77$ & $+0,70$ & $(125/2,121/2)$\\
11. & $f_2(2010)$ & $1995,58$ & $-0,72$ & $(63,61)$\\
12. & $f_2(2300)$ & $2293,37$ & $-0,29$ & $(135/2,131/2)$\\
13. & $f_2(2340)$ & $2327,73$ & $-0,52$ & $(68,66)$\\
14. & $D^\ast_2(2460)^0$ -- $2462,6\pm 0,6$ & $2467,75$ & $+0,20$ & $(70,68)$\\
15. & $D^\ast_2(2460)^\pm$ -- $2464,3\pm 1,6$ & $2467,75$ & $+0,14$ & $(70,68)$\\
16. & $\chi_{c2}(1P)$ -- $3556,2$ & $3562,30$ & $+0,17$ & $(84,82)$\\
17. & $\chi_{c2}(2P)$ -- $3927,2\pm 2,6$ & $3911,83$ & $-0,39$ & $(88,86)$\\
18. & $B^\ast_2(5747)^0$ -- $5739\pm 5$ & $5741,08$ & $+0,04$ & $(213/2,209/2)$\\
19. & $B^\ast_{s2}(5840)^0$ & $5849,92$ & $+0,17$ & $(215/2,211/2)$\\
20. & $\chi_{b2}(1P)$ -- $9912,21$ & $9943,67$ & $+0,32$ & $(140,138)$\\
21. & $\Upsilon(1D)$ -- $10163,7\pm 1,4$ & $10158,68$ & $-0,04$ & $(283/2,279/2)$\\
22. & $\chi_{b2}(2P)$ -- $10268,65$ & $10230,87$ & $-0,37$ & $(142,140)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\textbf{Table\,IV.} Mesons: spin-3 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $\omega_3(1670)$ -- $1667\pm 4$ & $1659,09$ & $-0,47$ & $(58,55)$\\
2. & $\rho_3(1690)$ -- $1688,8\pm 2,1$ & $1688,34$ & $-0,03$ & $(117/2,111/2)$\\
3. & $K^\ast_3(1780)$ -- $1776\pm 7$ & $1777,64$ & $+0,09$ & $(60,57)$\\
4. & $\phi_3(1850)$ -- $1854\pm 7$ & $1838,45$ & $-0,84$ & $(61,58)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\textbf{Table\,V.} Mesons: spin-4 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $a_4(2040)$ -- $1995\pm 10$ & $1994,05$ & $-0,05$ & $(64,60)$\\
2. & $f_4(2050)$ -- $2018\pm 11$ & $2026,11$ & $+0,40$ & $(129/2,121/2)$\\
3. & $K^\ast_4(2045)$ -- $2045\pm 9$ & $2058,43$ & $+0,66$ & $(65,61)$\\
\hline
\end{tabular}
}
\end{center}
\section{Baryon sector}
The baryon sector is divided (with respect to a charge) on the two sets of coherent subspaces: charged baryons with half-integer spin (all baryons have half-integer spin) from the subspaces $\bsH^\pm_{\rm phys}(b,0)$; neutral baryons of half-integer spin (states from the coherent subspaces of the type $\bsH^0_{\rm phys}(b,0)$).
\begin{center}
{\textbf{Table\,VI.} Baryons: spin-1/2 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $p$ -- $938,27$ & $933,85$ & $-0,47$ & $(85/2,42)$\\
2. & $n$ -- $939,56$ & $933,85$ & $-0,60$ & $(85/2,42)$\\
3. & $\Lambda$ -- $1115,68$ & $1116,79$ & $+0,09$ & $(93/2,46)$\\
4. & $\Sigma$ -- $1189,37$ & $1189,60$ & $+0,02$ & $(48,95/2)$\\
5. & $\Xi$ -- $1314,86$ & $1316,08$ & $+0,09$ & $(101/2,50)$\\
6. & $\Lambda(1405)$ & $1395,03$ & $-0,70$ & $(52,103/2)$\\
7. & $N(1440)$ & $1448,94$ & $+0,60$ & $(53,105/2)$\\
8. & $N(1535)$ & $1531,72$ & $-0,21$ & $(109/2,54)$\\
9. & $\Lambda(1600)$ & $1588,19$ & $-0,73$ & $(111/2,55)$\\
10. & $\Delta(1620)$ $\approx 1630$ & $1616,80$ & $-0,80$ & $(56,111/2)$\\
11. & $N(1650)$ $\approx 1655$ & $1645,67$ & $-0,56$ & $(113/2,56)$\\
12. & $\Sigma(1660)$ & $1674,80$ & $+0,89$ & $(57,113/2)$\\
13. & $\Lambda(1670)$ & $1674,80$ & $+0,28$ & $(57,113/2)$\\
14. & $N(1710)$ & $1704,18$ & $-0,34$ & $(115/2,57)$\\
15. & $\Sigma(1750)$ & $1733,82$ & $-0,92$ & $(58,115/2)$\\
16. & $\Lambda(1800)$ & $1793,86$ & $-0,34$ & $(59,117/2)$\\
17. & $\Lambda(1810)$ & $1824,27$ & $+0,78$ & $(119/2,59)$\\
18. & $\Delta(1910)$ $\approx 1890$ & $1885,84$ & $-0,22$ & $(121/2,60)$\\
19. & $\Lambda^+_c$ -- $2286,46$ & $2276,76$ & $-0,42$ & $(133/2,66)$\\
20. & $\Sigma_c(2455)$ -- $2453,97\pm 0,14$ & $2450,50$ & $-0,16$ & $(69,137/2)$\\
21. & $\Xi_c$ -- $2467,93\pm{}^{0,28}_{0,40}$ & $2486,01$ & $+0,60$ & $(139/2,69)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\renewcommand{\arraystretch}{1.0}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
22. & $\Xi^\prime_c(2578)$ & $2557,81$ & $-0,78$ & $(141/2,70)$\\
23. & $\Lambda_c(2595)^+$ -- $2592,25\pm 0,28$ & $2594,09$ & $+0,07$ & $(71,141/2)$\\
24. & $\Omega^0_c(2697)$ & $2704,46$ & $+0,27$ & $(145/2,72)$\\
25. & $\Xi_c(2790)$ & $2779,32$ & $-0,38$ & $(147/2,73)$\\
26. & $\Lambda^0_b$ -- $5620,2\pm 1,6$ & $5660,60$ & $+0,72$ & $(105,209/2)$\\
27. & $\Sigma^+_b$ -- $5807,8\pm 2,7$ & $5823,10$ & $+0,26$ & $(213/2,106)$\\
28. & $\Xi^0_b$ -- $5792,4\pm 3,0$ & $5768,68$ & $-0,40$ & $(106,211/2)$\\
29. & $\Xi^-_b$ -- $5792,4\pm 3,0$ & $5768,68$ & $-0,40$ & $(106,211/2)$\\
30. & $\Sigma^-_b$ -- $5815,2$ & $5823,10$ & $+0,08$ & $(213/2,106)$\\
31. & $\Lambda_b(5912)^0$ -- $5912,11\pm 0,26$ & $5932,71$ & $+0,35$ & $(215/2,107)$\\
32. & $\Xi^\prime_b(5935)^-$ -- $5935,02\pm 0,5$ & $5932,71$ & $-0,04$ & $(215/2,107)$\\
33. & $\Omega^-_b$ -- $6048,0\pm 1,9$ & $6043,34$ & $-0,08$ & $(217/2,108)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\textbf{Table\,VII.} Baryons: spin-3/2 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $\Delta(1232)$ & $1239,17$ & $+0,58$ & $(99/2,48)$\\
2. & $\Sigma(1385)$ & $1394,77$ & $+0,70$ & $(105/2,51)$\\
3. & $N(1520)$ & $1531,47$ & $+0,75$ & $(55,107/2)$\\
4. & $\Lambda(1520)$ & $1531,47$ & $+0,75$ & $(55,107/2)$\\
5. & $\Xi(1530)$ & $1531,47$ & $+0,09$ & $(55,107/2)$\\
6. & $\Delta(1600)$ & $1587,93$ & $-0,75$ & $(56,109/2)$\\
7. & $\Sigma(1670)$ & $1674,55$ & $+0,27$ & $(115/2,56)$\\
8. & $\Omega^-$ -- $1672,45$ & $1674,55$ & $+0,12$ & $(115/2,56)$\\
9. & $\Lambda(1690)$ & $1703,93$ & $+0,82$ & $(58,113/2)$\\
10. & $N(1700)$ & $1703,93$ & $+0,23$ & $(58,113/2)$\\
11. & $\Delta(1700)$ & $1703,93$ & $+0,23$ & $(58,113/2)$\\
12. & $N(1720)$ & $1733,57$ & $+0,79$ & $(117/2,57)$\\
13. & $\Xi(1820)$ & $1824,01$ & $+0,22$ & $(60,117/2)$\\
14. & $N(1875)$ & $1885,59$ & $+0,56$ & $(61,119/2)$\\
15. & $\Lambda(1890)$ & $1885,59$ & $-0,23$ & $(61,119/2)$\\
16. & $N(1900)$ & $1916,76$ & $+0,88$ & $(123/2,60)$\\
17. & $\Delta(1920)$ & $1916,76$ & $-0,17$ & $(123/2,60)$\\
18. & $\Sigma(1940)$ & $1948,19$ & $+0,42$ & $(62,121/2)$\\
19. & $\Sigma_c(2520)$ -- $2518,41\pm{}^{0,21}_{0,19}$ & $2521,53$ & $+0,12$ & $(141/2,69)$\\
20. & $\Lambda_c(2625)^+$ -- $2628,11\pm 0,19$ & $2630,37$ & $+0,08$ & $(72,141/2)$\\
21. & $\Xi_c(2645)$ & $2630,37$ & $-0,55$ & $(72,141/2)$\\
22. & $\Omega_c(2770)^0$ -- $2765,9\pm 2,0$ & $2779,07$ & $+0,33$ & $(74,145/2)$\\
23. & $\Xi_c(2815)$ -- $2816,6\pm 0,9$ & $2816,89$ & $+0,07$ & $(149/2,73)$\\
24. & $\Sigma^{\ast+}_b$ -- $5829,0\pm 3,4$ & $5822,85$ & $-0,10$ & $(107,211/2)$\\
25. & $\Sigma^{\ast-}_b$ -- $5836,4\pm 2,8$ & $5822,85$ & $-0,23$ & $(107,211/2)$\\
26. & $\Lambda_b(5920)^0$ -- $5919,81\pm 0,23$ & $5932,45$ & $+0,21$ & $(108,213/2)$\\
27. & $\Xi(5945)^0$ -- $5948,9\pm 1,5$ & $5987,64$ & $+0,65$ & $(217/2,107)$\\
28. & $\Xi^\ast_b(5955)^-$ -- $5955,33\pm 0,13$ & $5987,64$ & $+0,54$ & $(217/2,107)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\textbf{Table\,VIII.} Baryons: spin-5/2 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $N(1675)$ & $1674,04$ & $-0,06$ & $(58,111/2)$\\
2. & $N(1680)$ $\approx 1685$ & $1674,04$ & $-0,35$ & $(58,111/2)$\\
3. & $\Sigma(1775)$ & $1762,95$ & $-0,66$ & $(119/2,57)$\\
4. & $\Lambda(1820)$ & $1823,5$ & $+0,19$ & $(121/2,58)$\\
5. & $\Lambda(1830)$ & $1823,5$ & $-0,35$ & $(121/2,58)$\\
6. & $\Delta(1905)$ $\approx 1880$ & $1885,08$ & $+0,27$ & $(123/2,59)$\\
7. & $\Sigma(1915)$ & $1916,25$ & $+0,06$ & $(62,119/2)$\\
8. & $\Delta(1930)$ $\approx 1950$ & $1947,67$ & $-0,12$ & $(125/2,60)$\\
9. & $\Xi(2030)$ & $2043,49$ & $+0,66$ & $(64,123/2)$\\
10. & $\Lambda(2110)$ & $2108,64$ & $-0,06$ & $(65,125/2)$\\
11. & $\Lambda_c(2880)^+$ -- $2881,53\pm 0,35$ & $2892,77$ & $+0,39$ & $(76,147/2)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\textbf{Table\,IX.} Baryons: spin-7/2 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $\Delta(1950)$ $\approx 1930$ & $1933,88$ & $+0,20$ & $(125/2,59)$\\
2. & $\Sigma(2030)$ & $2042,72$ & $+0,63$ & $(129/2,61)$\\
3. & $\Lambda(2100)$ & $2107,87$ & $+0,37$ & $(131/2,62)$\\
4. & $N(2190)$ & $2174,05$ & $-0,73$ & $(133/2,63)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\textbf{Table\,X.} Baryons: spin-9/2 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $N(2220)$ $\approx 2250$ & $2240,22$ & $-0,43$ & $(68,127/2)$\\
2. & $N(2250)$ $\approx 2275$ & $2274,20$ & $+0,03$ & $(137/2,64)$\\
3. & $\Lambda(2350)$ & $2342,93$ & $-0,30$ & $(139/2,65)$\\
\hline
\end{tabular}
}
\end{center}
\begin{center}
{\textbf{Table\,XI.} Baryons: spin-11/2 line.}
{\renewcommand{\arraystretch}{1}
\begin{tabular}{|c||l|l|c|l|}\hline
& State and mass (exp.) -- MeV & Mass (theor.) & Error \% & $(l,\dot{l})$\\ \hline\hline
1. & $\Delta(2420)$ & $2411,40$ & $-0,35$ & $(71,131/2)$\\
2. & $N(2600)$ & $2590,26$ & $-0,37$ & $(147/2,68)$\\
\hline
\end{tabular}
}
\end{center}
\section{Mass quantization}
The tables I--XI show that masses of elementary particles are proportional to the rest mass of electron $m_e=0,511$ MeV with an accuracy of $0,41\%$. Taking into account mass-energy equivalence principle, one can say that the mass formula
\[
m^{(s)}=m_e\left(l+\frac{1}{2}\right)\left(\dot{l}+\frac{1}{2}\right),
\]
defining the mass (energy) of state (cyclic representation $(l,\dot{l})$), in some sense is equivalent to the well-known relation
\[
E=h\nu,
\]
where the electron mass $m_e$ plays a role of ``mass quantum''.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,902 |
Let's face it. Lately, I have been S.T. Rugglin. Which means that once again, you get something that i drew and colored years ago, instead of a fresh selection from my drawing board today. I'm going to work hard this weekend to get ahead on my blog posts, because I know the 5.7 people who read this blog rely on me for 19 seconds of diversion, twice a week. I promise there'll be all new stuff next week.
Eating: Nothing, I'm starved right now!
You're reading this impossibly dorky blog, and asking yourself, what kind of a person is this enigmatic J.Ho? Well let me tell you something–the other day my boss gave me a Transformers pencil (because it's well known throughout the office that I am a zealot for Transformers), and the first thing I did with that pencil… was sketch a Transformer. I did it, as if compelled by some greater force; as if inaugurating that Transformers pencil appropriately with a drawing of a Transformer was ensuring that all was right throughout the universe–nay, the multiverse. That is the kind of person that I am.
Though I never owned the Grotusque toy, I always thought the character looked cool: (sabre-toothed tiger) + (dragon) = WINNER, as far as I'm concerned. Unfortunately, because I don't own the toy, I have no idea what color it really is–in various photos I found online, the main torso appeared anywhere in the range of magenta, maroon, or burgundy. In the end, I think my colors skewed too close to the magenta end of the spectrum. Oh yeah, there's also no rhyme or reason to the light sources in this pic.
Close-up photos revealed that Grotusque's face was molded with a slight texture–in my mind, this implied fur, so I decided to give my interpretation an organic face.
The wing is cut off because that's where the paper stopped. And on that awkward note, I will end this post.
Transformers came out on DVD this week, and I'm glad to say that after repeat viewings I feel the same about it as when it first came out. I got an itch to draw the movie version of Bumblebee, which you can compare to my depiction of the cartoon version from a few months ago.
Those who know me have probably been baffled and confused that my blog has been so primarily focused on the world of He-Man. Indeed, even I am shocked that it has taken almost three full months for an illustration of a full-fledged Transformer to show up here (sorry Battle Beasts, being a part of the Transformers universe isn't the same as being a Transformer).
Bumblebee was the fresh-faced rookie of the original Transformers cartoon–he transformed from a Volkswagen Beetle into a robot. Since then, there have been, like, a million iterations of him in the toyline, but I won't get into that. A new version of the character is also going to be one of the main characters in the upcoming Transformers live-action movie.
My sketch is a pretty faithful rendition of the original cartoon version, and I was able to complete most of the drawing without needing to look at reference. Whether that's sad or awesome, I leave to you, dear reader. My pencil drawing was a little tighter, and therefore the inks were as well. The coloring on this one was fast and simple (but maybe a little bit plain and flat)–you'll note that I have left the black lines intact for the most part. The type treatment just sort of came to life on its own after the drawing was done. All in all, this was smooth-going, and I wish all my pieces came together this easily! | {
"redpajama_set_name": "RedPajamaC4"
} | 1,606 |
package com.intel.bugkoops;
import android.app.AlertDialog;
import android.app.Fragment;
import android.content.ContentResolver;
import android.content.CursorLoader;
import android.content.DialogInterface;
import android.content.Intent;
import android.database.Cursor;
import android.net.Uri;
import android.os.Bundle;
import android.app.LoaderManager;
import android.content.Loader;
import android.support.design.widget.FloatingActionButton;
import android.util.SparseBooleanArray;
import android.view.ActionMode;
import android.view.LayoutInflater;
import android.view.Menu;
import android.view.MenuItem;
import android.view.View;
import android.view.ViewGroup;
import android.widget.AbsListView;
import android.widget.AdapterView;
import android.widget.ListView;
import com.intel.bugkoops.Data.BugKoopsContract;
public class ReportListFragment extends Fragment implements LoaderManager.LoaderCallbacks<Cursor> {
public static final String LOG_TAG = ReportListFragment.class.getSimpleName();
private ReportListAdapter mReportListAdapter;
private FloatingActionButton mAddFAB;
private ListView mListView;
private int mPosition = ListView.INVALID_POSITION;
private boolean mUseTodayLayout;
private static final String SELECTED_KEY = "selected_position";
private static final int REPORT_LOADER = 0;
private static final String[] REPORT_COLUMNS = {
BugKoopsContract.ReportEntry._ID,
BugKoopsContract.ReportEntry.COLUMN_DATE,
BugKoopsContract.ReportEntry.COLUMN_TITLE,
BugKoopsContract.ReportEntry.COLUMN_TEXT
};
static final int COL_REPORT_ID = 0;
static final int COL_REPORT_DATE = 1;
static final int COL_REPORT_TITLE = 2;
static final int COL_REPORT_TEXT = 3;
public interface Callback {
void onItemSelected(Uri dateUri);
}
public ReportListFragment() {
}
@Override
public void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
}
@Override
public void onResume() {
super.onResume();
getLoaderManager().restartLoader(0, null, ReportListFragment.this);
}
@Override
public View onCreateView(LayoutInflater inflater, ViewGroup container,
Bundle savedInstanceState) {
mReportListAdapter = new ReportListAdapter(getActivity(), null, 0);
View rootView = inflater.inflate(R.layout.fragment_report, container, false);
mAddFAB = (FloatingActionButton) rootView.findViewById(R.id.action_report_list_add);
mAddFAB.setOnClickListener(new View.OnClickListener() {
@Override
public void onClick(View v) {
Intent intent = new Intent(getActivity(), ReportDetailActivity.class);
startActivity(intent);
}
});
mListView = (ListView) rootView.findViewById(R.id.listview_report);
mListView.setAdapter(mReportListAdapter);
mListView.setChoiceMode(ListView.CHOICE_MODE_MULTIPLE_MODAL);
mListView.setOnItemClickListener(new AdapterView.OnItemClickListener() {
@Override
public void onItemClick(AdapterView<?> adapterView, View view, int position, long l) {
Cursor cursor = (Cursor) adapterView.getItemAtPosition(position);
if (cursor != null) {
((Callback) getActivity())
.onItemSelected(BugKoopsContract.ReportEntry.buildUriFromId(cursor.getLong(COL_REPORT_ID)
));
}
mPosition = position;
}
});
mListView.setMultiChoiceModeListener(new AbsListView.MultiChoiceModeListener() {
@Override
public void onItemCheckedStateChanged(ActionMode mode, int position, long id, boolean checked) {
final int checkedCount = mListView.getCheckedItemCount();
mode.setTitle(checkedCount + " " + getString(R.string.report_list_fragment_word_selected));
}
@Override
public boolean onCreateActionMode(ActionMode mode, Menu menu) {
mode.getMenuInflater().inflate(R.menu.menu_report_list_modal, menu);
return true;
}
@Override
public boolean onPrepareActionMode(ActionMode mode, Menu menu) {
return false;
}
@Override
public boolean onActionItemClicked(ActionMode mode, MenuItem item) {
final SparseBooleanArray checked = mListView.getCheckedItemPositions();
switch (item.getItemId()) {
case R.id.action_report_list_modal_select_all:
for (int position = 0; position < mListView.getAdapter().getCount(); ++position) {
if (!checked.get(position)) {
mListView.performItemClick(
mListView.getAdapter().getView(position, null, null),
position,
mListView.getAdapter().getItemId(position));
}
}
return false;
case R.id.action_report_list_modal_delete:
DialogInterface.OnClickListener dialogClickListener = new DialogInterface.OnClickListener() {
@Override
public void onClick(DialogInterface dialog, int which) {
switch (which) {
case DialogInterface.BUTTON_POSITIVE:
final ContentResolver contentResolver = getActivity().getContentResolver();
for (int i = 0; i < checked.size(); i++) {
Cursor cursor = (Cursor) mReportListAdapter.getItem(checked.keyAt(i));
long id = cursor.getLong(COL_REPORT_ID);
contentResolver.delete(BugKoopsContract.ReportEntry.buildUriFromId(id),
null, null);
}
getLoaderManager().restartLoader(0, null, ReportListFragment.this);
break;
case DialogInterface.BUTTON_NEGATIVE:
break;
}
}
};
AlertDialog.Builder alertDialog = new AlertDialog.Builder(getActivity());
alertDialog.setMessage(ReportListFragment.this.getString(R.string.dialog_delete_reports_question))
.setPositiveButton(ReportListFragment.this.getString(R.string.dialog_positive), dialogClickListener)
.setNegativeButton(ReportListFragment.this.getString(R.string.dialog_negative), dialogClickListener).show();
return false;
default:
return false;
}
}
@Override
public void onDestroyActionMode(ActionMode mode) {
}
});
if (savedInstanceState != null && savedInstanceState.containsKey(SELECTED_KEY)) {
mPosition = savedInstanceState.getInt(SELECTED_KEY);
}
mReportListAdapter.setUseTodayLayout(mUseTodayLayout);
return rootView;
}
@Override
public void onActivityCreated(Bundle savedInstanceState) {
getLoaderManager().initLoader(REPORT_LOADER, null, this);
super.onActivityCreated(savedInstanceState);
}
@Override
public void onSaveInstanceState(Bundle outState) {
if (mPosition != ListView.INVALID_POSITION) {
outState.putInt(SELECTED_KEY, mPosition);
}
super.onSaveInstanceState(outState);
}
@Override
public Loader<Cursor> onCreateLoader(int i, Bundle bundle) {
String sortOrder = BugKoopsContract.ReportEntry.COLUMN_DATE + " DESC";
Uri reportUri = BugKoopsContract.ReportEntry.buildUriFromStartDate(0);
return new CursorLoader(getActivity(),
reportUri,
REPORT_COLUMNS,
null,
null,
sortOrder);
}
@Override
public void onLoadFinished(Loader<Cursor> loader, Cursor data) {
mReportListAdapter.swapCursor(data);
if (mPosition != ListView.INVALID_POSITION) {
mListView.smoothScrollToPosition(mPosition);
}
}
@Override
public void onLoaderReset(Loader<Cursor> loader) {
mReportListAdapter.swapCursor(null);
}
public void setUseTodayLayout(boolean useTodayLayout) {
mUseTodayLayout = useTodayLayout;
if (mReportListAdapter != null) {
mReportListAdapter.setUseTodayLayout(mUseTodayLayout);
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,119 |
James MacGregor (1830-1894) trained for the ministry under William Cunningham, whom he regarded as Scotland's master theologian. After MacGregor had been a pastor for ten years, he was called in 1868 to the chair of systematic theology at the Free Church College, Edinburgh, in succession to James Buchanan. He responded to rising errors of his day by writing in defense of the Sabbath and against Amyrauldianism. Illness forced him to migrate to New Zealand in 1881, where he was again the pastor of a church, and published expositions of the confessional teaching about election and eternal punishment. The following material is excerpted from his book, The Sabbath Question, Historical, Scriptural, and Practical (Edinburgh 1866). | {
"redpajama_set_name": "RedPajamaC4"
} | 4,949 |
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COVID-19: Lockdown retrospection and future
/ DigiQure Updates / By Team DigiQure
Corona, a global virus that kept us confined in our homes for months has already reorienting our relationship with the outside world. But crises like these also led us to seek new opportunities like the use of technology, less polarization and life's simple pleasures.
Firstly let us talk on how India proved to be an impressive model to implement measures changing the lifestyle of its 1.3 billion citizens. Statistics have shown a relative comparison worldwide wherein India's fight against the Covid-19 outbreak has been distinctive. Clampdowns had been imposed in India much earlier than in many countries which failed to contain the spread of the virus. The Indian government had announced a number of preventive measures to minimize the entry and spread of coronavirus such as introducing the Aarogya Setu mobile app for contact tracing and educating citizens about coronavirus.
We have a way ahead of us wherein the objective is to 'flatten' the curve so that there is slower growth in cases, or spreading out the number of cases over a longer period of time by enforcing prevention methods so that the steep mountain of cases is 'flattened' into a more gentle hillock.
With two months into quarantine life, it's hard to remember a time before COVID-19. The virus has touched all aspects of our lives, and it's hard to see how its impact won't ripple into the future. But there is light at the end of this coronavirus tunnel. The COVID-19 saga will undoubtedly come to an end.
In the present scenario, the effective exit strategy states there is no demarcation of zones like before whereas the containment zones with active cases shall continue practicing lockdown. Except medical shops, all the stand-alone shops are allowed to be open from 07:00hrs to 20:30hrs following a night curfew between 21:00hrs to 05:00hrs. However, the shops at a densely populated market are to be open as per the roster prepared for these areas, that asserts the opening of one third shops in that particular market at a particular time-interval. Private offices are allowed to start functioning with 50% of the staff and schools and colleges to remain closed. Nonetheless, 12th exams to be held as per the new schedule. An odd-even system to be used in schools after opening. Cinema halls to remain closed till further order, even so, the malls, the hotels and religious places to open from June 8, 2020. Further, the industries have been allowed to function with 50% of their capacities. With the series of lockdowns and all the restrictive movements it brought along; maybe it is time we start to adapt to the new normal.
"Paradigm shift" is a term most applied in this pandemic considering all the changes it inculcated in our lifestyle. It has shifted focus on healthcare delivery. Further virtual platforms allowed us to have the experiences we want even if we were isolated, quarantined or alone. For years, telemedicine, teleconsultations and electronic record-keeping that seemed to be a luxury are now going to be a necessity. The importance of digital health solutions was made clear during these challenging times. They are handy options to bring healthcare to patients, rather than the other way round. These eliminate doctor-patient visits whenever it's avoidable.
Since the beginning of March this year, when the pandemic hit India, team DigiQure has been active in ensuring that they do their bit. We kept on updating, revamping and streamlining our services so that all the Doctors with us continue their noble duties. So much so that for a good duration during this time, DigiQure has also provided all its services for free. Thus, if we contemplate the dynamics so far, we only plan to grow to the fore from here only to serve you better with even more exciting offers. Stay tuned till then.
It's two months into this pandemic and we already want to skip this year. Coronavirus has caused a lot of damage with its lockdown and the standstill it brought along with it for us as a community. The pandemic came with shattering effects on the economy, the real estate sector, the travel and hospitality industry and healthcare sector. It resulted in reduced availability of essential goods and the restrictions on travelling. The lockdown evocatively has had a disastrous impact on the hospitality sector, especially for hotels. Nevertheless, speculations say that the occupancy in India is going to be very low, that the hotels will have to either shut down or run in a very limited manner. With all the schools and colleges being shut down it has also impacted the education system, even though online classes are being held but those from financially weaker sections fear an uncertain future with no laptops or internet facilities. The disconnectedness of lockdown has also given rise to mental health issues among the older population. The daily wagers and migrant laborers have been left to rags with no source of income and no buffer of savings. Lastly let's not forget to mention the vulnerability and risk our healthcare professionals and the police have faced with the frustration they went through round the clock working for the masses.
It is not easy to stand strong against this global pandemic, especially when we as a community are surrounded by its negatives from all sides. But as we all know crisis moments also present opportunities and this one has a silver lining to it as well. The lockdown gave us time for our families and gave us a new perspective to practise hygiene. It also emphasised on remote working without physical presence in offices and also helped reduce the carbon footprint. The most important of all is it made us realise how our healthcare professionals and police working on the frontline have risked their lives for our safety. The present scenario will pay dividends in future by preparing us for any such instances in future.
As the end note we would say that every coin has two faces and with bad comes good. Countries worldwide are still fighting this pandemic race and even though the battle seems hard and long we shall overcome it by focusing on the brighter side. One such news being finding the vaccine for the coronavirus has become a public priority and several pharmaceutical companies and researchers across the world are rigorously working for it. Some of them being Moderna Inc. of Cambridge, Massachusetts, has already begun Phase-I human testing of its mRNA-1273 at Kaiser Permanente Washington Health Research Institute in Seattle and Regeneron Pharmaceuticals of Tarrytown of New York, is working on an antibody treatment that uses the virus itself⁽¹⁾. It is easy to get sucked in this endless road of despair but we need to try to pull through and rise stronger than ever.
We will get back to our lives and visit the great outdoors. But that life will be significantly different. Moreover, reaching that point will depend on our current actions. We must respect social distancing measures and reduce the spread of the disease. Only then will we experience the post-pandemic world.
So all and all we would say that here onwards, "Stay physically distant but socially connected!"
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,610 |
\section{Introduction}
The standard model (SM) of elementary particles has been tested to a very high accuracy.
It can be considered to be completed in the sense that all particles in the SM have been observed
and their properties have been confirmed to be consistent with the SM expectations.
However, there are still problems that this model itself cannot address, and hence motivating us to go beyond the SM.
The discovery of the Higgs boson not only fulfills the SM particle content, but also provides us with a hint
that the SM needs to be extended according to the requirement of naturalness.
Cosmological observations confirmed the existence of dark matter that goes beyond the SM prediction.
On the other hand, the measurement for the muon anomalous magnetic dipole moment ($g-2$) \cite{Exp_g-2}
reveals a 3-4 $\sigma$ discrepancy between the measured central value and the SM prediction \cite{SM_g-2}.
Supersymmetry (SUSY) has been investigated for a long time as one of the most promising candidates beyond the SM.
The gauge hierarchy problem, in other words, the instability of the electroweak scale under quantum corrections can be
solved by a SUSY extension of the SM such as the minimal supersymmetric SM (MSSM).
Assuming the conservation of R-parity, SUSY models can provide good candidates for the cold dark matter in the universe.
Additionally, the muon $g-2$ also receives contributions from superpartners (smuons, charginos and neutralinos) and
shifts to the allowed measured interval when their masses lie at the electroweak scale \cite{SUSY(g-2)enhance}.
The Higgs boson mass measurement at the Large Hadron Collider (LHC) together with other experiments have put severe constraints on SUSY breaking parameters.
At the tree level, the SM-like Higgs boson mass $m_h$ is just about the Z boson mass $m_Z$.
To reproduce the Higgs boson mass of about 125 GeV \cite{mHiggs}, quantum corrections to the Higgs boson mass play a crucial role.
The approximate formula for $m_h$ with radiative corrections
(in case $A_t$ is relatively large compared to $\mu$, and $m_A \gg m_Z$) is given by \cite{mHapproximation}
\begin{eqnarray}
m_h^2 & \simeq & m_Z^2 \cos^2 2 \beta
+ \frac{3}{4\pi^2} y_t^2 m_t^2 \sin^2 \beta
\left[ \log
\left( \frac{m^2_{\tilde{t}}}{m_t^2}
\right)
+ \frac{X_t^2}{m^2_{\tilde{t}}}
- \frac{X_t^4}{12 m^4_{\tilde{t}}}
\right],
\label{Higgs}
\end{eqnarray}
where $X_t = A_t - \mu \cot \beta$ is the stop mixing parameter.
In this formula, a large stop mass plays a crucial role to push up the Higgs boson mass
from $m_Z$ to the measured value of about 125 GeV.
In many SUSY breaking models, heavy stops imply that other sfermions are also heavy,
such that squark masses are of $\mathcal{O}(10\text{TeV})$, and slepton masses lie around a few TeV \cite{Okada:2012nr}.
However, heavy smuons make their loop contributions to the muon anomalous magnetic moment, $a_\mu=\frac{1}{2}(g_\mu-2)$,
too small to explain the 3-4 $\sigma$ discrepancy.
This fact can be easily seen in the formula of SUSY contributions to the muon anomalous magnetic moment \cite{amu-formula}:
\begin{eqnarray}
\Delta a_\mu &=&
\frac{\alpha m_\mu^2 \, \mu M_2 \tan \beta}{4 \pi \sin^2 \theta_W m^2_{{\tilde{\mu}}_L}}
\left[
\frac{f_\chi (M_2^2 / m^2_{{\tilde{\mu}}_L}) - f_\chi (\mu^2 / m^2_{{\tilde{\mu}}_L})} {M_2^2 - \mu^2}
\right] \nonumber \\
& &
+ \; \frac{\alpha m_\mu^2 \, \mu M_1 \tan \beta}{4 \pi \cos^2 \theta_W
(m^2_{{\tilde{\mu}}_R} - m^2_{{\tilde{\mu}}_L})}
\left[
\frac{f_N (M_1^2 / m^2_{{\tilde{\mu}}_R})}{m^2_{{\tilde{\mu}}_R}} -
\frac{f_N (M_1^2 / m^2_{{\tilde{\mu}}_L})}{m^2_{{\tilde{\mu}}_L}}
\right],
\label{Delta-a_mu}
\end{eqnarray}
where the loop functions are defined as
\begin{eqnarray}
f_\chi (x) = \frac{x^2 - 4x + 3 + 2 \ln x}{(1-x)^3} , \; \; \;
f_N (x) &=& \frac{x^2 - 1 - 2x \ln x}{(1-x)^3}.
\end{eqnarray}
For $x={\cal O}(1)$, they are of order one, for example, $f_\chi (1) = -\frac{2}{3}$ and $f_N (1) = -\frac{1}{3}$.
To yield $\Delta a_\mu \sim 10^{-9}$ to fill the discrepancy between the experimental result
and the SM prediction, light smuons and charginos/neutralinos are necessary,
while a large $\tan \beta$ works to enhance $\Delta a_\mu$.
A solution to the tension between the Higgs boson mass and the muon $g-2$ may come from a large mass splitting
between stops (squarks in general) and smuons (leptons in general)/charginos/neutralinos \cite{mass_splitting}.
According to Eq.~(\ref{Higgs}), beside heavy stops the Higgs boson mass can also be improved
by large $X_t$ \cite{Example_Xt-enhancement, Babu:2014lwa,LargeAt}.
There are also other proposals to solve this tension \cite{Other_g-2}.
In this paper, we investigate the MSSM in the 5D space-time
with the Randall-Sundrum (RS) background metric \cite{Randall:1999ee}.
Originally, the RS model was proposed to solve the gauge hierarchy problem of the SM,
where all the SM particles are confined on the so-called infrared (IR) brane
at a fixed point of the $S^1/Z_2$ orbifold on which the 5th dimension is compactified.
The large hierarchy between the electroweak and the Planck scales is naturally generated
via the so-called warp factor induced by the RS warped background metric.
Soon after the original work, the RS model was extended to have the SM fields to reside in the bulk
while the SM Higgs field is confined on the IR brane to maintain the solution to the gauge hierarchy problem \cite{bulkSM}.
SUSY extensions of the RS model then came up with the component field formulation \cite{componentSUSY-RS}
and the superfield formulation \cite{superfield-RS}.
This context provides not only an elegant explanation of the diversity of particle masses \cite{Huber:2000ie},
but also a variety of possibilities for SUSY breaking mediation mechanisms with the 5th dimension.%
\footnote{Beside the RS scenario, the flat extra dimension scenario also brings an interesting landscape for discussions on SUSY breaking. See, for example, \cite{largeY} and references therein. }
In SUSY RS models, the SUSY can solve the gauge hierarchy problem as usual, so that a very strong warp factor
is not necessary.
SUSY RS models have the ability to simultaneously solve both hierarchy problems:
the gauge hierarchy and the fermion mass (Yukawa) hierarchy.
On the other hand, the AdS/CFT correspondence brings an interesting point to our study setup.
This conjecture maps the physics in the AdS$_5$ space on to its dual 4D picture
with a strongly coupled conformal field theory \cite{Gherghetta:2000kr}.
A connection of the models to string theories would be possible \cite{string}.
Our setup is similar to Ref. \cite{Okada:2011ed} that all matter and gauge superfields reside in the bulk.
But we arrange the Higgs superfields to reside in the bulk as well, while the SUSY breaking hidden sector
is confined on the so-called ultraviolet (UV) brane.
In particular, quark superfields localize around the UV brane, while slepton superfields delocalize from the UV brane.
We will consider that the 5D MSSM can have a universal coupling between the MSSM multiplets and the hidden sector field.
However, because of this geometrical configuration of wave functions, we can naturally realize a large mass splitting
between squarks and sleptons.
Since gravitino, which is the superpartner of the massless 4D graviton, localizes around the UV brane,
its mass is large.
Hence, the lightest neutralino serves as a dark matter candidate as usual in the MSSM.
Taking into account a variety of experimental constraints, we find bulk field configurations
which are suitable to account for the muon $g-2$
while reproducing the observed SM-like Higgs boson mass.
The structure of this paper is as follows.
In Section 2, we describe the 5D MSSM with bulk superfields in the Randall-Sundrum background metric,
and derive the 4D MSSM as a low-energy effective theory.
In Section 3, we consider various phenomenological constraints, and
present the benchmark particle spectra of the model.
Section 4 is devoted for conclusion.
\section{
5D MSSM in the RS background metric
}
We consider a 5D space-time $(x^\mu, y)$, where the fifth dimension is compactified on the $S_1/Z_2$ orbifold,
and $y$ defined in the range of $-\pi \leq y \leq \pi $ is an angle of $S_1$ with a radius $R$.
Because of $Z_2$ parity, $y$ is identified with $-y$, so that the orbifold possesses two fixed points at $y = 0$ and $y = \pi $.
Introducing two ``3-branes" located at these orbifold fixed points and assigning suitable brane tensions to them,
a solution to the Einstein's equation is found to be \cite{Randall:1999ee}
\begin{eqnarray}
ds^2 &=& e^{-2R\sigma} \eta_{\mu\nu} dx^\mu dx^\nu - R^2 dy^2 ,
\end{eqnarray}
where $\sigma = k|y|$, and $k$ is the AdS curvature.
The 4D Minkowski space is realized as a slice of this AdS$_5$ space.
With this metric, a relation between the 5D Planck mass ($M_5$) and
the Planck mass ($M_4$) in the 4D effective theory is given by
\begin{eqnarray}
M_{4}^2 = \frac{M_{5}^3}{k} \left( 1 - \omega^2 \right)
\simeq \frac{M_5^3}{k},
\label{Planck}
\end{eqnarray}
where $\omega = e^{-kR\pi}$ is the so-called warp factor, and we have assumed $\omega \ll 1$.
In the following calculation, we simply take $k \simeq M_5 \simeq M_4$.
Because of the warped metric, an effective cutoff on the UV brane at $y=0$ is $M_{5}$ itself,
while that on the IR brane at $y=\pi$ is warped down to $M_{\rm cut} =M_{5} \, \omega$.
This effective cutoff at the IR brane is used to solve the gauge hierarchy problem
in the original paper by Randall and Sundrum \cite{Randall:1999ee}.
In this paper, we assume that all the MSSM superfields propagate in the 5D bulk,
while the SUSY breaking hidden sector is confined on the UV brane.
Since the gravity multiplet localizes toward the UV brane, the gravitino interacts strongly with the hidden sector field due to the large overlapping between their wave functions.
Therefore, when the SUSY is broken, the gravitino acquires a large mass.
On the other hand, the MSSM gauge multiplets have flat configurations in the 5th dimensions,
and gaugino masses are suppressed by the volume of the 5th dimension.
Hence the lightest neutralino is a dark matter candidate as usual in the MSSM.
The wave function configuration for the MSSM matter multiplets depends on the bulk mass parameters.
A sfermion mass becomes smaller, as its wave function is more delocalized from the UV brane.
Now we describe our $N=1$ 5D MSSM Lagrangian in terms of familiar ``4D-like" $N=1$ supermultiplets.\footnote{
In this paper, we assume some mechanism to stabilize the 5th dimensional radius, and
simply replace the radion supermultiplet as the 5th diminutional radius $R$.
We refer Ref.~\cite{Maru:2003mq} for a very simple mechanism to stabilize the radion potential.
}
In the Kaluza-Klein (KK) decomposition, only the $Z_2$-even 5D fields have massless modes.
After integrating over the extra 5th dimension $y$, these massless zero modes are identified
as usual 4D MSSM supermultiplets.
The 5D action for a bulk vector multiplet is described by using a 4D-like vector superfield
\begin{eqnarray}
V(x,y,\theta)
&=& -\theta \sigma^\mu \bar\theta A_\mu(x,y)
- i \bar\theta^2 \theta \lambda_1(x,y)
+ i \theta^2 \bar\theta \bar\lambda_1(x,y)
+ \frac{1}{2} \bar\theta^2 \theta^2 D(x,y) ,
\end{eqnarray}
and a 4D-like adjoint chiral superfield
\begin{eqnarray}
\chi(x,y,\theta)
&=& \frac{1}{\sqrt{2}} (\Sigma(x,y) + i A_5(x,y))
+ \sqrt{2} \theta \lambda_2(x,y)
+ \theta^2 F_\chi(x,y) .
\end{eqnarray}
Under the $Z_2$ parity, the former is even while the latter is odd.
The gauge invariant 5D action for the gauge multiplet is given by
\begin{eqnarray}
S_5^{gauge} &=& \int d^4 x \int_{-\pi}^\pi dy
\left\lbrace
\frac{1}{4g_5^2} \int d^2 \theta R \; \text{Tr} \left[W^\alpha W_\alpha \right] + \text{h.c.}
\right. \nonumber \\
& & \left.
+ \frac{2}{g_5^2}
\int d^4 \theta \frac{e^{-2R\sigma}}{2R} \text{Tr}
\left[
\{ e^{V/2}, \partial_y e^{-V/2} \} +
\frac{1}{\sqrt{2}}
(e^{V/2} \chi^\dagger e^{-V/2} + (e^{-V/2} \chi e^{V/2})
\right]^2
\right\rbrace ,
\end{eqnarray}
where the 5D gauge coupling $g_5$ has the mass dimension of $-1/2$.
Since the wave function of the vector superfield zero-mode is found to be independent of the $y$-coordinate,
we have rescaled it as $V \to V/\sqrt{2 \pi R}$, by which the zero-mode is canonically normalized in the 4D effective theory
with the relation between the 5D and 4D gauge couplings, $g_5 = \sqrt{2 \pi R} \; g_4$.
A hypermultiplet in the bulk is used to describe matter and Higgs multiplets,
which is decomposed into a pair of vector-like chiral superfields $\Phi$ and $\Phi^c$:
\begin{eqnarray}
\Phi(x,y,\theta)
&=& \phi(x,y) + \sqrt{2} \theta \psi(x,y) + \theta^2 F_\Phi(x,y) \; , \\
\Phi^c(x,y,\theta)
&=& \phi^c(x,y) + \sqrt{2} \theta \psi^c(x,y) + \theta^2 F_{\Phi^c}(x,y) \;.
\end{eqnarray}
Under the $Z_2$ parity, we assign an even parity for $\Phi$ while $\Phi^c$ is odd.
The 5D action for the hypermultiplet is given by
\begin{eqnarray}
S_5^{matter} &=& \int d^4 x \int_{-\pi}^\pi dy
\left\lbrace
\int d^4 \theta R e^{-2R\sigma}
\left( \Phi^\dagger e^{-V} \Phi + \Phi^c e^{V} \Phi^{c \dagger} \right)
\right. \nonumber \\
& & +
\left.
\int d^2 \theta e^{-3R\sigma} \Phi^c
\left[ \partial_y - \frac{1}{\sqrt{2}} \chi
- \left( \frac{3}{2} - c_\Phi \right) R \sigma'
\right] \Phi + \text{h.c.}
\right\rbrace ,
\label{S5matter}
\end{eqnarray}
where $c_\Phi$ is a bulk mass parameter.
Due to the $Z_2$ parity assignment of $\Phi$ and $\Phi^c$,
only the $Z_2$-even chiral multiplet $\Phi$ has a zero-mode in the Kaluza-Klein decomposition.
By solving the SUSY vacuum condition,
\begin{eqnarray}
\left[ \partial_y - \left( \frac{3}{2} - c_\Phi \right) R \sigma' \right] \Phi &=& 0,
\end{eqnarray}
we find the zero-mode wave function as
\begin{eqnarray}
\Phi(x,y,\theta) \vert_\text{zero-mode}
&=& {\hat \Phi}(x,\theta) e^{(\frac{3}{2} - c_\Phi)R\sigma} .
\label{masslessZeroMode}
\end{eqnarray}
Here, the 4D chiral superfiled ${\hat \Phi}(x,\theta)$ has a mass dimension $\frac{3}{2}$.
The canonically normalized chiral superfield $\varphi_0(x,\theta)$ in the 4D effective theory is given by
\begin{eqnarray}
{\hat \Phi}(x,\theta) = \sqrt{k} \mathcal{C}_\Phi \varphi_0(x,\theta) \, ,
\label{redefine}
\end{eqnarray}
where $\varphi_0$ represents the 4D MSSM chiral superfields ($H_u$, $H_d$, $Q_i$, $U_i$, $D_i$, $L_i$, $E_i$), and
\begin{eqnarray}
\mathcal{C}_\Phi = \sqrt{ \frac{(1-2c_\Phi)}{2 \left( \omega^{(-1+2c_\Phi)} -1 \right)}} \quad .
\end{eqnarray}
Note that the bulk mass parameter $c_\Phi$ controls the configuration of the zero-mode:
for $c_\Phi > 1/2$ ($c_\Phi < 1/2$), the zero-mode is localized toward the UV (IR) brane.\footnote{
In order to have the canonical Kahler potential in Eq.~(\ref{S5matter}),
we have redefined the hypermultiplet in Eq.~(\ref{masslessZeroMode}) as
$\Phi \rightarrow \Phi e^{-R\sigma}$ when discussing about field localization in the extra dimension.
}
Now we introduce interaction terms among the bulk multiplets and a chiral multiplet
in the hidden sector on the UV brane.
Because of the 5D $N=1$ SUSY, such interaction terms can be written only at the orbifold fixed points.
In order to forbid phenomenologically dangerous terms such as $R$-parity violating terms,
we introduce an $R$-symmetry with the charge assignments listed in Table~\ref{R-charge}.
Here, a chiral superfield $X$ in the hidden sector has been introduced,
and we assume that both the SUSY and the $R$-symmetry are broken by a vacuum expectation value (VEV)
of the $F$-component of $X$, $\langle F_X \rangle \neq 0$.
\begin{table}
\begin{center}
\begin{math}
\begin{array}{|c||c|c|c|c|c|c|c|c||c|}
\hline
\text{Bulk field} & V_a & Q_i^h & U_i^h & D_i^h & L_i^h & E_i^h & H_u^h & H_d^h & X \\
\hline
R{\rm -charge} & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\
\hline
\end{array}
\end{math}
\caption{
$R$-charge assignments for the 5D MSSM vector multiplet ($a = 1,2,3$), hypermultiplets and the hidden sector field $X$
(R-charge of $\theta$ is 1).
Here, for example, $Q_i^h$ is a $Z_2$-even component of the bulk quark doublet hypermultiplet,
whose zero mode is identified as the quark doublet chiralsuperfield in the 4D MSSM.
The generation index is denoted as $i=1,2,3$.
}
\label{R-charge}
\end{center}
\end{table}
In the 5D MSSM, a Yukawa coupling is symbolically given by
\begin{eqnarray}
S_5^{\rm Yukawa} =
\int d^4 x \int_{-\pi}^\pi dy \int d^2 \theta e^{-3R \sigma}
\frac{1}{M_{5}^{3/2}} \Phi_1 \Phi_2 \Phi_3
\left[
Y_0 \, \delta(y) + Y_\pi \, \left\{ \delta(y+\pi) + \delta(y-\pi) \right\}
\right] \, ,
\label{5DYukawa}
\end{eqnarray}
where $Y_0$ and $Y_\pi$ are dimensionless coupling constants,
and $M_5^{3/2}$ is introduced to yield the correct mass dimension.
Here, $\Phi_1$ stands for the MSSM Higgs doublets, and the other two $\Phi_2$ and $\Phi_3$
stand for the MSSM matter multiplets.
After the $y$-integration, a 4D effective Yukawa coupling is obtained as
\begin{eqnarray}
Y_4 \simeq
\left[
Y_0 + Y_\pi \, \omega^{-(\frac{3}{2} - c_{\Phi_1} - c_{\Phi_2} - c_{\Phi_3}) }
\right]
\mathcal{C}_{\Phi_1} \mathcal{C}_{\Phi_2} \mathcal{C}_{\Phi_3} \, ,
\end{eqnarray}
where we have used $k/M_5 \simeq 1$.
Note that an appropriate choice of the bulk mass parameters can derive
an exponentially suppressed Yukawa coupling even for $Y_0, Y_\pi ={\cal O}(1)$.
Although this feature implies a possibility to naturally explain the Yukawa hierarchy in the SM,
in this paper we do not attempt to explain the Yukawa hierarchy, but concentrate on soft SUSY breaking parameters.
Let us consider $R$-symmetric contact terms between the hidden sector field $X$ and the 5D MSSM multiplets in the bulk.
We introduce a contact term between the gauge multiplets and $X$ of the form:
\begin{eqnarray}
S_5^{Xg}
= \int d^4 x \int dy
\left\{ \int d^2 \theta \; d_a
\frac{X}{M^2_5} \text{Tr} \left[\tilde{W}^\alpha \tilde{W}_\alpha \right] + \text{h.c.} \right\}
\delta(y) \, ,
\label{Xg5D}
\end{eqnarray}
where the original $\tilde{W}^\alpha$ has the mass dimension of $2$ before normalizing $V$.
The contact terms between the Higgs hypermultiplets and the hidden sector field $X$ are written as
\begin{eqnarray}
S_5^{Xh}
&=& \int d^4 x \int dy \int d^4 \theta
\left\lbrace
\left[
d_\mu \frac{X^\dagger}{M_{5}^2} H_u^h H_d^h +
d_{B_\mu} \frac{X^\dagger X}{M_{5}^3} H_u^h H_d^h + \text{h.c.}
\right]
\right. \nonumber \\
& & \qquad\qquad +
\left[
d_A^{H_u} \frac{X + X^\dagger}{M_{5}^2} H_u^{h\dagger} H_u^h +
d_m^{H_u} \frac{X^\dagger X}{M_{5}^3} H_u^{h\dagger} H_u^h
\right. \nonumber \\
& & \qquad\qquad +
\left.
\left.
d_A^{H_d} \frac{X + X^\dagger}{M_{5}^2} H_d^{h\dagger} H_d^h +
d_m^{H_d} \frac{X^\dagger X}{M_{5}^3} H_d^{h\dagger} H_d^h
\right]
\right\rbrace
\delta(y) \, ,
\label{Xh5D}
\end{eqnarray}
and those between the matter hypermultiplets and $X$ are
\begin{eqnarray}
S_5^{Xm}
= \int d^4 x \int dy \int d^4 \theta
\left[
(d_A^\Phi)_{ij} \frac{X + X^\dagger}{M_{5}^2} \Phi_i^\dagger \Phi_j +
(d_m^\Phi)_{ij} \frac{X^\dagger X}{M_{5}^3} \Phi_i^\dagger \Phi_j
\right] \delta(y) \, ,
\label{Xm5D}
\end{eqnarray}
where $\Phi$ stands for $\{Q^h, U^h, D^h, L^h, E^h \}$ hypermultiplets,
and $\{i,j\}$ are generation indices.
We can also introduce contact terms in the superpotential as follows:
\begin{eqnarray}
S_5^{Xa}
&=& \int d^4 x \int dy \int d^2 \theta
\left\lbrace
\frac{(a_u)_{ij}}{M_{5}^{5/2}} X H_u^h Q_i^h U_j^h +
\frac{(a_d)_{ij}}{M_{5}^{5/2}} X H_d^h Q_i^h D_j^h
\right. \nonumber \\
& & \left. \qquad \qquad \qquad + \;
\frac{(a_e)_{ij}}{M_{5}^{5/2}} X H_d^h L_i^h E_j^h + \text{h.c.}
\right\rbrace \delta(y) \, .
\label{Xa5D}
\end{eqnarray}
The SUSY breaking by $\langle F_X \rangle$ induces the soft SUSY breaking terms
in the MSSM through the above contact terms at the effective 4D cutoff scale $M_{\rm cut} = M_4 \omega $.
The gaugino masses are given by
\begin{eqnarray}
M_a & \simeq & - \sqrt{3} \left( \frac{d_a}{2 \pi R M_4 } \right) g_a^2 \; m_{3/2} , \quad (a=1,2,3) \, .
\label{gaugino_softmasses}
\end{eqnarray}
where $g_a$ is the SM gauge coupling, and the gravitino mass $m_{3/2}$ is given by
\begin{eqnarray}
m_{3/2} &=& \frac{\left< F_X \right>}{\sqrt{3} M_4} \quad .
\end{eqnarray}
Note that the gaugino mass is suppressed by the so-called volume suppression factor of $1/(2 \pi R M_4)$.
Soft masses of the Higgs sector can be obtained from Eq.~(\ref{Xh5D}):
\begin{eqnarray}
m_{H_u}^2 &=&
3 \left[
- d_m^{H_u}
+ (d_A^{H_u})^2 \mathcal{C}_{H_u}^2
\right] \mathcal{C}_{H_u}^2 m_{3/2}^2
\, , \\
m_{H_d}^2 &=&
3 \left[
- d_m^{H_d}
+ (d_A^{H_d})^2 \mathcal{C}_{H_d}^2
\right] \mathcal{C}_{H_d}^2 m_{3/2}^2
\, , \\
B_\mu &=&
3 \, d_{B_\mu} \mathcal{C}_{H_u} \mathcal{C}_{H_d} m_{3/2}^2
-
\sqrt{3}
\left(
d_A^{H_u} \mathcal{C}_{H_u}^2
+ d_A^{H_d} \mathcal{C}_{H_d}^2
\right) \mu \, m_{3/2} \, .
\label{Higgs_softmasses}
\end{eqnarray}
In our $R$-charge assignment, the $\mu$-term is forbidden, but it is generated through the SUSY breaking \cite{Giudice:1988yz}:
\begin{eqnarray}
\mu &=&
\sqrt{3} \, d_\mu
\mathcal{C}_{H_u} \mathcal{C}_{H_d}
m_{3/2} \, .
\label{Higgsmu}
\end{eqnarray}
Scalar soft masses of sparticles are generated from Eq.~(\ref{Xm5D}):
\begin{eqnarray}
(m_\Phi)_{ij}^2 &=&
3 \left[
- (d_m^\Phi)_{ij}
+ \sum_{n=1}^3
(d_A^\Phi)_{in} (d_A^\Phi)_{nj}
\mathcal{C}_{\Phi_n}^2
\right]
\mathcal{C}_{\Phi_i} \mathcal{C}_{\Phi_j}
m_{3/2}^2 \, ,
\label{sparticle_softmasses}
\end{eqnarray}
where $\Phi$ stands for $Q, U, D, L, E$, and $i,j = \{1,2,3 \}$.
Last but not least, the trilinear couplings A-terms arise from Eq.~(\ref{Xa5D}):
\begin{eqnarray}
(A_u)_{ij} &=&
\frac{\sqrt{3} \, m_{3/2}}{(Y_u)_{ij}}
\left[
(a_u)_{ij} \mathcal{C}_{H_u} \mathcal{C}_{Q_i} \mathcal{C}_{Q_j}
\right. \nonumber \\
&&- \left.
d_A^{H_u} (Y_u)_{ij} \mathcal{C}_{H_u}^2
- \sum_{n=1}^3
(d_A^Q)_{ni} (Y_u)_{nj} \mathcal{C}_{Q_n} \mathcal{C}_{Q_i}
- \sum_{n=1}^3
(d_A^U)_{nj} (Y_u)_{in} \mathcal{C}_{U_n} \mathcal{C}_{U_j}
\right]
, \\
(A_d)_{ij} &=&
\frac{\sqrt{3} \, m_{3/2}}{(Y_d)_{ij}}
\left[
(a_d)_{ij} \mathcal{C}_{H_d} \mathcal{C}_{Q_i} \mathcal{C}_{D_j}
\right. \nonumber \\
&&- \left.
d_A^{H_d} (Y_d)_{ij} \mathcal{C}_{H_d}^2
- \sum_{n=1}^3
(d_A^Q)_{ni} (Y_d)_{nj} \mathcal{C}_{Q_n} \mathcal{C}_{Q_i}
- \sum_{n=1}^3
(d_A^D)_{nj} (Y_d)_{in} \mathcal{C}_{D_n} \mathcal{C}_{D_j}
\right]
, \\
(A_e)_{ij} &=&
\frac{\sqrt{3} \, m_{3/2}}{(Y_e)_{ij}}
\left[
(a_d)_{ij} \mathcal{C}_{H_d} \mathcal{C}_{L_i} \mathcal{C}_{E_j}
\right. \nonumber \\
&&- \left.
d_A^{H_d} (Y_e)_{ij} \mathcal{C}_{H_d}^2
- \sum_{n=1}^3
(d_A^L)_{ni} (Y_e)_{nj} \mathcal{C}_{L_n} \mathcal{C}_{L_i}
- \sum_{n=1}^3
(d_A^E)_{nj} (Y_e)_{in} \mathcal{C}_{E_n} \mathcal{C}_{E_j}
\right]
\, .
\label{Aterms}
\end{eqnarray}
To avoid the SUSY flavor changing neutral currents (FCNCs), we assume
that the couplings $d_m^\Phi$, $d_A^\Phi$, $a_u$, $a_d$, $a_e$ are all flavor diagonal
and, in particular, flavor-universal for the first two generations.
\begin{figure}[ht]
\begin{center}
\scalebox{1.2}[1.2]{
\includegraphics[width=3.5in]{Geometrical_coefficient.eps}
}
\caption{Behavior of geometrical coefficient as a function of the bulk mass parameter:
$\mathcal{C}_\Phi = \sqrt{ \frac{(1-2c_\Phi)}{2 \left( \omega^{(-1+2c_\Phi)} -1 \right)}}$. The plot is a demonstration for the case with
$\omega = 10^{-12}$.
}
\label{Geometrical_coefficient}
\end{center}
\end{figure}
All terms induced by the SUSY breaking are controlled by the gravitino mass
and the coupling constants for the contact interactions between the MSSM multiplets and
the hidden sector field $X$.
In addition, the warped background geometry plays a crucial role in determining the size of the parameters.
The gaugino masses are volume-suppressed from the gravitino mass.
The scalar masses squared, the $A$-terms and the $\mu$-term are controlled by the geometrical coefficients
of bulk hypermultiplets $\mathcal{C}_\Phi$.
In Figure \ref{Geometrical_coefficient}, we show a geometrical coefficient $\mathcal{C}_\Phi$ as a function of
the bulk mass parameter $c_\Phi$.
In this example, we have set $\omega=10^{-12}$ which generates the low cutoff scale of $\mathcal{O}(10^6)$ GeV.
\footnote{Basically, the choice of $\omega$ is arbitrary. But we have found that high cutoff scales result in tachyonic staus. Therefore, the choice of the cutoff scale of $\mathcal{O}(10^{6})$ GeV is preferable.}
For $c_\Phi=1/2$, the wave function is independent of $y$,
and $\mathcal{C}_\Phi ={\cal O}(0.1)$ in this case corresponds to the volume suppression factor.
As $c_\Phi >1/2$ increases, the wave function tends to localize towards the UV brane,
and hence $\mathcal{C}_\Phi$ is approaching to $1$.
On the other hand, as $c_\Phi < 1/2$ decreases, the wave function tends to localize towards the IR brane,
and $\mathcal{C}_\Phi$ is being exponentially suppressed.
Therefore, with a suitable choice of the bulk parameters, we can easily achieve a hierarchy
between soft SUSY breaking parameters.
From Eqs.~(\ref{gaugino_softmasses})-(\ref{Aterms}), we see that the maximum values of the soft parameters are of
${\cal O}(m_{3/2})$ when the coupling constants are of the order one.
For $\omega \ll 1$, the gaugino masses are roughly an order of magnitude smaller than the gravitino mass.
Thus, the model predicts the dark matter candidate to be the lightest neutralino.
We find that soft parameters for the scalars localized around the UV brane are of ${\cal O}(m_{3/2})$,
while they can be much smaller for the scalars localized around the IR brane.
Interestingly, once all the couplings between the 5D MSSM multiplet and the hidden sector field are set to be universal, for instance of $\mathcal{O}(1)$, the diversity of soft masses and couplings of the 4D MSSM can be derived from the warped geometry with appropriate localization.
\section{
Benchmark particle mass spectra
}
In this section, we investigate realistic particle mass spectra which satisfy all phenomenological constraints.
As we discussed in the previous section, a suitable choice of the bulk mass parameters can naturally generate a hierarchy
between sparticle masses.
In the following analysis, we consider the 4D effective MSSM
with the inputs of soft SUSY breaking parameters
at the 4D effective cutoff scale of $M_{\rm cut} \simeq M_4 \omega$.
The low energy mass spectrum is obtained through the renormalization group (RG) evolutions.
We employ SOFTSUSY package (version 3.6.2) \cite{SOFTSUSY} to numerically solve the RG equations.
With the output at low energies, other physical observables and constraints are computed
by using MicrOMEGAs package (version 4.2.3) \cite{MicrOMEGAs}.
Regarding to the inputs for the MSSM gaugino masses, we simply assume the universal couplings, $d_1=d_2=d_3$.
Since the ratio $m_g = M_a/g_a^2 $ is RG invariant at the 1-loop level, the resultant mass ratio among
the gauginos is the same as those in the constrained MSSM when $m_g$ is set as a common input for the gaugino sector at the cutoff scale.
Hence the bino and wino are lighter than the gluino.
To avoid the severe experimental constraints on the SUSY FCNCs for the first two generations,
we assume that the couplings of the hidden sector with the first two generation matter fields are flavor-blind.
In order to simplify our analysis, we set the universal soft mass inputs for the two Higgs doublets ($m^0_h$),
the sleptons and squarks in the first two generations ($m^0_l$, $m^0_q$).
The other free parameters in our analysis are the universal A-term $A_0$ at $M_{\rm cut}$ and $\tan\beta$.
We choose $\text{sign}(\mu) = +1$ to yield a positive $\Delta a_\mu$
which can fill up the discrepancy between the experimental value and the SM prediction.
In our study, we consider various phenomenological constraints.
We employ the combined result for the Higgs boson mass measured by the ATLAS and the CMS collaborations \cite{mHiggs}.
The lower mass bounds on squarks and gluino in the simplified model \cite{gluino} are taken into account as a reference.
As a motivation of this paper, the benchmark points are chosen such that the muon anomalous magnetic moment
$a_\mu = \frac{g_\mu - 2}{2}$ satisfies the current experimental value \cite{Exp_g-2, SM_g-2}.
Other constraints are from the branching ratios of rare decay processes:
$b \rightarrow s + \gamma $ \cite{bsg},
$B_s \rightarrow \mu^+ + \mu^- $ \cite{Bsmumu},
$B \rightarrow \tau + \nu_\tau $ \cite{Btaunu},
$D_s \rightarrow \tau + \nu_\tau$ \cite{dtaunu-dmunu},
$D_s \rightarrow \mu + \nu_\mu$ \cite{dtaunu-dmunu},
and the Kaon decay parameter \cite{Rl23}:
\begin{equation}
R_{l23} = \left| \frac{V_{us}(K_{l2})}{V_{us}(K_{l3})} \times
\frac{V_{ud}(0^+ \rightarrow 0^+)}{V_{ud}(\pi_{l2})} \right|,
\end{equation}
where the CKM matrix elements, $V_{us}$ and $V_{ud}$, are measured
from the corresponding 3-body semileptonic Kaon decay ($K_{l3}$),
2-body leptonic Kaon and pion decay ($K_{l2}$, $\pi_{l2}$),
and super-allowed nuclear beta decay ($0^+ \rightarrow 0^+$).
The constraints which we employ are listed below:
\begin{eqnarray}
&&
m_h = 125.09 \pm 0.21 (\text{stat.}) \pm 0.11 (\text{syst.}) \; \text{GeV},
\label{mH} \\
&&
m_{\tilde{g}} \gtrsim 1.4 \; \text{TeV} ,
\label{mgluino}
\\
&&
\Delta a_\mu = a_\mu^{\text{exp}} - a_\mu^{\text{SM}}
= (28.6 \pm 8.0) \times 10^{-10} ,
\label{gmu-2}\\
&&
2.99 \times 10^{-4} < \text{BR}(b \rightarrow s + \gamma) < 3.87 \times 10^{-4},
\quad \quad (2 \sigma) \\
&&
2.1 \times 10^{-9} < \text{BR}(B_s \rightarrow \mu^+ + \mu^-) < 4.0 \times 10^{-9},
\quad (1 \sigma) \\
&&
0.15 < \frac{\text{BR}^{exp}(B_u \rightarrow \tau + \nu_\tau)}
{\text{BR}^{SM}(B_u \rightarrow \tau + \nu_\tau)} < 2.41 ,
\qquad \qquad \qquad (3 \sigma) \\
&&
5.07 \times 10^{-2} < \text{BR}(D_s \rightarrow \tau + \nu_\tau) < 6.03 \times
10^{-2} , \quad (2 \sigma) \\
&&
5.31 \times 10^{-3} < \text{BR}(D_s \rightarrow \mu + \nu_\mu) < 5.81 \times 10^{-3} , \quad (1 \sigma) \\
&&
R_{l23} = 1.004 \pm 0.007 \; .
\end{eqnarray}
Since the LHC constraints require that sparticles must be heavy, their contributions to the precision electroweak observables are negligibly small \cite{RamseyMusolf:2006vr}.
Assuming R-parity conservation, the lightest neutralino is a primary candidate of the cold dark matter.
Beside the above constraints, we also consider the cosmological constraint
on the neutralino dark matter relic abundance.
Here we apply the result by the Planck satellite experiment \cite{PlanckCDM}:
\begin{eqnarray}
\Omega h^2 &=& 0.1188 \pm 0.0010 \quad (68\% \text{CL}) \; .
\label{Omega}
\end{eqnarray}
Finally, the constraints from the results of the direct and indirect dark matter searches are taken into account.
The most stringent upper limit on the spin-independent cross section of the neutralino dark matter
with nucleon has been reported by the LUX experiment \cite{LUX},
while the IceCube experiment has set the most severe upper limit on the spin-dependent cross section
between the neutralino dark matter and nucleon \cite{IceCube}:
\begin{eqnarray}
\sigma_\text{SI}^{\chi-p} & \lesssim &
7 \times 10^{-9} \; \text{pb} \; (90\% \; \text{CL}), \quad
\text{for} \quad m_\text{WIMP} \approx 600 \; \text{GeV}, \\
\sigma_\text{SD}^{\chi-p} & \lesssim &
10^{-4} \; \text{pb} \ (90\% \; \text{CL}), \quad \quad \; \;
\text{for} \quad m_\text{WIMP} \approx 150-600 \; \text{GeV}.
\end{eqnarray}
The benchmark mass spectra along with the observables satisfying the above phenomenological constraints
are shown in Tables \ref{benchmark1}, \ref{benchmark2}, and \ref{benchmark3}
for three cutoff scales, $M_\text{cut} = 10^{5}, 10^{6}$ and $10^{7}$ GeV, respectively.
On Tables, $m_q^0 = 8500$ GeV is the common input soft mass for all squarks in the first two generations,
while the common masses for the third generation sleptons and squarks are fixed to be $m_{l3}^0 = 800$ GeV
and $m_{q3}^0 = 9500$ GeV, respectively.
The choice of $m_{l3}^0$ for the benchmark point of the last column of Table~\ref{benchmark3} is a bit larger.
The other four input parameters at the cutoff scale $\{ m_g, m^0_l, m^0_h, A_0\}$
are chosen so as to satisfy the four most important constraints:
the Higgs boson mass, gluino mass,
the muon anomalous magnetic dipole moment, and
the dark matter relic density.
The mass hierarchy between squarks and sleptons/gauginos is crucial to reproduce $m_h \simeq 125$ GeV
and $\Delta a_\mu = \mathcal{O}(10^{-9})$ simultaneously.
The benchmark points satisfy all these phenomenological constraints.
The dark matter neutralinos in the benchmarks are all bino-like.
Since we have chosen $m^0_{l3}$ larger than $m^0_l$ to avoid stau being the lightest sparticle (LSP),
the next-to-LSP (NLSP) is muon-sneutrino which almost degenerate with electron-sneutrino.
The right dark matter relic abundance is achieved through the co-annihilation processes
between the neutralino LSP and the electron/muon-sneutrinos,
which is ensured by a correlation between the free inputs $m_g$ and $m^0_l$.
As can be seen in Eq.~(\ref{Delta-a_mu}), the sparticle contribution to the muon $g-2$ is proportional to $\tan\beta$.
Hence, as the input of $\tan\beta$ is raised, the inputs of $m_g$ and $m^0_l$ are increased
to satisfy the constraint from the muon $g-2$.
The cutoff scales in all the tables are just about a few orders of magnitude higher than typical squark masses.
Therefore, in our model, the distance of the RG evolutions of soft SUSY breaking parameters
are very short compared to, for example, the constrained MSSM, and hence
the RG evolution effects are much less.
In addition, the inputs of the scalar squared masses are non-universal.
In the slepton sector, we can see from the tables that the slepton masses at low energy
are smaller than the corresponding inputs at the boundary.
This is the effect from the higher order corrections in the RG equations with the hierarchically large
inputs of the squark masses.
Not as in the constrained MSSM, the left-handed sleptons of the first two generations
become lighter than right-handed ones.
As the consequence, the NLSP in the provided spectra is muon-sneutrino.
\begin{table}
\begin{center}
\scalebox{1}[1]{
\begin{math}
\begin{array}{|c|cccc|}
\hline
M_\text{cut} & 10^5 & 10^5 & 10^5 & 10^5 \\
m_g & 1120 & 1178 & 1330 & 1615 \\
m^0_l, m^0_q & 306.0, 8500 & 312.1, 8500 & 331.0, 8500 & 370.1, 8500 \\
m^0_{l3}, m^0_{q3} & 800, 9500 & 800, 9500 & 800, 9500 & 800, 9500 \\
m^0_h & 1000 & 2500 & 2600 & 2800 \\
A_0 & -6800 & -2200 & -1000 & 0 \\
\tan\beta & 10 & 20 & 30 & 40 \\
\hline
h^0 & 125.27 & 125.28 & 125.29 & 125.22 \\
H^0, A^0 & 3716 & 3307 & 3057 & 2766 \\
H^\pm & 3717 & 3308 & 3059 & 2767 \\
\tilde{g} & 1405 & 1469 & 1639 & 1953 \\
\tilde{\chi}^0_{1,2} & 245, 484 & 257, 507 & 290, 571 & 352, 689 \\
\tilde{\chi}^0_{3,4} & 3600, 3601 & 2426, 2427 & 2278, 2279 & 2029, 2030 \\
\tilde{\chi}^\pm_{1,2} & 484, 3602 & 507, 2428 & 571, 2280 & 689, 2031 \\
\tilde{u},\tilde{c}_{L,R} & 8572, 8560 & 8573, 8561 & 8577, 8565 & 8585, 8573 \\
\tilde{d},\tilde{s}_{L,R} & 8572, 8559 & 8573, 8560 & 8577, 8564 & 8585, 8572 \\
\tilde{t}_{1,2} & 9018, 9317 & 9112, 9339 & 9124, 9317 & 9130, 9283 \\
\tilde{b}_{1,2} & 9307, 9555 & 9336, 9525 & 9316, 9474 & 9281, 9401 \\
\tilde{\nu}^{e,\mu}_L & 253, 253 & 265, 265 & 298, 298 & 358, 358 \\
\tilde{e}, \tilde{\mu}_L & 265, 265 & 277, 277 & 308, 308 & 367, 367 \\
\tilde{e}, \tilde{\mu}_R & 335, 335 & 337, 337 & 354, 354 & 393, 392 \\
\tilde{\nu}^\tau_L & 765 & 766 & 760 & 751 \\
\tilde{\tau}_{1,2} & 726, 819 & 716, 827 & 677, 835 & 633, 833 \\
\hline
\Delta a_\mu & 2.58 \times 10^{-9} & 2.94 \times 10^{-9} & 3.23 \times 10^{-9} & 2.62 \times 10^{-9} \\
\text{BR}(b \rightarrow s + \gamma) & 3.34 \times 10^{-4} & 3.34 \times 10^{-4} & 3.35 \times 10^{-4} & 3.36 \times 10^{-4} \\
\text{BR}(B_s \rightarrow \mu^+ + \mu^-) & 3.08 \times 10^{-9} & 3.07 \times 10^{-9} & 3.04 \times 10^{-9} & 2.98 \times 10^{-9} \\
\frac{\text{BR}^{exp}(B_u \rightarrow \tau + \nu_\tau)}
{\text{BR}^{SM}(B_u \rightarrow \tau + \nu_\tau)}
& 1.00 & 9.98 \times 10^{-1} & 9.95 \times 10^{-1} & 9.89 \times 10^{-1} \\
\text{BR}(D_s \rightarrow \tau + \nu_\tau) & 5.17 \times 10^{-2} & 5.17 \times 10^{-2} & 5.17 \times 10^{-2} & 5.17 \times 10^{-2} \\
\text{BR}(D_s \rightarrow \mu + \nu_\mu) & 5.33 \times 10^{-3} & 5.33 \times 10^{-3} & 5.33 \times 10^{-3} & 5.33 \times 10^{-3} \\
R_{l23} & 1.000 & 1.000 & 1.000 & 1.000 \\
\hline
\Omega h^2 & 0.119 & 0.119 & 0.119 & 0.119 \\
\sigma_\text{SI}^{\chi-p} \; ({\rm pb}) & 9.35 \times 10^{-13} & 1.31 \times 10^{-12} & 1.46 \times 10^{-12} & 2.75 \times 10^{-12} \\
\sigma_\text{SD}^{\chi-p} \; ({\rm pb}) & 6.22 \times 10^{-10} & 3.88 \times 10^{-9} & 5.17 \times 10^{-9} & 8.74 \times 10^{-9} \\
\hline
\end{array}
\end{math}}
\caption{
Benchmark particle mass spectra in GeV units for $M_\text{cut} = 10^5$ GeV.
Input soft masses for the first two generation squarks,
the third generation slepton and squark are fixed as
$m^0_q = 8500$ GeV,
$m^0_{l3} = 800$ GeV,
and $m^0_{q3} = 9500$ GeV.
Other parameters including
the gaugino sector input $m_g$,
the soft masses for the first two generation sleptons $m^0_l$, and for two Higgs doublets $m^0_h$,
the universal trilinear coupling $A_0$,
and $\tan \beta$ are allowed to vary in this table.}
\label{benchmark1}
\end{center}
\end{table}
\begin{table}
\begin{center}
\scalebox{1}[1]{
\begin{math}
\begin{array}{|c|cccc|}
\hline
M_\text{cut} & 10^6 & 10^6 & 10^6 & 10^6 \\
m_g & 1114 & 1300 & 1350 & 1400 \\
m^0_l, m^0_q & 349.4, 8500 & 365.3, 8500 & 370.5, 8500 & 374.0, 8500 \\
m^0_{l3}, m^0_{q3} & 800, 9500 & 800, 9500 & 800, 9500 & 800, 9500 \\
m^0_h & 3200 & 3500 & 4000 & 4300 \\
A_0 & -6450 & -2600 & -2000 & -400 \\
\tan\beta & 10 & 20 & 30 & 40 \\
\hline
h^0 & 125.00 & 125.16 & 125.21 & 125.22 \\
H^0, A^0 & 4834 & 4343 & 4036 & 3541 \\
H^\pm & 4835 & 4344 & 4036 & 3542 \\
\tilde{g} & 1400 & 1606 & 1661 & 1715 \\
\tilde{\chi}^0_{1,2} & 243, 480 & 283, 557 & 294, 578 & 304, 596 \\
\tilde{\chi}^0_{3,4} & 3675, 3676 & 2945, 2946 & 2239, 2240 & 1558, 1560 \\
\tilde{\chi}^\pm_{1,2} & 480, 3676 & 558, 2947 & 578, 2241 & 596, 1561 \\
\tilde{u},\tilde{c}_{L,R} & 8557, 8546 & 8564, 8554 & 8566, 8556 & 8569(8), 8558 \\
\tilde{d}, \tilde{s}_{L,R} & 8557, 8546 & 8564, 8553 & 8567, 8555 & 8569, 8557 \\
\tilde{t}_{1,2} & 8666, 9130 & 8788, 9163 & 8784, 9113 & 8791, 9045 \\
\tilde{b}_{1,2} & 9125, 9535 & 9161, 9489 & 9111, 9396 & 9044, 9259 \\
\tilde{\nu}^{e,\mu}_L & 252, 252 & 291, 291 & 302, 301 & 312, 311 \\
\tilde{e}, \tilde{\mu}_L & 264, 264 & 302, 302 & 312, 312 & 322, 321 \\
\tilde{e},\tilde{\mu}_R & 368, 368 & 382, 381 & 386, 385 & 387, 386 \\
\tilde{\nu}^\tau_L & 736 & 729 & 680 & 631 \\
\tilde{\tau}_{1,2} & 699, 797 & 657, 799 & 554, 745 & 440, 681 \\
\hline
\Delta a_\mu & 2.31 \times 10^{-9} & 2.58 \times 10^{-9} & 2.88 \times 10^{-9} & 2.84 \times 10^{-9} \\
\text{BR}(b \rightarrow s + \gamma) & 3.33 \times 10^{-4} & 3.33 \times 10^{-4} & 3.33 \times 10^{-4} & 3.34 \times 10^{-4} \\
\text{BR}(B_s \rightarrow \mu^+ + \mu^-) & 3.08 \times 10^{-9} & 3.07 \times 10^{-9} & 3.06 \times 10^{-9} & 3.02 \times 10^{-9} \\
\frac{\text{BR}^{exp}(B_u \rightarrow \tau + \nu_\tau)}
{\text{BR}^{SM}(B_u \rightarrow \tau + \nu_\tau)}
& 1.00 & 9.99 \times 10^{-1} & 9.97 \times 10^{-1} & 9.93 \times 10^{-1} \\
\text{BR}(D_s \rightarrow \tau + \nu_\tau) & 5.17 \times 10^{-2} & 5.17 \times 10^{-2} & 5.17 \times 10^{-2} & 5.17 \times 10^{-2} \\
\text{BR}(D_s \rightarrow \mu + \nu_\mu) & 5.33 \times 10^{-3} & 5.33 \times 10^{-3} & 5.33 \times 10^{-3} & 5.33 \times 10^{-3} \\
R_{l23} & 1.000 & 1.000 & 1.000 & 1.000 \\
\hline
\Omega h^2 & 0.119 & 0.119 & 0.119 & 0.119 \\
\sigma_\text{SI}^{\chi-p} \; ({\rm pb})& 8.82 \times 10^{-13} & 7.78 \times 10^{-13} & 1.44 \times 10^{-12} & 4.96 \times 10^{-12} \\
\sigma_\text{SD}^{\chi-p} \; ({\rm pb}) & 5.65 \times 10^{-10} & 1.66 \times 10^{-9} & 5.59 \times 10^{-9} & 2.66 \times 10^{-8} \\
\hline
\end{array}
\end{math}}
\caption{
Same as Table~\ref{benchmark1}, but for $M_\text{cut} = 10^6$ GeV.
}
\label{benchmark2}
\end{center}
\end{table}
\begin{table}
\begin{center}
\scalebox{1}[1]{
\begin{math}
\begin{array}{|c|cccc|}
\hline
M_\text{cut} & 10^7 & 10^7 & 10^7 & 10^7 \\
m_g & 1280 & 1260 & 1230 & 1320 \\
m^0_l,m^0_q & 388.9, 8500 & 397.6, 8500 & 396.4, 8500 & 400.6, 8500 \\
m^0_{l3},m^0_{q3} & 800, 9500 & 800, 9500 & 800, 9500 & 1000, 9500 \\
m^0_h & 1000 & 4500 & 5000 & 5100 \\
A_0 & -7500 & -4000 & -500 & 0 \\
\tan\beta & 10 & 20 & 30 & 40 \\
\hline
h^0 & 125.02 & 125.13 & 125.08 & 125.11 \\
H^0, A^0 & 5611 & 5186 & 4723 & 4142 \\
H^\pm & 5612 & 5187 & 4724 & 4143 \\
\tilde{g} & 1589 & 1563 & 1524 & 1624 \\
\tilde{\chi}^0_{1,2} & 280, 551 & 275, 540 & 267, 524 & 286, 561 \\
\tilde{\chi}^0_{3,4} & 5548, 5548 & 3113, 3114 & 1966, 1968 & 1698, 1700 \\
\tilde{\chi}^\pm_{1,2} & 551, 5549 & 540, 3114 & 524, 1969 & 561, 1701 \\
\tilde{u}, \tilde{c}_{L,R} & 8553, 8544 & 8551, 8542 & 8549, 8541 & 8555(4), 8546 \\
\tilde{d}, \tilde{s}_{L,R} & 8553, 8542 & 8551, 8541 & 8550, 8540 & 8555, 8545(4) \\
\tilde{t}_{1,2} & 8377, 8984 & 8435, 8972 & 8476, 8926 & 8478, 8830 \\
\tilde{b}_{1,2} & 8979, 9525 & 8970, 9448 & 8924, 9323 & 8829, 9136 \\
\tilde{\nu}^{e,\mu}_L & 288, 288 & 283, 282 & 276, 275 & 295, 293 \\
\tilde{e}, \tilde{\mu}_L & 298, 298 & 294, 293 & 287, 286 & 306, 304 \\
\tilde{e}, \tilde{\mu}_R & 393, 392 & 404, 403 & 400, 399 & 403, 401 \\
\tilde{\nu}^\tau_L & 713 & 651 & 598 & 745 \\
\tilde{\tau}_{1,2} & 643, 788 & 536, 717 & 432, 648 & 471, 778 \\
\hline
\Delta a_\mu & 2.48 \times 10^{-9} & 2.69 \times 10^{-9} & 2.84 \times 10^{-9} & 3.13 \times 10^{-9} \\
\text{BR}(b \rightarrow s + \gamma) & 3.32 \times 10^{-4} & 3.32 \times 10^{-4} & 3.33 \times 10^{-4} & 3.33 \times 10^{-4} \\
\text{BR}(B_s \rightarrow \mu^+ + \mu^-) & 3.08 \times 10^{-9} & 3.08 \times 10^{-9} & 3.06 \times 10^{-9} & 3.03 \times 10^{-9} \\
\frac{\text{BR}^{exp}(B_u \rightarrow \tau + \nu_\tau)}
{\text{BR}^{SM}(B_u \rightarrow \tau + \nu_\tau)}
& 1.00 & 9.99 \times 10^{-1} & 9.98 \times 10^{-1} & 9.95 \times 10^{-1} \\
\text{BR}(D_s \rightarrow \tau + \nu_\tau) & 5.17 \times 10^{-2} & 5.17 \times 10^{-2} & 5.17 \times 10^{-2} & 5.17 \times 10^{-2} \\
\text{BR}(D_s \rightarrow \mu + \nu_\mu) & 5.33 \times 10^{-3} & 5.33 \times 10^{-3} & 5.33 \times 10^{-3} & 5.33 \times 10^{-3} \\
R_{l23} & 1.000 & 1.000 & 1.000 & 1.000 \\
\hline
\Omega h^2 & 0.119 & 0.119 & 0.119 & 0.119 \\
\sigma_\text{SI}^{\chi-p} \; ({\rm pb}) & 3.49 \times 10^{-13} & 6.34 \times 10^{-13} & 1.89 \times 10^{-12} & 3.17 \times 10^{-12} \\
\sigma_\text{SD}^{\chi-p} \; ({\rm pb}) & 5.81 \times 10^{-11} & 1.29 \times 10^{-9} & 9.70 \times 10^{-9} & 1.83 \times 10^{-8} \\
\hline
\end{array}
\end{math}}
\caption{
Benchmark particle mass spectra in GeV units for $M_\text{cut} = 10^7$ GeV.
Input soft masses for the first two generation squarks, the third generation slepton and squark
are fixed as $m^0_q = 8500$ GeV, $m^0_{l3} = 800$ GeV, and $m^0_{q3} = 9500$ GeV.
In the last column, the input for the 3rd generation slepton mass is taken a bit larger, $m^0_{l3} = 1000$ GeV.
}
\label{benchmark3}
\end{center}
\end{table}
\section{Conclusions}
In order to reconcile the Higgs boson mass $m_h \simeq 125$ GeV
and the discrepancy of the muon anomalous magnetic dipole moment
$\Delta a_\mu \sim 10^{-9}$,
a hierarchical mass splittings between squarks and sleptons/gauginos are usually necessary.
In this paper, we have presented a 5D MSSM in the RS warped background metric
with the warp factor $\omega \ll 1$.
All the MSSM multiplets reside in the bulk, while the SUSY is broken on the UV brane
where a hidden chiral field is localized.
The zero-modes of the 5D MSSM fields are identified as the MSSM fields in the 4D effective theory.
The SUSY breaking mediation to the MSSM sector is controlled by how much
the MSSM sparticles in the bulk overlap with the hidden field on the UV brane.
Since the gravitino is localizing around the UV brane, the SUSY breaking parameters in the MSSM
are characterized by the gravitino mass $m_{3/2}$ and geometrical factors corresponding
to the zero-mode configurations.
The gaugino masses are volume-suppressed $\sim 0.1 \; m_{3/2}$.
Squarks are localized around the UV brane with a bulk mass parameter $> 1/2$,
while leptons acquire much smaller masses with a suitable choice of
the bulk mass parameter $< 1/2$.
Interestingly, assuming a common coupling between the hidden sector and the 5D MSSM sector, the diversity of the 4D MSSM soft terms can be derived from the universality of the underlying theory with the warped geometry and appropriate localization.
In our setup, a factor deference between bulk mass parameters,
which are the original parameters in the model, results in a hierarchy
because of the warped metric.
With the hierarchical mass spectrum generated by the warped geometry,
we have demonstrated with the benchmarks that
not only $m_h \simeq 125$ GeV and $\Delta a_\mu \sim 10^{-9}$ can be reconciled,
but also various phenomenological constraints such as
the right abundance of the neturinalino dark matter,
the SUSY FCNC constraints and the LHC bounds on sparticle masses are all satisfied.
In the benchmark points, squarks are too heavy to be produced at the LHC,
while sleptons, light charginos and neutralinos can be explored
at the LHC Run-2 in the future.
\section*{Acknowledgment}
H.M.T. would like to thank the Department of Physics and Astronomy
at the University of Alabama for hospitality during his visit.
The work of N.O. is supported in part by the United States Department of Energy grant (DE-SC0013680).
The work of H.M.T. is supported in part by Vietnam National Foundation for Science
and Technology Development (NAFOSTED) under the grant No.~103.01-2014.22.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 582 |
{"url":"https:\/\/math.libretexts.org\/Courses\/Remixer_University\/Username%3A_hdagnew@ucdavis.edu\/SCC%3A_CHEM_300_-_Beginning_Chemistry_(Alviar-Agnew)\/13%3A_Solutions\/13.04%3A_Solutions_of_Gases_in_Water%3A_How_Soda_Pop_Gets_Its_Fizz","text":"\n# 13.4: Solutions of Gases in Water: How Soda Pop Gets Its Fizz\n\n\nLearning Objectives\n\n\u2022 Explain how temperature and pressure affect the solubility of gases.\n\nIn an earlier module of this chapter, the effect of intermolecular attractive forces on solution formation was discussed. The chemical structures of the solute and solvent dictate the types of forces possible and, consequently, are important factors in determining solubility. For example, under similar conditions, the water solubility of oxygen is approximately three times greater than that of helium, but 100 times less than the solubility of chloromethane, CHCl3. Considering the role of the solvent\u2019s chemical structure, note that the solubility of oxygen in the liquid hydrocarbon hexane, C6H14, is approximately 20 times greater than it is in water.\n\nOther factors also affect the solubility of a given substance in a given solvent. Temperature is one such factor, with gas solubility typically decreasing as temperature increases (Figure $$\\PageIndex{1}$$). This is one of the major impacts resulting from the thermal pollution of natural bodies of water.\n\nstyle=\"width: 449px; height: 469px;\" width=\"449px\" height=\"469px\" src=\"\/@api\/deki\/files\/59218\/CNX_Chem_11_03_gasdissolv.jpg\" \/> Figure $$\\PageIndex{1}$$: The solubilities of these gases in water decrease as the temperature increases. All solubilities were measured with a constant pressure of 101.3 kPa (1 atm) of gas above the solutions.\n\nWhen the temperature of a river, lake, or stream is raised abnormally high, usually due to the discharge of hot water from some industrial process, the solubility of oxygen in the water is decreased. Decreased levels of dissolved oxygen may have serious consequences for the health of the water\u2019s ecosystems and, in severe cases, can result in large-scale fish kills (Figure $$\\PageIndex{2}$$).\n\n\" style=\"width: 741px; height: 257px;\" width=\"741px\" height=\"257px\" src=\"\/@api\/deki\/files\/59220\/CNX_Chem_11_03_O2dissolv.1.jpg\" \/> Figure $$\\PageIndex{2}$$: (a) The small bubbles of air in this glass of chilled water formed when the water warmed to room temperature and the solubility of its dissolved air decreased. (b) The decreased solubility of oxygen in natural waters subjected to thermal pollution can result in large-scale fish kills. (Credit a: modification of work by Liz West; credit b: modification of work by U.S. Fish and Wildlife Service.)\n\nThe solubility of a gaseous solute is also affected by the partial pressure of solute in the gas to which the solution is exposed. Gas solubility increases as the pressure of the gas increases. Carbonated beverages provide a nice illustration of this relationship. The carbonation process involves exposing the beverage to a relatively high pressure of carbon dioxide gas and then sealing the beverage container, thus saturating the beverage with CO2 at this pressure. When the beverage container is opened, a familiar hiss is heard as the carbon dioxide gas pressure is released, and some of the dissolved carbon dioxide is typically seen leaving solution in the form of small bubbles (Figure $$\\PageIndex{3}$$). At this point, the beverage is supersaturated with carbon dioxide and, with time, the dissolved carbon dioxide concentration will decrease to its equilibrium value and the beverage will become \u201cflat.\u201d\n\nFigure 1$$\\PageIndex{3}$$: Opening the bottle of carbonated beverage reduces the pressure of the gaseous carbon dioxide above the beverage. The solubility of CO2 is thus lowered, and some dissolved carbon dioxide may be seen leaving the solution as small gas bubbles. (Credit: modification of work by Derrick Coetzee.)\n\n\"Fizz\"\n\nThe dissolution in a liquid, also known as fizz, usually involves carbon dioxide under high pressure. When the pressure is reduced, the carbon dioxide is released from the solution as small bubbles, which causes the solution to become effervescent, or fizzy. A common example is the dissolving of carbon dioxide in water, resulting in carbonated water.\n\nCarbon dioxide is weakly soluble in water, therefore it separates into a gas when the pressure is released. This process is generally represented by the following reaction, where a pressurized dilute solution of carbonic acid in water releases gaseous carbon dioxide at decompression:\n\n$H_2CO_{3(aq)} \u2192 H_2O_{(l)} + CO_{2(g)}$\n\nIn simple terms, it is the result of the chemical reaction occurring in the liquid which produces a gaseous product.\n\nFor many gaseous solutes, the relation between solubility, Cg, and partial pressure, Pg, is a proportional one:\n\n$C_\\ce{g}=kP_\\ce{g}$\n\nwhere k is a proportionality constant that depends on the identities of the gaseous solute and solvent, and on the solution temperature. This is a mathematical statement of Henry\u2019s law: The quantity of an ideal gas that dissolves in a definite volume of liquid is directly proportional to the pressure of the gas.\n\nExample $$\\PageIndex{1}$$: Application of Henry\u2019s Law\n\nAt 20 \u00b0C, the concentration of dissolved oxygen in water exposed to gaseous oxygen at a partial pressure of 101.3 kPa (760 torr) is 1.38 \u00d7 10\u22123 mol L\u22121. Use Henry\u2019s law to determine the solubility of oxygen when its partial pressure is 20.7 kPa (155 torr), the approximate pressure of oxygen in earth\u2019s atmosphere.\n\nSolution\n\nAccording to Henry\u2019s law, for an ideal solution the solubility, Cg, of a gas (1.38 \u00d7 10\u22123 mol L\u22121, in this case) is directly proportional to the pressure, Pg, of the undissolved gas above the solution (101.3 kPa, or 760 torr, in this case). Because we know both Cg and Pg, we can rearrange this expression to solve for k.\n\n\\begin{align} C_\\ce{g}&=kP_\\ce{g}\\\\ k&=\\dfrac{C_\\ce{g}}{P_\\ce{g}}\\\\ &=\\mathrm{\\dfrac{1.38\u00d710^{\u22123}\\:mol\\:L^{\u22121}}{101.3\\:kPa}}\\\\ &=\\mathrm{1.36\u00d710^{\u22125}\\:mol\\:L^{\u22121}\\:kPa^{\u22121}}\\\\ &\\hspace{15px}\\mathrm{(1.82\u00d710^{\u22126}\\:mol\\:L^{\u22121}\\:torr^{\u22121})} \\end{align}\n\nNow we can use k to find the solubility at the lower pressure.\n\n$C_\\ce{g}=kP_\\ce{g}$\n\n$$\\mathrm{1.36\u00d710^{\u22125}\\:mol\\:L^{\u22121}\\:kPa^{\u22121}\u00d720.7\\:kPa\\\\ (or\\:1.82\u00d710^{\u22126}\\:mol\\:L^{\u22121}\\:torr^{\u22121}\u00d7155\\:torr)\\\\ =2.82\u00d710^{\u22124}\\:mol\\:L^{\u22121}}$$\n\nNote that various units may be used to express the quantities involved in these sorts of computations. Any combination of units that yield to the constraints of dimensional analysis are acceptable.\n\nExercise $$\\PageIndex{1}$$\n\nA 100.0 mL sample of water at 0 \u00b0C to an atmosphere containing a gaseous solute at 20.26 kPa (152 torr) resulted in the dissolution of 1.45 \u00d7 10\u22123 g of the solute. Use Henry\u2019s law to determine the solubility of this gaseous solute when its pressure is 101.3 kPa (760 torr).\n\n7.25 \u00d7 10\u22123 g\n\n## Case Study: Decompression Sickness (\u201cThe Bends\u201d)\n\nDecompression sickness (DCS), or \u201cthe bends,\u201d is an effect of the increased pressure of the air inhaled by scuba divers when swimming underwater at considerable depths. In addition to the pressure exerted by the atmosphere, divers are subjected to additional pressure due to the water above them, experiencing an increase of approximately 1 atm for each 10 m of depth. Therefore, the air inhaled by a diver while submerged contains gases at the corresponding higher ambient pressure, and the concentrations of the gases dissolved in the diver\u2019s blood are proportionally higher per Henry\u2019s law.\n\nAs the diver ascends to the surface of the water, the ambient pressure decreases and the dissolved gases becomes less soluble. If the ascent is too rapid, the gases escaping from the diver\u2019s blood may form bubbles that can cause a variety of symptoms ranging from rashes and joint pain to paralysis and death. To avoid DCS, divers must ascend from depths at relatively slow speeds (10 or 20 m\/min) or otherwise make several decompression stops, pausing for several minutes at given depths during the ascent. When these preventative measures are unsuccessful, divers with DCS are often provided hyperbaric oxygen therapy in pressurized vessels called decompression (or recompression) chambers (Figure $$\\PageIndex{4}$$).\n\nFigure $$\\PageIndex{4}$$: (a) US Navy divers undergo training in a recompression chamber. (b) Divers receive hyperbaric oxygen therapy.\n\nDeviations from Henry\u2019s law are observed when a chemical reaction takes place between the gaseous solute and the solvent. Thus, for example, the solubility of ammonia in water does not increase as rapidly with increasing pressure as predicted by the law because ammonia, being a base, reacts to some extent with water to form ammonium ions and hydroxide ions.\n\n\" height=\"115\" width=\"594\" src=\"\/@api\/deki\/files\/59223\/CNX_Chem_11_02_ammonia1_img.jpg\" \/>\n\nGases can form supersaturated solutions. If a solution of a gas in a liquid is prepared either at low temperature or under pressure (or both), then as the solution warms or as the gas pressure is reduced, the solution may become supersaturated.","date":"2021-02-26 18:19:50","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6351161599159241, \"perplexity\": 1705.1345017323586}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-10\/segments\/1614178357935.29\/warc\/CC-MAIN-20210226175238-20210226205238-00572.warc.gz\"}"} | null | null |
\section{Introduction} \label{sec:intro}
Natural disasters impacting coastlines have long been some of the most dangerous
and unpredictable of all natural hazards, and among these tsunamis are particularly devastating.
Due to their rarity, it is extremely challenging to accurately understand and predict these events, owing to the
uncertainties in their generation, primarily subduction zone earthquakes, and
evolution, primarily the characterization of physical processes and bathymetric
measurements. Quantifying such uncertainties using
available past event data is
critical to help guide decision making during and after an event and also assists in building more accurate models.
One of the greatest sources of uncertainty in tsunami modeling lies with the
earthquake that generates the tsunami. This is mitigated in the far field by
the nature of the shallow water equations but in the near-field this uncertainty
can lead to significant discrepancies between predicted and actual flooding.
This is particularly troublesome when attempting to forecast tsunami run-up as
the immediately available fault movement is coarse in resolution and highly
uncertain itself. To mitigate this and improve the understanding of these
predictions, we propose an avenue for reconstructing the slip motion based on tsunami
observations immediately available via the DART buoy system.
A number of efforts towards quantification of uncertainty in the context of
tsunamis have been undertaken. Some studies have looked at fitting multiple
earthquake models, attempting to ascertain the best fit to available data while
allowing for simple variation in their initiation \cite{MacInnes:2013cr}, while
others have looked at other types of generation mechanisms such as land-slide
generated tsunamis \cite{Sarri2012}. Similar approaches to other problems
within the context of the ocean have also been presented. Examples of these
include studies examining tidal simulations that employed an adjoint or Kalman
filtering based approach \cite{Das:1992uo, Lardner:1995kn,Verlaan:1997te,
Heemink:2002vt, Mayo:2014}. Recently, the authors also presented an efficient
method for the inversion of Manning's $n$ coefficients that used water surface
elevation data collected during the T\={o}hoku\xspace earthquake and
tsunami~\cite{sraj:2014}. The efficiency of the method stems from using a
Polynomial Chaos (PC) surrogate model that approximated the forward model
{\sc GeoClaw}\xspace simulating the tsunami. The surrogate was constructed using a
non-intrusive spectral projection (NISP) method and was used within a Bayesian
inference formalism to avoid multiple runs of the forward model. We note that
Bayesian inversion of the distribution of fault slip has also been studied using synthetic data of surface displacement~\cite{Fukuda2008}.
The PC method uses polynomials to approximate a forward model (or a function)
and has been employed in the literature in various applications
including large-scale models~\citep{Iskandarani2015,Winokur2013,sraj:2013a,sraj:2013b,MatternFennelDowd2012}.
In those applications, traditional spectral projection methods~\citep{sraj:2013a,Reagan:2003,Alexanderian2012}
to construct the PC model were successfully implemented. In recent
studies, however, the spectral projection technique failed to construct
faithfully a PC expansion that represents the forward model~\citep{wang2015,Sraj2016}.
This was due to the non-linearity of the forward model and
to the internal noise that was present, leading
to PC expansion convergence issues. Instead, a compressed sensing technique called Basis-Pursuit-DeNoising (BPDN) was implemented to determine the PC expansion coefficients~\citep{Doostan:2014}. This technique first estimates the noise in the model (if any) and then solves an optimization problem to determine the PC expansion coefficients by
assuming sparsity in the coefficients and fitting the PC surrogate to a set of random model runs subject to the estimated noise.
BPDN was also recently implemented to build a proxy model for an ocean model with initial and wind forcing uncertainties~\citep{li2015}.
In that application, there was no noise in the model outputs, however, the BPDN method was used
as it does not require simulations at pre-specified sets of parameters which is a requirement by the NISP method.
In this work, we seek to quantify the uncertainties of the generating earthquake by
parameterizing the slip field in space. The basic approach is the same as the one employed in~\cite{sraj:2014}
where a Polynomial Chaos (PC) surrogate is constructed~\citep{MarzoukNajmRahn:2007,MarzoukNajm2009} and used for the inversion process using Bayesian inference~\citep{Malinverno2002}. In the case of the parameterized slip field, however, the specific method of constructing a PC surrogate using the NISP method was not successful. Instead the BDPN method proved more effective and capable of overcoming the convergence issues of the NISP approach and is the primary contribution presented in this paper. We also present results that show the ability of inferring the fault slip distribution using the DART buoys.
The remainder of the article is laid out as follows. In Section~\ref{sec:setup}, the essential setup of the
forward model is briefly described as well as the earthquake parameterization
considered. In Section~\ref{sec:formu}, the formulation of the inverse problem
including the approaches explored for the construction of the polynomial chaos
surrogate are detailed. Section~\ref{sec:results} presents results of the PC construction
using both NISP and BPDN methods in addition to results of the forward and inverse problems. Finally a discussion of the results and some conclusions are outlined in Section~\ref{sec:conc}.
\section{Problem Setup} \label{sec:setup}
The T\={o}hoku\xspace tsunami of 2011 was the most observed tsunami in
history providing us with a wealth of observational data. The earthquake had an
estimated magnitude of 9.0 ($\text{M}_\text{w}$) causing massive damage across
Japan due to the earthquake alone. The epicenter of the earthquake was located
approximately 72 km east of the T\={o}hoku\xspace region as indicated in
Figure~\ref{fig:setup}(Left). This section is devoted to the
description of the forward model used to simulate the tsunami and the
parameterization of the earthquake slip field.
\subsection{Forward Model}
The forward numerical model employed in this study is {\sc GeoClaw}\xspace, a package that has been
used to model a number of geophysical phenomena, mostly notably tsunamis for which it has been validated and approved for hazard mapping projects \cite{GonzalezLeVequeEtAl2011}. It
solves the non-linear, two-dimensional shallow water equations
\begin{equation} \label{eq:swe}
\begin{aligned}
&\pard{}{t} h + \pard{}{x} (hu) + \pard{}{y} (hv) = 0, \\
&\pard{}{t}(hu) + \pard{}{x} \left(hu^2 + \frac{1}{2} g h^2 \right ) + \pard{}{y} (huv) = ~~ fhv - gh \pard{}{x} b - C_f |\vec{u}| hu, \\
&\pard{}{t} (hv) + \pard{}{x} (huv) + \pard{}{y} \left (hv^2 + \frac{1}{2} gh^2 \right) = -fhu - gh \pard{}{y} b - C_f |\vec{u}| hv,
\end{aligned}
\end{equation}
where $h$ is the depth of the water column, $u$ and $v$ the velocities in the
longitudinal and latitudinal directions respectively, $g$ the acceleration due
to gravity, $b$ the bathymetry, $f$ the Coriolis parameter, and $C_f$ the bottom
friction coefficient. The sea-surface anomaly $\eta$, the difference between a
specified datum, such as mean tide level, and the modeled sea-surface, is $\eta
= h + b$.
{\sc GeoClaw}\xspace is an off-shoot of {\sc Clawpack}\xspace that solves systems of hyperbolic
equations in conservative and non-conservative form. The primary computational
kernel is the Riemann solver which determines fluctuations, wave speeds and
strengths. The Riemann solver in {\sc GeoClaw}\xspace contains a number of features
relevant to tsunami modeling including: (1) inundation (flooding at the shore);
(2) well-balanced formulation, providing the ability to handle topographical features
while maintaining steady-states (most notably an ocean at rest); and (3)
inclusion of entropy correction that handle rarefaction of the flow
\cite{George:2008aa}. One of the key components that makes {\sc GeoClaw}\xspace effective
at modeling trans-oceanic tsunamis is its use of adaptive mesh refinement (AMR).
AMR allows resolution of the model to follow features of the solution of
interest, such as the wave height difference from sea-level. {\sc GeoClaw}\xspace
implements these schemes via block-structured AMR as detailed in
\cite{Berger:1984ui, Berger:1998aa}.
Much of the setup for the T\={o}hoku\xspace simulations presented was adapted from the
{\sc GeoClaw}\xspace simulations presented in \cite{MacInnes:2013cr} including the
refinement strategy. This includes resolutions ranging from 1 degree in both
longitude and latitude to 75" resolution. The bathymetry used here is a
combination of ETOPO 1' and 4' resolution data~\cite{Amante:2009ud}; the finer bathymetry used in
\cite{MacInnes:2013cr} to model inundation appropriately was excluded as this
study does not include inundation data in the inversion.
\subsection{Parametric Representation of the Slip Distribution} \label{sec:parameters}
The overall goal of this article is to invert for the source earthquake using
observational data available immediately after the earthquake. In order to
simplify the investigation of the problem formulation, the base geometry of the fault
was assumed fixed while the slip on the fault is assumed to be uncertain.
Based on previous inversions, the slip magnitude was constrained between the
similar slips proposed in \cite{Ammon:2011dm} of $s_{max} = 30~m$ and no-slip
$s_{min} = 0~m$ (see Figure~\ref{fig:setup} right). Additionally the fault was
broken up into 6 sub-regions of which each can have a unique slip value in the
inversion (see Figure~\ref{fig:slips}) and cover the largest area of slip. The
initial uncertainty was represented as a non-informative, uniform distribution
with the limits mentioned above. The uncertainty is then quantified through PC
expansions as in \cite{sraj:2013a,sraj:2013b}.
\section{Formulation} \label{sec:formu}
In this section, we describe the different steps of our method to numerically
solve the inverse problem stated above. In Section~\ref{sec:obs}, we analyze the
available observations used in the Bayesian inference step, outlined in Section~\ref{sec:inference}.
Finally, in Section~\ref{sec:uq}, we provide some details on a key ingredient of
our methodology i.e.\ constructing a surrogate of the forward model for
the sake of accelerating the Bayesian inference.
\subsection{Observations}
\label{sec:obs}
We use observations consisting of water surface elevation
measurements collected for a period of around $4$ hours during the event at four
different gauge locations. These gauges are part of the Deep-ocean
Assessment and Reporting of Tsunamis (DART) buoy system developed and maintained
by the National Oceanic and Atmospheric Administration (NOAA) with the purpose
of providing early-warning detection and forecasting of tsunami propagation in
the Pacific Ocean \cite{Milburn:1996wm}. The four selected gauges are the
closest to the earthquake source of the T\={o}hoku\xspace tsunami denoted by Gauge 21401,
21413, 21418, and 21419. The locations of these buoys are shown in
Figure~\ref{fig:setup} (Left) where the bathymetry and topography of the
numerical domain is also shown. The de-tided water surface elevation data for
the event at the four gauges are shown in Figure~\ref{fig:observations} (Left). The
readers are referred to~\cite{Mungov2013} for details on the data processing
methodologies used for the DART buoy data.
Prior to using these observations for the inference of the fault slip
distribution, we verify the ability of {\sc GeoClaw}\xspace to realistically simulate water
surface elevation during the T\={o}hoku\xspace tsunami. To this end, we ran a single
simulation of {\sc GeoClaw}\xspace with default parameters and fault slip
distribution from Ammon \emph{et al.}
\cite{Ammon:2011dm} to predict the water surface elevation at the four gauges.
We compare these with their DART counterparts and plot them in
Figure~\ref{fig:observations} (Right) as a scatter plot for the gauges 21401, 21413, 21418
and 21419. The data points are colored differently for the different gauges and
the variance of the difference between observations and simulations was
calculated to be $7.99\times 10^{-3}~m^2, 9.65\times 10^{-3}~m^2, 4.62 \times 10^{-2}~m^2$
and $5.86\times 10^{-3}~m^2$, respectively. These variances are consistent with the
distance from the gauges to the epicenter of the earthquake located
approximately 72 kilometers east of Japan. The smallest variance was at gauge
21419 (the farthest gauge from the epicenter) while the higher
variance was at gauge 21418 that can be attributed to its proximity to the
epicenter of the earthquake as well as to the shore region. The scatter plot
along with the calculated variances indicate a reasonable agreement between the
simulations and the observations at the different gauges. The overall
differences between the simulations and observations can likely be attributed to
uncertainties in the input data such as the Manning's $n$
coefficients~\cite{sraj:2014}, fault slip distribution, errors in the earthquake rupture model,
insufficiently accurate bathymetry in the near-shore region, and to model errors,
such as unresolved effects and approximations inherent in the shallow water
model.
\subsection{Inverse problem}
\label{sec:inference}
Bayesian inference is a well-established probabilistic approach to inverse problems in
which all forms of uncertainty are expressed in terms of random variables. This method
provides complete posterior statistics and not just a single value for the
quantity of interest ($QoI$)~\cite{Tarantola:2005}. Consider a set of $N$ water surface
elevation observations $\vec{\eta}_j =\{{\eta}_j^k\}_{k=1}^N$ measured at the
different DART buoy gauges $j=1,2,3$ and $4$, corresponding to gauges 21401,
21413, 21418 and 21419, respectively. Let $\vec{s}=\{s_i\}_{i=1}^{m=6}$ be a
vector of uncertain parameters representing the six fault slip values. We
consider the forward model $\vec{G}_j(\vec s) =\{{G}_j^k(\vec s)\}_{k=1}^N$
represented by {\sc GeoClaw}\xspace that predicts the $N$ data at the $j^{th}$ gauge as a
function of the vector of parameters $\vec{s}$ given observations $\vec{\eta}_j$. Bayes's theorem can be applied
that yields:
\begin{equation} \label{eq:bayes}
\pi(\vec{s}| {\vec \eta}_j) \propto
\pi({\vec \eta}_j | \vec{s}) \ \pi(\vec{s}),
\end{equation}
where $\pi(\vec{s})$ is the prior of $\vec{s}$, $\pi({\vec \eta}_j| \vec s)$ is
the likelihood function and $\pi(\vec{s}| {\vec \eta}_j)$ is the
posterior of $\vec{s}$. The likelihood function $L(\vec{s} | {\vec \eta}_j) =
\pi({\vec \eta}_j| \vec s)$ can be formulated assuming that independent additive
errors account for the discrepancy between the predicted, $\vec{G}_j(\vec s)
=\{{G}_j^k(\vec{s})\}_{k=1}^N$, and observed $\vec{\eta}_j
=\{{\eta}_j^k\}_{k=1}^N$, values of water surface elevation such that:
\[
{\epsilon}_j^k = {G}_j^k(\vec s) - {\eta}_j^k, \quad j=1 \ldots 4 , \quad k=1 \ldots N,
\]
where ${\vec \epsilon}_j = \{{\epsilon}_j^k\}_{k=1}^N$ are assumed to be i.i.d.
random variables with density $p_{\epsilon_j}$. The likelihood function can
then be written as
\begin{equation} \label{eq:likelihood}
L(\vec{s} | {\vec \eta}_j) = \prod_{j=1}^4 \prod_{k=1}^N p_{\epsilon_j} (G_j^k(\vec s) - {\eta}_j^k ).
\end{equation}
In our application, the measurements may vary significantly from
one gauge to another and the observations collected may be exposed to different
measurement errors; therefore, it is reasonable to assume that the errors are normally distributed with
zero mean and a variance that depends on location, i.e. \ $\epsilon_j^k \sim N(0,\sigma_j^2)$
where $\sigma_j^2$ ($j=1 \ldots 4$) is the variance at the different gauges.
Thus the likelihood function can be expressed as
\begin{equation} \label{eq:likelihood2}
L(\vec{s} | {\vec \eta}_j) = \prod_{j=1}^4\prod_{k=1}^N \frac{1}{\sqrt{2
\pi \sigma_j^2}} \exp \left\lbrace \frac{-(G_j^k(\vec s)-\eta^k_j )^2}{2 \sigma_j^2} \right\rbrace,
\end{equation}
and the joint posterior in Equation~\ref{eq:bayes} becomes
\[
\pi(\vec{s}| \eta^k_j) \propto \prod_{j=1}^4 \prod_{k=1}^N \frac{1}{\sqrt{2 \pi \sigma_j^2}} \exp \left\lbrace \frac{-(G_j^k(\vec s) - \eta^k_j )^2}{2 \sigma_j^2} \right\rbrace \prod_{i=1}^6 \pi(s_i).
\]
The variance $\sigma_j^2$ is not well known \emph{a priori}, thus it is treated as a hyper-parameter
that becomes an additional parameter for Bayesian inference endowed with a prior which is updated based on available observations. In this
case the joint posterior is finally expressed as
\begin{equation} \label{eq:post_coef}
\pi(s_i,\sigma_j^2 | \eta_j^k)
\propto
\prod_{j=1}^4
\prod_{k=1}^N
\frac{1}{\sqrt{2 \pi \sigma_j^2}} \exp \left\lbrace \frac{-( G_j^k(\vec s)-\eta^k_j)^2}{2 \sigma_k^2} \right\rbrace
\ \prod_{i=1}^6
\pi(s_i) \prod_{j=1}^4 \pi(\sigma_j^2).
\end{equation}
Finally, proper priors are chosen for the uncertain parameters based on some
\emph{a priori} knowledge about them. In our case, we chose a non-informative
uniform prior for all six fault slip values, with $s_i$ in the range $[s_{min}
- s_{max}]$ so that $\pi(s_i) = \frac{1}{s_{max}-s_{min}}$. Regarding the noise
variance, the only information known is that $\sigma_j^2$ is always positive.
We thus assume a Jeffreys prior \citep{sivia} for $\sigma_j^2$, expressed as:
\begin{equation}
\pi(\sigma_j^2) = \begin{cases}
\displaystyle \frac{1}{\sigma_j^2} &\text{for~} \sigma_j^2 > 0, \\
0 &\text{otherwise}.
\end{cases}
\label{eq:var_pr}
\end{equation}
The described Bayesian formulation requires sampling the resulting posterior
(Equation~\ref{eq:post_coef}) to estimate the joint posterior of the parameters. Markov
Chain Monte Carlo (MCMC) methods are convenient and popular sampling strategies
that require a large number of posterior evaluations. We rely on an
adaptive Metropolis MCMC algorithm ~\cite{Haario2001,Gareth2009} to efficiently
sample the posterior distribution. In addition, we build a surrogate model of
the model response for further reduction in computational time as explained below.
\subsection{Surrogate model}
\label{sec:uq}
To accelerate the process of sampling the
posterior~(Equation~\ref{eq:post_coef}) using MCMC, we build a surrogate
model of the $QoIs$, namely the $\vec{\eta}_j$'s using a small ensemble of {\sc GeoClaw}\xspace model runs. For this
purpose, we apply a probabilistic method to express the $QoI$ as a function of
the uncertain model inputs, namely the Polynomial Chaos (PC)
method~\citep{LeMaitreKnio2010,Xiu2004}. As the name indicates, the function
would be in the form of a polynomial expansion~\citep{GhanemSpanos1991,Xiu2004}
that is truncated at a specific order. This approach was adopted
in~\cite{sraj:2014} to build a surrogate model for the water surface elevation
and then used to determine statistical properties (mean and variance) as well as
sensitivities~\citep{Crestaux}. Additionally the surrogate model was used for
efficient sampling of the posteriors. We briefly show here the process of
constructing a PC surrogate for the $QoI$; for more details on the PC method the
reader is referred to~\cite{LeMaitreKnio2010}.
\subsubsection{Polynomial Chaos}
\label{sec:pc}
We denote by $G=G(\vec{\xi})$ our $QoI$ which is the water surface elevation produced by {\sc GeoClaw}\xspace;
$\vec{\xi}=[\xi_1,...,\xi_m]$ denotes the canonical vector of $m$ random variables that parameterize the uncertain fault slip values
as follows:
\[
\xi_{i} = \frac{2s_i-(s_{min}+s_{min})}{(s_{min}-s_{max})}.
\]
The PC method seeks to represent $G$ as a function of the uncertain input
variables $\vec{\xi}$ as
\begin{equation}
G(\vec{\xi}) \approx \sum_{k = 0}^R g_k \psi_k(\vec{\xi}),
\label{eq:stochseries}
\end{equation}
where $g_k$ are the polynomial coefficients to be determined, and
$\psi_k(\vec{\xi})$ are tensor products of the scaled Legendre polynomials~\citep{LeMaitreKnio2010} forming an orthogonal basis
of the space of square integrable functions of the underlying uniform probability
distributions $\rho(\vec{\xi})$ with
\begin{equation}
\left<\psi_i,\psi_j\right> = \int \psi_i(\vec{\xi}) \;\psi_j(\vec{\xi}) \; \rho(\vec{\xi}) \; \mbox{d}\vec{\xi}=\delta_{ij}\ave{\psi_i^2},
\label{eq:inner}
\end{equation}
The PC coefficients $g_k$ can be determined using a number of methods.
In this work, we rely on non-intrusive approaches~\cite
{Berveiller:2006,Reagan:2003}
that use a set of deterministic model runs $G(\vec{\xi})$ evaluated
at particular realizations of $\vec{\xi}$. In particular, we relied on two non-intrusive methods
described in Section~\ref{sec:nisp} and Section~\ref{sec:bpdn} below. The reasoning behind using
these two methods is explained in the results section.
\subsubsection{Non-Intrusive Spectral Projection}
\label{sec:nisp}
The Non-Intrusive Spectral Projection (NISP) method makes use
of the orthogonality of the polynomial basis and applies a Galerkin projection
to find the PC expansion coefficients~\citep{Constantine:2012,Conrad:2013} as
\[
g_k = \frac{\left< G, \psi_k \right>}{\left< \psi_k, \psi_k \right>} =
\frac{1}{\left< \psi_k, \psi_k \right>}
\int G \psi_k(\vec{\xi}) \rho(\vec{\xi}) \mbox{ d}\vec{\xi}.
\]
A numerical quadrature is used to approximate the integrals with
\[
\int G \psi_k(\vec{\xi}) \rho(\vec{\xi}) \mbox{ d}\vec{\xi}
\approx \sum_{q=1}^{Q} G(\vec{\xi}_q) \psi_k(\vec{\xi}_q) \omega_q,
\]
where $\vec{\xi}_q$ and $\omega_q$ are the multi-dimensional quadrature points and weights,
respectively, and $Q$ is the total number of nodes in the multi-dimensional quadrature.
$G(\vec{\xi}_q)$ is the model prediction evaluated at the quadrature values $\vec{\xi}_q$.
We note that the order of quadrature should be commensurated with the PC truncation order,
and should be high enough to avoid aliasing artifacts.
\subsubsection{Basis-Pursuit DeNoising}
\label{sec:bpdn}
Basis-Pursuit DeNoising (BPDN) is a non-intrusive method for finding the PC
coefficients using a number of random model evaluations. BPDN is based on
the compressed sensing methodology that assumes sparsity in a signal, in our case
the PC coefficients, and seeks to determine the non-zero coefficients. using
optimization techniques~\citep{Berveiller:2006,Blatman:2011,Doostan:2014}. Let
${\vec{g}}=[g_0,...,g_R]$ be the vector of PC coefficients to be determined and
$\vec G = [G(\vec{\xi}_1),...,G(\vec{\xi}_S)]$ be the vector of random model evaluations
at the sampled $\vec{\xi}_s$. We also let $\Psi$ be a matrix whose rows are evaluations
of the PC basis functions $\psi_k(\vec{\xi})$ at the sampled $\vec{\xi}_s$. We therefore
transform Equation~\ref{eq:stochseries} into the following system in matrix
form to solve for:
\[
\vec{G} = \Psi \vec{g}.
\]
The sparsity in the system is exploited by constraining the system and minimizing its "energy", which is its $\ell_1$-norm,
and thus solving the optimization problem
\begin{equation} \label{eq:optim}
{\cal{O}}_{1,\delta} \approx \left\lbrace \arg\!\min_{{\vec g}} || {\vec{g}} ||_1 : || \vec G - \Psi \vec{g} ||_2 \le \delta \right\rbrace.
\end{equation}
In this specific method, we assumed the presence of noise $\delta$ in the signal
that is estimated \emph{a priori} in contrast to the Basis-Pursuit (BP)
technique where no noise is assumed~\cite{Donoho:2006}. The noise $\delta$ is
determined using a cross-validation method that assures the computed PC
coefficients not only fit the random model evaluations but also accurately
approximate the model~\cite{Doostan:2014}. The system ${\cal{O}}_{1,\delta}$ is
then solved using standard $\ell_1$-minimization solvers such as the MATLAB package
SPGL1~\citep{spgl1:2007}, that is based on the spectral projected gradient
algorithm~\citep{BergFriedlander:2008}.
\section{Results} \label{sec:results}
\subsection{PC Expansion Construction and Validation}
The construction of the PC surrogate for the water surface elevation using non-intrusive methods
requires an ensemble of forward model runs. The shape (distribution) of the ensemble and number of
members (model runs) is dictated by the particular method employed. In this work, we employ two different methods that require two different ensembles as follows:
\begin{enumerate}
\item NISP requires a quadrature to compute the PC coefficients~\cite{sraj:2014}. Here, we adopted a sparse nested
Smolyak quadrature~\citep{Petras:2000,Gerstner:2003,Smolyak:1963}. In particular,
Smolyak level 5 grid rule was used requiring a total number of $Q = 1889$
quadrature nodes for the case of $m=6$ uncertain parameters to accurately
approximate PC expansion of order $p = 5$. A two-dimensional projection of the quadrature grid
is shown in Figure~\ref{fig:sample}~(Left) on the $\vec{\xi}_1 - \vec{\xi}_2$ plane.
The evolution of the water surface elevation predicted by {\sc GeoClaw}\xspace at these nodes
is shown in Figure~\ref{fig:quadrature} at the four different gauges.
\vspace{6mm}
\item BPDN accommodates both regular and random sampling to determine the PC coefficients.
Here, we used a Latin-Hyper-Cube (LHS) sample consisting
of 729 {\sc GeoClaw}\xspace realizations whose nodes are shown in
Figure~\ref{fig:sample}~(Right) when projected on the $\vec{\xi}_1 - \vec{\xi}_2$ plane.
The evolution of the water surface elevation predicted by {\sc GeoClaw}\xspace at these nodes
is shown in Figure~\ref{fig:lhs_sample} at the four different gauges.
\end{enumerate}
In both sets of realizations, we notice that the variability in water surface elevation
is significant at all gauges. This variability in the prediction of water surface
elevation persists till the end of the simulations for all gauges as well.
It is noticed that this variability is present in the arrival time in addition to the Maximum Wave Amplitude (MWA).
To confirm, we estimate the arrival time and MWA of the 1889 realizations corresponding to the quadrature sample
and plot them as functions of the different slip values $s_i$ on the subfaults (other values are set to $s_j = 15$) in Figure~\ref{fig:quad_pt} and Figure~\ref{fig:quad_mwa}, respectively. We clearly notice the significant variation of arrival time with the slip values and similarly for the MWA. These variations are expected to be challenging when computing the PC coefficients as it might require
a high order PC expansion~\cite{Alen:2011}.
Finally, we note that the average arrival time and average MWA are both consistent with the distance from the gauge to the epicenter of the earthquake (located approximately 72 kilometer east of Japan). For instance,
gauge 21418 is the closest to the source as shown in Figure~\ref{fig:setup} with the shortest arrival time and largest MWA, while
on the other hand, gauge 21419 is the farthest from the source with the longest arrival time and smallest MWA.
\label{sec:pccs}
\subsubsection{Non-Intrusive Spectral Projection}
\label{sec:pcnisp}
The PC expansion coefficients are first computed using the output of the 1889
quadrature ensemble. The constructed PC surrogate is validated using the normalized
relative error (NRE) that measures the accuracy of predicted values by the PC surrogate
using an independent set of {\sc GeoClaw}\xspace simulations as follows:
\begin{equation}
NRE = \frac{\displaystyle
\left(\sum_{q=1}^S \left|G(\vec{\xi}_s) - \sum_{k = 0}^{R}
g_k\psi_k(\vec{\xi}_q)\right|^2
\right)^{1/2}}
{\displaystyle
\left(\sum_{q=1}^S \left|G(\vec{\xi}_s)\right|^2\right)^{1/2}
},
\label{eq:error}
\end{equation}
where $G(\vec{\xi}_s)$ is the $QoI$ corresponding to the LHS sample
that were not used in the PC construction process.
The evolution of NRE is shown in Figure~\ref{fig:error_lhs_nisp} for different PC orders
as indicated. The horizontal dotted lines are guides to the eye indicating the $5\%$ and $10\%$ errors.
The calculated NRE appears to be larger than $10\%$ for PC order $p=1$ at certain times
that amplifies with increasing PC order. This indicates convergence issues in the PC that leads to inaccuracies in
the representation of the $QoI$. This is noticed for all the gauges.
We conclude that the construction of a converging PC expansion using the NISP method was not successful which promoted us to use an to alternative method. The large errors can be attributed to the large variation in the arrival times
and the MWA that is not tolerated by the NISP method.
One option to overcome this issue is preconditioning the $QoI$.
This idea was proposed in~\cite{Alexanderian2011a,Alexanderian2012}, where appropriate transformations of
the original time-dependent $QoI$ into a new one having a tight sparse PC expansion, thus
requiring less effort to be projected. Instead we resort here to a recent compressed technique as explained above.
\subsubsection{Basis-Pursuit DeNoising}
\label{sec:pcbpdn}
We next applied the BPDN method to estimate the PC
coefficients~\cite{Doostan:2014} using the LHS sample consisting of 729 {\sc GeoClaw}\xspace
realizations. We again quantified the agreement between the PC surrogate and the {\sc GeoClaw}\xspace
realizations where we now calculate the NRE using the Smolyak quadrature sample
(not used in the PC coefficients estimation).
The evolution of error shown in Figure~\ref{fig:error_quad_bpdn} indicate a better agreement (compared to NISP)
whereas the maximum error was found to decrease as the PC order is increased. The average error is less than $5 \%$, indicating that BPDN is successful in constructing a surrogate that yields accurate $QoI$ predictions.
We also computed the empirical CDF of water surface elevation
at the different gauges using samples from the PC surrogate for different orders.
We also computed the CDF using the 1889 {\sc GeoClaw}\xspace model runs and compare them
to the PC-estimated ones and plot them in Figure~\ref{fig:cdfs}.
These different panel show that the CDFs obtained using higher order bases agree with each other
and with the CDF obtained from the full model runs directly.
In conclusion, these tests provide confidence that the PC expansion is a faithful
model surrogate that can be used in both the forward and inverse problems.
\subsection{Statistical Analysis}
\label{sec:sens}
The PC expansion created using an ensemble of {\sc GeoClaw}\xspace simulations
simplifies the calculations of the statistical moments of model output $G$ as
the expectation and variance can be computed from the PC coefficients as follows:
\begin{equation}
\mu_G = \int G \, \rho(\vec{\xi}) \, \mbox{d}\vec{\xi} \approx \left< G,\psi_0\right>_{\cal Q} = G_0,
\label{eq:mean}
\end{equation}
\begin{equation}
\sigma^2_G = \int (G- \mu_G)^2 \, \rho(\vec{\xi}) \, \mbox{d}\vec{\xi} \approx \sum_{k=1}^R G_k^2
\left<\psi_k,\psi_k\right>.
\label{eq:sigma}
\end{equation}
The evolution of the mean of the sea-surface elevation $\mu_G$ along with two
standard deviation bounds ($\pm 2\sigma_G$) are thus computed from the PC
coefficients and plotted in Figure~\ref{fig:ave} at the four gauges.
Note that the evolution shown starts at $t=2 hrs$ when the
uncertainty becomes significant. An interesting observation is that the standard
deviation in water surface elevations waxes and wanes as the tsunami evolves.
The narrowing of the variance at these instances is possibly associated with the
waves that arrive due to reflections from a single source and then move away
from the gauge location imposing no variance in the water surface
elevation.
\subsection{Fault Slip Inference}
\label{sec:infer}
Finally with our PC surrogate in hand we can solve the inverse problem, estimating the fault slip values as well as the variance of the noise in the measured data
using Bayesian inference. For this purpose, we implement an adaptive MCMC method ~\citep{Gareth2009,Haario2001} to sample
the posterior distributions in Equation~\ref{eq:post_coef} and consequently update the uncertain parameters.
The posterior was sampled $10^6$ times after which we find negligible change in the estimated posteriors of the fault slip values: $s_{1} \ldots s_6$ as well as for the noise variance $\sigma^2_1 \ldots \sigma^2_4$ with further iterations.
Figure \ref{fig:chains_p} plots the sample chains for the input parameters for different
iterations of the MCMC algorithm. The different panels show well-mixed chains for all input parameters
where the chains of $s_{1},s_{2},s_{4}$ and $s_{5}$ appear to be concentrated in an area of
the parameter prior range. In contrast, the $s_{3}$ and $s_6$ chains appear to be concentrated in the lower end of
the parameter range. The running mean plotted in Figure~\ref{fig:running_mean} is an indication of the convergence of the MCMC.
The chains for the noise variances ($\sigma^2_1 \ldots \sigma^2_4$)
are shown in Figure~\ref{fig:chains_s} at the different gauges and appear to be well mixed with a well defined
posterior range. The maximum variance appears to be at gauge 21418 and its range lies between 0.025 and 0.045.
We used Kernel Density Estimation (KDE)~\citep{Parzen1962,Silverman1986} to determine the marginalized posterior
probability distribution functions (\emph{pdfs}) using the computed MCMC chains and plot them in Figure~\ref{fig:pdfs_p} for the different parameters.
The first $2\times 10^5$ MCMC iterations were considered as the burn-in period and thus discarded.
The shapes of the marginalized posterior \emph{pdfs} are consistent with the chains shown in Figure~\ref{fig:chains_p}
where the \emph{pdfs} of $s_{1},s_{2},s_{4}$ and $s_{5}$ appear to have a Gaussian-like shape with a well-defined peak;
the Maximum A Posteriori (MAP) values are estimated to be $2.7,~23,~6.5$ and $21.5$ respectively. On the other hand, for $s_3$ and $s_6$ and the \emph{pdfs} exhibit also a well-defined peak,
but with an extended tail towards the smaller slip values; the mean values are
estimated to be $0.3$ for both. The 95\% intervals of high posterior probability
are shown as shaded regions for the inferred parameters.
Regarding the noise variances, their \emph{pdfs} are shown in Figure~\ref{fig:pdfs_s} at the different gauges.
The \emph{pdfs} appear to be well-defined and Gaussian shaped with a clear MAP values.
These MAP values can be used to estimate the maximum water surface elevation standard deviation that was found to
be $\sigma_3=0.182~m$ at gauge 21418. This value is a reflection of the mismatch between the model and
observed data. The $\sigma^2_i$ estimates are noticeably lower than those obtained with {\sc GeoClaw}\xspace default slip distribution (shown in Figure~\ref{fig:observations} (Right)):
$2.27\times 10^{-3}~m^2$ versus $7.99\times 10^{-3}~m^2$, $1.22\times 10^{-2}~m^2$ versus $9.65\times 10^{-3}~m^2$, $3.32 \times 10^{-2}~m^2$ versus $4.62 \times 10^{-2}~m^2$, $2.38\times 10^{-3}~m^2$ versus $5.86\times 10^{-3}~m^2$ at gauges 20401, 21413, 21418 and 21419, respectively.
The scatter plot shown in Figure~\ref{fig:scatter_inf} uses inferred MAP
values. Thus, the parameters MAP values have reduced the discrepancies between
simulated water surface elevation and DART buoy data. This comparison can be
seen as an evaluation of the \emph{a posteriori} goodness-of-fit. Additionally
Figure~\ref{fig:map_inversion} shows the comparison between the MAP values and
the Ammon \emph{et al.} model~\cite{Ammon:2011dm}. Note that the inverted fault leads to a moment
and magnitude of $M_o = 3.43900\times 10^{22}$, $M_w = 8.99095$, respectively, whereas the Ammon \emph{et al.} model yields a moment and magnitude of $M_o = 3.63595\times 10^{22}$ and
$M_w = 9.00708$.
\section{Discussion and Conclusions}
\label{sec:conc}
In this study, we sought to estimate the fault slip distribution that
plays a critical role in earthquake and tsunami modeling, mainly in the
prediction of water surface elevations. To this end, we proposed
a low-dimensional parameterization of the fault slip distribution
in which we assumed the fault consists of six sub-faults that
have different slip magnitudes. The estimation of the fault slip distribution thus boiled down into a six-parameter inverse problem.
A Bayesian inference approach was employed
that sharpens the initial estimates of the six uncertain parameters based on measured observations.
In our test case, the T\={o}hoku\xspace tsunami, we used water surface elevations information collected at four DART buoy gauges.
Discrepancies with measurements were accounted for using a Gaussian noise model, whose variance was treated as a hyper parameter that was inferred along with the uncertain fault parameters.
Bayesian inference was accelerated using a surrogate
model constructed based on the Polynomial Chaos approach where
the output of the forward model {\sc GeoClaw}\xspace was approximated using PC expansions.
The PC expansions were constructed based on a compressed sensing approach that uses basis-pursuit denoising technique,
to produce a faithful surrogate. This PC surrogate model was additionally
used to quantify the uncertainties in the predicted water surface
elevations due to the uncertainties in slip values. This included the mean and standard deviation
of water surface elevations.
The present study focused on formulating and estimating a low-dimensional
representation of the fault slip distribution using UQ techniques, namely
Bayesian inference and PC expansions. A high-dimensional representation of the fault slip distribution
would, however, require a large number of forward runs that is computational prohibitive.
Instead, one could exploit order-reduction techniques to
reduce the dimensionality such as Karhunen-Lo\`eve expansions~\cite{Sraj2016}. This will be the objective of a future study.
\section*{Acknowledgment}
Research reported in this publication was supported by the King Abdullah
University of Science and Technology (KAUST) in Thuwal, Saudi Arabia grant number CRG3-2156.
The authors would like to thank Dr. Olivier Le Maitre for the helpful discussions of the results.
\bibliographystyle{elsarticle-num}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,593 |
El ke (en pinyin: ke) és una unitat xinesa tradicional de temps decimal que dura aproximadament un quart d'una hora occidental. Tradicionalment el ke divideix un dia en cent intervals iguals de 14.4 minuts (14 min 24 s). El ke és equivalent al centidía (c d), un prefix d'una unitat que no pertany al sistema SI. En forma literal l ke signidfica 'marcar' o 'tallar', i és part del substantiu Kedu que fa a marques tallades en els dispositius de mesura.
Juntament amb l ke, els antics xinesos mesuraven el temps amb hores dobles (tradicional 时辰, simplificat 时辰, pinyin shíchen ) també anomenats "torns ". Atès que no és possible dividir 12 hores dobles en 100 ke en forma uniforme, cada ke va ser subdividit en 60 fen (分; pinyin fen).
Hi va haver diversos intents de redefinir el ke en 96, 108, o 120 de manera de poder dividir en forma uniforme les 12 hores dobles. Durant la dinastia Qing per l'època en què van arribar els missioners jesuïtes, la durada del ke havia estat redefinida a un 96 avo (1/96) d'un dia, o exactament 1/4 d'hora occidental. En l'actualitat ke és el terme estàndard xinès per denominar al quart d'hora. A més, en l'actualitat el fen és utilitzat per referir-se a un lapse de temps que no és 1/60 del ke sinó 1/60 d'una hora, o sigui 1 minuts.
Referències
Bibliografia
Colin Ronan, p 247-250 in Walker, Ch ed.: Astronomy before the telescope. Brit. Museum P., UK (1999).
Calendari
Temps | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 518 |
Hofkirchen – gmina targowa w Niemczech, w kraju związkowym Bawaria, w rejencji Dolna Bawaria, w regionie Donau-Wald, w powiecie Pasawa. Leży około 25 km na północny zachód od Pasawy, nad Dunajem, przy autostradzie A3.
Dzielnice
W skład gminy wchodzą trzy dzielnice: Hilgartsberg, Hofkirchen, Garham.
Demografia
Polityka
Wójtem od 2002 jest Wilhelm Wagenpfeil (SPD), jego poprzednikiem był Josef Weiß (CSU).
Współpraca
Miejscowość partnerska:
Hofkirchen an der Trattnach, Austria
Oświata
(na 1999)
W gminie znajduje się przedszkole (132 miejsc i 101 dzieci) oraz 2 szkoły podstawowe (12 nauczycieli, 280 uczniów).
Powiat Pasawa
Gminy w Bawarii | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,727 |
We're setting up new deposition systems in our lab so I had to do some welding using a Swagelok orbital tube welder.
This time I had to weld 1/2 inch OD tubing which was cool because you can look into the electropolished cylinder and watch the welding process as the welding tip orbits around the tube. You can see white/blue light from the welding arc between tip and tube.
This page contains a single entry by Franz Koeck published on March 12, 2011 7:00 PM.
What a sky... was the previous entry in this blog.
Fresh green looks. is the next entry in this blog. | {
"redpajama_set_name": "RedPajamaC4"
} | 47 |
\section*{Acknowledgements}
This research of Collins, Mokhtari, and Shakkottai is supported in part by NSF Grants 2019844 and 2112471, ARO Grant W911NF2110226, ONR Grant N00014-19-1-2566, the Machine Learning Lab (MLL) at UT Austin, and the Wireless Networking and Communications Group (WNCG) Industrial Affiliates Program. The research of Hassani is supported by NSF Grants 1837253, 1943064, AFOSR Grant FA9550-20-1-0111, DCIST-CRA, and the AI Institute for Learning-Enabled Optimization at Scale (TILOS).
\newpage
\section{Experimental Details} \label{app:experiments}
\subsection{Multi-task linear regression}
The multi-task linear regression experiments consist of two stages: training and fine-tuning. During training, we track $\operatorname{dist}(\mathbf{B}_t, \mathbf{B}_\ast)$ in Figure \ref{fig:1} and the Frobenius norm of the gradient of \ref{glob_pop}, i.e. $(\|\mathbf{B}_t^\top(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast})\|^2_2 + \|(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast})\mathbf{w}_t^\top\|_F^2)^{1/2}$, in Figure \ref{fig:linear}(left). For fine-tuning, we track the squared Euclidean distance of the post-fine-tuned model from the ground-truth in Figure \ref{fig:linear}(right) for various numbers of fine-tuning samples $n$.
Each training trial consists of first sampling $M$ ground truth heads $\mathbf{w}_{\ast,i} \sim \mathcal{N}(\mathbf{0},\mathbf{I}_k)$ and a ground truth representation $\mathbf{\check{B}}_\ast \in \mathbb{R}^{d \times k}$ such that each element is i.i.d. sampled from a standard Gaussian distribution. Then, $\mathbf{B}_\ast$ is formed by computing the QR factorization of $\mathbf{\check{B}}_\ast$, i.e. $\mathbf{B}_\ast\mathbf{R}_\ast = \mathbf{\check{B}}$, where $\mathbf{R}_\ast \in \mathbb{R}^{k\times k}$ is upper triangular and $\mathbf{B}_\ast\in \mathcal{O}^{d \times k}$ has orthonormal columns. To initialize the model we set $\mathbf{w}_0= \mathbf{0}\in \mathbb{R}^k$ and sample $\mathbf{\check{B}}_0 \in \mathbb{R}^{d \times k}$ such that each element is i.i.d. sampled from a standard Gaussian distribution, then compute $\mathbf{{B}}_0 = \tfrac{1}{\sqrt{\alpha}}\mathbf{\hat{B}}_0$ where $\mathbf{\hat{B}}_0 \in \mathcal{O}^{d\times k}$ is the matrix with orthonormal columns resulting from the QR factorization of $\mathbf{\check{B}}_0$. Then we run FedAvg with $\tau=2$ and D-SGD on the population objective \ref{glob_pop}, with both sampling $m=M$ clients per round and using step size $\alpha = 0.4$. The training plots show quantities averaged over 10 independent trials.
For each fine-tuning trial, we similarly draw a new head $\mathbf{w}_{\ast,M+1}\sim \mathcal{N}(\mathbf{0},\mathbf{I}_k)$, and data $\mathbf{x}_{M+1,j}\sim \mathcal{N}(\mathbf{0},\mathbf{I}_k)$, $y_{M+1,j} = \langle \mathbf{B}_\ast \mathbf{w}_{\ast,i}, \mathbf{x}_{M+1,j}\rangle+\zeta_{M+1,j}$ where $\zeta_{M+1,j} \sim \mathcal{N}(0,0.01)$.
Then we run GD on the empirical loss $\frac{1}{2n}\sum_{j=1}^n (\langle \mathbf{Bw}, \mathbf{x}_{M+1,j}\rangle - \mathbf{y}_{M+1,j})^2$ for $\tau'=200$ iterations with step size $\alpha = 0.01$. The fine-tuning plot shows average results over 10 independent, end-to-end trials (starting with training), and the error bars give standard deviations.
\subsection{Image classification}
The CNN used in the image classification experiments has six convolutional layers with ReLU activations and max pooling after every other layer. On top of the six convolutional layers is a 3-layer MLP with ReLU activations.
All models are trained with a step size of $\alpha = 0.1$ after tuning in $\{ 0.5,0.1, 0.05, 0.01,0.005\}$ and selecting the best $\alpha$ that yields the smallest training loss. In all cases, $m = 0.1M$. We use the SGD optimizer with weight decay $10^{-4}$ and momentum 0.5. We train all models such that $T\tau = 125000$. Thus, D-SGD trains for $T=125000$ rounds, since $\tau=1$ in this case. Likewise, for FedAvg with $\tau=50$, $T=2500$ training rounds are executed. The batch size is 10 in all cases. We also experimented with larger batch sizes for D-SGD but they did not improve performance.
Each client has 500 training samples in all cases. Thus, FedAvg with $\tau=50$ is equivalent to FedAvg with one local epoch. For the experiments with $C$ classes per client for all clients, each client has the same number of images from each class.
For the experiment testing fine-tuning performance on new classes from the same dataset, the first 80 classes for CIFAR100 are used for training, while classes 80-99 are reserved for new clients. For fine-tuning, 10 epochs of SGD are executed on the training data for the new client. For fine-tuning on CIFAR10, each new client has images from all 10 classes, and equal numbers of samples per class for training. For fine-tuning on CIFAR100, each new client has images from all 20 classes, with equal numbers of samples from each class for training when possible, and either 2 or 3 samples from each class otherwise (when the number of fine-tuning samples equals 50). Accuracies are top 1 accuracies evaluated on 2000 test samples per client for CIFAR10 and 400 test samples per client for the last 20 classes of CIFAR100.
To compute the layer-wise similarities in {Figure \ref{fig:2}}, we use the Centered Kernel Alignment (CKA) similarity metric, which is the most common metric used to measure the similarity between neural networks \cite{kornblith2019similarity}. CKA similarity between model layers is evaluated by feeding the same input through both networks and computing the similarity between the outputs of the layers. The similarity metric is invariant to rotations and isotropic scaling of the layer outputs \cite{kornblith2019similarity}. We use the code from \cite{subramanian2021torch_cka} to compute CKA similarity.
For {Figure \ref{fig:sim}}, the cosine similarity is evaluated by first feeding $n$ images from class $c$ through the trained network and storing the output of the network layer before the final linear layer to obtain the features $\{ \mathbf{f}_1^c,\dots,\mathbf{f}_n^c \}$, where each $\mathbf{f}_i^c\in\mathbb{R}^{512}$. Then, to obtain the average cosine similarity between features from classes $c$ and $c'$, we compute $\frac{1}{n}\sum_{i=1}^n\frac{|\langle \mathbf{f}_{i}^c , \mathbf{f}_{i}^{c'} \rangle |}{\|\mathbf{f}_{i}^{c} \|\|\mathbf{f}_{i}^{c'} \|}$. We use $n=25$.
All experiments were performed on two 8GB NVIDIA GeForce RTX 2070 GPUs.
\section{Finite-Sample Case}
\subsection{Concentration lemmas}
\begin{lemma} \label{lem:concen1}
Let $\mathbf{\Sigma}\coloneqq \frac{1}{b} \sum_{j=1}^b \mathbf{x}_j \mathbf{x}_j^\top$ be the empirical gram matrix formed by $b$ samples from a mean-zero, $\mathbf{I}_d$-sub-gaussian distribution.
Let $\mathbf{U}\in \mathbb{R}^{d \times d_1}$ and $\mathbf{V}\in\mathbb{R}^{d \times d_2}$ be two matrices independent of the randomness in $\mathbf{\Sigma}$.
Then for any $\gamma: 0 <\gamma< c (b - d_1 - d_2)$ and absolute constants $c,c',c''$,
\begin{align}
\|\mathbf{U}^\top \mathbf{{\Sigma}}\mathbf{V} - \mathbf{U}^\top \mathbf{V}\|_2\leq c' \|\mathbf{U}\|\|\mathbf{V}\|\frac{\sqrt{d_1+d_2} +{\gamma}}{\sqrt{b}}
\end{align}
with probability at least $1-\exp(c''\gamma^2)$.
\end{lemma}
\begin{proof}
The proof follows by sub-exponential concentration combined with an $\epsilon$-net argument as in the proof of Theorem 4.6.1. in \cite{vershynin2018high}.
First note that \begin{align}\| \mathbf{U}^\top \mathbf{{\Sigma}}\mathbf{V} - \mathbf{U}^\top \mathbf{V}\|_2 = \sup_{\mathbf{\bar{w}}_1 \in \mathcal{S}^{d_1-1},\mathbf{\bar{w}}_2 \in \mathcal{S}^{d_2-1}} \bigg| \tfrac{1}{b} \sum_{j=1}^b\mathbf{\bar{w}}_1^\top \mathbf{U}^\top \mathbf{x}_j\mathbf{x}_j^\top\mathbf{V} \mathbf{\bar{w}}_2 - \mathbf{\bar{w}}_1^\top\mathbf{U}^\top \mathbf{V} \mathbf{\bar{w}}_2 \bigg| \end{align}
Let $\mathcal{M}_1$ be an $\tfrac{\epsilon}{4}$-net over $\mathcal{S}^{d_1 - 1} \coloneqq \{ \mathbf{w}_1\in\mathbb{R}^{d_1}: \|\mathbf{w}_1\| = 1 \}$ and let $\mathcal{M}_2$ be an $\tfrac{\epsilon}{4}$-net over $\mathcal{S}^{d_2 - 1} \coloneqq \{ \mathbf{w}_2\in\mathbb{R}^{d_2}: \|\mathbf{w}_2\| = 1 \}$. By Corollary 4.2.13 in \cite{vershynin2018high}, we have that such nets exist with at most $9^{d_1}$ and $9^{d_2}$ elements, respectively.
Consider any fixed $\mathbf{w}_1\in \mathcal{M}_1$ and $\mathbf{w}_2 \in \mathcal{M}_{2}$. By the $\mathbf{I}_d$-sub-gaussianity of $\mathbf{x}_j$, the random variable
$\mathbf{w}_1^\top \mathbf{U}^\top \mathbf{x}_j\mathbf{x}_j^\top \mathbf{V} \mathbf{w}_2 - \mathbf{w}_1^\top\mathbf{U}^\top \mathbf{V} \mathbf{w}_2$ is sub-exponential with mean zero and variance proxy $c\|\mathbf{U}\|\|\mathbf{V}\|$, independently for each $j$.
Thus, by Bernstein's Inequality, for any $\gamma > 0, (\sqrt{d_1+d_2} + \gamma)^2 \leq b$ and an absolute constant $c$,
\begin{align}
\mathbb{P}\bigg( \bigg| \frac{1}{b} \sum_{j=1}^b &\mathbf{w}_1^\top \mathbf{U}^\top \mathbf{x}_j\mathbf{x}_j^\top \mathbf{V} \mathbf{w}_2 - \mathbf{w}_1^\top\mathbf{U}^\top \mathbf{V} \mathbf{w}_2 \bigg| < \|\mathbf{U}\|\|\mathbf{V}\|\tfrac{\sqrt{d_1+d_2} + \gamma}{\sqrt{b}} \bigg) \nonumber \\
&\geq 1 - 2 \exp\bigg( - cb\min \bigg( \tfrac{\sqrt{d_1+ d_2} + \gamma}{\sqrt{b}}, \bigg(\tfrac{\sqrt{d_1+ d_2} + \gamma}{\sqrt{b}}\bigg)^2 \bigg) \bigg)\nonumber \\
&\geq 1 - 2 \exp\big( - c' (d_1+d_2 + \gamma^2) \big)
\end{align}
where $\delta = \tfrac{\sqrt{d_1+ d_2} + \gamma}{\sqrt{b}}$ and the second inequality follows since $b \geq (\sqrt{d_1+d_2} + \gamma)^2$.
Union bounding over all $\mathbf{w}_1 \in \mathcal{M}_1$ and $\mathbf{w}_2 \in \mathcal{M}_2$ yields
\begin{align}
\mathbb{P}\bigg( \max_{\mathbf{w}_1 \in \mathcal{M}_1,\mathbf{w}_2 \in \mathcal{M}_2} &\bigg| \tfrac{1}{b} \sum_{j=1}^b \mathbf{w}_1^\top \mathbf{U}^\top \mathbf{x}_j\mathbf{x}_j^\top \mathbf{V} \mathbf{w}_2 - \mathbf{w}_1^\top\mathbf{U}^\top \mathbf{V} \mathbf{w}_2 \bigg| < \|\mathbf{U}\|\|\mathbf{V}\|\tfrac{\sqrt{d_1+d_2} + \gamma}{\sqrt{b}} \bigg) \nonumber \\ &\geq 1 - 2 \times 9^{d_1+d_2} \exp\big( - c' (d_1+d_2 + \gamma^2) \big)\nonumber \\
&\geq 1 - 2\exp\big( - c' \gamma^2 \big) \nonumber
\end{align}
for a sufficiently large constant $c'$.
Finally, since any $\mathbf{\bar{w}}_1 \in \mathcal{S}^{d_1-1}$ and $\mathbf{\bar{w}}_2 \in \mathcal{S}^{d_2-1}$ are each $\tfrac{\epsilon}{4}$-close in Euclidean distance to some $\mathbf{w}_1\in \mathcal{M}_1$ and $\mathbf{w}_2 \in \mathcal{M}_{2}$, respectively, we have
\begin{align}
\mathbb{P}\bigg(& \sup_{\mathbf{\bar{w}}_1 \in \mathcal{S}^{d_1-1},\mathbf{\bar{w}}_2 \in \mathcal{S}^{d_2-1}} \bigg| \tfrac{1}{b} \sum_{j=1}^b \mathbf{\bar{w}}_1^\top \mathbf{U}^\top \mathbf{x}_j\mathbf{x}_j^\top \mathbf{V} \mathbf{\bar{w}}_2 - \mathbf{\bar{w}}_1^\top\mathbf{U}^\top \mathbf{V} \mathbf{\bar{w}}_2 \bigg| \geq \|\mathbf{U}\|\|\mathbf{V}\|\tfrac{\sqrt{d_1+d_2} + \gamma}{\sqrt{b}} \bigg) \nonumber \\
&\leq 2 \mathbb{P}\bigg(\max_{\mathbf{w}_1 \in \mathcal{M}_1,\mathbf{w}_2 \in \mathcal{M}_2} \bigg| \tfrac{1}{b} \sum_{j=1}^b \mathbf{w}_1^\top \mathbf{U}^\top \mathbf{x}_j\mathbf{x}_j^\top \mathbf{V} \mathbf{w}_2 - \mathbf{w}_1^\top\mathbf{U}^\top \mathbf{V} \mathbf{w}_2 \bigg| < \|\mathbf{U}\|\|\mathbf{V}\|\tfrac{\sqrt{d_1+d_2} + \gamma}{\sqrt{b}} \bigg) \nonumber
\end{align}
thus
\begin{align}
\mathbb{P}\bigg(& \sup_{\mathbf{\bar{w}}_1 \in \mathcal{S}^{d_1-1},\mathbf{\bar{w}}_2 \in \mathcal{S}^{d_2-1}} \bigg| \tfrac{1}{b} \sum_{j=1}^b \mathbf{\bar{w}}_1^\top \mathbf{U}^\top \mathbf{x}_j\mathbf{x}_j^\top \mathbf{V} \mathbf{\bar{w}}_2 - \mathbf{\bar{w}}_1^\top\mathbf{U}^\top \mathbf{V} \mathbf{\bar{w}}_2 \bigg| \geq \|\mathbf{U}\|\|\mathbf{V}\|\tfrac{\sqrt{d_1+d_2} + \gamma}{\sqrt{b}} \bigg) \nonumber \\
&\geq 1 - 4 \exp\big( - c' \gamma^2 \big) \nonumber
\end{align}
as desired.
\end{proof}
\begin{lemma}\label{lem:concen2}
Let $\mathbf{\Sigma}\coloneqq \frac{1}{b}\sum_{j=1}^b \mathbf{x}_j \mathbf{x}_j^\top$ be the empirical gram matrix formed by $b$ samples from a mean-zero, $\mathbf{I}_d$-sub-gaussian distribution.
Let $\mathbf{U}\in \mathbb{R}^{d \times d_1}$ and $\mathbf{V}\in\mathbb{R}^{d \times d_2}$ be two matrices independent of the randomness in $\mathbf{\Sigma}$.
Then for any $\gamma: 0 <\gamma< c (Mb - d_1 - d_2)$ and absolute constants $c,c',c''$,
\begin{align}
\left\|\frac{1}{M}\sum_{i=1}^M \mathbf{U}_i^\top \mathbf{{\Sigma}}\mathbf{V}_i - \mathbf{U}_i^\top \mathbf{V}_i\right\|_2\leq c'\max_{i\in [M]}\{\|\mathbf{U}_i\|\|\mathbf{V}_i\|\}\frac{\sqrt{d_1+d_2} +{\gamma}}{\sqrt{M b}}
\end{align}
with probability at least $1-\exp(c''\gamma^2)$.
\end{lemma}
\begin{proof}
The argument is analogous to that in in Lemma \ref{lem:concen1} but with $Mb$ independent sub-exponential random variables rather than $b$, and each with maximum sub-exponential variance proxy $c \max_{i \in [M]} \|\mathbf{U}_i\|\|\mathbf{V}_i\|$.
\end{proof}
\begin{lemma}\label{lem:concen3}
Let $\mathbf{\Sigma}$ be the empirical covariance formed by $b$ samples from a mean-zero, $\mathbf{I}_d$-sub-gaussian distribution.
Let $\mathbf{U}\in \mathbb{R}^{d \times d_1}$ and $\mathbf{V}\in\mathbb{R}^{d \times d_2}$ be two matrices independent of the randomness in $\mathbf{\Sigma}$.
Then for any $\gamma: 0 <\gamma< c (Mb - d_1 - d_2)$ and absolute constants $c,c',c''$,
\begin{align}
\left\|\frac{1}{M}\sum_{i=1}^M \mathbf{U}_i^\top \mathbf{{\Sigma}}\mathbf{V}_i - \mathbf{U}_i^\top \mathbf{V}_i\right\|_2\leq c'\max_{i\in [M]}\{\|\mathbf{U}_i\|\|\mathbf{V}_i\|\}\frac{\sqrt{d_1+d_2} +{\gamma}}{\sqrt{M b}}
\end{align}
with probability at least $1-\exp(c''\gamma^2)$.
\end{lemma}
\begin{proof}
The argument is analogous to that in in Lemma \ref{lem:concen1} but with $Mb$ independent sub-exponential random variables rather than $b$, and each with maximum sub-exponential variance proxy $c \max_{i \in [M]} \|\mathbf{U}_i\|\|\mathbf{V}_i\|$.
\end{proof}
\begin{lemma}
concentration holds for all k-dim instances in the algorithm execution
\end{lemma}
\begin{proof}
take union bound, add an extra $\log(\tau \log(1\epsilon))$ factor to the batch complexity
\end{proof}
\subsection{Representation learning proofs}
Table of notations.
\begin{table}[h]
\begin{tabular}{|c|l|}
\hline
\textbf{Notation} & \textbf{Definition} \\ \hline
$\boldsymbol{\Delta}_t$ & $\mathbf{I}_k - \alpha \mathbf{B}_t^\top \mathbf{B}_t$ \\
$\boldsymbol{\bar{\Delta}}_t$ & $\mathbf{I}_d - \alpha \mathbf{B}_t \mathbf{B}_t^\top$ \\
$L_\ast$ & $\max_{t\in [T]} \sigma_{\max}^{0.5}\left(\tfrac{1}{n}\sum_{i=1}^n \mathbf{w}_{\ast,t,i}\mathbf{w}_{\ast,t,i}^\top\right)\leq L_\ast$ almost surely \\
$\mu_\ast$ & $0< \mu_\ast \leq \min_{t\in [T]} \sigma_{\min}^{0.5}\left(\tfrac{1}{n}\sum_{i=1}^n \mathbf{w}_{\ast,t,i}\mathbf{w}_{\ast,t,i}^\top\right)$ almost surely \\
$\eta_\ast$ & $\max_{t\in [T]} \left\|\tfrac{1}{n}\sum_{i=1}^n \mathbf{w}_{\ast,t,i}\right\|_2 \leq \eta_\ast \leq L_\ast$ almost surely \\
$L_{\max}$ & $\max_{t\in [T],i\in[n]}\|\mathbf{w}_{\ast,t,i}\|_2 \leq L_{\max}\leq c\sqrt{k} L_\ast$ almost surely for constant $c$ \\
$\kappa_\ast$ & $\nicefrac{L_\ast}{\mu_\ast}$ \\
$\kappa_{\ast,\max}$ & $\nicefrac{L_{\max}}{\mu_\ast}$ \\
$\boldsymbol{\delta}_{t,i,s}$ & $\coloneqq \mathbf{I}_k - \alpha\mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top $, i.e. the product error for the $s$-th local iteration for task $i$ at round $t$ \\
$\mathbf{e}_{t,i,s}$ & $\coloneqq \mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_{\ast}\mathbf{w}_{\ast,t,i} $, i.e. the product error for the $s$-th local iteration for task $i$ at round $t$ \\
$\mathbf{X}_{t,i,s}$ & $\coloneqq [\mathbf{x}_{t,i,s,j}^\top]_{j\in [b]} \in \mathbb{R}^{m \times d}$, i.e. the matrix of data vectors at update $(t,i,s)$ \\
$\mathbf{{\Sigma}}_{t,i,s}$ & $\coloneqq \tfrac{1}{b}\sum_{j=1}^{b}\mathbf{x}_{t,i,s,j}\mathbf{x}_{t,i,s,j}^\top$, i.e. the empirical covariance for the $s$-th local iteration for task $i$ at round $t$ \\
$\mathbf{z}_{t,i,s}$ & $\coloneqq [z_{t,i,s,j}]_{j\in [b]} \in \mathbb{R}^{b}$, i.e. the vector of noise values for the batch at update $(t,i,s)$ \\
\hline
\end{tabular}
\end{table}
\begin{proof}
\begin{enumerate}
\item $A_{1,t,i}(s) \coloneqq \{\|\mathbf{w}_{t,i,s'}- \alpha \mathbf{B}_{t,i,s'-1}^\top \mathbf{B}_{\ast}\mathbf{w}_{\ast,t,i}\|_2 \leq c_1'\alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2 \quad \forall s'\in \{1,\dots,s\}\}$
\item $A_{2,t,i}(s) \coloneqq \{\|\boldsymbol{\Delta}_{t,i,s'}\|_2 \leq c_2'\alpha^2 L_\ast^2 \kappa_{\max}^2(1 + \tfrac{\sqrt{k} + \sqrt{\log(M\tau)}}{\sqrt{n_i}}) \quad \forall s'\in \{1,\dots,s\} \}$
\item $A_{3,t,i}(s)\coloneqq \{ \operatorname{dist}(\mathbf{B}_{t,i,s'}, \mathbf{B}_\ast) \leq 2 \operatorname{dist}(\mathbf{B}_{t}, \mathbf{B}_\ast)\quad \forall s'\in \{1,\dots,s\}\}$
\end{enumerate}
The second set of inductions controls the global behavior, starting from $t=1$ as the base case:
\begin{enumerate}
\item $A_1(t) \coloneqq \{ \|\mathbf{w}_{t'} - \alpha(\mathbf{I}_k + \boldsymbol{\Delta}_{t'}) \mathbf{B}_{t'}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t'}\|_2 \leq \alpha^{2.5}\tau L_{\max}^3 + c \alpha^{4.5}\tau^2 L_{\max} c_{\boldsymbol{\Delta}}^2 \quad \forall t'\in \{1,\dots, t\}\}$
\item $A_2(t) \coloneqq \{ \|\boldsymbol{\Delta}_{t'} \|_2 \leq c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 \quad \forall t'\in \{1,\dots, t\}\}$
\item $A_3(t) \coloneqq \{ \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t'}\|_2 \leq (1 - 0.4 \alpha^2 \mu_\ast^2 E_0)\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t'-1} \|_2 \quad \forall t'\in \{1,\dots, t\} \}$
\item $A_4(t) \coloneqq \{ \operatorname{dist}_{t} \leq (1 - 0.4 \alpha^2 \mu_\ast^2 E_0)^{t-1} \quad \forall t'\in \{1,\dots, t\} \}$
\end{enumerate}
\end{proof}
\begin{lemma}[$A_{1,t,i}(s+1)$] \label{lem:la1s}
\begin{align}
\|\mathbf{w}_{t,i,s+1} - \alpha \mathbf{B}_{t,i,s}\mathbf{B}_\ast\mathbf{w}_{\ast,t,i} \| &\leq c' \alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2 + c \alpha^{0.5}(L_{\max}+\sigma)
\end{align}
\end{lemma}
\begin{proof}
Since $\mathbf{w}_{t,i,s+1} = \boldsymbol{\Delta}_{t,i,s-1}\mathbf{w}_{t,i,s-1} + \alpha \mathbf{B}_{t,i,s-1}\mathbf{B}_\ast\mathbf{w}_{\ast,t,i}$,
\begin{align}
\| \mathbf{w}_{t,i,s+1} - \alpha \mathbf{B}_{t,i,s}\mathbf{B}_\ast\mathbf{w}_{\ast,t,i} &=\|\boldsymbol{\Delta}_{t,i,s-1}\mathbf{w}_{t,i,s-1} \|_2 \nonumber \\
&\leq c \alpha^3 \tau L_{\max}^2 \kappa_{\max}^2 \|\mathbf{B}_{t,i,s-2}^\top\mathbf{B}_\ast \mathbf{w}_{\ast,t,i}\|_2\nonumber \\
&\leq c' \alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2
\end{align}
by $A_{1,t,i}(s)$ and $A_{2,t,i}(s)$.
\end{proof}
\begin{lemma}[$A_{2,t,i}(s+1)$]
\end{lemma}
\begin{proof}
We argue similarly as in Lemma \ref{lem:a2s}. Let $\mathbf{\hat{G}}_{t,i,s} \coloneqq \tfrac{1}{\alpha}(\mathbf{B}_{t,i,s} - \mathbf{B}_{t,i,s+1})= \mathbf{\Sigma}_{t,i,s} \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top + \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}\mathbf{w}_{t,i,s}^\top$ and
$\mathbf{N}_{t,i,s} \coloneqq \mathbf{G}_{t,i,s}-\mathbf{\hat{G}}_{t,i,s} = (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s}) \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top - \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}\mathbf{w}_{t,i,s}^\top$.
We have
\begin{align}
\boldsymbol{\Delta}_{t,i,s+1} &= \boldsymbol{\Delta}_{t,i,s} + \alpha^2 \mathbf{B}_{t,i,s}^\top \mathbf{\hat{G}}_{t,i,s} +\alpha^2 \mathbf{\hat{G}}_{t,i,s}^\top \mathbf{B}_{t,i,s} - \alpha^3 \mathbf{\hat{G}}_{t,i,s}^\top \mathbf{\hat{G}}_{t,i,s} \nonumber \\
&= \boldsymbol{\Delta}_{t,i,s} + \alpha^2 \mathbf{B}_{t,i,s}^\top \mathbf{{G}}_{t,i,s} +\alpha^2 \mathbf{{G}}_{t,i,s}^\top \mathbf{B}_{t,i,s} - \alpha^3 \mathbf{{G}}_{t,i,s}^\top \mathbf{{G}}_{t,i,s} \nonumber \\
&\quad - \alpha^2 \mathbf{{B}}_{t,i,s}^\top \mathbf{N}_{t,i,s} - \alpha^2 \mathbf{N}_{t,i,s}^\top\mathbf{{B}}_{t,i,s} - \alpha^3 \mathbf{N}_{t,i,s}^\top \mathbf{G}_{t,i,s} +\alpha^3 \mathbf{\hat{G}}_{t,i,s}^\top \mathbf{N}_{t,i,s}
\end{align}
Note that
\begin{align}
\| \mathbf{{B}}_{t,i,s}^\top \mathbf{N}_{t,i,s}\| &= \|\mathbf{{B}}_{t,i,s}^\top(\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s}) \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top - \tfrac{1}{b}\mathbf{{B}}_{t,i,s}^\top\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}\mathbf{w}_{t,i,s}^\top\|\nonumber \\
&\leq \|\mathbf{{B}}_{t,i,s}^\top(\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s}) \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top\| + \|\tfrac{1}{b}\mathbf{{B}}_{t,i,s}^\top\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}\mathbf{w}_{t,i,s}^\top\|\nonumber \\
&\leq c L_{\max}(L_{\max} +\sigma) \tfrac{\sqrt{k} + \gamma }{\sqrt{b}} \label{hp}
\end{align}
where \eqref{hp} follows with probability at least $1 - c e^{-c' \gamma^2}$ for any $\gamma: 0< \gamma < b - k -1$ by Lemma \ref{lem:concen1}.
Similarly,
\begin{align}
\|\mathbf{N}_{t,i,s}^\top \mathbf{G}_{t,i,s} \| &\leq \|((\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s}) \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top - \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}\mathbf{w}_{t,i,s}^\top)^\top \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top \| \nonumber \\
&\leq |\langle \mathbf{e}_{t,i,s}, (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s}) \mathbf{e}_{t,i,s}\rangle| \|\mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top\| + |\langle \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s} , \mathbf{e}_{t,i,s} \rangle| \|\mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top\| \nonumber \\
&\leq c \alpha L_{\max}^3(L_{\max}+\sigma)\tfrac{1 + \gamma}{\sqrt{b}} \nonumber
\end{align}
with probability at least $1- c e^{-c' \gamma^2}$. Lastly, we have
\begin{align}
\|&\mathbf{\hat{G}}_{t,i,s}^\top \mathbf{N}_{t,i,s}\| \nonumber \\
&= \|( \mathbf{\Sigma}_{t,i,s}\mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top + \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}\mathbf{w}_{t,i,s}^\top)^\top((\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s}) \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top - \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}\mathbf{w}_{t,i,s}^\top) \| \nonumber \\
&\leq |\langle \mathbf{\Sigma}_{t,i,s} \mathbf{e}_{t,i,s}, (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s}) \mathbf{e}_{t,i,s}\rangle| \|\mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top\| \nonumber \\
&\quad + | \langle \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}, (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s}) \mathbf{e}_{t,i,s}\rangle | \|\mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top\| \nonumber \\
&\quad + | \langle \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}, \mathbf{\Sigma}_{t,i,s} \mathbf{e}_{t,i,s}\rangle | \|\mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top\| \nonumber \\
&\quad + | \langle \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}, \tfrac{1}{b}\mathbf{X}_{t,i,s}^\top\mathbf{z}_{t,i,s}\rangle | \|\mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top\| \nonumber \\
&\leq \label{hhh}
\end{align}
where \eqref{hhh} follows with probability at least $ 1- c\exp ()$ by Lemma \ref{lem:concen3}.
---
Next, by Lemma \ref{lem:a2s}, we have almost surely
\begin{align}
\|\boldsymbol{\Delta}_{t,i,s} + \alpha^2 \mathbf{B}_{t,i,s}^\top \mathbf{\hat{G}}_{t,i,s} +\alpha^2 \mathbf{{G}}_{t,i,s}^\top \mathbf{B}_{t,i,s} - \alpha^3 \mathbf{{G}}_{t,i,s}^\top \mathbf{{G}}_{t,i,s}\| &\leq \|\boldsymbol{\Delta}_{t,i,s}\| + O(\alpha^4 \tau L_{\max}^4) \nonumber
\end{align}
which means that
\begin{align}
\|\boldsymbol{\Delta}_{t,i,s+1}\|_2 &\leq \|\boldsymbol{\Delta}_{t,i,s}\| + O(\alpha^4 \tau L_{\max}^4 + \alpha^2L_{\max}(L_{\max} +\sigma) \tfrac{\sqrt{k} + \gamma }{\sqrt{b}} \nonumber \\
&\quad \quad \quad \quad + \alpha^4 L_{\max}^3(L_{\max}+\sigma)\tfrac{1 + \gamma}{\sqrt{b}} ) \nonumber \\
&\quad\vdots \nonumber \\
&\leq \|\boldsymbol{\Delta}_{t}\| + O(\alpha^4 \tau^2 L_{\max}^4 + \alpha^2\tau L_{\max}(L_{\max} +\sigma) \tfrac{\sqrt{k} + \gamma }{\sqrt{b}} \nonumber \\
&\quad \quad \quad \quad + \alpha^4 \tau L_{\max}^3(L_{\max}+\sigma)\tfrac{1 + \gamma}{\sqrt{b}} ) \nonumber \\
&= \|\boldsymbol{\Delta}_{t}\| + O(\alpha^4 \tau^2 L_{\max}^4 + \alpha^2\tau L_{\max}(L_{\max} +\sigma) \tfrac{\sqrt{k} + \gamma }{\sqrt{b}} )...
\end{align}
\end{proof}
\begin{lemma}[$A_{3,t,i}(s+1)$] \label{lem:la3s}
Distance can get worse locally only by a constant factor.
\begin{align}
\operatorname{dist}(\mathbf{B}_{t,i,s}, \mathbf{B}_\ast) &\leq 2 \operatorname{dist}(\mathbf{B}_{t}, \mathbf{B}_\ast)
\end{align}
\end{lemma}
\begin{proof}
Note that
\begin{align}
\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t,i,s+1}\|_2 &= \|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{t,i,s} (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top) \|_2\nonumber \\
&\leq \|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{t,i,s} \|_2 \nonumber \\
&\quad \vdots \nonumber \\
&\leq \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t} \|_2
\end{align}
where the first inequality follows since $\|\mathbf{w}_{t,i,s}\|\leq c \sqrt{\alpha}L_{\max}$ (by $A_{1,t,i}(s)$ and $A_{2,t,i}(s)$) and $\alpha$ is sufficiently small, and the last inequality follows by recursively applying the first inequality for all local iterations leading up to $s$.
Thus
\begin{align}
\operatorname{dist}_{t,i,s} \leq \frac{\|\mathbf{B}_{t}\|_2 }{\sigma_{\min}(\mathbf{B}_{t,i,s})} \operatorname{dist}_{t} \leq \sqrt{\tfrac{1+ \alpha^2 \tau c_{\boldsymbol{\Delta}}}{1 - \alpha^2 \tau c_{\boldsymbol{\Delta}}}} \operatorname{dist}_{t} \leq 2 \operatorname{dist}_t
\end{align}
where $c_{\boldsymbol{\Delta}}\coloneqq L_{\max}^2 \kappa_{\max}^2$.
\end{proof}
\subsection{Global induction lemmas}
\begin{lemma}[$A_1(t+1)$] \label{lem:a1fs}
\begin{align}
\| \mathbf{w}_{t+1} - \alpha (\mathbf{I}_k& +\boldsymbol{\Delta}_{t+1})\mathbf{B}_{t+1}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} \|_2 \nonumber \\
&\leq c\alpha^{0.5} (L_{\max}+ \sigma) \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{Mb}} + c \alpha^{2.5}\tau L_{\max}^3\nonumber \\
&\quad + c\alpha^{2.5}\tau c_{\boldsymbol{\Delta}}(L_{\max} + \sigma ) \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{{Mb}}} + c \alpha^{4.5}\tau^2 L_{\max} c_{\boldsymbol{\Delta}}^2
\end{align}
\end{lemma}
\begin{proof} We argue similarly to Lemma \ref{lem:a1}.
Expanding $\mathbf{w}_{t+1}$ yields
\begin{align}
\mathbf{w}_{t+1} &= \frac{1}{M}\sum_{i=1}^M \mathbf{w}_{t,i,\tau} \nonumber \\
&= \frac{1}{M}\sum_{i=1}^M \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1} +\alpha \mathbf{B}_{t,i,\tau-1}^\top \mathbf{B}_\ast\mathbf{w}_{\ast,t,i} + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} \nonumber \\
&\quad \quad \quad \quad + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-1}^\top \mathbf{z}_{t,i,\tau-1}) \nonumber \\
&= \alpha \mathbf{B}_{t}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \frac{1}{M}\sum_{i=1}^M \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1} +\alpha (\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,t,i} \nonumber \\
&\quad + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-1}^\top \mathbf{z}_{t,i,\tau-1}) \nonumber
\end{align}
Next, expanding $\mathbf{w}_{t,i,\tau-1}$, we obtain
\begin{align}
\mathbf{w}_{t+1} &= \alpha \mathbf{B}_{t}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \frac{1}{M}\sum_{i=1}^M \alpha(\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,t,i} + \alpha \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-2}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,t,i} \nonumber \\
&\quad
+ \alpha \boldsymbol{\Delta}_{t,i,\tau-1} \boldsymbol{\Delta}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2} + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-1}^\top \mathbf{z}_{t,i,\tau-1}) \nonumber \\
&\quad + \alpha \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-1}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} + \alpha \boldsymbol{\Delta}_{t,i,\tau-1} \mathbf{B}_{t,i,\tau-1}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-1}^\top \mathbf{z}_{t,i,\tau-1}) \nonumber \\
&= \alpha \mathbf{B}_{t}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \alpha \boldsymbol{\Delta}_{t} \mathbf{B}_{t}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} \nonumber \\
&\quad + \frac{1}{M}\sum_{i=1}^M \alpha(\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,t,i} + \alpha^2 ( \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-2}^\top - \boldsymbol{\Delta}_{t}\mathbf{B}_{t}^\top )\mathbf{B}_\ast\mathbf{w}_{\ast,t,i} \nonumber \\
&\quad + \boldsymbol{\Delta}_{t,i,\tau-1} \boldsymbol{\Delta}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2} + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-1}^\top \mathbf{z}_{t,i,\tau-1}) \nonumber \\
&\quad + \alpha \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-1}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} + \alpha \boldsymbol{\Delta}_{t,i,\tau-1} \mathbf{B}_{t,i,\tau-1}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-1}^\top \mathbf{z}_{t,i,\tau-1}) \nonumber \\
&= \alpha \mathbf{B}_{t+1}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \alpha \boldsymbol{\Delta}_{t+1} \mathbf{B}_{t+1}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} \nonumber \\
&\quad + \alpha (\mathbf{B}_t -\mathbf{B}_{t+1})^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \alpha (\boldsymbol{\Delta}_t\mathbf{B}_t -\boldsymbol{\Delta}_{t+1}\mathbf{B}_{t+1})^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} \nonumber \\
&\quad + \frac{1}{M}\sum_{i=1}^M \alpha(\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,t,i} + \alpha^2 ( \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-2}^\top - \boldsymbol{\Delta}_{t}\mathbf{B}_{t}^\top )\mathbf{B}_\ast\mathbf{w}_{\ast,t,i} \nonumber \\
&\quad + \boldsymbol{\Delta}_{t,i,\tau-1} \boldsymbol{\Delta}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2} + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} + \alpha \mathbf{B}_{t,i,\tau-1}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-1}^\top \mathbf{z}_{t,i,\tau-1}) \nonumber \\
&\quad + \alpha \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-2}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-2})\mathbf{e}_{t,i,\tau-2} + \alpha \boldsymbol{\Delta}_{t,i,\tau-1} \mathbf{B}_{t,i,\tau-2}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-2}^\top \mathbf{z}_{t,i,\tau-2}) \label{chara11}
\end{align}
Therefore
\begin{align}
& \|\mathbf{w}_{t+1} - \alpha (\mathbf{I}_k +\boldsymbol{\Delta}_{t+1})\mathbf{B}_{t+1}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} \|_2 \nonumber \\
&\leq \alpha L_{\max} \| (\mathbf{B}_t - \mathbf{B}_{t+1})^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \| + \alpha L_{\max} \|(\boldsymbol{\Delta}_t \mathbf{B}_t - \boldsymbol{\Delta}_{t+1}\mathbf{B}_{t+1})^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t}\| \nonumber \\
&\quad + \alpha\left\|\frac{1}{M}\sum_{i=1}^M (\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,t,i} \right\| + \alpha^2\left\|\frac{1}{M}\sum_{i=1}^M (\boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-2} - \boldsymbol{\Delta}_t\mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,t,i} \right\| \nonumber \\
&\quad +\left\|\frac{1}{M}\sum_{i=1}^M \boldsymbol{\Delta}_{t,i,\tau-1} \boldsymbol{\Delta}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2} \right\| + \alpha \left\|\frac{1}{M}\sum_{i=1}^M \mathbf{B}_{t,i,\tau-1}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} \right\| \nonumber \\
&\quad + \alpha \left\|\frac{1}{M}\sum_{i=1}^M \mathbf{B}_{t,i,\tau-1}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-1}^\top \mathbf{z}_{t,i,\tau-1}) \right\| + \alpha \left\|\frac{1}{M}\sum_{i=1}^M\boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-2}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,\tau-2})\mathbf{e}_{t,i,\tau-2} \right\| \nonumber \\
&\quad + \alpha \left\|\frac{1}{M}\sum_{i=1}^M \boldsymbol{\Delta}_{t,i,\tau-1} \mathbf{B}_{t,i,\tau-2}^\top (\tfrac{1}{b} \mathbf{X}_{t,i,\tau-2}^\top \mathbf{z}_{t,i,\tau-2}) \right\| \nonumber \\
&\leq \alpha L_{\max} \| (\mathbf{B}_t - \mathbf{B}_{t+1})^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \| + \alpha L_{\max} \|(\boldsymbol{\Delta}_t \mathbf{B}_t - \boldsymbol{\Delta}_{t+1}\mathbf{B}_{t+1})^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t}\| \nonumber \\
&\quad + \alpha\left\|\frac{1}{M}\sum_{i=1}^M (\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,t,i} \right\| + \alpha^2\left\|\frac{1}{M}\sum_{i=1}^M (\boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-1} - \boldsymbol{\Delta}_t\mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,t,i} \right\| \nonumber \\
&\quad +c\alpha^{0.5} \|\boldsymbol{\Delta}\|^2 L_{\max} + c\alpha^{0.5} (L_{\max}+ \sigma) \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{Mb}} + c \alpha^{0.5} \|\boldsymbol{\Delta}_t\| (L_{\max}+\sigma)\tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{b}}\label{march}
\end{align}
where the last inequality follows with probability at least $1-$ by Lemmas \ref{lem:concen1} and \ref{lem:concen2}. To bound the rest of the norms in the RHS of \eqref{march}, we use
\begin{align}
&\left\|\frac{1}{M}\sum_{i=1}^M \mathbf{B}_{\ast}^\top( \mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})\right\|_2\nonumber \\
&\leq \sum_{s=1}^{\tau-1} \left\|\frac{1}{M}\sum_{i=1}^M \mathbf{B}_{\ast}^\top( \mathbf{B}_{t,i,s}- \mathbf{B}_{t,i,s-1})\right\|_2 \nonumber \\
&\leq \alpha\sum_{s=1}^{\tau-1} \|\mathbf{e}_{t,i,s-1}\mathbf{w}_{t,i,s-1}^\top\|_2 +\alpha \sum_{s=1}^{\tau-1} \left\|\frac{1}{M}\sum_{i=1}^M \mathbf{B}_{\ast}^\top (\mathbf{I}_k - \mathbf{\Sigma}_{t,i,s-1})\mathbf{e}_{t,i,s-1}\mathbf{w}_{t,i,s-1}^\top \right\| \nonumber \\
&\quad + \alpha \sum_{s=1}^{\tau-1} \left\|\frac{1}{M}\sum_{i=1}^M \mathbf{B}_{\ast}^\top (\tfrac{1}{b}\mathbf{X}_{t,i,s-1}^\top\mathbf{z}_{t,i,s-1})\mathbf{w}_{t,i,s-1}^\top \right\| \nonumber \\
&\leq \alpha^{1.5}\tau L_{\max}^2 + \alpha^{1.5}\tau L_{\max}(L_{\max} + \sigma ) \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{{Mb}}} \label{chara22}
\end{align}
where \eqref{chara22} follows with probability at least $1-$. Using this, we obtain
\begin{align}
\|\mathbf{B}_\ast^\top(\mathbf{B}_{t+1} - \mathbf{B}_{t})\|_2 &= \left\|\frac{1}{M}\sum_{i=1}^M\mathbf{B}_\ast^\top(\mathbf{B}_{t,i,\tau} - \mathbf{B}_{t})\right\|_2\nonumber \\
&\leq c\alpha^{1.5}\tau L_{\max}^2 + \alpha^{1.5}\tau L_{\max}(L_{\max} + \sigma ) \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{{Mb}}}, \nonumber
\end{align}
\begin{align}
& \left\|\frac{1}{M}\sum_{i=1}^M \mathbf{B}_\ast^\top( \mathbf{B}_{t,i,\tau-2}\boldsymbol{\Delta}_{t,i,\tau-1} - \mathbf{B}_{t}\boldsymbol{\Delta}_{t})\right\|_2\nonumber \\
&\leq \left\|\frac{1}{M}\sum_{i=1}^M \mathbf{B}_\ast^\top(\mathbf{B}_{t,i,\tau-2} - \mathbf{B}_{t})\right\|_2 + \alpha\left\|\frac{1}{M}\sum_{i=1}^M\mathbf{B}_\ast^\top(\mathbf{B}_{t,i,\tau-2}\mathbf{B}_{t,i,\tau-1}^\top\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t}\mathbf{B}_{t}^\top\mathbf{B}_{t})\right\|_2 \nonumber \\
&\leq \left\|\frac{1}{M}\sum_{i=1}^M \mathbf{B}_\ast^\top(\mathbf{B}_{t,i,\tau-2} - \mathbf{B}_{t})\right\|_2 + \alpha\left\|\frac{1}{M}\sum_{i=1}^M\mathbf{B}_\ast^\top(\mathbf{B}_{t,i,\tau-2} - \mathbf{B}_{t})\mathbf{B}_{t,i,\tau-1}^\top\mathbf{B}_{t,i,\tau-1}\right\|_2 \nonumber \\
&\quad + \alpha \left\| \frac{1}{M}\sum_{i=1}^M\mathbf{B}_t (\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_t)^\top \mathbf{B}_{t,i,\tau-1} \right\|_2 + \alpha \left\| \frac{1}{M}\sum_{i=1}^M\mathbf{B}_t \mathbf{B}_{t}^\top (\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_t) \right\|_2 \nonumber \\
&\leq c \alpha^{1.5}\tau L_{\max}^2 + \alpha^{1.5}\tau L_{\max}(L_{\max} + \sigma ) \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{{Mb}}}, \nonumber
\end{align}
and, similarly (using $\mathbf{B}_{t+1}= \tfrac{1}{M}\sum_{i=1}^M \mathbf{B}_{t,i,\tau}$),
\begin{align}
\|\mathbf{B}_t\boldsymbol{\Delta}_t - \mathbf{B}_{t+1}\boldsymbol{\Delta}_{t+1}\|_2 &\leq \left\|\frac{1}{M}\sum_{i=1}^M\mathbf{B}_{t,i,\tau} - \mathbf{B}_{t}\right\|_2 + \alpha\left\|\frac{1}{M}\sum_{i=1}^M(\mathbf{B}_{t,i,\tau} - \mathbf{B}_{t})\mathbf{B}_{t+1}^\top\mathbf{B}_{t}\right\|_2 \nonumber \\
&\quad + \alpha \left\| \frac{1}{M}\sum_{i=1}^M\mathbf{B}_t (\mathbf{B}_{t,i,\tau} - \mathbf{B}_t)^\top \mathbf{B}_{t+1} \right\|_2 + \alpha \left\| \frac{1}{M}\sum_{i=1}^M\mathbf{B}_t \mathbf{B}_{t}^\top (\mathbf{B}_{t,i,\tau} - \mathbf{B}_t) \right\|_2 \nonumber \\
&\leq c \alpha^{1.5}\tau L_{\max}^2 + \alpha^{1.5}\tau L_{\max}(L_{\max} + \sigma ) \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{{Mb}}}.
\end{align} with probability at least .
Also, we have
\begin{align}
\| \boldsymbol{\Delta}_{t,i,\tau-1} \boldsymbol{\Delta}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2} \|_2 &\leq c \alpha^{4.5} \tau^2 L_{\max} c_{\boldsymbol{\Delta}}^2
\end{align}
Thus, using \eqref{chara}, we have
\begin{align}
\| \mathbf{w}_{t+1} - \alpha (\mathbf{I}_k& +\boldsymbol{\Delta}_{t+1})\mathbf{B}_{t+1}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} \|_2 \nonumber \\
&\leq c\alpha^{0.5} (L_{\max}+ \sigma) \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{Mb}} + c \alpha^{2.5}\tau L_{\max}^3\nonumber \\
&\quad + c\alpha^{2.5}\tau c_{\boldsymbol{\Delta}}(L_{\max} + \sigma ) \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{{Mb}}} + c \alpha^{4.5}\tau^2 L_{\max} c_{\boldsymbol{\Delta}}^2
\end{align}
where $c_{\boldsymbol{\Delta}}\coloneqq L_{\max}^2 \kappa_{\max}^2$ (i.e. $c\alpha^2\tau L_{\max}^2 \kappa_{\max}^2$ upper bounds $\|\boldsymbol{\Delta}_t\|_2$).
\end{proof}
\input{App_Finite_A2}
\begin{lemma}[$A_3(t+1)$] \label{lem:1a3}
Suppose ... hold, then
\begin{align}
\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t+1}\|_2 &\leq (1 - E_0 ... \alpha^2 \tau)\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t}\|_2 + ...
\end{align}
\end{lemma}
\begin{proof}
Let $\mathbf{\tilde{B}}_{t+1}$ denote the update in the population case, namely
\begin{align}
\mathbf{\tilde{B}}_{t+1} = \mathbf{{B}}_{t} \left(\frac{1}{n} \sum_{i=1}^n \prod_{s=0}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top)\right) + \mathbf{{B}}_\ast \left(\frac{\alpha}{n} \sum_{i=1}^n \mathbf{w}_{\ast,i} \sum_{s=0}^{\tau-1}\mathbf{w}_{t,i,s}^\top \prod_{r=s+1}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,r}\mathbf{w}_{t,i,r}^\top) \right)
\end{align}
We have
\begin{align}
\mathbf{B}_{t+1} &= \tfrac{1}{n}\sum_{i=1}^n \mathbf{B}_{t,i,\tau} \nonumber \\
&= \tfrac{1}{n}\sum_{i=1}^n \mathbf{B}_{t,i,\tau-1}\boldsymbol{\delta}_{t,i,\tau-1} + \alpha \mathbf{B}_{\ast}\mathbf{w}_{\ast,t,i}\mathbf{w}_{t,i,\tau-1}^\top + (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} \mathbf{w}_{t,i,\tau-1}^\top\nonumber \\
&= \tfrac{1}{n}\sum_{i=1}^n \mathbf{B}_{t,i,\tau-2}\boldsymbol{\delta}_{t,i,\tau-2}\boldsymbol{\delta}_{t,i,\tau-1} + \alpha \mathbf{B}_{\ast} \mathbf{w}_{\ast,t,i} \mathbf{w}_{t,i,\tau-2}^\top \boldsymbol{\delta}_{t,i,\tau-1} + \alpha \mathbf{B}_{\ast}\mathbf{w}_{\ast,t,i}\mathbf{w}_{t,i,\tau-1}^\top \nonumber \\
&\quad + \alpha (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,\tau-2})\mathbf{e}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2}^\top \boldsymbol{\delta}_{t,i,\tau-1} + {\alpha} (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,\tau-1})\mathbf{e}_{t,i,\tau-1} \mathbf{w}_{t,i,\tau-1}^\top\nonumber \\
&= \mathbf{{B}}_{t} \left(\frac{1}{n} \sum_{i=1}^n \prod_{s=0}^{\tau-1}\boldsymbol{\delta}_{t,i,s}\right) + \mathbf{{B}}_\ast \left(\frac{\alpha}{n} \sum_{i=1}^n \mathbf{w}_{\ast,i} \sum_{s=0}^{\tau-1}\mathbf{w}_{t,i,s}^\top \prod_{r=s+1}^{\tau-1}\boldsymbol{\delta}_{t,i,r} \right) \nonumber \\
&\quad + \frac{\alpha}{n} \sum_{i=1}^n \sum_{s=1}^\tau (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})\mathbf{e}_{t,i,s} \mathbf{w}_{t,i,s}^\top \prod_{r=s}^\tau \boldsymbol{\delta}_{t,i,r} \nonumber \\
&= \mathbf{\tilde{B}}_{t+1} + \frac{\alpha}{n} \sum_{i=1}^n \sum_{s=1}^\tau (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})\mathbf{e}_{t,i,s} \mathbf{w}_{t,i,s}^\top \prod_{r=s}^\tau \boldsymbol{\delta}_{t,i,r}
\end{align}
therefore
\begin{align}
\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t+1}\|_2 &\leq \|\mathbf{B}_{\ast,\perp}^\top \mathbf{\tilde{B}}_{t+1}\|_2 + \alpha\left\| \frac{1}{n} \sum_{i=1}^n \mathbf{B}_{\ast,\perp}^\top \sum_{s=1}^\tau (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})\mathbf{e}_{t,i,s} \mathbf{w}_{t,i,s}^\top \prod_{r=s}^\tau \boldsymbol{\delta}_{t,i,r} \right\|_2
\end{align}
The error term due to the noise can be controlled as
\begin{align}
\alpha\left\| \frac{1}{n} \sum_{i=1}^n \mathbf{B}_{\ast,\perp}^\top \sum_{s=1}^\tau (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})\mathbf{e}_{t,i,s} \mathbf{w}_{t,i,s}^\top \prod_{r=s}^\tau \boldsymbol{\delta}_{t,i,r} \right\|_2
&\leq \alpha\left\| \frac{1}{n} \sum_{i=1}^n \sum_{s=1}^\tau (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})\mathbf{e}_{t,i,s} \mathbf{w}_{t,i,s}^\top \prod_{r=s}^\tau \boldsymbol{\delta}_{t,i,r} \right\|_2 \nonumber
\end{align}
By standard sub-gaussian concentration results, we have that as long as $N= \Omega(d)$. with probability at least $1 - \exp(cd)$.
\begin{align}
\alpha \left\| \frac{1}{n} \sum_{i=1}^n \sum_{s=1}^\tau (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})\mathbf{e}_{t,i,s} \mathbf{w}_{t,i,s}^\top \prod_{r=s}^\tau \boldsymbol{\delta}_{t,i,r} \right\|_2 &\leq c' \alpha \tau \frac{\sqrt{d}}{\sqrt{N}} \max_{i\in [n], s\in [\tau]} \|\mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top\|_2 \leq c'' \alpha^{1.5}\tau \frac{\sqrt{d}}{\sqrt{N}} L_{\max}^2 \nonumber
\end{align}
for absolute constants $c,c',c''$.
Next, we have
\begin{align}
\|\mathbf{B}_{\ast,\perp}^\top \mathbf{\tilde{B}}_{t+1}\|_2 &= \left\|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_t \tfrac{1}{M} \sum_{i=1}^M \prod_{s=0}^\tau (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top)\right\|_2 \nonumber \\
&\leq \left\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_t \right\|_2 \left\|\mathbf{I}_k -\alpha \mathbf{w}_t\mathbf{w}_t^\top\right\| \left\| \tfrac{1}{M} \sum_{i=1}^M \prod_{s=1}^\tau (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top)\right\|_2 \nonumber
\end{align}
We can expand the right product of $\mathbf{B}_t (\mathbf{I} - \alpha \mathbf{w}_t \mathbf{w}_t^\top)$ using the binomial expansion as follows:
\begin{align}
\frac{1}{n} \sum_{i=1}^n \prod_{s=1}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top) &= \mathbf{I}_k - \frac{\alpha}{n} \sum_{i=1}^n \sum_{s = 1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top + \frac{\alpha^2}{n} \sum_{i=1}^n \sum_{s=1}^{\tau-2} \sum_{s^{(1)}=s+1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top\mathbf{w}_{t,i,s^{(1)}}\mathbf{w}_{t,i,s^{(1)}}^\top \nonumber \\
&\quad - \dots + \operatorname{sign}(\tau)\frac{\alpha^{\tau}}{n} \sum_{i=1}^n \prod_{s=1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \nonumber
\end{align}
Recall that each $\|\mathbf{w}_{t,i,s}\|_2 = \mathcal{O}(\sqrt{\alpha}L_{\max})$. Thus, after the identity, the spectral norm of the first set of summations scales as $\mathcal{O}(\alpha^2 \tau L_{\max}^2 )$, the second set scales as $\mathcal{O}(\alpha^4 \tau^2 L_{\max}^4)$, and so on.
We in fact use the first set of summations as a negative term, and bound all subsequent sets of summations as errors, exploiting the fact that their norms are geometrically decaying. In particular, we have:
\begin{align}
\left\|\frac{1}{n} \sum_{i=1}^n \prod_{s=1}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top) \right\|_2 &\leq \left\| \mathbf{I}_k - \frac{\alpha}{n} \sum_{i=1}^n \sum_{s = 1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \right\|_2 + \sum_{z=2}^{\tau-1}(\alpha^2 \tau L_{\max}^2)^z \nonumber \\
&\leq \left\| \mathbf{I}_k - \frac{\alpha}{n} \sum_{i=1}^n \sum_{s = 1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \right\|_2 + \frac{\alpha^4 \tau^2 L_{\max}^4}{1 - \alpha^2 \tau L_{\max}^2} \label{sslast}
\end{align}
Next, we use $\mathbf{w}_{t,i,s} = \alpha \mathbf{B}_{t,i,s-1}^\top \mathbf{B}_\ast \mathbf{w}_{\ast,t,i} + \boldsymbol{\Delta}_{t,i,s-1}\mathbf{w}_{t,i,s-1}$ for all $s\geq 1$, where $\|\boldsymbol{\Delta}_{t,i,s-1}\mathbf{w}_{t,i,s-1}\|_2 \leq c\sqrt{\alpha} \|\boldsymbol{\Delta}_{t}\|_2 L_{\max}\leq c \alpha^{2.5} \tau L_{\max} c_{\boldsymbol{\Delta}}$ to obtain
\begin{align}
\left\| \mathbf{I}_k - \frac{\alpha}{n} \sum_{i=1}^n \sum_{s = 1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \right\|_2 &\leq \left\| \mathbf{I}_k - \frac{\alpha^3}{n} \sum_{i=1}^n \sum_{s = 1}^{\tau-1} \mathbf{B}_{t,i,s-1}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,t,i}\mathbf{w}_{\ast,t,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t,i,s-1} \right\|_2 \nonumber \\
&\quad + \alpha^2\tau^2 L_{\max}^2 \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{N}} + 3 c \alpha^4 \tau^2 L_{\max}^2 c_{\boldsymbol{\Delta}}\label{slast}
\end{align}
Next, we have for any $s-1 \in \{1,\dots,\tau-1\}$,
\begin{align}
\| \mathbf{B}_{t,i,s-1} - \mathbf{B}_t \|_2 = \| \mathbf{B}_{t,i,s-1} - \mathbf{B}_{t,i,0} \|_2 &\leq \sum_{r = 1}^{s-1} \| \mathbf{B}_{t,i,r} - \mathbf{B}_{t,i,r-1} \|_2 \nonumber \\
&\leq \alpha \sum_{r = 1}^{s-1} \|\mathbf{e}_{t,i,r-1}\|_2 \|\mathbf{w}_{t,i,r-1}\|_2 \nonumber \\
&\leq c'\alpha^{1.5} (\tau-1) L_{\max}^2 \nonumber
\end{align}
Thus we have
\begin{align}
\bigg\| \mathbf{I}_k - \frac{\alpha^3}{n} \sum_{i=1}^n &\sum_{s = 1}^{\tau-1} \mathbf{B}_{t,i,s-1}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,t,i}\mathbf{w}_{\ast,t,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t,i,s-1} \bigg\|_2 \nonumber \\
&\leq \left\| \mathbf{I}_k - \frac{\alpha^3}{n} \sum_{i=1}^n \sum_{s = 1}^{\tau-1} \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,t,i}\mathbf{w}_{\ast,t,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t} \right\|_2 \nonumber \\
&\quad + \left\|\frac{\alpha^3}{n} \sum_{i=1}^n \sum_{s = 1}^{\tau-1} (\mathbf{B}_{t} - \mathbf{B}_{t,i,s-1} )^\top\mathbf{B}_\ast\mathbf{w}_{\ast,t,i}\mathbf{w}_{\ast,t,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t,i,s-1} \right\|_2 \nonumber \\
&\quad + \left\|\frac{\alpha^3}{n} \sum_{i=1}^n \sum_{s = 1}^{\tau-1} \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,t,i}\mathbf{w}_{\ast,t,i}^\top\mathbf{B}_\ast^\top(\mathbf{B}_t - \mathbf{B}_{t,i,s-1}) \right\|_2 \nonumber\\
&\leq \left\| \mathbf{I}_k - \frac{\alpha^3}{n} \sum_{i=1}^n \sum_{s = 1}^{\tau-1} \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,t,i}\mathbf{w}_{\ast,t,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t} \right\|_2 + 2c \alpha^4 \tau^2 L_{\max}^4 \nonumber \\
&\leq 1 - \alpha^2 (\tau-1) E_0 \mu_\ast^2 + 2c \alpha^4 (\tau -1)^2 L_{\max}^4 \label{last}
\end{align}
\end{proof}
\begin{lemma}[$A_4(t+1)$] \label{lem:la4}
Distance is converging at rate
\end{lemma}
\begin{proof}
fresh samples every time:
\begin{align}
\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t+1}\|_2 &\leq ( 1 - \alpha^2 \tau) \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t}\|_2 + \alpha^{1.5} \frac{\sqrt{d\tau}}{\sqrt{N}} \nonumber \\
&\leq (1 - \alpha^2 \tau)^{t} \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{0}\|_2 + \alpha^{1.5} \frac{\sqrt{d\tau}}{\sqrt{N}} \sum_{s = 1}^t (1 - \alpha^2 \tau)^s
\end{align}
\begin{align}
\operatorname{dist}_{t+1} &\leq c (1 - \alpha^2 \tau) \operatorname{dist}_0 + \frac{\alpha^2 \sqrt{d \tau}}{(1-\|\boldsymbol{\Delta}\|_2)\alpha^2 \tau \sqrt{N}} \leq c (1 - \alpha^2 \tau) \operatorname{dist}_0 + \frac{ \sqrt{d}}{(1-\|\boldsymbol{\Delta}\|_2) \sqrt{N\tau}}
\end{align}
\begin{align}
\end{align}
\end{proof}
\begin{lemma}
\end{lemma}
\begin{proof}
\end{proof}
-------
\begin{align}\nabla_{\mathbf{B}} \hat{f}_{t,i,s}(\mathbf{B}_{t,i,s}, \mathbf{w}_{t,i,s}; \mathbf{X}_{t,i,s}) &= \mathbf{{\Sigma}}_{t,i,s} (\mathbf{B}_{t,i,s} \mathbf{w}_{t,i,s} - \mathbf{B}_{\ast} \mathbf{w}_{\ast,t,i}) \mathbf{w}_{t,i,s}^\top \nonumber \\
&= (\mathbf{B}_{t,i,s} \mathbf{w}_{t,i,s}
- \mathbf{B}_{\ast} \mathbf{w}_{\ast,t,i}) \mathbf{w}_{t,i,s}^\top - (\mathbf{I}_d-\mathbf{{\Sigma}}_{t,i,s})( \mathbf{B}_{t,i,s} \mathbf{w}_{t,i,s}
- \mathbf{B}_{\ast} \mathbf{w}_{\ast,t,i} )\mathbf{w}_{t,i,s}^\top \nonumber \\
\nabla_{\mathbf{w}}\hat{f}_{t,i,s}(\mathbf{B}_{t,i,s}, \mathbf{w}_{t,i,s}; \mathbf{X}_{t,i,s}) &= \mathbf{B}_{t,i,s}^\top\mathbf{{\Sigma}}_{t,i,s} (\mathbf{B}_{t,i,s} \mathbf{w}_{t,i,s} - \mathbf{B}_{\ast} \mathbf{w}_{\ast,t,i}) \nonumber \\
&= \mathbf{B}_{t,i,s}^\top (\mathbf{B}_{t,i,s} \mathbf{w}_{t,i,s}
- \mathbf{B}_{\ast} \mathbf{w}_{\ast,t,i})- \mathbf{B}_{t,i,s}^\top (\mathbf{I}_d-\mathbf{{\Sigma}}_{t,i,s})( \mathbf{B}_{t,i,s} \mathbf{w}_{t,i,s}
- \mathbf{B}_{\ast} \mathbf{w}_{\ast,t,i} )\nonumber \\
\mathbf{e}_{t,i,s}
\end{align}
\begin{align}
\mathbf{B}_{t+1} &= \tfrac{1}{n}\sum_{i=1}^n \mathbf{B}_{t,i,\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1}^\top) + \alpha \mathbf{B}_{\ast}\mathbf{w}_{\ast,t,i}\mathbf{w}_{t,i,\tau-1}^\top \nonumber \\
&\quad + \tfrac{1}{n}\sum_{i=1}^n (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,\tau-1})(\mathbf{B}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1} - \mathbf{B}_{\ast}\mathbf{w}_{\ast,t,i}) \mathbf{w}_{t,i,\tau-1}^\top\nonumber \\
&= \tfrac{1}{n}\sum_{i=1}^n \mathbf{B}_{t,i,\tau-2}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,\tau-2}\mathbf{w}_{t,i,\tau-2}^\top)(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1}^\top) \nonumber \\
&\quad + \alpha \mathbf{B}_{\ast} \mathbf{w}_{\ast,t,i} \mathbf{w}_{t,i,\tau-2}^\top (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1}^\top) + \alpha \mathbf{B}_{\ast}\mathbf{w}_{\ast,t,i}\mathbf{w}_{t,i,\tau-1}^\top \nonumber \\
&\quad + \tfrac{\alpha}{n}\sum_{i=1}^n (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,\tau-2})(\mathbf{B}_{t,i,\tau-2}\mathbf{w}_{t,i,\tau-2} - \mathbf{B}_{\ast}\mathbf{w}_{\ast,t,i}) \mathbf{w}_{t,i,\tau-2}^\top (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1}^\top)\nonumber\\
&\quad + \tfrac{\alpha}{n}\sum_{i=1}^n (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,\tau-1})(\mathbf{B}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1} - \mathbf{B}_{\ast}\mathbf{w}_{\ast,t,i}) \mathbf{w}_{t,i,\tau-1}^\top\nonumber
\end{align}
Error terms will accumulate as:
\begin{align}
\left\| \sum_{s=1}^\tau \tfrac{\alpha}{n} \sum_{i=1}^n (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})\mathbf{e}_{t,i,s} \mathbf{w}_{t,i,s}^\top \prod_{r=s}^\tau (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,r}\mathbf{w}_{t,i,r}^\top) \right\|_2 &\leq \tau \alpha^{1.5} \tfrac{\sqrt{d}}{\sqrt{nm}}
\end{align}
which is fine.
Local updates:
\begin{align}
\mathbf{B}_{t,i,s+1} &= \mathbf{B}_{t,i,s} - \alpha \mathbf{\hat{G}}_{t,i,s} \nonumber \\
\mathbf{\hat{G}}_{t,i,s} &= (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\mathbf{w}_{t,i,s}^\top - (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\mathbf{w}_{t,i,s}^\top \nonumber \\
\boldsymbol{\Delta}_{t,i,s+1} &= \boldsymbol{\Delta}_{t,i,s} + \alpha^2 \mathbf{B}_{t,i,s}^\top \mathbf{\hat{G}}_{t,i,s} + \alpha^2 \mathbf{\hat{G}}_{t,i,s}^\top \mathbf{B}_{t,i,s} - \alpha^3 \mathbf{\hat{G}}_{t,i,s}^\top \mathbf{\hat{G}}_{t,i,s} \nonumber \\
&= \boldsymbol{\Delta}_{t,i,s} + \alpha^2 \mathbf{B}_{t,i,s}^\top (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\mathbf{w}_{t,i,s}^\top + \alpha^2 \mathbf{w}_{t,i,s}(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})^\top \mathbf{B}_{t,i,s} \nonumber \\
&\quad - \alpha^3 \|\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i}\|_2^2 \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \nonumber \\
&\quad - \alpha^2 \mathbf{B}_{t,i,s}^\top (\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\mathbf{w}_{t,i,s}^\top \nonumber \\
&\quad - \alpha^2 \mathbf{w}_{t,i,s}\left((\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\right)^\top \mathbf{B}_{t,i,s} \nonumber \\
&\quad + \alpha^2\mathbf{w}_{t,i,s}\left((\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\right)^\top\left((\mathbf{I}_d - \mathbf{\Sigma}_{t,i,s})(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\right) \mathbf{w}_{t,i,s}^\top \nonumber \\
\| \boldsymbol{\Delta}_{t,i,s+1}\|_2 &\leq \| \boldsymbol{\Delta}_{t,i,s}\|_2 + \alpha^4 \|\mathbf{e}_{t,i,s}\|_2^2 L_{\max}^2 + \alpha^2 \tfrac{\sqrt{k}+\sqrt{\log(n)}}{\sqrt{m}}\|\mathbf{e}_{t,i,s}\|_2 \nonumber \\
\|\mathbf{e}_{t,i,s+1}\|_2 &\leq (1 - \alpha^2 \|\mathbf{\Sigma}_{t,i,s}\|_2 \|\mathbf{w}_{\ast,t,i}\|_2^2)\|\mathbf{e}_{t,i,s}\|_2 \nonumber \\
\mathbf{w}_{t,i,s+1} &= \boldsymbol{\Delta}_{t,i,s}\mathbf{w}_{t,i,s} +\alpha \mathbf{B}_{t,i,s}^\top \mathbf{B}_\ast \mathbf{w}_{\ast,t,i} +
\end{align}
Need $\alpha^2 (1+ \tfrac{\sqrt{d}}{\sqrt{m}})\|\mathbf{w}_{\ast,t,i}\|_2^2$
Need $\alpha = O(1/\sqrt{d})$. There is no getting around this.
But we can choose $\tau = d$. But then we need to invoke concentration lemma d times. This is fine because it fails with exp small probability. Succeeds with prob $1 - e^{-n_i}$. Now, $1 - de^{-n_i}$ --> need $n_i = \Theta(\log(d))$. How many times do we need to invoke in total?
$ (1 - alpha2 \tau)^T \leq \epsilon$ --> $\poly(\kappa)\log(1/\epsilon)$ iters. Thus we need to invoke $$d\poly(\kappa)\log(1/\epsilon)$$ times.
\subsection{Proof of Proposition \ref{cor:1}}
\begin{proof}
Let $\mathbf{e}_{M+1,s} := \mathbf{B}_{T,M+1,s}\mathbf{w}_{T,M+1,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,M+1}$ be the error for Client $M+1$ after fine-tuning the model trained by FedAvg for $T$ rounds.
For any $s$, note that $\mathbf{e}_{T,M+1,s}\coloneqq \mathbf{B}_{T,M+1,s}\mathbf{w}_{T,M+1,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,M+1}$ can be written as:
\begin{align}
\mathbf{e}_{T,M+1,s+1} = \mathbf{\hat{B}}_T \mathbf{\hat{B}}_T^\top \mathbf{e}_{T,M+1,s+1} + (\mathbf{I}_k - \mathbf{\hat{B}}_T \mathbf{\hat{B}}_T^\top) \mathbf{e}_{T,M+1,s+1}
\end{align}
where
\begin{align}
(\mathbf{I}_k - \mathbf{\hat{B}}_T \mathbf{\hat{B}}_T^\top) \mathbf{e}_{T,M+1,s} &= (\mathbf{I}_k - \mathbf{\hat{B}}_T \mathbf{\hat{B}}_T^\top) \mathbf{B}_{\ast} \mathbf{w}_{\ast,M+1} \leq \operatorname{dist}_T \|\mathbf{w}_{\ast,M+1}\|_2.
\end{align}
by the Cauchy-Schwarz Inequality and the fact that $\|(\mathbf{I}_k - \mathbf{\hat{B}}_T \mathbf{\hat{B}}_T^\top) \mathbf{B}_{\ast}\|_2 = \operatorname{dist}_T$. On the other hand,
\begin{align}
&\mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top \mathbf{e}_{M+1,s+1} \nonumber \\
&= \mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top \big(\mathbf{I}_d - \alpha \mathbf{{B}}_{T,M+1,s} \mathbf{B}_{T,M+1,s}^\top\mathbf{\Sigma}_{T,M+1,s} + \alpha^2 \langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top\mathbf{\Sigma}_{T,M+1,s}\mathbf{e}_{T,M+1,s}\rangle \mathbf{\Sigma}_{T,M+1,s} \nonumber \\
&\quad - \alpha \| \mathbf{{w}}_{T,M+1,s}\|_2^2 \mathbf{\Sigma}_{T,M+1,s} \big) \mathbf{e}_{T,M+1,s}
- \alpha \mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top\mathbf{B}_{t,M+1,s+1}\mathbf{B}_{T,M+1,s}^\top \tfrac{1}{b}\mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s}\nonumber \\
&\quad - \alpha \mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top \tfrac{1}{b}\mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s}\langle\mathbf{w}_{T,M+1,s},\mathbf{w}_{t,i,s+1}\rangle \nonumber \\
&= \mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top \big(\mathbf{I}_d - \alpha \mathbf{{B}}_{T,M+1,s} \mathbf{B}_{T,M+1,s}^\top + \alpha^2 \langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top\mathbf{e}_{T,M+1,s}\rangle \mathbf{I}_d - \alpha \| \mathbf{{w}}_{T,M+1,s}\|_2^2 \mathbf{I}_{d} \big)\mathbf{e}_{T,M+1,s} \nonumber \\
&\quad + \alpha \mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top\mathbf{{B}}_{T,M+1,s} \mathbf{B}_{T,M+1,s}^\top (\mathbf{\Sigma}_{T,M+1,s}- \mathbf{I}_d)\mathbf{e}_{T,M+1,s} \nonumber \\
&\quad - \mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top( \alpha^2 \langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top\mathbf{e}_{T,M+1,s}\rangle \mathbf{I}_{d} \nonumber \\
&\quad - \alpha^2 \langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top\mathbf{\Sigma}_{T,M+1,s}\mathbf{e}_{T,M+1,s}\rangle \mathbf{\Sigma}_{T,M+1,s} )\mathbf{e}_{T,M+1,s} \nonumber \\
&\quad + \alpha \| \mathbf{{w}}_{T,M+1,s}\|_2^2 \mathbf{\hat{B}}_{T} \mathbf{\hat{B}}_{T}^\top(\mathbf{I}_d - \mathbf{\Sigma}_{T,M+1,s} ) \mathbf{e}_{T,M+1,s} \nonumber \\
&\quad - \alpha \mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top\mathbf{B}_{t,M+1,s+1}\mathbf{B}_{T,M+1,s}^\top \tfrac{1}{b}\mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s} - \alpha \mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top \tfrac{1}{b}\mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s}\langle\mathbf{w}_{T,M+1,s},\mathbf{w}_{t,i,s+1}\rangle
\end{align} The terms in the first two lines of the last equation are equivalent to the update in the population case. Define $\mathbf{P}_{\mathbf{B}_{T,M+1,s}} \coloneqq \mathbf{I}_d - \mathbf{\hat{B}}_{T,M+1,s}\mathbf{\hat{B}}_{T,M+1,s}^\top$
These terms can be bounded as
\begin{align}
&\|\mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top \big(\mathbf{I}_d - \alpha \mathbf{{B}}_{T,M+1,s} \mathbf{B}_{T,M+1,s}^\top + \alpha^2 \langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top\mathbf{e}_{T,M+1,s}\rangle \mathbf{I}_d - \alpha \| \mathbf{{w}}_{T,M+1,s}\|_2^2 \mathbf{I}_{d} \big)\mathbf{e}_{T,M+1,s}\|_2 \nonumber \\
&= \|\mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top \big(\mathbf{P}_{\mathbf{B}_{T,M+1,s}} + \mathbf{\hat{B}}_{T,M+1,s} \mathbf{\hat{B}}_{T,M+1,s}^\top - \alpha \mathbf{{B}}_{T,M+1,s} \mathbf{B}_{T,M+1,s}^\top + \alpha^2 \langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top\mathbf{e}_{T,M+1,s}\rangle \mathbf{I}_d \nonumber \\
&\quad - \alpha \| \mathbf{{w}}_{T,M+1,s}\|_2^2 \mathbf{I}_{d} \big)\mathbf{e}_{T,M+1,s}\|_2 \nonumber \\
&\leq \|\mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top\mathbf{P}_{\mathbf{B}_{T,M+1,s}}
\mathbf{B}_\ast \mathbf{w}_{\ast,i} \|_2 + ( \|\boldsymbol{\Delta}_{T,M+1,s}\|_2 + c \alpha^2 L^2 )\|\mathbf{e}_{T,M+1,s}\|_2 \nonumber \\
&\leq \min(1, \alpha^2 \tau' L_l^2 ) L_l \operatorname{dist}_T + \|\boldsymbol{\Delta}\| \|\mathbf{e}_{T,M+1,s}\|_2
\end{align}
Now we consider the finite-sample error terms. We have
\begin{align}
\|\alpha \mathbf{\hat{B}}_{T}&\mathbf{\hat{B}}_{T}^\top\mathbf{{B}}_{T,M+1,s} \mathbf{B}_{T,M+1,s}^\top (\mathbf{\Sigma}_{T,M+1,s}- \mathbf{I}_d)\mathbf{e}_{T,M+1,s} \|_2
\leq c \tfrac{\sqrt{k}+\sqrt{\log()}}{\sqrt{b}} \|\mathbf{e}_{T,M+1,s} \|_2, \nonumber
\end{align}
and
\begin{align}
&\alpha^2 \|\mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top( \langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top\mathbf{e}_{T,M+1,s}\rangle \mathbf{I}_{d} - \langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top\mathbf{\Sigma}_{T,M+1,s}\mathbf{e}_{T,M+1,s}\rangle \mathbf{\Sigma}_{T,M+1,s} )\mathbf{e}_{T,M+1,s} \| \nonumber \\
&\leq \alpha^2 |\langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top\mathbf{e}_{T,M+1,s}\rangle| \|\mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top( \mathbf{I}_{d} - \mathbf{\Sigma}_{T,M+1,s})\mathbf{e}_{T,M+1,s} \|_2 \nonumber \\
&\quad + \alpha^2 |\langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top(\mathbf{I}_k - \mathbf{\Sigma}_{T,M+1,s})\mathbf{e}_{T,M+1,s}\rangle|\|\mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top \mathbf{\Sigma}_{T,M+1,s}\mathbf{e}_{T,M+1,s} \|_2\nonumber \\
&\leq c\alpha^2 L^2 \tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} \|\mathbf{e}_{T,M+1,s}\|_2,
\end{align}
and
\begin{align}
\alpha \| \mathbf{{w}}_{T,M+1,s}\|_2^2 \|\mathbf{\hat{B}}_{T} \mathbf{\hat{B}}_{T}^\top(\mathbf{I}_d - \mathbf{\Sigma}_{T,M+1,s} ) \mathbf{e}_{T,M+1,s}\|_2 &\leq c\alpha^2 L^2 \tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} \|\mathbf{e}_{T,M+1,s}\|_2
\end{align}
all with high probability. Further,
note that the noise terms can be written as
\begin{align}
&\tfrac{\alpha}{b} \mathbf{B}_{t,i,s+1}\mathbf{B}_{T,M+1,s}^\top \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s} \nonumber \\
&= \tfrac{\alpha}{b} \mathbf{B}_{T,M+1,s}\mathbf{B}_{T,M+1,s}^\top \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s} - \tfrac{\alpha^2}{b}(\mathbf{w}_{T,M+1,s}^\top \mathbf{B}_{T,M+1,s}^\top \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s}) \mathbf{e}_{T,M+1,s} \nonumber \\
&\quad - \tfrac{\alpha^2}{b} (\mathbf{w}_{T,M+1,s}^\top \mathbf{B}_{T,M+1,s}^\top \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s}) (\mathbf{I}_d - \mathbf{\Sigma}_{T,M+1,s})\mathbf{e}_{T,M+1,s} \nonumber \\
&\quad + \tfrac{\alpha^2}{b^2} (\mathbf{w}_{T,M+1,s}^\top \mathbf{B}_{T,M+1,s}^\top \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s}) \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s} \nonumber
\end{align}
and
\begin{align}
& \tfrac{\alpha}{b} \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s}\langle\mathbf{w}_{T,M+1,s},\mathbf{w}_{t,i,s+1}\rangle \nonumber \\
&= \tfrac{\alpha}{b} \|\mathbf{w}_{T,M+1,s}\|_2^2 \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s} - \tfrac{\alpha^2}{b} \langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{T,M+1,s}^\top \mathbf{\Sigma}_{T,M+1,s} \mathbf{e}_{T,M+1,s}\rangle \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s} \nonumber \\
&\quad \quad - \tfrac{\alpha^2}{b^2}\langle \mathbf{w}_{T,M+1,s}, \mathbf{B}_{t,M+1,s}^\top \mathbf{X}_{T,M+1,s}^\top \mathbf{z}_{t,M+T,s}\rangle\mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s} \nonumber
\end{align}
thus, if $b \geq k+\log$,
\begin{align}
\| \tfrac{\alpha}{b} \mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top&\mathbf{B}_{t,i,s+1}\mathbf{B}_{T,M+1,s}^\top \mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s}\| \nonumber \\
&\leq c \tfrac{\sigma(\sqrt{k}+\sqrt{\log})}{\sqrt{b}} + c \alpha^2 \tfrac{L\sigma(\sqrt{k}+\sqrt{\log})}{\sqrt{b}} \|\mathbf{e}_{T,M+1,s}\|_2 + c \alpha^2 \tfrac{L\sigma^2({k}+{\log})}{{b}} \nonumber \\
\|\tfrac{\alpha}{b}\mathbf{\hat{B}}_{T}\mathbf{\hat{B}}_{T}^\top&\mathbf{X}_{T,M+1,s}^\top\mathbf{z}_{T,M+1,s}\langle\mathbf{w}_{T,M+1,s},\mathbf{w}_{t,i,s+1}\rangle \| \nonumber \\
&\leq c \alpha^2 \tfrac{L^2\sigma(\sqrt{k}+\sqrt{\log})}{\sqrt{b}} + c \alpha^2 \tfrac{(L+\sigma)\sigma({k}+ {\log})}{{b}} \|\mathbf{e}_{T,M+1,s}\|_2. \nonumber
\end{align}
with high probability.
Putting these together and using $\alpha^2 (L+\sigma)^2 \leq 1$, we have that all of the stochastic terms can be bounded by
\begin{align}
c\tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} (\sigma+ \|\mathbf{e}_{T,M+1,s}\|_2), \nonumber
\end{align}
Combining all terms in the projection onto the column space of $\mathbf{B}_T$, we obtain
\begin{align}
\|\mathbf{\hat{B}}_T \mathbf{\hat{B}}_T^\top \mathbf{e}_{T,M+1,s+1}\| &\leq \min(1, \alpha^2 \tau' L_l^2 ) L_l \operatorname{dist}_T + c \alpha^2 L^2 \kappa^2 \|\mathbf{e}_{T,M+1,s}\|_2 +c\tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} (\sigma+ \|\mathbf{e}_{T,M+1,s}\|_2) \nonumber \\
&\leq +c\tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} \|\mathbf{e}_{T,M+1,s}\|_2 + \min(1, \alpha^2 \tau' L_l^2 ) L_l \operatorname{dist}_T + c \sigma \tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} \nonumber
\end{align}
for an absolute constant $c$. Recursively applying this inequality yields
\begin{align}
\|\mathbf{\hat{B}}_T \mathbf{\hat{B}}_T^\top \mathbf{e}_{T,M+1,s+1}\| &\leq \big(\tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} \big)^s \|\mathbf{\hat{B}}_T \mathbf{\hat{B}}_T^\top \mathbf{e}_{T,M+1,s}\| + \sum_{r = 1}^s \big(\tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} \big)^{s-r} (\operatorname{dist}_T + \sigma \tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} ) \nonumber \\
&\leq \big(\tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} \big)^s c L + c\tfrac{\sqrt{b}}{\sqrt{b} - \sqrt{k} - \sqrt{\log()}}(\operatorname{dist}_T + \sigma \tfrac{\sqrt{k}+\sqrt{\log}}{\sqrt{b}} ) \nonumber
\end{align}
{
Need to show:
\begin{align}
\|(\mathbf{B}_T-\mathbf{B}_{T,M+1,s})^\top(\mathbf{I}_k - \mathbf{\hat{B}}_{T,M+1,s} \mathbf{\hat{B}}_{T,M+1,s}^\top)\mathbf{B}_\ast \| &\leq \alpha^{1.5} s \operatorname{dist}_T
\end{align}
major issue: only projected distance stays small locally. so we do not know for sure if the above expression is proportional to the distance...
... we can get an $\alpha^4 \tau^2$ term for the population terms in the finite-sample case. But this is not good enough.
\begin{align}
&\|\mathbf{B}_t^\top (\mathbf{I}_d - \alpha \mathbf{B}_{t,i,s} \mathbf{B}_{t,i,s}^\top)(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\| \nonumber \\
&\leq \|\mathbf{B}_t^\top (\mathbf{I}_d - \alpha \mathbf{B}_{t} \mathbf{B}_{t}^\top)(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\| \nonumber \\
&\quad + \alpha\|\mathbf{B}_t^\top (\mathbf{B}_{t} \mathbf{B}_{t}^\top - \mathbf{B}_{t,i,s} \mathbf{B}_{t,i,s}^\top)(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\| \nonumber \\
&\leq \|\mathbf{B}_t^\top (\mathbf{I}_d - \mathbf{\hat{B}}_{t} \mathbf{\hat{B}}_{t}^\top + \mathbf{\hat{B}}_{t} \mathbf{\hat{B}}_{t}^\top -\alpha \mathbf{B}_{t} \mathbf{B}_{t}^\top)(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\| \nonumber \\
&\quad + \alpha\|\mathbf{B}_t^\top (\mathbf{B}_{t} \mathbf{B}_{t}^\top - \mathbf{B}_{t} \mathbf{B}_{t,i,s}^\top)(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i}) \|\nonumber \\
&\quad + \alpha\| \mathbf{B}_t^\top(\mathbf{B}_{t} \mathbf{B}_{t,i,s}^\top- \mathbf{B}_{t,i,s} \mathbf{B}_{t,i,s}^\top)(\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,t,i})\| \nonumber \\
&\leq c \alpha^{1.5}\tau \mathbf{e}_{t,i,s} + noise
\end{align}
but still need to deal with past noise and current iterates being a function of them
}
\end{proof}
\begin{lemma}
For all $r\leq s$,
\begin{align}
\| \mathbf{B}_{t,i,s}^\top \mathbf{N}_{t,i,r}\| &\leq \tfrac{\sqrt{k}+ \sqrt{\log()}}{\sqrt{b}}
\end{align}
with high probability
\end{lemma}
\begin{proof}
We know
\begin{align}
\| \mathbf{B}_{t,i,s-1}^\top \mathbf{N}_{t,i,r}\| &\leq \tfrac{\sqrt{k}+ \sqrt{\log()}}{\sqrt{b}}
\end{align} whp
for all $r\leq s-1$.
We have
\begin{align}
\| \mathbf{B}_{t,i,s}^\top \mathbf{N}_{t,i,r}\| &\leq \| \mathbf{B}_{t,i,s-1}^\top \mathbf{N}_{t,i,r}\|
\end{align}
\end{proof}
\begin{lemma}
Distance does not get worse locally.
\end{lemma}
\begin{proof}
\begin{align}
\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t,i,s+1}\|_2 &= \|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{T,M+1,s} (\mathbf{I}_k - \alpha \mathbf{w}_{T,M+1,s}\mathbf{w}_{T,M+1,s}^\top) \|_2\nonumber \\
&\leq \|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{t,i,s} \|_2 \nonumber \\
&\leq \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t} \|_2
\end{align}
Thus
\begin{align}
\operatorname{dist}_{t,s} \leq \frac{\|\mathbf{B}_{t}\|_2 }{\sigma_{\min}(\mathbf{B}_{t,i,s})} \operatorname{dist}_{t} \leq \sqrt{\tfrac{1+ \alpha^2 \tau c_{\boldsymbol{\Delta}}}{1 - c\alpha^2 \tau c_{\boldsymbol{\Delta}}}} \operatorname{dist}_{t}
\end{align}
With finite samples, we have:
just need to control:
\begin{align}
\end{align}
\end{proof}
\subsection{Proof of Proposition \ref{prop:dgd}.}
\begin{proof}
Let $\mathbf{\bar{w}}_\ast \coloneqq \tfrac{1}{M}\sum_{i=1}^M \mathbf{w}_{\ast,i}$.
Note that for D-GD the global update for the representation is
\begin{align}
\mathbf{B}_{t+1} = \mathbf{B}_t - \frac{\alpha}{M}\sum_{i=1}^M \nabla_{\mathbf{B}} f_i(\mathbf{B}_t, \mathbf{w}_t) = \mathbf{B}_t - \alpha (\mathbf{B}_t \mathbf{w}_t -\mathbf{B}_\ast \mathbf{\bar{w}}_{\ast}) \mathbf{w}_t^\top,
\end{align}
and similarly, the update for the head is $\mathbf{w}_{t+1} = \mathbf{w}_t - \alpha\mathbf{B}_t^\top(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast})$. Thus, the behavior of D-GD is invariant for all settings with ground-truth representation $\mathbf{B}_{\ast}'$ and average ground-truth head $\mathbf{w}_\ast'$ satisfying $\mathbf{B}_\ast' \mathbf{\bar{w}}_\ast' = \mathbf{B}_\ast \mathbf{\bar{w}}_\ast$.
Suppose $\operatorname{dist}(\mathbf{B}_T(\mathbf{B}_0,\mathbf{B}_\ast), \mathbf{B}_\ast) < \delta_0$ for some such $\mathbf{B}_\ast$. There exists $\mathbf{B}_\ast'\in \mathcal{O}^{d\times k}$ such that $\operatorname{dist}(\mathbf{B}_0,\mathbf{B}_\ast')$ and $\operatorname{dist}(\mathbf{B}_\ast,\mathbf{B}_\ast')\geq 2 \delta_0$ such that $\mathbf{B}_\ast \mathbf{\bar{w}}_\ast = \mathbf{B}_\ast' \mathbf{\bar{w}}_\ast $. Since behavior of Distributed GD depends only on the product $\mathbf{B}_\ast \mathbf{\bar{w}}_\ast$ and not the factors $\mathbf{B}_\ast$ and $\mathbf{\bar{w}}_\ast$, $\mathbf{B}_T(\mathbf{B}_0,\mathbf{B}_\ast) = \mathbf{B}_T(\mathbf{B}_0,\mathbf{B}_\ast')$. Using this equality with the triangle inequality yields
\begin{align}
\operatorname{dist}(\mathbf{B}_T(\mathbf{B}_0,\mathbf{B}_\ast'), \mathbf{B}_\ast' ) = \operatorname{dist}(\mathbf{B}_T(\mathbf{B}_0,\mathbf{B}_\ast), \mathbf{B}_\ast' ) &\geq \operatorname{dist}( \mathbf{B}_\ast, \mathbf{B}_\ast') - \operatorname{dist}(\mathbf{B}_T(\mathbf{B}_0,\mathbf{B}_\ast), \mathbf{B}_\ast ) \nonumber \\
&\geq 2 \delta_0 - \delta_0 \geq \delta_0 \nonumber
\end{align}
\end{proof}
\section{Proof of Theorem Main Results}\label{app:proof}
\subsection{Proof of Theorem \ref{thm:main_pop}}
In this section we provide the proof of Theorem \ref{thm:main_pop}. We make use of the notations in Table \ref{table:notations}.
\begin{table}[H]
\caption{Notations.}
\label{table:notations}
\centering
\begin{tabular}{lll}
\toprule
Notation & Definition \\
\midrule
$\mu$ & $ \sigma_{\min}^{0.5}\left(\tfrac{1}{M}\sum_{i=1}^M (\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast})(\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast})^\top\right)$ \\
$L_{\max}$ & $\max_{i\in[M]}\|\mathbf{w}_{\ast,i}\|_2 $ \\
$\kappa_{\max}$ & $\nicefrac{L_{\max}}{\mu}$ \\
$\mathbf{\bar{w}}_{\ast} $ & $\tfrac{1}{M}\sum_{i=1}^M \mathbf{w}_{\ast,i}$ \\
$\mathbf{\bar{w}}_{\ast,t}$ & $ \tfrac{1}{m}\sum_{i\in \mathcal{I}_t} \mathbf{w}_{\ast,i}$ \\
$ \mathbf{B}_{t,i,s},\mathbf{w}_{t,i,s}$ & the results of $s$ local updates of the global model at round $t$ by the $i$-th client\\
$ \mathbf{B}_{t,i,0},\mathbf{w}_{t,i,0}$ & $ \mathbf{B}_{t},\mathbf{w}_{t}$, respectively \\
$\mathbf{e}_{t,i,s}$ & $\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_{\ast}\mathbf{w}_{\ast,i} $, i.e. product error for $s$-th local update for task $i$, round $t$ \\
$ \mathbf{G}_{t,i,s}$ & $(\mathbf{B}_{t,i,s+1} - \mathbf{B}_{t,i,s})/\alpha$, such that $\mathbf{B}_{t,i,s+1} = \mathbf{B}_{t,i,s} -\alpha \mathbf{G}_{t,i,s}$ \\
$ \mathbf{G}_{t}$ & $(\mathbf{B}_{t+1} - \mathbf{B}_{t})/\alpha$, such that $\mathbf{B}_{t+1} = \mathbf{B}_{t} -\alpha \mathbf{G}_{t}$ \\
$\boldsymbol{\Delta}_t$ & $\mathbf{I}_k - \alpha \mathbf{B}_t^\top \mathbf{B}_t$ \\
$\boldsymbol{\bar{\Delta}}_t$ & $\mathbf{I}_d - \alpha \mathbf{B}_t \mathbf{B}_t^\top$ \\
$\operatorname{dist}_t$ & $\operatorname{dist}(\mathbf{B}_t,\mathbf{B}_\ast)$ \\
$\delta_0$ & $\operatorname{dist}_0$ \\
$E_0$ & $1-\operatorname{dist}_0^2$ \\
$\operatorname{col}(\mathbf{B}), \operatorname{col}(\mathbf{B})^\perp$ & column space of $\mathbf{B}$, orthogonal complement to column space of $\mathbf{B}$, respectively \\
\bottomrule
\end{tabular}
\end{table}
Here the local updates are given by
\begin{align}
\mathbf{B}_{t,i,s+1} &= \mathbf{B}_{t,i,s} - \alpha (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_{t,i,s}^\top \nonumber \\
\mathbf{w}_{t,i,s+1} &= \mathbf{w}_{t,i,s} - \alpha \mathbf{B}_{t,i,s}^\top (\mathbf{B}_{t,i,s} \mathbf{w}_{t,i,s} - \mathbf{B}_{\ast} \mathbf{w}_{\ast,i}) \nonumber \\
&= \boldsymbol{\Delta}_{t,i,s}\mathbf{w}_{t,i,s} + \alpha \mathbf{B}_{t,i,s}^\top \mathbf{B}_{\ast} \mathbf{w}_{\ast,i} \nonumber
\end{align}
and the global updates are given by
\begin{align}
\mathbf{B}_{t+1} &= \tfrac{1}{m}\sum_{i \in \mathcal{I}_t} \mathbf{B}_{t,i,\tau} \nonumber \\
\mathbf{w}_{t+1} &= \tfrac{1}{m}\sum_{i \in \mathcal{I}_t} \mathbf{w}_{t,i,\tau}. \nonumber
\end{align}
First we control the ground-truth heads sampled on each round.
\begin{lemma}\label{lem:concen}
Suppose $m\geq \min(M, 20((\nicefrac{\gamma}{L_{\max}})^2 + (\nicefrac{H}{L_{\max}})^4)(\alpha L_{\max})^{-4}\log(kT))$. Then the event
\begin{align}
A_0\coloneqq \Bigg\{& \bigg\| \tfrac{1}{m}\sum_{i\in \mathcal{I}_t} \mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast} \bigg\| \leq 4 \alpha^2 L_{\max}^3,\nonumber \\
& \bigg\| \tfrac{1}{m}\sum_{i\in \mathcal{I}_t} \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top - \tfrac{1}{M}\sum_{i'=1}^M \mathbf{w}_{\ast,i'}\mathbf{w}_{\ast,i'}^\top \bigg\| \leq 4\alpha^2 L_{\max}^4 \quad \forall t \in [T]\Bigg\} \nonumber
\end{align}
with probability at least $ 1- 4 (kT)^{-99}$.
\end{lemma}
\begin{proof}
If $m=M$ then $A_0$ holds almost surely. Otherwise, first let $\mathbf{W}_{\ast,i} := \text{diag}(\mathbf{w}_{\ast,i}) \in \mathbf{R}^{k\times k}$, and let $\mathbf{\bar{W}}_{\ast} := \tfrac{1}{M}\sum_{i=1}^M\text{diag}(\mathbf{w}_{\ast,i})$. For any $t\in [T]$, $\{\mathbf{W}_{\ast,i}\}_{i \in\mathcal{I}_t}$ is a set of Hermitian matrices sampled uniformly without replacement from $\{\mathbf{W}_{\ast,i}\}_{i \in[M]}$, $\|\mathbf{W}_{\ast,i}\|\leq L_{\max}$ almost surely, and $\left\|\tfrac{1}{M}\sum_{i=1}^M (\mathbf{W}_{\ast,i}-\mathbf{\bar{W}}_{\ast})^2 \right\| \leq \tfrac{1}{M}\sum_{i=1}^M \|\mathbf{w}_{\ast,i}-\mathbf{\bar{w}}_{\ast}\|^2 =\gamma^2$ by the triangle and Cauchy-Schwarz inequalities and Definition \ref{def:var}. Thus, we can apply Theorem 1 in \cite{gross2010note} to obtain
\begin{align}
\mathbb{P}\left( \left\|\sum_{i \in \mathcal{I}_t} \mathbf{W}_{\ast,i} - \mathbf{\bar{W}}_{\ast}\right\|> t \right) &\leq 2 k \exp( \tfrac{-t^2}{4m\gamma^2} )
\end{align}
as long as $t\leq 2 m \gamma^2/L_{\max}$. Choose $t = 4 m \alpha^2 L_{\max}^3$. Note that indeed $t \leq 2 m \gamma^2/L_{\max}$ since $\gamma^2 = \sum_{l=1}^k\tfrac{1}{M}\sum_{i=1}^M \mathbf{u}_l^\top (\mathbf{w}_{\ast,i}- \mathbf{\bar{w}}_{\ast})(\mathbf{w}_{\ast,i}- \mathbf{\bar{w}}_{\ast})^\top \mathbf{u}_l\geq k\mu^2$, where $\mathbf{u}_l$ is the $l$-th standard basis vector, and $\alpha \leq \mu^2/(2L_{\max}^4)$. Thus we obtain
\begin{align}
\mathbb{P}\left( \left\|\sum_{i \in \mathcal{I}_t} \mathbf{W}_{\ast,i} - \mathbf{\bar{W}}_{\ast}\right\|> 4m \alpha^2 L_{\max}^3 \right) &\leq 2 k \exp\left( \tfrac{- 4m \alpha^4 L_{\max}^6 }{ \gamma^2} \right) \nonumber \\
\implies \mathbb{P}\left( \left\|\tfrac{1}{m}\sum_{i \in \mathcal{I}_t} \mathbf{W}_{\ast,i} - \mathbf{\bar{W}}_{\ast}\right\|> 4\alpha^2 L_{\max}^3 \right) &\leq 2 k \exp\left( - 100 \log(kT) \right) \nonumber
\end{align}
since $m \geq 20 (\tfrac{L_{\max}^2}{\gamma^2})\alpha^4 L_{\max}^4 \log(kT)$.
An analogous argument, without needing to lift the matrices to higher dimensions, yields
\begin{align}
\mathbb{P}\left( \left\|\tfrac{1}{m}\sum_{i \in \mathcal{I}_t}\left( \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top - \tfrac{1}{M}\sum_{i'=1}^M\mathbf{{w}}_{\ast,i'}\mathbf{{w}}_{\ast,i'}^\top\right) \right\|> 4 \alpha^2 L_{\max}^4 \right) &\leq 2 k \exp\left( - 100 \log(kT) \right) \nonumber
\end{align}
Union bounding, we obtain that $ \left\|\tfrac{1}{m}\sum_{i \in \mathcal{I}_t} \mathbf{W}_{\ast,i} - \mathbf{\bar{W}}_{\ast}\right\|\leq 4\alpha^2 L_{\max}^3 $ and \\
$ \left\|\tfrac{1}{m}\sum_{i \in \mathcal{I}_t}\left( \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top - \tfrac{1}{M}\sum_{i'=1}^M\mathbf{{w}}_{\ast,i'}\mathbf{{w}}_{\ast,i'}^\top\right) \right\|\leq 4 \alpha^2 L_{\max}^3 $ with probability at least \\
$1 - 4k\exp(-100\log(kT)) = 1 - 4k^{-99}T^{-100}$.
Union bounding over all $t\in [T]$ completes the proof.
\end{proof}
Next we state and prove the version of Theorem \ref{thm:main_pop} with explicit constants. Note that the constants are not optimized.
\begin{theorem}[FedAvg Representation Learning]
\label{thm:app_pop} Consider the case that each client takes gradient steps with respect to their population loss $f_i(\mathbf{B},\mathbf{w})\coloneqq \tfrac{1}{2}\|\mathbf{Bw}-\mathbf{B}_{\ast}\mathbf{w}_{\ast,i}\|^2$ and all losses are weighted equally in the global objective.
Suppose Assumptions \ref{assump:n} and \ref{assump:td} hold, the number of clients participating each round satisfies $m \geq \min(M, 20((\nicefrac{\gamma}{L_{\max}})^2 + (\nicefrac{H}{L_{\max}})^4)(\alpha L_{\max})^{-4}\log(kT))$, and the initial parameters satisfy (i) $ \delta_0 \coloneqq \operatorname{dist}(\mathbf{B}_0, \mathbf{B}_\ast)\leq \sqrt{1\! -\! E_0}$ for any $E_0 \in (0,1]$, (ii) $\|\mathbf{I}- \alpha \mathbf{B}_0^\top \mathbf{B}_0\|_2 \leq \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2$ and (iii) $\|\mathbf{w}_0\|_2 \leq \alpha^{2.5} \tau L_{\max}^3$.
Choose step size $\alpha \leq \tfrac{1-\delta_0}{4800{ \sqrt{\tau}L_{\max}\kappa_{\max}^{2} }}$.
Then for any $\epsilon \in (0, 1)$, the distance of the representation learned by FedAvg with $\tau\geq 2$ local updates satisfies $\operatorname{dist}(\mathbf{B}_T, \mathbf{B}_\ast) <\epsilon$ after at most
\begin{align}
T \leq \tfrac{25}{\alpha^2 \tau \mu^2 E_0}\log(\nicefrac{1}{\epsilon}) \nonumber
\end{align}
communication rounds with probability at least $1 - 4 (kT)^{-99}$.
\end{theorem}
\begin{proof}
First we condition on the event $A_0$, which occurs with probability at least $1 - 4(kT)^{-99}$ by Lemma \ref{lem:concen}. Conditioned on this event, we will show that that the following two sets of inductive hypotheses hold for all $s\in [\tau]$, $i\in \mathcal{I}_t$, and $t\in[T]$. The first set of inductive hypotheses controls local behavior. We apply the below local induction in parallel for each client $i \in [M]$ at every communication round $t \geq 0$, starting from the base case $s=1$.
\begin{enumerate}
\item $A_{1,t,i}(s) \coloneqq \{\|\mathbf{w}_{t,i,s'}- \alpha \mathbf{B}_{t,i,s'-1}^\top \mathbf{B}_{\ast}\mathbf{w}_{\ast,i}\|_2 \leq 4 c_3 \alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2 E_0^{-1} \quad \forall s'\in \{1,\dots,s\}\}$
\item $A_{2,t,i}(s) \coloneqq \{\|\mathbf{w}_{t,i,s'}\|_2 \leq 2 \alpha^{0.5} L_{\max} \quad \forall s'\in \{1,\dots,s\} \}$
\item $A_{3,t,i}(s) \coloneqq \{\|\boldsymbol{\Delta}_{t,i,s'}\|_2 \leq 2c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} \quad \forall s'\in \{1,\dots,s\} \}$
\item $A_{4,t,i}(s)\coloneqq \{ \operatorname{dist}(\mathbf{B}_{t,i,s'}, \mathbf{B}_\ast) \leq 1.1 \operatorname{dist}(\mathbf{B}_{t}, \mathbf{B}_\ast)\quad \forall s'\in \{1,\dots,s\}\}$
\end{enumerate}
The second set of inductions controls the global behavior, starting from $t=1$ as the base case:
\begin{enumerate}
\item $A_1(t) \coloneqq \{ \|\mathbf{w}_{t'} - \alpha(\mathbf{I}_k + \boldsymbol{\Delta}_{t'}) \mathbf{B}_{t'}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t'}\|_2 \leq 91\alpha^{2.5}\tau L_{\max}^3
\quad \forall t'\in \{1,\dots, t\}\}$
\item $A_2(t) \coloneqq \{ \|\mathbf{w}_{t'}\|_2 \leq 2\alpha^{0.5} L_{\max} \quad \forall t'\in \{1,\dots, t\}\}$
\item $A_3(t) \coloneqq \{ \|\boldsymbol{\Delta}_{t'} \|_2 \leq c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} \quad \forall t'\in \{1,\dots, t\}\}$
\item $A_4(t) \coloneqq \{ \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t'}\|_2 \leq (1 - 0.04 \alpha^2 \tau \mu^2 E_0)\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t'-1} \|_2 \quad \forall t'\in \{1,\dots, t\} \}$
\item $A_5(t) \coloneqq \{ \operatorname{dist}_{t} \leq (1 - 0.04 \alpha^2 \tau \mu^2 E_0)^{t-1} \quad \forall t'\in \{1,\dots, t\} \}$
\end{enumerate}
where $c_3 = 4800$.
Without loss of generality let $\alpha \leq \frac{1-\delta_0}{{c_3} \sqrt{\tau}L_{\max}\kappa_{\max}^2}$. For ease of presentation we refer to $c_3$ symbolically rather than by its value throughout the proof.
The above inductions are applied in the following manner. First, the global initialization at $t=0$ implies that the local inductive hypotheses hold after one local update (the base case). Then, by the local inductive argument, these conditions continue to hold for all subsequent local updates. This in turn implies that the global inductive hypotheses hold after the first global averaging step, i.e. $A_1(1), A_2(1)$ and $A_3(1)$ hold. Next, the global hypotheses holding at $t=1$ implies that the local inductions hold in their base case at $t=1$ (after one local update, i.e. $s=1$), which implies they continue to hold for all subsequent local updates. Again, this implies the global hypotheses hold at $t=2$, which implies the base case for the local inductions at $t=2$, and so on. In summary, the ordering of the inductions is:
\begin{align}
\text{Initialization at $t\!=\!0$}\! \implies\! & \text{Local inductions at $t\!=\!0$} \! \implies \! \text{Global inductions at $t\!=\!1$} \! \nonumber \\
&\implies\!\text{Local inductions at $t\!=\!1$}\! \implies\! \dots \nonumber
\end{align}
We start by showing that the base case $s=1$ holds for the local inductions. The proof is identical for all $i\in [M]$ and $t\geq 0$.
\begin{itemize}
\item \textbf{If $t=0$: initial conditions $\implies$ $A_{1,t,i}(1)$, else $A_2(t) \cap A_3(t) \implies A_{1,t,i}(1)$.}
Note that at initialization, $\|\boldsymbol{\Delta}_0\mathbf{w}_0\|\leq \|\boldsymbol{\Delta}_0\|\|\mathbf{w}_0\| \leq \alpha^{2.5}\tau L_{\max}^3 \kappa_{\max}^2 \leq 4c_3 \alpha^{2.5}\tau L_{\max}^3 \kappa_{\max}^2 E_0^{-1}$. Likewise, at arbitrary $t$, $\|\boldsymbol{\Delta}_t\mathbf{w}_t\|\leq 4c_3 \alpha^{2.5}\tau L_{\max}^3 \kappa_{\max}^2 E_0^{-1} $ due to $A_2(t)$ and $A_3(t)$. Thus, since
$\mathbf{w}_{t,i,1} = \boldsymbol{\Delta}_t \mathbf{w}_t + \alpha \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i}$, we have
\begin{align}
\| \mathbf{w}_{t,i,1} - \alpha \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i} \| &= \|\boldsymbol{\Delta}_t \mathbf{w}_t \|
\leq \|\boldsymbol{\Delta}_t \| \| \mathbf{w}_t \| \leq 4 c_3 \alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2 E_0^{-1} \nonumber
\end{align}
as desired (recall that $\mathbf{B}_{t,i,0}\equiv \mathbf{B}_t$).
\item \textbf{If $t=0$: initial conditions $ \cap \; A_{1,t,i}(1) \implies$ $A_{2,t,i}(1)$, else $ A_3(t) \cap A_{1,t,i}(1) \implies A_{2,t,i}(1)$.}
For any $t \geq 0$, we have $\|\boldsymbol{\Delta}_t\| \leq c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}$ due to either the initialization $(t=0)$ or $A_3(t)$ $(t> 0)$. This implies that $\|\mathbf{B}_t\| \leq \sqrt{\tfrac{1 + c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}}{\alpha}} \leq \tfrac{1.1}{\sqrt{\alpha}}$ since $\alpha$ is sufficiently small (noting that $\tfrac{(1-\delta)^2}{E_0} = \tfrac{(1-\delta)^2}{1-\delta^2}\leq 1$ . Now we use $A_{1,t,i}(1)$ and the triangle inequality to obtain:
\begin{align}
\|\mathbf{w}_{t,i,1}\| &\leq \| \mathbf{w}_{t,i,1} - \alpha \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i} \| + \| \alpha \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i} \|\nonumber \\
&\leq 4c_3 \alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2 E_0^{-1} + \alpha \|\mathbf{B}_t\| \|\mathbf{w}_{\ast,i}\|\nonumber \\
&\leq {2\sqrt{\alpha}}L_{\max}. \nonumber
\end{align}
as desired.
\item \textbf{If $t=0$: initial conditions $\implies$ $A_{3,t,i}(1)$, else $A_2(t) \cap A_3(t) \implies A_{3,t,i}(1)$.}
We have
\begin{align}
\boldsymbol{\Delta}_{t,i,1} &= \mathbf{I}_k - \alpha \mathbf{B}_{t,i,1}^\top \mathbf{B}_{t,i,1} \nonumber \\
&= \boldsymbol{\Delta}_t + \alpha^2 \mathbf{B}_t^\top( \mathbf{B}_{t} \mathbf{w}_t - \mathbf{B}_{\ast} \mathbf{w}_{\ast,i}) \mathbf{w}_t^\top \nonumber \\
&\quad + \alpha^2 \mathbf{B}_t^\top( \mathbf{B}_{t} \mathbf{w}_t - \mathbf{B}_{\ast} \mathbf{w}_{\ast,i}) \mathbf{w}_t^\top - \alpha^3 \mathbf{w}_t \mathbf{w}_t^\top \|\mathbf{B}_{t} \mathbf{w}_t - \mathbf{B}_{\ast} \mathbf{w}_{\ast,i}\|_2^2 \label{12}
\end{align}
By the initial conditions and by inductive hypotheses $A_1(t)$ and $A_2(t)$, for any $t\geq 0$ we have $\|\mathbf{w}_t\|_2\leq 2\sqrt{\alpha}L_{\max}$, $\|\boldsymbol{\Delta}_t\|\leq c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2E_0^{-1}$, and $ \|\mathbf{B}_t\|_2\leq \tfrac{1.1}{\sqrt{\alpha}}$. This implies
$\|\mathbf{B}_t \mathbf{w}_{t} - \mathbf{B}_\ast \mathbf{w}_{\ast,i}\|_2\leq \|\mathbf{B}_t\| \|\mathbf{w}_{t}\| +\| \mathbf{B}_\ast \mathbf{w}_{\ast,i}\|\leq 3.2 L_{\max}$.
Therefore using \eqref{12}, we obtain
\begin{align}
\|\boldsymbol{\Delta}_{t,i,1}\| _2
&\leq \|\boldsymbol{\Delta}_t\|_2 + 2 \alpha^2 \|\mathbf{B}_t^\top( \mathbf{B}_{t} \mathbf{w}_t - \mathbf{B}_{\ast} \mathbf{w}_{\ast,i}) \mathbf{w}_t^\top\|_2 + \alpha^3 \|\mathbf{w}_t \|^2_2 \|\mathbf{B}_{t} \mathbf{w}_t - \mathbf{B}_{\ast} \mathbf{w}_{\ast,i}\|_2^2 \nonumber \\
&\leq \|\boldsymbol{\Delta}_t\|_2 + 15 \alpha^2 L_{\max}^2 + 41\alpha^4 L_{\max}^4 \nonumber \\
&\leq 2 c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}
\end{align}
as desired.
\item \textbf{If $t=0$: initial conditions $\implies$ $A_{4,t,i}(1)$, else $A_{3,t,i}(1)\cap A_2(t) \cap A_3(t) \implies A_{4,t,i}(1)$.}
Note that
\begin{align}
\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t,i,1}\|_2\! &= \|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{t} (\mathbf{I}_k\! -\! \alpha \mathbf{w}_{t}\mathbf{w}_{t}^\top) \|_2 \leq\|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{t}\| \|\mathbf{I}_k\! -\! \alpha \mathbf{w}_{t}\mathbf{w}_{t}^\top \|_2 \leq \|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{t} \|_2 \nonumber
\end{align}
as $\alpha\|\mathbf{w}_t\|^2 \leq 1$ by either the initialization (if $t=0$) or $A_2(t)$ (if $t\geq 1$) and the choice of $\alpha$ sufficiently small.
Thus, letting $\mathbf{\hat{B}}_{t,i,1}\mathbf{R}_{t,i,1} = \mathbf{B}_{t,i,1}$ denote the QR-decomposition of $\mathbf{B}_{t,i,1}$, we have
\begin{align}
\operatorname{dist}(\mathbf{B}_{t,i,1},\mathbf{B}_\ast) &= \|\mathbf{B}_{\ast,\perp}^\top \mathbf{\hat{B}}_{t,i,1}\|_2 \nonumber \\
&\leq \tfrac{1}{\sigma_{\min}(\mathbf{B}_{t,i,1})}\|\mathbf{B}_{\ast,\perp}^\top \mathbf{{B}}_{t,i,1}\|_2 \nonumber \\
&\leq \tfrac{1}{\sigma_{\min}(\mathbf{B}_{t,i,1})}\|\mathbf{B}_{\ast,\perp}^\top \mathbf{{B}}_{t}\|_2 \nonumber \\
&\leq \tfrac{\|\mathbf{B}_t\|}{\sigma_{\min}(\mathbf{B}_{t,i,1})}\operatorname{dist}(\mathbf{B}_t, \mathbf{B}_{\ast}) \nonumber \\
&\leq \sqrt{\tfrac{1+ c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}}{1 - 2c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}}} \operatorname{dist}_{t} \label{jgj} \\
&\leq 1.1 \operatorname{dist}(\mathbf{B}_t, \mathbf{B}_{\ast})\label{gbg}
\end{align}
where the \eqref{jgj} follows by $A_{3,t,i}(1)$ and either the initial condition on $\|\boldsymbol{\Delta}_t\|$ (if $t=0$) or $A_3(t)$ (if $t>0$), and \eqref{gbg} follows as $\alpha$ is sufficiently small.
\end{itemize}
Now we show that the global inductions hold at global round $t=1$ following the local updates at round $t=0$.
\begin{itemize}
\item \textbf{Initialization $\cap \big(\cap_{i\in\mathcal{I}_0}A_{1,0,i}(\tau)\cap A_{2,0,i}(\tau)\cap A_{3,0,i}(\tau)\big) \implies A_1(1)\cap A_2(1)\cap A_4(1)\cap A_5(1)$.}
To show each of these hypotheses hold we can apply the proofs of Lemmas \ref{lem:a1}, \ref{lem:1.5} \ref{lem:a2} and \ref{lem:a4} respectively, since they only rely on inductive hypotheses $ A_{1,0,i}(\tau)$, $ A_{2,0,i}(\tau)$ and $ A_{3,0,i}(\tau)$ and appropriate scaling of $\|\mathbf{B}_0\|$ and $\|\mathbf{w}_0\|$, which is guaranteed by the initialization. In particular, the proof of these inductive hypotheses is identical for all $t\geq 1$.
\item \textbf{Initialization $ \cap \big(\cap_{i\in\mathcal{I}_0} A_{2,0,i}(\tau)\cap A_{3,0,i}(\tau)\big) \implies A_2(1)$.}
In the proof of $A_2(t)$ for $t\geq 2$ (Lemma \ref{lem:a2}) we leverage the fact that $\mathbf{w}_{t-1}$ is close to a matrix times the average of the $\mathbf{\bar{w}}_{\ast,t-1}$. Our initialization cannot guarantee that this holds for $\mathbf{w}_0$. Instead, we show that $\|\boldsymbol{\Delta}_1\|$ may increase from $\|\boldsymbol{\Delta}_0\|$ at a large rate that would cause $\|\boldsymbol{\Delta}_t\|$ to blow up if continued indefinitely, but since it only grows at this rate for the first round, this is ok. In particular, let $\mathbf{G}_0 = \tfrac{1}{\alpha}(\mathbf{B}_0 - \mathbf{B}_1)$ such that $\mathbf{B}_1 = \mathbf{B}_0 - \alpha \mathbf{G}_0$. Then
\begin{align}
\boldsymbol{\Delta}_{1} &= \boldsymbol{\Delta}_0 + \alpha^2 \mathbf{B}_0^\top \mathbf{G}_0 + \alpha^2 \mathbf{G}_0^\top \mathbf{B}_0 - \alpha^3 \mathbf{G}_0^\top \mathbf{G}_0 \nonumber
\end{align}
Moreover,
\begin{align}
\| \mathbf{G}_0 \| &= \left\|\frac{1}{m}\sum_{i\in\mathcal{I}_0} \sum_{s=0}^{\tau-1} ( \mathbf{B}_{0,i,s} \mathbf{w}_{0,i,s} - \mathbf{B}_{\ast}\mathbf{w}_{\ast,i})\mathbf{w}_{0,i,s}^\top \right\|
\leq 7 \sqrt{\alpha} \tau L_{\max}^2 \nonumber
\end{align}
by the initialization and $A_{2,0,i}(\tau)$ and $A_{3,0,i}(\tau)$, thus
\begin{align}
\| \mathbf{B}_0^\top \mathbf{G}_0 \| &\leq 8 \tau L_{\max}^2, \quad \quad \| \mathbf{G}_0^\top \mathbf{G}_0 \| \leq 49 \alpha \tau^2 L_{\max}^4 \nonumber
\end{align}
which implies that $\|\boldsymbol{\Delta}_1\|\leq \|\boldsymbol{\Delta}_0\| + 10 \alpha^2 \tau L_{\max}^2 \leq c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}$, as desired.
\end{itemize}
Assume that the inductive hypotheses hold up to time $t$ and local round $s\geq 1$. We first show that the local inductive hypotheses hold for local round $s+1$. Then, we show that the global inductions hold at time $t+1$. This is achieved by the following lemmas.
{\textbf{Local inductions.}}
\begin{itemize}
\item $A_{2,t,i}(s) \cap A_{3,t,i}(s) \implies A_{1,t,i}(s+1). $ This is Lemma \ref{lem:a1s}.
\item $A_{1,t,i}(s+1) \cap A_{2,t,i}(s) \cap A_{3,t,i}(s) \implies A_{2,t,i}(s+1). $ This is Lemma \ref{lem:a1.5s}.
\item $ A_{2,t,i}(s) \cap A_{3,t,i}(s) \implies A_{3,t,i}(s+1). $ This is Lemma \ref{lem:a2s}.
\item $A_{2,t,i}(s) \cap A_{3,t,i}(s+1) \cap A_{3}(t) \implies A_{4,t,i}(s+1)$. This is Lemma \ref{lem:a3s}.
\end{itemize}
{\textbf{Global inductions.}}
\begin{itemize}
\item $ \cap_{i\in \mathcal{I}_t} \big(A_{1,t,i}(\tau-1) \cap A_{3,t,i}(\tau-1)\big) \cap A_1(t) \cap A_2(t)\cap A_3(t) \implies A_{1}(t+1). $ This is Lemma \ref{lem:a1}.
\item $ \cap_{i\in \mathcal{I}_t} A_{2,t,i}(\tau) \implies A_{2}(t+1). $ This is Lemma \ref{lem:1.5}.
\item $ \cap_{i\in \mathcal{I}_t} \big(\cap_{h=1}^4 A_{h,t,i}(\tau) \big) \cap A_1(t) \cap A_2(t) \cap A_3(t) \cap A_5(t)\implies A_3(t+1).$ This is Lemma \ref{lem:a2}.
\item $ \cap_{i\in \mathcal{I}_t} \big( A_{1,t,i}(\tau) \cap A_{2,t,i}(\tau) \cap A_{3,t,i}(\tau) \big) \cap A_2(t) \cap A_3(t) \implies A_{4}(t+1). $ This is Lemma \ref{lem:a3}.
\item $ A_3(t+1) \cap A_4(t+1) \cap A_5(t) \implies A_{5}(t+1).$ This is Lemma \ref{lem:a4}.
\end{itemize}
These inductions complete the proof.
\end{proof}
\begin{lemma}$A_{2,t,i}(s) \cap A_{3,t,i}(s) \implies A_{1,t,i}(s+1)$. \label{lem:a1s}
\end{lemma}
\begin{proof}
Since $\mathbf{w}_{t,i,s+1} = \boldsymbol{\Delta}_{t,i,s}\mathbf{w}_{t,i,s} + \alpha \mathbf{B}_{t,i,s}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}$, we have
\begin{align}
\| \mathbf{w}_{t,i,s+1} - \alpha \mathbf{B}_{t,i,s}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i} \| &=\|\boldsymbol{\Delta}_{t,i,s}\mathbf{w}_{t,i,s} \|_2 \nonumber \\
&\leq \|\boldsymbol{\Delta}_{t,i,s}\|\|\mathbf{w}_{t,i,s} \|_2 \nonumber \\
&\leq 4 c_3 \alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2
\end{align}
where the last inequality follows by $A_{2,t,i}(s)$ and $A_{3,t,i}(s)$.
\end{proof}
\begin{lemma}$A_{1,t,i}(s+1) \cap A_{3,t,i}(s) \implies A_{2,t,i}(s+1)$. \label{lem:a1.5s}
\end{lemma}
\begin{proof}
Note that by the triangle inequality,
\begin{align}
\| \mathbf{w}_{t,i,s+1}\| &\leq \| \mathbf{w}_{t,i,s+1}- \alpha \mathbf{B}_{t,i,s}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i} \| + \|\alpha \mathbf{B}_{t,i,s}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i} \| \nonumber\\
&\leq 4 c_3 \alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2 E_0^{-1} + \|\alpha \mathbf{B}_{t,i,s}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i} \| \label{vf} \\
&\leq 4 c_3 \alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2 E_0^{-1} + 1.1 \sqrt{\alpha} L_{\max} \label{vf1} \\
&\leq 2 \sqrt{\alpha} L_{\max} \nonumber
\end{align}
where \eqref{vf} follows by $A_{1,t,i}(s)$ and \eqref{vf1} follows by the fact that $\|\mathbf{B}_{t,i,s}\|\leq \tfrac{1.1}{\sqrt{\alpha}}$ by $A_{3,t,i}(s)$, and choice of $\alpha \leq (1-\delta_0)(c_3\sqrt{ \tau } L_{\max}\kappa_{\max}^{2})^{-1}$.
\end{proof}
\begin{lemma}$ A_{2,t,i}(s) \cap A_{3,t,i}(s) \implies A_{3,t,i}(s+1)$. \label{lem:a2s}
\end{lemma}
\begin{proof}
Let $\mathbf{e}_{t,i,s}\coloneqq \mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s} - \mathbf{B}_\ast \mathbf{w}_{\ast,i}$ and $\mathbf{G}_{t,i,s} \coloneqq \mathbf{e}_{t,i,s} \mathbf{w}_{t,i,s}$.
We have
\begin{align}
\boldsymbol{\Delta}_{t,i,s+1} &= \boldsymbol{\Delta}_{t,i,s} + \alpha^2 \mathbf{B}_{t,i,s}^\top \mathbf{G}_{t,i,s} +\alpha^2 \mathbf{G}_{t,i,s}^\top \mathbf{B}_{t,i,s} - \alpha^3 \mathbf{G}_{t,i,s}^\top \mathbf{G}_{t,i,s} \nonumber
\end{align}
We use $A_{2,t,i}(s)$ and $A_{3,t,i}(s)$ throughout the proof. Recall that $A_{3,t,i}(s)$ directly implies $\|\mathbf{B}_{t,i,s}\|\leq \tfrac{1.1}{\sqrt{\alpha}}$.
This bound as well as the bound on $\|\mathbf{w}_{t,i,s}\|$ from $A_{2,t,i}(s)$ and the Cauchy Schwarz inequality implies $\|\mathbf{e}_{t,i,s}\|\leq 3.2 L_{\max}$ and $\|\mathbf{G}_{t,i,s}\|_2 \leq 7\sqrt{\alpha}L_{\max}^2$, thus $\|\alpha^3 \mathbf{G}_{t,i,s}^\top \mathbf{G}_{t,i,s} \|\leq 49\alpha^{4} L_{\max}^4$. Next,
\begin{align}
\mathbf{B}_{t,i,s}^\top \mathbf{G}_{t,i,s} &= \mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top \nonumber \\
&= \alpha\mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s-1} + \mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s-1}^\top \boldsymbol{\Delta}_{t,i,s-1} \nonumber \\
&= \alpha\mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s} + \alpha\mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top (\mathbf{B}_{t,i,s-1} -\mathbf{B}_{t,i,s}) \nonumber \\
&\quad + \mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s-1}^\top \boldsymbol{\Delta}_{t,i,s-1} \nonumber
\end{align}
where, by the Cauchy-Schwarz inequality and $A_{2,t,i}(s)$ and $A_{3,t,i}(s)$
\begin{align}
\|\alpha\mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top (\mathbf{B}_{t,i,s-1} -\mathbf{B}_{t,i,s})\| &= \alpha^2 \|\mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{e}_{t,i,s-1}\mathbf{w}_{t,i,s-1}^\top\| \leq 23 \alpha^2 L_{\max}^4, \nonumber \\
\| \mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s-1}^\top \boldsymbol{\Delta}_{t,i,s-1} \| &\leq 15 c_3 \alpha^2 \tau L_{\max}^4 \kappa_{\max}^2 E_0^{-1},
\end{align}
and
\begin{align}
\|\alpha&\mathbf{B}_{t,i,s}^\top \mathbf{e}_{t,i,s}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s} \| \nonumber \\
&= \| \alpha^2\mathbf{B}_{t,i,s}^\top \mathbf{B}_{t,i,s}\mathbf{B}_{t,i,s-1}^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i} \mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s} - \alpha\mathbf{B}_{t,i,s}^\top \mathbf{B}_{\ast}\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s} \nonumber \\
&\quad + \alpha^2\mathbf{B}_{t,i,s}^\top \mathbf{B}_{t,i,s}\boldsymbol{\Delta}_{t,i,s-1} \mathbf{w}_{t,i,s-1} \mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s} \| \nonumber \\
&= \| - \alpha \boldsymbol{\Delta}_{t,i,s}\mathbf{B}_{t,i,s}^\top \mathbf{B}_{\ast}\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s} \nonumber \\
&\quad + \alpha^2\mathbf{B}_{t,i,s}^\top \mathbf{B}_{t,i,s}(\mathbf{B}_{t,i,s-1} - \mathbf{B}_{t,i,s})^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i} \mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s} \nonumber \\
&\quad + \alpha^2\mathbf{B}_{t,i,s}^\top \mathbf{B}_{t,i,s}\boldsymbol{\Delta}_{t,i,s-1} \mathbf{w}_{t,i,s-1} \mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s} \| \nonumber \\
&\leq \alpha\| \boldsymbol{\Delta}_{t,i,s}\mathbf{B}_{t,i,s}^\top \mathbf{B}_{\ast}\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s}\| \nonumber \\
&\quad + \alpha^2\|\mathbf{B}_{t,i,s}^\top \mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s-1}\mathbf{e}_{t,i,s-1}^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i} \mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s}\| \nonumber \\
&\quad + \alpha^2\| \mathbf{B}_{t,i,s}^\top \mathbf{B}_{t,i,s}\boldsymbol{\Delta}_{t,i,s-1} \mathbf{w}_{t,i,s-1} \mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_{t,i,s} \| \nonumber \\
&= 7 c_3 \alpha^2 \tau L_{\max}^4 \kappa_{\max}^2 E_0^{-1} + 9 \alpha^2 L_{\max}^4 .
\end{align}
Thus,
\begin{align}
\| \boldsymbol{\Delta}_{t,i,s+1}\|_2 &\leq \|\boldsymbol{\Delta}_{t,i,s} \|_2 + 2 \alpha^2 \| \mathbf{B}_{t,i,s}^\top \mathbf{G}_{t,i,s}\| + \alpha^3 \| \mathbf{G}_{t,i,s}^\top \mathbf{G}_{t,i,s}\| \nonumber \\
&\leq \|\boldsymbol{\Delta}_{t,i,s} \|_2 + 46 c_3 \alpha^4 \tau L_{\max}^4 \kappa_{\max}^2 E_0^{-1} + 81 \alpha^4 L_{\max}^4 \nonumber \\
&\vdots \nonumber \\
&\leq \|\boldsymbol{\Delta}_{t} \|_2 + 46 c_3 \alpha^4 \tau^2 L_{\max}^4 \kappa_{\max}^2 E_0^{-1} + 81 \alpha^4 \tau L_{\max}^4 \nonumber \\
&\leq c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} + 46 c_3 \alpha^4 \tau^2 L_{\max}^4 \kappa_{\max}^2 E_0^{-1} + 81 \alpha^4 \tau L_{\max}^4 \nonumber \\
&\leq 2 c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}
\end{align}
by choice of $c_3$ and $\alpha$ sufficiently small.
\end{proof}
\begin{lemma}$A_{2,t,i}(s) \cap A_{3,t,i}(s+1) \cap A_{3}(t) \implies A_{4,t,i}(s+1)$. \label{lem:a3s}
\end{lemma}
\begin{proof}
Note that
\begin{align}
\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t,i,s+1}\|_2 &= \|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{t,i,s} (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top) \|_2\nonumber \\
&\leq \|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{t,i,s} \|_2 \nonumber \\
&\quad \vdots \nonumber \\
&\leq \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t} \|_2
\end{align}
where the first inequality follows since $\|\mathbf{w}_{t,i,s}\|\leq 2 \sqrt{\alpha}L_{\max}$ (by $A_{2,t,i}(s)$) and $\alpha$ is sufficiently small, and the last inequality follows by recursively applying the first inequality for all local iterations leading up to $s$.
Thus
\begin{align}
\operatorname{dist}_{t,i,s} \leq \frac{\|\mathbf{B}_{t}\|_2 }{\sigma_{\min}(\mathbf{B}_{t,i,s})} \operatorname{dist}_{t} \leq \sqrt{\tfrac{1+ c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}}{1 - 2c_3 \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}}} \operatorname{dist}_{t} \leq 2 \operatorname{dist}_t. \nonumber
\end{align}
\end{proof}
\begin{lemma}$\cap_{i\in \mathcal{I}_t} \big(A_{2,t,i}(\tau-1) \cap A_{3,t,i}(\tau-1)\big) \cap A_2(t) \cap A_3(t) \implies A_{1}(t+1)$. \label{lem:a1}
\end{lemma}
\begin{proof}
Expanding $\mathbf{w}_{t+1}$ yields
\begin{align}
\mathbf{w}_{t+1} &= \tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\mathbf{w}_{t,i,\tau} \nonumber \\
&= \tfrac{1}{m}\sum_{i\in \mathcal{I}_t} \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1} +\alpha \mathbf{B}_{t,i,\tau-1}^\top \mathbf{B}_\ast\mathbf{w}_{\ast,i} \nonumber \\
&= \alpha \mathbf{B}_{t}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \tfrac{1}{m}\sum_{i\in \mathcal{I}_t} \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{w}_{t,i,\tau-1} +\alpha (\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,i} \nonumber \\
&= \frac{1 }{n}\sum_{i\in \mathcal{I}_t} \alpha(\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,i} + \alpha \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-2}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i} \nonumber \\
&\quad \quad \quad \quad\quad \quad + \alpha \boldsymbol{\Delta}_{t,i,\tau-1} \boldsymbol{\Delta}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2} +\alpha \mathbf{B}_{t}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} \nonumber \\
&= \alpha \mathbf{B}_{t}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \alpha \boldsymbol{\Delta}_{t} \mathbf{B}_{t}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} \nonumber \\
&\quad + \tfrac{1}{m}\sum_{i\in \mathcal{I}_t} \alpha(\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,i} + \alpha ( \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-2}^\top - \boldsymbol{\Delta}_{t}\mathbf{B}_{t}^\top )\mathbf{B}_\ast\mathbf{w}_{\ast,i} \nonumber \\
&\quad \quad \quad \quad\quad \quad + \boldsymbol{\Delta}_{t,i,\tau-1} \boldsymbol{\Delta}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2} \nonumber \\
&= \alpha \mathbf{B}_{t+1}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t+1} + \alpha \boldsymbol{\Delta}_{t+1} \mathbf{B}_{t+1}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t+1} \nonumber \\
&\quad + \alpha \mathbf{B}_{t+1}^\top \mathbf{B}_\ast(\mathbf{\bar{w}}_{\ast,t}-\mathbf{\bar{w}}_{\ast,t+1}) + \alpha \boldsymbol{\Delta}_{t+1} \mathbf{B}_{t+1}^\top \mathbf{B}_\ast(\mathbf{\bar{w}}_{\ast,t} - \mathbf{\bar{w}}_{\ast,t+1}) \nonumber \\
&\quad + \alpha (\mathbf{B}_t -\mathbf{B}_{t+1})^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \alpha (\boldsymbol{\Delta}_t\mathbf{B}_t -\boldsymbol{\Delta}_{t+1}\mathbf{B}_{t+1})^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} \nonumber \\
&\quad + \tfrac{1}{m}\sum_{i\in \mathcal{I}_t} \alpha(\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t})^\top \mathbf{B}_\ast\mathbf{w}_{\ast,i} + \alpha ( \boldsymbol{\Delta}_{t,i,\tau-1}\mathbf{B}_{t,i,\tau-2}^\top - \boldsymbol{\Delta}_{t}\mathbf{B}_{t}^\top )\mathbf{B}_\ast\mathbf{w}_{\ast,i} \nonumber \\
&\quad \quad \quad \quad\quad \quad + \boldsymbol{\Delta}_{t,i,\tau-1} \boldsymbol{\Delta}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2} \label{chara}
\end{align}
The remainder of the proof lies in bounding the error terms, which are all terms in the RHS of \eqref{chara} besides the terms in the first line.
First, by $A_0$ and the triangle inequality, we have
\begin{align}
\|\mathbf{\bar{w}}_{\ast,t}-\mathbf{\bar{w}}_{\ast,t+1} \| &\leq \|\mathbf{\bar{w}}_{\ast,t}-\mathbf{\bar{w}}_{\ast}\| + \|\mathbf{\bar{w}}_{\ast,t+1}-\mathbf{\bar{w}}_{\ast}\| \leq 8\alpha^2 L_{\max}^3 \nonumber
\end{align}
Thus, by $A_3(t+1)$, we have
\begin{align}
\|\alpha \mathbf{B}_{t+1}^\top \mathbf{B}_\ast(\mathbf{\bar{w}}_{\ast,t}-\mathbf{\bar{w}}_{\ast,t+1}) \| &\leq 1.1 \sqrt{\alpha} \|\mathbf{\bar{w}}_{\ast,t}-\mathbf{\bar{w}}_{\ast,t+1} \| \leq 9 \alpha^{2.5} L_{\max}^3 \nonumber \\
\|\alpha \boldsymbol{\Delta}_{t+1} \mathbf{B}_{t+1}^\top \mathbf{B}_\ast(\mathbf{\bar{w}}_{\ast,t}-\mathbf{\bar{w}}_{\ast,t+1}) \| &\leq 1.1 \sqrt{\alpha} \|\boldsymbol{\Delta}_{t+1}\| \|\mathbf{\bar{w}}_{\ast,t}-\mathbf{\bar{w}}_{\ast,t+1} \| \leq 18 c_3 \alpha^{4.5} \tau L_{\max}^5 \kappa_{\max}^2 E_0^{-1} \nonumber
\end{align}
Next, we can bound the difference between the locally-updated representation and the global representation as follows, for any $s\in \{1,\dots,\tau\}$
\begin{align}
\|\mathbf{B}_{t,i,s} - \mathbf{B}_{t}\|_2 &\leq \sum_{r=1}^{s} \|\mathbf{B}_{t,i,r}- \mathbf{B}_{t,i,r-1}\|_2 \leq \alpha\sum_{r=1}^{s} \|\mathbf{e}_{t,i,r-1}\mathbf{w}_{t,i,r-1}^\top\|_2 \leq 7 \alpha^{1.5}s L_{\max}^2 \label{chara2}
\end{align}
using $A_2(t), A_3(t), A_{2,t,i}(\tau-1)$ and $A_{3,t,i}(\tau-1)$ to control the norms of $\mathbf{w}_{t,i,s-1}$ and $\mathbf{B}_{t,i,s-1}$.
From \eqref{chara2} it follows that
\begin{align}
\|\mathbf{B}_{t+1} - \mathbf{B}_{t}\|_2 &\leq \tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\|\mathbf{B}_{t,i,\tau} - \mathbf{B}_{t}\|_2 \leq 7\alpha^{1.5}\tau L_{\max}^2 \nonumber \\
\|\mathbf{B}_{t,i,\tau-2}\boldsymbol{\Delta}_{t,i,\tau-1} - \mathbf{B}_{t}\boldsymbol{\Delta}_{t}\|_2 &\leq \|\mathbf{B}_{t,i,\tau-2} - \mathbf{B}_{t}\|_2 + \alpha\|\mathbf{B}_{t,i,\tau-2}\mathbf{B}_{t,i,\tau-1}^\top\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_{t}\mathbf{B}_{t}^\top\mathbf{B}_{t}\|_2 \nonumber \\
&\leq \|\mathbf{B}_{t,i,\tau-2} - \mathbf{B}_{t}\|_2 +\alpha\|(\mathbf{B}_{t,i,\tau-2} - \mathbf{B}_{t})\mathbf{B}_{t,i,\tau-1}^\top\mathbf{B}_{t,i,\tau-1}\|_2 \nonumber \\
&\quad + \alpha \| \mathbf{B}_t (\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_t)^\top \mathbf{B}_{t,i,\tau-1} \|_2 \nonumber \\
&\quad + \alpha \| \mathbf{B}_t \mathbf{B}_{t}^\top (\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_t) \|_2 \nonumber \\
&\leq \|\mathbf{B}_{t,i,\tau-2} - \mathbf{B}_{t}\|_2 +\alpha\|\mathbf{B}_{t,i,\tau-2} - \mathbf{B}_{t}\|\|\mathbf{B}_{t,i,\tau-1}^\top\mathbf{B}_{t,i,\tau-1}\|_2 \nonumber \\
&\quad + \alpha \| \mathbf{B}_t \|\|\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_t\|\|\mathbf{B}_{t,i,\tau-1} \|_2\nonumber \\
&\quad + \alpha \| \mathbf{B}_t \mathbf{B}_{t}^\top \|\|\mathbf{B}_{t,i,\tau-1} - \mathbf{B}_t \| \nonumber \\
&\leq 31 \alpha^{1.5}\tau L_{\max}^2 \nonumber \\
\|\mathbf{B}_t\boldsymbol{\Delta}_t - \mathbf{B}_{t+1}\boldsymbol{\Delta}_{t+1}\|_2 &\leq 31 \alpha^{1.5}\tau L_{\max}^2
\end{align}
Also, we have by $A_{2,t,i}(\tau-1)$ and $A_{3,t,i}(\tau-1)$,
\begin{align}
\| \boldsymbol{\Delta}_{t,i,\tau-1} \boldsymbol{\Delta}_{t,i,\tau-2} \mathbf{w}_{t,i,\tau-2} \|_2 &\leq 8 c_3^2 \alpha^{4.5} \tau^2 L_{\max}^5 \kappa_{\max}^4 E_0^{-2}.
\end{align}
Thus, using these bounds with \eqref{chara}, we obtain
\begin{align}
\| \mathbf{w}_{t+1} - \alpha (\mathbf{I}_k +\boldsymbol{\Delta}_{t+1})\mathbf{B}_{t+1}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t+1} \|_2 &\leq 82 \alpha^{2.5}\tau L_{\max}^3 + (8c_3^2 + 12c_3) \alpha^{4.5}\tau^2 L_{\max}^5 \kappa_{\max}^4 E_0^{-2}\nonumber \\
&\leq 91 \alpha^{2.5}\tau L_{\max}^3 \nonumber
\end{align} to complete the proof, where we have used that $\alpha$ is sufficiently small in the last inequality.
\end{proof}
\begin{lemma}$\cap_{i\in \mathcal{I}_t} A_{2,t,i}(\tau) \implies A_{2}(t+1)$ \label{lem:1.5}
\end{lemma}
\begin{proof}
By the triangle inequality and $\cap_{i\in \mathcal{I}_t} A_{2,t,i}(\tau)$, we have
\begin{align}
\|\mathbf{w}_{t+1}\| &= \bigg\|\tfrac{1}{m}\sum_{i\in\mathcal{I}_t} \mathbf{w}_{t,i,\tau} \bigg\|\leq \tfrac{1}{m}\sum_{i\in\mathcal{I}_t} \|\mathbf{w}_{t,i,\tau}\| \leq 2 \sqrt{\alpha} L_{\max} \nonumber
\end{align}
as desired.
\end{proof}
\begin{lemma} \label{lem:distlb}
$A_{3}(t)\cap A_4(t) \implies \sigma_{\min}^2(\mathbf{B}_{t}^\top\mathbf{B}_\ast)\geq \tfrac{0.1}{\alpha} E_0$.
\end{lemma}
\begin{proof}
First note that
\begin{align}
\sigma_{\min}^2(\mathbf{B}_{t}^\top\mathbf{B}_\ast)&\geq \sigma_{\min}^2 (\mathbf{R}_t) \sigma_{\min}^2(\mathbf{\hat{B}}_{t}^\top\mathbf{B}_\ast) \nonumber \\
&\geq \tfrac{0.9}{\alpha} \sigma_{\min}^2(\mathbf{\hat{B}}_{t}^\top\mathbf{B}_\ast) \label{rtrt} \\
&= \tfrac{0.9}{\alpha}( 1 - \|\mathbf{\hat{B}}_{t}^\top\mathbf{B}_{\ast,\perp}\|_2^2 ) \nonumber \\
&= \tfrac{0.9}{\alpha} (1 - \operatorname{dist}_t^2) \label{whrr}
\end{align}
where $\mathbf{\hat{B}}_{t}\mathbf{R}_t = \mathbf{B}_t$ is the QR factorization of $\mathbf{B}_t$.
Next, we would like to show the RHS is at most $(2+\delta_0)/3$.
Using $A_3(t)$ and $A_4(t)$, we obtain
\begin{align}
\operatorname{dist}_{t}&= \|\mathbf{B}_{\ast,\perp}^\top \mathbf{\hat{B}}_{t}\|_2 \nonumber \\
&\leq\tfrac{1}{ \sigma_{\min}(\mathbf{B}_{t})}\|\mathbf{B}_{\ast,\perp}^\top \mathbf{{B}}_{t}\|_2\nonumber \\
&\quad \vdots \nonumber \\
&\leq \tfrac{1}{ \sigma_{\min}(\mathbf{{B}}_{t+1})}(1-0.04\alpha^2 \tau E_0 \mu^2 )^t\|\mathbf{B}_{\ast,\perp}^\top \mathbf{{B}}_{0}\|_2\nonumber \\
&\leq \tfrac{\sigma_{\max}(\mathbf{B}_0)}{ \sigma_{\min}(\mathbf{{B}}_{t})}(1-0.04\alpha^2 \tau E_0 \mu^2 )^t\delta_0 \nonumber \\
&\leq \tfrac{\sqrt{1 +\|\boldsymbol{\Delta}_0\|_2}/\sqrt{\alpha}}{ \sqrt{1-\|\boldsymbol{\Delta}_{t}\|_2}/\sqrt{\alpha}}\delta_0\nonumber
\end{align}
Next we use that $\|\boldsymbol{\Delta}_0\|\leq\alpha^2\tau L_{\max}^2 \kappa_{\max}^2 \leq 0.1 (1 - \delta_0)^2$ by choice of initialization and choice of $\alpha$, and similarly $\|\boldsymbol{\Delta}_t\|\leq \alpha^2\tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} \leq 0.1 (1 - \delta_0)^2/(1 - \delta_0^2)$. Let $c\coloneqq 0.1$. Then we have
\begin{align}
\tfrac{\sqrt{1 +\|\boldsymbol{\Delta}_0\|_2}/\sqrt{\alpha}}{ \sqrt{1-\|\boldsymbol{\Delta}_{t}\|_2}/\sqrt{\alpha}}\delta_0 &\leq \tfrac{\sqrt{1 + c(1-\delta_0)^2}}{ \sqrt{1-c(1-\delta_0)^2/(1 -\delta_0^2)}} \delta_0 \nonumber \\
&= \tfrac{\sqrt{1 + c(1-\delta_0)^2}}{ \sqrt{1-c(1-\delta_0)/(1 +\delta_0)}} \delta_0 \nonumber \\
&= \tfrac{\sqrt{1+\delta_0 + c(1-\delta_0)^2(1+\delta_0)}}{ \sqrt{1-c +(1+c)\delta_0}} \delta_0 \nonumber
\end{align}
Now, observe that
\begin{align}
\tfrac{\sqrt{1+\delta_0 + c(1-\delta_0)^2(1+\delta_0)}}{ \sqrt{1-c +(1+c)\delta_0}} \delta_0 &\leq \tfrac{2+\delta_0}{3} \nonumber \\
\iff \tfrac{{1+\delta_0 + c(1-\delta_0)^2(1+\delta_0)}}{ {1-c +(1+c)\delta_0}}\delta_0^2 &\leq \tfrac{4+4\delta_0+\delta_0^2}{9} \nonumber\\
\iff (1+c)\delta_0^2 + \delta_0^3 -c\delta_0^4 +c\delta_0^5 &\leq
(4-4c+ 8\delta_0 +8\delta_0^2 +(1+c)\delta_0^3)/9
\nonumber
\end{align}
\begin{align}
\iff c\delta_0^5 - c\delta_0^4 + \tfrac{8-c}{9}\delta_0^3 + \tfrac{1+9c}{9} \delta_0^2 -\tfrac{8}{9}\delta_0 - \tfrac{4-4c}{9} &\leq 0 \label{where}
\end{align}
where \eqref{where} holds for all $\delta_0 \in [0,1)$ and $c=0.1$, therefore we have
\begin{align}
\operatorname{dist}_t \leq \tfrac{\sqrt{1 +\|\boldsymbol{\Delta}_0\|_2}/\sqrt{\alpha}}{ \sqrt{1-\|\boldsymbol{\Delta}_{t}\|_2}/\sqrt{\alpha}}\delta_0 \leq \tfrac{2+\delta_0}{3}. \label{uhu}
\end{align}
Thus, using \eqref{whrr}, we obtain
\begin{align}
\sigma_{\min}^2(\mathbf{B}_{t}^\top\mathbf{B}_\ast)&\geq \tfrac{0.9}{\alpha} \left(1 - \tfrac{4+4\delta_0 +\delta_0^2}{9}\right) \nonumber \\
&\geq \tfrac{0.9}{\alpha} \left(1 - \tfrac{8 +\delta_0^2}{9}\right) \nonumber \\
&= \tfrac{0.9}{9\alpha} E_0\nonumber \\
&= \tfrac{0.1}{\alpha} E_0 \nonumber
\end{align}
as desired.
\end{proof}
\begin{lemma} $\cap_{i\in \mathcal{I}_t} \big(\cap_{h=1}^4 A_{h,t,i}(\tau) \big) \cap A_1(t) \cap A_2(t) \cap A_3(t) \cap A_5(t) \implies A_{3}(t+1).$ \label{lem:a2}
\end{lemma}
\begin{proof}
We aim to write $\boldsymbol{\Delta}_{t+1} = \tfrac{1}{2}(\mathbf{I}_k - \mathbf{P}_t)\boldsymbol{\Delta}_t + \tfrac{1}{2}\boldsymbol{\Delta}_t(\mathbf{I}_k - \mathbf{P}_t) + \mathbf{Z}_t$ for a positive definite matrix $\mathbf{P}_t$ and a perturbation matrix $\mathbf{Z}_t$. This will yield the inequality $\|\boldsymbol{\Delta}_{t+1}\|_2 \leq (1 - \lambda_{\min}(\mathbf{P}_t))\|\boldsymbol{\Delta}_{t}\|_2 + \|\mathbf{Z}_t\|_2$. Assuming $\lambda_{\min}(\mathbf{P}_t)$ and $\|\mathbf{Z}_t\|_2$ scale appropriately (defined later), this inequality combined with inductive hypothesis $A_5(t)$ will give the desired upper bound on $\|\boldsymbol{\Delta}_{t+1}\|_2$ (this is because the upper bound on $\|\mathbf{Z}_t\|_2$ scales with $\operatorname{dist}_t$, so $A_5(t)$ contributes to controlling $\|\mathbf{Z}_t\|_2$). The proof therefore relies on showing the existence of appropriate $\mathbf{P}_t$ and $\mathbf{Z}_t$.
First recall $\boldsymbol{\Delta}_t \coloneqq \mathbf{I} - \alpha\mathbf{B}_t^\top \mathbf{B}_t$ and $\boldsymbol{\bar{\Delta}}_t \coloneqq \mathbf{I}_d - \alpha \mathbf{B}_t \mathbf{B}_t^\top$. Let $\mathbf{G}_t \coloneqq \tfrac{1}{\alpha}(\mathbf{B}_t - \mathbf{B}_{t+1})$, i.e. $\mathbf{G}_t$ satisfies $\mathbf{B}_{t+1}= \mathbf{B}_t - \alpha \mathbf{G}_t$.
Then
\begin{align}
\boldsymbol{\Delta}_{t+1} &= \mathbf{I}_k - \alpha \mathbf{B}_{t+1}^\top \mathbf{B}_{t+1} = \boldsymbol{\Delta}_t + \alpha^2 \mathbf{B}_t^\top \mathbf{G}_t + \alpha^2 \mathbf{G}_t^\top \mathbf{B}_t - \alpha^3 \mathbf{G}_t^\top \mathbf{G}_t \label{del}
\end{align}
The key is showing that $\alpha^2 \mathbf{B}_t^\top \mathbf{G}_t = -\tfrac{1}{2}\boldsymbol{\Delta}_t \mathbf{P}_t + \mathbf{Z}_t'$ for appropriate $\mathbf{P}_t$ and $\mathbf{Z}_t'$. Then, by \eqref{del}, we will have $\boldsymbol{\Delta}_{t+1} = \tfrac{1}{2}(\mathbf{I}_k - \mathbf{P}_t)\boldsymbol{\Delta}_t + \tfrac{1}{2}\boldsymbol{\Delta}_t(\mathbf{I}_k - \mathbf{P}_t) + \mathbf{Z}_t $ as desired, where $\mathbf{Z}_t = \mathbf{Z}_t' + (\mathbf{Z}_t')^\top - \alpha^3 \mathbf{G}_t^\top \mathbf{G}_t$.
Notice that $\mathbf{G}_t$ is the average across clients of the sum of their local gradients on every local update. In particular, we have
\begin{align}
\mathbf{G}_t = (\mathbf{B}_{t}\mathbf{w}_{t}- \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t})\mathbf{w}_{t}^\top +\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\sum_{s = 1}^{\tau-1} (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s}- \mathbf{B}_\ast\mathbf{w}_{\ast,i})\mathbf{w}_{t,i,s}^\top
\end{align}
We will unroll the gradients for the first two local updates only, in order to obtain a negative term that will contribute to the contraction of $\|\boldsymbol{\Delta}_t\|$ (i.e. $\mathbf{P}_t$ will be extracted from the gradients for the first two local updates).
The remaining terms will belong to $\mathbf{Z}_t$ and must be upper bounded (i.e. $\|\boldsymbol{\Delta}_{t+1}\|$ can grow due to local updates beyond the second local update, but we will show that it can't grow too much). In particular, we have
\begin{align}
\mathbf{G}_t &= (\mathbf{B}_{t}\mathbf{w}_{t}- \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t})\mathbf{w}_{t}^\top +\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}(\mathbf{B}_{t,i,1}\mathbf{w}_{t,i,1}- \mathbf{B}_\ast\mathbf{w}_{\ast,i})\mathbf{w}_{t,i,1}^\top \nonumber \\
&\quad +\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\sum_{s = 2}^{\tau-1} (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s}- \mathbf{B}_\ast\mathbf{w}_{\ast,i})\mathbf{w}_{t,i,s}^\top \nonumber \\
&= (\mathbf{B}_{t}\mathbf{w}_{t}- \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t})\mathbf{w}_{t}^\top - \alpha \boldsymbol{\bar{\Delta}}_t \mathbf{B}_\ast \tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top \mathbf{B}_t - \boldsymbol{\bar{\Delta}}_t \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t}\mathbf{w}_t^\top \boldsymbol{\Delta}_t \nonumber \\
&\quad + \tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\alpha^2(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_t^\top \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{t,i,1}^\top
\nonumber \\
&\quad + \tfrac{1}{m}\sum_{i\in \mathcal{I}_t}(\mathbf{B}_t - \alpha(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_t^\top) \boldsymbol{\Delta}_t \mathbf{w}_{t}\mathbf{w}_{t,i,1}^\top \nonumber \\
&\quad+\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\sum_{s = 2}^{\tau-1} (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s}- \mathbf{B}_\ast\mathbf{w}_{\ast,i})\mathbf{w}_{t,i,s}^\top \nonumber
\end{align}
Multiplying both sides by $\mathbf{B}_t^\top$, and using the fact that $\mathbf{B}_t^\top \boldsymbol{\bar{\Delta}}_t = \boldsymbol{\Delta}_t \mathbf{B}_t^\top$, we obtain
\begin{align}
\mathbf{B}_t^\top \mathbf{G}_t &= \mathbf{B}_t^\top(\mathbf{B}_{t}\mathbf{w}_{t}- \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t})\mathbf{w}_{t}^\top - \alpha \boldsymbol{\Delta}_t \mathbf{B}_t^\top \mathbf{B}_\ast \tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top \mathbf{B}_t - \boldsymbol{\Delta}_t \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t}\mathbf{w}_t^\top \boldsymbol{\Delta}_t \nonumber \\
&\quad - \mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\alpha^2(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_t^\top \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{t,i,1}^\top
\nonumber \\
&\quad + \mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}(\mathbf{B}_t - \alpha(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_t^\top) \boldsymbol{\Delta}_t \mathbf{w}_{t}\mathbf{w}_{t,i,1}^\top\nonumber \\
&\quad +\mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\sum_{s = 2}^{\tau-1} (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s}- \mathbf{B}_\ast\mathbf{w}_{\ast,i})\mathbf{w}_{t,i,s}^\top \nonumber \\
&= - \alpha \boldsymbol{\Delta}_t \mathbf{B}_t^\top \mathbf{B}_\ast \tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top \mathbf{B}_t + \mathbf{N}_t \label{61}
\end{align}
where the first term is a negative term that helps $\|\boldsymbol{\Delta}_{t+1}\|$ stay small, and the remaining terms are given by
\begin{align}
\mathbf{N}_t &\coloneqq \mathbf{B}_t^\top(\mathbf{B}_{t}\mathbf{w}_{t}- \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t})\mathbf{w}_{t}^\top - \boldsymbol{\Delta}_t \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t}\mathbf{w}_t^\top \boldsymbol{\Delta}_t \nonumber \\
&\quad - \mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\alpha^2(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_t^\top \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{t,i,1}^\top
\nonumber \\
&\quad + \mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}(\mathbf{B}_t - \alpha(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_t^\top) \boldsymbol{\Delta}_t \mathbf{w}_{t}\mathbf{w}_{t,i,1}^\top \nonumber \\
&\quad+\mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\sum_{s = 2}^{\tau-1} (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s}- \mathbf{B}_\ast\mathbf{w}_{\ast,i})\mathbf{w}_{t,i,s}^\top \nonumber \\
&=\mathbf{B}_t^\top(\mathbf{B}_{t}\mathbf{w}_{t}- \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t})\mathbf{w}_{t}^\top + \mathbf{B}_t^\top\mathbf{B}_t\boldsymbol{\Delta}_t \mathbf{w}_{t}\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\mathbf{w}_{t,i,1}^\top
\nonumber \\
&\quad - \mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\alpha^2(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_t^\top \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{t,i,1}^\top\nonumber \\
&\quad - \mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\alpha(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_t^\top \boldsymbol{\Delta}_t \mathbf{w}_{t}\mathbf{w}_{t,i,1}^\top \nonumber\\
&\quad - \boldsymbol{\Delta}_t \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t}\mathbf{w}_t^\top \boldsymbol{\Delta}_t +\mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\sum_{s = 2}^{\tau-1} (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s}- \mathbf{B}_\ast\mathbf{w}_{\ast,i})\mathbf{w}_{t,i,s}^\top \nonumber \\
&= \underbrace{\mathbf{B}_t^\top(\mathbf{B}_{t}\mathbf{w}_{t}- \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t})\mathbf{{w}}_{t}^\top + \alpha \mathbf{B}_t^\top\mathbf{B}_t\boldsymbol{\Delta}_t \mathbf{w}_{t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t}_{=:\mathbf{E}_1}
\nonumber \\
&\quad -\underbrace{ \tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\alpha \mathbf{B}_t^\top(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{w}_{\ast,i})\mathbf{w}_t^\top \mathbf{w}_{t,i,1}\mathbf{w}_{t,i,1}^\top}_{=:\mathbf{E}_2} \nonumber\\
&\quad + \underbrace{\boldsymbol{\Delta}_t \mathbf{B}_t^\top (\mathbf{B}_t \mathbf{w}_{t} - \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t})\mathbf{w}_t^\top \boldsymbol{\Delta}_t}_{=:\mathbf{E}_3} +\underbrace{\mathbf{B}_t^\top\tfrac{1}{m}\sum_{i\in \mathcal{I}_t}\sum_{s = 2}^{\tau-1} (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s}- \mathbf{B}_\ast\mathbf{w}_{\ast,i})\mathbf{w}_{t,i,s}^\top}_{=:\mathbf{E}_4} \label{split}
\end{align}
To get from the first to the second equation we expanded the fourth term in the first equation. We need to upper bound the spectral norm of each of these terms.
The matrices $\mathbf{E}_2$ and $\mathbf{E}_3$ are straightforward to control; we will take care of them shortly. For now we are concerned with $\mathbf{E}_1$. In order to control this matrix, we must use the fact that $\mathbf{w}_t$ is close to a matrix times $\mathbf{\bar{w}}_{\ast,t}$. This will allow us to subsume the dominant term from $\mathbf{E}_1$ into the negative term in \eqref{61}.
In particular, note that by $A_1(t)$, we have $\mathbf{w}_t = \alpha \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} + \alpha\boldsymbol{\Delta}_{t} \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} + \mathbf{h}_t$, where $\|\mathbf{h}_t\|_2 \leq 91 \alpha^{2.5} \tau L_{\max}^3 $.
This implies that
\begin{align}
\mathbf{B}_t^\top(\mathbf{B}_{t}\mathbf{w}_{t}- \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t}) &= \mathbf{B}_t^\top(\alpha \mathbf{B}_{t}\mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} - \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t}) + \alpha \boldsymbol{\Delta}_t\mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{h}_{t} \nonumber\\
&= -\boldsymbol{\Delta}_t \mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \alpha \boldsymbol{\Delta}_t\mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{h}_{t} \nonumber\\
&= -\boldsymbol{\Delta}_t^2 \mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t} + \mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{h}_{t}
\end{align}
Making this substitution in $\mathbf{E}_1$, we obtain,
\begin{align}
\mathbf{E}_1&= -\boldsymbol{\Delta}_t^2 \mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t}\mathbf{{w}}_{t}^\top + \mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{h}_{t} \mathbf{{w}}_{t}^\top + \alpha \mathbf{B}_t^\top\mathbf{B}_t\boldsymbol{\Delta}_t \mathbf{w}_{t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t \nonumber \\
&= -\boldsymbol{\Delta}_t^2 \mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t}\mathbf{{w}}_{t}^\top + \mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{h}_{t} \mathbf{{w}}_{t}^\top -\boldsymbol{\Delta}_t^2 \mathbf{w}_{t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t + \boldsymbol{\Delta}_t \mathbf{w}_{t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t \nonumber \\
&= -\boldsymbol{\Delta}_t^2 \mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t}\mathbf{{w}}_{t}^\top + \mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{h}_{t} \mathbf{{w}}_{t}^\top -\boldsymbol{\Delta}_t^2 \mathbf{w}_{t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t \nonumber \\
&\quad + \boldsymbol{\Delta}_t(\alpha\boldsymbol{\Delta}_{t} \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t}+\mathbf{h}_t) \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t + \alpha \boldsymbol{\Delta}_t \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t. \label{above}
\end{align}
The dominant term in \eqref{above} is the last term. Specifically, we have,
\begin{align}
\|\mathbf{E}_1 - &\alpha \boldsymbol{\Delta}_t \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t \|\nonumber \\
&\leq \| \boldsymbol{\Delta}_t^2 \mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t}\mathbf{{w}}_{t}^\top\| + \|\mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{h}_{t} \mathbf{{w}}_{t}^\top\| + \|\boldsymbol{\Delta}_t^2 \mathbf{w}_{t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t \| \nonumber \\
&\quad + \|\boldsymbol{\Delta}_t(\alpha\boldsymbol{\Delta}_{t} \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t}+\mathbf{h}_t) \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t\| \nonumber \\
&\leq \| \boldsymbol{\Delta}_t^2 \mathbf{B}_t^\top\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t}\mathbf{{w}}_{t}^\top\| + \|\boldsymbol{\Delta}_t^2 \mathbf{w}_{t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t \| +\alpha\|\boldsymbol{\Delta}_t^2 \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t\| \nonumber \\
&\quad +\|\mathbf{B}_t^\top \mathbf{B}_{t}\mathbf{h}_{t} \mathbf{{w}}_{t}^\top\| + \|\boldsymbol{\Delta}_t\mathbf{h}_t \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t\| \nonumber \\
&\leq 5.5 c_3^2 \alpha^4 \tau^2 L_{\max}^6 \kappa_{\max}^4 E_0^{-2} + 2.2\times 91 \alpha^2 \tau L_{\max}^4 + 1.1 \times 91 c_3\alpha^4 \tau^2 L_{\max}^6 \kappa_{\max}^2 E_0^{-1} \label{rrmm} \\
&\leq (206 + 101/c_3) \alpha^2 \tau L_{\max}^4
\label{rrm}
\end{align}
where \eqref{rrmm} follows by applying the Cauchy-Schwarz inequality to each of the terms in the previous inequality, and using $A_2(t), A_3(t)$, and our bound on $\mathbf{h}_t$ (from $A_1(t)$), and \eqref{rrm} follows as $\alpha$ is sufficiently small.
The last first term term can be subsumed by completing a square as follows.
Combining \eqref{61}, \eqref{split} and \eqref{above} yield
\begin{align}
\mathbf{B}_t^\top \mathbf{G}_t &= - \alpha \boldsymbol{\Delta}_t \mathbf{B}_t^\top \mathbf{B}_\ast \tfrac{1}{m}\sum_{i\in\mathcal{I}_t}\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top \mathbf{B}_t + \mathbf{E}_1 - \mathbf{E}_2 +\mathbf{E}_3 + \mathbf{E}_4 \nonumber \\
&= - \alpha \boldsymbol{\Delta}_t \mathbf{B}_t^\top \mathbf{B}_\ast \tfrac{1}{m}\sum_{i\in\mathcal{I}_t}\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top \mathbf{B}_t + \alpha \boldsymbol{\Delta}_t \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t \nonumber \\
&\quad + (\mathbf{E}_1 - \alpha \boldsymbol{\Delta}_t \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t) - \mathbf{E}_2 +\mathbf{E}_3 + \mathbf{E}_4
\nonumber \\
&= - \alpha \boldsymbol{\Delta}_t \mathbf{B}_t^\top \mathbf{B}_\ast \tfrac{1}{m}\sum_{i\in\mathcal{I}_t} (\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})(\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})^\top\mathbf{B}_\ast^\top \mathbf{B}_t \nonumber \\
&\quad + (\mathbf{E}_1 - \alpha \boldsymbol{\Delta}_t \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t) - \mathbf{E}_2 +\mathbf{E}_3 + \mathbf{E}_4
\nonumber \\
&= - \tfrac{1}{2\alpha^2} \boldsymbol{\Delta}_t \mathbf{P}_t + \tfrac{1}{\alpha^2}\mathbf{Z}'_t
\end{align}
where $\mathbf{P}_t = 2\alpha^3\mathbf{B}_t^\top \mathbf{B}_\ast \tfrac{1}{m}\sum_{i\in\mathcal{I}_t} (\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})(\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})^\top\mathbf{B}_\ast^\top \mathbf{B}_t$ and
\begin{align}
\mathbf{Z}'_t &:= \alpha^2(\mathbf{E}_1 - \alpha \boldsymbol{\Delta}_t \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t) - \alpha^2\mathbf{E}_2 +\alpha^2\mathbf{E}_3 + \alpha^2\mathbf{E}_4 \nonumber
\end{align}
we have performed the desired decomposition; it remains to show that $\lambda_{\min}(\mathbf{P}_t)$ and $\|\mathbf{Z}'_t\|_2$ scale appropriately.
First we lower bound $\lambda_{\min}(\mathbf{P}_t)$.
\begin{align}
\lambda_{\min}(\mathbf{P}_t) &= \lambda_{\min}\left(2\alpha^3\mathbf{B}_t^\top \mathbf{B}_\ast \tfrac{1}{m}\sum_{i\in\mathcal{I}_t} (\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})(\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})^\top\mathbf{B}_\ast^\top \mathbf{B}_t\right) \nonumber \\
&\geq 2 \alpha^3 \sigma_{\min}(\mathbf{B}_t^\top \mathbf{B}_\ast)^2 \lambda_{\min}\left(\tfrac{1}{m}\sum_{i\in\mathcal{I}_t} (\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})(\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})^\top\right) \nonumber \\
&\geq 0.2 \alpha^2 E_0 \lambda_{\min}\left(\tfrac{1}{m}\sum_{i\in\mathcal{I}_t} (\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})(\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast,t})^\top\right) \label{e0} \\
&\geq 0.2 \alpha^2 E_0 \lambda_{\min}\left(\tfrac{1}{M }\sum_{i=1}^M (\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast})(\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast})^\top\right) \nonumber \\
&\quad - 0.2 \alpha^2 E_0 \bigg\|\tfrac{1}{m}\sum_{i\in\mathcal{I}_t} \mathbf{w}_{\ast,i} \mathbf{w}_{\ast,i}^\top - \tfrac{1}{M}\sum_{i'=1}^M \mathbf{w}_{\ast,i'} \mathbf{w}_{\ast,i'}^\top \bigg\| \nonumber \\
&\quad - 0.2 \alpha^2 E_0 \big\| \mathbf{w}_{\ast,t} \mathbf{w}_{\ast,t}^\top - \mathbf{\bar{w}}_{\ast} \mathbf{\bar{w}}_{\ast}^\top \big\| \nonumber \\
&\geq 0.15 \alpha^2 E_0 \mu^2 - 6\alpha^4 E_0 L_{\max}^4 \label{e00} \\
&\geq 0.15 \alpha^2 E_0 \mu^2 \label{e000}
\end{align}
where \eqref{e0} follows by Lemma \ref{lem:distlb}, \eqref{e00} follows by Assumption \ref{assump:td} and $A_0$, and \eqref{e000} follows as $\alpha^2\leq \frac{1}{120\kappa_\ast^2 L_{\max}^2}$.
Now we upper bound $\|\mathbf{Z}'_t\|_2$. We have already upper bounded $\|\mathbf{E}_1 - \alpha \boldsymbol{\Delta}_t \mathbf{B}_{t}^\top \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast,t} \mathbf{\bar{w}}_{\ast,t}^\top \mathbf{B}_\ast^\top \mathbf{B}_t\|$ in \eqref{rrm}. We next upper bound $\|\mathbf{E}_2\|_2$ and $\|\mathbf{E}_3\|_2$ by $A_2(t), A_{3}(t),$ and $A_{2,i,t}(1)$. We have
\begin{align}
\|\alpha^2\mathbf{E}_2\|_2 &\leq 32
\alpha^4 L_{\max}^4 \nonumber \\
\|\alpha^2\mathbf{E}_3\|_2 &\leq 28c_3^2 \alpha^6 \tau^2 L_{\max}^6\kappa_{\max}^2 E_0^{-2} \nonumber
\end{align}
using the triangle and Cauchy-Schwarz inequalities. Now we turn to $\|\alpha^2\mathbf{E}_4\|_2$. Recall that $\mathbf{E}_4$ is the sum of local gradients across all clients and all local updates beyond the first local update. We show that these gradients are sufficiently small such that $\|\boldsymbol{\Delta}_{t+1}\|_2$ cannot grow beyond the desired threshold.
Recall that $\mathbf{E}_4 = \sum_{s=2}^{\tau-1} \mathbf{B}_t^\top \mathbf{e}_{t,i,s}\mathbf{w}_{t,i,s}^\top$. To bound this sum it is critical to control the evolution of $\mathbf{e}_{t,i,s}$. The idea is to split $\mathbf{e}_{t,i,s}$ into its projection onto $\operatorname{col}(\mathbf{B}_{t,i,s-1})\approx \operatorname{col}(\mathbf{B}_t)$ and its projection onto $\operatorname{col}(\mathbf{B}_{t,i,s-1})^\perp\approx \operatorname{col}(\mathbf{B}_t)^\perp.$ Then, we can show that the magnitude of the projection onto $\operatorname{col}(\mathbf{B}_{t,i,s-1})$ is going to zero very fast (the head is quickly learned, meaning it fits the product as much as it can with what it has to work with, i.e. $\operatorname{col}(\mathbf{B}_{t,i,s-1})$). On the other hand, the magnitude of the projection onto $\operatorname{col}(\mathbf{B}_{t,i,s-1})^\perp$ is slowly going to zero, since this reducing this error requires changing the representation and the representation changes slower than the head. The saving grace is that this error is proportional to $\operatorname{dist}(\mathbf{B}_{t,i,s-1},\mathbf{B}_\ast)$, which for all $s$ is linearly converging to zero with $t$.
To show this, pick any $i\in\mathcal{I}_t$ and let
$\mathbf{\hat{B}}_{t,i,s},\mathbf{R}_{t,i,s}$ denote the QR-factorization of $\mathbf{B}_{t,i,s}$. Define $\tilde{\boldsymbol{\Delta}}_{t,i,s-1} \coloneqq \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top - \alpha \mathbf{B}_{t,i,s-1}\mathbf{B}_{t,i,s-1}^\top$ and $\omega_{t,i,s-1} \coloneqq \alpha \mathbf{w}_{t,i,s-1}^\top \boldsymbol{\Delta}_{t,i,s-1}\mathbf{w}_{t,i,s} + \alpha^2 \mathbf{w}_{t,i,s-1}^\top \mathbf{B}_{t,i,s-1}^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i}$. By expanding $\mathbf{e}_{t,i,s}$, we find
\begin{align}
&\mathbf{e}_{t,i,s}\nonumber \\
&= (\mathbf{I}_d - \alpha \mathbf{B}_{t,i,s-1}\mathbf{B}_{t,i,s-1}^\top - \alpha \mathbf{w}_{t,i,s-1}^\top \boldsymbol{\Delta}_{t,i,s-1}\mathbf{w}_{t,i,s}\mathbf{I}_d - \alpha^2 \mathbf{w}_{t,i,s-1}^\top \mathbf{B}_{t,i,s-1}^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i}\mathbf{I}_d)\mathbf{e}_{t,i,s-1} \nonumber \\
&= (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{e}_{t,i,s-1} + \big( \tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big)\mathbf{e}_{t,i,s-1} \nonumber \\
&= (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{e}_{t,i,s-1} + \big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big) (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2} \nonumber \\
&\quad + \big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big) \big(\tilde{\boldsymbol{\Delta}}_{t,i,s-2} - \omega_{t,i,s-2}\mathbf{I}_d\big)\mathbf{e}_{t,i,s-2}
\end{align}
Therefore,
\begin{align}
\mathbf{B}_t^\top \mathbf{e}_{t,i,s}
&= \mathbf{B}_t^\top (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{e}_{t,i,s-1} \nonumber \\
& \quad + \mathbf{B}_t^\top\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big) (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2} \nonumber \\
&\quad + \mathbf{B}_t^\top\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big) \big(\tilde{\boldsymbol{\Delta}}_{t,i,s-2} - \omega_{t,i,s-2}\mathbf{I}_d\big)\mathbf{e}_{t,i,s-2} \label{3terms}
\end{align}
For the first term, we have
\begin{align}
\|\mathbf{B}_t^\top (\mathbf{I}_d -& \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{e}_{t,i,s-1}\|_2\nonumber \\
&\leq \|\mathbf{B}_{t,i,s-1}^\top (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{e}_{t,i,s-1}\|_2\nonumber \\
&\quad + \|(\mathbf{B}_t - \mathbf{B}_{t,i,s-1})^\top (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{e}_{t,i,s-1}\|_2 \nonumber \\
&= \|(\mathbf{B}_t - \mathbf{B}_{t,i,s-1})^\top (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{e}_{t,i,s-1}\|_2 \label{eq}\\
&\leq \| (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{e}_{t,i,s-1}\|_2 \sum_{r=1}^{s-1}\|\mathbf{B}_{t,i,r} - \mathbf{B}_{t,i,r-1} \|_2 \label{suum} \\
&\leq 7 \| (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{B}_\ast \mathbf{w}_{\ast,i}\|_2 \alpha^{1.5} \tau L_{\max}^2 \label{suuum} \\
&\leq 8\alpha^{1.5} \tau L_{\max}^3 \operatorname{dist}_t \label{laast}
\end{align}
where \eqref{eq} follows since $\mathbf{B}_{t,i,s-1}^\top(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top) = \mathbf{0}$, \eqref{suum} follows using the Cauchy-Schwarz and triangle inequalities, \eqref{suuum} follows using that $(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{B}_{t,i,s-1} = \mathbf{0}$ and applying $A_{2,t,i}(\tau)$ and $A_{3,t,i}(\tau)$, \eqref{laast} follows by the fact that $\|(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-1}\mathbf{\hat{B}}_{t,i,s-1}^\top)\mathbf{B}_\ast\|= \operatorname{dist}(\mathbf{B}_{t,i,s}, \mathbf{B}_\ast) \leq 1.1\operatorname{dist}_t$ by $A_{4,t,i}(\tau)$.
For the second term in \eqref{3terms}, note that
\begin{align}
|\omega_{t,i,s-1}| &\leq \alpha|\mathbf{w}_{t,i,s-1}^\top \boldsymbol{\Delta}_{t,i,s-1}\mathbf{w}_{t,i,s-1}| + \alpha^2|\mathbf{w}_{t,i,s-1}^\top \mathbf{B}_{t,i,s-1}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}|\nonumber \\
&\leq 8 c_3 \alpha^{4} \tau L_{\max}^4 \kappa_{\max}^2 E_0^{-1} + 2.2 \alpha^{1.5} L_{\max}^2 \nonumber\\
&\leq 3\alpha^{2} L_{\max}^2
\end{align}
As a result, we have
\begin{align}
\| \mathbf{B}_t^\top\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1}& - \omega_{t,i,s-1}\mathbf{I}_d\big) (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber \\
&\leq \| \mathbf{B}_t^\top \tilde{\boldsymbol{\Delta}}_{t,i,s-1} (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber \\
&\quad + |\omega_{t,i,s-1} |\| \mathbf{B}_t^\top (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber \\
&\leq \| \mathbf{B}_t^\top \tilde{\boldsymbol{\Delta}}_{t,i,s-1} (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber \\
&\quad + 3.3 \alpha^{1.5} L_{\max}^2\| (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{B}_{\ast}\mathbf{w}_{\ast,i}\|_2 \nonumber \\
&\leq \| \mathbf{B}_t^\top \tilde{\boldsymbol{\Delta}}_{t,i,s-1} (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber \\
&\quad + 3.7 \alpha^{1.5} L_{\max}^3 \operatorname{dist}_t \label{42}
\end{align}
where \eqref{42} follows by $A_{4,t,i}(\tau)$, and
\begin{align}
\| &\mathbf{B}_t^\top \tilde{\boldsymbol{\Delta}}_{t,i,s-1} (\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber\\
&\leq \| \mathbf{B}_t^\top \mathbf{\hat{B}}_{t,i,s-1} \mathbf{\hat{B}}_{t,i,s-1}^\top(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber \\
&\quad + \alpha\| \mathbf{B}_t^\top \mathbf{{B}}_{t,i,s-1} \mathbf{{B}}_{t,i,s-1}^\top(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber \\
&= \| \mathbf{B}_t^\top \mathbf{\hat{B}}_{t,i,s-1} (\mathbf{R}^{-1}_{t,i,s-1})^\top \mathbf{{B}}_{t,i,s-1}^\top(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber \\
&\quad + \alpha\| \mathbf{B}_t^\top \mathbf{{B}}_{t,i,s-1} \mathbf{{B}}_{t,i,s-1}^\top(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber \\
&=\alpha \| \mathbf{B}_t^\top \mathbf{\hat{B}}_{t,i,s-1} (\mathbf{R}^{-1}_{t,i,s-1})^\top \mathbf{{w}}_{t,i,s-2} \mathbf{e}_{t,i,s-2}^\top(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \nonumber\\
&\quad + \alpha^2\| \mathbf{B}_t^\top \mathbf{{B}}_{t,i,s-1} \mathbf{{w}}_{t,i,s-2} \mathbf{{e}}_{t,i,s-2}^\top(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top)\mathbf{e}_{t,i,s-2}\|_2 \label{hgh} \\
&\leq 44 \alpha^{1.5} L_{\max}^3 \operatorname{dist}_t \label{44}
\end{align}
where \eqref{hgh} follows since $\mathbf{B}_{t,i,s-2}(\mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-2}\mathbf{\hat{B}}_{t,i,s-2}^\top) = \mathbf{0}$ and \eqref{44} follows using the Cauchy-Schwarz inequality, $A_3(t)$, $A_{2,t,i}(\tau)$, $A_{3,t,i}(\tau)$, and $A_{4,t,i}(\tau)$. Next, recalling that $\mathbf{\hat{B}}_{t,i,s}\mathbf{R}_{t,i,s}$ is the QR-factorization of $\mathbf{{B}}_{t,i,s}$, we have, for any $s$,
\begin{align}
\|\tilde{\boldsymbol{\Delta}}_{t,i,s-1}\| &= \|\mathbf{\hat{B}}_{t,i,s-1} \mathbf{\hat{B}}_{t,i,s-1}^\top - \alpha \mathbf{{B}}_{t,i,s-1} \mathbf{{B}}_{t,i,s-1}^\top\| \nonumber \\
&\leq \|\mathbf{\hat{B}}_{t,i,s-1}(\mathbf{I}_k - \alpha \mathbf{R}_{t,i,s-1} \mathbf{R}_{t,i,s-1}^\top)\mathbf{\hat{B}}_{t,i,s-1}^\top \| \nonumber \\
&\leq \|\mathbf{I}_k - \alpha \mathbf{R}_{t,i,s-1} \mathbf{R}_{t,i,s-1}^\top \| \nonumber \\
&\leq \max(|1 - \alpha \sigma_{\min}^2(\mathbf{B}_{t,i,s-1})|, |1 - \alpha \sigma_{\max}^2(\mathbf{B}_{t,i,s-1})| ) \label{ggg} \\
&\leq \max(|1 - \alpha \tfrac{1 - \|\boldsymbol{\Delta}_{t,i,s-1}\|}{\alpha}|, |1 - \alpha \tfrac{1 + \|\boldsymbol{\Delta}_{t,i,s-1}\|}{\alpha})| ) \nonumber \\
&= \|\boldsymbol{\Delta}_{t,i,s-1}\| \nonumber \\
&\leq 2c_3\alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} \label{gg}
\end{align}
where \eqref{ggg} follows by Weyl's inequality and \eqref{gg} follows
by $A_{3,t,i}(s-1)$. Furthermore,
$
\|\tilde{\boldsymbol{\Delta}}_{t,i,s-1} +\omega_{t,i,s-1}\mathbf{I}_d\| \leq 2c_3\alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} + 3 \alpha^2L_{\max}^2 \leq 3 c_3\alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1}
$
for any $s$.
Thus, for the third term in \eqref{3terms}, for any $s>2$,
\begin{align}
\| &\mathbf{B}_t^\top\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big) \big(\tilde{\boldsymbol{\Delta}}_{t,i,s-2} - \omega_{t,i,s-2}\mathbf{I}_d\big)\mathbf{e}_{t,i,s-2} \|_2 \nonumber \\
&= \| \mathbf{B}_t^\top\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big) \big(\tilde{\boldsymbol{\Delta}}_{t,i,s-2} - \omega_{t,i,s-2}\mathbf{I}_d\big)( \tilde{\boldsymbol{\Delta}}_{t,i,s-3} - \omega_{t,i,s-3}\mathbf{I}_d)\mathbf{e}_{t,i,s-3} \|_2\nonumber \\
&\quad + \|\mathbf{B}_t^\top\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big) \big(\tilde{\boldsymbol{\Delta}}_{t,i,s-2} - \omega_{t,i,s-2}\mathbf{I}_d\big)( \mathbf{I}_d - \mathbf{\hat{B}}_{t,i,s-3}\mathbf{\hat{B}}_{t,i,s-3}^\top)\mathbf{e}_{t,i,s-3} \|_2 \nonumber \\
&\leq \| \mathbf{B}_t^\top\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big) \big(\tilde{\boldsymbol{\Delta}}_{t,i,s-2} - \omega_{t,i,s-2}\mathbf{I}_d\big)( \tilde{\boldsymbol{\Delta}}_{t,i,s-3} - \omega_{t,i,s-3}\mathbf{I}_d)\mathbf{e}_{t,i,s-3} \|_2 \nonumber \\
&\quad + 10 c_3^2\alpha^{3.5} \tau^2 L^5_{\max} \kappa_{\max}^4 E_0^{-2} \operatorname{dist}_t \nonumber \\
&\vdots \nonumber \\
&\leq \bigg\|\mathbf{B}_t^\top\prod_{r=1}^s\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-r} - \omega_{t,i,s-r}\mathbf{I}_d\big) \mathbf{e}_{t,i,s-r}\bigg\|_2 \nonumber \\
&\quad + 10 c_3^2 \alpha^{3.5} \tau^2 L^5_{\max} \kappa^4_{\max}E_0^{-2} \operatorname{dist}_t \sum_{r=0}^s (3c_3)^r\alpha^{2r}\tau^r L_{\max}^{2r} \kappa_{\max}^{2r} E_0^{-r}\nonumber \\
&\leq \bigg\|\mathbf{B}_t^\top\prod_{r=1}^s\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-r} - \omega_{t,i,s-r}\mathbf{I}_d\big) \mathbf{e}_{t,i,s-r}\bigg\|_2 + \frac{ 10c_3^2 \alpha^{3.5} \tau^2 L^5_{\max} \kappa_{\max}^4 E_{0}^{-2} \operatorname{dist}_t}{1 - 3c_3 \alpha^{2} \tau L^2_{\max} \kappa_{\max}^2 E_0^{-1}} \nonumber \\
&\leq 3.5 \times (3 c_3)^s \alpha^{2s -0.5}\tau^s{L_{\max}^{2s+1} }\kappa_{\max}^{2s}E_0^{-s} + { 15 c_3^2 \alpha^{3.5} \tau^2 L_{\max}^5 \kappa_{\max}^4 E_0^{-2} \operatorname{dist}_t} \label{45}
\end{align}
and for $s=2$ we have
\begin{align}
\| \mathbf{B}_t^\top\big(\tilde{\boldsymbol{\Delta}}_{t,i,s-1} - \omega_{t,i,s-1}\mathbf{I}_d\big)& \big(\tilde{\boldsymbol{\Delta}}_{t,i,s-2} - \omega_{t,i,s-2}\mathbf{I}_d\big)\mathbf{e}_{t,i,s-2} \|_2 \nonumber \\
&\leq 3.5\times (3c_3)^2 \alpha^{3.5} \tau^{2} L_{\max}^{5}\kappa_{\max}^{4}E_0^{-2}. \label{46}
\end{align}
Thus, using $\|\mathbf{w}_{t,i,s}\|_2\leq 2 \sqrt{\alpha}L_{\max}$ with \eqref{3terms}, \eqref{laast}, \eqref{42}, \eqref{44}, \eqref{45}, and \eqref{46}, we have
\begin{align}
\| \alpha^2 \mathbf{E}_4 \|_2 &\leq 2 \alpha^{2.5} L_{\max} \sum_{s=2}^{\tau-1} \bigg(3.5 \times (3c_3)^2\alpha^{2s-0.5}\tau^s L_{\max}^{2s+1}\kappa_{\max}^{2s} E_0^{-2s}\nonumber\\
&\quad \quad \quad \quad \quad \quad \quad\quad + 15c_3^2\alpha^{3.5} \tau^2 L_{\max}^5 \kappa_{\max}^4 \operatorname{dist}_t + (8 \tau + 48)\alpha^{1.5} L_{\max}^3 \operatorname{dist}_t \bigg)\nonumber \\
&\leq \frac{ 63 c_3^2 \alpha^{6}\tau^{2} L_{\max}^6 \kappa_{\max}^4 E_0^{-2} }{1 - 3 c_s \alpha^{2}\tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} } + (30c_3^2\alpha^{6} \tau^3 L_{\max}^6 \kappa_{\max}^4E_0^{-2} + 66\alpha^{4} \tau^2 L_{\max}^4 )\operatorname{dist}_t \nonumber \\
&\leq
90 c_3^2 \alpha^{6}\tau^{2} L_{\max}^6 \kappa_{\max}^4 E_0^{-2} + 94\alpha^{4} \tau^2 L_{\max}^4 \operatorname{dist}_t \nonumber
\end{align}
where the last inequality follows by choice of $\alpha$.
Combining all terms, we obtain
\begin{align}
\|\boldsymbol{\Delta}_{t+1}\|_2 &\leq (1 - 0.15 \alpha^2 E_0 \mu^2 )\|\boldsymbol{\Delta}_t\|_2 + (206 + 101/c_3) \alpha^4 \tau L_{\max}^4 + 32
\alpha^4 L_{\max}^4 \nonumber
\\
&\quad + 118 c_3^2\alpha^{6}\tau^{2} L_{\max}^6 \kappa_{\max}^4 E_0^{-2} + 94\alpha^{4} \tau^2 L_{\max}^4 \operatorname{dist}_t \nonumber \\
&\leq (1 - 0.15 \alpha^2 E_0 \mu^2 )\|\boldsymbol{\Delta}_t\|_2 + (340 + 101/c_3) \alpha^4 \tau L_{\max}^4 + 94\alpha^{4} \tau^2 L_{\max}^4 \operatorname{dist}_t \label{leq} \\
&\quad \vdots \nonumber \\
&\leq (1 - 0.15 \alpha^2 E_0 \mu^2 )^t\|\boldsymbol{\Delta}_0\|_2 \nonumber \\
&\quad + \sum_{t' = 1}^t (1 - 0.15 \alpha^2 E_0 \mu^2)^{t-t'} \big( (340 + 101/c_3) \alpha^4 \tau L_{\max}^4 + 94\alpha^{4} \tau^2 L_{\max}^4 \operatorname{dist}_{t'}\big) \nonumber \\
&\leq \|\boldsymbol{\Delta}_0\|_2 + (340 + 101/c_3) \alpha^4 \tau L_{\max}^4 \sum_{t' = 1}^t (1 - 0.15\alpha^2 E_0 \mu^2)^{t-t'} \nonumber \\
&\quad + 94\alpha^{4} \tau^2 L_{\max}^4\sum_{t' = 1}^t (1 - 0.04 \alpha^2 \tau E_0 \mu^2 )^{t'} \label{ms13} \\
&\leq \|\boldsymbol{\Delta}_0\|_2 + ({7(340 + 101/c_3)+25\times 94} ) \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} \nonumber \\
&\leq \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 + ({4730+ 101/c_3} ) \alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} \nonumber \\
&\leq c_3\alpha^2 \tau L_{\max}^2 \kappa_{\max}^2
\end{align}
where \eqref{leq} follows by choice of $\alpha \leq \tfrac{1 - \delta_0}{c_3\sqrt{\tau} L_{\max}^2 \kappa_{\max}^2}\leq \tfrac{E_0}{c_3\sqrt{\tau} L_{\max}^2 \kappa_{\max}^2 }$, \eqref{ms13} follows from $A_5(t)$, and the last inequality is due to $c_3 = 4800$.
\end{proof}
\begin{lemma} \label{lem:a3}
$\cap_{i\in \mathcal{I}_t}\big(A_{1,t,i}(\tau) \cap A_{2,t,i}(\tau)\cap A_{3,t,i}(\tau)\big) \cap A_2(t) \implies A_{4}(t+1)$.
\end{lemma}
\begin{proof}
We have \begin{align}
\mathbf{B}_{t+1} &= \mathbf{{B}}_{t} \bigg(\frac{1}{m} \sum_{i\in \mathcal{I}_t} \prod_{s=0}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top)\bigg)\nonumber \\
& \quad+ \mathbf{\hat{B}}_\ast \bigg(\frac{\alpha}{m} \sum_{i\in \mathcal{I}_t} \mathbf{w}_{\ast,i} \sum_{s=0}^{\tau-1}\mathbf{w}_{t,i,s}^\top \prod_{r=s+1}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,r}\mathbf{w}_{t,i,r}^\top) \bigg) \nonumber
\end{align}
which implies
\begin{align}
\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t+1} &= \mathbf{B}_{\ast,\perp}^\top\mathbf{{B}}_{t} (\mathbf{I} - \alpha \mathbf{w}_t \mathbf{w}_t^\top) \left(\frac{1}{m} \sum_{i\in \mathcal{I}_t} \prod_{s=1}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top)\right) \label{ssslast}
\end{align}
We can expand the right product of $\mathbf{B}_t (\mathbf{I} - \alpha \mathbf{w}_t \mathbf{w}_t^\top)$ using the binomial expansion as follows:
\begin{align}
\frac{1}{m} \sum_{i\in \mathcal{I}_t} \prod_{s=1}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top) &= \mathbf{I}_k - \frac{\alpha}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top\nonumber \\
&\quad + \frac{\alpha^2}{m} \sum_{i\in \mathcal{I}_t} \sum_{s=1}^{\tau-1} \sum_{s^{(1)}=s+1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top\mathbf{w}_{t,i,s^{(1)}}\mathbf{w}_{t,i,s^{(1)}}^\top \nonumber \\
&\quad - \dots + \operatorname{sign}(\tau)\frac{\alpha^{\tau}}{m} \sum_{i\in \mathcal{I}_t} \prod_{s=1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \nonumber
\end{align}
Recall that each $\|\mathbf{w}_{t,i,s}\|_2 \leq 2\sqrt{\alpha}L_{\max}$. Thus, after the identity, the spectral norm of the first set of summations has spectral norm at most $4\alpha^2 \tau L_{\max}^2 $, the second set has specral norm at most $16\alpha^4 \tau^2 L_{\max}^4$, and so on.
We in fact use the first set of summations as a negative term, and bound all subsequent sets of summations as errors, exploiting the fact that their norms are geometrically decaying. In particular, we have:
\begin{align}
\left\|\frac{1}{m} \sum_{i\in \mathcal{I}_t} \prod_{s=1}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top) \right\|_2 &\leq \left\| \mathbf{I}_k - \frac{\alpha}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \right\|_2 + \sum_{z=2}^{\tau-1}(4\alpha^2 \tau L_{\max}^2)^z \nonumber \\
&\leq \left\| \mathbf{I}_k - \frac{\alpha}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \right\|_2 + \frac{4\alpha^4 \tau^2 L_{\max}^4}{1 - 4\alpha^2 \tau L_{\max}^2}\nonumber \\
&\leq \left\| \mathbf{I}_k - \frac{\alpha}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \right\|_2 + {5\alpha^4 \tau^2 L_{\max}^4} \label{sslast}
\end{align}
Next, we use $\|\mathbf{w}_{t,i,s} - \alpha \mathbf{B}_{t,i,s-1}^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i}\| \leq 4 c_3 \alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2 E_0^{-1} $ for all $s\geq 1$
to obtain
\begin{align}
\left\| \mathbf{I}_k - \frac{\alpha}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top \right\|_2 &\leq \left\| \mathbf{I}_k - \frac{\alpha^3}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{B}_{t,i,s-1}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t,i,s-1} \right\|_2 \nonumber \\
&\quad + 13 c_3 \alpha^4 \tau^2 L_{\max}^4 \kappa_{\max}^2 E_0^{-1} \label{slast}
\end{align}
Next, we have for any $s-1 \in \{1,\dots,\tau-1\}$,
\begin{align}
\| \mathbf{B}_{t,i,s-1} - \mathbf{B}_t \|_2 = \| \mathbf{B}_{t,i,s-1} - \mathbf{B}_{t,i,0} \|_2 &\leq \sum_{r = 1}^{s-1} \| \mathbf{B}_{t,i,r} - \mathbf{B}_{t,i,r-1} \|_2 \nonumber \\
&\leq \alpha \sum_{r = 1}^{s-1} \|\mathbf{e}_{t,i,r-1}\|_2 \|\mathbf{w}_{t,i,r-1}\|_2 \nonumber \\
&\leq 7\alpha^{1.5} (s-1) L_{\max}^2 \nonumber
\end{align}
Thus,
\begin{align}
\bigg\| \mathbf{I}_k - \frac{\alpha^3}{m} \sum_{i\in \mathcal{I}_t} &\sum_{s = 1}^{\tau-1} \mathbf{B}_{t,i,s-1}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t,i,s-1} \bigg\|_2 \nonumber \\
&\leq \left\| \mathbf{I}_k - \frac{\alpha^3}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t} \right\|_2 \nonumber \\
&\quad + \left\|\frac{\alpha^3}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} (\mathbf{B}_{t} - \mathbf{B}_{t,i,s-1} )^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t,i,s-1} \right\|_2 \nonumber \\
&\quad + \left\|\frac{\alpha^3}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top(\mathbf{B}_t - \mathbf{B}_{t,i,s-1}) \right\|_2 \nonumber\\
&\leq \left\| \mathbf{I}_k - \frac{\alpha^3}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t} \right\|_2 + 16 \alpha^4 (\tau-1)^2 L_{\max}^4. \label{comb}
\end{align}
Furtheromre,
\begin{align}
&\left\| \mathbf{I}_k - \tfrac{\alpha^3}{m} \sum_{i\in \mathcal{I}_t} \sum_{s = 1}^{\tau-1} \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t} \right\|_2 \nonumber \\
&= \left\| \mathbf{I}_k - \tfrac{\alpha^3(\tau-1)}{m} \sum_{i\in \mathcal{I}_t} \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t} \right\|_2 \nonumber \\
&\leq \left\| \mathbf{I}_k - \tfrac{\alpha^3(\tau-1)}{M} \sum_{i=1}^M \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t} \right\|_2 \nonumber \\
&\quad + {\alpha^3(\tau-1)} \|\mathbf{B}_{t}^\top\mathbf{B}_\ast\|^2_2 \left\| \tfrac{1}{m}\sum_{i\in\mathcal{I}_t} \left(\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top - \tfrac{1}{M}\sum_{i=1}^M \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\right)\right\|_2\nonumber \\
&\leq \left\| \mathbf{I}_k - \tfrac{\alpha^3(\tau-1)}{M} \sum_{i=1}^M \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t} \right\|_2 + 6{\alpha^4(\tau-1)} L_{\max}^4,\label{cond}
\end{align}
noting that \eqref{cond} follows since we are conditioning on the event $A_0$. Finally,
\begin{align}
&\left\| \mathbf{I}_k - \tfrac{\alpha^3(\tau-1)}{M} \sum_{i=1}^M \mathbf{B}_{t}^\top\mathbf{B}_\ast\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\mathbf{B}_\ast^\top\mathbf{B}_{t} \right\|_2\nonumber \\ &\leq 1 - \alpha^3 (\tau-1) \sigma_{\min}^2(\mathbf{B}_t^\top\mathbf{B}_\ast)\sigma_{\min}\left(\tfrac{1}{M} \sum_{i=1}^M \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top\right) \nonumber \\
&\leq 1 - \alpha^3 (\tau-1) \sigma_{\min}^2(\mathbf{B}_t^\top\mathbf{B}_\ast)\sigma_{\min}\left(\tfrac{1}{M} \sum_{i=1}^M \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top - \mathbf{\bar{w}}_{\ast}\mathbf{\bar{w}}_{\ast}^\top\right) \nonumber \\
&= 1 - \alpha^3 (\tau-1) \sigma_{\min}(\mathbf{B}_t^\top\mathbf{B}_\ast)^2\sigma_{\min}\left(\tfrac{1}{M} \sum_{i=1}^M (\mathbf{w}_{\ast,i}-\mathbf{\bar{w}}_{\ast} )(\mathbf{w}_{\ast,i}-\mathbf{\bar{w}}_{\ast})^\top \right) \nonumber \\
&\leq 1 - 0.1\alpha^2 (\tau-1)E_0\mu \label{nnnnn} \\
&\leq 1 - 0.05\alpha^2 \tau E_0\mu \label{nn}
\end{align}
where \eqref{nnnnn} follows by Lemma \ref{lem:distlb} and Assumption \ref{assump:td}, and \eqref{nn} follows since $\tau \geq 2$.
Combining \eqref{nn}, \eqref{cond}, \eqref{comb}, \eqref{slast}, \eqref{sslast}, and \eqref{ssslast}, we obtain
\begin{align}
\| \mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t+1} \|_2 &\leq \bigg(1 - 0.05\alpha^2 \tau E_0 \mu^2 + 6\alpha^4 (\tau-1)L_{\max}^4 + 16 \alpha^4 (\tau-1)^2 L_{\max}^4 \nonumber\\
&\quad \quad \quad \quad + 13 c_3 \alpha^4 \tau^2 L_{\max}^4 \kappa_{\max}^2 E_0^{-1} + {5\alpha^4 \tau^2 L_{\max}^4} \bigg) \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t} \|_2 \nonumber \\
&\leq \big(1 - 0.05\alpha^2 \tau E_0 \mu^2 + (24/c_3^2) \alpha^2 \tau E_0 \mu^2 + (13/c_3) \alpha^2 \tau E_0 \mu^2 \big) \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t} \|_2 \nonumber \\
&\leq (1 - 0.04 \alpha^2 \tau E_0 \mu^2 ) \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t} \|_2
\end{align}
using $\alpha^2 \tau \leq \tfrac{(1-\delta_0)^2}{c_3^2\tau\kappa_{\max}^4 L_{\max}^2}\leq \tfrac{E_0^2}{c_3^3\tau\kappa_{\max}^4 L_{\max}^2 }$ and $c_3> 1305$.
\end{proof}
\begin{lemma} \label{lem:a4}
$A_3(t+1) \cap A_4(t+1) \cap A_5(t) \implies A_{5}(t+1)$
\end{lemma}
\begin{proof}
We use the contraction of $\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{s}\|_2$ ($A_4(t)$) and the fact that $\|\boldsymbol{\Delta}_{s}\|_2$ is small for all $s\in [t]$ ($A_5(t)$), as in Lemma \ref{lem:distlb}, to obtain
\begin{align}
\operatorname{dist}_{t+1}&= \|\mathbf{B}_{\ast,\perp}^\top \mathbf{\hat{B}}_{t+1}\|_2 \nonumber \\
&\leq\tfrac{1}{ \sigma_{\min}(\mathbf{B}_{t+1})}\|\mathbf{B}_{\ast,\perp}^\top \mathbf{{B}}_{t+1}\|_2\nonumber \\
&\leq\tfrac{1}{ \sigma_{\min}(\mathbf{{B}}_{t+1})}(1-0.04\alpha^2 \tau E_0 \mu^2 )\|\mathbf{B}_{\ast,\perp}^\top \mathbf{{B}}_{t}\|_2\nonumber \\
&\quad \vdots \nonumber \\
&\leq \tfrac{1}{ \sigma_{\min}(\mathbf{{B}}_{t+1})}(1-0.04\alpha^2 \tau E_0 \mu^2 )^t\|\mathbf{B}_{\ast,\perp}^\top \mathbf{{B}}_{0}\|_2\nonumber \\
&\leq \tfrac{\sigma_{\max}(\mathbf{B}_0)}{ \sigma_{\min}(\mathbf{{B}}_{t+1})}(1-0.04\alpha^2 \tau E_0 \mu^2 )^t\delta_0 \nonumber \\
&\leq \tfrac{\sqrt{1+\|\boldsymbol{\Delta}_{0}\|_2}/\sqrt{\alpha}}{ \sqrt{1-\|\boldsymbol{\Delta}_{t+1}\|_2}/\sqrt{\alpha}}(1-0.04\alpha^2 \tau E_0 \mu^2 )^t\delta_0 \nonumber
\end{align}
Now, we argue as in \eqref{uhu} (with $\|\boldsymbol{\Delta}_t\|$ replaced by $\|\boldsymbol{\Delta}_{t+1}$ without anything changing in the analysis) to find
$\tfrac{\sqrt{1+\|\boldsymbol{\Delta}_{0}\|_2}/\sqrt{\alpha}}{ \sqrt{1-\|\boldsymbol{\Delta}_{t+1}\|_2}/\sqrt{\alpha}}\delta_0\leq \tfrac{2+\delta_0}{3}\leq 1 $. Thus $ \operatorname{dist}_{t+1}\leq (1-0.04\alpha^2 \tau E_0 \mu^2 )^t$ as desired.
\end{proof}
\subsection{Proof of Proposition \ref{prop:dgd}} \label{app:prooflb}
\begin{proposition}[Distributed GD lower bound]
Suppose we are in the setting described in Section \ref{sec:linear} and $k > 1$. Then for any set of ground-truth heads $\{\mathbf{w}_{\ast,i}\}_{i=1}^M$, full-rank initialization $\mathbf{B}_0\in\mathbb{R}^{d\times k}$, initial distance $\delta_0 \in (0,1/2]$, step size $\alpha > 0$, and number of rounds $T$, there exists $\mathbf{B}_\ast\in \mathcal{O}^{d \times k}$ such that $\operatorname{dist}(\mathbf{B}_0, \mathbf{B}_\ast) = \delta_0$ and $\operatorname{dist}(\mathbf{B}_T^{\text{D-GD}}, \mathbf{B}_\ast) \geq \delta_0$, where $\mathbf{B}_T^{\text{D-GD}}\equiv \mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_\ast,\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha)$ is the result of D-GD with step size $\alpha$ and initialization $\mathbf{B}_0$ on the system with ground-truth representation $\mathbf{B}_\ast$ and ground-truth heads $\{\mathbf{w}_{\ast,i}\}_{i=1}^M$.
\end{proposition}
\begin{proof}
Recall that $\mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_\ast,\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha)$ is the result of D-GD with step size $\alpha$ and initialization $\mathbf{B}_0$ on the system with ground-truth representation $\mathbf{B}_\ast$ and ground-truth heads $\{\mathbf{w}_{\ast,i}\}_{i=1}^M$.
There are two disjoint cases: (1) for all $\mathbf{B}_\ast \in \mathcal{B} \coloneqq \{\mathbf{B}\in \mathcal{O}^{d\times k}:\operatorname{dist}(\mathbf{B}_0,\mathbf{B}) = \delta_0, \mathbf{B}\mathbf{\bar{w}}_{\ast}\in\operatorname{col}(\mathbf{B}_0)\}$, $\operatorname{dist}(\mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_\ast,\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha), \mathbf{B}_\ast)\geq 0.7 \delta_0$, or (2) there exists some $\mathbf{B}_\ast \in \mathcal{B}$ such that \\ $\operatorname{dist}(\mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_\ast,\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha), \mathbf{B}_\ast)< 0.7 \delta_0$. If case (1) holds then the proof is complete. Otherwise, let
$\mathbf{B}_\ast \in \mathcal{B}$ such that $\operatorname{dist}(\mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_\ast,\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha), \mathbf{B}_\ast)< 0.7 \delta_0$. We will show that there exists another $\mathbf{B}_{\ast'}\in \mathcal{B}$ such that $\operatorname{dist}(\mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_{\ast'},\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha), \mathbf{B}_{\ast'})\geq \delta_0$, so D-GD cannot guarantee to recover the ground-truth representation, completing the proof.
Consider case (2). Without loss of generality we can write $\mathbf{B}_0 =\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{v}_0^\top + \mathbf{\tilde{B}}_0\mathbf{\tilde{V}}_0^\top$ for some $\mathbf{v}_0\in \mathbb{R}^k: \|\mathbf{v}_0\|=1$, $\mathbf{\tilde{B}}_0\in \mathcal{O}^{d \times k-1}: \mathbf{\tilde{B}}_0^\top \mathbf{B}_\ast \mathbf{\bar{w}}_\ast=\mathbf{0}$, $\mathbf{\tilde{V}}_0\in \mathcal{O}^{k \times k-1}:\mathbf{\tilde{V}}_0^\top \mathbf{v}_0=\mathbf{0}$ using the SVD, since $\mathbf{B}_\ast \mathbf{\bar{w}}_\ast \in \operatorname{col}(\mathbf{B}_0)$. Likewise, we can write $\mathbf{B}_\ast = \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top + \mathbf{\tilde{B}}_\ast\mathbf{\tilde{V}}_\ast^\top$ for some $\mathbf{\tilde{B}}_\ast\in \mathcal{O}^{d \times k-1}: \mathbf{\tilde{B}}_\ast^\top \mathbf{{B}}_\ast\mathbf{\bar{w}}_{\ast}=\mathbf{0}$, $\mathbf{\tilde{V}}_\ast\in \mathcal{O}^{k \times k-1}: \mathbf{\tilde{V}}_\ast^\top \mathbf{\bar{w}}_\ast=\mathbf{0}$.
Using these decompositions, we can see that
\begin{align}
\mathbf{B}_\ast \mathbf{B}_\ast^\top &= \big(\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top\! +\! \mathbf{\tilde{B}}_\ast\mathbf{\tilde{V}}_\ast^\top\big) \big(\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top\! +\! \mathbf{\tilde{B}}_\ast\mathbf{\tilde{V}}_\ast^\top)^\top \nonumber \\
&= \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^4} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top + \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{\tilde{V}}_\ast \mathbf{\tilde{B}}_\ast^\top
+ \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{\tilde{B}}_\ast\mathbf{\tilde{V}}_\ast^\top \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top \nonumber \\
&\quad + \mathbf{\tilde{B}}_\ast\mathbf{\tilde{V}}_\ast^\top \mathbf{\tilde{V}}_\ast \mathbf{\tilde{B}}_\ast^\top \nonumber \\
&= \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top
+ \mathbf{\tilde{B}}_\ast \mathbf{\tilde{B}}_\ast^\top \nonumber
\end{align}
and
\begin{align}
\delta_0&\coloneqq \operatorname{dist}(\mathbf{B}_{0},\mathbf{B}_\ast) \nonumber \\
&\coloneqq \|(\mathbf{I}_d - \mathbf{B}_\ast \mathbf{B}_\ast^\top)\mathbf{B}_0\|\nonumber \\
&= \big\|\big(\mathbf{I}_d - \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top
- \mathbf{\tilde{B}}_\ast \mathbf{\tilde{B}}_\ast^\top
\big)\big(\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{v}_0^\top \!+\! \mathbf{\tilde{B}}_0\mathbf{\tilde{V}}_0^\top \big)\big\|\nonumber \\
&= \big\|\big(\mathbf{I}_d - \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top
- \mathbf{\tilde{B}}_\ast \mathbf{\tilde{B}}_\ast^\top
\big)\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{v}_0^\top \nonumber\\
&\quad + \big(\mathbf{I}_d - \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top
- \mathbf{\tilde{B}}_\ast \mathbf{\tilde{B}}_\ast^\top
\big)\mathbf{\tilde{B}}_0\mathbf{\tilde{V}}_0^\top \big\|\nonumber \\
&= \big\| \big(\mathbf{I}_d - \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top
- \mathbf{\tilde{B}}_\ast \mathbf{\tilde{B}}_\ast^\top
\big)\mathbf{\tilde{B}}_0\mathbf{\tilde{V}}_0^\top \big\|\nonumber \\
&= \big\| \big(\mathbf{I}_d
- \mathbf{\tilde{B}}_\ast \mathbf{\tilde{B}}_\ast^\top
\big)\mathbf{\tilde{B}}_0\mathbf{\tilde{V}}_0^\top \big\|\nonumber \\
&= \big\| \big(\mathbf{I}_d
- \mathbf{\tilde{B}}_\ast \mathbf{\tilde{B}}_\ast^\top
\big)\mathbf{\tilde{B}}_0 \big\|\nonumber \\
&= \operatorname{dist}(\mathbf{\tilde{B}}_0, \mathbf{\tilde{B}}_\ast). \label{dist}
\end{align}
Next, let $\mathbf{B}_{\ast'} = \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top + (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast)\mathbf{\tilde{V}}_\ast^\top$. We first check that $\mathbf{B}_{\ast'}\in \mathcal{O}^{d\times k}$:
\begin{align}
\mathbf{B}_{\ast'}^\top \mathbf{B}_{\ast'}&= \big(\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top + (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast)\mathbf{\tilde{V}}_\ast^\top\big)^\top \big(\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top + (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast)\mathbf{\tilde{V}}_\ast^\top\big)\nonumber \\
&= \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top + \mathbf{\tilde{V}}_\ast (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast)^\top (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast) \mathbf{\tilde{V}}_\ast^\top \label{zero}\\
&= \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top + \mathbf{\tilde{V}}_\ast (4 \mathbf{\tilde{B}}_\ast^\top\mathbf{\tilde{B}}_0\mathbf{\tilde{B}}_0^\top\mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - 4\mathbf{\tilde{B}}_\ast^\top\mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast + \mathbf{\tilde{B}}_\ast^\top\mathbf{\tilde{B}}_\ast) \mathbf{\tilde{V}}_\ast^\top \nonumber \\
&= \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top + \mathbf{\tilde{V}}_\ast \mathbf{\tilde{V}}_\ast^\top\nonumber \\
&= [\mathbf{\tilde{V}}_\ast, \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|} \mathbf{\bar{w}}_\ast ] [\mathbf{\tilde{V}}_\ast, \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|} \mathbf{\bar{w}}_\ast ]^\top\nonumber \\
&= \mathbf{I}_k \label{bg}
\end{align}
as desired, where \eqref{zero} follows since $\mathbf{\tilde{B}}_\ast^\top \mathbf{B}_\ast \mathbf{\bar{w}}_\ast= \mathbf{\tilde{B}}_0^\top \mathbf{B}_\ast \mathbf{\bar{w}}_\ast=\mathbf{0}$, and \eqref{bg} follows since $ [\mathbf{\tilde{V}}_\ast, \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|} \mathbf{\bar{w}}_\ast ] \in \mathcal{O}^{k \times k}$ by the definition of the SVD.
Furthermore,
\begin{align}
\operatorname{dist}(\mathbf{B}_0, \mathbf{B}_{\ast'}) &= \|(\mathbf{I}_d - \mathbf{B}_0\mathbf{B}_0^\top)\mathbf{B}_{\ast'} \|\nonumber \\
&= \|(\mathbf{I}_d \!-\! \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top \! -\! \mathbf{\tilde{B}}_0\mathbf{\tilde{B}}_0^\top)\big(\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top + (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast)\mathbf{\tilde{V}}_\ast^\top\big)\|\nonumber \\
&= \|(\mathbf{I}_d - \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top - \mathbf{\tilde{B}}_0\mathbf{\tilde{B}}_0^\top)\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \nonumber \\
&\quad + (\mathbf{I}_d - \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top - \mathbf{\tilde{B}}_0\mathbf{\tilde{B}}_0^\top) (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast)\mathbf{\tilde{V}}_\ast^\top\|\nonumber \\
&= \| (\mathbf{I}_d - \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top - \mathbf{\tilde{B}}_0\mathbf{\tilde{B}}_0^\top) (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast)\mathbf{\tilde{V}}_\ast^\top\|\nonumber \\
&= \| (\mathbf{I}_d - \mathbf{\tilde{B}}_0\mathbf{\tilde{B}}_0^\top) (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast)\mathbf{\tilde{V}}_\ast^\top\|\nonumber \\
&= \| (\mathbf{I}_d - \mathbf{\tilde{B}}_0\mathbf{\tilde{B}}_0^\top) \mathbf{\tilde{B}}_\ast \mathbf{\tilde{V}}_\ast^\top\|\nonumber \\
&= \| (\mathbf{I}_d - \mathbf{\tilde{B}}_0\mathbf{\tilde{B}}_0^\top) \mathbf{\tilde{B}}_\ast\|\nonumber \\
&= \operatorname{dist}(\mathbf{\tilde{B}}_\ast, \mathbf{\tilde{B}}_0) \nonumber \\
&=\delta_0 \label{fhf}
\end{align}
where \eqref{fhf} follows from \eqref{dist}. Moreover, $\mathbf{B}_{\ast'}\mathbf{\bar{w}}_{\ast} = \mathbf{B}_{\ast}\mathbf{\bar{w}}_{\ast} \in \operatorname{col}(\mathbf{B}_0)$, thus $\mathbf{B}_{\ast'}\in \mathcal{B}$. Next,
\begin{align}
\operatorname{dist}(\mathbf{B}_\ast, \mathbf{B}_{\ast'}) &= \|(\mathbf{I}_d - \mathbf{B}_\ast\mathbf{B}_\ast^\top)\mathbf{B}_{\ast'} \|\nonumber \\
&= \|(\mathbf{I}_d \!-\! \tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top \mathbf{B}_\ast^\top \! -\! \mathbf{\tilde{B}}_\ast\mathbf{\tilde{B}}_\ast^\top)\big(\tfrac{1}{\|\mathbf{\bar{w}}_{\ast}\|^2} \mathbf{B}_\ast \mathbf{\bar{w}}_\ast \mathbf{\bar{w}}_\ast^\top + (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast - \mathbf{\tilde{B}}_\ast)\mathbf{\tilde{V}}_\ast^\top\big)\|\nonumber \\
&= \|(\mathbf{I}_d \! -\! \mathbf{\tilde{B}}_\ast\mathbf{\tilde{B}}_\ast^\top) (2 \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast \!-\! \mathbf{\tilde{B}}_\ast)\| \nonumber \\
&= 2\|(\mathbf{I}_d \! -\! \mathbf{\tilde{B}}_\ast\mathbf{\tilde{B}}_\ast^\top) \mathbf{\tilde{B}}_0 \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast\| \nonumber \\
&\geq 2 \|(\mathbf{I}_d \! -\! \mathbf{\tilde{B}}_\ast\mathbf{\tilde{B}}_\ast^\top) \mathbf{\tilde{B}}_0\|\sigma_{\min}( \mathbf{\tilde{B}}_0^\top \mathbf{\tilde{B}}_\ast) \nonumber \\
&= 2 \operatorname{dist}(\mathbf{\tilde{B}}_0,\mathbf{\tilde{B}}_\ast)\sqrt{1 - \operatorname{dist}^2( \mathbf{\tilde{B}}_0,\mathbf{\tilde{B}}_\ast ) } \label{swrt} \\
&= 2 \delta_0\sqrt{1-\delta_0} \nonumber
\end{align}
where \eqref{swrt} follows since $\sigma_{\min}^2(\mathbf{\tilde{B}}_1^\top \mathbf{\tilde{B}}_2 ) + \sigma_{\max}^2( (\mathbf{I}_d \! -\! \mathbf{\tilde{B}}_1\mathbf{\tilde{B}}_1^\top) \mathbf{\tilde{B}}_2) = 1$ for any $\mathbf{\tilde{B}}_1,\mathbf{\tilde{B}}_2\in\mathcal{O}^{d,k-1}$.
Note that for D-GD the global update for the representation is
\begin{align}
\mathbf{B}_{t+1} = \mathbf{B}_t - \frac{\alpha}{M}\sum_{i=1}^M \nabla_{\mathbf{B}} f_i(\mathbf{B}_t, \mathbf{w}_t) = \mathbf{B}_t - \alpha (\mathbf{B}_t \mathbf{w}_t -\mathbf{B}_\ast \mathbf{\bar{w}}_{\ast}) \mathbf{w}_t^\top,
\end{align}
and similarly, the update for the head is $\mathbf{w}_{t+1} = \mathbf{w}_t - \alpha\mathbf{B}_t^\top(\mathbf{B}_t\mathbf{w}_t - \mathbf{B}_\ast \mathbf{\bar{w}}_{\ast})$. Thus, the behavior of D-GD is indistinguishable in the settings with ground-truth representations $\mathbf{B}_{\ast'}, \mathbf{B}_\ast$ since $\mathbf{B}_{\ast'} \mathbf{\bar{w}}_\ast = \mathbf{B}_\ast \mathbf{\bar{w}}_\ast$.
In particular, $\mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_{\ast},\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha) = \mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_{\ast'},\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha)$
Using this equality along with the triangle inequality yields
\begin{align}
\operatorname{dist}(\mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_{\ast'},\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha), \mathbf{B}_{\ast'} ) &= \operatorname{dist}(\mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_{\ast},\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha), \mathbf{B}_{\ast'} ) \nonumber \\
&\geq \operatorname{dist}( \mathbf{B}_\ast, \mathbf{B}_{\ast'}) - \operatorname{dist}(\operatorname{dist}(\mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_{\ast},\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha), \mathbf{B}_\ast ) \nonumber \\
&\geq 2 \delta_0 \sqrt{1-\delta_0^2} - 0.7\delta_0 \label{lk} \\
&\geq (\sqrt{3}-0.7)\delta_0 \label{klk} \\
&\geq \delta_0 \nonumber
\end{align}
as desired, where \eqref{lk} follows by the definition of case (2) and \eqref{swrt}, and \eqref{klk} follows by $\delta_0 \in (0,1/2]$.
\end{proof}
\section{Additional Related Work} \label{app:rw}
In this section we provide further discussion of the related works.
\textbf{Convergence of FedAvg.} The convergence of FedAvg, also known as Local SGD, has been the subject of intense study in recent years, due to the algorithm's effectiveness combined with the difficulties of analyzing it. In homogeneous data settings, local updates are easier to reconcile with solving the global objective, allowing much progress to be made in understanding convergence rates in this case \cite{stich2018local,haddadpour2019local,stich2019error,yu2019parallel,wang2019cooperative,haddadpour2019local,spiridonoff2021communication,woodworth2020local,zhou2017convergence}.
In the heterogeneous case multiple works have shown that FedAvg with fixed learning rate may not solve the global objective because the local updates induce a non-vanishing bias by drifting towards local solutions,
even with full gradient steps and and strongly convex objectives \cite{li2019convergence,malinovskiy2020local,pathak2020fedsplit,charles2021convergence, wang2020tackling,karimireddy2020scaffold,charles2020outsized,wang2019federated,wang2021local}. As a remedy, several papers have analyzed FedAvg with learning rate that decays over communication rounds, and have shown that this approach indeed reaches a stationary point of the global objective, but at sublinear rates \cite{khaled2020tighter,koloskova2020unified,li2019convergence,qu2020federated,karimireddy2020scaffold} that can be strictly slower than the convergence rates of D-SGD \cite{woodworth2020minibatch,karimireddy2020scaffold}.
Nevertheless, in overparameterized settings with strongly convex losses, multiple works have shown that FedAvg achieves linear convergence to a global optimum \cite{koloskova2020unified,qu2020federated}.
Here overparameterized means that the model class contains a single model that achieves zero loss for all clients. Our setting is not overparameterized in this sense, nor is it convex.
\textbf{Multi-task representation learning.} Multiple works have studied the multi-task linear representation learning setting \cite{maurer2016benefit} in recent years.
\cite{tripuraneni2020provable} and \cite{kong2020robust} give statistical rates for a method-of-moments estimator for learning the representation and \cite{sun2021towards} analyze a projection and eigen-weighting based algorithm designed for the case in which ground-truth representation is unknown.
Other works have studied alternating minimization procedures for learning $\operatorname{col}(\mathbf{B}_\ast)$ in the context of meta-learning \cite{thekumparampil2021statistically} and federated learning \cite{collins2021exploiting}. However, these methods require a unique head for each client, which greatly simplifies the analysis since head diversity is guaranteed prior to local updates and is not applicable to some cross-device FL settings which cannot tolerate stateful clients.
Outside of the multi-task linear regression setting, \cite{tripuraneni2020theory} and \cite{xu2021representation} have demonstrated the necessity of task diversity to learning generalizable representations from a learning theoretic perspective, and \cite{du2020fewshot} considered the statistical rates of representation learning by solving an ERM with unique heads per task.
\section{Experiments} \label{sec:experiments}
In this section we conduct experiments to (I) verify our theoretical results in the linear setting and (II) determine whether our established insights generalize to deep neural networks. Notably, demonstrating the competitive performance of FedAvg plus fine-tuning for personalized FL is {\em not} a goal of this section, as this is evident from prior experiments \cite{yu2020salvaging,li2020ditto,collins2021exploiting,cheng2021fine}. Rather, to achieve (II) we test whether FedAvg learns effective representations when trained with neural networks in heterogeneous data settings via three popular benchmarks for evaluating the quality of learned representations. Since our main claim is that local updates are key to representation learning, we use distributed SGD as our baseline in all experiments.
\begin{figure}
\centering
\begin{subfigure}[b]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{linear24.pdf}
\end{subfigure}
\qquad
\begin{subfigure}[b]{0.42\textwidth}
\centering
\includegraphics[width=\textwidth]{ftacc_linear.pdf}
\end{subfigure}
\caption{(Left) D-GD converges to a stationary point of the global objective \eqref{glob_pop}, unlike FedAvg, yet (Right) FedAvg achieves smaller error after fine-tuning with various numbers of samples.
}
\label{fig:linear}
\end{figure}
\subsection{Multi-task linear regression} We first experiment with the regression setting from our theory. We randomly generate $\mathbf{B}_\ast \in \mathbb{R}^{d \times k}$ and $\{\mathbf{w}_{\ast,i}\}_{i\in [M]}$ by sampling each element i.i.d. from the normal distribution, where $d\!=\!100, k\!=\!5$ and $M\!=\!40$, and then orthogonalizing $\mathbf{B}_\ast$. Then we run FedAvg with $\tau\!=\!2$ local updates and D-GD, both sampling $m\!=\!M$ clients per round. We have seen in Figure \ref{fig:1} that the principal angle distance between the representation learned by FedAvg and the ground-truth representation linearly converges to zero, whereas D-GD does not learn the ground-truth representation. Conversely, Figure \ref{fig:linear} (left) tracks the gradient of the global loss \eqref{glob_pop} and shows that D-GD linearly converges to stationary point of \eqref{glob_pop}, while FedAvg does not converge to one at all. Although D-GD optimizes the global loss, it does not generalize as well as FedAvg to new clients as demonstrated by Figure \ref{fig:linear} (right). Here, we fine-tune the models learned by FedAvg and D-GD on a new client with $n$ samples generated by $\mathbf{x}_{M+1}\!\sim\! \mathcal{N}(\mathbf{0},\mathbf{I}_d)$, $\zeta_{M+1}\!\sim\! \mathcal{N}(0,0.01)$, and $y_{M+1}\! =\! \langle \mathbf{B}_{\ast}\mathbf{w}_{\ast,M+1} ,\mathbf{x}_{M+1}\rangle + \zeta_{M+1}$. We fine-tune using GD for $\tau'\!=\!200$ iterations with batch size $b\!=\!n$, and plot the final error $\|\mathbf{B}_{T,M+1,\tau'}\mathbf{w}_{T,M+1,\tau'}\! -\! \mathbf{B}_\ast\mathbf{w}_{\ast,M+1}\|^2$.
Both plots are generated by averaging 10 runs.
\subsection{Image classification with neural networks} Next we evaluate FedAvg's representation learning ability on nonlinear neural networks. For fair comparison, in every experiment all methods make the same total amount of local updates during the course of training (e.g. D-SGD is trained for $50\times$ more rounds than FedAvg with $\tau=50$).
\textbf{Datasets and models.} We use the image classification datasets CIFAR-10 and CIFAR-100 \cite{krizhevsky2009learning}, which consist of 10 and 100 classes of RGB images, respectively.
We use a convolutional neural network (CNN) with three convolutional blocks followed by a three-layer multi-layer perceptron, with each convolutional block consisting of two convolutional layers and a max pooling layer.
\begin{figure}[t]
\begin{center}
\vspace{-2mm}
\centerline{\includegraphics[width=\columnwidth]{featmat.pdf}}
\vspace{-0mm}
\caption{Average cosine similarity for features learned by D-SGD and FedAvg with varying numbers of local updates on a heterogeneous partition of CIFAR-10. }
\label{fig:sim}
\end{center}
\vspace{-6mm}
\end{figure}
\textbf{Cosine similarity of features.} A desirable property of representations for downstream classification tasks is that features of examples from the same class are similar to each other, while features of examples from different classes are dissimilar \cite{hadsell2006dimensionality}. In Figure \ref{fig:sim} we examine whether the representations learned by FedAvg satisfy this property. Here we have trained FedAvg with varying $\tau$ and D-SGD (FedAvg with $\tau\! =\! 1$) on CIFAR-10. Image classes are heterogeneously allocated to $M=100$ clients according to the Dirichlet distribution with parameter 0.6 as in \cite{acar2021federated}. Each subplot is a 10x10 matrix whose $(i,j)$-th element gives the average cosine similarity between features of images from the $i$-th and $j$-th classes learned by the corresponding model. Ideally, diagonal elements are close to 1 (high similarity) and off-diagonal elements are close to 0 (low similarity).
Figure \ref{fig:sim} shows that FedAvg indeed learns features with high intra-class similarity and low inter-class similarity, with representation quality improving with more local updates between communications.
Meanwhile, D-SGD does not learn such features. The leftmost subplot shows that all of the features learned by D-SGD are dissimilar, regardless of whether two images belong to the same class.
\begin{figure}
\centering
\begin{subfigure}[b]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{ftacc_cif100_20.pdf}
\end{subfigure}
\qquad
\begin{subfigure}[b]{0.43\textwidth}
\centering
\includegraphics[width=\textwidth]{ftacc_cif100_10.pdf}
\end{subfigure}
\caption{Average fine-tuning accuracies on new clients for models trained by FedAvg and D-SGD. (Left) Models trained on 80 classes from CIFAR-100 (with $C$ classes/client) and fine-tuned on new clients from 20 new classes from CIFAR-100. (Right) Models trained on CIFAR-100 with $C$ classes/client and fine-tuned on new clients from CIFAR-10 (10 classes/client). For FedAvg, $\tau=50$ in all cases, and error bars give standard deviations over five trials with five new clients tested/trial.
}
\label{fig:CIFAR-FT}
\end{figure}
\textbf{Fine-tuning performance.} We evaluate the generalization ability of the representations learned by FedAvg to new classes and also new datasets. An effective representation identifies universally important features, so it should generalize to new data, with perhaps a small amount of fine-tuning needed to learn a new mapping from feature space to label space. The transfer learning performance of fine-tuned models is a popular metric for evaluating the quality of learned representations \cite{whitney2020evaluating,chen2020simple}.
We first study how models trained by FedAvg and D-SGD generalize to unseen classes from the same dataset. To do so, we train models on heterogeneous partitions of CIFAR-100 using both FedAvg with $\tau = 50$ as well as D-SGD. In the left plot of Figure~\ref{fig:CIFAR-FT}, we illustrate the case that models are trained on 80 clients each with 500 total images from $C$ classes sub-selected from 80 classes of CIFAR-100, and tested on new clients with images from the remaining 20 classes of CIFAR-100. We fine-tune the trained models on the new clients with 10 epochs of SGD, with varying numbers of samples per epoch as listed on the x-axis, before testing.
Next, we investigate how well models trained by FedAvg and D-SGD generalize to an unseen dataset. In the right plot of Figure~\ref{fig:CIFAR-FT}, we train models with $C$ classes/client from CIFAR-100, then test on new clients with samples drawn from CIFAR-10 (a different dataset, but with presumably similar ``basic'' features). Specifically, for these new clients, we fine-tune for 10 epochs as previously, then test the post-fine-tuned models on the test data for each client.
In both left and right plots, we observe that FedAvg significantly outperforms D-SGD, indicating that FedAvg has learned a representation that generalizes better to new classes. Additional details are provided in Appendix \ref{app:experiments}.
\section{Introduction} \label{sec:intro}
Federated Learning (FL) \cite{mcmahan2017communication} provides a communication-efficient and privacy preserving means to learn from data distributed across clients such as cell phones, autonomous vehicles, and hospitals.
FL aims for each client to benefit from collaborating in the learning process without sacrificing data privacy or paying a substantial communication cost.
Federated Averaging (FedAvg) \cite{mcmahan2017communication} is the predominant FL algorithm. In FedAvg, also known as Local SGD \cite{stich2018local,stich2019error,wang2019cooperative}, the clients achieve communication efficiency by making multiple local updates of a shared global model before sending the result to the server, which averages the locally updated models to compute the next global model.
FedAvg is motivated by settings with {\em homogeneous} data across clients, since multiple local updates should improve model performance on all other clients' data when their data is similar. In contrast, FedAvg faces two major challenges in more realistic {\em heterogeneous} data settings: learning a single global model may not necessarily yield good performance for each individual client, and, multiple local updates may cause the FedAvg updates to drift away from solutions of the global objective \cite{karimireddy2020scaffold,malinovskiy2020local,pathak2020fedsplit,charles2021convergence, wang2020tackling}.
Despite these challenges, several empirical studies \cite{yu2020salvaging,reddi2020adaptive,li2020ditto} have observed that this shared global model trained by FedAvg {\em with several local updates per round} when further fine-tuned for individual clients is surprisingly effective in heterogeneous FL settings.
These studies motivate us to explore the impact of local updates on post-fine-tuning performance.
Meanwhile, a large number of recent works have shown that representation learning is a powerful paradigm for attaining high performance in multi-task settings, including FL. This is because the tasks' data often share a small set of features which are useful for downstream tasks, even if the datasets as a whole are heterogeneous. Consider, for example, heterogeneous federated image classification in which each client (task) may have images of different types of animals. It is safe to assume the images share a small number of features, such as body shape and color, which admit a simple and accurate mapping from feature space to label space. Since the number of important features is much smaller than the dimension of the data, knowing these features greatly simplifies each client's task.
\begin{figure*}[t]
\centering
\begin{minipage}{.48\linewidth}
\centering
\includegraphics[width=0.94\linewidth]{linear22.pdf}
\vspace{-.2cm}
\caption{
In multi-task linear regression with population losses, FedAvg linearly converges to the ground-truth representation, while D-GD (FedAvg with one local update) fails to learn it.}
\label{fig:1}
\end{minipage}%
\hspace{4mm}
\begin{minipage}{.48\linewidth}
\centering
\includegraphics[width=0.9\linewidth]{ftsim1intro1.pdf}
\vspace{-.2cm}
\caption{The NN representation learned by FedAvg on CIFAR-100 with 5 classes/client does not change significantly when fine-tuned on a new dataset (CIFAR-10), unlike D-SGD.
\label{fig:2}
\end{minipage}
\end{figure*}
To explore the connection between local updates and representation learning, we
first study multi-task linear regression
sharing a common ground-truth representation (Figure \ref{fig:1}).
We observe that FedAvg converges (exponentially fast) to the ground-truth representation in principal angle distance, while Distributed-GD (D-GD), which is effectively FedAvg with one local gradient update, fails to learn the shared representation. A similar concept can be shown in the nonlinear setting. We study a multi-layer CNN on a heterogeneous partition of CIFAR-100 (Figure \ref{fig:2}). Since there is not necessarily a ground-truth model here, we evaluate representation learning as follows. We first train the models with FedAvg and Distributed-SGD (D-SGD) then fine-tune the pre-trained models on clients from a new dataset, CIFAR-10.
Finally we evaluate the quality of the learned representation by measuring the amount that each model layer changes during fine-tuning using CKA similarity \cite{kornblith2019similarity}. Observe that the early layers of FedAvg's pre-trained model (corresponding to the representation) change much less than those of D-SGD.
More details for both experiments are in Section \ref{sec:experiments} and Appendix \ref{app:experiments}.
These observations suggest that FedAvg learns a shared representation that generalizes to new clients, even when trained in a heterogeneous setting. Hence, a natural question that arises is:
\vspace{-1.5mm}
\begin{quote}
\centering
{\em {Does FedAvg provably learn effective representations of heterogeneous data?}}
\vspace{-1.5mm}
\end{quote}
We answer ``yes'' to this question by proving that FedAvg recovers the ground-truth representation in the case of multi-task linear regression.
Critically, we show that FedAvg's local updates leverage the diversity among client data distributions to learn their common representation. This is surprising because FedAvg is a general-purpose algorithm not designed for representation learning.
Our analysis thus yields new insights on how FedAvg finds generalizable models. Our contributions are:
\vspace{-2mm}
\begin{itemize}[leftmargin=25pt, labelindent=1.5pt]
\item \textbf{Representation learning guarantees.} We study the behavior of FedAvg in multi-task linear regression with common representation. Here, each client aims to solve a $d$-dimensional regression with ground-truth solution that belongs to a shared $k$-dimensional subspace of $\mathbb{R}^d$, where $k\ll d$.
Our results show that FedAvg with $\tau\geq 2$ local updates learns the representation at a linear rate when each client accesses population gradients.
{\em To the best of our knowledge, this is the first result showing that FedAvg learns an effective representation in any setting.}
\item \textbf{Insights on the importance of local updates.} Our analysis reveals that executing more than one local update between communication rounds \textit{exploits the diversity} of the clients' ground truth regressors to improve the learned representation in all $k$ directions in the linear setting.
In contrast,
we prove that D-GD (FedAvg with one local update) fails to learn the representation.
\item \textbf{Empirical evidence of representation learning.} We provide experimental results showing Fedavg learns a generalizable representation when we use deep neural networks on real-world data sets. This confirms the main massage of our theoretical results in the bilinear setting and suggest that our results can generalize to more complex scenarios.
\end{itemize}
\subsection{Related work}
Recently there has been a surge of interest motivated by FL in analyzing FedAvg/Local SGD in heterogeneous settings. Multiple works have shown that FedAvg converges to a global optimum (resp. stationary point) of the global objective in convex (resp. nonconvex) settings but with decaying learning rate \cite{khaled2020tighter,koloskova2020unified,li2019convergence,qu2020federated,karimireddy2020scaffold}, leading to sublinear rates and communication complexity sometimes dominated by Distributed-SGD \cite{woodworth2020minibatch}.
These results are tight in the sense that FedAvg with fixed learning rate may {\em not} converge to a stationary point of the global objective in the presence of data heterogeneity, as its multiple local updates cause it to optimize a distinct, unknown objective \cite{malinovskiy2020local,mitra2021linear,pathak2020fedsplit,charles2021convergence, wang2020tackling,wang2019federated,li2019convergence}. Several methods have tried to correct this objective inconsistency via gradient tracking \cite{karimireddy2020scaffold, mitra2021linear, haddadpour2020federated,liang2019variance,murata2021bias,gorbunov2021local}, local regularization \cite{li2018federated,wang2019federated,zhang2020federated,t2020personalized}, operator splitting \cite{pathak2020fedsplit}, and strategic client sampling \cite{ribero2020communication,chen2020optimal,cho2020client}.
We take an orthogonal approach by arguing that FedAvg's local updates actually {\em benefit} convergence in heterogeneous settings by resulting in more generalizable models.
Several papers have also analyzed FedAvg from a generalization perspective. It was shown in \cite{chen2021theorem} that in a setting with strongly convex losses, either local training or FedAvg with fine-tuning (but not both) achieves minimax risk, depending on the level of data heterogeneity.
Similarly, \cite{cheng2021fine} argued that FedAvg with fine-tuning generalizes as well as more sophisticated methods, including model-agnostic meta-learning (MAML) \cite{finn2017model,fallah2020personalized}, in a strongly convex regularized linear regression setting. Additional work has studied the generalization of FedAvg in kernel regression, but for convex objectives that do not allow for representation learning \cite{su2021achieving}, and the generalization of a variant of FedAvg, known as Reptile \cite{nichol2018reptile}, on wide two-layer ReLU networks with homogeneous data \cite{huang2021fl}.
We focus on the multi-task linear representation learning setting \cite{maurer2016benefit}, which has become popular in recent years as it is an expressive but tractable nonconvex setting for studying the sample-complexity benefits of learning representations and the representation learning abilities of popular algorithms in data heterogeneous settings \cite{ collins2021exploiting,du2020fewshot, tripuraneni2020provable,kong2020robust, thekumparampil2021statistically,collins2022maml,sun2021towards}. Remarkably, our study of FedAvg reveals that it can learn an effective representation even though it was not designed for this goal, unlike a variety of personalized FL methods specifically tailored for representation learning \cite{collins2021exploiting,liang2020think,arivazhagan2019federated,oh2021fedbabu}.
\textbf{Notations.} We use $\mathcal{N}(\mathbf{u}, \mathbf{\Sigma})$ to signify the multivariate Gaussian distribution with mean $\mathbf{u}$ and covariance $\mathbf{\Sigma}$. $\mathcal{O}^{d \times k}$ denotes the set of matrices in $\mathbb{R}^{d \times k}$ with orthonormal columns. The notation $\operatorname{col}(\mathbf{B})$ represents the column space of the matrix $\mathbf{B}$, and $\operatorname{col}(\mathbf{B})^\perp$ is the orthogonal complement to this space. The norm $\|\cdot\|$ is the spectral norm and $\mathbf{I}_d$ is the identity matrix in $\mathbb{R}^{d \times d}$. We use $[m]$ to indicate the set of natural numbers up to and including $m$.
\section{Main Results} \label{sec:linear}
We employ the standard setting used for algorithmic representation learning analysis: multi-task linear regression \cite{tripuraneni2020provable,thekumparampil2021sample,collins2021exploiting,chua2021fine}. In this setting, samples $(\mathbf{x}_{i,j},y_{i,j})$ for each client $i$ are drawn independently from a distribution $\mathcal{D}_i$ on $\mathbb{R}^d\times \mathbb{R}$ such that
\begin{align}
\mathbf{x}_{i,j} \stackrel{\text{i.i.d.}}{\sim} p_{\mathbf{x}}, \;\; y_{i,j} = \langle \boldsymbol{\beta}_{\ast,i}, \mathbf{x}_{i,j} \rangle + \zeta_{i,j} \; \text{ where } \; \zeta_{i,j} \stackrel{\text{i.i.d.}}{\sim} p_{\zeta} \nonumber
\end{align}
for an unobserved ground-truth regressor $\boldsymbol{\beta}_{\ast,i}\!\in \!\mathbb{R}^d$ and label noise $\zeta_{i,j}$. We assume the distributions $p_{\mathbf{x}}$ and $p_{\zeta}$ are such that $\mathbb{E}[\mathbf{x}_{i,j}]\! =\! \mathbf{0}, \mathbb{E}[\mathbf{x}_{i,j}\mathbf{x}_{i,j}^\top]\! =\! \mathbf{I}_d$ and $\mathbb{E}[\zeta_{i,j}]\! =\! 0$.
To incentivize representation learning, each $\boldsymbol{\beta}_{\ast,i}$ belongs to the same $k$-dimensional subspace of $\mathbb{R}^d$, where $k\ll d$. Let $\mathbf{B}_\ast \in \mathcal{O}^{d\times k}$ have columns that form an orthogonal basis for the shared subspace, so that $\boldsymbol{\beta}_{\ast,i} = \mathbf{B}_\ast \mathbf{w}_{\ast,i}$ for some $\mathbf{w}_{\ast,i}\in\mathbb{R}^k$ for each $i$. In other words, there exists a low-dimensional set of parameters known as the ``head'' that can specify the ground-truth model for client $i$ once the shared representation, i.e., $\operatorname{col}(\mathbf{B}_\ast)$, is known. It is advantageous to learn $\operatorname{col}(\mathbf{B}_\ast)$ because once it is known, all clients (including potentially new clients entering the system) have sample complexity $O(k)\ll d$ as they only need to learn the parameters of their head \cite{tripuraneni2020provable,du2020fewshot}.
Each client $i$ ultimately aims to learn a model $\hat{\boldsymbol{\beta}}_i$ that approximates $\boldsymbol{\beta}_{\ast,i}$ in order to achieve good generalization on its local distribution.
To eventually achieve this for each client, FedAvg with fine-tuning first aims to learn a global model consisting of a representation $\mathbf{B}\in\mathbb{R}^{d \times k}$ and a head $\mathbf{w}\in\mathbb{R}^k$ that minimizes the average loss across clients. The loss for client $i$ is $f_i(\mathbf{B}, \mathbf{w}) \coloneqq \frac{1}{2n_i}\sum_{j=1}^{n_i} (y_{i,j} - \langle \mathbf{Bw}, \mathbf{x}_{i,j} \rangle)^2$, i.e. the average squared loss on the local data, so
FedAvg tries to learn a global model that solves the nonconvex problem:
\begin{align}
\min_{\mathbf{B}\in\mathbb{R}^{d\times k}, \mathbf{w}\in \mathbb{R}^{k}} \frac{1}{N} \sum_{i=1}^M n_i\bigg\{ f_{i}(\mathbf{B},\mathbf{w}) \coloneqq \frac{1}{2n_i}\sum_{j=1}^{n_i} (y_{i,j} - \langle \mathbf{Bw}, \mathbf{x}_{i,j} \rangle)^2\bigg\}. \label{global_linear}
\end{align}
To solve \eqref{global_linear} in a distributed manner, FedAvg dictates that each client makes a series of local updates of the current global model before returning the models to the server for averaging, as discussed in Section \ref{sec:formulation}.
We aim to show that the FedAvg training procedure learns the column space of $\mathbf{B}_\ast$.
The first step is to make standard diversity and normalization assumptions on the ground-truth heads.
\begin{assumption}[Client normalization] \label{assump:n}
There exists $L_{\max}<\infty$ s.t. $\forall i \in [M]$, $\|\mathbf{w}_{\ast,i}\|_2 \leq L_{\max}$.
\end{assumption}
\begin{assumption}[Client diversity] \label{assump:td}
There exists $\mu \!>\! 0$ s.t. $\sigma_{\min}(\tfrac{1}{M}\sum_{i=1}^M (\mathbf{w}_{\ast,i}-\mathbf{\bar{w}}_{\ast})(\mathbf{w}_{\ast,i}-\mathbf{\bar{w}}_{\ast})^\top) \geq \mu^2 $, where $\mathbf{\bar{w}}_{\ast} \coloneqq \tfrac{1}{M} \sum_{i=1}^M \mathbf{w}_{\ast,i}$. Define $\kappa_{\max}\coloneqq \nicefrac{L_{\max}}{\mu}$.
\end{assumption}
Assumption \ref{assump:td} is very similar to typical task diversity assumptions except that it quantifies the diversity of the centered rather than un-centered tasks \cite{du2020fewshot,tripuraneni2020provable}. Intuitively, task diversity is required so that all of the directions in $\operatorname{col}(\mathbf{B}_\ast)$ are observed.
Next, to obtain convergence results we must define the variance of the ground-truth heads and the principal angle distance between representations.
\begin{definition}[Client variance] \label{def:var}
For $\gamma > 0$, define: $\gamma^2 \coloneqq \frac{1}{M}\sum_{i=1}^M \|\mathbf{w}_{\ast,i} - \mathbf{\bar{w}}_{\ast}\|^2$, where $\mathbf{\bar{w}}_{\ast}$ is defined in Assumption \ref{assump:td}. For $H > 0$, define $H^4 \coloneqq \frac{1}{M}\sum_{i=1}^M \| \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top - \tfrac{1}{M}\sum_{i'=1}^M\mathbf{\bar{w}}_{\ast,i}\mathbf{\bar{w}}_{\ast,i}^\top\|^2$.
\end{definition}
\begin{definition}[Principal angle distance]
For two matrices $\mathbf{B}_1, \mathbf{B}_2 \in \mathbb{R}^{d \times k}$, the {\em principal angle distance} between $\mathbf{B}_1$ and $\mathbf{B}_2$ is defined as $\operatorname{dist}(\mathbf{B}_1, \mathbf{B}_2) \coloneqq \|\mathbf{\bar{B}}_{1,\perp}^\top \mathbf{\bar{B}}_{2}\|_2$,
where the columns of $\mathbf{\bar{B}}_{1,\perp} \in \mathcal{O}^{d \times d-k}$ and $\mathbf{\bar{B}}_{2} \in \mathcal{O}^{d \times k}$ form orthonormal bases for $\operatorname{col}(\mathbf{B}_1)^\perp$ and $\operatorname{col}(\mathbf{B}_2)$, respectively.
\end{definition}
Intuitively, the principal angle distance between $\mathbf{B}_1$ and $\mathbf{B}_2$ is the sine of the largest angle between the subspaces spanned by their columns.
Now we are ready to state our main result. We consider the case that each client has access to gradients of the population loss on its local data distribution.
\begin{theorem}[FedAvg Representation Learning] \label{thm:main_pop} Consider the case that each client takes gradient steps with respect to their population loss $f_i(\mathbf{B},\mathbf{w})\coloneqq \tfrac{1}{2}\|\mathbf{Bw}-\mathbf{B}_{\ast}\mathbf{w}_{\ast,i}\|^2$ and all losses are weighted equally in the global objective.
Suppose Assumptions \ref{assump:n} and \ref{assump:td} hold, the number of clients participating each round satisfies $m \geq \min(M, 20((\nicefrac{\gamma}{L_{\max}})^2 + (\nicefrac{H}{L_{\max}})^4)(\alpha L_{\max})^{-4}\log(kT))$, and the initial parameters satisfy (i) $ \delta_0 \coloneqq \operatorname{dist}(\mathbf{B}_0, \mathbf{B}_\ast)\leq \sqrt{1\! -\! E_0}$ for any $E_0 \in (0,1]$, (ii) $\|\mathbf{I}- \alpha \mathbf{B}_0^\top \mathbf{B}_0\|_2 = O(\alpha^2 \tau L_{\max}^2 \kappa_{\max}^2)$ and (iii) $\|\mathbf{w}_0\|_2 = O(\alpha^{2.5} \tau L_{\max}^3)$.
Choose step size $\alpha = O(\tfrac{1-\delta_0}{ \sqrt{\tau} L_{\max} \kappa_{\max}^2})$.
Then for any $\epsilon \in (0, 1)$, the distance of the representation learned by FedAvg with $\tau\geq 2$ local updates satisfies $\operatorname{dist}(\mathbf{B}_T, \mathbf{B}_\ast) <\epsilon$ after at most
\begin{align}
T = O \big(\tfrac{1}{\alpha^2 \tau \mu^2 E_0}\log(\nicefrac{1}{\epsilon})\big)
\end{align}
communication rounds with probability at least $1 - 4 (kT)^{-99}$.
\end{theorem}
Theorem \ref{thm:main_pop} shows that FedAvg converges exponentially fast to the ground-truth representation when executed on the clients' population losses.
We provide intuition for the proof in Section \ref{sec:sketch} and the full proof in Appendix \ref{app:proof}. First, some comments are in order.
\textbf{Mild initial conditions.}
Theorem \ref{thm:main_pop} holds under benign initial conditions. In particular, condition ($i$) requires that the initial distance is only a constant away from 1. Condition ($ii$) ensures that the initial representation is well-conditioned with appropriate scaling, and ($iii$) guarantees the initial head is not too large. The last two conditions can be easily achieved by normalizing the inputs.
\textbf{Generalization without convergence in terms of the global loss.} When each client accesses its population loss as in Theorem \ref{thm:main_pop}, the global objective is:
\begin{align}
\min_{\mathbf{B}\in\mathbb{R}^{d\times k}, \mathbf{w}\in \mathbb{R}^{k}} \frac{1}{M} \sum_{i=1}^M \|\mathbf{Bw}-\mathbf{B}_\ast\mathbf{w}_{\ast,i}\|^2 \label{glob_pop}
\end{align}
However, Theorem \ref{thm:main_pop} does not imply that FedAvg solves \eqref{glob_pop}. In fact, our simulations in Section \ref{sec:experiments} show that it does not even reach a stationary point of \eqref{glob_pop}. This is consistent with prior works that have noticed the ``objective inconsistency'' phenomenon of FedAvg: it solves an unknown objective distinct from the global objective due to the fact that after multiple local updates, local gradients are no longer unbiased estimates of gradients of \eqref{glob_pop} \cite{wang2020tackling}.
Nevertheless, our results show that FedAvg is able to learn a generalizable model {\em even when it does not optimize the global loss in data heterogeneous settings}.
\textbf{Multiple local updates critically harness diversity, whereas Distributed GD (D-GD) does not learn the representation.} Key to the proof of Theorem \ref{thm:main_pop} is that the locally-updated heads become {\em diverse}, meaning that they cover all directions in $\mathbb{R}^k$, with greater diversity corresponding to more evenly covering in all directions. We will show in Section \ref{sec:sketch} that the locally-updated heads become roughly as diverse as the ground-truth heads, and this causes the representation to move towards the ground-truth at rate depending on the diversity level. Theorem \ref{thm:main_pop} reflects this: the convergence rate improves with the diversity metric $\nicefrac{\mu}{L_{\max}}$. In this way FedAvg {\em exploits} data heterogeneity to learn the representation, as more diverse $\{\mathbf{w}_{\ast,i}\}_{i\in [M]}$ implies more heterogeneous data.
Importantly, head diversity only benefits the global representation update if $\tau\geq 2$. We formally prove that D-GD (equivalent to FedAvg with $\tau\!=\!1$ and $m\!=\!M$) cannot recover $\operatorname{col}(\mathbf{B}_\ast)$ in the following result.
\begin{proposition}[Distributed GD lower bound] \label{prop:dgd}
Suppose we are in the setting described in Section \ref{sec:linear} and $d\! >\! k \!>\! 1$. Then for any set of ground-truth heads $\{\mathbf{w}_{\ast,i}\}_{i=1}^M$, full-rank initialization $\mathbf{B}_0\in\mathbb{R}^{d\times k}$, initial distance $\delta_0 \in (0,1/2]$, step size $\alpha > 0$, and number of rounds $T$, there exists $\mathbf{B}_\ast\in \mathcal{O}^{d \times k}$ such that $\operatorname{dist}(\mathbf{B}_0, \mathbf{B}_\ast) = \delta_0$, $\mathbf{B}_\ast\mathbf{\bar{w}}_{\ast}\in \operatorname{col}(\mathbf{B}_0)$ and $\operatorname{dist}(\mathbf{B}_T^{\text{D-GD}}, \mathbf{B}_\ast) \geq 0.7\delta_0$, where $\mathbf{B}_T^{\text{D-GD}}\equiv \mathbf{B}_T^{\text{D-GD}}(\mathbf{B}_0,\mathbf{B}_\ast,\{\mathbf{w}_{\ast,i}\}_{i=1}^M, \alpha)$ is the result of D-GD with step size $\alpha$ and initialization $\mathbf{B}_0$ on the system with ground-truth representation $\mathbf{B}_\ast$ and ground-truth heads $\{\mathbf{w}_{\ast,i}\}_{i=1}^M$.
\end{proposition}
Proposition \ref{prop:dgd} shows that for any choice of $\delta_0 \in (0,1/2]$, non-degenerate initialization $\mathbf{B}_0$, and ground-truth heads, there exists a $\mathbf{B}_\ast$ whose column space is $\delta_0$-close to $\operatorname{col}(\mathbf{B}_0)$, yet is at least $0.7\delta_0$-far from the representation learned by D-GD in the setting with $\mathbf{B}_\ast$ as ground-truth.
Therefore, even allowing for a strong initialization, D-GD cannot guarantee to recover the ground-truth representation. This negative result
combined with our previous results suggest even if we had an infinite communication budget, it would still be advantageous to execute multiple local updates between communication rounds in order to achieve better generalization through representation learning.
\section{Problem Formulation} \label{sec:formulation}
Consider a federated setting with a central server and $M$ clients. Each client $i\in [M]$ has a training dataset $\mathcal{\hat{D}}_i$ of $n_i$ labeled samples drawn from a distribution $\mathcal{D}_i$ over $\mathcal{X}\times \mathcal{Y}$, where $\mathcal{X}$ is the input space and $\mathcal{Y}$ is the label space. The learning model is given by $h_{\boldsymbol{\theta}}:\mathcal{X}\rightarrow \mathcal{Y}$ for model parameters $\boldsymbol{\theta}\in \mathbb{R}^D$. The loss of the model on a sample
$(\mathbf{x}, \mathbf{y}) \in \mathcal{X}\times \mathcal{Y}$ is given by $\ell( h_{\boldsymbol{\theta}}(\mathbf{x}), \mathbf{y} )$, which may be, for example, the squared or cross entropy loss.
The loss of model parameters $\boldsymbol{\theta}$ on the $i$-th client is the average loss of the model $h_{\boldsymbol{\theta}}$ on the samples in $\mathcal{\hat{D}}_i$, namely $f_i(\boldsymbol{\theta}) \coloneqq \tfrac{1}{n_i}\sum_{j=1}^{n_i}\ell(h_{\boldsymbol{\theta}}( \mathbf{x}_{i,j}), \mathbf{y}_{i,j})$, where $(\mathbf{x}_{i,j}, \mathbf{y}_{i,j})$ is the $j$-th sample in $\mathcal{\hat{D}}_i$.
The server aims to leverage all of the data across clients to find models that achieve small loss $f_i(\boldsymbol{\theta})$ for each client. To do so, the standard approach is to find a single model $\boldsymbol{\theta}$ that minimizes the average of the client losses weighted by number of samples:
\begin{equation}
\min_{\boldsymbol{\theta}} \frac{1}{N}\sum_{i=1}^M n_i f_i(\boldsymbol{\theta}) \label{global}\ = \
\frac{1}{N}\sum_{i=1}^M
\sum_{j\in \mathcal{\hat{D}}_i}\ell(h_{\boldsymbol{\theta}}( \mathbf{x}_{i,j}),\mathbf{y}_{i,j})),
\end{equation}
where $N= \sum_{i=1}^M n_i$. Due to communication and privacy constraints, the clients cannot share their local data $\mathcal{\hat{D}}_i$, so \eqref{global} must be solved in a federated manner.
\textbf{FedAvg.} The most common FL method is FedAvg. On each round $t$ of FedAvg, the server uniformly samples a set $\mathcal{I}_t$ of $m\leq M$ clients.
Each selected client receives the current global parameters $\boldsymbol{\theta}_t$, executes multiple SGD steps on its local data starting from $\boldsymbol{\theta}_t$, then sends the result back to the server. The server then computes $\boldsymbol{\theta}_{t+1}$ as the weighted average of the updates. Specifically, upon receiving the global model $\boldsymbol{\theta}_t$, client $i$ computes
\begin{align}
\boldsymbol{\theta}_{t,i,s+1} &= \boldsymbol{\theta}_{t,i,s} - \alpha \mathbf{g}_{t,i,s}(\boldsymbol{\theta}_{t,i,s}), \label{eq_local_updates}
\end{align}
for $s=1,\dots,\tau-1$,
where $\tau$ is the number of local steps, $\boldsymbol{\theta}_{t,i,0} = \boldsymbol{\theta}_t$ and $\mathbf{g}_{t,i,s}(\boldsymbol{\theta}_{t,i,s})$ is a stochastic gradient of $f_i$ evaluated at $\boldsymbol{\theta}_{t,i,s}$ using $b$ samples from $\mathcal{\hat{D}}_i$. The client then sends $\boldsymbol{\theta}_{t,i,\tau}$ back to the server, which computes the next global iterate as:
\begin{equation}
\boldsymbol{\theta}_{t+1} = \frac{1}{N_t}\sum_{i \in \mathcal{I}_t} n_i \boldsymbol{\theta}_{t,i,\tau},
\end{equation} where $N_t \!\coloneqq\! \sum_{i \in \mathcal{I}_t} n_i$.
Note that $\tau\!=\!1$ corresponds to D-SGD, also known as mini-batch SGD whose convergence properties are well-understood \cite{woodworth2020minibatch,nguyen2018sgd,shamir2014distributed,gower2019sgd}. FedAvg improves the communication efficiency of D-SGD by making $\tau\!\geq\! 2$ local updates between communication rounds.
\textbf{Fine-tuning.} After training for $T$ communication rounds, the global parameters $\boldsymbol{\theta}_T$ learned by FedAvg are typically fine-tuned on each client before testing. In particular, starting from $\boldsymbol{\theta}_T$, client $i$ executes $\tau'$ steps of SGD on its local data as follows:
\begin{align}
\boldsymbol{\theta}_{T,i,s+1} = \boldsymbol{\theta}_{T,i,s} - \alpha \mathbf{g}_{T,i,s}(\boldsymbol{\theta}_{t,i,s})
\end{align}
for $s\in [\tau'-1]$. The fine-tuned model ultimately used for testing is $\boldsymbol{\theta}_{T,i,\tau'}$. Note that a new client, indexed by $M+1$, entering the system after FedAvg training has completed can also fine-tune $\boldsymbol{\theta}_{T}$ using the same procedure to obtain a personalized solution $\boldsymbol{\theta}_{T,M+1,\tau'}$.
\textbf{Representation learning.} We aim to answer why the fine-tuned models $\{\boldsymbol{\theta}_{T,i,\tau'}\}_{i=1}^{M+1}$ perform well in practice by taking a representation learning perspective. We show that the output of FedAvg, i.e., $\mathbf{\theta}_T$, has learned the common data representation among clients. To formalize this result, we consider a class of models that can be written as the composition of a representation $h^{\text{rep}}$ and a prediction module, i.e. head, denoted as $h^{\text{head}}$. Let the model parameters be split as $\boldsymbol{\theta} := [\boldsymbol{\phi}, \boldsymbol{\psi}]$, where $\boldsymbol{\phi}$ contains the representation parameters and $\boldsymbol{\psi}$ contains the head parameters. Then, for any $\mathbf{x}\in \mathcal{X}$, the prediction of the learning model is $h_{\boldsymbol{\theta}}(\mathbf{x}) = (h_{\boldsymbol{\psi}}^{\text{head}} \circ h_{\boldsymbol{\phi}}^{\text{rep}})(\mathbf{x}) = h_{\boldsymbol{\psi}}^{\text{head}} (h_{\boldsymbol{\phi}}^{\text{rep}}(\mathbf{x}))$.
For instance, if $h_{\boldsymbol{\theta}}$ is a neural network with weights $\boldsymbol{\theta}$, then $h_{\boldsymbol{\phi}}^{\text{rep}}$ is the first many layers of the network with weights $\boldsymbol{\phi}$, and $h_{\boldsymbol{\psi}}^{\text{head}}$ is the network last few layers with weights $\boldsymbol{\psi}$.
A standard assumption in multi-task settings is existence of a common representation $h_{\boldsymbol{\phi}_\ast}^{\text{rep}}$ that admits an easily learnable head $h_{\boldsymbol{\psi}_{\ast,i}}^{\text{rep}}$ such that $h_{\boldsymbol{\psi}_{\ast,i}}^{\text{head}} \circ h_{\boldsymbol{\phi_*}}^{\text{rep}}$ performs well for task $i$. It is thus of interest to all the clients to learn $h_{\boldsymbol{\phi}_\ast}^{\text{rep}}$.
\section{Intuitions and Proof Sketch} \label{sec:sketch}
Next we highlight the key ideas behind the importance of local updates and why FedAvg learns $\operatorname{col}(\mathbf{B}_\ast)$, while D-GD fails to achieve this goal.
\textbf{Global update $\mathbf{B}_{t+1}$.} To build intuition for why FedAvg can learn $\operatorname{col}{(\mathbf{B}_\ast)}$, we examine the global update of the representation in the full participation case ($m=M$):
\begin{align}
\mathbf{B}_{t+1} &= \mathbf{{B}}_{t}\bigg(\underbrace{ \tfrac{1}{M} \sum_{i=1}^M \prod_{s=0}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top}_{\text{prior weight}})\bigg) + \mathbf{{B}}_\ast \bigg(\underbrace{\tfrac{\alpha}{M}\sum_{i=1}^M \mathbf{w}_{\ast,i} \sum_{s=0}^{\tau-1}\mathbf{w}_{t,i,s}^\top \prod_{r=s+1}^{\tau-1}(\mathbf{I}_k - \alpha \mathbf{w}_{t,i,r}\mathbf{w}_{t,i,r}^\top}_{\text{signal weight}}) \bigg)\nonumber
\end{align}
Notice that $\mathbf{B}_{t+1}$ is a mixture of $\mathbf{B}_t$ and $\mathbf{B}_\ast$ with weight matrices in $\mathbb{R}^{k\times k}$. We aim to show that
\vspace{-1mm}
\begin{enumerate}[(I), leftmargin=25pt, labelindent=1.5pt]
\item the `prior weight' on $\mathbf{B}_t$ has spectral norm strictly less than 1, and
\item the `signal weight' on $\mathbf{B}_\ast$ adds energy from $\operatorname{col}(\mathbf{B}_\ast)$ to $\mathbf{B}_{t+1}$ so that $\sigma_{\min}(\mathbf{B}_{t+1}) \approx \sigma_{\min}(\mathbf{B}_t)$.
\end{enumerate}
\vspace{-1mm}
These properties ensure that the contribution from $\operatorname{col}(\mathbf{B}_t)$ in $\operatorname{col}(\mathbf{B}_{t+1})$ contracts, while energy from $\operatorname{col}(\mathbf{B}_\ast)$ replaces the lost energy from $\operatorname{col}(\mathbf{B}_t)$. Consequently, $\operatorname{col}(\mathbf{B}_{t+1})$ moves closer to $\operatorname{col}(\mathbf{B}_\ast)$ in all $k$ directions.
\textbf{The role of head diversity and multiple local updates.} To show {(I)} and {(II)}, it is imperative to use the diversity of the locally-updated heads when $\tau\geq 2$. First consider {(I)}. Notice that for each $i$, $\prod_{s=0}^{\tau-1}({\mathbf{I}_k \!-\! \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top})$ has singular values at most 1, and strictly less than 1 corresponding to directions spanned by $\{ \mathbf{w}_{t,i,s}\}_{s\in[\tau-1]}$. Thus, the maximum singular value of the average of these matrices should be strictly less than 1 as long as $\{ \mathbf{w}_{t,i,s}\}_{s\in[\tau-1],i \in [M]}$ spans $\mathbb{R}^k$, i.e. the locally-updated heads are diverse. Similarly, the signal weight is rank-$k$ if the locally-updated heads span $\mathbb{R}^k$, which leads to (II) as discussed below.
In contrast, if $\tau=1$, then the global update of the representation does {\em not} leverage head diversity, as it is only a function of the global head and the average ground-truth head: $\mathbf{B}_{t+1} = \mathbf{B}_t({\mathbf{I}_k - \alpha \mathbf{w}_t \mathbf{w}_t^\top}) + \alpha\mathbf{B}_{\ast}{\mathbf{\bar{w}}_{\ast} \mathbf{w}_t^\top}$ in this case. As a result, $\operatorname{col}(\mathbf{B}_{t+1})$ can only improve in one direction, so D-GD ultimately fails to learn $\operatorname{col}(\mathbf{B}_\ast)$ (Prop. \ref{prop:dgd}).
\textbf{Achieving head diversity: the necessity of controlling $\mathbf{I}_k\!- \alpha\mathbf{B}_{t}^\top \mathbf{B}_t$.} We have discussed the intuition for why head diversity implies (I) and (II) for FedAvg. Next, we investigate why the heads become diverse.
Let us examine client $i$'s first local update for the head at round $t$:
\begin{align}
\mathbf{w}_{t,i,1} = (\mathbf{I}_k-\alpha \mathbf{B}_{t}^\top \mathbf{B}_{t}) \mathbf{w}_{t} + \alpha \mathbf{B}_{t}^\top \mathbf{B}_{\ast}\mathbf{w}_{\ast,i} \nonumber
\end{align}
{From this equation we see that if $\boldsymbol{\Delta}_t \coloneqq \mathbf{I}_k - \alpha \mathbf{B}_t^\top \mathbf{B}_t \approx \mathbf{0}$ and $\|\mathbf{w}_t\|$ is bounded, then $\mathbf{w}_{t,i,1} \approx {\alpha} \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i}$. If this approximation holds, then $\{\mathbf{w}_{t,i,1}\}_{i \in [M]}$ inherits the diversity of $\{\mathbf{w}_{\ast,i}\}_{i \in [M]}$, which is indeed diverse due to Assumption \ref{assump:td}, meaning that the local heads are diverse after just one local update.
Moreover, it can be shown that if $\boldsymbol{\Delta}_t \approx \mathbf{0}$ and the heads become diverse after one local update, then they remain diverse for all local updates due to the observation that each $\mathbf{B}_{t,i,s}$ changes slowly over $s$.
Note that in addition to implying local head diversity, $\boldsymbol{\Delta}_t \approx \mathbf{0}$ for all $t$ implies $\sigma_{\min}(\mathbf{B}_t) \approx \sigma_{\min}(\mathbf{B}_{t+1}) \approx \tfrac{1}{\sqrt{\alpha}}$, which directly ensures {(II)}. Thus we aim to show $\boldsymbol{\Delta}_t \approx \mathbf 0$ for all communication rounds, i.e. $\mathbf{B}_t$ remains close to a scaled orthonormal matrix.
However, it is surprising why $\|\boldsymbol{\Delta}_t\|$ remains small:
$\mathbf{B}_{t+1}$ is the average of nonlinearly locally-updated representations, and the local updates could `overfit' by adding more energy to some columns than others, and/or lead to cancellation when summed, so it is not intuitive why $\sqrt{\alpha}\mathbf{B}_t$ remains almost orthonormal. Nor does the expression above for $\mathbf{B}_{t+1}$ provide any clarity on this.} Nevertheless, through a careful induction we show that $\boldsymbol{\Delta}_t$ indeed stays close to zero since the local heads converge quickly and the projection of the local representation gradient onto $\operatorname{col}(\mathbf{B}_t)$ is exponentially decaying.
\textbf{Inductive argument.} While the above intuitions seem to simplify the behavior of FedAvg, showing that they all hold simultaneously is not at all obvious. To study this, we are inspired by recent work \cite{collins2022maml} that developed an inductive argument for representation learning in the context of gradient based-meta-learning.
To formalize our intuition discussed previously, in our proof we need to show that (i) the learned representation does not overfit to each client's loss despite {\em many local updates} and simultaneously the heads quickly become diverse, and (ii) the update at the global server preserves the learned representation despite {\em averaging} many nonlinearly perturbed representations gathered from clients after local updates. To address these challenges, we construct a pair of intertwined induction hypotheses over time, one for tracking the effect of local updates, and another for tracking the global averaging. Each induction hypothesis (local and global) itself consists of several hypotheses (in effect, a nested induction) that evolve both within and across communication rounds.
\textit{Local induction.} The proof leverages the following local inductive hypotheses for every $t,i$:
\begin{enumerate}
\item $A_{1,t,i}(s) \coloneqq \{\|\mathbf{w}_{t,i,s'}- \alpha \mathbf{B}_{t,i,s'-1}^\top \mathbf{B}_{\ast}\mathbf{w}_{\ast,i}\|_2 = c_1\alpha^{2.5} \tau L_{\max}^3 \kappa_{\max}^2 E_0^{-1} \quad \forall s'\in \{1,\dots,s\}\}$
\item $A_{2,t,i}(s) \coloneqq \{\|\mathbf{w}_{t,i,s'}\|_2 \leq c_2 \sqrt{\alpha} L_{\max} \quad \forall s'\in \{1,\dots,s\} \}$
\item $A_{3,t,i}(s) \coloneqq \{\|\mathbf{I}_k - \alpha \mathbf{B}_{t,i,s'}^\top \mathbf{B}_{t,i,s'}\|_2 = c_3\alpha^2 L_{\max}^2 \kappa_{\max}^2 E_0^{-1} \quad \forall s'\in \{1,\dots,s\} \}$
\item $A_{4,t,i}(s)\coloneqq \{ \operatorname{dist}(\mathbf{B}_{t,i,s'}, \mathbf{B}_\ast) \leq c_4 \operatorname{dist}(\mathbf{B}_{t}, \mathbf{B}_\ast)\quad \forall s'\in \{1,\dots,s\}\}$
\end{enumerate}
The local induction tracks the effect of updates at each client node: At the end of $\tau$ local updates, $A_{1,t,i}(\tau)$ captures the diversity of the local heads, $A_{2,t,i}(\tau)$ ensures that the heads remain uniformly bounded,
$A_{3,t,i}(\tau)$ shows that the locally adapted representations stay close to a scaled orthonormal matrix, and $A_{4,t,i}(\tau)$ shows that the locally adapted representations do not diverge too quickly from the ground-truth.
The second set of inductions below controls the global behavior.
\textit{Global induction.} The global induction utilizes a similar set of inductive hypotheses.
\begin{enumerate}
\item $A_1(t) \coloneqq \{ \|\mathbf{w}_{t'} - \alpha(\mathbf{I}_k + \boldsymbol{\Delta}_{t'}) \mathbf{B}_{t'}^\top \mathbf{B}_\ast\mathbf{\bar{w}}_{\ast,t'}\|_2 = c_1'\alpha^{2.5}\tau L_{\max}^3 \quad \forall t'\in \{1,\dots, t\}\}$
\item $A_2(t) \coloneqq \{ \|\mathbf{w}_{t'}\|_2 \leq c_2'\sqrt{\alpha} L_{\max} \quad \forall t'\in \{1,\dots, t\}\}$
\item $A_3(t) \coloneqq \{ \|\boldsymbol{\Delta}_{t'}\|_2 = c_3'\alpha^2 \tau L_{\max}^2 \kappa_{\max}^2 E_0^{-1} \quad \forall t'\in \{1,\dots, t\}\}$
\item $A_4(t) \coloneqq \{ \|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t'}\|_2 \leq (1 - c_4' \alpha^2 \tau \mu^2 E_0)\|\mathbf{B}_{\ast,\perp}^\top \mathbf{B}_{t'-1} \|_2 \quad \forall t'\in \{1,\dots, t\} \}$
\item $A_5(t) \coloneqq \{ \operatorname{dist}(\mathbf{B}_{t},\mathbf{B}_\ast) \leq (1 - c_5'\alpha^2 \tau \mu^2 E_0)^{t-1} \quad \forall t'\in \{1,\dots, t\} \}$
\end{enumerate}
Hypotheses $A_1(t)$, $A_2(t)$ and $A_3(t)$ are analogous to $A_{1,t,i}(s)$, $A_{2,t,i}(s)$ and $A_{3,t,i}(s)$, respectively. $A_4(t)$ shows that the energy of $\operatorname{col}(\mathbf{B}_t)$ that is orthogonal to the ground-truth subspace is contracting, and $A_5(t)$ finally shows that the principal angle distance between the learned and ground-truth representations is exponentially decreasing.
Our main claim follows from $A_5(T)$.
However, proving this result requires showing that all the above local and global hypotheses hold for all times $t\geq1$, as these hypotheses are heavily coupled.
As mentioned previously, the most difficult challenge is controlling $\|\boldsymbol{\Delta}_t\|$ ($A_3(t)$) despite many local updates, and doing so requires leveraging both local and global properties.
The details of this local-global induction argument are in Appendix \ref{app:proof}.
\section{Meeting 4/8}
Still cannot complete the proof when $\alpha^2 \tau \gtrsim 1$...
Notations:
\begin{align}
\hat{\mu}_{\ast}^2 &= \sigma_{\min}\left(\tfrac{1}{n}\sum_{i=1}^n \frac{1}{\|\mathbf{w}_{\ast,i} \|_2^2}\mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top \right) \nonumber \\
\bar{\mathbf{w}}_{\ast} &= \tfrac{1}{n}\sum_{i=1}^n \mathbf{w}_{\ast,i} \nonumber \\
\bar{\mu}_\ast^2 &= \sigma_{\min}\left(\tfrac{1}{n}\sum_{i=1}^n (\mathbf{w}_{\ast,i} - \bar{\mathbf{w}}_{\ast} )(\mathbf{w}_{\ast,i} - \bar{\mathbf{w}}_{\ast} )^\top \right) \nonumber
\end{align}
Two difficulties:
\begin{enumerate}
\item Cannot show that the distance is converging: we have
\begin{align}
\mathbf{B}_{t+1} &= \mathbf{B}_t\left(\tfrac{1}{n}\sum_{i=1}^n \prod_{s=1}^\tau (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top ) \right) + \mathbf{B}_\ast \left(\tfrac{\alpha}{n}\sum_{i=1}^n \mathbf{w}_{\ast,i}\sum_{s=1}^\tau\mathbf{w}_{t,i,s}^\top\prod_{r=s}^{\tau}(\mathbf{I}- \alpha\mathbf{w}_{t,i,r}\mathbf{w}_{t,i,r}^\top) \right) \nonumber \\
\| \mathbf{B}_{\ast,\perp}^\top\mathbf{B}_{t+1}\|_2 &= \|\mathbf{B}_{\ast,\perp}^\top\mathbf{B}_t\|_2\left\|\tfrac{1}{n}\sum_{i=1}^n \prod_{s=1}^\tau (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top ) \right\|_2 \nonumber
\end{align}
Empirically,
\begin{align}
\left\|\tfrac{1}{n}\sum_{i=1}^n \prod_{s=1}^\tau (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top ) \right\|_2 &\approx 1 - \alpha \sigma_{\min}^2(\mathbf{B}_\ast^\top \mathbf{B}_t) \hat{\mu}_\ast^2 \label{recov}
\end{align}
this approximation is tight when $\alpha \sigma_{\min}^2(\mathbf{B}_\ast^\top \mathbf{B}_t) \hat{\mu}_\ast^2 \ll 1$ (note that this quantity scales independently of $\alpha$). If we assume that {\color{red}
\begin{align}
\prod_{s=1}^\tau (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top ) \approx (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,\tau}\mathbf{w}_{t,i,\tau}^\top )^\tau \label{54}
\end{align}}
and $\mathbf{w}_{t,i,\tau}\approx \alpha \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i}$, then we recover \eqref{recov} since
\begin{align}
\left\|\tfrac{1}{n}\sum_{i=1}^n \prod_{s=1}^\tau (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,s}\mathbf{w}_{t,i,s}^\top ) \right\|_2 &\approx \left\|\tfrac{1}{n}\sum_{i=1}^n (\mathbf{I}_k - \alpha \mathbf{w}_{t,i,\tau}\mathbf{w}_{t,i,\tau}^\top )^\tau \right\|_2 \nonumber \\
&\approx \left\|\tfrac{1}{n}\sum_{i=1}^n (\mathbf{I}_k - \alpha^3 \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_t )^\tau \right\|_2 \nonumber \\
&= \left\| \mathbf{I}_k - \tfrac{1}{n}\sum_{i=1}^n\frac{1}{\| \mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i}\|_2^2}\mathbf{B}_t^\top \mathbf{B}_\ast \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top \mathbf{B}_\ast^\top \mathbf{B}_t \right\|_2 \nonumber \\
&\leq \left\| \mathbf{I}_k -\alpha^2{\sigma_{\min}^2(\mathbf{B}_t^\top \mathbf{B}_\ast)} \sigma_{\min}(\tfrac{1}{n}\sum_{i=1}^n\frac{1}{\| \mathbf{w}_{\ast,i}\|_2^2} \mathbf{w}_{\ast,i}\mathbf{w}_{\ast,i}^\top) \right\|_2 \nonumber \\
&\leq 1 - \alpha^2 \sigma_{\min}^2(\mathbf{B}_\ast^\top \mathbf{B}_t) \hat{\mu}_\ast^2
\end{align}
The difficulty is in showing that \eqref{54} holds.
Assume $\alpha \sigma_{\min}^2(\mathbf{B}_\ast^\top \mathbf{B}_t) = 0.5$. Then, since \eqref{54} is tight when $\hat{\mu}_\ast^2$ is small, the error in the approximation in \eqref{54} must scale with something smaller than $\hat{\mu}_\ast^2$. Empirically, it scales with $\alpha^4 \hat{\mu}_\ast^2 \ll \hat{\mu}_\ast^2 $. However, we are only able to upper bound the error by a constant. Approaches we have tried:
\begin{itemize}
\item \textbf{Simply use the fast convergence of $\mathbf{w}_{t,i,s}$.}
Let $\|\mathbf{I}_k - \alpha \mathbf{B}_{t,i,s}^\top \mathbf{B}_{t,i,s} \|_2 \leq D$ for all $s$ (we can show this is true if $\|\mathbf{I}_k - \alpha \mathbf{B}_{t}^\top \mathbf{B}_{t} \|_2 = O(D)$). Then we can show:
\begin{align}
\|\mathbf{w}_{t,i,s+1}- \mathbf{w}_{t,i,s}\|_2 &\leq \sqrt{\alpha} D^s + \alpha^{2.5} (1 - \alpha^2 \|\mathbf{w}_{\ast,i}\|_2^2 )^{2s} \| \mathbf{B}_{t}\mathbf{w}_{t} - \mathbf{B}_{\ast} \mathbf{w}_{\ast,i}\|_2^2
\end{align}
This implies that
\begin{align}
\|\mathbf{w}_{t,i,\tau}- \mathbf{w}_{t,i,s}\|_2 &\leq \sqrt{\alpha} \sum_{r=s}^\tau D^r + \alpha^{2.5} \| \mathbf{B}_{t}\mathbf{w}_{t} - \mathbf{B}_{\ast} \mathbf{w}_{\ast,i}\|_2^2 \sum_{r=s}^\tau (1 - \alpha^2 \|\mathbf{w}_{\ast,i}\|_2^2 )^{2r} \nonumber \\
&\lesssim \sqrt{\alpha} \frac{ D^s}{1 - D} + 0.5 \sqrt{\alpha} (1 - \alpha^2 \|\mathbf{w}_{\ast,i}\|_2^2 )^{2s}\label{55}
\end{align}
Now make two-stage argument:
Let $\mathbf{w}_s = \mathbf{w}_{t,i,s}$ and $\boldsymbol{\delta}_s \coloneqq \mathbf{I}_k - \alpha \mathbf{w}_{s}\mathbf{w}_{s}^\top$.
\begin{align}
\prod_{s=1}^\tau \boldsymbol{\delta}_s - \boldsymbol{\delta}_\tau^\tau = (\prod_{s=1}^{\tau'} \boldsymbol{\delta}_s) (\prod_{z=\tau'}^{\tau} \boldsymbol{\delta}_z - \boldsymbol{\delta}_\tau^{\tau-\tau'}) + \prod_{s=1}^{\tau'} (\boldsymbol{\delta}_s - \boldsymbol{\delta}_\tau^{\tau'})\boldsymbol{\delta}_\tau^{\tau - \tau'}
\end{align}
for some $\tau' : \alpha^2 \tau' \ll 1$.
We know:
\begin{align}
\| \prod_{s=1}^{\tau'} (\boldsymbol{\delta}_s - \boldsymbol{\delta}_\tau^{\tau'})\|_2 &\leq \sum_{s = 1}^{\tau'} \alpha\|\mathbf{w}_{s}\mathbf{w}_{s}^\top - \mathbf{w}_{\tau}\mathbf{w}_{\tau}^\top\| + \sum_{s = 1}^{\tau'}\sum_{s' = 1}^{\tau'} \alpha^2\|\mathbf{w}_{s}\mathbf{w}_{s}^\top - \mathbf{w}_{\tau}\mathbf{w}_{\tau}^\top\|\|\mathbf{w}_{s'}\mathbf{w}_{s'}^\top - \mathbf{w}_{\tau}\mathbf{w}_{\tau}^\top\| + \dots \nonumber \\
&\leq \alpha^2 \tau' + \alpha^4 (\tau')^2 + \dots \nonumber \\
&= c\alpha^2 \tau'
\end{align}
Meanwhile, using \eqref{55} and assuming $D < (1 - \alpha^2 \|\mathbf{w}_{\ast,i}\|_2^2)$, we can show
\begin{align}
\left \| \prod_{z=\tau'}^{\tau} (\boldsymbol{\delta}_z - \boldsymbol{\delta}_\tau^{\tau-\tau'})\right\|_2 &\leq (1 - \alpha^2 \|\mathbf{w}_{\ast,i}\|_2^2)^{2\tau'}
\end{align}
So
\begin{align}
\left \|(\prod_{s=1}^{\tau'} \boldsymbol{\delta}_s) (\prod_{z=\tau'}^{\tau} \boldsymbol{\delta}_z - \boldsymbol{\delta}_\tau^{\tau-\tau'}) + \prod_{s=1}^{\tau'} (\boldsymbol{\delta}_s - \boldsymbol{\delta}_\tau^{\tau'})\boldsymbol{\delta}_\tau^{\tau - \tau'}\right\|_2 &\leq c \alpha^2 \tau' + (1 - \alpha^2 \|\mathbf{w}_{\ast,i}\|_2^2)^{2\tau'}
\end{align}
but there is no $\tau'$ such that the RHS is small (i.e. $O(\alpha^2)$)
\item \textbf{Recursive approach.} Let
\begin{align}
\mathbf{E}_s &\coloneqq \prod_{r=1}^s \boldsymbol{\delta}_r - \boldsymbol{\delta}_s^s
\end{align}
and note that our goal is to control $\|\mathbf{E}_\tau\|_2$. We have:
\begin{align}
\mathbf{E}_{s+1} &= \prod_{r=1}^{s+1} \boldsymbol{\delta}_r - \boldsymbol{\delta}_{s+1}^{s+1} \nonumber \\
&= (\prod_{r=1}^{s} \boldsymbol{\delta}_r - \boldsymbol{\delta}_{s}^{s})\boldsymbol{\delta}_{s+1} \nonumber \\
&\quad +(\boldsymbol{\delta}_s^s - \boldsymbol{\delta}_{s+1}^{s})\boldsymbol{\delta}_{s+1} \nonumber \\
&= \mathbf{E}_s\boldsymbol{\delta}_{s+1} +(\boldsymbol{\delta}_s^s - \boldsymbol{\delta}_{s+1}^{s})\boldsymbol{\delta}_{s+1}
\end{align}
from which we can show
\begin{align}
\|\mathbf{E}_{s+1}\|_2 &\leq \|\mathbf{E}_s\boldsymbol{\delta}_{s+1}\|_2 +\|(\boldsymbol{\delta}_s^s - \boldsymbol{\delta}_{s+1}^{s})\boldsymbol{\delta}_{s+1}\|_2 \nonumber \\
&\leq \|\mathbf{E}_s\|_2 +\|\boldsymbol{\delta}_s^s - \boldsymbol{\delta}_{s+1}^{s}\|_2 \label{loose?} \\
&\leq \|\mathbf{E}_s\|_2 +c\alpha^2 (1 - \alpha^2 \|\mathbf{w}_{\ast,i}\|_2^2)^{2s} \nonumber
\end{align}
which implies $\|\mathbf{E}_\tau\|_2\leq c$, which is not good enough.
There may be looseness in \eqref{loose?} because it ignores the fact that multiplication by $\boldsymbol{\delta}_{s+1}$ causes contraction in exactly one direction ($\mathbf{w}_{s+1}$). However, for this to be useful we must show that most of the energy in $\mathbf{E}_s$ is concentrated in the direction $\mathbf{w}_{s+1}$. But I have not been able to show this...
\item Other approaches:
- Instead of trying to bound the error for each client separately, consider the average error over all clients. But averaging does not seem to give any benefit.
-
\end{itemize}
\item $\|\boldsymbol{\Delta}_t\|_{t+1}\leq \kappa_\ast^{-1}$
Recall $\boldsymbol{\Delta}_{t} \coloneqq \mathbf{I}_k - \alpha\mathbf{B}_t^\top \mathbf{B}_t$ and:
\begin{align}
\|\boldsymbol{\Delta}_{t+1}\|_2 &\leq \underbrace{(1 - \alpha^2 \tilde{\mu}_{\ast}^2)\|\boldsymbol{\Delta}_t\|_2}_{\text{contraction due to first two local updates}} + \underbrace{\alpha^2 L_{\max}^2 \|\boldsymbol{\Delta}_t\|_2^2}_{\text{perturbation due to first two local updates}} \nonumber \\
&\quad + {\color{red}\alpha^2\underbrace{\bigg\|\mathbf{B}_t^\top\tfrac{1}{n}\sum_{i=1}^n \sum_{s = 2}^{\tau-1} (\mathbf{B}_{t,i,s}\mathbf{w}_{t,i,s}- \mathbf{B}_\ast\mathbf{w}_{\ast,t,i})\mathbf{w}_{t,i,s}^\top\bigg\|_2}_{\text{perturbation due to local updates $>2$}}}
\end{align}
When $\alpha^2 \tau \gtrsim 1$ we do not know to bound the perturbation due to more than 2 local updates. Currently we have that this term is upper bounded by $\operatorname{dist}_t^2$, which means
\begin{align}
\|\boldsymbol{\Delta}_{t+1}\|_2 \leq \sum_{s=1}^t(1 - \alpha^2 \bar{\mu}_\ast^2)^{t-s}
\operatorname{dist}_s^2
\end{align}
But even if $\operatorname{dist}_s$ is linearly converging, this bound is not tight enough to show $\|\boldsymbol{\Delta}_t\|_{t+1}\leq \kappa_\ast^{-1}$ (the looseness is in the bound of $\operatorname{dist}_t^2$ on the perturbation term).
\end{enumerate}
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
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{"url":"https:\/\/www.tutorialspoint.com\/c-cplusplus-program-to-find-product-of-unique-prime-factors-of-a-number","text":"# C\/C++ Program to find Product of unique prime factors of a number?\n\nCServer Side ProgrammingProgrammingC++\n\n#### C in Depth: The Complete C Programming Guide for Beginners\n\n45 Lectures 4.5 hours\n\n#### Practical C++: Learn C++ Basics Step by Step\n\nMost Popular\n\n50 Lectures 4.5 hours\n\n#### Master C and Embedded C Programming- Learn as you go\n\nBest Seller\n\n66 Lectures 5.5 hours\n\nIn this section we will see how we can get the product of unique prime factor of a number in an efficient way. There is a number say n = 1092, we have to get product of unique prime factors of this. The prime factors of 1092 are 2, 2, 3, 7, 13. So the unique prime factors are {2, 3, 7, 13}, the product is 546. To solve this problem, we have to follow this rule \u2212\n\n\u2022 When the number is divisible by 2, then multiply 2 with product, and divide the number by 2 repeatedly, then next 2s will be ignored.\n\n\u2022 Now the number must be odd. Now starting from 3 to square root of the number, if the number is divisible by current value, then multiply the factor into product, and change the number by divide it with the current number then continue. Next are ignored like above\n\n\u2022 And finally if the number is greater than 2, then it is not 1, so multiply the remaining number.\n\nLet us see the algorithm to get better idea.\n\n## Algorithm\n\n#### uniquePrimeProduct(n)\n\nbegin\nprod := 1\nif n is divisible by 2, then\nprod := prod * 2\nn := n \/ 2\nend if\nwhile n is divisible by 2, do\nn := n \/ 2\ndone\nfor i := 3 to \u221a\ud835\udc5b, increase i by 2, do\nif n is divisible by i, then\nprod := prod * i\nn := n \/ i\nend if\nwhile n is divisible by i, do\nn := n \/ i\ndone\ndone\nif n > 2, then\nprod := prod * n\nend if\nend\n\n## Example\n\n#include<stdio.h>\n#include<math.h>\nint uniquePrimeProduct(int n){\nint i, prod = 1;\nif(n % 2 == 0){\nprod *= 2;\nn = n\/2;\n}\nwhile(n % 2 == 0){\/\/skip next 2s\nn = n\/2;\n}\nfor(i = 3; i <= sqrt(n); i=i+2){ \/\/i will increase by 2, to get only odd numbers\nif(n % i == 0){\nprod *= i;\nn = n\/i;\n}\nwhile(n % i == 0){ \/\/skip next i's\nn = n\/i;\n}\n}\nif(n < 2){\nprod *= n;\n}\nreturn prod;\n}\nmain() {\nint n;\nprintf(\"Enter a number: \");\nscanf(\"%d\", &n);\nprintf(\"Product of prime factors: %d\", uniquePrimeProduct(n));\n}\n\n## Output\n\nEnter a number: 1092\nProduct of prime factors: 546\nUpdated on 30-Jul-2019 22:30:26\n\nAdvertisements","date":"2022-11-28 16:35:08","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2681562006473541, \"perplexity\": 2501.8367531826902}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710533.96\/warc\/CC-MAIN-20221128135348-20221128165348-00315.warc.gz\"}"} | null | null |
Илья Алексеевич Хворостянов (20 июля 1914, с. Салтыково, Курская губерния — 19 февраля 1988, Ленинград) — советский военачальник, вице-адмирал (25.10.1967). Герой Советского Союза (14.09.1945).
Биография
Родился 7 июля 1914 года в селе Салтыково (ныне Губкинского городского округа Белгородской области). Окончил Салтыковскую начальную школу, школу-семилетку в городе Старый Оскол, два курса рабфака и Орловский техникум семеноводства. Работал техником-нормировщиком в совхозе в Россошанском районе.
В Военно-Морском Флоте с июня 1935 года. В 1939 году окончил Военно-морское береговой обороны имени ЛКСМУ в Севастополе. С июня 1939 года по декабрь 1952 года служил на Амурской военной флотилии (АВФ) — командир катера, с декабря 1940 года — командир отряда бронекатеров Иманского отдельного дивизиона речных кораблей. С марта по июль 1943 года учился на отделении штабных командиров Высших специальных классов командного состава ВМФ. Член ВКП(б) с 1940 года.
С июля 1943 года — начальник штаба Уссурийского отдельного дивизиона речных кораблей АВФ. С октября 1943 года — командир Ханкайского отдельного отряда речных бронекатеров АВФ. Отряд базировался на озере Ханка, часть побережья которого находилась под контролем японских войск, оккупировавших Маньчжурию.
Командир Ханкайского отдельного отряда бронекатеров капитан-лейтенант Илья Алексеевич Хворостянов проявил отвагу и геройство в советско-японской войне в августе 1945 года. Лично руководил серией десантных и набеговых операций 1-го отряда в период с 9-го по 14 августа 1945 года на озере Ханка. В районе Юнфандунь был разгромлен штаб японской комендатуры, в базе японского отряда речных кораблей были уничтожены 2 сторожевых речных катеров японцев, уничтожены укреплённые позиции и захвачено боевое знамя. Совместно с пограничниками капитан-лейтенант Хворостянов И. А. успешно высадил армейский десант, овладевший этим населённым пунктом. Дивизион разгромил прибрежные оборонительные позиции японских войск и способствовал успешному наступлению сухопутных войск на этом участке фронта. Дивизион был награждён орденом Нахимова и получил почётное наименование «Ханкайский», десятки краснофлотцев и командиров были представлены к награждению орденами, а командир дивизиона — к присвоению звания Героя Советского Союза.
Указом Президиума Верховного Совета СССР от 14 сентября 1945 года за мужество и героизм, проявленные в борьбе, капитан-лейтенанту Хворостянову Илье Алексеевичу присвоено звание Героя Советского Союза с вручением ордена Ленина и медали «Золотая Звезда».
После войны И. А. Хворостянов продолжал службу в ВМФ СССР. С февраля 1946 года — командир 6-го отдельного дивизиона бронекатеров Амурской военной флотилии. С декабря 1948 года — начальник отдела в штабе этой флотилии, в декабре 1949 года убыл на учёбу.
В декабре 1952 года окончил с отличием Военно-морскую академию имени К. Е. Ворошилова. С декабря 1952 года служил в Морском Генеральном штабе. С января 1953 года — военный советник командующего Дунайской военной флотилии Болгарской народной армии. Когда 1 ноября 1954 года в посёлке Нёнокса в 40 километрах от города Молотовска было начато формирование 21-го полигона Военно-Морских Сил СССР, первым его начальником в марте 1955 года был назначен капитан 2-го ранга Хворостянов И. А. В декабре 1964 года контр-адмирал (воинское звание присвоено 7 мая 1960 года) Хворостянов И. А. был назначен заместителем начальника 4-го института ВМФ по ракетному вооружению в Ленинграде. С января 1965 года — начальник Черноморского Высшего военно-морского училища имени П. С. Нахимова. С ноября 1971 года — заместитель начальника ордена Ленина Высших специальных офицерских классов по учебной работе.
С июня 1974 года вице-адмирал И. А. Хворостянов в запасе. Жил в городе-герое Ленинграде. Скончался 19 февраля 1988 года. Похоронен на (3-й вязовый участок) в Санкт-Петербурге.
Награды
Герой Советского Союза (14.09.1945)
Орден Ленина (14.09.1945)
Четыре ордена Красного Знамени (23.08.1945, 20.09.1945, 30.12.1956, 26.06.1959)
Орден Отечественной войны 1-й степени (11.03.1985)
Два ордена Трудового Красного Знамени (1959, 1970)
Орден Красной Звезды (15.11.1950)
Медаль «За боевые заслуги» (10.11.1945)
медали СССР.
Память
Почётный гражданин города Губкина.
На здании школы № 10 в городе Губкин установлена мемориальная доска в честь Героя.
Мемориальная доска установлена в городе Северодвинске на доме, в котором жил И. А. Хворостянов.
Примечания
Литература
Алексенко Н. П. Герои — губкинцы // История Губкинского района. — Губкин, 1999. — С. 97.
Белгородская энциклопедия. — Белгород, 2000. — С.409-410.
Герои-белгородцы. — 2-е изд. — Воронеж, 1972. — С.244—245.
Золотые Звёзды тихоокеанцев. — Владивосток, 1982. — С.347—350.
Золотые имена губкинцев. — Белгород, 2013. — С.78.
Королёв В. Т. Герои Великого океана. — 2-е изд. — Владивосток, 1972. — С.304—307.
Ратная доблесть белгородцев: Герои Советского Союза и полные кавалеры ордена Славы. — Белгород, 1995. — С.316-317.
Словарь биографический морской. — СПб., 2000. — С.403.
Строкач Л. В. Дорогой ратной славы. — Белгород, 2003. — С.128-130.
Ссылки
Послужной список И. А. Хворостянова на сентябрь 1945 // ОБД «Память народа».
Члены КПСС
Выпускники Военно-морской академии имени Н. Г. Кузнецова
Начальники Черноморского высшего военно-морского училища имени П. С. Нахимова
Моряки Великой Отечественной войны
Участники советско-японской войны (СССР) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,009 |
{"url":"http:\/\/molecularmodelingbasics.blogspot.com\/","text":"## Sunday, March 1, 2015\n\n### Computational Chemistry Highlights: February issue\n\nThe February issue of\u00a0Computational Chemistry Highlights\u00a0is out.\n\nCCH is an\u00a0overlay journal\u00a0that identifies the most important papers in computational and theoretical chemistry published in the last 1-2 years. CCH is not affiliated with any publisher: it is a free resource run by scientists for scientists.\u00a0You can read more about it here.\n\nTable of content for this issue features contributions from CCH editors Dean Tantillo, Marcel Swart, Martin Korth, Johannes Hachmann, Steven Bachrach, and Jan Jensen:\n\nWater\u2013Water and Water\u2013Solute Interactions in Microsolvated Organic Complexes\n\n## Sunday, February 1, 2015\n\n### Computational Chemistry Highlights: January issue\n\nThe January issue of\u00a0Computational Chemistry Highlights\u00a0is out.\n\nCCH is an\u00a0overlay journal\u00a0that identifies the most important papers in computational and theoretical chemistry published in the last 1-2 years. CCH is not affiliated with any publisher: it is a free resource run by scientists for scientists.\u00a0You can read more about it here.\n\nTable of content for this issue features contributions from CCH editors Al\u00e1n Aspuru-Guzik, Andres Cisneros, Steven Bachrach, David Bowler, and Jan Jensen:\n\nConstruction of a Highly Distorted Benzene Ring in a Double Helicene\n\n## Saturday, January 24, 2015\n\n### The conformationally averaged free energy\n\nThe free energy averaged over $N_\\mathrm{conf}$ conformations of molecule X is\n\n$G^\\circ=-RT \\ln \\left( \\sum_I^{N_\\mathrm{conf}} e^{-G^\\circ_I\/RT} \\right)$ \u00a0(1)\n\nHowever, the way to compute an average property of the conformations $\\left\\langle x\\right\\rangle$ is\n\n$\\left\\langle x\\right\\rangle=\\sum_I^{N_\\mathrm{conf}} p_Ix_I$ \u00a0(2)\n\nwhere\n\n$p_I=\\frac{e^{-G_I^\\circ\/RT}}{\\sum_J^{N_\\mathrm{conf}} e^{-G_J^\\circ\/RT}}$ (3)\n\nBut this equation cannot be used to compute the conformationally averaged free energy because\n\n$G^\\circ \\ne \\left\\langle G^\\circ \\right\\rangle$\n\nWhy not? First, let's see where the first equation comes from.\n\nObtaining equation (1)\n\nThe first equation comes from the statistical mechanical definition of the Helmholtz free energy found any any p-chem textbook\n\n$A^\\circ = -RT \\ln \\left( \\sum_i^{\\mathrm{states}} e^{-\\varepsilon_i\/kT} \\right)=-RT \\ln \\left( q \\right)$\n\nThe sum over microstates can be split into sums over microstates of each conformation I\n\n$A^\\circ = -RT \\ln \\left( \\sum_I^{N\\mathrm{conf}} \\sum_{i\\in I}^{\\mathrm{states}} e^{-\\varepsilon_i\/kT} \\right)$\n\n$= -RT \\ln \\left( \\sum_I^{N\\mathrm{conf}} q_I \\right) = -RT \\ln \\left( \\sum_I^{N_\\mathrm{conf}} e^{-A_I^\\circ\/RT} \\right)$\n\nTo get the corresponding expression for the Gibbs free energy [Eq (1)]:\n\n$G^\\circ = A^\\circ +p^\\circ V$\n\n$=-RT \\ln \\left( \\sum_I^{N_\\mathrm{conf}} e^{-A^\\circ_I\/RT} \\right)-RT \\ln \\left( e^{-p^\\circ V\/RT} \\right)$\n\n$=-RT \\ln \\left( \\sum_I^{N_\\mathrm{conf}} e^{-G_I^\\circ\/RT} \\right)$\n\nThe difference between equation (1) and (3) is the conformational entropy\n$G^\\circ - \\left\\langle G^\\circ \\right\\rangle=-RT \\ln \\left( \\sum_J^{N_\\mathrm{conf}} e^{-G_J^\\circ\/RT} \\right)\\sum_I^{N_\\mathrm{conf}} p_I$\n\n$+RT\\sum_I^{N_\\mathrm{conf}} p_I\\frac{-G_I}{RT}$\n\n$=RT \\sum_I^{N_\\mathrm{conf}} p_I \\left( \\frac{-G_I}{RT}- \\ln \\left( \\sum_J^{N_\\mathrm{conf}} e^{-G_J^\\circ\/RT} \\right) \\right)$\n\n$=RT \\sum_I^{N_\\mathrm{conf}} p_I \\left( \\ln \\left( e^{-G_I^\\circ\/RT} \\right) - \\ln \\left( \\sum_J^{N_\\mathrm{conf}} e^{-G_J^\\circ\/RT} \\right) \\right)$\n\n$=RT \\sum_I^{N_\\mathrm{conf}} p_I \\ln(p_I) =-TS_{\\mathrm{conf}}$\n\n## Wednesday, January 7, 2015\n\n### Predicting binding free energies with electronic structure theory: thermodynamic considerations - Part 3\n\n2015.01.25: \u00a0I have summarized discussion of this and related issues in this paper.\n\nPredicting absolute binding free energies of biologically relevant molecules (in aqueous solution at pH 7 using electronic structure theory without empirical adjustments to within 1 kcal\/mol) is one of the holy grails of computational chemistry. Recent work by Grimme and co-workers (here and here) have come close with mean absolute deviations of about 2 kcal\/mol for host-guest complexes. This and other work has shed some light on why it is so difficult to predict binding free energies in aqueous solution, which I will discuss here and in two previous posts (Part 1\u00a0and Part 2). In addition I'll talk about further improvements that could potentially increase the accuracy further.\n\nThe approach is based on the following equation\n\n$\\Delta G^\\circ = \\Delta E_\\mathrm{gas} + \\Delta G^\\circ_{\\mathrm{gas,RRHO}}+\\Delta \\delta G^\\circ_{\\mathrm{solv}}$\n\nwhere $\\Delta E_\\mathrm{gas}$ is the change in electronic energy and $\\Delta G^\\circ_{\\mathrm{gas,RRHO}}$ the change in the translational, rotational, and vibrational free energy computed using the rigid-rotor and harmonic oscillator approximation, respectively - both evaluated in the gas phase. The vibrational frequencies are computed at a lower level of theory compared to that used to compute $\\Delta E_{\\mathrm{gas}}$. $\\Delta \\delta G^\\circ_{\\mathrm{solv}}$ is the change in solvation free energy computed using a continuum model of the solvent, such as COSMO.\n\nSolvation Thermodynamics\nBackground.\u00a0Most continuum models (CMs) of solvation compute the solvation free energy as the difference between the free energy in solution and the gas phase electronic energy\n\n$\\delta G^\\circ\\mathrm{_{solv}(X)}=G\\mathrm{^{\\circ,CM}_{soln}(X)}-E\\mathrm{_{gas}(X)}$\n\n$G\\mathrm{^{CM}_{soln}(X)}$ typically contain energy terms describing the electrostatic interaction of the molecule and the continuum as well as the van der Waal inteactions with the solvent and free energy required to create the molecular cavity in the solvent (cavitation). The electrostatic interaction with the solvent alters the molecular wavefunction and is computed self-consistently.\n\nSome software packages automatically compute $G\\mathrm{^{\\circ,CM}_{soln}(X)}$ and $E\\mathrm{_{gas}(X)}$ in one run, while others only compute $G\\mathrm{^{\\circ,CM}_{soln}(X)}$. Also, some programs just compute the electrostatic component of $G\\mathrm{^{\\circ,CM}_{soln}(X)}$ by default. \u00a0However, the van der Waals and, especially, the cavitation component can make sizable contributions to the binding free energy and must be included for accurate results. \u00a0It is worth noting that any hydrophobic contribution to binding will derive primarily from the change in cavitation energy.\n\n$G\\mathrm{^{CM}_{soln}(X)}$ contain parameters (e.g. atomic radii) that are adjusted to reproduce experimentally measured solvation free energies\n\n$\\delta G\\mathrm{^\\circ_{solv}(X)}=G\\mathrm{^{\\circ,exp}_{soln}(X)}-G\\mathrm{^{\\circ,exp}_{gas}(X)}$\n\nThe standard state for both $G\\mathrm{^{\\circ,exp}_{soln}(X)}$ and $G\\mathrm{^{\\circ,exp}_{gas}(X)}$ is generally 1 M. \u00a0The latter is the reason why a 1 M reference state also must be used when computing $\\Delta G^\\circ_{\\mathrm{RRHO}}$\n\nAtomic radii. The solvation energy is computed using a set of atomic radii that define the solute-solvent boundary surface. These radii are usually obtained by fitting to experimentally measured solvation energies. Accurate solvation energies should not be expected from methods that use iso-electron density surfaces or van der Waals radii without additional empirical fitting. When using fitted radii one should use the same level of theory for the solute as was used in the parameterization.\n\nIons. For neutral molecules solvation free energies can be measured with an accuracy of roughly 0.2 kcal\/mol and reproduced theoretically to within roughly 0.5 kcal\/mol. \u00a0However, the solvation energies of ions cannot be directly measured and must be indirectly inferred relative to a standard (typically the solvation energy of the proton). The experimentally obtained solvation energies are typically accurate to within 3 kcal\/mol and can be reproduced computationally with roughly the same accuracy. \u00a0The solvation energy of ions are therefore an especially likely source of error in binding free energies - especially if the ionic regions of the molecules become significantly desolvated due to binding.\n\nGas phase vs solution optimization. \u00a0The fitting of the radii described above is usually done using gas phase optimized structures only, i.e. any change in structure and corresponding rotational and vibrational effects are \"included\" in the radii via the parameterization. \u00a0However, for ionic species gas phase optimization can lead to significantly distorted structures or even proton transfer and in these cases solution phase optimizations and, hence, vibrational frequency calculations, tend to be used. However, numerical instability in the continuum models can make it necessary to increase (i.e. make less stringent) the geometry convergence criteria and can lead to more imaginary frequencies than in the gas phase. One option is to compute the vibrational contribution to $\\Delta G^\\circ_{\\mathrm{RRHO}}$ using gas phase optimized structures.\n\nWhen using solution phase geometries the gas phase single point energies needed to evaluate $\\delta G\\mathrm{^\\circ_{solv}(X)}$ represent added computational expense and it can be tempting to use solution phase free energies to evaluate the binding free energies\n\n$\\Delta G^\\circ = \\Delta G\\mathrm{^{\\circ,CM}_{soln}}- \\Delta G\\mathrm{^{\\circ,CM,RRHO}_{soln}}$\n\nOne problem with this approach is that $\\Delta G\\mathrm{^{\\circ,CM}_{soln}}$, unlike $\\Delta E_{\\mathrm{gas}}$, is not systematically improveable due to the empirical parameterization.\n\nCavities.\u00a0The atomic radii and corresponding cavity generation algorithms are parameterized for small molecules. For more complex molecules such as receptors this can lead to continuum solvation of regions of molecules, e.g. deep in the binding pocket, that are not accessible to the molecular solvent. Furthermore, any solvent molecule inside such pocket is likely to be quite \"un-bulk-like\" and not well-represented by the bulk solvent or fixed by the underlying parametrization. \u00a0However, how big an error this may introduce to the binding free energy is not really known, but certain models for the cavitation energy have been shown to give unrealistically large contributions to the binding free energy.\n\nExplicit water molecules. Adding explicit solvent molecules to the receptor and\/or ligand can potentially lead to more accurate results. For example, including explicit water molecules around ionic sites reduces the strong dependence of the solvation energy on the corresponding atomic radii. Also, \"un-bulk-like\" water molecules now are treated more naturally and the risk of solvating non-solvent-acesssible regions is reduced somewhat. \u00a0However, adding explicit solvent molecules increases the computational cost by increasing the CPU time needed to compute energies, perform conformational searches, and compute vibrational frequencies.\n\nThere are several approaches to include the effect of explicit solvent molecules in the binding free energy. \u00a0Bryantsev and co-workers suggest computing the solvation energy by\n\n$\\delta G^\\circ_{\\mathrm{solv},n}\\mathrm{(X)}=\\Delta G^\\circ_{\\mathrm{gas}}\\mathrm{(X(H_2O)_n})+\\delta G^\\circ_{\\mathrm{solv}}\\mathrm{(X(H_2O)_n)}-$\n\n$\\delta G^{\\circ,liq}_{\\mathrm{solv}}\\mathrm{((H_2O)_n)}$\n\nwhere\n\n$\\Delta G^\\circ_{\\mathrm{gas}}\\mathrm{(X(H_2O)_n})=G^\\circ_{\\mathrm{gas}}\\mathrm{(X(H_2O)_n})-G^\\circ_{\\mathrm{gas}}\\mathrm{(X})-G^\\circ_{\\mathrm{gas}}\\mathrm{((H_2O)_n})$\n\nand\n\n$\\delta G^{\\circ,liq}_{\\mathrm{solv}}\\mathrm{((H_2O)_n)}=\\delta G^\\circ_{\\mathrm{solv}}\\mathrm{((H_2O)_n)}+RT\\ln(\\mathrm{[H_2O]\/n})$\n\nwith \"$\\circ$\" and \"$liq$\" referring to a standard state of 1 M and 55.34, respectively. \u00a0The term $RT\\ln(\\mathrm{[H_2O]\/n})$ is the free energy required to change the standard state of (H$_2$O)$_n$ from 1 M to 55.34\/n M.\n\nBryantsev et al. have shown that using this water cluster approach leads to a smooth convergence of the solvation free energy with respect to the cluster size $n$. \u00a0The optimum choice of $n$ is this one where an additional water does changes the solvation energy by less than a certain user defined amount. \u00a0One can thereby compute the optimum number of water molecules for the receptor ($n$), ligand ($m$) and receptor-ligand complex ($l$) and then compute the binding free energy as\n\n$\\Delta \\delta G^\\circ_{\\mathrm{solv},x}=\\delta G^\\circ_{\\mathrm{solv},l}\\mathrm{(RL)}-\\delta G^\\circ_{\\mathrm{solv},n}\\mathrm{(L)}-\\delta G^\\circ_{\\mathrm{solv},m}\\mathrm{(R)}$\n\nand computing $\\Delta E_{\\mathrm{gas}}$ and $\\Delta G^\\circ_{\\mathrm{RRHO}}$ as before. \u00a0One can show that this corresponds to the free energy change for this reaction\n\n$\\mathrm{L(H_2O)_n(aq)+R(H_2O)_m(aq)+(H_2O)_l(liq) \\rightleftharpoons RL(H_2O)_l(aq)}+$\n$\\mathrm{(H_2O)_n(liq)+L(H_2O)_m(liq)}$ (1)\n\nIn principle the free energy change is zero for\n\n$\\mathrm{(H_2O)_l(liq) \\rightleftharpoons+(H_2O)_n(liq)+L(H_2O)_m(liq)+sgn(d)(H_2O)_{|d|}(liq)}$\n\nwhere $d=l-m-n$ and sgn(d) returns the sign of d. So the free energy change for Reaction (1) can also be computed as the free energy change for\n\n$\\mathrm{L(H_2O)_n(aq)+R(H_2O)_m(aq) \\rightleftharpoons RL(H_2O)_l(aq)+sgn(d)(H_2O)_{|d|}}$ (2)\n\nHowever, this is only approximately true in practice due to errors in the computed gas phase and solvation free energies. Furthermore, Reaction 2 does not really lead to any significant reduction in CPU time because the water cluster free energies only have to be computed once. However, if Reaction (2) is used then one must add an additional term correcting for the indistinguishability of water molecules\n\n$G^\\circ_{\\mathrm{RRHO}}\\mathrm{(X(H_2O)_n)} \\rightarrow G^\\circ_{\\mathrm{RRHO}}\\mathrm{(X(H_2O)_n)}-RT\\ln (n!)$\n\nand similarly for the water clusters. \u00a0Using Reaction (1) leads to a cancellation of this term and also maximizes error cancellation in the other energy terms. Similar considerations apply to when using individual water molecules to the balance the reaction instead of water clusters\n\n$\\mathrm{(H_2O)_l(liq) \\rightleftharpoons (H_2O)_n(liq)+L(H_2O)_m(liq)+sgn(d)|d|H_2O}$\n\nWhen using many explicit water molecules the error in the continuum solvation energies can be reduced by ensuring that the continuum solvation energy of a single water molecule matches the experimental value of -6.32 kcal\/mol at 298.15K as close as possible.\n\n## Thursday, January 1, 2015\n\n### Computational Chemistry Highlights: December issue\n\nThe December issue of\u00a0Computational Chemistry Highlights\u00a0is out.\n\nCCH is an\u00a0overlay journal\u00a0that identifies the most important papers in computational and theoretical chemistry published in the last 1-2 years. CCH is not affiliated with any publisher: it is a free resource run by scientists for scientists.\u00a0You can read more about it here.\n\nTable of content for this issue features contributions from CCH editors Al\u00e1n Aspuru-Guzik, Robert Paton, Steven Bachrach, David Bowler, and Jan Jensen:\n\nDiscovering chemistry with an ab initio nanoreactor\n\nTautomerism in Neutral Histidine\n\nInterested in more?\u00a0There are many ways to subscribe to CCH updates.\n\nAlso, for your daily computational chemistry fix subscribe to\u00a0Computational Chemistry Daily\n\n## Monday, December 29, 2014\n\n### Predicting binding free energies with electronic structure theory: thermodynamic considerations - Part 2\n\n2015.01.25: \u00a0I have summarized discussion of this and related issues in this paper. \u00a0I have also made some changes in the post to reflect what I have learned since I wrote it.\n\nPredicting absolute binding free energies of biologically relevant molecules (in aqueous solution at pH 7 using electronic structure theory without empirical adjustments to within 1 kcal\/mol) is one of the holy grails of computational chemistry. Recent work by Grimme and co-workers (here and here) have come close with mean absolute deviations of about 2 kcal\/mol for host-guest complexes. This and other work has shed some light on why it is so difficult to predict binding free energies in aqueous solution, which I will discuss here and in a previous post. In addition I'll talk about further improvements that could potentially increase the accuracy further.\n\nThe general approach is based on the following equation\n\n$\\Delta G^\\circ = \\Delta E + \\Delta G^\\circ_{\\mathrm{RRHO}}+\\Delta \\delta G_{\\mathrm{solv}}$\n\nwhere $\\Delta E$ is the change in electronic energy and $\\Delta G^\\circ_{\\mathrm{RRHO}}$ the change in the translational, rotational, and vibrational free energy computed using the rigid-rotor and harmonic oscillator approximation, respectively. The vibrational frequencies are computed at a lower level of theory compared to that used to compute $\\Delta E$. $\\Delta \\delta G_{\\mathrm{solv}}$ is the change in solvation free energy computed using a polarizable continuum model such as COSMO.\n\npH and molecular charge. Virtually all binding measurements in aqueous solution are performed in buffer with a constant pH and many ligands and or receptors contain one or more ionizable groups. The charge of an ionizable (acid\/base) group in aqueous solution depends on its pK$_a$ and the pH:\n\n$q= \\frac{1}{1+10^{\\mathrm{pH}-\\mathrm{p}K_a}}-\\delta$\n\nwhere $\\delta$ is 1 for an acid and 0 for a base. \u00a0In most cases, selecting the wrong charge for the ligand and\/or host will result in a significant error in the computed binding free energy. \u00a0The pK$_a$ can be computed using electronic structure theory or empirically using software such Marvin. However, if the pK$_a$ value is perturbed by the binding the situation may be complicated further. Here I illustrate this point for a simple example where the ligand (L) has a basic group that is neutral when deprotonated and the receptor (R) is non-ionizable.\n\n$\\mathrm{R + L(H^+) \\rightleftharpoons RL(H^+)}$\n\nThe (apparent) experimental binding constant is then\n\n$K^\\prime=\\mathrm{\\frac{[RL]+[RLH^+]}{[R]([L]+[LH^+])}}$\n\nand the corresponding binding free energy is\n\n$\\Delta G^{\\prime\\circ}=\\Delta G^{\\circ}(+)-RT\\ln \\left( \\frac{1+10^{\\mathrm{pH}-\\mathrm{p}K_a^c}}{1+10^{\\mathrm{pH}-\\mathrm{p}K_a^f}} \\right)$ \u00a0 (1)\n\nwhere $\\Delta G^{\\circ}(+)$ is the binding free energy computed using the charged (protonated) form of the ligand and pK$_a^c$ and pK$_a^f$ are the\u00a0pK$_a$\u00a0values the ligand bound to the receptor and the free ligand, respectively.\n\nIf the pK$_a$ is unaffected by the binding, the binding free energy is unaffected by pH and the chosen protonation state of the ligand. For the remaining scenarios it is instructive to plug in some numbers. For example, for pH = 7, pK$_a^f$ = 9 and pK$_a^c$ = 11, the ligand is protonated before and after binding and $\\Delta G^{\\prime\\circ}=\\Delta G^{\\circ}(+)$ is a good approximation. However, if pH = 7,\u00a0pK$_a^f$ = 5 and pK$_a^c$ = 3, the ligand is neutral before and after binding and assuming it is charged leads to a 2.7 kcal\/mol error in the binding free energy (unless corrected by this equation). \u00a0Finally, if pH = 7,\u00a0pK$_a^f$ = 8 and pK$_a^c$ = 6, the ligand is (91%) charged before and (91%) neutral after binding and assuming it remains charged leads to a 1.4 kcal\/mol error in the binding free energy.\n\nFor many ligands of interest the pK$_a^f$ can be estimated fairly accurately in a matter of second using programs such as Marvin. The effect of binding on pK$_a^f$ can often be estimated by chemical intuition since hydrogen bonds to charged acid and basic groups tend to, respectively, lower or raise the pK$_a$ even further. \u00a0For example, if an amine with pK$_a^f$ = 9 binds to the receptor via hydrogen bonding, then pK$_a^c$ is likely higher than 9 and $\\Delta G^{\\prime\\circ}=\\Delta G^{\\circ}(+)$ is a good approximation. \u00a0However, if pK$_a^f$ is close to 7 then pK$_a^c$ should be computed. \u00a0Also, it is possible for charged ligands to change to their neutral state if they bind to hydrophobic or similarly charged receptors.\n\nIf pK$_a^f$ is known with some degree of confidence then pK$_a^c$ can be estimated by\n\n$\\mathrm{p}K_a^c=\\mathrm{p}K_a^f-\\Delta G^\\circ \/RT\\ln(10)$\n\nwhere $\\Delta A^\\circ$ is the free energy change for\n\n$\\mathrm{RLH^+ + L \\rightleftharpoons RL + LH^+}$\n\nIf there are several ionizable groups then Eq (1) generalizes to\n\n$\\Delta G^{\\prime\\circ}=\\Delta G^{\\circ}(-\/+)-RT\\ln \\left(\\sum_i \\frac{1+10^{n_i(\\mathrm{pH}-\\mathrm{p}K_{a,i}^c)}}{1+10^{n_i(\\mathrm{pH}-\\mathrm{p}K_{a,i}^f)}} \\right)$\n\nwhere $\\Delta G^{\\circ}(-\/+)$ is the binding free energy when all acids and bases are deprotonated and protonated, respectively, the sum runs over all ionizable groups and $n_i$ is 1 and -1 if $i$ is a base or acid, respectively.\n\nHowever, this assumes that the ionizable groups\u00a0titrate independently of one another, i.e. that the pK$_a$\u00a0value of one group is independent of the protonation states of all other ionizable groups. \u00a0If that is not the case then it is difficult to give a general expression for the pH-dependent free energy correction in terms of pK$_a$\u00a0values (though it can easily be derived for a specific case).\n\nInstead a general expression can be written in terms of Legendre transformed free energies as suggested by Alberty\u00a0(modified here to electronic structure calculations):\n\n$G^{\\prime\\circ}(\\overline{X})=-RT\\ln \\left( \\sum_i \\exp{(-G^{\\prime\\circ}(X_i)\/RT)} \\right)$\n\nHere the sum runs over all possible protonation states and\n\n$G^{\\prime\\circ}(X_i)=G^{\\circ}(X_i)-n(\\mathrm{H^+})[\\delta G^\\circ (\\mathrm{H^+}) -RT\\ln(10)\\mathrm{pH}]$\n\nwhere $G^{\\circ}(X_i)$ is the usual standard free energy of protonation state $i$, $n(\\mathrm{H^+})$ is the number of ionizable proton in pronation state $i$, and $\\delta G^\\circ (\\mathrm{H^+})$ is the solvation free energy of the proton. \u00a0So in the case of ligand L considered above, $n(\\mathrm{H^+})$ is 0 and 1 for L and LH$^+$, respectively. $\\delta G^\\circ (\\mathrm{H^+})$ is usually taken from the literature where estimates vary between -265.8 and -268.6 kcal\/mol.\n\nThus, Eq (1) can be rewritten as\n\n$\\Delta G^{\\prime\\circ}=G^{\\prime\\circ}(\\overline{RL})-G^{\\prime\\circ}(\\overline{L})-G^{\\circ}(R)$\n\nSince the electronic energy contribution to the standard free energy can be very large in magnitude this form is more easily evaluated\n\n$G^{\\prime\\circ}(\\overline{X})=G^{\\prime\\circ}({X_0})-RT\\ln \\left( 1+\\sum_{i\\ne0} \\exp{(-G^{\\prime\\circ}(X_i)\/RT)} \\right)$\n\nwhere $X_0$ is some arbitrarily chosen reference protonation state, for example that for which $n(\\mathrm{H^+})$ = 0. \u00a0The sum can be combined with that over different conformations, discussed in a previous post.\n\nOther ions\nThe buffers that are commonly used to regulate the pH also contain other ions, such as Na$^+$, Mg$^{2+}$, Cl$^-$. \u00a0At high ion concentrations, it is possible that these ions bind at certain sites in the ligand, receptor, or ligand-receptor complex with sufficient probability that they must be included in the thermodynamics. If so the exact same equations and considerations outlined above for H$^+$ also apply to, e.g. Cl$^-$ and pCl$^-$ (computed from the specified buffer concentration) is used instead of pH.\n\n## Saturday, December 27, 2014\n\n### Predicting binding free energies with electronic structure theory: thermodynamic considerations - Part 1\n\n2015.01.25: \u00a0I have summarized discussion of this and related issues in this paper. \u00a0I have also made some changes in the post to reflect what I have learned since I wrote it.\n\nPredicting absolute binding free energies of biologically relevant molecules (in aqueous solution at pH 7 using electronic structure theory without empirical adjustments to within 1 kcal\/mol) is one of the holy grails of computational chemistry. Recent work by Grimme and co-workers (here and here) have come close with mean absolute deviations of about 2 kcal\/mol for host-guest complexes. This and other work has shed some light on why it is so difficult to predict binding free energies in aqueous solution, which I will discuss here and in subsequent posts. In addition I'll talk about further improvements that could potentially increase the accuracy further.\n\nThe approach is based on the following equation\n\n$\\Delta G^\\circ = \\Delta E + \\Delta G^\\circ_{\\mathrm{RRHO}}+\\Delta \\delta G_{\\mathrm{solv}}$\n\nwhere $\\Delta E$ is the change in electronic energy and $\\Delta G^\\circ_{\\mathrm{RRHO}}$ the change in the translational, rotational, and vibrational free energy computed using the rigid-rotor and harmonic oscillator approximation, respectively. The vibrational frequencies are computed at a lower level of theory compared to that used to compute $\\Delta E$. $\\Delta \\delta G_{\\mathrm{solv}}$ is the change in solvation free energy computed using a polarizable continuum model such as COSMO.\n\nElectronic energy\nGrimme has shown that dispersion typically makes a very big (>10 kcal\/mol) contribution to binding free energies of host-guest complexes. Dispersion corrections are therefore a must if DFT is used to compute the electronic binding energy. Furthermore, Grimme has shown that three-body dispersion makes a non-negligible (2-3 kcal\/mol) contribution to the electronic binding energy. \u00a0For convergent methods this effect is only included in rather expensive methods that involve triple-excitations such as MP4 and CCSD(T).\n\nMolecular Thermodynamics\nThe translational, rotational and vibrational thermodynamic contribution to the binding free energy is very large (>10 kcal\/mol) and must be included for accurate results. \u00a0Some years ago there was a bit of confusion in the literature about whether the RRHO approach was appropriate for condenses phase systems, but Zhou and Gilson have clarified this beautifully.\n\nStandard state.\u00a0 Most electronic structure codes compute the RRHO energy corrections for an ideal gas, where the standard state is a pressure of 1 bar. \u00a0The standard state for solution is 1 M, so the free energy of a molecule X must be corrected accordingly\n\n$G^\\circ_{\\mathrm{RRHO}}(\\mathrm{X}) = G^{\\circ,\\mathrm{1 bar}}_{\\mathrm{RRHO}}(\\mathrm{X})-RT\\ln (V^{-1})$\n\nwhere $V$ is the volume of an ideal gas at 1 bar and temperature $T$. At 298K $-RT\\ln (V^{-1})$ = 1.90 kcal\/mol. \u00a0This correction is already included in the solvation energy $\\delta G_{\\mathrm{solv}}$\n\nSymmetry. Many host molecules and some guest molecules are symmetric, which affects the rotational entropy through the symmetry number ($\\sigma$) which is a function of the point group.\n\n$S_{rot}=R\\ln\\left(\\frac{8\\pi^2}{\\sigma}\\left(\\frac{2\\pi ekT}{h^2}\\right)^{3\/2}\\sqrt{I_1I_2I_3}\\right)$\n\nIt can be very difficult to build large molecules with the correct point group and most studies use $C_1$ symmetry. \u00a0In this case the effect of symmetry must be added manually to the free energy\n\n$G^\\circ_{\\mathrm{RRHO}}(\\mathrm{X}) \\rightarrow G^\\circ_{\\mathrm{RRHO}}(\\mathrm{X})+RT \\ln(\\sigma_X)$\n\nAs an example, the popular host molecule corcubit[7] has $D_{7h}$ symmetry and a corresponding $\\sigma$ value of 14, in which case the correction contributes 1.56 kcal\/mol to the free energy at 298K.\n\nAnharmonicity and low frequency modes. Host-guest complexes can exhibit very low frequency vibrations on the order of 50 cm$^{-1}$ or less, which tend to dominate the vibrational entropy contribution. \u00a0Grimme (and many others) have questioned whether the harmonic approximation is valid for such low frequency modes and this is an open research question. \u00a0The main problem is that it is very difficult to compute the vibrational entropy exactly. \u00a0Most methods for computing anharmonic vibrational are developed to obtain the 2 or 3 lowest energy states, but for very low frequency modes 10-20 states likely significantly populated at room temperature and therefore contribute to the entropy.\n\nIn the absence of theoretical benchmarks, comparison to experiment can prove constructive. Kj\u00e6rgaard and co-workers have recently measured standard binding free energies for small gas phase compounds and compared them to CCSD(T)\/aug-cc-pV(T+d) calculations. \u00a0For example, in the case of acetronitrile-HCl the measured binding free energy at 295K is between 1.2 and 1.9 kcal\/mol, while the predicted value is 2.3 kcal\/mol using the harmonic approximation. \u00a0Since the errors in $\\Delta E$ and the rigid-rotor approximation presumably are quite low, this suggest and error in the vibrational free energy of at most 1.1 kcal\/mol, despite the fact that the lowest vibrational frequency is only about 30 cm$^{-1}$. \u00a0Furthermore, the error can be reduced by 0.4 kcal\/mol by scaling the harmonic frequencies by anharmonic scaling factors suggested by Shields and co-workers. \u00a0Similar results were found for dimethylsulfide-HCl. \u00a0So there are some indications that the harmonic approximation yields free energy corrections that are reasonable and that can be improved upon by relatively minor corrections.\n\nGrimme has taken a different approach by arguing that low-frequency modes resemble free rotations and using the corresponding entropy term for low frequency modes. \u00a0This changes the RRHO free energy correction by 0.5 - 4 kcal\/mol, depending on the system.\n\nImaginary frequencies.\u00a0Low frequencies are especially susceptible to numerical error and it is not unusual to see 1 or 2 imaginary frequencies of low magnitude in a vibrational analysis of a host-guest complex. \u00a0Since imaginary frequencies are excluded from the vibrational free energy this effectively removes 1 or 2 low frequency contributions to the vibrational free energy. For example, a 30 cm$^{-1}$ frequency contributes about 1.7 kcal\/mol to the free energy at 298K.\n\nImaginary frequencies resulting from a flat PES and numerical errors can often be removed by making the convergence criteria for the geometry optimization and electronic energy minimization more stringent and making the grid size finer in the case of DFT calculations. If the Hessian is computed using finite difference it is important to use double-differencing. \u00a0If all else fails, it is probably better to pretend that the imaginary frequency is real and add the corresponding vibrational free energy contribution.\n\nConformations. One of the main problems in computing accurate binding free energies is to identify the structures of the host, guest and (especially) the host-guest complex with the lowest free energy. Because both the RRHO and solvation energy contributions contribute greatly to the binding free energy change, simply finding the structure with the lowest electronic energy and computing the free energy only for that conformation is probably not enough.\n\nThe free energy for a molecule (X) with N conformations the standard free energy is\n\n$G^\\circ(\\mathrm{X})= G^\\circ _0(\\mathrm{X})-RT\\ln\\left(\\sum^N_{i=1} \\left( 1+\\exp{\\left( -(G^\\circ _i- G^\\circ _0)\/RT\\right)} \\right)\\right)$\n\nwhere $G^\\circ _0(\\mathrm{X})$ is the conformation with lowest free energy. \u00a0Conformations with free energies higher than 1.36 kcal\/mol contribute less than 0.1 to the sum at 298K. \u00a0So a significant number of very low free energy structures is needed to make even a 0.5 kcal\/mol contribution to the free energy. \u00a0Conformations related by symmetry should not be included here as their effects are accounted for in the rotational entropy (see above). \u00a0Also, conformationally flexible regions of the ligand or host that are unaffected by binding need not be explored since the effect on the binding free energy will cancel.","date":"2015-03-30 02:18:50","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.760523796081543, \"perplexity\": 1151.6772395601326}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-14\/segments\/1427131298889.70\/warc\/CC-MAIN-20150323172138-00063-ip-10-168-14-71.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}
\label{sec:intro}
The $\pi$-calculus \cite{milner.parrow.ea:calculus-mobile,sangiorgi.walker:theory-mobile}
holds an honoured position amongst process calculi as a succinct calculus that can capture topological changes in a network, as well as encode computation as represented by $\l$-calculus \cite{Barendregt85}.
Interaction in $\pi$-calculus is done by matching upon a single name known by both the input and output primitives.
The polyadic $\pi$-calculus extends this by also matching on the length of the tuple of names to be communicated.
Linda \cite{Gel85} extends this further by allowing matching on any number of names known by both processes.
A more symmetric approach to communication is taken in Fusion calculus \cite{parrow.victor:fusion-calculus}
that matches a channel name and tuple length, like polyadic $\pi$-calculus, but allows symmetric information exchange.
Other calculi consider structured information rather than simply names \cite{gordon1997ccp},
even matching arbitrary structures asymmetrically during communication \cite{BJPV11}.
Hence it is natural to explore how a concurrent pattern calculus can unify structured patterns with symmetric matching and communication mechanisms.
This paper develops pattern unification in a setting that supports
parallel composition, name restriction, and replication. This yields
{\em concurrent pattern calculus} (CPC), where prefixes for input and
output are generalised to patterns whose {\em unification} triggers a
symmetric flow of information, as represented by the sole interaction
rule
\[
(p\pre P \bnf q\pre Q) \quad \rew \quad \sigma P\bnf \rho Q
\]%
where $\sigma$ and $\rho$ are the substitutions on names resulting
from the unification of the patterns $p$ and $q$.
The flexibility of the pattern unification and the symmetry of exchange
in CPC align closely with the world of trade. Here the support for
discovering a compatible process and exchanging information mirrors
the behaviour of trading systems such as a stock market.
The main features of CPC are illustrated in the following sample trade interaction:
\[
\begin{array}{r}
\res{\mathit{\ sharesID}}\pro{\mathit{ABCShares}}\bullet\mathit{sharesID}\bullet\l x
\to \xangle{\mathit{charge\ x\ for\ sale}}
\\ \bnf \quad
\res{\mathit{\ bankAcc}}\pro{\mathit{ABCShares}}\bullet\l y\bullet\mathit{bankAcc}
\to \xangle{\mathit{save\ y\ as\ proof}}
\vspace*{.3cm}
\\
\redar
\res{\mathit{\ sharesID}}\res{\mathit{\ bankAcc}}
(\xangle{\mathit{charge\ bankAcc\ for\ sale}}\\
\bnf \xangle{\mathit{save\ sharesID\ as\ proof}})
\end{array}
\]
The first line models a seller that will synchronise with a buyer, using the protected
information $\mathit{ABCShares}$, and exchange its shares ($\mathit{sharesID}$) for bank
account information (bound to $x$).
The second line models a buyer. Notice that the information exchange is bidirectional
and simultaneous: {\it sharesID} replaces $y$ in the (continuation of the) buyer and
{\it bankAcc} replaces $x$ in the (continuation of the) seller.
Moreover, the two patterns $\pro{\mathit{ABCShares}}\bullet\mathit{sharesID}\bullet\l x$
and $\pro{\mathit{ABCShares}}\bullet\l y\bullet\mathit{bankAcc}$ also specify the
details of the stock being traded, that must be matched for equality in the pattern
matching, as indicated by the syntax $\pro {\,\cdot\,}$.
Pattern unification in CPC is even richer than indicated in this example, as unification
may bind a compound pattern to a single name; that is, patterns do not need to be
fully decomposed in unification.
For example, the bank account information could be specified, and matched upon, in
much more detail.
The buyer could provide the account name and number such as in the following pattern:
$\res{\mathit{\ accName}}\res{\mathit{\ accNum}}
\pro{\mathit{ABCShares}}\bullet\l y\bullet
(\mathit{name}\bullet\mathit{accName}\bullet\mathit{number}\bullet\mathit{accNum})$.
This more detailed buyer would still match against the seller, now yielding
$\xangle{\mathit{charge\ \mathit{name}\bullet\mathit{accName}\bullet\mathit{number}\bullet\mathit{accNum}\ for\ sale}}$.
Indeed, the seller could also specify a desire to only accept bank account information
whose structure includes some name and number (bound to $a$ and $b$ respectively) with the following pattern:
$\pro{\mathit{ABCShares}}\bullet\mathit{sharesID}\bullet
(\pro{\mathit name}\bullet\l a\bullet\pro{\mathit number}\bullet\l b)$
and continuation $\xangle{\mathit{charge\ a\ b\ for\ sale}}$.
This would also match with the detailed buyer information by
unifying $name$ with $\pro{name}$, $number$ with $\pro{number}$, and binding
$accName$ and $accNum$ to $a$ and $b$ respectively.
The second seller exploits the structural matching of CPC to only interact with a
buyer whose pattern is of the right structure (four sub-patterns) and contains
the right information (the protected names $name$ and $number$, and shared information
in the other two positions).
The structural patterns of CPC are inspired by those of {\em pattern calculus} \cite{JK09,pcb}
that supports even more computations than $\l$-calculus, since pattern-matching functions may
be {\em intensional} with respect to their arguments \cite{JayGW10}.
For example, the pattern $x~y$ can decompose any compound data structure
$u~v$ into its components $u$ and $v$.
This is different from {\em extensional} computation, like those of
$\l$- and $\pi$-calculus, where arguments are `atomic'.
This rich form of structural interaction, combined with concurrency, makes CPC very expressive, as
illustrated by the following diamond \cite{GivenWilsonPHD}:
\begin{center}
\begin{picture}(240,85)(0,0)
\put(95,1){\mbox{$\l_v$-calculus}}
\put(12,38){\mbox{$SF$-calculus}}
\put(169,38){\mbox{~$\pi$-calculus}}
\put(58,78){\mbox{Concurrent Pattern Calculus}}
\put(90,6){\vector(-1,1){28}}
\put(148,6){\vector(1,1){28}}
\put(62,47){\vector(1,1){28}}
\put(174,47){\vector(-1,1){28}}
\end{picture}
\end{center}
The $\l$-calculus sits at the bottom and can be generalised either by
$SF$-calculus \cite{JayGW10}, by considering intensionality in the sequential setting,
or by $\pi$-calculus, by considering concurrency in the extensional setting.
CPC completes the diamond by adding either concurrency to $SF$-calculus, or
intensionality to $\pi$-calculus. Thus, CPC is the most expressive of all
by supporting intensional concurrent computation.
The definition of CPC also includes a behavioural theory that defines
when two processes are behaviourally equivalent. This is done using a
standard approach in concurrency. First, define an intuitive notion of
equivalence that equates processes with the same behaviour (i.e., with
the same interaction capabilities), in any context and along any reduction sequence, to yield a
notion of {\em barbed congruence}. Second, provide a more effective
characterisation of such equivalence by means of a {\em labelled
transition system} (LTS) and a {\em bisimulation-based} equivalence.
Although this path is familiar, some delicacy is required for each
definition. For example, as unification of patterns may require
testing of names for equality, the {\em barbs} of CPC (i.e. the
predicate describing the interactional behaviour of a CPC process)
must account for names that {\em might} be matched, not just those
that {\em must} be matched. This is different from the standard barbs
of, say, the $\pi$-calculus. Further, as some patterns are more
discriminating than others, the bisimulation defined here will rely on
a notion of {\em compatibility} of patterns, yielding a bisimulation
game in which a challenge can be replied to with a different, though
compatible, reply. This is reminiscent of the asynchronous
bisimulation for the asynchronous $\pi$-calculus
\cite{amadio.castellani.ea:bisimulations-asynchronous}
or the symbolic characterization of open bisimilarity in the $\pi$-calculus
\cite{San96}.
CPC's support for interaction that is both structured and symmetrical
allows CPC to simulate many approaches to interaction and reduction in the
literature \cite{G:IC08}. For example, checking equality of channel names, as in
$\pi$-calculus \cite{milner.parrow.ea:calculus-mobile}, can be viewed
as a trivial form of pattern unification. It also supports
unification of tuples of names, as in Linda \cite{Gel85}, or fusing names,
as in Fusion \cite{parrow.victor:fusion-calculus}. Spi calculus
\cite{gordon1997ccp} adds patterns for numbers (zero and successors)
and encryptions. Also the Psi calculus \cite{BJPV11} introduces
support for structures, albeit with a limited symmetry.
More formally, $\pi$-calculus, Linda and Spi calculus can all be
encoded into CPC but CPC cannot be encoded into any of them. By
contrast, the way in which name fusion is modeled in fusion calculus
is not encodable into CPC; conversely, the richness of CPC's pattern
unification is not encodable in fusion calculus. Similarly, the
implicit computation of name equivalence
in Psi calculus cannot be encoded within CPC;
the converse separation result is ensured by CPC's symmetry.
A natural objection to CPC is that its unification is too complex to
be an atomic operation. In particular, any limit to the size of
communicated messages could be violated by some match. Also, one
cannot, in practice, implement a simultaneous exchange of information,
so that pattern unification must be implemented in terms of simpler
primitives.
This objection applies to many other calculi.
For example, neither polyadic $\pi$-calculus' arbitrarily large tuple communication
nor Linda's pattern matching are atomic, but both underpin many existing programming environments
\cite{Pierce97pict:a,cpplinda,Klava,Lime}.
Indeed the arbitrary complexity of both Psi calculus and CPC patterns can
exceed the capability of any computer, yet both have implementations
\cite{Khorsandiaghai603139,cbondi}.
Simlar comments apply to other process calculi
\cite{20110201:jocaml,nomadic-pict}.
A further complexity is the secure synchronisation and information exchange between agents
in distinct locations \cite{DY83,Fournet07atype,bengtson2011refinement},
however since the focus here is on exploring structured, symmetric, pattern unification
and not implementations, we do not attempt to address these details.
The structure of the paper is as follows. Section \ref{sec:cpc}
introduces symmetric matching through a concurrent pattern calculus
and an illustrative example. Section \ref{sec:bisim} defines the
behavioural theory of the language: its barbed congruence, LTS and the
alternative characterization via a bisimulation-based equivalence. %
Section \ref{sec:compare} formalises the relation between CPC and
other process calculi.
Section \ref{sec:conclusions} concludes the paper.
Standard proofs have been moved to the Appendix.
\section{Concurrent Pattern Calculus}
\label{sec:cpc}
This section presents a {\em concurrent pattern calculus} (CPC) that
uses symmetric pattern unification as the basis of communication. Both
symmetry and pattern matching appear in existing models of
concurrency, but in more limited ways. For example, $\pi$-calculus
requires a sender and receiver to share a channel, so that knowledge
of the channel is symmetric but information flows in one direction
only. Fusion calculus achieves symmetry by fusing names together but
has no intensional patterns. Linda's matching is more intensional as
it can test equality of an arbitrary number of names, and the number
of names to be communicated, in an atomic interaction. Spi calculus
has even more intensional patterns, e.g.~for natural numbers, and can
check equality of terms (i.e.\ patterns), but does not perform
matching in general. Neither Linda or Spi calculus support much
symmetry beyond that of the $\pi$-calculus.
The expressiveness of CPC comes from extending the class of
communicable objects from raw names to a class of {\em patterns} that
can be unified. This merges equality testing and bi-directional
communication in a single step.
\subsection{Patterns}
Suppose given a countable set of {\em names} ${\cal N}$ (meta-variables $n,m,x,y,z,\ldots$).
The {\em patterns} (meta-variables $p,p',p_1,q,q',q_1,\ldots$)
are built using names and have the following forms:
\[
\begin{array}{lll}
{\it Patterns}\quad p \ ::= \
& \lambda x & \mbox{binding name} \\
& x & \mbox{variable name} \\
& \pro x & \mbox{protected name} \\
& p\bullet p \quad & \mbox{compound}
\end{array}
\]%
A binding name $\lambda x$ denotes information sought, e.g.\ by a
trader; a variable name $x$ represents such information. Note that a
binding name binds the underlying process, defined in
Section~\ref{subsec:processes}. Protected names $\pro x$ represent
information that can be checked but not traded. A compound combines
two patterns $p$ and $q$, its {\em components}, into a pattern
$p\bullet q$. Compounding is left associative, similar to application
in $\l$-calculus, and pure pattern calculus.
The {\em atoms} are patterns that are not compounds. The
atoms $x$ and $\pro x$ {\em know} $x$.
Binding, variable and protected names are all well established
concepts in the literature. Indeed, there is a correspondence between
patterns and prefixes of more familiar process calculi, such as
$\pi$-calculus: binding names correspond to input arguments and
variable names to output arguments. Moreover, a form of protected
names appear in Linda.
There is some subtlety in the relationship of protected names to
variable names. As protected names specify a requirement, it is
natural that they unify with the variable form of the name.
Similarly, as protected names can be used to support
channel-based communication, it is also natural that protected names
unify with themselves.
Given a pattern $p$ the sets of: {\em variables names}, denoted ${\sf
vn}(p)$; {\em protected names}, denoted ${\sf pn}(p)$; and {\em
binding names}, denoted ${\sf bn}(p)$, are defined as expected with
the union being taken for compounds. The {\em free names} of a
pattern $p$, written ${\sf fn}(p)$, is the union of the variable names
and protected names of $p$. A pattern is {\em well formed} if its
binding names are pairwise distinct and different from the free ones.
All patterns appearing in the rest of this paper are assumed to be
well formed.
As protected names are limited to recognition and binding names are
being sought, neither should be communicable to another process.
This leads to the following definition.
\begin{defi}[Communicable Pattern]
\label{def:communicable}
A pattern is {\em communicable} if it contains no protected or binding names.
\end{defi}
Protection can be extended from names to communicable patterns by
defining
$$
\pro {p\bullet q} = \pro p \bullet \pro q
$$
A {\em substitution} $\sigma$ is defined as a partial function from names to communicable patterns.
The {\em domain} of $\sigma$ is denoted $\textsf{dom}(\sigma)$;
the free names of $\sigma$, written $\textsf{fn}(\sigma)$, is given by the union of the sets $\textsf{fn}(\sigma x)$ where $x \in \textsf{dom}(\sigma)$.
The {\em names} of $\sigma$, written $\textsf{names}(\sigma)$, are $\textsf{dom}(\sigma)\cup\textsf{fn}(\sigma)$.
A substitution $\sigma$ {\em avoids} a name $x$ (or a collection of names $\wt n$) if $x\notin\textsf{names}(\sigma)$ (respectively $\wt n\cap\textsf{names}(\sigma)=\{\}$).
Note that all substitutions considered in this paper have finite domain.
For later convenience, we denote by $\idsub_X$ the identity
substitution on a finite set of names $X$; it maps every name in $X$ to
itself, i.e. $\idsub_X(x) = x$, for every $x\in X$.
Substitutions are applied to patterns as follows
\begin{eqnarray*}
\sigma x &=&
\left\{
\begin{array}{ll}
\sigma (x) & \mbox{if $x \in \textsf{dom}(\sigma)$}\\
x & \mbox{otherwise}
\end{array}
\right. \\
\sigma \pro x &=&
\left\{
\begin{array}{ll}
\pro{\sigma (x)} & \mbox{if $x \in \textsf{dom}(\sigma)$}\\
\pro x & \mbox{otherwise}
\end{array}
\right. \\
\sigma (\l x)&=& \l x\\
\sigma (p\bullet q)&=& (\sigma p)\bullet (\sigma q)
\end{eqnarray*}
The action of a substitution
$\sigma$ on patterns can be adapted to produce a function $\hat\sigma$
that acts on binding names rather than on free names. In CPC, it is
defined by
\begin{eqnarray*}
\hat\sigma x &=& x\\
\hat\sigma \pro x &=& \pro x\\
\hat\sigma (\l x) &=&
\left\{
\begin{array}{ll}
\sigma(x) &\mbox{if $x \in \textsf{dom}(\sigma)$}\\
\l x &\mbox{otherwise}
\end{array}
\right. \\
\hat\sigma (p\bullet q)&=& (\hat\sigma p)\bullet (\hat\sigma q)
\end{eqnarray*}
When $\sigma$ is of the form $\{p_i/x_i\}_{i \in I}$,
then $\{p_i/\l x_i\}_{i \in I}$ may be used to denote $\hat\sigma$.
The {\em symmetric matching} or {\em unification} $\{p \pmatch q\}$ of
two patterns $p$ and $q$ attempts to unify $p$ and $q$ by generating
substitutions upon their binding names. When defined, the result is
a pair of substitutions whose domains are the binding names of $p$
and of $q$, respectively. The rules to generate the substitutions are:
\begin{eqnarray*}
\begin{array}{rcll}
\left.
\begin{array}{r}
\{x\pmatch x\}\\
\{x\pmatch \pro{x}\}\\
\{\pro{x}\pmatch x\}\\
\{\pro{x}\pmatch \pro{x}\}
\end{array}
\right\}\!\!\! &=\!\!\!& (\{\}, \{\})\\
\{\lambda x\pmatch q\} &=\!\!\!& (\{q/x\}, \{\}) & \mbox{if $q$ is communicable}\\
\{p\pmatch \lambda x\} &=\!\!\!& (\{\}, \{p/x\}) & \mbox{if $p$ is communicable}\\
\{p_1\bullet p_2\pmatch q_1\bullet q_2\} &=\!\!\!& ((\sigma_1\cup\sigma_2), (\rho_1\cup\rho_2))
& \mbox{if } \{p_i\pmatch q_i\}= (\sigma_i, \rho_i) \mbox{ for } i \in \{1,2\}\\
\{p\pmatch q\} &=\!\!\!& \mbox{undefined} & \mbox{otherwise}
\end{array}
\end{eqnarray*}
Two atoms unify if they know the same name. A name that seeks
information (i.e., a binding name) unifies with any communicable pattern to
produce a binding for its underlying name. Two compounds unify if
their corresponding components do; the resulting substitutions are
given by taking unions of those produced by unifying the components
(necessarily disjoint as patterns are well-formed). Otherwise the
patterns cannot be unified and the unification is undefined.
\begin{prop}
\label{prop:free_n_match}
If the unification of patterns $p$ and $q$ is defined then any protected
name of $p$ is a free name of $q$.
\end{prop}
\begin{proof}
By induction on the structure of $p$.
\end{proof}
\subsection{Processes}
\label{subsec:processes}
The processes of CPC are given by:
\[
\begin{array}{lll}
{\it Processes}\quad P \ ::= \
& \zero & \mbox{null} \\
& P|P & \mbox{parallel composition} \\
& !P & \mbox{replication} \\
& \res x P & \mbox{restriction} \\
& p\pre P \quad & \mbox{case}
\end{array}
\]%
The null process, parallel composition, replication and restriction
are the classical ones for process calculi: $\zero$ is the inactive
process; $P\bnf Q$ is the parallel composition of processes $P$ and
$Q$, allowing the two processes to evolve independently or to
interact; the replication $!P$ provides as many parallel copies of $P$
as desired; $\res x P$ binds $x$ in $P$ so that it is not visible from
the outside. The
traditional input and output primitives are replaced by the {\em
case}, viz. $p\pre P$, that has a {\em pattern} $p$ and a {\em body} $P$. If
$P$ is $\zero$ then $p\to \zero$ may be denoted by $p$.
The free names of processes, denoted ${\sf fn}(P)$, are defined as
usual for all the traditional primitives and
\[
{\sf fn}(p\pre P) \quad =\quad {\sf fn}(p)\cup({\sf fn}(P)\backslash{\sf bn}(p))
\]%
for the case. As expected the binding names of the pattern bind their free occurrences in the body.
\subsection{Operational Semantics}
\label{s:reduction-new}
The application $\sigma P$ of a substitution $\sigma$ to a process $P$
is defined in the usual manner, provided that there is no name
capture.
Name capture can be avoided by $\alpha$-conversion (written $=_\alpha$) that
is the congruence relation generated by the following axioms:
\[
\begin{array}{rcll}
\res x P &=_\alpha& \res y (\{y/x\}P) & \quad y\notin{\sf fn}(P)\\
p\pre P &=_\alpha& (\{\l y/\l x\}p)\pre (\{y/x\}P) &
\quad x\in{\sf bn}(p),y\notin{\sf fn}(P)\cup{\sf bn}(p)
\end{array}
\]%
The {\em structural congruence relation} $\equiv$ is defined
just as in $\pi$-calculus \cite{milner:polyadic-tutorial}: it includes
$\alpha$-conversion and its defining axioms are:
\begin{equation*}
\begin{array}{c}
\vspace*{.3cm}
P\bnf \stoppr \equiv P
\qquad
P \bnf Q \equiv Q \bnf P
\qquad
P \bnf (Q \bnf R) \equiv (P \bnf Q) \bnf R
\\
\vspace*{.3cm}
\res n \stoppr \equiv \stoppr
\qquad
\res n \res m P \equiv \res m \res n P
\qquad
!P \equiv P\bnf !P
\\
P\bnf\res n Q \equiv \res n (P\bnf Q)
\quad \mbox{if $n \not\in{\sf fn}(P)$}
\end{array}
\end{equation*}
It states that: $|$ is a commutative, associative, monoidal operator,
with $\zero$ acting as the identity; that restriction has no effect
on the null process; that the order of restricted names is
immaterial; that replication can be freely unfolded; and that the
scope of a restricted name can be freely extended, provided that no
name capture arises.
For later convenience, $\wt x$ denotes a sequence of $x$'s, for example
$\wt n$ can denote the names $n_1,\ldots,n_i$.
Similarly, $\res {n_1} (\ldots (\res {n_i} P))$ will be written $\rest n P$;
however, due to structural congruence, these shall be considered as a set of names.
\withsetnot{}{For clarity set notation is used, for example
$\res {m_1} \res {m_2}\ldots \res {m_i} \res {n_1} \res {n_2} \ldots \res {n_j} P$
shall be denoted $\res {\wt m \cup \wt n} P$.}
The operational semantics of CPC is formulated via a {\em reduction
relation} $\redar$ between pairs of CPC processes. Its defining
rules are:
\begin{eqnarray*}
\begin{array}{c}
\Rule{}
{}
{(p\pre P)\bnf(q\pre Q) \redar (\sigma P)\bnf(\rho Q)}{if $\{p\pmatch q\}=(\sigma,\rho)$}\\
\vspace*{.0cm}
\\
\Rule{}
{P \rew P'}{P|Q \rew P'|Q}{}
\
\Rule{}
{P \rew P'}{\res n P \rew \res n P'}{}
\
\Rule{}
{P \equiv Q \ \ Q \rew Q'\ \ Q' \equiv P'}{P \rew P'}{}
\vspace*{.1cm}
\end{array}
\end{eqnarray*}
CPC has one interaction axiom, stating that, if the unification of two
patterns $p$ and $q$ is defined and generates $(\sigma, \rho)$, then
the parallel composition of two cases $p\pre P$ and $q\pre Q$ reduces
to the parallel composition of $\sigma P$ and $\rho Q$.
Alternatively, if the unification of $p$ and $q$ is undefined, then no
interaction occurs.
Unlike the sequential setting, there is no need for a rule to capture failure
of unification since failure to interact with one process does not
prevent interactions with other processes.
The interaction rule is then closed under parallel composition,
restriction and structural congruence in the usual manner. Unlike
pure pattern calculus, but like pi-calculus, computation does not occur within the body of a
case. As usual, $\redar^k$ denotes $k$ interactions, and $\Redar$ denotes the reflexive and transitive closure
of $\redar$.
The section concludes with three simple properties of substitutions and the reduction relation.
\begin{prop}
\label{lem:fn-sub}
For every process $P$ and substitution $\sigma$, it holds that ${\sf
fn}(\sigma P)\subseteq {\sf fn}(P)\cup{\sf fn}(\sigma)$.
\end{prop}
\begin{proof}
By definition of the application of $\sigma$.
\end{proof}
\begin{prop}
\label{prop:free_name_subset}
If $P\Redar P'$, then ${\sf fn}(P')\subseteq {\sf fn}(P)$.
\end{prop}
\begin{proof}
$P\Redar P'$ means that $P\redar\!\!\!^k\, P'$, for some $k \geq 0$. The proof is by induction on $k$
and follows by Proposition~\ref{lem:fn-sub}.
\end{proof}
\begin{prop}
\label{red:renaming}
If $P \redar P'$, then $\sigma P \redar \sigma P'$, for every $\sigma$.
\end{prop}
\begin{proof}
By induction on the derivation of $P \redar P'$.
\end{proof}
\begin{prop}
\label{prop:free_n_match_proc}
Suppose a process $p\to P$ interacts with a process $Q$. If $x$ is a protected
name in $p$ then $x$ must be a free name in $Q$.
\end{prop}
\begin{proof}
For $Q$ to interact with $p\to P$ it must be that $Q\Redar \rest n
(q\to Q_1\bnf Q_2)$ such that $\wt n \cap {\sf fn}(p \to P) =
\emptyset$ and $\{p\pmatch q\}$ is defined. Then, by
Proposition~\ref{prop:free_n_match}, the free names of $q$ include
$x$ and, consequently, $x$ must be free in $q\to Q_1\bnf Q_2$. By
Proposition~\ref{prop:free_name_subset}, $x$ is free in $Q$. Further,
$x$ cannot belong to $\wt n$, since $x \in {\sf fn}(p \to P)$ and
$\wt n \cap {\sf fn}(p \to P) = \emptyset$.
\end{proof}
\subsection{Trade in CPC}
\label{subsec:cpc-trade}
This section uses the example of share trading to explore the
potential of CPC. The scenario is that two traders, a buyer
and a seller, wish to engage in trade. To complete a transaction, the
traders need to progress through two stages: {\em discovering} each
other and {\em exchanging} information. Both traders begin with a
pattern for their desired transaction.
The discovery phase can be characterised as a pattern-unification
problem, where traders' patterns are used to find a compatible
partner.
The exchange phase occurs when a buyer and seller have agreed upon a
transaction. Now each trader wishes to exchange information in a
single interaction, preventing any incomplete trade from occurring.
The rest of this section develops three solutions of increasing
sophistication that: demonstrate discovery; introduce a registrar to
validate the traders; and protects names to ensure privacy.
\enlargethispage{\baselineskip}
\subsubsection*{Solution 1}
\label{sec:example:sol1}
Consider two traders, a buyer and a seller. The buyer $\buy_1$ with
bank account $b$ and desired shares $s$ can be given by
\begin{eqnarray*}
\buy_1 &=& s\bullet\lambda m \pre m\bullet b\bullet \lambda x \pre B(x)
\end{eqnarray*}
The first pattern $s\bullet \lambda m$ is used to match with a
compatible seller using share information $s$, and to input a name $m$
to be used as a channel to exchange bank account information $b$ for
share certificates bound to $x$. The transaction successfully
concludes with $B(x)$.
The seller $\sel_1$ with share certificates $c$ and desired share sale
$s$ is given by
\begin{eqnarray*}
\sel_1 &=& \res n s\bullet n\pre n\bullet \lambda y\bullet c\pre S(y)
\end{eqnarray*}
The seller creates a channel name $n$ and then tries to find a buyer
for the shares described in $s$, offering $n$ to the buyer to
continue the transaction. The channel is then used to exchange
billing information, bound to $y$, for the share certificates $c$.
The seller then concludes with the successfully completed transaction
as $S(y)$.
The discovery phase succeeds when the traders are placed in a parallel
composition and discover each other by unification on $s$
\begin{eqnarray*}
\buy_1|\sel_1
&\equiv&
\res n (s\bullet \lambda m \pre m\bullet b \bullet \lambda x \pre B(x)
\bnf s\bullet n \pre n\bullet \lambda y \bullet c \pre S(y))\\
&\rew&
\res n (n\bullet b \bullet \lambda x \pre B(x)
\bnf n\bullet \lambda y \bullet c \pre S(y))
\end{eqnarray*}
The next phase is to exchange billing information for share certificates, as in
$$
\res n (n\bullet b \bullet \lambda x \pre B(x)
\bnf n\bullet \lambda y \bullet c \pre S(y))
\ \ \rew\ \ \res n (B(c)\bnf S(b))
$$
The transaction concludes with the buyer having the share
certificates $c$ and the seller having the billing account $b$.
This solution allows the traders to discover each other and exchange
information atomically to complete a transaction. However, there is no way to
determine if a trader is trustworthy.
\subsubsection*{Solution 2}
\label{sec:example:sol2}
Now add a registrar that keeps track of registered
traders. Traders offer their identity to potential partners
and the registrar confirms if the identity belongs to a valid trader.
The buyer is now
\begin{eqnarray*}
\buy_2 &=& s\bullet i_B\bullet\lambda j \pre n_B\bullet j\bullet\lambda m \pre
m\bullet b\bullet \lambda x \pre B(x)
\end{eqnarray*}
The first pattern now swaps the buyer's identity $i_B$ for the seller's,
bound to $j$. The buyer then consults the registrar using the
identifier $n_B$ to validate $j$; if valid, the exchange continues as before.
Now define the seller symmetrically by
\begin{eqnarray*}
\sel_2 &=& s\bullet \lambda j\bullet i_S \pre n_S\bullet j\bullet\lambda m \pre
m\bullet \lambda y\bullet c\pre S(y)
\end{eqnarray*}
Also define the registrar $\reg_2$ with identifiers $n_B$ and $n_S$ to
communicate with the buyer and seller, respectively, by
\begin{eqnarray*}
\reg_2 &=& \res n (n_B\bullet{i_S}\bullet n\bnf n_S\bullet{i_B}\bullet n)
\end{eqnarray*}
The registrar creates a new identifier $n$ and delivers it to traders who
have been validated; then it makes the identifier available to known
traders who attempt to validate another known trader. Although rather
simple, the registrar can easily be extended to support a multitude of
traders.
Running these processes in parallel yields the following interaction
\begin{eqnarray*}
& & \buy_2 \bnf \sel_2 \bnf \reg_2\\
&\equiv& \res n (\ s\bullet i_B\bullet\lambda j \pre n_B\bullet j\bullet\lambda m \pre
m\bullet b\bullet \lambda x \pre B(x)
\bnf n_B\bullet\ {i_S}\bullet n\\
&& \qquad |\ s\bullet \lambda j\bullet i_S\ \pre n_S\bullet j\bullet\lambda m \pre
m\bullet \lambda y\bullet c\pre S(y)
\bnf n_S\bullet {i_B}\bullet n)\\
&\rew& \res n (n_B\bullet i_S\bullet\lambda m \pre
m\bullet b\bullet \lambda x \pre B(x)
\bnf n_B\bullet {i_S}\bullet n\\
&& \qquad |\ n_S\bullet i_B\bullet\lambda m \pre
m\bullet \lambda y\bullet c\pre S(y)
\bnf n_S\bullet {i_B}\bullet n)
\end{eqnarray*}
The share information $s$ allows the buyer and seller to discover
each other and swap identities $i_B$ and $i_S$. The next two
interactions involve the buyer and seller validating each other's
identity and inputting the identifier to complete the transaction
\begin{eqnarray*}
&& \res n (n_B\bullet i_S\bullet\lambda m \pre
m\bullet b\bullet \lambda x \pre B(x)
\bnf n_B\bullet {i_S}\bullet n\\
&& \qquad |\ n_S\bullet i_B\bullet\lambda m \pre
m\bullet \lambda y\bullet c\pre S(y)
\bnf n_S\bullet {i_B}\bullet n)\\
&\rew&\res n (n\bullet b\bullet \lambda x \pre B(x)\\
&& \qquad |\ n_S\bullet i_B\bullet\lambda m \pre
m\bullet \lambda y\bullet c\pre S(y)
\bnf n_S\bullet {i_B}\bullet n)\\
&\rew&\res n (n\bullet b\bullet \lambda x \pre B(x)\bnf
n\bullet \lambda y\bullet c\pre S(y))
\end{eqnarray*}
Now that the traders have validated each other, they can continue
with the exchange step from before
\begin{eqnarray*}
\res n (n\bullet b\bullet \lambda x \pre B(x)\bnf n\bullet \lambda y\bullet c\pre S(y))
& \rew & \res n (B(c)\bnf S(b))
\end{eqnarray*}
The traders exchange information and successfully complete with
$B(c)$ and $S(b)$.
\subsubsection*{Solution 3}
\label{sec:example:sol3}
Although Solution 2 satisfies the desire to validate that
traders are legitimate, the freedom of unification allows for
malicious processes to interfere. Consider the promiscuous
process $\prom$ given by
\begin{eqnarray*}
\prom &=& \lambda z_1\bullet \lambda z_2\bullet a\pre P(z_1,z_2)
\end{eqnarray*}
This process is willing to match any other process that will swap
two pieces of information for some arbitrary name $a$. Such a
process could interfere with the traders trying to complete the
exchange phase of a transaction. For example,
\begin{eqnarray*}
\res n (n\bullet b\bullet \lambda x \pre B(x)\bnf n\bullet \lambda y\bullet c\pre S(y))\bnf\prom\\
\qquad \qquad \rew \quad \res n (B(a)\bnf n\bullet \lambda y\bullet c\pre S(y) \bnf P(n,b))
\end{eqnarray*}
where the promiscuous process has stolen the identifier $n$ and the
bank account information $b$. The unfortunate buyer is left with some
useless information $a$ and the seller is waiting to complete the
transaction.
This vulnerability (emerging both in Solution 1 and 2) can be repaired by using protected
names.
For example, the buyer, seller and registrar of Solution 2 can become
\begin{eqnarray*}
\buy_3 &=& s\bullet i_B\bullet\lambda j \pre \pro {n_B}\bullet j\bullet\lambda m \pre
\pro m\bullet b\bullet \lambda x \pre B(x) \\
\sel_3 &=& s\bullet \lambda j\bullet i_S \pre \pro {n_S}\bullet j\bullet\lambda m \pre
\pro m\bullet \lambda y\bullet c\pre S(y) \\
\reg_3 &=& \res n (\pro {n_B}\bullet\pro{i_S}\bullet n\bnf \pro {n_S}\bullet\pro{i_B}\bullet n)
\end{eqnarray*}
Now all communications between the buyer, seller and registrar
use protected identifiers: $\pro {i_B}, \pro {i_S}, \pro {n_B},\pro {n_S}$ and $\pro m$.
Thus, we just need to add the appropriate restrictions:
\begin{eqnarray*}
\res {i_B}\res {i_S}\res {n_B} \res {n_S} (\buy_3\bnf\sel_3\bnf\reg_3)
\end{eqnarray*}
Therefore, other processes can only interact with the traders during
the discovery phase, which will not lead to a successful
transaction. The registrar will only interact with the
traders as all the registrar's patterns have protected names
known only to the registrar and a trader (Proposition~\ref{prop:free_n_match_proc}).
\section{Behavioural Theory}
\label{sec:bisim}
\newcommand{\usedby}[1]{}
This section follows a standard approach in concurrency to defining
behavioural equivalences, beginning with a barbed congruence and
following with a labelled transition system (LTS) and a bisimulation
for CPC. We will prove that the two semantics do coincide. Then the
bisimulation technique will be used to prove some sample equational
laws for CPC.
\nobreak
\subsection{Barbed Congruence}
The first step is to characterise the interactions a process can participate in via
{\em barbs}.
Since a barb is an opportunity for interaction, a simplistic
definition could be the following:
\begin{equation}
\label{def-one}
P \barb{} \mbox{ iff }\ P \equiv p \pre P'\bnf P'' \mbox{, for some $p,P'$ and $P''$}
\end{equation}
However, this definition is too strong: for example, $\res n(n \pre P)$ does not
exhibit a barb according to \eqref{def-one}, but it can interact with an external
process, e.g. $\lambda x \pre \zero$.
Thus, an improvement to \eqref{def-one} is as follows:
\begin{equation}
\label{def-two}
P \barb{} \mbox{ iff }\ P \equiv \rest n(p \pre P'\bnf P'') \mbox{, for some $\wt n, p, P'$ and $P''$}
\end{equation}
However, this definition is too weak. Consider $\res n(\pro n \pre P)$: it exhibits
a barb according to \eqref{def-two}, but cannot interact with any external
process.
A further refinement on \eqref{def-two} could be:
\begin{equation}
\label{def-three}
P \barb{} \mbox{ iff }\ P \equiv \rest n(p \pre P'\bnf P'') \mbox{, for some $\wt n, p, P',P''$ s.t. }
{\sf pn}(p) \cap \wt n = \emptyset
\end{equation}
This definition is not yet the final one, as it is not sufficiently discriminating to have
only a single kind of barb.
Because of the rich form of interactions in CPC, there is no single identifier such as in CCS
and $\pi$-calculus $\pi$-calculus \cite{milner.sangiorgi:barbed-bisimulation},
thus CPC barbs include the set of names that {\em may} be tested for equality
in an interaction, not just those that {\em must} be equal. This leads to the following definition:
\begin{defi}[Barb]
\label{def:barb}
Let $P\barb{\wt m}$ mean that
$P\equiv \rest n (p\pre P'\bnf P'')$
for some $\wt n$ and $p$ and $P'$ and $P''$ such that
${\sf pn}(p)\cap \wt n = \emptyset$ and $\wt m = {\sf fn}(p) \backslash \wt n$.
\end{defi}
For later convenience, define $P\suc_{\wt m}$ to mean that there exists some $P'$
such that $P\Redar P'$ and $P'\barb{\wt m}$.
Using this definition, a barbed congruence can be defined in the standard way
\cite{milner.sangiorgi:barbed-bisimulation,HY95} by requiring three properties.
Let $\Re$ denote a binary relation on CPC processes, and let a {\em context}
$\context C \cdot$ be a CPC process with the hole `$\,\cdot\,$'.
\begin{defi}[Barb preservation]
\label{def:barb-pres}
$\Re$ is barb preserving iff, for every $(P,Q) \in \Re$ and set of names ${\wt m}$, it holds that $P \barb{\wt m}$
implies $Q \barb{\wt m}$.
\end{defi}
\begin{defi}[Reduction closure]
\label{def:barb-close}
$\Re$ is reduction closed iff, for every $(P,Q) \in \Re$, it holds that $P \redar P'$
implies $Q \redar Q'$, for some $Q'$ such that $(P',Q') \in \Re$.
\end{defi}
\begin{defi}[Context closure]
\label{def:cont-close}
$\Re$ is context closed iff, for every $(P,Q) \in \Re$ and CPC context
$\context C \cdot$,
it holds that $(\context C P, \context C Q) \in \Re$.
\end{defi}
\begin{defi}[Barbed congruence]
\label{def:barb-con}
Barbed congruence, $\beq$, is the least binary relation on CPC processes that is symmetric, barb preserving, reduction closed and
context closed.
\end{defi}
Barbed congruence relates processes with the same
behaviour, as captured by barbs: two equivalent processes must exhibit the same behaviours,
and this property should hold along every sequence of reductions and in every execution context.
The challenge in proving barbed congruence is to prove
context closure. The typical way of solving the problem is by giving
a coinductive (bisimulation-based) characterization of barbed
congruence, that provides a manageable proof technique. In turn, this
requires an alternative operational semantics, by means of a labelled
transition system, on top of which the bisimulation equivalence can be
defined.
\subsection{Labelled Transition System}
\label{sec:LTS}
The following is an adaption of the late LTS for the
$\pi$-calculus \cite{milner.parrow.ea:calculus-mobile}.
{\em Labels} are defined as follows:
$$
\mu\ ::=\ \tau \quad |\quad \rest n p
$$
where $\tau$ is used to label silent transitions.
\begin{figure}[t]
$$
\begin{array}{ll}
{\sf case:}&
(p \pre P) \ltsred p P\\
\\
{\sf resnon:}&
\prooftree P \ltsred\mu P'
\justifies \res n P\ltsred\mu \res n P'
\endprooftree\quad n \notin {\sf names}(\mu)
\vspace*{.5cm}
\\
{\sf open:}&
\prooftree P \ltsred{\rest n p} P'
\justifies \res m P\ltsred{\res {\withsetnot{\wt n,m}{\wt n\cup \{m\}}} p} P'
\endprooftree\quad m \in {\sf vn}(p) \setminus (\wt n \cup {\sf pn}(p) \cup {\sf bn}(p))
\vspace*{.5cm}
\\
{\sf unify:}&
\prooftree P \ltsred{\rest m p} P' \quad Q \ltsred{\rest n q} Q'
\justifies P\bnf Q \ltsred\tau \res{\withsetnot{\wt m,\wt n}{\wt m\cup \wt n}}(\sigma P'\bnf \rho Q')
\endprooftree\quad
\begin{array}{l}
\{p \pmatch q\} = (\sigma, \rho)\\
\wt m \cap {\sf fn}(Q) = \wt n \cap {\sf fn}(P) = \emptyset\\
\wt m \cap \wt n = \emptyset
\end{array}
\vspace*{.5cm}
\\
{\sf parint:}&
\prooftree P \ltsred\tau P'
\justifies P\bnf Q \ltsred\tau P'\bnf Q
\endprooftree
\vspace*{.5cm}
\\
{\sf parext:}&
\prooftree P \ltsred{\rest n p} P'
\justifies P\bnf Q \ltsred{\rest n p} P'\bnf Q
\endprooftree\quad (\wt n \cup {\sf bn}(p)) \cap {\sf fn}(Q) = \emptyset
\vspace*{.5cm}
\\
{\sf rep:}&
\prooftree !P|P \ltsred\mu P'
\justifies !P \ltsred\mu P'
\endprooftree
\end{array}
$$
\caption{Labelled Transition System for CPC (the symmetric versions of {\sf parint} and {\sf parext} have been omitted)}
\label{fig:lts}
\end{figure}
Labels are used in {\em transitions} $P\ltsred\mu P'$ between CPC
processes, whose defining rules are given in Figure~\ref{fig:lts}. If
$P\ltsred\mu P'$ then $P'$ is a {\em $\mu$-reduct} of $P$, alternatively the transition $P\ltsred\mu P'$
indicates that $P$ is able to {\em perform} $\mu$ and reduces to $P'$.
Rule {\sf case} states that a case's pattern can be used to interact with external processes.
Rule {\sf resnon} is used when a restricted name does not appear in the names of the label: it simply maintains the restriction on the process after the transition.
By contrast, rule {\sf open} is used when a restricted name occurs in the label: as the restricted name is going to be shared with other processes, the restriction is moved from the process to the label (this is called {\em extrusion}, in $\pi$-calculus terminology).
Rule {\sf unify} defines when two processes can interact to perform an internal action:
this can occur whenever the processes exhibit labels with unifiable patterns and with no possibility of clash or capture due to restricted names.
Rule {\sf parint} states that, if either process in a parallel composition can evolve with an internal action, then the whole process can evolve with an internal action.
Rule {\sf parext} is similar, but is used when the label is visible: when one of the processes in parallel exhibits an external action, then the whole composition exhibits the same external action, as long as the restricted or binding names of the label do not appear free in the parallel component that does not generate the label.
Finally, rule {\sf rep} unfolds the replicated process to infer the action.
Note that $\alpha$-conversion is always assumed, so that the side conditions can always be satisfied in practice.
The presentation of the LTS is concluded with the following two
results. First, for every $P$ and $\mu$, there are finitely many
$\equiv$-equivalence classes of $\mu$-reducts of $P$
(Proposition~\ref{prop:imfin}). Second, the LTS induces the same
operational semantics as the reductions of CPC
(Proposition~\ref{prop:tau-red}). As CPC reductions only involve
interaction between processes and not external actions, it is
sufficient to show that any internal action of the LTS is mimicked by
a reduction in CPC, and vice versa. All proofs are in Appendix A, because they are quite standard.
\begin{defi}
An LTS is {\em structurally image finite} if, for every $P$ and $\mu$, it holds that
$\{P' :\, P \ltsred\mu P'\}/_\equiv$ contains finitely many elements.
\end{defi}
\begin{prop}
\label{prop:imfin}
The LTS defined in Figure~\ref{fig:lts} is structurally image finite.
\end{prop}
\usedby{Lemma \ref{lem:bisim-rep}}
\begin{lem}
\label{lem:lts-exhibit-p}
If $P\ltsred{\rest m p}P'$ then
there exist $\wt n$ and $Q_1$ and $Q_2$ such that
$P \equiv \rest m \rest n (p\to Q_1\bnf Q_2)$ and
$P' \equiv \rest n (Q_1\bnf Q_2)$ and
$\wt n\cap{\sf names}(\rest m p)=\emptyset$ and ${\sf bn}(p)\cap{\sf fn}(Q_2)=\emptyset$.
\end{lem}
\usedby{Prop \ref{prop:tau-red} and Lemma \ref{lem:sound-one}}
\begin{prop}
\label{prop:tau-red}
If $P \ltsred\tau P'$ then $P \redar P'$.
Conversely, if $P \redar P'$ then there exists $P''$ such that $P \ltsred\tau P'' \equiv P'$.
\end{prop}
\usedby{Lemma \ref{lem:sound-two}, Lemma \ref{lem:succ-beq} and Thm \ref{thm: complete}}
To conclude, it is known that $\alpha$-conversion must be handled with care \cite{UBN07}.
A way in which we can leave it out from our presentation is to follow \cite{BP09}, that
also has the advantage of being implementable in Isabelle/HOL \cite{NPW02}.
However, we prefer to follow a more traditional approach in our presentation.
\subsection{Bisimulation}
\label{sec:bis}
We now develop a {\em bisimulation} relation for CPC that equates processes with the same interactional behaviour; this is captured by the labels of the LTS.
The complexity for CPC is that the labels for external actions contain patterns, and some patterns are more general than others, in that they unify with more things.
For example, a transition $P\ltsred{\pro n}P'$ performs the action $\pro n$; however a similar external action of another process could be the variable name $n$ and the transition $Q\ltsred n Q'$.
Both transitions have the same barb, that is $P\barb{n}$ and $Q\barb{n}$; however their labels are not identical
and, indeed, the latter can interact with a process performing a transition labeled with $\l x$ whereas the former cannot.
Thus, a {\em compatibility} relation is defined on patterns that can be used to develop the bisimulation.
The rest of this section discusses the development of compatibility and concludes with the definition of bisimulation for CPC.
Bisimilarity of two processes $P$ and $Q$ can be captured by a challenge-reply game
based upon the actions the processes can take.
One process, say $P$, issues a {\em challenge} and evolves to a new state $P'$.
Now $Q$ must perform an action that is a {\em proper reply} and evolve to a state $Q'$.
If $Q$ cannot perform a proper reply then the challenge issued by $P$ can distinguish $P$ and $Q$,
and shows they are not equivalent.
If $Q$ can properly reply then the game continues with the processes $P'$ and $Q'$.
Two processes are bisimilar (or equivalent) if any challenge by one
can be answered by a proper reply from the other.
The main complexity in defining a bisimulation to capture this challenge-reply game is the choice of actions, i.e.\ challenges and replies.
In most process calculi, a challenge is replied to with an identical action \cite{Mil89,milner.parrow.ea:calculus-mobile}.
However, there are situations in which an exact reply would make the bisimulation equivalence too fine for characterising barbed congruence \cite{amadio.castellani.ea:bisimulations-asynchronous,DGP:IC07}.
This is due to the impossibility for the language contexts to force barbed congruent processes to execute the same action; in such calculi more liberal replies must be allowed.
That CPC lies in this second group of calculi is demonstrated by the following two examples.
\begin{exa}{Example 1}
\label{ex:input}
Consider the processes
\[
P = \l x \bullet \l y \to x\bullet y
\qquad \mbox{and} \qquad
Q = \l z \to z
\]
together with the challenge $P \ltsred{\l x \bullet \l y} x \bullet y$.
One may think that a possible context
$\context {C_{{\it \l x \bullet \l y}}} \cdot$
to enforce a proper reply could be $\ \cdot\bnf w \bullet w \pre \pro w$, for $w$ fresh.
Indeed, $\context {C_{{\it \l x\bullet\l y}}} P\redar w\bullet w \bnf \pro w$
and the latter process exhibits a barb over $w$.
However, the exhibition of action $\l x \bullet \l y$ is {\em not} necessary
for the production of such a barb: indeed,
$\context {C_{{\it \l x\bullet\l y}}} Q\redar w\bullet w \bnf \pro w$,
but in doing so $Q$ performs $\l z$ instead of $\l x \bullet \l y$.
\end{exa}
\begin{exa}{Example 2}
\label{ex:pro}
Consider the processes
\[
P = \pro n \pre \zero
\qquad \mbox{and} \qquad
Q = n\pre \zero
\]
together with the context $\context {C_{{\it \pro n}}} \cdot = n\pre\pro w$, for $w$ fresh.
Although $\context {C_{{\it \pro n}}} P\redar\pro w$ and the latter process exhibits a barb over $w$,
the exhibition of action $\pro n$ is {\em not} necessary for the production of such a barb:
$\context {C_{{\it \pro n}}} Q\redar\pro w$ also exhibits a barb on $w$,
but in doing so $Q$ performs $n$ instead of $\pro n$.
\end{exa}
\medskip
Example~1 shows that CPC pattern-unification allows binding names to be contractive:
it is not necessary to fully decompose a pattern to bind it.
Thus a compound pattern may be bound to a single name or to more than one name in unification.
Example~2 illustrates that CPC pattern-unification on protected names only requires the other pattern know the name, but such a name is not necessarily protected in the reply.
These two observations make it clear that some patterns are more discerning than others,
i.e.\ unify with fewer patterns than others. This leads to the following definitions.
\begin{defi}
\label{def:match}
Define a {\em match} $(p,\sigma)$ to be a pattern $p$ and substitution $\sigma$ such that
${\sf bn}(p)={\sf dom}(\sigma)$.
\end{defi}
\begin{defi}
\label{def:compat}
Let $(p,\sigma)$ and $(q,\rho)$ be matches.
Define inductively that $p$ is {\em compatible} with $q$ by $\sigma$ and $\rho$,
denoted $p,\sigma\compat q,\rho$ as follows:
$$
\begin{array}{rcll}
p,\sigma &\compat& \l y,\{\hat\sigma p/y\} & \mbox{if } {\sf fn}(p)=\emptyset\\
n,\{\} &\compat& n,\{\}\\
\pro n ,\{\} &\compat& \pro n ,\{\}\\
\pro n ,\{\}&\compat& n,\{\}\\
p_1\bullet p_2,\sigma_1\cup\sigma_2 &\compat& q_1\bullet q_2,\rho_1\cup\rho_2
\quad& \mbox{if } p_i,\sigma_i\compat q_i,\rho_i \mbox{, for } i \in \{1,2\}
\end{array}
$$
\end{defi}
The idea behind this definition is that a pattern $p$ is compatible
with another pattern $q$ with substitutions $(\sigma,\rho)$ if and only if every other pattern $r$ that
unifies $p$ by some substitutions $(\theta,\sigma)$ also unifies with
$q$ with substitutions $(\theta,\rho)$.
That is, the patterns that unify with $p$ are a subset of
the patterns that unify with $q$. This will be proved later in
Proposition~\ref{lem:pat-lessthan}.
The compatibility relation on patterns provides the concept of proper reply in the challenge-reply game.
\begin{defi}[Bisimulation]
\label{def:bisim}
A symmetric binary relation on CPC processes $\Re$ is a bisimulation if,
for every $(P,Q) \in \Re$ and $P \ltsred\mu P'$, it holds that:
\begin{itemize}
\item if $\mu = \tau$, then $Q \ltsred\tau Q'$, for some $Q'$ such that $(P',Q') \in \Re$;
\item if $\mu = \rest n p$ and $({\sf bn}(p)\cup \wt n)\cap {\sf fn}(Q)=\emptyset$,
then, for all matches $(p,\sigma)$ with
${\sf fn}(\sigma)\cap \wt n = \emptyset$,
there exist a match $(q,\rho)$ and $Q'$
such that
$p,\sigma \compat q,\rho$ and
$Q\ltsred {\rest n q}Q'$
and $(\sigma P',\rho Q')\in \Re$.
\end{itemize}
Denote by $\bisim$ the largest bisimulation closed under any substitution.
\end{defi}
The definition is inspired by the early bisimulation congruence for the
$\pi$-calculus \cite{milner.parrow.ea:calculus-mobile} (actually, it is what
in \cite{sangiorgi.walker:theory-mobile} is called {\em strong full bisimilarity} -- see Definition 2.2.2 therein):
for every possible instantiation $\sigma$ of the binding names,
there exists a proper reply from $Q$.
Of course, $\sigma$ cannot be chosen arbitrarily:
it cannot use in its range names that were opened by $P$.
Also the action $\mu$ cannot be arbitrary, as in the $\pi$-calculus:
its restricted and binding names cannot occur free in $Q$.
Unlike the $\pi$-calculus, however, the reply from $Q$ can be
different from the challenge from $P$:
this is due to the fact that contexts in CPC are not powerful enough to
enforce an identical reply (as highlighted in Examples~1 and~2).
Indeed, this notion of bisimulation allows a challenge $p$ to be replied to by
any compatible $q$, provided that $\sigma$ is properly adapted (yielding $\rho$, as
described by the compatibility relation) before being applied to $Q'$.
This feature somehow resembles the symbolic characterization of
open bisimilarity given in \cite{San96,BM08}. There, labels are pairs made up
of an action and a set of equality constraints. A challenge can be replied to by a
smaller (i.e.~less constraining) set. However, the action in the reply must be
the same (in \cite{San96}) or becomes the same once we apply the name identifications
induced by the equality constraints (in \cite{BM08}).
An alternative approach may consider a standard bisimulation defined on top of an LTS that directly captures
the difficulties of Examples 1 and 2.
That is, allow $\l z\to z$ to reduce with label $\l x\bullet \l y$ to $x\bullet y$; similarly, allow
$n\to 0$ to reduce with label $\pro n$ to $0$. For example, this would allow the transition
$\l w\bullet \l x\bullet n \to P \ltsred{\l w\bullet (\l y\bullet \l z)\bullet \pro n} \{y\bullet z/x\}P$.
The difficulty with this approach is that, for every binding name in a pattern, there would be an
infinite collection of transitions. For example, $\l x \to P$ would have transitions $\l x\to P\ltsred\mu \sigma P$,
where $\mu$ can be $\l x_1\bullet \ldots\bullet \l x_i$ (for every $i \geq 1$), but also
$(\l y_1\bullet \ldots\bullet \l y_j)\bullet \l z$ and $\l y\bullet(\l z_1\bullet\ldots\bullet \l z_k)$,
and so forth (with $\sigma$ adapted appropriately).
This would make working with the LTS very heavy (the LTS would not be finitely branching anymore);
so the simplicity of relating patterns by compatibility is used here.
\subsection{Properties of Compatibility}
This section considers some properties of the compatibility relation on patterns introduced in Section~\ref{sec:bis};
they are formalised for later exploitation, even though some of them also illustrate some general features of patterns.
In particular, we show that compatibility preserves information used for barbs, is stable under substitution, is reflexive and transitive.
\begin{lem}
\label{prop:compat-fn}
If $p,\sigma\compat q,\rho$ then ${\sf fn}(p)={\sf fn}(q)$ and ${\sf vn}(p) \subseteq {\sf vn}(q)$
and ${\sf pn}(q) \subseteq {\sf pn}(p)$.
\end{lem}
\usedby{Lemma \ref{lem:sound-one} and \ref{lem:bisim-nuR}}
\begin{proof}
By definition of compatibility and induction on the structure of $q$.
\end{proof}
Given two substitutions $\sigma$ and $\theta$, denote with $\theta[\sigma]$
the composition of $\sigma$ and $\theta$,
with domain limited to the domain of $\sigma$,
i.e.\ the substitution mapping every $x\in{\sf dom}(\sigma)$ to $\theta(\sigma(x))$.
\begin{lem}
\label{lem:compat-compose-subs}
If $p,\sigma \compat q,\rho$ then $p,\theta[\sigma] \compat q,\theta[\rho]$, for every $\theta$.
\end{lem}
\usedby{Lemma \ref{lem:succ-beq} and Thms \ref{thm: complete} and \ref{eq-grrr}}
\begin{proof}
By induction on the structure of $q$. The only interesting base case is when $q = \l y$.
Since ${\sf dom}(\theta[\sigma]) = {\sf dom}(\sigma)$, we have that
$p,\theta[\sigma] \compat q,\vartheta$, for $\vartheta = \{ \widehat{\theta[\sigma]}(p)/y\}
= \{\theta(\rho(y))/y\} = \theta[\rho]$.
\end{proof}
\begin{prop}[Compatibility is reflexive]
\label{prop:compat-reflexive}
For all matches $(p,\sigma)$, it holds that $p,\sigma\compat p,\sigma$.
\end{prop}
\usedby{Lemma \ref{lem:bisim-case}, Lemma \ref{lem:bisim-nuR} and Thms \ref{thm: complete} and \ref{eq-grrr}}
\begin{proof}
By definition of compatibility.
\end{proof}
\begin{prop}[Compatibility is closed under substitution]
\label{prop:compat-sub-closed}
If $p,\sigma\compat q,\rho$ then for all substitutions $\theta$ there exists
$\sigma '$ and $\rho '$ such that
$\theta p, \sigma '\compat \theta q,\rho '$.
\end{prop}
\usedby{Lemma~\ref{lem:bisim-case}}
\begin{proof}
By induction on the structure of $q$.
\end{proof}
\begin{prop}[Compatibility is transitive]
\label{prop:trans-pattern}
If $p,\sigma \compat q,\rho$ and $q,\rho \compat r,\theta$ then $p,\sigma \compat r,\theta$.
\end{prop}
\usedby{Lemma \ref{lem:trans-bisim}}
\begin{proof}
By induction on $r$. We have three possible base cases:
\begin{itemize}
\item $r = \l z$: in this case, $q = \l y_1 \bullet \ldots \bullet \l y_n$, for some $n \geq 1$, and
$$\theta = \{\hat\rho q/z\} = \{\rho(y_1) \bullet \ldots \bullet \rho(y_n) / z\}.$$
Again by definition of compatibility,
$p = \l x_1^1 \bullet \ldots \bullet \l x_1^{k_1} \bullet \ldots \bullet \l x_n^1 \bullet \ldots \bullet \l x_n^{k_n}$,
for some $k_1,.., k_n \geq 1$, and
$$\rho = \{\hat\sigma (x_i^1 \bullet \ldots \bullet x_i^{k_i})/y_i\}_{i = 1,..,n} =
\{\sigma(x_i^1) \bullet \ldots \bullet \sigma(x_i^{k_i})/y_i\}_{i = 1,..,n}.$$
Thus, $\theta = \{\sigma(x_1^1) \bullet \ldots \bullet \sigma(x_1^{k_1}) \bullet \ldots \bullet
\sigma(x_n^1) \bullet \ldots \bullet \sigma(x_n^{k_n})/z\} = \{\hat\sigma p/z\}$
and $p,\sigma \compat r,\theta$, as desired.
\item $r = \pro n$: in this case $q = \pro n$ and $\theta = \rho = \{\}$. Again by compatibility,
$p = \pro n$ and $\sigma = \{\}$; thus $p,\sigma \compat r,\theta$.
\item $r = n$: in this case $q$ can either be $\pro n$ or $n$, and $\theta = \rho = \{\}$. Again by compatibility,
$p = \pro n$ or $p = n$ (this is possible only when $q = n$), and $\sigma = \{\}$; in all cases,
$p,\sigma \compat r,\theta$.
\end{itemize}
For the inductive step, let $r = r_1 \bullet r_2$. By compatibility, $q = q_1 \bullet q_2$ and
$\theta = \theta_1 \cup \theta_2$ and $\rho = \rho_1 \cup \rho_2$, with
$q_i,\rho_i \compat r_i,\theta_i$, for $i = 1,2$. Similarly, $p = p_1 \bullet p_2$ and
$\sigma = \sigma_1 \cup \sigma_2$, with $p_i,\sigma_i \compat q_i,\rho_i$, for $i = 1,2$.
By two applications of the inductive hypothesis, we obtain $p_i,\sigma_i \compat r_i,\theta_i$, for $i = 1,2$,
and by definition of compatibility we can conclude.
\end{proof}
The next result captures the idea behind the definition of
compatibility: the patterns that unify with $p$ are a subset of the
patterns that unify with $q$.
\begin{prop}
\label{lem:pat-lessthan}
If $p,\sigma\compat q,\rho$ then, for every $r$ and $\theta$ such that $\{r\pmatch p\}=(\theta,\sigma)$,
we have that $\{r\pmatch q\}=(\theta,\rho)$.
\end{prop}
\proof
The proof is by induction on $q$. There are three possible base cases:
\begin{itemize}
\item If $q = \l y$ then ${\sf fn}(p)=\emptyset$ and $\rho = \{\hat\sigma p/y\}$; for the unification of
$r$ and $p$ to be defined, it must be $\theta = \{\}$ and
$\sigma=\{r_i/x_i\}_{x_i\in{\sf bn}(p)}$, each $r_i$ is communicable and $\hat\sigma p=r$.
It follows that $\{r\pmatch q\}=(\{\},\{r/y\})=(\{\},\{\hat\sigma p/y\}) = (\theta, \rho)$.
\item If $q = \pro n$ then $p = \pro n$ and $\sigma = \rho = \{\}$.
For $r$ to unify with $p$, it must be that $r$ is $n$ or $\pro n$; in both cases $\theta = \{\}$.
Hence, $\{r\pmatch q\}=(\{\},\{\})=(\theta,\rho)$.
\item If $q = n$ then $p$ is either $n$ or $\pro n$, and $\sigma = \rho = \{\}$.
In both cases, $r$ can as well be either $n$ or $\pro n$.
The proof is similar to the previous case.
\end{itemize}
For the inductive step, $q = q_1\bullet q_2$; by comparability, $p = p_1\bullet p_2$.
There are two possible cases for $r$ to unify with $p$:
\begin{itemize}
\item If $r = \l z$, then $p$ must be communicable and $\theta = \{p/z\}$;
thus, by definition of comparability, $q=p$ and $\sigma = \rho = \{\}$.
Hence, $\{r\pmatch q\}=(\{q/z\},\{\})=(\{p/z\},\{\})=(\theta,\rho)$.
\item Otherwise, for $r$ to unify with $p$, it must be $r = r_1\bullet r_2$
with $\{r_i \pmatch p_i\} = (\theta_1,\sigma_i)$, for $i \in \{1,2\}$,
and $\sigma = \sigma_1 \uplus \sigma_2$ and $\theta = \theta_1 \uplus \theta_2$.
Conclude by two applications of induction and by definition of compatibility.\qed
\end{itemize}
\noindent Notice that the converse does not hold. Take $p = n$ and $q = \pro n$; we have that, for every
$r$ such that $\{r\pmatch p\}=(\theta,\sigma)$, we have that $\{r\pmatch q\}=(\theta,\rho)$ (the only
such $r$'s are $n$ and $\pro n$, for which $\sigma = \theta = \rho = \{\}$); however, $n , \{\} \not\compat
\pro n , \{\}$.
The following result is a variation of the previous lemma, that fixes $\sigma$ to ${\sf id}_{{\sf bn}(p)}$ but
allows an arbitrary substitution in the unification with $r$.
\begin{prop}
\label{lem:compat-match}
If $p,{\sf id}_{{\sf bn}(p)} \compat q,\rho$ and $\{p\pmatch r\}=(\vartheta,\theta)$,
then $\{q\pmatch r\}=(\vartheta[\rho],\theta)$.
\end{prop}
\usedby{Thm \ref{eq-grrr}}
\proof
By induction on $q$. There are three possible base cases:
\begin{itemize}
\item $q = \l x$: by Definition~\ref{def:compat}, it must be that ${\sf fn}(p) = \emptyset$, i.e.
$p = \l x_1 \bullet \ldots \bullet \l x_k$, for some $k$. Thus, $\rho = \{x_1 \bullet \ldots \bullet x_k / x\}$,
$r = r_1 \bullet \ldots \bullet r_k$ communicable, $\vartheta = \{r_1/x_1 \ldots r_k/x_k\}$ and $\theta = \{\}$.
By definition of unification, $\{q\pmatch r\}=(\{r/x\},\{\})$ and conclude, since
$\{r/x\} = \{r_1 \bullet \ldots \bullet r_k / x\} = \vartheta[\rho]$.
\item $q = n$: in this case, it must be either $p = n$ or $p = \pro n$; in both cases, $\rho = \{\}$.
If $p = n$, then conclude, since $q = p$ and $\vartheta[\rho] = \vartheta$.
If $p = \pro n$, obtain that $r$ can be either $n$ or $\pro n$; in both cases $\vartheta = \theta = \{\}$
and conclude.
\item $q = \pro n$: in this case $p = \pro n$, $\rho = \{\}$ and work like in the previous case.
\end{itemize}
For the inductive case, $q = q_1 \bullet q_2$; thus, by Definition~\ref{def:compat},
$p = p_1 \bullet p_2$ and $p_i,{\sf id}_{{\sf bn}(p_i)} \compat q_i,\rho_i$, where
$\rho_i = \rho|_{{\sf bn}(q_i)}$, for $i \in \{1,2\}$. We have two possibilities for $r$:
\begin{itemize}
\item $r = r_1 \bullet r_2$, where $\{p_i\pmatch r_i\}=(\vartheta_i,\theta_i)$, for $i \in \{1,2\}$;
moreover, $\vartheta = \vartheta_1 \uplus \vartheta_2$
and $\theta = \theta_1 \uplus \theta_2$. Apply induction two times and to conclude.
\item $r = \l x$ and $p$ is communicable; thus, $\vartheta = \{\}$ and $\theta = \{p/x\}$.
By definition of compatibility, $q = p$ and $\rho = \{\}$. Conclude
with $\{\} = \{\}[\{\}]$.\qed
\end{itemize}
\noindent As compatibility is an ordering on matches,
it is interesting to observe that, for every pattern $p$, there is a unique (up to $\alpha$-conversion)
maximal pattern w.r.t. $\compat$. Note that, as in Proposition~\ref{lem:compat-match} the substitution can be
fixed (or indeed entirely elided).
\begin{prop}
\label{prop:maximal}
For every pattern $p$ there exists a maximal pattern $q$ with respect to $\compat$;
this pattern is unique up-to $\alpha$-conversion of binding names.
\end{prop}
\usedby{Lemma \ref{lem:bisim-rep}}
\begin{proof}
The proof is by induction on the structure of $p$:
\begin{itemize}
\item If ${\sf fn}(p)=\emptyset$, then the largest $q$ w.r.t. $\compat$ is $\l y$ for some fresh $y$.
\item If $p$ is $n$ or $\pro n$, then the largest $q$ w.r.t. $\compat$ is $n$.
\item Otherwise, if $p=p_1\bullet p_2$, then proceed by induction on $p_1$ and $p_2$.
\end{itemize}
The only arbitrary choice is the $y$ used in the first item, that can be $\alpha$-converted to
any other fresh name.
\end{proof}
To conclude the properties of the compatibility, it is worth remarking that it does not yield a lattice: there is no supremum for the two patterns $\l x$ and $n$.
\subsection{Soundness of the Bisimulation}
\label{sec:sound}
This section proves soundness by showing that the bisimulation relation is included in barbed congruence.
This is done by showing that the bisimilarity relation is an equivalence, it is
barb preserving, reduction closed and context closed.
\begin{lem}
\label{lem:trans-bisim}
If $P\bisim Q$ and $Q\bisim R$ then $P\bisim R$.
\end{lem}
\usedby{Lemma \ref{lem:bisim-rep}}
\begin{proof}
Standard, by exploiting Proposition~\ref{prop:trans-pattern}.
\end{proof}
\begin{lem}
\label{lem:sound-one}
$\bisim$ is barb preserving.
\end{lem}
\usedby{Thm \ref{thm: sound}}
\begin{proof}
Straightforward by Lemmata~\ref{prop:compat-fn} and~\ref{lem:lts-exhibit-p}, and by definition of the LTS.
\end{proof}
Closure under any context is less easy to prove.
The approach here is as follows:
prove bisimilarity is closed under case prefixing,
name restriction and parallel composition; finally, prove closure under replication.
Proofs of these lemmata are in Appendix B, because they are adaptions
of the corresponding results for the $\pi$-calculus.
These three results will easily entail closure under arbitrary contexts (Lemma~\ref{lem:sound-three}).
\begin{lem}
\label{lem:bisim-case}
If $P\bisim Q$ then $p \to P \bisim p \to Q$.
\end{lem}
\usedby{Lemma \ref{lem:sound-three}}
\begin{lem}
\label{lem:bisim-nu}
If $P\bisim Q$ then $\rest n P \bisim \rest n Q$.
\end{lem}
\usedby{Lemma \ref{lem:bisim-rep}, Lemma \ref{lem:sound-three} and Thm \ref{eq-grrr}}
\begin{lem}
\label{lem:bisim-par}
If $P\bisim Q$ then $P\bnf R \bisim Q\bnf R$.
\end{lem}
\usedby{Lemma \ref{lem:bisim-rep}, Lemma \ref{lem:sound-three} and Thm \ref{eq-grrr}}
\begin{lem}
\label{lem:bisim-rep}
If $P\bisim Q$ then $!P\bisim\,\, !Q$.
\end{lem}
\usedby{Lemma \ref{lem:sound-three}}
\begin{lem}
\label{lem:sound-three}
$\bisim$ is contextual.
\end{lem}
\usedby{Thm \ref{thm: sound}}
\begin{proof}
Given two bisimilar processes $P$ and $Q$, it is necessary to show that for any context
$\context C \cdot$ it holds that $\context C P \bisim \context C Q$.
The proof is by induction on the structure of the context.
If $\context C \cdot\define \cdot$ then the result is immediate.
For the inductive step, we reason by case analysis on the outer operator of $\context C \cdot$:
then, we simply use the inductive hypothesis and Lemmata~\ref{lem:bisim-case}, \ref{lem:bisim-nu},
\ref{lem:bisim-par} and~\ref{lem:bisim-rep}, respectively.
\end{proof}
Finally, we have to prove that bisimilarity is reduction closed; to this aim, we first need
to prove that structural congruence is contained in bisimilarity.
\begin{lem}
\label{lem:struct-is-a-bisim}
$\equiv$ is a bisimulation closed under substitutions.
\end{lem}
\usedby{Thm \ref{lem:sound-two}}
\proof
For every structural axiom $LHS \equiv RHS$ it suffices to show that $\{(LHS,RHS)\} \cup \bisim$
is a bisimulation. Closure under contexts follows from Lemma~\ref{lem:sound-three}. Closure under
substitutions follows from the fact that the axioms only involve bound names. The only exception
is the rule for scope extension; however, the fact that substitution application is capture-avoiding
allows us to conclude.
\qed
\begin{lem}
\label{lem:sound-two}
$\bisim$ is reduction closed.
\end{lem}
\usedby{Thm \ref{thm: sound}}
\begin{proof}
By Proposition~\ref{prop:tau-red} and Lemma~\ref{lem:struct-is-a-bisim}.
\end{proof}
The soundness of bisimilarity w.r.t. barbed congruence now follows.
\begin{thm}[Soundness of bisimilarity]
\label{thm: sound}
$\bisim\ \subseteq\ \beq$.
\end{thm}
\begin{proof}
Lemma~\ref{lem:sound-one}, Lemma~\ref{lem:sound-three} and Lemma~\ref{lem:sound-two}
entail that $\bisim$ satisfies the conditions of Definition~\ref{def:barb-con}.
\end{proof}
\subsection{Completeness of the Bisimulation}
Completeness is proved by showing that barbed congruence is a bisimulation.
There are two results required:
showing that barbed congruence is closed under substitutions,
and showing that, for any challenge, a proper reply can be obtained via closure under an appropriate context.
To this aim, we define notions of success and failure that can be reported.
A fresh name $w$ is used for reporting success, with a barb $\barb{w}$ indicating success, and $\suc_w$ indicating a reduction sequence that can eventually report success. Failure is handled similarly using the fresh name $f$.
A process $P$ {\em succeeds}
if $P\suc_w$ and $P\not\suc_f$;
$P$ is {\em successful} if $P \equiv \rest n(\pro w\bullet p\ |\ P')$, for some $\wt n$ and $p$ and $P'$
such that $w \not\in \wt n$ and $P'\not\suc_f$.
The next lemma shows that barbed congruence is closed under any substitution.
\begin{lem}
\label{lem:bcon-sub}
If $P\beq Q$ then $\sigma P\beq\sigma Q$, for every $\sigma$.
\end{lem}
\usedby{Lemma \ref{lem:succ-beq} and Thm \ref{thm: complete}}
\begin{proof}
Given a substitution $\sigma$, choose patterns $p$ and $q$ such that $\{p\pmatch q\}=(\sigma,\{\})$;
to be explicit, $p = \l x_1 \bullet \ldots\bullet \l x_k$ and $q = \sigma(x_1) \bullet \ldots \bullet \sigma(x_k)$,
for $\{x_1,\ldots,x_k\} = {\sf dom}(\sigma)$.
Define $\context C \cdot \define p\to \cdot\ \bnf q$;
by context closure, $\context C P\beq\context C Q$.
By reduction closure, the reduction $\context C P\redar \sigma P$ can be replied to
only by $\context C Q\redar \sigma Q$; hence, $\sigma P\beq \sigma Q$, as desired.
\end{proof}
The other result to be proved is that challenges can be tested for a proper reply by a context.
When the challenge is an internal action, the reply is also an internal action; thus, the empty
context suffices, as barbed congruence is reduction closed.
The complex scenario is when the challenge is a pattern together with a set of restricted names,
i.e., a label of the form $\rest n p$.
Observe that in the bisimulation such challenges also fix a substitution $\sigma$ whose domain is the binding names of $p$.
Most of this section develops a reply for a challenge of the form $(\rest n p,\idsub_{{\sf bn}(p)})$;
the general setting (with an arbitrary $\sigma$) will be recovered in Theorem~\ref{thm: complete}
by relying on Lemma~\ref{lem:compat-compose-subs}.
The context for forcing a proper reply for a challenge of the form $(\rest n p,\idsub_{{\sf bn}(p)})$ is developed in three steps.
The outcome will be a process that interacts by some pattern $p'$ and reduces to a collection of tests $T$ such that $\theta T$ succeeds
if and only if $\{p\pmatch p'\}=(\sigma,\theta)$.
The first step presents the {\em specification} of a pattern and a set of names $N$ (to be thought of as the free names of the processes being compared for bisimilarity); this is the information required to build a reply context.
The second step develops auxiliary processes to test specific components of a pattern, based on information from the specification.
The third step combines these into a reply context that succeeds if and only if it interacts
with a process that exhibits a proper reply to the challenge.
For later convenience, we define the {\em first projection} ${\sf fst}(-)$ and
{\em second projection} ${\sf snd}(-)$ of a set of pairs: e.g.,
${\sf fst}(\{(x,m),(y,n)\})=\{x,y\}$ and ${\sf snd}(\{(x,m),(y,n)\})=\{m,n\}$, respectively.
\begin{defi}
\label{def:bchar}
The {\em specification} ${\sf spec}^{N}(p)$ of a pattern $p$ with respect to a finite set of names $N$ is defined follows:
$$
\begin{array}{rcl}
\vspace{.2cm}
{\sf spec}^{N}(\l x) &=& x,\{\},\{\} \\
\vspace{.2cm}
{\sf spec}^{N}(n) &=&
\left\{\!\!\!
\begin{array}{ll}
\vspace{.2cm}
\l x,\{(x,n)\},\{\} &\mbox{if $n\in N$ and $x$ is fresh for $N$ and $p$}\\
\l x,\{\},\{(x,n)\} &\mbox{if $n\notin N$ and $x$ is fresh for $N$ and $p$}
\end{array}
\right.
\\
{\sf spec}^{N}(\pro n) &=& \pro n,\{\},\{\}\\
{\sf spec}^{N}(p\bullet q) &=& p'\bullet q',F_p\uplus F_q,R_p\uplus R_q \ \mbox{ if }\left\{\!\!
\begin{array}{l}
{\sf spec}^{N}(p) = p',F_p,R_p\\
{\sf spec}^{N}(q) = q',F_q,R_q
\end{array}\right.
\end{array}
$$
where $F_p\uplus F_q$ denotes $F_p\cup F_q$, provided that ${\sf fst}(F_p) \cap {\sf fst}(F_q) = \emptyset$
(a similar meaning holds for $R_p\uplus R_q$).
\end{defi}
Observe that, since we only consider well formed patterns, the disjoint unions $F_p\uplus F_q$ and $R_p\uplus R_q$ are defined and the choices of the binding names for $p'$ are pairwise distinct.
Given a pattern $p$, the specification ${\sf spec}^{N}(p)=p',F,R$ of $p$ with respect to a set of names $N$ has three components:
\begin{enumerate}
\item $p'$, called the {\em complementary pattern}, is a pattern used to ensure that the context interacts with a
process that exhibits a pattern $q$ such that $p$ is compatible with $q$ (via some substitutions);
\item $F$ is a collection of pairs $(x,n)$ made up by a binding name in $p'$ and the expected
name (free in the process being tested) it will be bound to;
\item finally, $R$ is a collection of pairs $(x,n)$ made up by a binding name in $p'$ and the expected
name (restricted in the process being tested) it will be bound to.
\end{enumerate}
\noindent The specification is straightforward for binding names, protected names and compounds.
When $p$ is a variable name, $p'$ is a fresh binding name $\l x$ and the intended binding of $x$ to $n$
is recorded in $F$ or $R$, according to whether $n$ is free or restricted, respectively.
\begin{lem}
\label{prop:spec-pp}
Given a pattern $p$ and a finite set of names $N$, let ${\sf spec}^N(p)=p',F,R$.
Then, $\{p\pmatch p'\}=(\idsub_{{\sf bn}(p)},\{n/x\}_{(x,n) \in F \cup R})$.
\end{lem}
\usedby{Thm \ref{thm:lts-2-reply-succeed}}
\begin{proof}
By straightforward induction on the structure of $p$.
\end{proof}
\enlargethispage{\baselineskip}
To simplify the definitions, let $\prod_{x\in S} {\mathcal P}(x)$ be the parallel composition of
processes ${\mathcal P}(x)$, for each $x$ in $S$.
The tests also exploit a check ${\sf check}(x,m,y,n,w)$ to ensure equality or
inequality of name substitutions:
\[
{\sf check}(x,m,y,n,w) =
\left\{
\begin{array}{ll}
\res z (\pro z\bullet \pro x\bnf \pro z\bullet \pro y\to \pro w) & \mbox{if } m=n
\vspace*{.2cm}\\
\pro w\bnf \res z (\pro z\bullet \pro x\bnf \pro z\bullet \pro y\to \pro f\bullet\l z) &\mbox{otherwise}
\end{array}
\right.
\]
Observe that failure here is indicated by pattern $\pro f \bullet \l z$; in this way,
two failure barbs cannot unify and so they cannot disappear during computations.
\begin{defi}[Tests]
Let $w$ and $f$ be fresh names, i.e.\ different from all the other names around. Then define:
\begin{equation*}
\begin{array}{rcl}
{\sf free}(x,n,w) &=& \res m (\pro m\bullet \pro n\to \pro {w}\bnf \pro m\bullet\pro x)
\\
\
\\
{\sf rest}^{N}(x,w) &=& \pro {w}\bnf\res m \res z (\ \pro m\bullet x\bullet z\\
& & \qquad \qquad \bnf \pro m\bullet (\l y_1\bullet \l y_2)\bullet \l z\to \pro f\bullet \l z
\\
& & \qquad \qquad \bnf \prod_{n\in N} \pro m\bullet \pro n\bullet \l z\to \pro f\bullet \l z\ )
\\
\
\\
{\sf equality}^R(x,m,w) &=& \rest {w_y}(\ \pro {w_{y_1}}\to \ldots \to \pro {w_{y_i}} \to \pro w\\
\vspace*{.2cm}& & \qquad\quad\bnf \prod_{(y,n)\in R} {\sf check}(x,m,y,n,w_y)\ )\\
& \multicolumn{2}{l}{\mbox{where $\wt y = \{y_1,\ldots,y_i\}={\sf fst}(R)$}}
\end{array}
\end{equation*}
\end{defi}
The behaviour of the tests just defined is formalized by the following three results.
\begin{lem}
\label{lem:free-succ}
Let $\theta$ be such that $\{n,w\} \cap {\sf dom}(\theta) = \emptyset$; then,
$\theta({\sf free}(x,n,w))$ succeeds if and only if $\theta(x)=n$.
\end{lem}
\usedby{Lemma \ref{lem:theta-charP} and \ref{lem:reply-rename}}
\begin{proof}
Straightforward.
\end{proof}
\begin{lem}
\label{lem:rest-succ}
Let $\theta$ be such that $(N \cup \{w,f\}) \cap {\sf dom}(\theta) = \emptyset$; then,
$\theta({\sf rest}^N(x,w))$ succeeds if and only if $\theta(x) \in {\cal N} \setminus N$.
\end{lem}
\usedby{Lemma \ref{lem:theta-charP} and \ref{lem:reply-rename}}
\begin{proof}
Straightforward.
\end{proof}
\begin{lem}
\label{lem:equi-succ}
Let $\theta$ be such that $({\sf snd}(R) \cup \{w,f,m\}) \cap {\sf dom}(\theta) = \emptyset$; then,
$\theta({\sf equality}^R(x,m,w))$ succeeds if and only if, for every $(y,n)\in R$,
$m=n$ if and only if $\theta(x)=\theta(y)$.
\end{lem}
\usedby{Lemma \ref{lem:theta-charP} and \ref{lem:reply-rename}}
\begin{proof}
In order for $\theta({\sf equality}^R(x,m,w))$ to succeed by exhibiting a barb $\pro w$,
each check $\theta({\sf check}(x,m,y,n,w_y))$ must succeed by producing $\pro {w_y}$.
The rest of the proof is straightforward.
\end{proof}
\begin{lem}
\label{lem:exact-reduct-tests}
Let $T$ be a test and $\theta$ be a substitution such that $\theta(T)$ succeeds;
there are exactly $k$ reductions of $\theta(T)$ to a successful process, where $k$ depends only on the structure of $T$.
\end{lem}
\begin{proof}
Straightforward for free and restricted tests, for which $k = 1$ and $k = 0$, respectively.
For an equality test ${\sf equality}^R(x,m,w)$ it suffices to observe that each successful check has an exact
number of reductions to succeed (1, if $m=n$, 0 otherwise) and then there is a reduction to consume the success
barb of each check.
Thus, $k = |R|+h$, where $h$ is the number of pairs in $R$ whose second component equals $m$.
\end{proof}
From now on, we adopt the following notation: if $\wt n = n_1,\ldots,n_i$, then $\pro w \bullet \wt n$
denotes $\pro w \bullet n_1 \bullet \ldots \bullet n_i$. Moreover, $\theta(\wt n)$ denotes
$\theta(n_1),\ldots,\theta(n_i)$; hence, $\pro w \bullet \theta(\wt n)$ denotes
$\pro w \bullet \theta(n_1) \bullet \ldots \bullet \theta(n_i)$.
\begin{defi}
\label{def:char}
The {\em characteristic process} ${\sf char}^{N}(p)$ of a pattern $p$ with respect to a finite set of names $N$ is ${\sf char}^N(p)=p'\to {\sf tests}^N_{F,R}$ where ${\sf spec}^{N}(p)=p',F,R$ and
\begin{equation*}
\begin{array}{rcll}
{\sf tests}^N_{F,R} &\define& \rest {w_x} \rest {w_y}(\\
& & \qquad\pro {w_{x_1}}\to\ldots\to\pro{w_{x_i}}\to\pro {w_{y_1}}\to\ldots\to\pro {w_{y_j}}\to\pro w\bullet \wt x\\
& & \qquad\bnf \prod_{(x,n)\in R} {\sf equality}^R(x,n,w_x)\\
& & \qquad\bnf \prod_{(y,n)\in F} {\sf free}(y,n,w_y)\\
& & \qquad\bnf \prod_{(y,n)\in R} {\sf rest}^N(y,w_y)\ )
\end{array}
\end{equation*}
where $\wt x = \{x_1,\ldots,x_i\} = {\sf fst}(R)$ and
$\wt y = \{y_1,\ldots,y_j\} = {\sf fst}(F)\cup {\sf fst}(R)$.
\end{defi}
\begin{lem}
\label{lem:theta-charP}
Let $\theta$ be such that ${\sf dom}(\theta) = {\sf fst}(F) \cup {\sf fst}(R)$; then,
$\theta({\sf tests}^N_{F,R})$ succeeds if and only if
\begin{enumerate}
\item for every $(x,n) \in F$ it holds that $\theta(x) = n$;
\item for every $(x,n) \in R$ it holds that $\theta(x) \in {\cal N}\setminus N$;
\item for every $(x,n)$ and $(y,m) \in R$ it holds that $n=m$ if and only if $\theta(x)=\theta(y)$.
\end{enumerate}
\end{lem}
\usedby{Thm \ref{thm:lts-2-reply-succeed}}
\begin{proof}
By induction on $|F \cup R|$ and Lemmata~\ref{lem:free-succ},
\ref{lem:rest-succ} and \ref{lem:equi-succ}. Indeed, by Definition~\ref{def:bchar},
${\sf fst}(F \cup R) \cap ({\sf snd}(F\cup R) \cup N) = \emptyset$; moreover, freshness of
$w$ and $f$ implies that $\{w,f\} \cap {\sf dom}(\theta) = \emptyset$.
\end{proof}
Note that the following results will consider the number of reductions required to succeed.
These are significant to proving the results in the strong setting, but unimportant in
the weak setting, i.e.\ with $\redar$ replaced by $\Redar$.
\begin{lem}
\label{lem:min-reduct-charP}
Given ${\sf char}^N(p)$ and any substitution $\theta$
such that ${\sf dom}(\theta) = {\sf fst}(F)\cup{\sf fst}(R)$ and $\theta({\sf tests}^N_{F,R})$ succeeds,
then there are exactly $k$ reduction steps $\theta({\sf tests}^N_{F,R})\redar^k \pro w\bullet \theta(\wt x)\ |\ Z$,
where $\wt x = {\sf fst}(R)$ and $Z \beq \zero$ and $k$ depends only on $F$ and $R$ and $N$; moreover,
no sequence of reductions shorter than $k$ can yield a successful process.
\end{lem}
\usedby{Prop \ref{prop:reply-context-minimum} and Thm \ref{thm:lts-2-reply-succeed}}
\begin{proof}
By induction on $|F \cup R|$ and Lemma~\ref{lem:exact-reduct-tests}.
\end{proof}
Notice that $k$ does not depend on $\theta$; thus, we shall refer to $k$ as the number of
reductions for ${\sf tests}^N_{F,R}$ to become successful.
The crucial result we have to show is that the characterisation of a pattern $p$ with respect to a set of names $N$ can yield a reduction via a proper reply (according to Definition~\ref{def:bisim}) to the challenge $\rest n p$ when $\wt n$ does not intersect $N$.
A reply context for a challenge $(\rest n p,\idsub_{{\sf bn}(p)})$ with a finite set of names $N$ can be defined by exploiting the characteristic process.
\begin{defi}
\label{def:reply-context}
A {\em reply context} $\CopNnoarg C p N (\cdot)$ for the challenge $(\rest n p,\idsub_{{\sf bn}(p)})$ with a finite set of names $N$ such that $\wt n$ is disjoint from $N$ is defined as follows:
\begin{eqnarray*}
\CopNnoarg C p N (\cdot) &\define& {\sf char}^{N}(p)\bnf \cdot
\end{eqnarray*}
\end{defi}
\begin{prop}
\label{prop:reply-context-minimum}
Given a reply context $\CopNnoarg C p N (\cdot)$, the minimum number of reductions required for $\CopNnoarg C p N (Q)$
to become successful (for any $Q$) is the number of reduction steps for ${\sf tests}^N_{F,R}$ to become successful plus 1.
\end{prop}
\usedby{Thms \ref{thm:lts-2-succeed-reply} and \ref{thm: complete}}
\begin{proof}
By Definition~\ref{def:reply-context}, success can be generated only after removing the case $p'$ from ${\sf char}^{N}(p)$;
this can only be done via a reduction together with $Q$, i.e.\ $Q$ must eventually yield a pattern $q$
that unifies with $p'$. The minimum number of reductions is obtained when $Q$ already yields such a $q$, i.e.\ when $Q$ is a
process of the form $\rest m (q\to Q_1\bnf Q_2)$, for some $\wt m$ and $q$ and $Q_1$ and $Q_2$ such that $\{p'\pmatch q\}=(\theta,\rho)$ and $\theta({\sf tests}^N_{F,R})$ succeeds. In this case,
${\sf dom}(\theta) = {\sf bn}(p') = {\sf fst}(F\cup R)$;
by Lemma~\ref{lem:min-reduct-charP}, $\theta({\sf tests}^N_{F,R})$ is successful after
$k$ reductions; thus, $\CopNnoarg C p N (Q)$ is successful after $k+1$ reductions, and this is
the minimum over all possible $Q$'s.
\end{proof}
Denote the number of reductions put forward by Proposition~\ref{prop:reply-context-minimum} as $\lb N p$.
The main feature of $\CopNnoarg C p N (\cdot)$ is that, when the hole is filled with a process $Q$, it holds that
$\CopNnoarg C p N (Q)$ is successful after $\lb N p$ reductions if and only if
there exist $(q,\rho)$ and $Q'$ such that $Q\ltsred{\rest n q}Q'$ and $p,\idsub_{{\sf bn}(p)}\compat q,\rho$.
This fact is proved by Propositions~\ref{thm:lts-2-reply-succeed} and~\ref{thm:lts-2-succeed-reply}.
\begin{prop}
\label{thm:lts-2-reply-succeed}
Suppose given a challenge $(\rest n p,\idsub_{{\sf bn}(p)})$, a finite set of names $N$, a process $Q$ and fresh names $w$ and $f$ such that
$(\wt n \cup \{w,f\}) \cap N = \emptyset$ and $({\sf fn}(\rest n p) \cup {\sf fn}(Q)) \subseteq N$.
If $Q$ has a transition of the form $Q\ltsred{\rest n q}Q'$ and there is a substitution $\rho$ such that
$p,\idsub_{{\sf bn}(p)}\compat q,\rho$ then
$\CopNnoarg C p N (Q)$ succeeds and has a reduction sequence
$\CopNnoarg C p N (Q)\redar^k \rest n(\rho Q'\bnf\pro w\bullet\wt n\ |\ Z)$, where $k=\lb N p$ and $Z \beq \zero$.
\end{prop}
\usedby{Lemma \ref{lem:succ-beq} and Thm \ref{thm: complete}}
\begin{proof}
We assume, by $\alpha$-conversion, that binding names of $p$ are fresh, in particular do not appear in $Q$.
By Lemma~\ref{prop:spec-pp} $\{p\pmatch p'\}=(\sigma,\theta)$ where $\sigma=\idsub_{{\sf bn}(p)}$ and $\theta= \{n/x\}_{(x,n) \in F \cup R}$.
By Proposition~\ref{lem:pat-lessthan} $\{q\pmatch p'\}=(\rho,\theta)$; thus $\CopNnoarg C p N (Q)\redar \rest n (\rho Q'\bnf \theta ({\sf tests}^N_{F,R}))$. Since $w$ and $f$ do not appear in $Q$, the only possibility of producing a successful
process is when $\theta ({\sf tests}^N_{F,R})$ succeeds; this is ensured by Lemma~\ref{lem:theta-charP}. The thesis follows by Lemma~\ref{lem:min-reduct-charP}.
\end{proof}
The main difficulty in proving the converse result is the possibility of renaming restricted names.
Thus, we first need a technical lemma that ensures us the possibility of having the same set of restricted
names both in the challenge and in the reply, as required by the definition of bisimulation.
\begin{lem}
\label{lem:reply-rename}
Let $p$ and $N$ be such that ${\sf pn}(p) \subseteq N$, ${\sf bn}(p) \cap N = \emptyset$ and
${\sf spec}^{N}(p)=p',F,R$. If $q$ is such that ${\sf bn}(p) \cap {\sf fn}(q) = \emptyset$ and
$\{p'\pmatch q\}=(\theta,\rho)$ such that $\theta({\sf tests}^N_{F,R})$ succeeds, then:
\begin{itemize}
\item $|{\sf vn}(p) \setminus N| = |{\sf vn}(q) \setminus N|$;
\item there exists a bijective renaming $\zeta$ of ${\sf vn}(q) \setminus N$ into ${\sf vn}(p) \setminus N$
such that $p,\idsub_{{\sf bn}(p)}\compat \zeta q,\rho$;
\item $\theta = \{n/x\}_{(x,n) \in F}\ \cup\ \{\zeta^{-1}(n)/x\}_{(x,n)\in R}$.
\end{itemize}
\end{lem}
\usedby{Thm \ref{thm:lts-2-succeed-reply}}
\proof
The proof is by induction on the structure of $p$. We have three possible base cases:
\begin{enumerate}
\item If $p=\l x$, then $p' = x$ and $F = R = \emptyset$. By definition of pattern unification,
$q \in \{x,\pro x, \l y\}$, for any $y$. Since $x \in {\sf bn}(p)$ and ${\sf bn}(p) \cap {\sf fn}(q) = \emptyset$,
it can only be $q = \l y$; then, $\theta = \{\}$ and $\rho = \{x/y\}$. This suffices to conclude,
since ${\sf vn}(p) \setminus N = {\sf vn}(q) \setminus N = \emptyset$ and
$\l x,\idsub_{\{x\}} \compat \l y,\rho$.
\item If $p = n$, then $p' = \l x$, for $x$ fresh. Let us distinguish two subcases:
\begin{enumerate}
\item If $n \in N$, then $F = \{(x,n)\}$ and $R =
\emptyset$. By definition of pattern unification,
$q$ must be communicable, $\rho = \{\}$ and $\theta
= \{q/x\}$. Since ${\sf tests}^N_{F,R}$ only
contains ${\sf free}(x,n)$, by
Lemma~\ref{lem:free-succ} it holds that $q =
\theta(x) = n$. This suffices to conclude, since
${\sf vn}(p) \setminus N = {\sf vn}(q) \setminus N =
\emptyset$ and $n, \{\} \compat n,\{\}$.
\item If $n \not\in N$, then $F = \emptyset$ and $R = \{(x,n)\}$. Like before,
$q$ must be communicable, $\rho = \{\}$ and $\theta = \{q/x\}$.
Since ${\sf tests}^N_{F,R}$ contains ${\sf rest}^N(x)$,
by Lemma~\ref{lem:rest-succ} it holds that $q = \theta(x) = m \in {\cal N} \setminus N$;
thus, $|{\sf vn}(p) \setminus N| = |{\sf vn}(q) \setminus N| = 1$.
This suffices to conclude, by taking $\zeta = \{n/m\}$, since $n, \{\} \compat n,\{\}$.
\end{enumerate}
\item If $p = \pro n$, then $p' = \pro n$ and $F = R = \emptyset$. By definition of pattern unification,
$q \in \{n,\pro n\}$ and $\rho = \theta = \{\}$. In any case,
${\sf vn}(p) \setminus N = {\sf vn}(q) \setminus N = \emptyset$ and
$p,\{\} \compat q,\{\}$.
\end{enumerate}
For the inductive case, let $p = p_1\bullet p_2$. By definition of specification,
$p' = p_1'\bullet p_2'$, $F = F_1 \uplus F_2$ and $R = R_1 \uplus R_2$, where
${\sf spec}^{N}(p_i)=p_i',F_i,R_i$, for $i \in \{1,2\}$.
By definition of pattern unification, there are two possibilities for $q$:
\begin{enumerate}
\item If $q=\l z$, for some $z$, then $p'$ must be communicable and
$\theta = \{\}$ and $\rho = \{p'/z\}$.
If $p'$ is communicable then by definition of specification
${\sf vn}(p)=\emptyset={\sf vn}(q)$ and ${\sf vn}(p) \setminus N = {\sf vn}(q) \setminus N = \emptyset$
and conclude with $p,\idsub_{{\sf bn}(p)}\compat\l z,\rho$.
\item Otherwise, it must be that $q = q_1\bullet q_2$, with
$\{p'_i\pmatch q_i\} = (\theta_i,\rho_i)$, for $i \in \{1,2\}$; moreover,
$\theta = \theta_1 \cup \theta_2$ and $\rho = \rho_1 \cup \rho_2$.
Since the first components of $F_1$ and $F_2$ are disjoint (and similarly for $R_1$ and $R_2$),
$\theta({\sf tests}^N_{F,R})$ succeeds implies that both $\theta({\sf tests}^N_{F_1,R_1})$ and
$\theta({\sf tests}^N_{F_2,R_2})$ succeed, since every test of $\theta({\sf tests}^N_{F_i,R_i})$
is a test of $\theta({\sf tests}^N_{F,R})$. Now, by two applications of the induction hypothesis,
we obtain that, for $i \in \{1,2\}$:
\begin{itemize}
\item $|V_i| = |W_i|$, where $V_i = {\sf vn}(p_i) \setminus N$ and $W_i = {\sf vn}(q_i) \setminus N$;
\item there exists a bijective renaming $\zeta_i$ of $W_i$ into $V_i$
such that $p_i,\idsub_{{\sf bn}(p_i)}\compat \zeta_i q_i,\rho_i$;
\item $\theta_i = \{n/x\}_{(x,n) \in F_i}\ \cup\ \{\zeta_i^{-1}(n)/x\}_{(x,n)\in R_i}$.
\end{itemize}
We now show that every name $m\in W_i$ is in the domain of $\zeta_i$ and that $\zeta_i(m)\in V_i$.
Further, that if $m$ is in only one of $W_i$ then $\zeta_i(m)$ only appears in the
corresponding $V_i$, alternatively if $m$ is in both $W_1$ and $W_2$ then $\zeta_1(m) = \zeta_2(m)=n$
for some $n\in V_1\cap V_2$.
\begin{enumerate}
\item {\em if $m \in W_1 \setminus W_2$, then $\zeta_1(m) \in V_1 \setminus V_2$:}\\
by contradiction, assume that $\zeta_1(m) = n \in V_1 \cap V_2$ (indeed,
$\zeta_1(m) \in V_1$, by construction of $\zeta_1$). By construction of the specification,
there exists $(x,n) \in R_1$. Moreover, since $n \in V_2$, there exists $m' \in W_2$
such that $\zeta_2(m') = n$ but $m' \neq m$. Again by construction of the specification,
there exists $(y,n) \in R_2$. By inductive hypothesis, $\theta_1(x) = \zeta_1^{-1}(n) = m$
and $\theta_2(x) = \zeta_2^{-1}(n) = m'$. But then $\theta({\sf check}(x,n,y,n))$, that
is part of $\theta({\sf tests}^N_{F,R})$, cannot succeed, since $\theta_1(x) \neq \theta_2(y)$
(see Lemma~\ref{lem:equi-succ}). Contradiction.
\item {\em if $m \in W_2 \setminus W_1$, then $\zeta_2(m) \in V_2 \setminus V_1$:}\\
similar to the previous case.
\item {\em if $m \in W_1 \cap W_2$, then $\zeta_1(m) = \zeta_2(m) \in V_1 \cap V_2$:}\\
let $n_i = \zeta_i(m) \in V_i$; by construction of the specification,
there exists $(x_i,n_i) \in R_i$. By contradiction, assume that $n_1 \neq n_2$.
Then, $\theta({\sf check}(x_1,n_1,x_2,n_2))$, that is part of $\theta({\sf tests}^N_{F,R})$,
reports failure, since by induction $\theta_1(x_1) = \zeta_1^{-1}(x_1) = m = \zeta_2^{-1}(x_2) = \theta_2(x_2)$
(see Lemma~\ref{lem:equi-succ}). Contradiction.
\end{enumerate}
Thus, $V_1 \cup V_2$ and $W_1 \cup W_2$ have the same cardinality; moreover, $\zeta = \zeta_1 \cup \zeta_2$ is a
bijection between them and it is well-defined (in the sense that $\zeta_1$ and $\zeta_2$ coincide on all elements
of ${\sf dom}(\zeta_1) \cap {\sf dom}(\zeta_2)$ -- see point (c) above).
Thus, $p_1,\idsub_{{\sf bn}(p_1)}\compat \zeta q_1,\rho_1$ and $p_2,\idsub_{{\sf bn}(p_2)}\compat \zeta q_2,\rho_2$;
so, $p,\idsub_{{\sf bn}(p)}\compat \zeta q,\rho$. Moreover,
\[\eqalign{
\theta &= \theta_1 \cup \theta_2 \cr
&= \{n/x\}_{(x,n) \in F_1}\ \cup\ \{\zeta^{-1}(n)/x\}_{(x,n)\in R_1}
\cup \{n/x\}_{(x,n) \in
F_2}\ \cup\ \{\zeta^{-1}(n)/x\}_{(x,n)\in R_2}\cr
&= \{n/x\}_{(x,n) \in F}\ \cup\
\{\zeta^{-1}(n)/x\}_{(x,n)\in R},
}
\] as desired.\qed
\end{enumerate}
\enlargethispage{\baselineskip}
\begin{prop}
\label{thm:lts-2-succeed-reply}
Suppose given a challenge $(\rest n p,\idsub_{{\sf bn}(p)})$, a finite set of names $N$, a process $Q$ and fresh names $w$ and $f$ such that ${\sf bn}(p) \cap N = (\wt n \cup \{w,f\}) \cap N = \emptyset$ and $({\sf fn}(\rest n p) \cup {\sf fn}(Q)) \subseteq N$.
If $\CopNnoarg C p N (Q)$ is successful after $\lb N p$ reduction steps,
then there exist $(q,\rho)$ and $Q'$
such that $Q\ltsred{\rest n q}Q'$
and $p,\idsub_{{\sf bn}(p)}\compat q,\rho$.
\end{prop}
\usedby{Lemma \ref{lem:succ-beq} and Thm \ref{thm: complete}}
\begin{proof}
By Proposition~\ref{prop:reply-context-minimum},
there must be a reduction $\CopNnoarg C p N (Q) \redar \rest m (\theta ({\sf tests}^N_{F,R})\bnf\rho Q'')$
obtained because $Q\ltsred{\rest m q'}Q''$ and $\{p'\pmatch q'\}=(\theta,\rho)$.
Since $w\notin {\sf fn}(Q,p')$ and $\CopNnoarg C p N (Q)\suc_w$, it must be that
$\theta ({\sf tests}^N_{F,R})$ succeeds; by
Proposition~\ref{prop:reply-context-minimum}, this happens in $\lb N p -1$ reduction steps.
By hypothesis, ${\sf fn}(\rest n p) \subseteq N$; thus, ${\sf vn}(p) \setminus N = \wt n$.
Moreover, by $\alpha$-conversion, $\wt m \cap {\sf fn}(Q) = \emptyset$;
thus, by ${\sf fn}(\rest m q') \subseteq {\sf fn}(Q) \subseteq N$, we have
that ${\sf vn}(q') \setminus N = \wt m$. Since ${\sf bn}(p) \cap N = \emptyset$,
we also have that ${\sf bn}(p) \cap {\sf fn}(q') = \emptyset$; thus, we can
use Lemma~\ref{lem:reply-rename} and obtain a bijection $\zeta = \{\wt n / \wt m\}$
such that $p,\idsub_{{\sf bn}(p)}\compat \zeta q',\rho$; moreover, by $\alpha$-conversion,
$Q\ltsred{\rest n \zeta q'} \zeta Q''$. We can conclude by taking $q = \zeta q'$ and
$Q' = \zeta Q''$.
\end{proof}
We are almost ready to give the completeness result, we just need an auxiliary lemma that allows us to remove
success and dead processes from both sides of a barbed congruence, while also opening the scope of the names
exported by the success barb.
\begin{lem}
\label{lem:succ-beq}
Let $\rest m(P\bnf\pro w\bullet\wt m \bnf Z) \beq \rest m(Q\bnf\pro w\bullet\wt m \bnf Z)$,
for $w\notin{\sf fn}(P,Q,\wt m)$ and $Z \beq \zero$; then $P\beq Q$.
\end{lem}
\usedby{Thm \ref{thm: complete}}
\begin{proof}
By Theorem~\ref{thm: sound}, it suffices to prove that
$$
\begin{array}{ll}
\Re = \{(P,Q)\ : & \rest m(P\bnf\pro w\bullet\wt m \bnf Z) \beq \rest m(Q\bnf\pro w\bullet\wt m \bnf Z)
\\
& \wedge\ w\notin{\sf fn}(P,Q,\wt m)\ \wedge\ Z \beq \zero\}
\end{array}
$$
is a bisimulation. Consider the challenge $P \ltsred\mu P'$ and reason by case analysis on $\mu$.
\begin{itemize}
\item If $\mu = \tau$, then $\rest m(P\bnf\pro w\bullet\wt m \bnf Z) \ltsred\tau
\rest m(P'\bnf\pro w\bullet\wt m \bnf Z) = \hat P$.
By Proposition~\ref{prop:tau-red} and reduction closure,
$\rest m(Q\bnf\pro w\bullet\wt m \bnf Z) \ltsred\tau \hat Q$ such that $\hat P \beq \hat Q$.
By Proposition~\ref{prop:free_n_match_proc} (since $w \notin {\sf fn}(Q)$) and $Z \beq \zero$, it can only be that
$\hat Q = \rest m(Q'\bnf\pro w\bullet\wt m \bnf Z)$, where $Q \ltsred\tau Q'$.
By definition of $\Re$, we conclude that $(P',Q') \in \Re$.
\item If $\mu = \rest n p$, for $({\sf bn}(p) \cup \wt n) \cap {\sf fn}(Q) = \emptyset$.
By $\alpha$-conversion, we can also assume that ${\sf bn}(p) \cap (\wt n \cup \wt m \cup {\sf fn}(P)) = \emptyset$.
Let us now fix a substitution $\sigma$ such that ${\sf dom}(\sigma) = {\sf bn}(p)$ and
${\sf fn}(\sigma) \cap \wt n=\emptyset$. Consider the context
$$
\context C \cdot =\ \cdot\ \bnf\ \pro w\bullet \wt{\l m} \to(\sigma({\sf char}^{N}(p)) \bnf
\pro w \bullet \wt{\l n} \to \pro {w'\,} \bullet \wt n \bullet \wt m)
$$
for $w'$ fresh (in particular, different from $w$). Consider now the following sequence of reductions:
$$
\begin{array}{ll}
\multicolumn{2}{l}{\context C {\rest m(P|\pro w\bullet\wt m|Z)}\vspace*{.2cm}}
\\
\vspace*{.2cm}
\redar &
\rest m(\sigma(\CopNnoarg C p N (P)) \bnf Z \bnf
\pro w \bullet \wt{\l n} \to \pro {w'\,} \bullet \wt n \bullet \wt m)
\\
\vspace*{.2cm}
\redar^{\!_{\lb N p}} \!\!\!\!\! &
\rest m( \rest n(\sigma P'|\pro w\bullet \wt n|\sigma Z') \bnf Z \bnf
\pro w \bullet \wt{\l n} \to \pro {w'\,} \bullet \wt n \bullet \wt m)
\\
\redar &
\res{\withsetnot{\wt n, \wt m}{\wt n\cup\wt m}}(\sigma P'\bnf \pro {w'\,} \bullet \wt n \bullet \wt m \bnf Z|\sigma Z')
\ \ = \ \ \hat P
\end{array}
$$
The first reduction is obtained by unifying $\pro w\bullet \wt m$ with the first
case of $\context C \cdot$; this replaces the binding names $\wt m$ in the context with
the variable names $\wt m$ and the scope of the restriction is extended consequently.
Moreover, $\sigma({\sf char}^{N}(p)) \bnf P = \sigma({\sf char}^{N}(p) \bnf P) =
\sigma(\CopNnoarg C p N (P))$: the first equality holds because
${\sf dom}(\sigma) = {\sf bn}(p)$ and ${\sf bn}(p) \cap {\sf fn}(P) = \emptyset$;
the second equality holds by definition of reply context.
The second sequence of reductions follows by Proposition~\ref{thm:lts-2-reply-succeed}
(ensuring that $\CopNnoarg C p N (P) \redar^{\!_{\lb N p}} \rest n(P'|\pro w\bullet \wt n|Z')$, for $Z' \beq \zero$),
Proposition~\ref{red:renaming}
and by the fact that $\sigma(\rest n(P'|\pro w\bullet \wt n|Z')) = \rest n(\sigma P'|\pro w\bullet \wt n|\sigma Z')$
(indeed, $w$ is fresh and ${\sf names}(\sigma) \cap \wt n = \emptyset$).
Moreover, notice that $\sigma Z' \beq \sigma \zero \beq \zero$, because of
Lemma~\ref{lem:bcon-sub}.
The last reduction is obtained by unifying $\pro w\bullet \wt n$ with the
case $\pro w\bullet \wt {\l n}$ of the context; this replaces the binding names $\wt n$
in the context with the variable names $\wt n$ and the scope of the restriction
is extended consequently.
Consider now $\context C {\rest m(Q|\pro w\bullet\wt m|Z)}$; then
reduction closure yields
$\context C {\rest m(Q|\pro w\bullet\wt m|Z)} \redar^{{\lb N p+2}} \hat Q$ such
that $\hat P \beq \hat Q$. As $\hat P$ has a barb containing $w'$, so must $\hat Q$;
by definition of $\context C \cdot$, this can happen only if $\CopNnoarg C p N (Q)$
is successful after $\lb N p$ steps. By Proposition~\ref{thm:lts-2-succeed-reply},
this entails that there exist $(q,\rho)$ and $Q'$
such that $Q\ltsred{\rest n q}Q'$
and $p,\idsub_{{\sf bn}(p)}\compat q,\rho$. Moreover, with a reasoning similar to that
for the reductions of $\context C {\rest m(P|\pro w\bullet\wt m|Z)}$, we can conclude
that $\hat Q = \res{\withsetnot{\wt n, \wt m}{\wt n\cup \wt m}}
(\sigma[\rho](Q') \bnf \pro {w'\,} \bullet \wt n \bullet \wt m \bnf Z|\sigma Z')$;
indeed, in this case applying Proposition~\ref{thm:lts-2-reply-succeed} yields
$\CopNnoarg C p N (Q) \redar^{\!_{\lb N p}} \rest n(\rho Q'|\pro w\bullet \wt n|Z')$.
To state that $(\sigma P', \sigma[\rho](Q')) \in \Re$, it suffices to notice
that $Z|\sigma Z' \beq \zero$; this holds because of contextuality of barbed congruence.
Finally, Lemma~\ref{lem:compat-compose-subs} entails that $p,\sigma\compat q,\sigma[\rho]$:
indeed, $\sigma[\idsub_{{\sf bn}(p)}] = \sigma$ because ${\sf dom}(\sigma) = {\sf bn}(p)$.
This shows that $(q,\sigma[\rho])$ and $Q'$ is a proper reply to the challenge
$P \ltsred{\rest n p} P'$ together with $\sigma$.
\end{itemize}
Closure under substitution holds by definition of $\Re$.
\end{proof}
\begin{thm}[Completeness of the bisimulation]
\label{thm: complete}
$\beq\ \subseteq\ \bisim$.
\end{thm}
\begin{proof}
It is sufficient to prove that, for every pair of processes $P$ and $Q$ such that $P\beq Q$ and
for every transition $P\ltsred\mu P'$, there exists a proper reply (according to the definition of
the bisimulation) of $Q$ and the reducts are still barbed congruent.
This is straightforward when $\mu = \tau$, due to reduction closure and Proposition~\ref{prop:tau-red}.
The difficult case if when $\mu=\rest n p$, for $({\sf bn}(p)\cup\wt n) \cap {\sf fn}(Q)=\emptyset$.
In this case fix a substitution $\sigma$ such that ${\sf dom}(\sigma)={\sf bn}(p)$ and ${\sf fn}(\sigma)\cap\wt n=\emptyset$.
By Propositions~\ref{thm:lts-2-reply-succeed} and~\ref{prop:compat-reflexive},
$\CopNnoarg C p N (P)$ is successful after $k$ reduction steps, where $k=\lb N p$.
It follows by barbed congruence that $\CopNnoarg C p N (Q)$ is successful after $k$ reduction steps too;
Proposition~\ref{thm:lts-2-succeed-reply} then implies that $Q\ltsred{\rest n q}Q'$
for some $(q,\rho')$ and $Q'$
such that $p,\idsub_{{\sf bn}(p)}\compat q,\rho'$.
By two applications of Proposition~\ref{thm:lts-2-reply-succeed} it follows that
$\CopNnoarg C p N (P)\redar^k \rest n(P'\bnf \pro w\bullet \wt n \bnf Z)$, for $Z \beq \zero$, and
$\CopNnoarg C p N (Q)\redar^k \rest n(\rho'Q'\bnf \pro w\bullet \wt n \bnf Z)$.
Notice that, by Proposition~\ref{prop:reply-context-minimum} and definition of the reply context,
these are the only possibilities that yield a success barb in $k$ reductions.
Furthermore, reduction closure of $\beq$ and Lemma~\ref{lem:succ-beq} imply that $P'\beq \rho ' Q'$.
By Lemma~\ref{lem:bcon-sub}, we obtain $\sigma P'\beq \sigma (\rho' Q') = \sigma[\rho'](Q')$.
By Lemma~\ref{lem:compat-compose-subs}, $p,\idsub_{{\sf bn}(p)}\compat q,\rho'$
implies $p,\sigma\compat q,\sigma[\rho']$. This suffices to conclude.
\end{proof}
To conclude, we want to stress that we have developed our semantic theories
in the {\em strong} setting just for the sake of simplicity. Their {\em weak} counterparts,
consisting of allowing multiple $\tau$s/reductions in every predicate, can be obtained
in the usual manner \cite{milner.parrow.ea:calculus-mobile,milner.sangiorgi:barbed-bisimulation}.
As usual, the main difficulty is in the completeness proof just shown. Indeed, to force a proper
reply via contexts, we need to use ``fresh" barbs (viz, the $w$s and $f$ in our tests). Such barbs
have to be removed after the forced action; however, this can be done only if the left and right
hand side of the equated processes have the same shape (see Lemma~\ref{lem:succ-beq}).
This is straightforward in the strong case, where the number of reductions (viz, $\lb N p$ --
see Propositions~\ref{thm:lts-2-reply-succeed} and~\ref{thm:lts-2-succeed-reply}) ensures this property.
By contrast, in the weak case we can stop along this sequence of $\lb N p$ reductions, since the
weak barbs will cover the missing steps. This requires a different proof of Lemma~\ref{lem:succ-beq}.
To achieve this, we can follow the traditional path: instead of having a single success barb $w$,
our tests have two (say, $w$ and $w'$) in mutual exclusion (i.e., internal choice); we then
consider an additional reduction that excludes $w'$. This ensures that the other process must also reach
the reduction that excludes $w'$ and thus complete the proof.
\subsection{Example Equivalences}
\label{subsec:examples}
This section considers some examples where bisimulation can be used to show the equivalence of processes.
The first example exploits the unification of protected names with both variable and protected names:
\begin{eqnarray*}
\pro n\to P\bnf !n\to P &\bisim& !n\to P
\end{eqnarray*}
It states that the processes $\pro n\to P\bnf !n\to P$ can be subsumed by the more compact process $!n\to P$;
indeed, any interaction of the left hand processes can be properly responded to by the right hand process and vice versa.
The second example considers the contractive nature of binding names in CPC:
a case with the pattern $\l x\bullet\l y$ can be subsumed by a case with the pattern $\l z$ as long as some conditions are met.
For example:
\begin{equation*}
\begin{array}{rcll}
\l x\bullet \l y\to P \bnf !\l z \to Q &\bisim& !\l z\to Q &
\quad \mbox{if $P\bisim \{x\bullet y/z\}Q$}
\end{array}
\end{equation*}
The side condition requires that the bodies of the cases must be bisimilar under a substitution that preserves the structure of any pattern bound by $\l x\bullet\l y$ in the process $Q$.
These examples both arise from pattern unification and also appear in the compatibility relation.
Indeed, the examples above are instances of a general result:
\begin{prop}
\label{eq-grrr}
Let $P=p\to P'\bnf !q\to Q'$ and $Q=\ !q\to Q'$.
If there exists $\rho$ such that $p,\idsub_{{\sf bn}(p)}\compat q,\rho$ and $P'\bisim\rho Q'$,
then $P\bisim Q$.
\end{prop}
\begin{proof}
It suffices to prove that
$$
\Re = \{(p \to P'|Q|R,Q|R)\, :\, Q =\,\, !q \to Q'\ \wedge\
\exists \rho\,.\, p,{\sf id}_{{\sf bn}(p)}\compat q,\rho\ \wedge\ P'\bisim\rho Q'\}\ \cup\ \bisim
$$
is a bisimulation. To this aim, consider every challenge from $p \to P'|Q|R$ and show that
there exists a transition from $Q|R$ that is a proper reply (according to the bisimulation).
The converse (when the challenge comes from $Q \bnf R$) is easier.
Let $p \to P'|Q|R \ltsred\mu \hat P$; there are two possibilities for $\mu$:
\begin{enumerate}
\item $\mu = \rest n p'$: in this case, we also have to fix a substitution $\sigma$ such that
${\sf dom}(\sigma) = {\sf bn}(p')$ and ${\sf fn}(\sigma) \cap \wt n = \emptyset$.
There are three possible ways for producing $\mu$:
\begin{enumerate}[label=\({\alph*}]
\item $\mu = p$ and $\hat P = P'|Q|R$: in this case, since the action comes from $p \to P'$,
by the side condition of rule {\sf parext}, it must be that ${\sf bn}(p) \cap {\sf fn}(Q|R) = \emptyset$.
Now, consider $Q \ltsred q Q'|Q$ with ${\sf bn}(q) \cap {\sf fn}(Q|R) = \emptyset$ (ensured by
$\alpha$-conversion); thus, $Q|R \ltsred q Q'|Q|R = \hat Q$. Let $\rho$ be such that
$p,{\sf id}_{{\sf bn}(p)}\compat q,\rho$; by Lemma~\ref{lem:compat-compose-subs},
$p,\sigma \compat q,\sigma[\rho]$, where $\sigma[{\sf id}_{{\sf bn}(p)}] = \sigma$
because ${\sf dom}(\sigma) = {\sf bn}(p)$. Now it suffices to prove that
$(\sigma \hat P, \sigma[\rho]\hat Q) \in \Re$.
This follows from the hypothesis that $P'\bisim\rho Q'$: indeed, by closure of $\bisim$ under
substitutions, $\sigma P'\bisim \sigma (\rho Q') = \sigma[\rho]Q'$; by Lemma~\ref{lem:bisim-par},
$\sigma P'|Q|R \bisim \sigma[\rho]Q'|Q|R$. Now conclude:
since ${\sf dom}(\sigma) = {\sf bn}(p)$ and ${\sf bn}(p) \cap {\sf fn}(Q|R) = \emptyset$, it holds that
$\sigma \hat P = \sigma P'|Q|R$;
since ${\sf dom}(\sigma[\rho]) = {\sf dom}(\rho) = {\sf bn}(q)$ and ${\sf bn}(q) \cap {\sf fn}(Q|R) = \emptyset$,
it holds that $\sigma[\rho] \hat Q = \sigma[\rho] Q'|Q|R$;
finally, by definition, $\bisim\ \subseteq \Re$.
\item $\mu = q$ and $\hat P = p \to P'|Q'|Q|R$: in this case, since the action comes from $Q$,
by the side condition of rule {\sf parext}, it must be that ${\sf bn}(q) \cap {\sf fn}(p \to P'|R) = \emptyset$.
Now, consider $Q|R \ltsred q Q'|Q|R = \hat Q$. By Lemma~\ref{prop:compat-reflexive},
$q,\sigma \compat q,\sigma$. It suffices to prove that $(\sigma \hat P, \sigma \hat Q) \in \Re$.
This follows from the definition of $\Re$:
since ${\sf dom}(\sigma) = {\sf bn}(q)$ and ${\sf bn}(q) \cap {\sf fn}(p \to P'|R) = \emptyset$, it holds that
$\sigma \hat P = p \to P'|\sigma Q'|Q|R$ and $\sigma \hat Q = \sigma Q'|Q|R$.
\item $\mu = \rest n r$, $R \ltsred\mu R'$ and $\hat P = p \to P'|Q|R'$: in this case,
by the side condition of rule {\sf parext}, it must be that ${\sf bn}(r) \cap {\sf fn}(p \to P'|Q) = \emptyset$.
Now, consider $Q|R \ltsred \mu Q|R' = \hat Q$ and reason like in the previous case, obtaining that
$\sigma \hat P = p \to P'|Q|\sigma R'\ \Re\ \ Q|\sigma R' = \sigma \hat Q$.
\end{enumerate}
\item $\mu = \tau$: in this case, there are five possible ways for producing $\mu$:
\begin{enumerate}[label=\({\alph*}]
\item $R \ltsred\tau R'$ and $\hat P = p \to P'|Q|R'$: this case is straightforward.
\item $\hat P = \vartheta P'|\theta (Q'|Q)|R$, where $\{p\pmatch q\} = (\vartheta,\theta)$:
Let $\rho$ be such that $p,{\sf id}_{{\sf bn}(p)}\compat q,\rho$; by Proposition~\ref{lem:compat-match},
$\{q\pmatch q\} = (\vartheta[\rho],\theta)$. But a pattern can unify with itself only if it
contains no binding names;
this entails that $\theta = \{\}$ and $\vartheta = \{\}$.
Hence, $\hat P = P'| Q'|Q |R$ and conclude by
taking $Q|R \ltsred\tau Q'|Q'|Q|R = \hat Q$, since by hypothesis $P' \bisim Q'$.
\item $\hat P = \rest n(\vartheta P'|Q|\theta R')$, where $R \ltsred{\rest n r} R'$ and
$\{p\pmatch r\} = (\vartheta,\theta)$: by $\alpha$-conversion, now let ${\sf bn}(p) \cap {\sf fn}(Q) = \emptyset$
and $\wt n \cap {\sf fn}(p \to P'|Q) = \emptyset$. Now consider $Q \ltsred q Q'|Q$ with
${\sf bn}(q) \cap {\sf fn}(Q) = \emptyset$; by Proposition~\ref{lem:compat-match}, the hypothesis
$p,{\sf id}_{{\sf bn}(p)}\compat q,\rho$ entails $\{q\pmatch r\} = (\vartheta[\rho],\theta)$.
Thus, $Q|R \ltsred\tau \rest n(\vartheta[\rho](Q'|Q)|\theta R') = \rest n(\vartheta[\rho]Q'|Q|\theta R') = \hat Q$,
where the first equality holds because ${\sf dom}(\vartheta[\rho]) = {\sf dom}(\rho) = {\sf bn}(q)$
and ${\sf bn}(q) \cap {\sf fn}(Q) = \emptyset$. Conclude by using the hypothesis $P' \bisim \rho Q'$,
thanks to closure of $\bisim$ under substitutions, parallel and restriction.
\item $\hat P = p \to P'\ |\ \rest n(\vartheta (Q'|Q)|\theta R')$, where $R \ltsred{\rest n r} R'$ and
$\{q\pmatch r\} = \linebreak (\vartheta,\theta)$: this case is simple, by considering
$Q|R \ltsred\tau \linebreak \rest n(\vartheta (Q'|Q)|\theta R') = \hat Q$ and by observing that
${\sf dom}(\vartheta) = {\sf bn}(q)$, with ${\sf bn}(q) \cap {\sf fn}(Q) = \emptyset$.
\item $\hat P = p \to P'\ |\ \vartheta Q'|\theta Q'|Q|R$, where $\{q\pmatch q\} = (\vartheta,\theta)$:
this case is straightforward, by observing that $\vartheta = \theta = \{\}$.
\end{enumerate}
\end{enumerate}
Closure under substitution is straightforward by Proposition~\ref{prop:compat-sub-closed}.
\end{proof}
To conclude, notice that the more general claim
\begin{quote}
Let $P=p\to P'\bnf !q\to Q'$ and $Q= \,\,!q\to Q'$; if there are $\sigma$
and $\rho$ such that $p,\sigma\compat q,\rho$ and
$\sigma P'\bisim\rho Q'$, then $P\bisim Q$
\end{quote}
does {\em not} hold. To see this, consider the following two processes:
$$
\begin{array}{lll}
P = \l x \to P'\ |\ Q & \mbox{with} & P' = x\bnf m \to \pro w
\ \ \mbox{ for } x \neq m
\\
Q =\,\, !\l x \to Q' & \mbox{with} & Q' = m\bnf m \to \pro w
\end{array}
$$
Trivially $\l x, \{m/x\} \compat \l x, \{m/x\}$ and $\{m/x\}P' \bisim \{m/x\}Q' = Q'$;
however, $P$ is {\em not} bisimilar to $Q$. Indeed, in the context $\context C \cdot = \,\cdot\bnf k \to \zero$,
for $k \neq m$, they behave differently: $\context C P$ can reduce in one step to a process that is stuck and cannot
exhibit any barb on $w$; by contrast, every reduct of $\context C Q$ reduces in another step to a process that exhibits
a barb on $w$. (As usual, for proving equivalences it is easier to rely on bisimulation, while for proving
inequivalences it is easier to rely on barbed congruence, thanks to Theorems~\ref{thm: sound} and~\ref{thm: complete}.)
Proposition~\ref{eq-grrr} is more demanding: it does not leave us free to choose whatever $\sigma$ we want, but
it forces us working with ${\sf id}_{{\sf bn}(p)}$. Now, the only $\rho$ such that $\l x,\{x/x\} \compat \l x,\rho$
is $\{x/x\}$; with such a substitution, the second hypothesis of the theorem, in this case $P' \bisim Q'$, does not hold
and so we cannot conclude that $P \bisim Q$.
\section{Comparison with Other Process Calculi}
\label{sec:compare}
This section exploits the techniques developed in \cite{G:IC08,G:CONCUR08} to formally
assess the expressive power of CPC with respect to $\pi$-calculus, Linda, Spi calculus, Fusion and Psi calculus.
After briefly recalling these models and some basic material from \cite{G:CONCUR08}, the
relation to CPC is formalised. First, let each model, including CPC, be augmented with
a reserved process `$\ok$', used to signal successful termination.
This feature is needed to formulate what a {\em valid} encoding is in Definition~\ref{def:ve}.
\subsection{Some Process Calculi}
\label{subsec:calculi}
\paragraph{$\pi$-calculus \cite{milner.parrow.ea:calculus-mobile,sangiorgi.walker:theory-mobile}.}
The $\pi$-calculus processes are given by the following grammar:
$$
P \ ::= \ \zero \ \bnf \ \ok \ \bnf \ \oap a b.P\ \bnf \ \iap a x.P \ \bnf \
(\nu n) P \ \bnf \ P | Q \ \bnf \ !P
$$
and the only reduction axiom is
$$
\oap a b .P\bnf \iap a x.Q \quad\redar\quad P\bnf \{b/x\}Q
$$
The reduction relation is obtained by closing this interaction rule by parallel, restriction and the
same structural congruence relation defined for CPC.
\paragraph{Linda \cite{Gel85}.} Consider the following variant of Linda formulated to follow
CPC's syntax. Processes are defined as:
$$
P \ ::= \ \zero \ \bnf \ \ok \ \bnf \ \oap {} {b_1,\ldots,b_k} \ \bnf \ \iap {} {t_1,\ldots,t_k}.P \ \bnf \
(\nu n) P \ \bnf \ P | Q \ \bnf \ !P
$$
where $b$ ranges over names and $t$ denotes a template field, defined by:
$$
t \ ::=\ \lambda x\ \quad |\quad \ex {\,b\,}
$$
Assume that input variables occurring in templates are all distinct.
This assumption rules out template $(\l x,\l x)$, but accepts $(\l x,
\ex b,\ex b)$. Templates are used to implement Linda's pattern
matching, defined as follows:
$$
\begin{array}{c}
\vspace*{.4cm}
\pmtch(\ ; \, ) = \{\}
\qquad\qquad
\pmtch(\ex {\,b\,} ; b) = \{\}
\qquad\qquad
\pmtch(\lambda x ; b) = \{b/x\}
\\
\Rule{}
{\pmtch(t ; b) = \sigma_1 \qquad \pmtch(\wt t ; \wt b) = \sigma_2}
{\pmtch(t,\wt t\, ;\, b,\wt b) = \sigma_1 \uplus \sigma_2}
{}
\end{array}
$$
where
`$\uplus$' denotes the union of partial functions with disjoint domains. The interaction axiom is:
$$
\oap {} {\wt b}\bnf \iap{}{\wt t}.P \redar \sigma P
\qquad \mbox{ if }\ \pmtch(\wt t ; \wt b) = \sigma
$$
The reduction relation is obtained by closing this interaction rule by parallel, restriction and the
same structural congruence relation defined for CPC.
\paragraph{Spi calculus \cite{gordon1997ccp}.} This language is unusual as names
are now generalised to {\em terms} of the form
\begin{eqnarray*}
M,N \ &::=&\ n \ \bnf\ x \ \bnf\ (M,N)
\ \bnf\ 0 \ \bnf\ i \ \bnf\ {\it suc}(M) \ \bnf\ \encr M N
\end{eqnarray*}
\change{Thomas}
{They are rather similar to the patterns of CPC in that they may have
internal structure. Of
particular interest is the pair, that combines terms and allows the
construction of arbitrary structured data,
and the encryption construct.
Pairing is distinct from the polyadic data exchange
discussed previously, as compound messages may be bound to a single name
and then
decomposed later by some intensional reduction. Similarly, the encryption
requires they key to be known to gain access to the encrypted term.}
{They are rather similar to the patterns of CPC in that they may have internal
structure. Of particular interest are the pair, successor and encryption that
may be bound to a name and then decomposed later by an intensional reduction.
Note that $i$ denotes a natural number greater than zero, and is considered
equal to the $i$th successor of zero.}
The processes of the Spi calculus are:
\begin{eqnarray*}
P,Q &::=& \ \ 0\ \bnf \ \ok \ \bnf\ P|Q\ \bnf\ !P\ \bnf\ \res m P\ \bnf\ M(x).P\
\bnf\ \overline{M}\langle N\rangle .P\\
& & \ \bnf\ [M\ {\it is}\ N]P
\ \bnf\ {\it let}\ (x,y)=M\ {\it in}\ P\\
& & \ \bnf\ {\it case}\ M\ {\it of}\ \encr x N:P
\ \bnf\ {\it case}\ M\ {\it of}\ 0:P\ {\it suc}(x):Q
\end{eqnarray*}
The null process, parallel composition, replication and restriction
are all familiar.
The input $M(x).P$ and output $\overline{M}\langle N\rangle .P$ are generalised
from $\pi$-calculus to
allow arbitrary terms in the place of channel names and output arguments.
The match $[M\ {\it is}\ N]P$ determines equality of $M$ and $N$.
The splitting ${\it let}\ (x,y)=M\ {\it in}\ P$ decomposes pairs.
The decryption ${\it case}\ M\ {\it of}\ \encr x N:P$ decrypts $M$
and binds the encrypted message to $x$.
The integer test ${\it case}\ M\ {\it of}\ 0:P\ {\it suc}(x):Q$ branches
according to the number.
\change{Thomas}
{The last four can all get stuck if $M$ is an incompatible term.}
{Note that the last four processes can all get stuck if $M$ is an incompatible term.
Furthermore, the last three are intensional, i.e.\ they depend on the internal
structure of $M$.}
Concerning the operational semantics, we
consider a slightly modified version of Spi calculus where
interaction is generalised to
$$
\overline{M}\langle N\rangle .P\bnf M(x) .Q \quad\rew\quad P\bnf \{N/x\}Q
$$
where $M$ is any term of the Spi calculus. The remaining axioms are:
$$
\begin{array}{rcl}
[M\ {\it is}\ M]P &\redar& P
\vspace*{.1cm}
\\
{\it let}\ (x,y)=(M,N)\ {\it in}\ P &\redar& \{M/x,N/y\}P
\vspace*{.1cm}
\\
{\it case}\ \{M\}_N\ {\it of}\ \encr x N:P &\redar& \{M/x\}P
\vspace*{.1cm}
\\
{\it case}\ 0\ {\it of}\ 0:P\ {\it suc}(x):Q &\redar& P
\vspace*{.1cm}
\\
{\it case}\ suc(N)\ {\it of}\ 0:P\ {\it suc}(x):Q &\redar& \{N/x\}Q
\end{array}
$$
Again, the reduction relation is obtained by closing the interaction axiom
under parallel, restriction and the structural congruence of CPC.
\paragraph{Fusion \cite{parrow.victor:fusion-calculus}.}
Processes are defined as:
$$
P\ ::=\ \zero\ \bnf\ \ok \ \bnf \ P|P\ \bnf \ (\nu x)P\ \bnf \ !P\ \bnf \
\oap u {\wt x}.P\ \bnf \ \iap u {\wt x}.P
$$
The interaction rule for Fusion is taken from \cite{WG:explicit-fusions}:
$$
\begin{array}{ll}
(\nu \wt u)(\oap u {\wt x}.P\bnf \iap u {\wt y}.Q\ | \ R)
\redar \sigma P\ | \ \sigma Q\ | \ \sigma R\
& \mbox{with } {\sf dom}(\sigma) \cup {\sf ran}(\sigma) \subseteq \{\wt x,\wt y\}
\\
& \mbox{and } \wt u = {\sf dom}(\sigma) \setminus {\sf ran}(\sigma)
\\
& \mbox{and } \sigma(v) = \sigma(w)
\\
& \mbox{iff } (v,w) \in E(\wt x = \wt y)
\end{array}
$$
where $E(\wt x = \wt y)$ is the least equivalence relation on names
generated by the equalities $\wt x = \wt y$ (that is defined
whenever $|\wt x| = |\wt y|$).
Fusion's reduction relation is obtained by closing the interaction axiom
under parallel, restriction and the structural congruence of CPC.
\newcommand{\stackrel\cdot\leftrightarrow}{\stackrel\cdot\leftrightarrow}
\newcommand{{\bf T}}{{\bf T}}
\newcommand{{\bf A}}{{\bf A}}
\newcommand{{\bf 1}}{{\bf 1}}
\newcommand{\otimes}{\otimes}
\newcommand{\assert}[1]{\llparenthesis \, #1 \, \rrparenthesis}
\newcommand{\fram}[1]{{\cal F}(#1)}
\paragraph{Psi \cite{BJPV11}.}
For our purposes, Psi-calculi are parametrized w.r.t. two sets: terms ${\bf T}$,
ranged over by $M,N,\ldots$, and assertions ${\bf A}$, ranged over by $\Psi$.
The empty assertion is written ${\bf 1}$.
We also assume two operators: channel equivalence, $\stackrel\cdot\leftrightarrow \subseteq {\bf T} \times {\bf T}$,
and assertion composition, $\otimes: {\bf A} \times {\bf A} \rightarrow {\bf A}$.
It is also required that $\stackrel\cdot\leftrightarrow$ is transitive and
symmetric, and that $(\otimes,{\bf 1})$ is a commutative monoid.
Processes in Psi are defined as:
$$
P\ ::=\ \zero\ \bnf\ \ok \ \bnf \ P|P\ \bnf \ (\nu x)P\ \bnf \ !P\ \bnf \
\oap M N.P\ \bnf \ \iap M {\lambda\wt x} N.P \ \bnf\ \assert\Psi
$$
We now give a reduction semantics, by isolating the $\tau$ actions of the
LTS given in \cite{BJPV11}. To this aim, we recall the definiton of frame
of a process $P$, written $\fram P$, as the set of unguarded assertions
occurring in $P$. Formally:
$$
\fram{\assert \Psi} = \Psi
\qquad
\fram{(\nu x)P} = (\nu x)\fram P
\qquad
\fram{P|Q} = \fram P \otimes \fram Q
$$
and is ${\bf 1}$ in all other cases. We denote as $(\nu \wt b_P)\Psi_P$ the frame of $P$.
The structural laws are the same as in $\pi$-calculus.
The reduction relation is inferred by the following laws:
$$
\begin{array}{c}
\prooftree \Psi \vdash M \stackrel\cdot\leftrightarrow N
\justifies \Psi \triangleright \oap M K.P\ |\ \iap N {\lambda \wt x}H.Q \redar P\ |\ \{{\wt L}/{\wt x}\}Q
\endprooftree\ K = H[\wt x := \wt L]
\vspace*{.4cm}
\\
\prooftree \Psi \otimes \Psi_Q \triangleright P \redar P'
\justifies \Psi \triangleright P\ |\ Q \redar P' \ |\ Q
\endprooftree\ \fram Q = (\nu \wt b_Q)\Psi_Q, \wt b_Q \mbox{ fresh for } \Psi \mbox{ and } P
\vspace*{.4cm}
\\
\prooftree \Psi \triangleright P \redar P'
\justifies \Psi \triangleright (\nu x) P \redar (\nu x) P'
\endprooftree\ x \not\in \mbox{names}(\Psi)
\qquad
\prooftree P \equiv Q \quad \Psi \triangleright Q \redar Q' \quad Q' \equiv P'
\justifies \Psi \triangleright P \redar P'
\endprooftree
\end{array}
$$
We write $P \redar P'$ whenever ${\bf 1} \triangleright P \redar P'$.
\subsection{Valid Encodings and their Properties}
This section recalls and adapts the definition of valid encodings as well as some
useful theorems (details in \cite{G:CONCUR08}) for formally relating process calculi.
The validity of such criteria in developing expressiveness studies emerges from the
various works
\cite{G:IC08,G:DC10,G:CONCUR08}, that have also recently inspired similar works
\cite{LPSS10,LVF10,gla12}.
An {\em encoding} of a language $\Lang_1$ into another language $\Lang_2$ is a pair $(\encode\cdot,\renpol)$
where $\encode\cdot$ translates every $\Lang_1$-process into an $\Lang_2$-process
and $\renpol$ maps every name (of the source language) into a tuple of $k$ names (of the target language), for $k > 0$.
The translation $\encode\cdot$ turns every term of the source language into a term of the target; in doing this,
the translation may fix some names to play a precise r\^ole
or may translate a single name into a tuple of names. This can be obtained
by exploiting $\renpol$.
Now consider only encodings that satisfy the following properties.
Let a {\em $k$-ary
context} $\context C {\_\,_1; \ldots; \_\,_k}$ be a term where $k$
occurrences of $\zero$ are linearly replaced by the holes $\{\_\,_1;
\ldots; \_\,_k\}$ (every one of the $k$ holes must occur once and only once).
Moreover, denote with $\redar_i$ and $\Redar_i$
the relations $\redar$ and $\Redar$ in language $\Lang_i$;
denote with $\redar^\omega_i$ an infinite sequence of reductions in $\Lang_i$.
Moreover, we let $\beq_i$ denote the reference behavioural equivalence for language $\Lang_i$.
Also, let $P \suc_i$ mean that there exists $P'$ such that $P \Redar_i P'$ and $P' \equiv P''\bnf \ok$,
for some $P''$.
Finally, to simplify reading, let $S$ range
over processes of the source language (viz., $\Lang_1$) and $T$ range
over processes of the target language (viz., $\Lang_2$).
\begin{defi}[Valid Encoding]
\label{def:ve}
An encoding $(\encode\cdot,\renpol)$ of $\Lang_1$ into $\Lang_2$
is {\em valid} if it satisfies the following five properties:
\begin{enumerate}
\item {\em Compositionality:} for every $k$-ary operator $\op$ of $\Lang_1$
and for every subset of names $N$,
there exists a $k$-ary context $\CopN C \op N {\_\,_1; \ldots; \_\,_k}$ of $\Lang_2$
such that, for all $S_1,\ldots,S_k$ with ${\sf fn}(S_1,\ldots,S_k) = N$, it holds
that $\encode{\op(S_1,\ldots,S_k)} = \CopN C \op N {\encode{S_1};\ldots;\encode{S_k}}$.
\item {\em Name invariance:}
for every $S$ and name substitution $\sigma$, it holds that
$$
\encode{\sigma S}\ \left\{
\begin{array}{ll}
\ =\ \sigma'\encode S& \mbox{ if $\sigma $ is injective}\\
\ \beq_2\ \sigma'\encode S & \mbox{ otherwise}
\end{array}
\right.
$$
where $\sigma'$ is such that
$\renpol(\sigma(a)) = \sigma'(\renpol(a))$
for every name $a$.
\item {\em Operational correspondence:}
\begin{itemize}
\item for all $S \Redar_1 S'$, it holds that $\encode S \Redar_2 \beq_2 \encode {S'}$;
\item for all $\encode S \Redar_2 T$, there exists $S'$ such that $S \Redar_1\!\! S'$
and $T \Redar_2 \beq_2\!\! \encode {S'}$.
\end{itemize}
\item {\em Divergence reflection:}
for every $S$ such that
$\encode S \redar\!\!_2^\omega$, it holds that
\linebreak $S$ \mbox{$\redar\!\!_1^\omega$}.
\item {\em Success sensitiveness:}
for every $S$, it holds that $S \suc_1$ if and only if $\encode S \suc_2$.
\end{enumerate}
\end{defi}
The criteria we have just presented may seem quite demanding; for example,
they do not allow schemes including parameters that are changed along the
way of the encoding (the most notable of such examples is Milner's encoding
of $\lambda$-calculus into $\pi$-calculus \cite{Milner92}). Of course, this
makes our separation results slightly weaker and leaves room for further
improvement. Moreover, as fully explained in \cite{GN:MSCS14}, we do not
consider full abstraction as a validity criterion for expressiveness.
Now recall some results concerning valid encodings, in particular for showing
separation results, i.e.\ for proving that no valid encoding can exist between
a pair of languages ${\mathcal L}_1$ and ${\mathcal L}_2$ satisfying certain
conditions.
Here, these languages will be limited to CPC and those introduced in Section~\ref{subsec:calculi}.
Originally valid encodings considered were assumed to be {\em semi-homomorphic},
i.e.\ where the interpretation of parallel
composition is via a context of the form $\res {\wt n}(\_\,_1\bnf
\_\,_2\bnf R)$, for some $\wt n$ and $R$ that only depend on the
free names of the translated processes.
This assumption simplified the proofs of the following results in general, i.e.\ without
relying on any specific process calculus; in our setting, since the languages are fixed,
we can prove the same results without assuming semi-homomorphism.
\change{barry}{It is worth remarking that, since the calculi considered here have been already defined
(see Section~\ref{subsec:calculi}), we do not need any assumption on the context used
to translate the parallel operator. In \cite{G:CONCUR08} we needed to explicitly
assume that such an operator is translated ``semi"-homomorphically, i.e.\ via a context
of the form $\res {\wt n}(\_\,_1\bnf \_\,_2\bnf R)$, for some $\wt n$ and $R$ that only
depend on the free names of the translated processes. ``Semi"-homomorphism comes for free
by Proposition~\ref{deadlock} and by the kind of interactions that can occur in our sample
process calculi.}{}
\comments{barry}{The limitation to semi-homomorphisms that was
implicit in [9] is here made explicit. It is worth remarking that
the limitation to the given set of languages does not remove the
need for this assumption in the given proofs, even though it kills
of one particular counter-example. }
\begin{thm}
\label{autoriduz}
Assume that there exists $S$ such that $S \noredar\!\!_1$ and
$S \not\suc_1\ $ and $S\bnf S \suc_1$;
moreover, assume that every $T$
that does not reduce is such that $T\bnf T \noredar\!\!_2$. Then,
there cannot exist any
valid encoding of $\Lang_1$ into $\Lang_2$.
\end{thm}
To state the following proof technique, define the {\em matching degree}
of a language $\Lang$, written $\md\Lang$, as the least upper bound on the number
of names that must be matched to yield a reduction in $\Lang$. For example,
$\md{\pi\mbox{-calculus}} = 1$, since the only name matched for performing
a reduction is the name of the channel where the communication happens,
whereas $\md{\mbox{Linda}} = \md{\mbox{CPC}} = \infty$, since there is no upper bound
on the number of names that can be matched in a reduction.
\begin{thm}
\label{match}
If $\md{\Lang_1} > \! \md{\Lang_2}$, then there exists no
valid encoding of $\Lang_1$ into $\Lang_2$.
\end{thm}
The previous proof techniques can be directly used in some cases: for example,
we shall prove that CPC cannot be encoded in any other sample calculus by exploiting
Theorem~\ref{autoriduz}. However, not all separation results can be obtained as
corollaries of such results. The following technique provides a very useful tool when
the theorems above cannot be applied.
\begin{prop}
\label{deadlock}
Let $\encode\cdot$ be a valid encoding; then, $S \noredar\!\!_1$
implies that $\encode S \noredar\!\!_2$.
\end{prop}
The way in which we shall use this technique is the following. To prove that
$\Lang_1$ cannot be encoded into $\Lang_2$ we reason by contradiction and assume a
valid encoding $\encode\cdot$. Then, we pick an $\Lang_1$-process $P$ that reduces;
we first show that this implies that $\encode P$ also reduces. We then analyze how
the latter reduction may have happened and, for every possible case, show a process
$P'$ obtained from $P$ (usually, by just swapping two names) such that $\encode{P'}$
reduces whereas $P'$ does not. This contradicts Proposition~\ref{deadlock}
and allows us to conclude that no valid encoding exists.
\subsection{CPC vs $\pi$-calculus and Linda}
\label{subsec:pi-linda}
A hierarchy of sets of process calculi with different communication primitives is
obtained in
\cite{G:IC08} via combining four features:
synchronism (synchronous vs asynchronous),
arity (monadic vs polyadic data exchange),
communication medium (channels vs shared dataspaces),
and the presence of a form of pattern matching (that checks the arity of the
tuple of names and equality of some specific names).
This hierarchy is built upon a very similar notion of encoding to that presented
in Definition~\ref{def:ve} and, in particular, it is proved that Linda \cite{Gel85} (called $\lzuzu$ in \cite{G:IC08}) is more expressive than
monadic/polyadic $\pi$-calculus \cite{milner.parrow.ea:calculus-mobile,milner:polyadic-tutorial} (called $\luzuz$ and $\luuuz$, respectively, in \cite{G:IC08}).
As Linda is more expressive than $\pi$-calculus, it is sufficient to show that CPC is more expressive than Linda.
However, apart from being a corollary of such a result, the lack of a valid encoding of CPC into $\pi$-calculus can also be shown by exploiting the matching degree, i.e.\ Theorem~\ref{match}: the matching degree of $\pi$-calculus is one, while the matching degree of CPC is infinite.
\begin{thm}
\label{noCPCinLinda-1}
There is no valid encoding of CPC into Linda.
\end{thm}
\begin{proof}
The self-matching CPC process $S=x \pre \ok$ is such that $S\not\redar$ and $S\not\suc$, however $S\bnf S\redar$ and $S\bnf S\suc$. Every Linda process $T$ such that $T\bnf T\redar$ can reduce in isolation, i.e.\ $T\redar$: this fact can be proved by induction on the structure of $T$. Conclude by Theorem~\ref{autoriduz}.
\end{proof}
The next step is to show a valid encoding of Linda into CPC.
The encoding $\encode\cdot$ is homomorphic with
respect to all operators except for input and output which are encoded as follows:
\begin{eqnarray*}
\encode{\iap{}{\wt t}.P} &\define& \pref {\patt{\wt t}} {\encode P}\\
\encode{\oap{}{\wt b}} &\define& \pref {\patb{\wt b}} \zero
\end{eqnarray*}
The functions $\patt\cdot$ and $\patb\cdot$ are used to translate templates and data, respectively,
into CPC patterns. The functions are defined as follows:
$$
\begin{array}{rcll}
\patt{\ } & \define & \l x \bullet \n
& \mbox{for $x$ a fresh name}
\\
\patt{t,\wt t} & \define & t \bullet \n \bullet \patt{\wt t}
\\
\patb{\ } & \define & \n \bullet \l x
\\
\patb{b,\wt b} & \define & b \bullet \l x \bullet \patb{\wt b}
\qquad & \mbox{for $x$ a fresh name}
\end{array}
$$
where $\n$ is any name (a symbolic name is used for clarity but no result relies upon this choice).
Moreover, the function $\patb\cdot$ associates a bound variable to
every name in the sequence; this fact ensures that
a pattern that translates a datum and a pattern that translates
a template match only if they have the same length (this is a feature
of Linda's pattern matching but not of CPC's unification).
It is worth noting that the simpler translation
$
\encode{\oap{}{b_1,\ldots,b_n}} \ \define\
\pref {b_1 \bullet \ldots \bullet b_n} \zero
$
would not work: the Linda process $\oap{}{b}\bnf\oap{}{b}$
does not reduce, whereas its encoding would, in contradiction with Proposition~\ref{deadlock}.
Next is to prove that this encoding is valid.
This is a corollary of the following lemma, stating a strict
correspondence between Linda's pattern matching and CPC's unification
(on patterns arising from the translation).
\begin{lem}
\label{lem:twomatchs}
$\pmtch(\wt t;\wt b) = \sigma$ if and only if
\[\aaa {\patt{\wt t}}
{\patb{\wt b}} = (\sigma \cup \{\n/x\}, \{\n/x_0,\ldots,\n/x_n\}),\]
where $\{x_0,\ldots,x_n\} = {\sf bn}(\patb{\wt b})$ and
${\sf dom}(\sigma) \uplus \{x\} = {\sf bn}(\patt{\wt t})$
and $\sigma$ maps names to names.
\end{lem}
\proof
In both directions the proof is by induction on the length of $\wt t$.
The forward direction is as follows.
\begin{itemize}
\item The base case is when $\wt t$ is the empty sequence of template fields;
thus, $\patt{\wt t} = \l x \bullet \n$.
By definition of $\pmtch$, it must be that $\wt b$ is the empty sequence
and that $\sigma$ is the empty substitution.
Thus, $\patb{\wt b} = \n \bullet \l x$ and the thesis follows.
\item For the inductive step $\wt t= t,\wt{t'}$ and $\patt{\wt t} = t \bullet \n \bullet \patt{\wt{t'}}$.
By definition of $\pmtch$, it must be that $\wt b = b, \wt{b'}$ and $\pmtch(t,b) = \sigma_1$ and
$\pmtch(\wt{t'},\wt{b'}) = \sigma_2$ and $\sigma = \sigma_1 \uplus \sigma_2$.
By the induction hypothesis, $\aaa {\patt{\wt {t'}}} {\patb{\wt {b'}}} =
(\sigma_2 \cup \{\n/x\} ; \{\n/x_1,\ldots,\n/x_n\})$,
where $\{x_1,\ldots,x_n\} = {\sf bn}(\patb{\wt {b'}})$
and ${\sf dom}(\sigma_2) \uplus \{x\} = {\sf bn}(\patt{\wt {t'}})$.
There are now two sub-cases to consider according to the kind of template field $t$.
\begin{itemize}
\item If $t = \pro b$ then $\sigma_1 = \{\}$; therefore,
$\sigma
= \sigma_2$ as well as
$\aaa {\patt{\wt t}} {\patb{\wt b}} =
(\sigma\cup \{\n/x\}, \{\n/x_0,\ldots,\n/x_n\})$.
\item If $t = \l y$ then $\sigma_1 = \{b/y\}$ and $y \not\in {\sf dom}(\sigma_2)$.
Thus, $\patt{\wt t}$ is a pattern in CPC and it follows that
$\aaa {\patt{\wt t}} {\patb{\wt b}} =
(\sigma_1\cup\sigma_2\cup \{\n/x\}, \{\n/x_0,\ldots,\n/x_n\}) =
(\sigma \cup \{\n/x\}, \{\n/x_0,\ldots,\n/x_n\})$.
\end{itemize}
\end{itemize}
The reverse direction is as follows.
\begin{itemize}
\item The base case is when $\wt t$ is the empty sequence of template fields;
thus, $\patt{\wt t} = \l x \bullet \n$.
Now proceed by contradiction.
Assume that $\wt b$ is not the empty sequence.
In this case, $\patb{\wt b} = b_0 \bullet\l x_0\bullet(b_1 \bullet\l x_1\bullet(
\ldots(b_n \bullet\l x_n \bullet (\n \bullet \l x_{n+1}))\ldots)$,
for some $n > 0$.
By definition of pattern unification in CPC, $\patb{\wt b}$ and $\patt{\wt t}$ cannot unify,
and this would contradict the hypothesis. Thus, it must be that $\wt b$ is the empty sequence
and we conclude.
\item The inductive case is when $\wt t = t, \wt{t'}$ and thus,
$\patt{\wt t} = t \bullet \n \bullet \patt{\wt{t'}}$.
If $\wt b$ was the empty sequence, then
$\patb{\wt b} = \n \bullet \l x$ and it would not unify with $\patt{\wt t}$.
Hence, $\wt b = b, \wt{b'}$ and so
$\patb{\wt b} = b \bullet \l x \bullet \patb{\wt{b'}}$.
By definition of pattern-unification in CPC it follows that
$\aaa t b = (\sigma_1, \{\})$ and
$\aaa {\patt{\wt {t'}}} {\patb{\wt {b'}}} =(\sigma_2 \cup \{\n/x\},
\{\n/x_1,\ldots, \n/x_n\})$ and $\sigma=\sigma_1\cup\sigma_2$.
Now consider the two sub-cases according to the kind of the template field $t$.
\begin{itemize}
\item If $t = \ex b$ then $\sigma_1 = \{\}$ and so $\sigma_2 = \sigma$.
By induction hypothesis, $\pmtch(\wt{t'};\wt{b'}) = \sigma$,
and so $\pmtch(\wt{t};\wt{b}) = \sigma$.
\item If $t = \l y$ then $\sigma_1 = \{b/y\}$ and
$\sigma_2=\{n_i/y_i\}$ for $y_i\in{\sf dom}(\sigma)\backslash \{y\}$
and $n_i=\sigma y_i$.
Thus, $y \not\in {\sf dom}(\sigma_2)$ and so $\sigma = \sigma_1 \uplus \sigma_2$.
By the induction hypothesis, $\pmtch(\wt{t'};\wt{b'}) = \sigma_2$;
moreover, $\pmtch(t;b) = \sigma_1$.
Thus, $\pmtch(\wt{t};\wt{b}) = \sigma$.\qed
\end{itemize}
\end{itemize}
\begin{lem}
\label{lem:structenc-linda}
If $P \equiv Q$ then $\encode P \equiv \encode Q$.
Conversely, if $\encode P \equiv Q$ then $Q = \encode{P'}$, for some $P' \equiv P$.
\end{lem}
\begin{proof}
Straightforward, from the fact that $\equiv$ acts only on operators that $\encode\cdot$ translates homomorphically.
\end{proof}
\begin{thm}
\label{thm:opcorr}
The translation $\encode\cdot$ from Linda into CPC preserves and reflects reductions.
That is:
\begin{itemize}
\item If $P\redar P'$ then $\xtrans P \redar \xtrans {P'}$;
\item if $\xtrans P \redar Q$ then $Q=\xtrans {P'}$ for some $P'$ such that $P\redar P'$.
\end{itemize}
\end{thm}
\begin{proof}
Both parts can be proved by a straightforward induction
on judgements $P \redar P'$ and $\encode P \redar Q$, respectively.
In both cases, the base step is the most interesting one and
follows from Lemma~\ref{lem:twomatchs}; the inductive
cases where the last rule used is the structural one rely on
Lemma~\ref{lem:structenc-linda}.
\end{proof}
\begin{cor}
\label{cor:valid-linda}
The encoding of Linda into CPC is valid.
\end{cor}
\begin{proof}
Compositionality and name invariance hold by construction.
Operational correspondence and divergence reflection
follow from Theorem~\ref{thm:opcorr}. Success sensitiveness
can be proved as follows: $P \suc$ means that there exist $P'$
and $k \geq 0$ such that $P \redar^k P' \equiv P''\bnf \ok$;
by exploiting Theorem~\ref{thm:opcorr} $k$ times
and Lemma~\ref{lem:structenc-linda}, we obtain that $\encode P \redar^k
\encode{P'} \equiv \encode{P''}\bnf \ok$, i.e.\ that $\encode P \suc$.
The converse implication can be proved similarly.
\end{proof}
\subsection{CPC vs Spi}
\label{subsec:spi-new}
CPC cannot be encoded into Spi calculus, as a corollary of Theorem~\ref{autoriduz}.
This can be proved as in Theorem~\ref{noCPCinLinda-1}: the self-unifyinging CPC
process $x \pre \ok$ cannot be properly rendered in Spi.
The remainder of this section develops an encoding of Spi calculus into CPC.
The terms can be encoded as patterns using the reserved
names {\sf pair}, {\sf encr}, $0$, {\sf suc}, and the natural numbers $>0$ ranged over by $i$ with
\[
\begin{array}{rclrcl}
\encode n &\define& n
\qquad\qquad
&
\encode {{\it suc}(M)} &\define& {\sf suc} \bullet \encode M
\\
\encode x &\define& x
&
\encode {(M,N)} &\define& {\sf pair}\bullet \encode M \bullet \encode N
\\
\encode 0 &\define& 0
&
\encode {\encr M N} &\define& {\sf encr}\bullet \encode M \bullet \encode N
\\
\encode i &\define& {\sf suc}^i 0
\end{array}
\]
where ${\sf suc}^i 0$ denotes {\sf suc} compounded $i$ times with $0$.
The tagging is used for safety, as otherwise there are potential
pathologies in the translation: for example,
without tags, the representation of an encrypted term could be confused
with a pair.
The encoding of the familiar process forms are homomorphic as expected. The input and output
both encode as cases:
\begin{eqnarray*}
\begin{array}{rcll}
\encode {M(x).P} &\define& \encode M \bullet\l x\bullet \n \pre \encode P\\
\encode{\overline{M}\langle N\rangle .P} &\define& \encode M\bullet(\encode N)\bullet\l x\pre\encode P
&\quad \mbox{$x$ is a fresh name}
\end{array}
\end{eqnarray*}
The symbolic name $\n$ (input) and fresh name $x$ (output) are used to
ensure that encoded inputs will only unify with encoded outputs as for Linda.
The four remaining process forms all require pattern unification and so
translate to cases in parallel. In each encoding a fresh name $n$ is
used to prevent interaction with other processes, see
Proposition~\ref{prop:free_n_match_proc}. As in the Spi calculus,
the encodings will reduce only after a successful unification and will be
stuck otherwise. The encodings are
\begin{eqnarray*}
\encode {[M\ {\it is}\ N]P} &\define&
\res n (\pro n\bullet \encode M\pre \encode P \bnf \pro
n\bullet \encode N)\\
\encode {{\it let}\ (x,y)= M\ {\it in}\ P} &\define&
\res n (\pro n \bullet (\pro {{\sf pair}}\bullet\l x\bullet
\l y)\pre \encode P\\
& & \quad\quad | \pro n\bullet \encode M)\\
\encode {{\it case}\ M\ {\it of}\ \encr x N:P} &\define&
\res n (\pro n \bullet (\pro {{\sf encr}}\bullet\l x\bullet
\encode N)\pre \encode P\\
& & \quad\quad | \pro n\bullet \encode M)\\
\encode {{\it case}\ M\ {\it of}\ 0:P\ {\it suc}(x):Q} &\define&
\res n (\pro n\bullet \pro 0\pre \encode P \\
& & \quad\quad | \pro n\bullet (\pro {{\sf suc}}\bullet \l
x)\pre \encode Q \\
& & \quad\quad | \pro n\bullet \encode M )
\end{eqnarray*}
The unification $[M\ {\it is}\ N]P$ only reduces to $P$ if $M=N$, thus the
encoding creates two patterns using $\encode M$ and $\encode
N$ with one reducing to $\encode P$.
The encoding of pair splitting ${\it let}\ (x,y)= M\ {\it in}\ P$
creates a case with a pattern that unifies with a tagged pair and binds the
components to $x$ and $y$ in $\encode P$. This is put in parallel with
another case that has $\encode M$ in the pattern.
The encoding of a decryption ${\it case}\ M\ {\it of}\ \encr x N:P$ checks
whether $\encode M$ is encoded with key $\encode N$ and
retrieves the value encrypted by binding it to $x$ in the continuation.
Lastly the encoding of an integer test ${\it case}\ M\ {\it of}\ 0:P\ {\it
suc}(x):Q$ creates a case for each of the zero and the
successor possibilities. These cases unify the tag and the reserved
names $0$, reducing to $\encode P$, or ${\sf suc}$ and binding $x$ in
$\encode Q$. The term to be compared $\encode M$ is as in the other cases.
Let us now prove validity of this encoding.
\begin{lem}
\label{lem:structenc-spi}
If $P \equiv Q$ then $\encode P \equiv \encode Q$.
Conversely, if $\encode P \equiv Q$ then $Q = \encode{P'}$, for some $P' \equiv P$.
\end{lem}
\begin{proof}
Straightforward, from the fact that $\equiv$ acts only on operators that $\encode\cdot$ translates homomorphically.
\end{proof}
\begin{thm}
\label{spi2cpc-red}
The translation $\encode\cdot$ from Spi calculus into CPC preserves and reflects reductions, up-to CPC's barbed
congruence. That is:
\begin{itemize}
\item If $P\redar P'$ then $\xtrans P \redar \beq \xtrans {P'}$;
\item if $\xtrans P \redar Q$ then $Q \beq \xtrans {P'}$ for some $P'$ such that $P\redar P'$.
\end{itemize}
\end{thm}
\proof
The first claim can be proved by a straightforward induction
on judgement $P \redar P'$. The base case is proved by reasoning on the Spi axiom used to infer the reduction.
Although all the cases are straightforward, a reduction rule for integers is shown for illustration.
Consider the reduction for a successor as the reduction for zero is simpler.
In this case, $P = {\it case}\ {\it suc}(M)\ {\it of}\ 0:P_1\ {\it suc}(x):P_2$
and $P' = \{M/x\}P_2$. Then,
\begin{eqnarray*}
\encode P &\define&
\res n (\pro n\bullet \pro 0\pre \encode {P_1} \\
& & \quad\quad \bnf \pro n\bullet (\pro {{\sf suc}}\bullet \l x)\pre \encode {P_2}\\
& & \quad\quad \bnf \pro n\bullet ({\sf suc} \bullet \encode M) \pre \zero) \; .
\end{eqnarray*}
and it can only reduce to
$$
\{\encode M / x\}\encode{P_2} \bnf \res n \pro n\bullet \pro 0\pre \encode {P_1}
$$
A straightforward induction on the structure of $P_2$ proves
$\{\encode M / x\}\encode{P_2} = \encode{\{M / x\}P_2}$. Thus,
$\encode P \redar \encode{\{M / x\}P_2}\bnf
\res n \pro n\bullet \pro 0\pre \encode {P_1} \beq \encode{P'}$,
where the last equivalence follows from Proposition~\ref{prop:free_n_match_proc}.
The inductive case is straightforward, with the structural case relying on Lemma~\ref{lem:structenc-spi}.
The second part can be proved by induction on judgement $\encode P \redar Q$.
There is just one base case, i.e.\ when $\encode P = p \pre Q_1\bnf q \pre Q_2$ and
$Q = \sigma Q_1\bnf \rho Q_2$ and $\{p\pmatch q\} = (\sigma, \rho)$.
By definition of the encoding, it can only be that
$p= \encode M\bullet\l x\bullet \n$ and $Q_1 = \encode {P_1}$ and
$q = \encode M\bullet (\encode N)\bullet \l x$ and $Q_2 = \encode {P_2}$
for some $P_1$, $P_2$, $M$ and $N$. This means that $P = \iap M x.P_1\bnf \oap M N . P_2$
and that $Q = \{\encode N/x\}\encode{P_1}\bnf\encode{P_2} = \encode{\{N/x\}P_1\bnf P_2}$.
To conclude, it suffices to take $P' = \{N/x\}P_1\bnf P_2$.
For the inductive case there are two possibilities.
\begin{itemize}
\item The inference of $\encode P \redar Q$ ends with an application of the rule for
parallel composition or for structural congruence: this case can be proved by a
straightforward induction.
\item The inference of $\encode P \redar Q$ ends with an application of the rule for restriction;
thus, $\encode P = \res n Q'$, with $Q' \redar Q''$ and $Q = \res n Q''$.
If $Q' = \encode {P''}$, for some $P''$, apply a straightforward induction.
Otherwise, there are the following four possibilities.
\begin{itemize}
\item $Q' = \pro n\bullet\pro{\encode M}\pre\encode{P_1}\bnf\pro n\bullet\pro{\encode N}$
and, hence, $Q'' = \encode{P_1}$. By definition of the encoding,
$P = [M\ {\it is}\ N] P_1$. Notice that the reduction $Q' \redar Q''$ can happen only if
$\encode M$ and $\encode N$ unify; by construction of the encoding of Spi-terms,
this can happen only if $M = N$ and, hence, $P \redar P_1$.
The thesis follows by letting $P' = P_1$, since $n$ is a fresh name and so
$Q = \res n \encode {P_1} \equiv \encode {P_1}$.
\item $Q' =\pro n\bullet(\pro{{\sf pair}}\bullet(\l x\bullet\l y))\pre\encode{P_1}
\bnf\pro n\bullet({\sf pair}\bullet(\encode M\bullet\encode N))$
and, hence, $Q'' = \{\encode M/x,\encode N/y\}\encode{P_1}$.
This case is similar to the previous one, by letting $P$ be
${\it let}\ (x,y)= (M,N)\ {\it in}\ P_1$.
\item $Q' = \pro n\bullet (\pro {{\sf encr}}\bullet(\l x\bullet \encode N))\pre \encode {P_1}
\bnf \pro n\bullet ({\sf encr}\bullet (\encode M \bullet \encode N))$
and, hence, $Q'' = \{\encode M/x\}\encode{P_1}$.
This case is similar to the previous one, by letting $P$ be
${\it case}\ \encr M N\ {\it of}\ \encr x N:P_1$.
\item $Q' = \pro n\bullet \pro 0\pre \encode {P_1}
\bnf\pro n\bullet (\pro {{\sf suc}}\bullet \l x)\pre \encode {P_2}
\bnf\pro n\bullet \encode M$.
Hence, $P = {\it case}\ M\ {\it of}\ 0:P_1\ {\it suc}(x):P_2$.
According to the kind of $\encode M$, there are two sub-cases
(notice that, since $Q' \redar Q''$, no other possibility is allowed for $\encode M$).
\begin{itemize}
\item $\encode M = 0$: in this case, $Q'' = \encode {P_1}
\bnf \pro n\bullet (\pro {{\sf suc}}\bullet \l x)\pre\encode {P_2}$
and so $Q = \res n Q'' \equiv \encode {P_1}
\bnf\res n\pro n\bullet(\pro {{\sf suc}}\bullet\l x)\pre\encode {P_2}
\beq \encode {P_1}$.
In this case, $M = 0$ and so $P \redar P_1$; to conclude,
it suffices to let $P'$ be $P_1$.
\item $\encode M = {\sf suc} \bullet \encode {M'}$, for some $M'$:
in this case, $Q'' = \{\encode{M'}/x\}\encode {P_2} \bnf
\pro n\bullet \pro 0\pre \encode {P_1}$
and so $Q = \res n Q'' \equiv \encode {\{M'/x\}P_2}\bnf\res n
\pro n\bullet 0\pre \encode {P_1}
\beq \encode {\{M'/x\}P_2}$.
In this case, $M = {\it suc}(M')$ and so $P \redar \{M'/x\}P_2$; to conclude,
it suffices to let $P'$ be $\{M'/x\}P_2$.\qed
\end{itemize}
\end{itemize}
\end{itemize}
\begin{cor}
\label{cor:valid-spi}
The encoding of Spi calculus into CPC is valid.
\end{cor}
\begin{proof}
See the proof for Corollary~\ref{cor:valid-linda}.
\end{proof}
Notice that the criteria for a valid encoding do not imply full
abstraction of the encoding (actually, they were defined as an alternative to full abstraction
\cite{G:IC08,G:CONCUR08}). This means that the encoding of equivalent
Spi calculus processes can be distinguished by contexts in CPC that do not result from the
encoding of any Spi calculus context. Indeed, while this encoding allows Spi calculus to be modelled in
CPC, it does {\em not} entail that cryptography can be properly rendered.
Consider the pattern ${\sf encr}\bullet \l x \bullet \l y$ that could unify with the encoding of an encrypted term
to bind the message and key, so that CPC can break any encryption!
Indeed this is an artefact of the straightforward approach to encoding taken here.
Some discussion of alternative approaches to encryption in CPC are detailed in
\cite{GivenWilsonPHD}.
\subsection{CPC vs Fusion}
The separation results for CPC and the other process calculi presented so far have all been proved via symmetry;
thus, the relationship between Fusion and CPC is of particular interest.
Such calculi are {\em unrelated}, in the sense that there exists no valid
encoding from one into the other. The impossibility for a valid
encoding of CPC into Fusion can be proved in two ways, by exploiting either the matching degree or the symmetry of CPC.
\begin{thm}
\label{thm:nocpc2fusion-1}
There is no valid encoding of CPC into Fusion.
\end{thm}
\begin{proof}
The matching degree of Fusion is 1 while the matching degree of CPC is infinite;
conclude by Theorem~\ref{match}.
Alternatively, reuse the proof for Theorem~\ref{noCPCinLinda-1} as every Fusion process
$T$ is such that $T\bnf T\redar$ implies $T\redar$.
\end{proof}
The converse separation result is ensured by the following theorem.
\begin{thm}
\label{thm:fusionNoinCPC}
There exists no valid encoding of Fusion into CPC.
\end{thm}
\proof
By contradiction, assume that there exists a valid encoding $\encode\cdot$
of Fusion into CPC.
Consider the Fusion process $P \define \res x(\oap u x\bnf \iap u y.\ok)$,
for $x$, $y$ and $u$ pairwise distinct. By success sensitiveness, $P \suc$
entails that $\encode P \suc$.
We first show that $\encode P$ must reduce before reporting success,
i.e.\ every occurrence of $\ok$ in $\encode P$ falls underneath
some prefix. By compositionality, $\encode P \define \CopN C {\res x}
{\{u,x,y\}} {\CopN C | {\{u,x,y\}} {\encode{\oap u x};\\ \encode{\iap u
y.\ok}}}$. If $\encode P$ had a top-level unguarded occurrence
of $\ok$, then such an occurrence could be in $\CopN C {\res x}
{\{u,x,y\}} {\_\,}$, in $\CopN C | {\{u,x,y\}} {\_\,_1;\_\,_2}$, in
$\encode{\oap u x}$ or in $\encode{\iap u y.\ok}$; in any case, it
would also follow that at least one of:
\begin{equation}
\label{eq:fus:ex1}
\encode{\res x(\oap u x\bnf \iap y u.\ok)}
\end{equation}
that has $\iap u y$ replaced with $\iap y u$;
or
\begin{equation}
\label{eq:fus:ex2}
\encode{\res x(\oap x u\bnf \iap u y.\ok)}
\end{equation}
that has $\oap u x$ replaced with $\oap x u$,
would report success,
whereas both
Equation~\ref{eq:fus:ex1}$\not\suc$
and
Equation~\ref{eq:fus:ex2}$\not\suc$,
against success sensitiveness of $\encode\cdot$.
Thus, the only possibility for $\encode P$ to report success is
to perform some reduction steps (at least one) and then exhibit
a top-level unguarded occurrence of $\ok$.
We now prove that every possible reduction leads to contradiction of the validity of $\encode\cdot$;
this suffices to conclude. There are five possibilities for $\encode P \redar$.
\begin{enumerate}
\item Either $\CopNnoarg C {\res x} {\{u,x,y\}} \redar$, or
$\CopNnoarg C | {\{u,x,y\}} \redar$, or
$\encode{\oap u x}\redar$ or $\encode{\iap u y.\ok}\redar$. In any
of these cases, at least one out of
$\encode{\mbox{Equation~\ref{eq:fus:ex1}}}$ or
$\encode{\mbox{Equation~\ref{eq:fus:ex2}}}$ would reduce;
however, $\mbox{Equation~\ref{eq:fus:ex1}} \not\redar$ and
$\mbox{Equation~\ref{eq:fus:ex2}} \not\redar$,
against Proposition~\ref{deadlock} (that must hold whenever $\encode\cdot$
is valid).
\item Reduction is generated by interaction between
$\CopNnoarg C {\res x} {\{u,x,y\}}$ and
$\CopNnoarg C | {\{u,x,y\}}$. Then, as before,
$\encode{\mbox{Equation~\ref{eq:fus:ex1}}} \redar$
whereas $\mbox{Equation~\ref{eq:fus:ex1}} \not\redar$,
against Proposition~\ref{deadlock}.
\item Reduction is generated by interaction between
$\CopNnoarg C \op {\{u,x,y\}}$ and $\encode{\oap u x}$, for
$\op \in \{\res x,\,|\,\}$. Like case 2.
\item Reduction is generated by interaction between
$\CopNnoarg C \op {\{u,x,y\}}$ and
$\encode{\iap u y.\ok}$, for
$\op \in \{\res x,\,|\,\}$. As before it follows that
$\encode{\mbox{Equation~\ref{eq:fus:ex2}}} \redar$
whereas $\mbox{Equation~\ref{eq:fus:ex2}} \not\redar$,
against Proposition~\ref{deadlock}.
\item The reduction is generated by an interaction between the processes
$\encode{\oap u x}$ and
$\encode{\iap u y.\ok}$. In this
case, it follows that $\encode{\oap u x\bnf \iap u y.\ok}\redar$
whereas $\oap u x\bnf \iap u y.\ok\not\redar$: indeed, the interaction
rule of Fusion imposes that at least one between $x$ and $y$ must
be restricted to yield the interaction.\qed
\end{enumerate}
\subsection{CPC vs Psi}
CPC and Psi are {\em unrelated}, in the sense that there exists no valid
encoding from one into the other. As in Theorem~\ref{noCPCinLinda-1},
the impossibility for a valid
encoding of CPC into Psi can be proved by exploiting
the symmetry of CPC.
The converse separation result is ensured by the following theorem.
\begin{thm}
\label{thm:psiNoinCPC}
There exists no valid encoding of Psi into CPC.
\end{thm}
\proof
Assume that there exists a valid encoding $\encode\cdot$
of Psi into CPC. Consider the Psi process
$P \define (\bar a.c \ |\ b.(\ok\ |\ c))\ | \ \assert{a \stackrel\cdot\leftrightarrow b}$,
where we have omitted the argument of the actions to simplify the proofs,
and chosen $a$, $b$ and $c$ pairwise distinct; also consider the reduction
$$
\prooftree
\prooftree \{a \stackrel\cdot\leftrightarrow b\} \vdash a \stackrel\cdot\leftrightarrow b
\justifies \{a \stackrel\cdot\leftrightarrow b\} \triangleright \bar a.c \ |\ b.(\ok\ |\ c) \redar c \ |\ \ok\ |\ c
\endprooftree
\justifies {\bf 1} \triangleright P \redar (c\ |\ \ok\ |\ c)\ | \ \assert{a \stackrel\cdot\leftrightarrow b}
\endprooftree
$$
Therefore, $P \suc$ and, by success sensitiveness, $\encode P \suc$.
Hence, by compositionality, $\encode P \define \CopN C {|} {\{a,b,c\}}
{\CopN C | {\{a,b,c\}} {\encode{\bar a.c}; \encode{b.(\ok\ |\ c)}}; \encode{\assert{a \stackrel\cdot\leftrightarrow b}}}$.
Like in the proof of Theorem~\ref{thm:fusionNoinCPC}, it can be proven that the only possibility
for $\encode P$ to report success is to perform some reduction steps (at least one) and then exhibit
a top-level unguarded occurrence of $\ok$.
We now prove that every possible reduction leads to contradiction of the validity of $\encode\cdot$;
this suffices to conclude. Of course, none of $\encode{\bar a.c}$, $\encode{b.(\ok\ |\ c)}$
and $\encode{\assert{a \stackrel\cdot\leftrightarrow b}}$ can reduce, because $\bar a.c$, $b.(\ok\ |\ c)$ and $\assert{a \stackrel\cdot\leftrightarrow b}$
do not reduce. Thus, there are seven possibilities for $\encode P \redar$.
\begin{enumerate}
\item Either $\CopNnoarg C {|} {\{a,b,c\}} \redar$ or the reduction is obtained by synchronizing
the two copies of $\CopNnoarg C {|} {\{a,b,c\}}$. In both cases, $\encode{(\bar c.a \ |\ b.(\ok\ |\ c))\ | \ \assert{a \stackrel\cdot\leftrightarrow b}}$
(with $\bar a.c$ replaced by $\bar c.a$)
would also reduce, whereas $(\bar c.a \ |\ b.(\ok\ |\ c))\ | \ \assert{a \stackrel\cdot\leftrightarrow b} \not\redar$,
against Proposition~\ref{deadlock} (that must hold whenever $\encode\cdot$ is valid).
\item The reduction is obtained by synchronizing $\encode{\bar a.c}$
with (one of the two copies of) $\CopNnoarg C {|} {\{a,b,c\}}$. In this case,
also $\encode{(\bar a.c \ |\ c.(\ok\ |\ b))\ | \ \assert{a \stackrel\cdot\leftrightarrow b}}$
(with $b.(\ok\ |\ c)$ replaced by $c.(\ok\ |\ b)$)
would reduce, whereas $(\bar a.c \ |\ c.(\ok\ |\ b))\ | \ \assert{a \stackrel\cdot\leftrightarrow b} \not\redar$.
\item The reduction is obtained by synchronizing $\encode{b.(\ok\ |\ c)}$
with (one of the two copies of) $\CopNnoarg C {|} {\{a,b,c\}}$. This case is
proved impossible like case 1 above.
\item The reduction is obtained by synchronizing $\encode{\assert{a \stackrel\cdot\leftrightarrow b}}$
with (one of the two copies of) $\CopNnoarg C {|} {\{a,b,c\}}$. This case is
proved impossible like cases 1 and 2 above.
\item The reduction is obtained by synchronizing $\encode{\bar a.c}$
with $\encode{b.(\ok\ |\ c)}$. In this case,
also $\encode{\bar a.c \ |\ b.(\ok\ |\ c)}$
would reduce, whereas $\bar a.c \ |\ b.(\ok\ |\ c) \not\redar$.
\item The reduction is obtained by synchronizing $\encode{\bar a.c}$
with $\encode{\assert{a \stackrel\cdot\leftrightarrow b}}$. This case is
proved impossible like case 2 above.
\item The reduction is obtained by synchronizing $\encode{b.(\ok\ |\ c)}$
with $\encode{\assert{a \stackrel\cdot\leftrightarrow b}}$. This case is
proved impossible like case 1 above.\qed
\end{enumerate}
\section{Conclusions}
\label{sec:conclusions}
Concurrent pattern calculus uses patterns to represent input,
output and tests for equality, whose interaction is driven by
unification that allows a two-way flow of information. This symmetric
information exchange provides a concise model of trade in the
information age. This is illustrated by the example of traders who
can discover each other in the open and then close the deal
in private.
As patterns drive interaction in CPC,
their properties heavily influence CPC's behaviour theory. As pattern
unification may match any number of names these must all be accounted
for in the definition of barbs. More delicately, some patterns are
compatible with others, in that their unifications yield similar results.
The resulting bisimulation requires that the transitions be compatible
patterns rather than exact.
Further, the pattern-matching bisimulation developed for CPC can easily account
for other kinds of pattern-matching, such as in polyadic $\pi$-calculus and
Linda \cite{GivenWilsonGorla13}.
CPC supports valid encodings of many popular concurrent calculi such
as $\pi$-calculus, Spi calculus and Linda as its patterns describe
more structures. However, these three calculi do not support valid
encodings of CPC because, among other things, they are insufficiently
symmetric. On the other hand, while fusion calculus is completely
symmetric, it has an incompatible approach to interaction.
Similarly, Psi calculus is unrelated to CPC due to supporting implicit
computations, while also being less symmetric.
Another path of development for a process calculus is implementation in a
programming language \cite{Pierce97pict:a,Klava,cpplinda,20110201:jocaml}.
The {\bf bondi}\ programming language is based upon pattern matching as the core
of reduction and the theory of pattern calculus \cite{pcb,bondi}. A
\cbondi\ has also been developed that extends {\bf bondi}\ with concurrency
and interaction based on the pattern unification and theory of CPC
\cite{GivenWilsonPHD,cbondi}.
\bigskip
\noindent{\bf Acknowledgments } We would like to thank the anonymous reviewers for their
fruitful comments and for their constructive attitude towards our paper.
\section*{Appendix A: Proofs of Section~\ref{sec:LTS}}
\paragraph{Proof of Proposition~\ref{prop:imfin}}
First of all, let us define an alternative (but equivalent, up-to $\equiv$) LTS
for CPC, written $\!\!\llts\mu$: it is obtained by replacing {\sf rep} with the
following two rules (all the other rules are the same, with $\llts{}$ in place
of $\ltsred{}$ everywhere):
$$
\prooftree P \llts\mu P'
\justifies !P \llts\mu P'\bnf !P
\endprooftree
\qquad\qquad
\prooftree P \llts{\rest m p} P' \quad P \llts{\rest n q} P''
\justifies !P \llts\tau \res{\withsetnot{\wt m,\wt n}{\wt m\cup\wt n}}(\sigma P'\bnf \rho P'')\bnf !P
\endprooftree\
\begin{array}{l}
\{p \pmatch q\} = (\sigma, \rho)\\
\wt m \cap \wt n = \emptyset
\end{array}
$$
We can prove that: (1) if $P \llts\mu P'$ then $P \ltsred\mu P'$; and (2)
if $P \ltsred\mu P'$ then $P \llts\mu P''$, for some $P'' \equiv P'$
(both proofs are done by a straightforward induction on the derivation of
the premise, whose only interesting case is when $P =~!Q$, for some $Q$).
Now define the following measure associated to a process:
$$
\begin{array}{lll}
\meas \zero\ =\ 0
\qquad\qquad
&
\meas {p \pre P}\ =\ 1
&
\meas {\res n P}\ =\ \meas P
\vspace*{.2cm}
\\
\multicolumn{2}{l}{
\meas {P_1 \bnf P_2}\ =\ \meas {P_1}+\meas {P_2}+\meas {P_1}\cdot\meas {P_2}
}
\quad
&
\meas {\,!P}\ =\ \meas P+\meas P\cdot\meas P
\end{array}
$$
By induction on the structure of $P$, we can prove that $|\{P' : P \llts\mu P'\}| \leq \meas P$.
By exploiting this fact and (2) above, it follows that there are finitely many (up-to $\equiv$)
$P'$ such that $P \ltsred\mu P'$.
\qed
\paragraph{Proof of Lemma~\ref{lem:lts-exhibit-p}}
The proof is by induction on the inference for $P\ltsred{\rest m p} P'$.
The base case is when the last rule is {\sf case}, with $P = (p\to P_1)\ltsred p P_1 = P'$;
conclude by taking $\wt n = \emptyset$ and $Q_1 = P_1$ and $Q_2 = \zero$.
For the inductive step, consider the last rule in the inference.
\begin{itemize}
\item If the last rule is {\sf resnon} then $P = \res o P_1 \ltsred{\rest m p}\res o P_1' = P'$, where
$P_1 \ltsred{\rest m p} P_1'$ and $o\notin{\sf names}(\rest m p)$.
By induction, there exist $\wt n'$ and $Q_1'$ and $Q_2'$ such that
$P_1 \equiv (\nu \wt m)(\nu \wt n')(p\to Q_1'\bnf Q_2')$ and
$P_1' \equiv (\nu \wt n')(Q_1'\bnf Q_2')$ and
$\wt n'\cap{\sf names}(\rest m p)=\emptyset$ and ${\sf bn}(p)\cap{\sf fn}(Q_2')=\emptyset$.
As $o\notin{\sf names}(\rest m p)$ and by $\alpha$-conversion $o\notin\wt n'$,
conclude with $Q_1 = Q_1'$ and $Q_2 = Q_2'$ and $\wt n = \wt n',o$.
\item If the last rule is {\sf open} then $P = \res o P_1\ltsred{\res {\wt m' ,o} p} P_1' = P'$, where
$P_1\ltsred{\res {\wt m'} p}P_1'$ and
$o\in {\sf vn}(p)\backslash(\wt m'\cup{\sf pn}(p)\cup{\sf bn}(p))$
and $\wt m=\wt m',o$.
By induction, there exist $\wt n'$ and $Q_1'$ and $Q_2'$ such that
$P_1 \equiv (\nu \wt m')(\nu \wt n')(p\to Q_1'\bnf Q_2')$ and
$P_1' \equiv (\nu \wt n')(Q_1'\bnf Q_2')$ and
$\wt n'\cap{\sf names}(\res {\wt m'} p)=\emptyset$ and
${\sf bn}(p)\cap{\sf fn}(Q_2')=\emptyset$.
Conclude with $\wt n = \wt n'$ and $Q_1 = Q_1'$ and $Q_2 = Q_2'$.
\item If the last rule is {\sf parext} then $P = P_1\bnf P_2 \ltsred{\rest m p} P_1' \bnf P_2$,
where $P_1\ltsred{\rest m p} P_1'$
and ${\sf fn}(P_2)\cap(\wt m\cup{\sf bn}(p))=\emptyset$.
By induction, there exist $\wt n'$ and $Q_1'$ and $Q_2'$ such that
$P_1 \equiv (\nu \wt m)(\nu \wt n')(p\to Q_1'\bnf Q_2')$ and
$P_1' \equiv (\nu \wt n')(Q_1'\bnf Q_2')$ and
$\wt n'\cap{\sf names}(\rest m p)=\emptyset$ and ${\sf bn}(p)\cap{\sf fn}(Q_2')=\emptyset$.
As ${\sf bn}(p)\cap{\sf fn}(P_2) = \emptyset$, we can
conclude with $\wt n = \wt n'$ and $Q_1 = Q_1'$ and $Q_2 = Q_2'\bnf P_2$.
\item If the last rule is {\sf rep} then $P = \,\,!Q \ltsred{\rest m p} P'$,
where $Q\bnf !Q \ltsred{\rest m p} P'$. We conclude by induction
and by the fact that $P \equiv Q\bnf!Q$.
\qed
\end{itemize}
\paragraph{Proof of Proposition~\ref{prop:tau-red}}
The first claim is proved by induction on the inference for $P\ltsred\tau P'$.
The base case is with rule {\sf unify}: $P = P_1\bnf Q_1$, where
$P_1 \ltsred{\rest m p}P'_1$ and $Q_1 \ltsred{\rest n q} Q'_1$ and
$P' = \res{\withsetnot{\wt m, \wt n}{\wt m\cup \wt n}}(\sigma P'_1\bnf\rho Q'_1)$ and
$\{p\pmatch q\}=(\sigma,\rho)$ and
$\wt m \cap {\sf fn}(Q_1) = \wt n \cap {\sf fn}(P_1) = \emptyset$
and $\wt m\cap\wt n=\emptyset$. By Lemma~\ref{lem:lts-exhibit-p}, it follows that
$P_1 \equiv \rest m\rest o(p\to P''_1\bnf P''_2)$ and
$P_1' \equiv \rest o(P''_1\bnf P''_2)$, with $\wt o\cap{\sf names}(\rest m p)=\emptyset$
and ${\sf bn}(p)\cap{\sf fn}(P''_2)=\emptyset$; similarly,
$Q_1 \equiv \rest n\rest r(q\to Q''_1\bnf Q''_2)$ and $Q_1' \equiv \rest r(Q''_1\bnf Q''_2)$,
with $\wt r\cap{\sf names}(\rest n q)=\emptyset$
and ${\sf bn}(q)\cap{\sf fn}(Q''_2)=\emptyset$.
By exploiting $\alpha$-conversion on the names in $\wt o$ and $\wt r$, we have
$\withsetnot{\wt o,\wt r}{(\wt o\cup \wt r)}\cap({\sf names}(\rest m p)\cup{\sf names}(\rest n q))=\emptyset$;
thus, $P_1\bnf Q_1 \equiv \res{\withsetnot{\wt m, \wt n}{\wt m\cup \wt n}}
\res{\withsetnot{\wt o, \wt r}{\wt o\cup \wt r}} (p\to P''_1\bnf P''_2\bnf q\to Q''_1\bnf Q''_2)
\redar \res{\withsetnot{\wt m, \wt n}{\wt m\cup\wt n}}
\res{\withsetnot{\wt o, \wt r}{\wt o\cup \wt r}} (\sigma P''_1\bnf P''_2\bnf \rho Q''_1\bnf Q''_2)$.
Since $\sigma$ avoids $\wt o$, ${\sf dom}(\sigma)\cap{\sf fn}(P''_2)=\emptyset$ and
$\rho$ avoids $\wt r$, ${\sf dom}(\rho)\cap{\sf fn}(Q''_2)=\emptyset$ and
$\wt o\cap{\sf fn}(Q''_1\bnf Q''_2)=\wt r\cap{\sf fn}(P''_1\bnf P''_2)=\emptyset$, conclude
$P \redar \res{\withsetnot{\wt m, \wt n}{\wt m\cup \wt n}}
\res{\withsetnot{\wt o, \wt r}{\wt o\cup\wt r}} (\sigma P''_1\bnf P''_2\bnf \rho Q''_1\bnf Q''_2)
\equiv \res{\withsetnot{\wt m, \wt n}{\wt m\cup \wt n}}
(\sigma(\rest o (P''_1\bnf P''_2))\bnf \rho(\rest r(Q''_1\bnf Q''_2)))
\equiv \res{\withsetnot{\wt m, \wt n}{\wt m\cup\wt n}}(\sigma P'_1\bnf \rho Q'_1) = P'$.
For the inductive step, reason on the last rule used in the inference.
\begin{itemize}
\item If the last rule is {\sf parint} then $P = P_1\bnf P_2$,
for $P_1 \ltsred\tau P_1'$ and $P'=P_1'\bnf P_2$.
Apply induction to the transition $P_1 \ltsred\tau P_1'$ to obtain that $P_1\redar P_1'$;
thus, $P \redar P'$.
\item If the last rule is {\sf resnon} then $P = \res n P_1$, for $P_1 \ltsred\tau P_1'$ and $P'=\res n P_1'$.
Again, conclude by induction.
\item If the last rule is {\sf rep} then $P = \,\,!P_1$, for $P_1\bnf!P_1 \ltsred\tau P'$.
By induction, $P_1\bnf!P_1 \redar P'$ and conclude, since $P \equiv P_1\bnf!P_1$.
\end{itemize}
\medskip\noindent
The second claim is by induction on the inference for $P \redar P'$.
The base case is when $P = p\to P'_1\bnf q\to Q'_1$ and $P' =\sigma P'_1\bnf\rho Q'_1$,
for $\{p\pmatch q\}=(\sigma,\rho)$. By the {\sf unify} rule in the LTS
\begin{equation*}
\prooftree (p\to P'_1) \ltsred{p}P'_1 \qquad (q\to Q'_1) \ltsred{q}Q'_1
\justifies p\to P'_1\bnf q\to Q'_1\ \ltsred\tau\ \sigma P'_1\bnf\rho Q'_1
\endprooftree\ \ \{p\pmatch q\}=(\sigma,\rho)
\end{equation*}
and the result is immediate.
For the inductive step, reason on the last rule used in the inference.
\begin{itemize}
\item If $P=P_1\bnf P_2$, where $P_1\redar P'_1$ and $P' = P_1'\bnf P_2$,
then use the induction and exploit the {\sf parint} rule.
\item If $P=\res n P_1$, where $P_1\redar P'_1$ and $P' = \res n P'_1$,
then use the induction and exploit the {\sf resnon} rule.
\item Otherwise, it must be that $P \equiv Q \redar Q' \equiv P'$.
By induction, $Q \ltsred\tau Q'$ for some $Q'' \equiv Q'$.
We now have to prove that structurally equivalent processes have
the same $\tau$-transitions, up-to $\equiv$; this is done via
a second induction, on the inference of the judgement $P \equiv Q$.
The following are two representative base cases; the other base cases are easier,
as is the inductive case.
\begin{itemize}
\item $P =\, !R \equiv R\bnf!R = Q$: since $Q = R\bnf!R \ltsred\tau Q''$, for $Q'' \equiv Q'$,
we can use rule {\sf rep} of the LTS and obtain $P \ltsred\tau Q''$;
we can conclude, since $Q'' \equiv Q' \equiv P'$.
\item $P = \res n P_1\, \bnf\ P_2 \equiv \res n (P_1 \bnf\ P_2) = Q$, that holds since
$n \not\in {\sf fn}(P_2)$: by the first inductive hypothesis,
$\res n (P_1 \bnf\ P_2) \ltsred\tau Q''$, for $Q'' \equiv Q'$. Moreover, by definition
of the LTS, the last rule used in this inference must be {\sf resnon}; thus,
$P_1 \bnf\ P_2 \ltsred\tau Q'''$ and $Q'' = \res n Q'''$. There are three possible
ways to generate the latter $\tau$-transition:
\begin{itemize}
\item $P_1 \ltsred\tau P_1'$ and $Q''' = P_1'\bnf P_2$: in this case
$$
\prooftree
\prooftree P_1 \ltsred\tau P_1'
\justifies \res n P_1 \ltsred\tau \res n P_1'
\endprooftree
\justifies P = \res n P_1 \bnf P_2 \ltsred\tau \res n P_1'\bnf P_2
\endprooftree
$$
and conclude by noticing that $\res n P_1'\bnf P_2 \equiv \res n (P_1'\bnf P_2) = Q'' \equiv Q' \equiv P'$.
\item $P_2 \ltsred\tau P_2'$ and $Q''' = P_1\bnf P_2'$: this case is similar to the previous one, but simpler.
\item $P_1 \ltsred{\rest m p} P_1'$ and $P_2 \ltsred{\rest n q} P_2'$, and $Q''' =
(\nu \withsetnot{\wt m,\wt n}{\wt m\cup \wt n})(\sigma P_1'\bnf \rho P_2')$, where $\{p \pmatch q\} = (\sigma, \rho)$,
$\wt m \cap {\sf fn}(P_2) = \wt n \cap {\sf fn}(P_1) = \emptyset$ and $\wt m \cap \wt n = \emptyset$:
this case is similar to the base case of the first claim of this Proposition and, essentially, relies
on Lemma~\ref{lem:lts-exhibit-p}. The details are left to the interested reader.
\qed
\end{itemize}
\end{itemize}
\end{itemize}
\section*{Appendix B: Proofs of Section~\ref{sec:sound}}
\paragraph{Proof of Lemma~\ref{lem:bisim-case}}
It is necessary to prove that the relation
$$
\Re = \{(p \to P , p \to Q)\ :\ P \bisim Q\}\ \cup\ \bisim
$$
is a bisimulation. The only possible challenge of $p \to P$ is
$p \to P \ltsred p P$ such that ${\sf bn}(p) \cap {\sf fn}(Q) = \emptyset$;
moreover, fix any $\sigma$ such that ${\sf dom}(\sigma) = {\sf bn}(p)$.
The only possible reply from $p \to Q$ is $p \to Q \ltsred p Q$, that is
a valid reply (in the sense of Definition~\ref {def:bisim}). Indeed,
$p,\sigma \compat p,\sigma$, by Proposition~\ref{prop:compat-reflexive},
and $(\sigma P , \sigma Q) \in \Re$, because $P \bisim Q$ and
$\bisim$ is closed under substitutions by definition.
Closure under substitution holds by definition of $\Re$.
\qed
\paragraph{Proof of Lemmata~\ref{lem:bisim-nu} and~\ref{lem:bisim-par}}
The two lemmata have to be proved together; as in $\pi$-calculus, this is necessary because of name extrusion.
We can conclude if we show that the relation
$$
\Re = \{(\rest n (P\bnf R),\rest n (Q\bnf R))\ :\ P \bisim Q\}
$$
is a bisimulation.
Fix any transition $\rest n (P\bnf R) \ltsred{\mu} \hat P$ that,
by definition of the LTS, has been inferred as follows:
$$
\hspace*{3cm}
\prooftree
\prooftree P\bnf R \ltsred{\bar\mu} \bar P
\justifies \vdots
\endprooftree
\justifies \rest n (P\bnf R) \ltsred{\mu} \hat P
\endprooftree
\hspace*{3cm}
(\star)
$$
where $\mu = \rest m \bar\mu$ and $\hat P = \res{\ \wt n\! \setminus\!\! \wt m} \bar P$ and
the dots denote repeated applications of {\sf resnon} (one for every name in $\wt n \setminus \wt m$)
and {\sf open} (one for every name in $\wt m$).
If $\bar\mu = \tau$, then $\wt m = \emptyset$; moreover, $P\bnf R \ltsred{\bar\mu} \bar P$ can
be generated in three ways:
\begin{itemize}
\item If the transition is
\begin{equation*}
\prooftree P\ltsred\tau P'
\justifies P\bnf R\ltsred\tau P'\bnf R
\endprooftree
\end{equation*}
then because of $P\bisim Q$ there exists $Q\ltsred\tau Q'$
such that $P' \bisim Q'$; hence conclude with
$\rest n (Q\bnf R) \ltsred\tau \rest n(Q'\bnf R)$.
\item If the transition is
\begin{equation*}
\prooftree R\ltsred\tau R'
\justifies P\bnf R\ltsred\tau P\bnf R'
\endprooftree
\end{equation*}
consider $\rest n (Q\bnf R) \ltsred\tau \rest n(Q\bnf R')$ and conclude.
\item If the transition is
\begin{equation*}
\prooftree P \ltsred{\rest l p} P' \quad R \ltsred{\rest o r} R'
\justifies P\bnf R \ltsred\tau \res{\withsetnot{\wt l,\wt o}{\wt l\cup\wt o}}(\sigma P'\bnf\theta R')
\endprooftree
\end{equation*}
with $\{p \pmatch r\} = (\sigma, \theta)$ and
$\wt l \cap {\sf fn}(R) = \wt o \cap {\sf fn}(P) = \wt l\cap\wt o = \emptyset$.
Now, there exist $(q,\rho)$ and $Q'$
such that $Q\ltsred{\rest l q}Q'$ and
$p,\sigma\compat q,\rho$ and $\sigma P'\bisim\rho Q'$.
By Proposition~\ref{lem:pat-lessthan}, $\{q\pmatch r\}=(\rho,\theta)$
and so
\begin{equation*}
\prooftree Q \ltsred{\rest l q} Q' \quad R \ltsred{\rest o r} R'
\justifies Q\bnf R \ltsred\tau \res{\withsetnot{\wt l,\wt o}{\wt l\cup\wt o}}(\rho Q'\bnf\theta R')
\endprooftree
\end{equation*}
where, by $\alpha$-conversion, we can always let $\wt o\cap{\sf fn}(Q) = \emptyset$
(the other side conditions for applying rule {\sf unify} already hold).
By repeated applications of rule {\sf resnon}, infer
$\rest n (Q\bnf R) \ltsred\tau \rest n\res{\withsetnot{\wt l,\wt o}{\wt l\cup\wt o}}(\rho Q'\bnf\theta R')$
and conclude.
\end{itemize}
\noindent If $\bar\mu = \rest l p$, it must be that $({\sf bn}(p) \cup \wt l) \cap {\sf fn}(\rest n(Q\bnf R)) = \emptyset$.
Then, fix any $\sigma$ such that ${\sf dom}(\sigma) = {\sf bn}(p)$ and ${\sf fn}(\sigma) \cap \wt l = \emptyset$.
The transition $P\bnf R \ltsred{\bar\mu} \bar P$ can be now generated in two ways:
\begin{itemize}
\item The transition is
\begin{equation*}
\prooftree P\ltsred{\rest l p} P'
\justifies P\bnf R\ltsred{\rest l p} P'\bnf R
\endprooftree
\ \ (\wt l \cup {\sf bn}(p)) \cap {\sf fn}(R) = \emptyset
\end{equation*}
By $P\bisim Q$ there exist $(q,\rho)$ and $Q'$
such that $Q\ltsred{\rest l q} Q'$ and
$p,\sigma \compat q,\rho$ and $\sigma P' \bisim \rho Q'$. By $\alpha$-equivalence,
let ${\sf bn}(q) \cap {\sf fn}(R) = \emptyset$; thus, $Q \bnf R \ltsred{\rest l q} Q' \bnf R$.
By applying the same sequence of rules {\sf resnon} and {\sf open} used for $(\star)$
(this is possible since ${\sf fn}(p) = {\sf fn}(q)$, see Lemma~\ref{prop:compat-fn}),
conclude with $\rest n (Q\bnf R) \ltsred{\res{\wt l,\wt m} q} \res{\ \wt n\! \setminus\!\! \wt m}(Q'\bnf R)
= \hat Q$.
Since ${\sf dom}(\sigma) \cap {\sf fn}(R) = {\sf bn}(p) \cap {\sf fn}(R) = \emptyset$ and
substitution application is capture-avoiding by definition, obtain that $\sigma\hat P =
\sigma(\res{\ \wt n\! \setminus\! \wt m}(P'\bnf R)) =
\res{\ \wt n\! \setminus\!\! \wt m}(\sigma P'\bnf R)$.
Similarly, $\rho\hat Q = \res{\ \wt n\! \setminus\!\! \wt m}(\rho Q' \bnf R)$.
This suffices to conclude $(\sigma\hat P,\rho\hat Q) \in \Re$, as desired.
\item The transition is
\begin{equation*}
\prooftree R\ltsred{\rest l p} R'
\justifies P\bnf R\ltsred{\rest l p} P\bnf R'
\endprooftree
\ \ (\wt l \cup {\sf bn}(p)) \cap {\sf fn}(P) = \emptyset
\end{equation*}
By $\alpha$-equivalence, let $(\wt l \cup {\sf bn}(p)) \cap {\sf fn}(Q) = \emptyset$;
this allows us to infer $Q\bnf R\ltsred{\rest l p} Q\bnf R'$. The same sequence of
rules {\sf resnon} and {\sf open} used for $(\star)$, yields
$\rest n (Q\bnf R) \ltsred{\res{\withsetnot{\wt l,\wt m}{\wt l\cup\wt m}} p}
\res{\ \wt n\! \setminus\! \wt m}(Q\bnf R') = \hat Q$.
By Proposition~\ref{prop:compat-reflexive}, $p,\sigma \compat p,\sigma$. Moreover,
since ${\sf dom}(\sigma) \cap {\sf fn}(P,Q) = \emptyset$ and
substitution application is capture-avoiding, obtain that $\sigma\hat P =
\res{\ \wt n\! \setminus\!\! \wt m}(P\bnf \sigma R')$ and
$\sigma\hat Q = \res{\ \wt n\! \setminus\!\! \wt m}(Q \bnf \sigma R')$.
This suffices to conclude $(\sigma\hat P,\sigma\hat Q) \in \Re$, as desired.
\end{itemize}
Closure under substitution holds by definition of $\Re$.
\qed
\paragraph{Proof of Lemma~\ref{lem:bisim-rep}}
This proof rephrases the similar one in \cite{sangiorgi.walker:theory-mobile}.
First, define the $n$-th approximation of the bisimulation:
$$
\begin{array}{rcl}
\bisim_0 & = & Proc \times Proc
\\
\stackrel\bullet\bisim_{n+1} & = & \{(P,Q)\ :
\\
&& \quad \forall\ P\ltsred{\mu}P'\\
&& \quad\qquad \mu=\tau\ \Rightarrow\ \exists\ Q\ltsred\tau Q'.\ (P',Q')\in\ \bisim_n\\
&& \quad\qquad \mu=\rest n p \ \Rightarrow\ \forall \sigma\ s.t.\ \,{\sf dom}(\sigma)={\sf bn}(p)\ \wedge \\
&& \qquad\qquad\qquad\qquad\qquad\qquad {\sf fn}(\sigma)\cap\wt n=\emptyset\ \wedge \\
&& \qquad\qquad\qquad\qquad\qquad\qquad\! ({\sf bn}(p)\cup\wt n)\cap{\sf fn}(Q) =\emptyset\\
&& \quad\qquad\qquad\qquad\qquad\ \ \exists\ (q,\rho)\mbox{ and } Q' s.t.\ Q\ltsred{\rest n q}Q' \wedge \\
&& \qquad\qquad\qquad\qquad\qquad\qquad p,\sigma\compat q,\rho
\wedge (\sigma P',\rho Q')\in\ \bisim_n\\
&& \quad \mbox{Symmetrically for transitions of } Q \}
\\
\bisim_{n+1} & = & \mbox{the largest subrelation of $\stackrel\bullet\bisim_{n+1}$ closed under substitutions}
\end{array}
$$
Trivially, $\bisim_0\ \supseteq\ \bisim_1\ \supseteq\ \bisim_2\ \supseteq\ \cdots\,$.
We now prove that, since the LTS is structurally image finite (see Proposition~\ref{prop:imfin}),
it follows that
\begin{equation}
\label{eq:appr}
\bisim\ =\ \bigcap_{n \geq 0} \bisim_n
\end{equation}
One inclusion is trivial: by induction on $n$, it can be proved that $\bisim\ \subseteq\ \bisim_n$ for every $n$,
and so $\bisim\ \subseteq\ \bigcap_{n \geq 0} \bisim_n$.
For the converse, fix $P \ltsred\mu P'$ and consider the case for $\mu = \rest m p$, since
the case for $\mu = \tau$ can be proved like in $\pi$-calculus. For every $n \geq 0$, since $P \bisim_{n+1} Q$,
there exist $(q_n,\rho_n)$ and $Q_n$
such that $Q \ltsred{\rest m q_n} Q_n$ and $p,\sigma \compat q_n,\rho_n$
and $\sigma P' \bisim_n \rho_n Q_n$. However, by Proposition~\ref{prop:maximal},
there are finitely many (up-to $\alpha$-equivalence) such $q_n$'s; thus, there must exist
(at least) one $q_k$ that leads to infinitely many $Q_n$'s that, because of Proposition~\ref{prop:imfin},
cannot be all different (up-to $\equiv$). Fix one of such $q_k$'s; there must exist (at least) one $Q_h$
such that $Q\ltsred{\rest m q_k} Q_h$ and there are infinitely many $Q_n$'s such that
$Q\ltsred{\rest m q_k} Q_n$ and $Q_n \equiv Q_h$. Fix one of such $Q_h$'s. It suffices to prove that
$\sigma P' \bisim_n \rho_h Q_h$, for every $n$. This fact trivially holds whenever $n \leq h$:
in this case, we have that $\bisim_n\ \supseteq\ \bisim_h$. So, let $n > h$. If $Q_n \equiv Q_h$,
conclude, since $\equiv$ is closed under substitutions (notice that $\rho_n = \rho_h$ since
$q_n = q_h = q_k$) and $\equiv\ \subseteq\ \bisim_n$, for every $n$.
Otherwise, there must exist $m > n$ such that $Q_m \equiv Q_h$
(otherwise there would not be infinitely many $Q_n$'s structurally equivalent to $Q_h$):
thus, $\sigma P' \bisim_m \rho_h Q_h$ that implies $\sigma P' \bisim_n \rho_h Q_h$, since $m > n$.
\medskip
Thus, $!P \bisim\,\, !Q$ if and only if $!P \bisim_n \,!Q$, for all $n$.
Let $P^n$ denote the parallel composition of $n$ copies of the process $P$ (and similarly for $Q$).
Now, it can be proved that
\begin{equation}
\label{eq:n}
!P \bisim_n P^{2n} \quad\mbox{and}\quad !Q \bisim_n Q^{2n}
\end{equation}
The proof is by induction on $n$ and exploits a Lemma similar to Lemma~\ref{lem:bisim-par} (with $\bisim_n$ in
place of $\bisim$); the details are left to the interested reader.
By repeatedly exploiting Lemma~\ref{lem:bisim-par}, it follows that $P^{2n} \bisim Q^{2n}$
and so by \eqref{eq:appr}
\begin{equation}
\label{eq:PQ}
P^{2n} \bisim_n Q^{2n}
\end{equation}
Now by \eqref{eq:PQ} it follows that $P\bisim Q$ implies that $P^{2n}\bisim_n Q^{2n}$, for all $n$.
By \eqref{eq:n} and Lemma~\ref{lem:trans-bisim} (that also holds with $\bisim_n$ in place of $\bisim$),
it follows that $!P\bisim_n \,!Q$, for all $n$.
By \eqref{eq:appr}, conclude that $!P\bisim\,\, !Q$.
\qed
\bibliographystyle{abbrv}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,642 |
Лозà е село в Северна България, община Габрово, област Габрово.
География
Село Лоза се намира на около 8 km северозападно от центъра на град Габрово и около 2 km североизточно от село Враниловци, в близост със селата Златевци от изток и Петровци от запад. Разположено е в подножията на западната част на платото Стражата, между два малки притока на река Лопушница. Климатът е умереноконтинентален. Надморската височина нараства от около 355 m в южния край на селото до около 395 m в северния му край. Общинският път за Лоза е северно отклонение в село Янковци от второкласния републикански път II-44 (Севлиево – Габрово), минава през селата Милковци и Златевци, а след Лоза продължава през село Петровци до кръстовище с пътя от село Враниловци до село Армените.
Населението на село Лоза, наброявало 186 души при преброяването към 1934 г., намалява до 60 към 1992 г. и до 32 души (по текущата демографска статистика за населението) към 2019 г.
История
През 1951 г. дотогавашното населено място колиби Саламаните е преименувано на Лоза, а през 1995 г. колиби Лоза придобива статута на село..
Бележки
Външни препратки
Села в област Габрово
Населени места в община Габрово | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 742 |
\section*{Abstract}
The population-attributable fraction (PAF) quantifies the public health impact of a harmful exposure. Despite being a measure of significant importance an estimand accommodating complicated time-to-event data is not clearly defined. We discuss current estimands of the PAF used to quantify the public health impact of an internal time-dependent exposure for data subject to competing outcomes. To overcome some limitations, we proposed a novel estimand which is based on dynamic prediction by landmarking. In a profound simulation study, we discuss interpretation and performance of the various estimands and their estimators. The methods are applied to a large french database to estimate the health impact of ventilator-associated pneumonia for patients in intensive care.
\medskip
\textbf{Keywords: Population-attributable risk, time-dependent exposure, competing risks, hospital-acquired infection, mortality}
\section{Introduction}
An important intention of public health decisions is the containment of fatal exposures such as infectious diseases. A recent example is the fear of
an increasing spread of antimicrobial resistance \cite{laxminarayan2013antibiotic}. The need for action is based on the number of lives that could be spared if nosocomial infections (NIs) could be prevented or entirely cured. Thus, quantifying the threat of an exposure for a population is of main interest when
taking decisions about prevention programs and the development of new drugs.
To quantify the public health impact of a harmful exposure Levin \cite{Levin1953PAF} defined the population-attributable fraction (PAF). It expresses the fraction of all cases that are attributable to the exposure and is often interpreted as percentage of preventable cases.
The PAF is commonly estimated as a static measure over a specific time period. A generalization has been proposed for time-to-event data \cite{chen2006attributable, chen2010attributable, samuelsen2008attributable, laaksonen2010piecewise,laaksonen2010estimation, sjolander2016cautionary, zhao2017onestimation, sjolander2017doubly}. However, these approaches are not appropriate for data settings with an internal time-dependent exposure. We emphasize that harmful exposures are often naturally time-dependent since -- unlike in randomized clinical trials -- the time of onset cannot be chosen by the researcher. Moreover, the outcome is often unobservable due to competing risks. This is the case if attributable risk is quantified by cause-specific mortality or non-mortal endpoints. For example, in hospital epidemiology, the burden of a health-care associated infection (i.e. an NI) is often quantified in terms of death in the hospital or intensive care unit (ICU). Then, even though observational cohort studies in ICUs have often complete follow-up, one has to account for discharge alive as a competing risk to death in the ICU \cite{wolkewitz2014interpreting}. Additionally, infections occur over the course of time. Ignoring the fact that NI is a time-dependent exposure leads to the so-called time-dependent bias \cite{schumacher2013hospital}. Another challenging aspect in this data situation is the adjustment for time-varying confounding which is essential to draw conclusions from observational studies. Thus, major difficulties in defining and estimating the PAF arise when the exposure is time-dependent.
Literature on the PAF for time-dependent exposures and competing risks is sparse \cite{sjolander2017doubly} and inconsistent. Different proposed estimands \cite{schumacher2007attributable, bekaert2010adjusting} lead to different conclusions \cite{vonCube2019beweis}. In \cite{vonCube2019beweis}, we study the differences of the approaches by Schumacher et al. \cite{schumacher2007attributable} and Bekaert et al. \cite{bekaert2010adjusting}. In \cite{vonCube2019lm}, we propose a novel estimand of the PAF which is based on dynamic prediction by landmarking \cite{van2011dynamic}.
The novel approach overcomes some limitations of interpretation and estimation of the current approaches by Schumacher et al. \cite{schumacher2007attributable} and Bekaert et al. \cite{bekaert2010adjusting}. It provides clinically relevant implications and the estimator is easily adjustable for time-dependent confounders.
The purpose of this article is to introduce the various ways of defining the PAF for complex time-to-event data and to draw attention to the differences with regard to interpretation. Our investigations include also a study of basic aspects of the corresponding estimators of the PAF. In Section 2, we introduce the established approaches used to define and estimate the PAF in hospital epidemiology. Moreover, the novel approach which is discussed in detail in \cite{vonCube2019lm} is outlined. A discussion and comparison of the various estimands and their estimators based on a simulation study are presented in Section 3. In Section 4, we analyse a large sample of ventilated patients in intensive care to estimate attributable mortality and the percentage of preventable ICU death cases if ventilator-associated pneumonia (VAP) was avoided. For simplicity, all the methods are explained and discussed based on the example of attributable ICU death cases due to NIs. However, they are applicable to any other survival data setting with binary time-dependent exposure and competing risks. Even though our focus is on data settings with complete follow-up, all estimands can be estimated with censored time-to-event data.
\section{The population-attributable fraction for time-dependent exposures: Estimands and estimators}
\subsection{Initial definition of the PAF}
The PAF is defined by
\begin{equation}
\textrm{PAF}=\frac{P(D=1)-P(D=1|E=0)}{P(D=1)},
\label{PAFl}
\end{equation}
where $D$ is the random variable of a dichotomous outcome and $E$ of a dichotomous exposure \cite{benichou2001review}. The sampling schemes that correspond to such an estimand are usually cross-sectional studies and cohort studies of fixed length. Note that $D$ and $E$ are both observable random variables.
An equivalent definition in terms of the relative risk (RR) \cite{miettinen1974proportion} is
\begin{equation}
\textrm{PAF}=P(E=1|D=1)\times \frac{RR-1}{RR}.
\label{PAFm}
\end{equation}
This representation shows that the PAF takes both the prevalence of the exposure and the strength of association of exposure and outcome into account. In cross-sectional studies and cohort studies of fixed length with a time-independent exposure the PAF can be interpreted causally if it has been sufficiently adjusted for confounding.
Then, it can be interpreted as proportion of preventable death cases if exposure was completely extinct \cite{benichou2005attributable}.
\subsubsection{Defining $\textrm{PAF}_{crude}$}
If follow-up is complete, information on exposure and outcome is often summarized in a fourfold table. A patient that is discharged alive has the realization $D=0$. A patient that died in the ICU has the realization $D=1$. Patients acquiring an infection during their ICU stay have $E=1$, otherwise $E=0$. Then, the percentage of attributable ICU death cases is often accessed with \eqref{PAFl} or \eqref{PAFm}.
The resulting estimand relates the proportion of patients that were ever infected to the proportion of patients that remained uninfected until the end of their ICU stay. We denote this estimand with $\textrm{PAF}_{crude}$. In clinical literature this is still the most commonly used approach. However, $\textrm{PAF}_{crude}$ ignores the time-dependencies of exposure and outcome and is therefore only a crude measure of attributable risk.
\subsubsection{Estimating $\textrm{PAF}_{crude}$}
Estimation of $\textrm{PAF}_{crude}$ can be performed with the R-package 'AF' \cite{dahlqwist2016model} which is based on generalized-linear models (GLMs). The R-package allows for adjustment for confounding based on the maximum likelihood estimator from a logistic model as proposed by Greenland and Drescher \cite{greenland1993maximum}. Note that in case of censoring, $\textrm{PAF}_{crude}$ can be estimated by $\textrm{PAF}_o(\tau)$, where $\tau$ denotes the end of follow-up. This approach is explained in the following Section 2.2 and discussed in more detail in Section 3.
\subsection{Defining $\textrm{PAF}_o(t)$}
In order to account for the timing of exposure and outcome, Schumacher et al. \cite{schumacher2007attributable} extended the definition of $\textrm{PAF}_{crude}$ to
\begin{equation}
\textrm{PAF}_o(t)=\frac{P(D(t)=1)-P(D(t)=1|E(t)=0)}{P(D(t)=1)},
\label{eqPAF_S}
\end{equation}
where $D(t)$ is the random variable that indicates if the patient died in the ICU by time $t$ ($D(t)=1$ if the patient died) and $E(t)$ if the patient acquired an NI by $t$ ($E(t)=1$ if the patient acquired an NI within $(0,t]$). Both $E(t)$ and $D(t)$ are observable random variables. By definition of NIs patients are naturally unexposed at study entry. Thus, $E(0)=0$ for all patients. $\textrm{PAF}_o(t)$ relates the proportions of patients that died infection-free within $(0,t]$ to the proportion of all patients that died. Therefore, it is interpretable as the \textit{observable} proportion of attributable death cases until time $t$ among all initially admitted patients \cite{vonCube2019beweis}.
\subsubsection{Estimating $\textrm{PAF}_o(t)$}
For identification and estimation Schumacher et al. \cite{schumacher2007attributable} proposed to use the multi-state model shown in Figure \ref{fig:extendedIllnessDeath}. This model is often called 'extended illness-death model' \cite{beyersmann2011competing}. The exposure is modelled as an intermediate state (State 1), the outcome death in the ICU as State 3 if the patient died unexposed and as State 5 if the patient acquired an NI before death. Analogously, discharge alive is modelled as State 2 and State 4.
Based on the extended illness-death model and with the Bayes' Theorem the conditional probability of ICU death is identifiable by
\begin{equation}
P(D(t)=1|E(t)=0)=\frac{P_{03}(0,t)}{P_{00}(0,t)+P_{02}(0,t)+P_{03}(0,t)},
\label{condP03}
\end{equation}
where $P_{0j}(0,t)$ ($j=0,2,3$) denote the transition probabilities of the extended illness-death model \cite{schumacher2007attributable}.
Moreover, the sum of the risk to die without and with the exposure results in an estimand of overall mortality:
\begin{equation}
P(D(t)=1)=P_{03}(0,t)+P_{05}(0,t).
\label{P_Dt}
\end{equation}
\begin{figure*}
\centering
\includegraphics[width=\textwidth]{exIDMc.pdf}
\caption{Extended Illness-Death Model with hazard rates $\alpha_{01}(t)$, $\alpha_{02}(t)$, $\alpha_{03}(t)$, $\alpha_{14}(t)$ and $\alpha_{15}(t)$.}
\label{fig:extendedIllnessDeath}
\end{figure*}
Estimation of the transition probabilities can be, for example, performed with the Aalen-Johansen estimator. To adjust for confounding, \cite{coeurjolly2012attributable} proposed a semi-parametric modelling approach. Alternatively, the Aalen-Johansen estimators can be estimated within strata based on baseline covariates. Confidence-intervals can be obtained with a bootstrap approach.
\subsection{Defining $\textrm{PAF}_c(t)$}
An alternative definition of the PAF for data settings with time-dependent exposure and competing risks was motivated by Bekaert et al. \cite{bekaert2010adjusting} and formalized by von Cube et al. \cite{vonCube2019beweis}. We denoted this estimand with $\textrm{PAF}_c(t)$. The initial definition was based on counterfactual outcomes. In this article, we use a slightly different approach to define $\textrm{PAF}_c(t)$.
This approach is based on the definition of the PAF (for cross-sectional studies and cohort studies of fixed length) by Eide et al.\cite{eide2001attributable}
Let $D(t)$ be, as defined above, the observable random variable of death by time $t$ and $P$ the corresponding distribution in the target population. Thus, $P(D(t)=1)$ is - as in \eqref{eqPAF_S} - the (observable) overall death risk. To denote the hypothetical death risk of this population if the exposure could be eliminated - all other things left equal - we define the distribution $P_0$ of $D(t)$.
Then, $\textrm{PAF}_c(t)$ is given by
\begin{equation}
\textrm{PAF}_c(t)=\frac{P(D(t)=1)-P_0(D(t)=1)}{P(D(t)=1)},
\label{eqPAF_B}
\end{equation}
where $P_0(D(t)=1)$ is the hypothetical death risk at $t$ had all patients remained unexposed.
$\textrm{PAF}_c(t)$ is interpreted as the percentage of preventable ICU death cases over the course of time had all patients remained infection-free.
\subsubsection{Estimating $\textrm{PAF}_c(t)$}
To identify $\textrm{PAF}_c(t)$, we must identify the two distributions, $P$ and $P_0$, of the random variable $D(t)$.
$P$ corresponds to the distribution of $D(t)$ in the observable population and can be identified by \eqref{P_Dt}. $P_0$ is the hypothetical distribution after a manipulation of the transition intensities of the extended illness-death model (Figure \ref{fig:extendedIllnessDeath}). We only consider an indirect manipulation of the death risk by setting the infection hazard to zero. The resulting distribution of $D(t)$ corresponds to $P_0$. Now $P_0(D(t)=1)$ can be identified with the cumulative-incidence function (CIF) of death without NI. For estimation, patients that acquire an infection are treated as censored observations instead of accounting for NI as a competing risk. An estimator for the CIF is, for example, the Aalen-Johansen estimator. We denote this estimator with $\hat{P}_{03_0}(0,t)$. For details we refer to \cite{vonCube2019beweis} and the Appendix.
Bekaert et al. propose two estimators of $P_0(D(t)=1)$. The first is called naive, as it is not adjusted for counfounding factors. We emphasize that this naive estimator is an estimator for the conditional probability function \eqref{condP03} \cite{vonCube2019beweis}. Thus, the resulting estimand of the PAF is $\textrm{PAF}_o(t)$.
Furthermore, Bekaert et al. propose to adjust $\textrm{PAF}_c(t)$ by adjusting $P_0(D(t)=1)$ using inverse probability weights (IPWs). The weights denote the probability of being uninfected at time $t$ conditional on observable covariates (time-dependent and time-independent). The weights can be derived using pooled logistic regression. The causal interpretation is justified if the IPWs are correctly specified at each time $t$ and under the usual assumptions of marginal structural models \cite{robins2000marginal}. We emphasize that in the absence of confounding, this estimator is equivalent to $\hat{P}_{03_0}(0,t)$ \cite{vonCube2019beweis}. The resulting estimand is $\textrm{PAF}_c(t)$. In this article, we are mainly interested in the estimands of the PAF and consider simulation studies without confounding. However, in practice adjustment for time-varying confounding is essential to draw causal conclusions. Then, the IPW-approach by Bekaert et al. \cite{bekaert2010adjusting} provides a way to adjust $\widehat{\textrm{PAF}}_c(t)$ for time-varying confounding. To obtain confidence intervals a bootstrap approach can be used.
\subsection{Defining $\textrm{PAF}_{LM}$}
A different way to define the PAF while accounting for the time-dependencies of exposure and outcome is via dynamic prediction by landmarking \cite{vonCube2019lm}. Generally speaking, this is done by choosing a set of relevant time points on the study time scale (landmarks) and an adequate time window (e.g. the mean length of stay in the ICU). At each landmark the exposure state is updated and kept fixed over the time-window.
Then, at each landmark a PAF within the time window can be defined with the time-independent definitions \eqref{PAFl} or \eqref{PAFm}. The PAF at a specific landmark provides information for the patient population that remained in the ICU until that day. The exposed patients are those patients, that are still in the ICU at the landmark and acquired an infection some time before or at the landmark. The unexposed patients are those that are NI-free at the landmark. As the PAF is defined over a specific time window it quantifies the proportion of attributable death cases which occur within the time window.
These attributable cases could be prevented if NIs could be eliminated for patients being infected at the landmark if the Markov assumption holds \cite{vonCube2019lm}. By considering a whole set of landmarks, we account for the time-dependency of infections.
A graphical presentation of $\textrm{PAF}_{LM}$ is given in Figure \ref{fig:LM}.
Let $A_l$ indicate whether the patient is still at risk at landmark $l$, $E_l$ if the patient was exposed at $l$ and $D_{l,h}$ if the patient died within $(l,l+h]$. Then, the PAF at a landmark $l$ within a time window $(l,l+h]$ is defined by
\begin{equation}
\textrm{PAF}(l,h)=\frac{P(D_{l,h}=1|A_l=1)-P(D_{l,h}=1|E_l=0,A_l=1)}{P(D_{l,h}=1|A_l=1)}
\end{equation}
or equivalently as
\begin{align}
\textrm{PAF}(l,h)&=P(E_l=1|A_l=1, D_{l,h}=1)\times \frac{RR_{l,h}-1}{RR_{l,h}}\nonumber\\
&=P_{E_l}\times \frac{RR_{l,h}-1}{RR_{l,h}}
\label{PAF(s,t)_def}
\end{align}
where $P_{E_l}$ is the prevalence of infection at time $l$ among death cases occurring within the time window $(l,l+h]$ and $RR_{l,h}$ is the RR of death within $(l,l+h]$ depending on the infection state at time point $l$. $RR_{l,h}$ is formally defined by
\begin{equation}
\textrm{RR}_{l,h}=\frac{P(D_{l,h}=1|A_l=1,E_l=1)}{P(D_{l,h}=1|A_l=1, E_l=0)},
\end{equation}
$\textrm{PAF}_{LM}$ is the set of estimands $\textrm{PAF}(l,h)$s over all landmarks. It accounts for the time-dynamics of the study population by considering a range of time points $l$. Remark that at each landmark we consider a different target population.
\begin{figure*}
\centering
\includegraphics[scale=0.8]{LM_PrincipleC.pdf}
\caption{Dynamic prediction by landmarking: $l_1$, $l_2$ are landmarks, $h$ is the time window of fixed length; $PAF(l_1, h)$ is a summary measure over the time-interval $(l_1, l_1+h]$.}
\label{fig:LM}
\end{figure*}
\subsubsection{Estimating $\textrm{PAF}_{LM}$}
A major strength of $\textrm{PAF}_{LM}$ is the simplicity of its' estimation. Generally, time-dependent confounding is a major challenge in the estimation of the PAF for time-dependent exposures. However, at a landmark $l$ estimation of $\textrm{PAF}_{LM}$ is equivalent to estimation of the PAF in a data setting with baseline exposure and fixed length of follow-up.
More explicitly, estimation of $\textrm{PAF}(l,h)$ is based on estimation methods for $\textrm{PAF}_{crude}$ since at each landmark and for every chosen time window, information of exposure and outcome can be summarized in a fourfold table. Time-varying confounding is accounted for by updating the covariate values at every landmark.
For estimation, we must first identify a set of relevant landmarks. The choice of landmarks depends on the number of exposed and unexposed patients in the study sample. The number of patients in each group must be sufficiently large such that the regression model converges. Inference at a landmark $l$ is performed on a so-called landmark dataset \cite{van2011dynamic}. For a specific landmark $l$, it includes information on the patients that are still at risk at $l$. All other patients are excluded. The necessary information comprise exposure state at $l$, outcome state at $l+h$ and covariate values at $l$.
If the patient is still alive at $l+h$ or experienced a competing event, then $D_{l,h}=0$ otherwise $D_{l,h}=1$. In case of censoring pseudo-values for $D_{l,h}$ as proposed by Nicolaie et al. \cite{nicolaie2013dynamic} can be used \cite{vonCube2019lm}.
With the landmark dataset at landmark $l$, $\textrm{PAF}(l,h)$ can be estimated with any method available for the time-independent PAF (e.g. \cite{greenland1987variance, greenland1993maximum, sjolander2011estimation}). Confidence intervals can be obtained in the same way.
Finally, van Houweling and Putter \cite{van2011dynamic} proposed to smooth the separate estimates $\widehat{\textrm{PAF}}(l,h)$ to increase the efficiency of the estimators.
In principle, two different approaches can be used to obtain a smooth curve of the separate $\textrm{PAF}(l,h)$s over all landmarks. Firstly, smoothing methods like splines in a linear model or local smoothers such as "loess" can be applied on the separately estimated $\widehat{\textrm{PAF}}(l,h)$.
Secondly, a so-called supermodel can be used to obtain a smooth curve over all landmarks directly without first fitting the separate models \cite{van2011dynamic}. The supermodel is basically pooled logistic regression on the landmark datasets stacked together to one large dataset. A regression model is fitted by accounting for possible time-varying effects at the landmarks via interaction terms. For more details, we refer to \cite{vonCube2019lm}.
\section{Comparison of the estimands and estimators}
\subsection{General aspects on the estimands}
The estimands $\textrm{PAF}_o(t)$ and $\textrm{PAF}_c(t)$ are directly comparable, since they are both cumulative measures of attributable risk over the course of time. The target population of these two estimands are all patients admitted to the ICU or more generally all patients initially entering the study. The $\textrm{PAF}_{crude}$ can be viewed as a summary measure of $\textrm{PAF}_o(t)$ as - in the absence of censoring - we have $\textrm{PAF}_o(\tau)=\textrm{PAF}_{crude}$.
$\textrm{PAF}_o(t)$ and $\textrm{PAF}_c(t)$ differ in the choice of unexposed patients. In the definition of $\textrm{PAF}_o(t)$ the unexposed patients are those patients that did not acquire an infection until $t$. Thus, they are an \textit{observable} time-varying \textit{subpopulation} of the target population. In contrast, the unexposed patients considered in $\textrm{PAF}_c(t)$ are a \textit{hypothetical} patient population that differs from the factual one in being infection-free. As a consequence, in the definition of $\textrm{PAF}_c(t)$ the same population is compared under two distinct conditions.
The $\textrm{PAF}_{LM}$ differs from $\textrm{PAF}_o(t)$ and $\textrm{PAF}_c(t)$ in many aspects. Firstly, it is not a cumulative measure over the course of time. Instead, similarly to $\textrm{PAF}_{crude}$, it summarizes the information within a specific time window. Secondly, $\textrm{PAF}_{LM}$ conditions on patients being still at risk at certain time points (the landmarks). This means that - in contrast to $\textrm{PAF}_{crude}$, $\textrm{PAF}_o(t)$ and $\textrm{PAF}_c(t)$ - the \textit{target population} varies with time. The $\textrm{PAF}_{LM}$ is a summary measure of population-attributable risk of patients still in the ICU after a certain amount of days. In Table 2, we present the main characteristics of the four estimands and corresponding estimators of the PAF. The simulation study demonstrates not only the behaviour of the estimators but also the different interpretation of the estimands under ideal conditions (i.e. no confounding).
\subsection{Performance in a simulation study}
All the proposed estimands of the PAF can be identified with the transition probabilities of the extended illness-death model (Figure \ref{fig:extendedIllnessDeath}), which are determined by the five cause-specific hazard rates. Therefore, data generation was based on the extended illness-death model. The data was generated and evaluated with the statistical software R and the R code for the data simulation is an extension of the simulation code provided by Heggland et al. \cite{heggland2015estimating}. We assumed constant hazards and more generally time-varying Weibull hazards to obtain different data situations. The effect of the time-dependent exposure on the outcome of interest (death in ICU) was modelled either directly via an increased death hazard after an infection or indirectly via a decreased discharge hazard after an infection. The parameters of the various scenarios are presented in Table \ref{tab:scenarios}.
Each scenario was simulated 100 times with a sample size of 10,000 or 2,000 observations. In each run, we obtained estimates of $\textrm{PAF}_{crude}$, $\textrm{PAF}_o(t)$, $\textrm{PAF}_c(t)$ and $\textrm{PAF}_{LM}$. The estimates of $\textrm{PAF}_{crude}$ and $\textrm{PAF}_{LM}$ were obtained with generalized linear models using the R-function \textit{glm} \cite{stats2017}. Those for $\textrm{PAF}_o(t)$ and $\textrm{PAF}_c(t)$ were obtained with the R-function \textit{etm} \cite{etm2011}. To present the results we evaluated at each time point a summary (1st to 3rd quartile and the mean) of the 100 estimates.
\begin{table*}[htbp]
\begin{center}
\vspace{-3cm}
\begin{tabular}{cllllll}
\multicolumn{6}{c}{\large Data scenarios in the simulation study}\\
\hline
\hline
&&&&&\\
\multicolumn{6}{l}{ Scenarios with constant hazards} \\
\multicolumn{6}{l}{($\alpha_{ij}(t)=\alpha_{ij}$; $i=0,1$, $j=1,2,3,4,5$; cause specific hazard rates of the extended } \\
\multicolumn{6}{l}{illness-death model (Figure \ref{fig:extendedIllnessDeath})} \\
\hline
&&&&&\\
&\multicolumn{5}{c}{ Parameters of the cause-specific hazard rates}\\
&&&&&\\
Scenario (fig. w/results)& \hspace{0.5cm} NI & Discharge & Death & Discharge & Death\\
&&w/out NI&w/out NI&w/NI&w/NI\\
\multicolumn{3}{l}{No effect on mortality:} &&&\\
1 (fig. A1 (ESM)) &$\alpha_{01}=0.005$&$\alpha_{02}=0.02$&$\alpha_{03}=0.01$&$\alpha_{14}=0.02$&$\alpha_{15}=0.01$\\
2 (fig. A2 (ESM))&$\alpha_{01}=0.05$&$\alpha_{02}=0.02$&$\alpha_{03}=0.01$&$\alpha_{14}=0.02$&$\alpha_{15}=0.01$\\
&&&&&\\
\multicolumn{3}{l}{Direct effect on mortality:} &&&\\
3 (fig. A3 (ESM))&$\alpha_{01}=0.005$&$\alpha_{02}=0.02$&$\alpha_{03}=0.01$&$\alpha_{14}=0.02$&$\alpha_{15}=0.02$\\
4 (fig. \ref{fig:SimScene4})&$\alpha_{01}=0.05$&$\alpha_{02}=0.02$&$\alpha_{03}=0.01$&$\alpha_{14}=0.02$&$\alpha_{15}=0.02$\\
&&&&&\\
\multicolumn{3}{l}{Indirect effect on mortality:} &&&\\
5 (fig. A4 (ESM)) &$\alpha_{01}=0.005$&$\alpha_{02}=0.03$&$\alpha_{03}=0.01$&$\alpha_{14}=0.02$&$\alpha_{15}=0.01$\\
6 (fig. A5 (ESM))&$\alpha_{01}=0.05$&$\alpha_{02}=0.03$&$\alpha_{03}=0.01$&$\alpha_{14}=0.02$&$\alpha_{15}=0.01$\\
\multicolumn{6}{c}{}\\
\hline
\multicolumn{6}{c}{}\\
\multicolumn{6}{l}{ Scenarios with time-varying Weibull hazards (fig. A6 and A8 (ESM))}\\
\multicolumn{6}{l}{($\alpha_{ij}(t)=k_{ij}\lambda_{ij}(\lambda_{ij}t)^{k_{ij}-1}$; $i=0,1$, $j=1,2,3,4,5$); cause specific hazard rates of the extended } \\
\multicolumn{6}{l}{illness-death model (Figure \ref{fig:extendedIllnessDeath})} \\
\hline
&&&&&\\
&\multicolumn{5}{c}{ Parameters of the cause-specific hazard rates}\\
&&&&&\\
Scenario (fig. w/results)& \hspace{0.5cm} NI & Discharge & Death & Discharge & Death\\
&&w/out NI&w/out NI&w/NI&w/NI\\
\multicolumn{3}{l}{Indirect effect on mortality:} &&&\\
7 (fig. \ref{fig:SimScene7}) &$k_{01}=1$&$k_{02}=1.4$&$k_{03}=0.9$&$k_{14}=1.4$&$k_{15}=0.9$\\
&$\lambda_{01}=0.06$ &$\lambda_{02}=0.08$&$\lambda_{03}=0.05$&$\lambda_{14}=0.05$&$\lambda_{15}=0.05$\\
8 (fig. A7 (ESM)) &$k_{01}=1$&$k_{02}=0.9$&$k_{03}=1.4$&$k_{14}=0.9$&$k_{15}=1.4$\\
&$\lambda_{01}=0.06$ &$\lambda_{02}=0.08$&$\lambda_{03}=0.05$&$\lambda_{14}=0.05$&$\lambda_{15}=0.05$\\
&&&&&\\
\multicolumn{3}{l}{Direct effect on mortality:} &&&\\
9 (fig. A9 (ESM)) &$k_{01}=1$&$k_{02}=1.4$&$k_{03}=0.9$&$k_{14}=1.4$&$k_{15}=0.9$\\
&$\lambda_{01}=0.06$ &$\lambda_{02}=0.05$&$\lambda_{03}=0.05$&$\lambda_{14}=0.05$&$\lambda_{15}=0.08$\\
10 (fig. A10 (ESM)) &$k_{01}=1$&$k_{02}=0.9$&$k_{03}=1.4$&$k_{14}=0.9$&$k_{15}=1.4$\\
&$\lambda_{01}=0.06$ &$\lambda_{02}=0.05$&$\lambda_{03}=0.05$&$\lambda_{14}=0.05$&$\lambda_{15}=0.08$\\
\end{tabular}
\end{center}
\caption{\footnotesize Each scenarios was simulated 100 times with 10,000 and 2000 observations in each run. The R code was based on the simulation code provided by Heggland et al.\cite{heggland2015estimating}. In each run the four estimators of the PAF were calculated. Then, summary statistics over the 100 runs were obtained.}
\label{tab:scenarios}
\end{table*}
\subsection{Data settings with time-constant hazards}
We considered six different scenarios with constant hazards (see Table \ref{tab:scenarios}). In the following, we discuss Scenario 4 in more detail. In this scenario, we simulated a data setting with hazard rates $\alpha_{03}(t)=0.01$, $\alpha_{15}(t)=0.02$ and $\alpha_{02}(t)=\alpha_{14}(t)=0.02$. The infection hazard was quite high with $\alpha_{01}(t)=0.05$. Due to the inceased death hazard with infection, we expect an increased risk of death for exposed patients. The results of Scenario 4 (10,000 observations) are shown in Figure \ref{fig:SimScene4}. The results of Scenarios 1-3 and 5,6 lead to similar conclusions and are shown in the electronic supplementary material (ESM).
First, we consider $\widehat{\textrm{PAF}}_{LM}$ which is presented in the upper graphs of Figure \ref{fig:SimScene4} (separate models left, smoothed supermodel right). We find that due to an increasing prevalence of infection within the time window, $\widehat{\textrm{PAF}}_{LM}$ becomes higher at later landmarks. Thus, patients at risk at late time points would benefit most of a preventive intervention provided at the specific landmark. Regarding the estimators, the supermodel increases the efficiency of the separate models. However, variation of both estimators (separate models and supermodel) is quite large since the landmark datasets are much smaller in size than the initial population.
The $\textrm{PAF}_o(t)$ (lower graph on the left) is negative in the first part of the time frame. As explained previously \cite{schumacher2007attributable,von2017basic} this rather undesirable property results from death cases accumulating later among exposed patients than among unexposed patients. The apparent 'bump' resulting from this time delay is a characteristic of the \textit{estimand} and does not allow for a causal interpretation. The different simulation scenarios (see also the ESM) demonstrate that the infection hazard influences the depth of the bump and the speed of convergence of the estimand.
Furthermore, the limit of $\textrm{PAF}_o(t)$ equals $\textrm{PAF}_{crude}$ which relates the observable proportion of death cases of eventually exposed and unexposed patients. This becomes not only apparent from the simulation study but can be also shown mathematically \cite{von2017basic}.
In the presence of censoring, $\widehat{\textrm{PAF}}_{crude}$ is unobservable and $\widehat{\textrm{PAF}}_o(\tau)$ is the best approximation of it. Finally, variation of $\widehat{\textrm{PAF}}_o(t)$ is minor and decreases with increasing infection hazard.
The $\widehat{\textrm{PAF}}_c(t)$ (lower graph, right) is positive at all time points and overcomes the interpretational limitations of $\textrm{PAF}_o(t)$ (see especially Scenarios 1 and 2 in the ESM).
In Scenario 4, $\widehat{\textrm{PAF}}_c(t)$ increases quickly and first exceeds $\widehat{\textrm{PAF}}_{crude}$ before decreasing again. Thus, after removal of the exposure risk deaths accumulate more slowly. This means that some death cases that could have been prevented around day 50 would still occur later in time. For constant hazards (however not generally \cite{vonCube2019beweis}) it can be shown mathematically that $\widehat{\textrm{PAF}}_c(t)$ should equal $\widehat{\textrm{PAF}}_{crude}$ at the end of follow-up. Nevertheless, despite complete follow-up, this is not the case in Scenario 4 due to the large infection hazard and the accordingly high systematic censoring of infected patients. Remark that the estimand $\textrm{PAF}_c(t)$ is independent of the infection hazard. However, as patients with an infection are treated as censored observations, the estimator $\widehat{\textrm{PAF}}_c(t)$ loses precision with an increasing infection hazard. Moreover, compared to $\widehat{\textrm{PAF}}_o(t)$ , $\widehat{\textrm{PAF}}_c(t)$ seems to be less precise.
\begin{figure*}[htb!]
\centering
\includegraphics[width=\textwidth]{simulationScenario4.png}
\caption{Scenario 4: Simulation of a direct effect of the exposure on the death risk with constant cause-specific hazard rates ($\alpha_{01}(t)=0.05$, $\alpha_{02}(t)=0.02$, $\alpha_{03}(t)=0.01$, $\alpha_{14}(t)=0.02$ and $\alpha_{15}(t)=0.02$). Each sample consisted of 10,000 observations.
The time window of $\widehat{PAF}_{LM}$ was the approximate mean length of stay (30 days).}
\label{fig:SimScene4}
\end{figure*}
\subsection{Data settings with time-varying Weibull hazards}
To investigate the estimands and estimators of the PAF for a time-dependent exposure with time-varying hazards, we further simulated data based on Weibull hazards. We investigated four scenarios (see Table 1). In the following, we discuss Scenario 7 (Figure \ref{fig:SimScene7}, 10,000 observations) in detail. The argumentation and discussion are similar for the other scenarios (shown in the ESM; ESM Figures A7, A9 and A10). In Scenario 7, we assumed equal, decreasing death hazards and differential increasing discharge hazards. The discharge hazard of patients with infection was reduced compared to the one of patients without infection.
In Scenario 7, $\widehat{\textrm{PAF}}_{crude}$ is almost zero. This is rather surprising as we would expect an increased death risk due to a decreased discharge hazard with infection. The same applies for $\widehat{\textrm{PAF}}_o(t)$. It is negative in the first part of the time frame and then converges from below zero to $\widehat{\textrm{PAF}}_{crude}$.
In contrast, both $\widehat{\textrm{PAF}}_c(t)$ and $\widehat{\textrm{PAF}}_{LM}$ imply an increased death risk for infected patients and a significant amount of preventable death cases at later time points. Due to the fact that there is no administrative censoring and no confounding, we are able to draw direct conclusions on the estimands.
This simulation setting shows that $PAF_{crude}$ has no causal interpretation \cite{vonCube2019beweis}.
The discrepancy between the results is mainly explained by the death hazards which are strongly decreasing within the first days. At this time, only a few patients already had an infection and most patients are at risk to die without an infection. Later, when the death hazards are already considerably decreased, more and more patients become at risk to die with infection. Therefore, the absolute number of patients that die without infection and with infection within the complete study period is almost the same despite an indirect effect of the infection via a decreased discharge hazard. However, interpretation must be done carefully as this equal number is rather due to the time delay of the occurrence of infections than the severity of infections. The time delay is not a causal consequence (though a natural aspect) of the exposure.
In the landmark approach patients that died or were discharged before the landmark no longer influence the estimand/estimate. The difference compared to $\textrm{PAF}_o(t)$ or $\textrm{PAF}_{crude}$ arises from considering different target populations and different unexposed patients. The $\widehat{\textrm{PAF}}_c(t)$ remains zero until the difference of the discharge hazards without and with NI becomes more pronounced. Then, $\widehat{\textrm{PAF}}_c(t)$ starts to increase and finally converges. The difference to $\textrm{PAF}_o(t)$ and $\textrm{PAF}_{crude}$ arises from the different definition of unexposed patients.
The estimator $\widehat{\textrm{PAF}}_c(t)$ seems to give precise results as variation is small. However, due to the systematic censoring of infected patients, it can be unreliable.
All estimators performed better when the sample size was 10,000. A sample size of 2,000 led to higher variations especially of the landmark approach.
The main characteristics of the estimands and estimators of the PAF are summarized in Table 2.
\begin{figure*}[htb]
\centering
\includegraphics[width=\textwidth]{simulationScenario7m.png}
\caption{Scenario 7: Simulation of an indirect effect of the exposure on the death risk with time-varying cause-specific Weibull hazard rates (the according hazards are shown in the upper graph of ESM Figure A6). Each sample consisted of 10,000 observations.
The time window of $\widehat{PAF}_{LM}$ was the approximate mean length of stay (8 days).}
\label{fig:SimScene7}
\end{figure*}
\pagestyle{empty}
\begin{landscape}
\begin{table}[htbp]
\begin{center}
\begin{tabular}{l@{\hskip 0.5in}l@{\hskip 0.5in}l@{\hskip 0.35in}l}
\multicolumn{4}{c}{\large Estimands of the PAF for data with internal time-dependent exposure and competing risks}\\
\hline
\hline
\multicolumn{4}{c}{}\\
Definition & Time scale & Target population & Unexposed patients \\
\multicolumn{4}{c}{}\\
\hline
\multicolumn{4}{c}{}\\
$\textrm{PAF}_{crude}=\frac{P(D=1)-P(D=1|E=0)}{P(D=1)}$ &\begin{tikzpicture}
\draw[|-|, thick] [draw=black](0,0)node[below]{0 } --(4,0);
\draw [decorate,decoration={brace,amplitude=10pt},xshift=0pt,yshift=0pt, rotate=270]
(0,0) -- (0,4.0) node [black,midway,yshift=0.75cm]
{\footnotesize complete study time};
\foreach \x in {0}
\draw[xshift=\x cm] (0pt,2pt) -- (0pt,-1pt) node[below,fill=white]{0};
\foreach \x in {4}
\draw[xshift=\x cm] (0pt,2pt) -- (0pt,-1pt) node[below,fill=white]{$\tau$};
\end{tikzpicture} & All patients & Patients unexposed at
\\
\hspace{1.8cm}$=\textrm{PAF}_o(\tau)$& Summary measure && the end of their ICU-stay\\
&&&\\
&&&\\
$\textrm{PAF}_o(t)=\frac{P(D(t)=1)-P(D(t)=1|E(t)=0)}{P(D(t)=1)}$& \begin{tikzpicture}
\draw[|->, thick] [draw=black](0,0)node[below]{0 } --node[below]{t (study time)}++(4,0);
\foreach \x in {0}
\draw[xshift=\x cm] (0pt,2pt) -- (0pt,-1pt) node[below,fill=white]{0};
\end{tikzpicture}
& All patients & Patients unexposed at $t$\\
& Cumulative measure &&\\
&&&\\
&&&\\
$\textrm{PAF}_c(t)=\frac{P(D(t)=1)-P_0(D(t)=1)}{P(D(t)=1)}$&
\begin{tikzpicture}
\draw[|->, thick] [draw=black](0,0)node[below]{0 } --node[below]{t (study time)}++(4,0);
\foreach \x in {0}
\draw[xshift=\x cm] (0pt,2pt) -- (0pt,-1pt) node[below,fill=white]{0};
\end{tikzpicture}
& All patients & All patients (hypo-
\\
& Cumulative measure && thetically unexposed)\\
&&&\\
&&&\\
$\textrm{PAF}_{LM}=\{\textrm{PAF}(l,h)|l\in \mathcal{LM}\}$& \begin{tikzpicture}
\draw (0,0) -- (4,0);
\foreach \x in {0,1,2.5,4}
\draw (\x cm,3pt) -- (\x cm,-3pt);
\draw [decorate,decoration={brace,amplitude=10pt},xshift=0pt,yshift=0pt, rotate=270]
(0,1) -- (0,2) node [black,midway,yshift=0.5cm]
{\footnotesize h};
\draw (0,0) node[below=3pt] {$ 0 $};
\draw (1,0) node[below=3pt] {$ l_1 $};
\draw (2.5,0) node[below=3pt] {$ l_2 $};
\draw [decorate,decoration={brace,amplitude=10pt},xshift=0pt,yshift=0pt, rotate=270]
(0,2.5) -- (0,3.5) node [black,midway,yshift=0.5cm]
{\footnotesize h};
\draw (4,0) node[below=3pt] {$\tau$};
\end{tikzpicture}
& All patients still & Patients unexposed \\
\hspace{2.2cm}$\textrm{PAF}(l,h)=P_{E_l}\times \frac{RR_{l,h}-1}{RR_{l,h}}$ & Summary measure &at risk at the LM&at the LM
\\
\end{tabular}
\end{center}
\caption{\footnotesize D and D(t) are the variables of death at the end of the ICU stay and at time $t$ respectively; $P$ is the factual distribution of $D(t)$; $P_0$ the one after artificial removal of exposure risk; $P_{E_l}$ is the proportion of exposed at time $l$ among ICU death cases within $(l,l+h]$ of patients at risk at $l$; $RR_{l,h}$ is the relative risk of death in ICU within $(l, l+h]$ depending on exposure at landmark $l$ among patients at risk at $l$. $\mathcal{LM}$ is the set of landmarks.}
\end{table}
\label{tab:resultsSim}
\begin{table}[htbp]
\vspace{-2.5cm}
\begin{center}
\begin{tabular}{l@{\hskip 0.5in}l@{\hskip 0.5in}l@{\hskip 0.35in}l}
\multicolumn{4}{c}{\large Estimands of the PAF for data with internal time-dependent exposure and competing risks}\\
\hline
\hline
\multicolumn{4}{c}{}\\
Estimand & Interpretation & Advantages & Disadvantages \\
&(see also Section 3)&&\\
\hline
\multicolumn{4}{c}{}\\
$PAF_{crude}$ & \% of observable attributable & Based on observable & Cannot capture time-varying\\
& death cases at & random variables & effects;\\
& the end of follow-up &&No causal interpretation\\
&&&\\
$PAF_o(t)$ & \% of observable attributable & Based on observable & No causal interpretation\\
& death cases until $t$ & random variables & \\
&&&\\
$PAF_c(t)$ &\% of preventable death cases & Most consistent & \\
& until $t$ & with initial definition & \\
&&&\\
$PAF_{LM}$&\% of preventable death cases & Accounts for time dynamic& Depends on choice of LMs\\
& within time window $h$ & target population; & and time window;\\
& had the exposure been prevented &Based on observable variables;& Does not result in a single number\\
&at the LM & Causal interpretation possible & \\
&&&\\
\hline
&&&\\
Estimator& R-function & Advantages & Disadvantages\\
&&&\\
\hline
&&&\\
$\widehat{\textrm{PAF}}_{crude}$ & \textit{glm} & Easily adjusted for& No adjustment for\\
&&(time-independent) covariates;& time-dependent covariates\\
&& Efficient&\\
&&&\\
$\widehat{\textrm{PAF}}_o(t)$ &\textit{etm} &Efficient;& No adjustment for\\
&&& time-dependent covariates\\
&&&\\
$\widehat{\textrm{PAF}}_c(t)$ &\textit{etm} (Unadjusted; &Adjustable for& Adjustment for time-dependent cov. \\
&No R-functions for & time-dependent cov.&computer intensive and elaborate;\\
&adjusted analysis)&using inverse probability weights& Biased results if prevalence is high;\\
&&& Strong assumptions needed\\
&&&\\
$\widehat{\textrm{PAF}}_{LM}$ &\textit{glm} &Easily adjusted for time-& Large sample size needed\\
&& dependent covariates&\\
\end{tabular}
\end{center}
\end{table}
\end{landscape}
\pagestyle{plain}
\section{Data example: Preventable death cases among ventilated patients in intensive care}
In this section, we estimate the health impact of ventilator-associated pneumonia (VAP) for patients in intensive care. To do so, the four estimands of the PAF are derived and compared for a sample of the large French database Rea-Raisin (R\'{e}seau d'Alerte, d'Investigation et de Surveillance des Infections Nosocomiales). The data was collected from 2004 to 2015. The data sample includes information on 79,347 invasive-mechanically ventilated patients from 188 ICUs. All of these patients were at least two days ventilated with a mean length of stay (LOS) from first ventilation to discharge (dead or alive) of 17 days and a median of 12 days. After 21 days two third of the initial patient population has left the ICU. The shortest follow-up time was three days and the longest 403 days. A VAP was acquired by 8,320 patients of whom 2,746 died. Of the 71,027 patients that remained VAP-free until the end of their ICU stay 22,203 patients died.
We estimate the PAF using the four discussed methods. For the landmark approach we use a time window of 14 days and landmarks daily from day 3 until day 70. Due to the definition of VAP,
day three is the first time point where a patient may die/be discharged with VAP. Moreover, only a small part of the ventilated patients stay in the ICU for more than 70 days.
The time window was chosen to be between the mean and the median LOS. The landmarks are such that enough events are observable in both patient groups (exposed and unexposed). The results are presented in Figure \ref{fig:ReaR_PAFs}.
The $\widehat{\textrm{PAF}}_{crude}$ was approximately 0.6\% which is the observable proportion of attributable cases due to VAP at the end of follow-up (after 403 days). The total number of attributable cases was 145. The $\widehat{\textrm{PAF}}_o(t)$ equals $\widehat{\textrm{PAF}}_{crude}$ at the end of follow-up. In contrast, $\widehat{PAF}_c(t)$ being interpretable as the proportion of preventable death cases was clearly larger with 2.22\% at the end of follow-up. This corresponds to a total number of 555 preventable ICU death cases.
Both, $\textrm{PAF}_o(t)$ and $\textrm{PAF}_c(t)$, describe how the proportion of attributable or respectively preventable cases accumulate over the course of time.
As already observed in the simulation study, $\widehat{PAF}_o(t)$ was negative in the first days. As commonly observed in data on patients in intensive care, the discharge hazard among uninfected patients is large in the beginning. Thus, the number of unexposed patients decreased quickly. The $\widehat{\textrm{PAF}}_c(t)$ was also negative in the first days but eventually converged to 0.022. As the infection hazard is low systematic censoring of infected patients does not affect the estimate $\widehat{\textrm{PAF}}_c(t)$ strongly.
The $\widehat{\textrm{PAF}}_{LM}$ (separate models) was close to zero from the first landmarks until landmark 40. Then, it increased strongly reaching a peak of 11.8\% at day 50. Thus, if VAP could've been prevented at day 50 for patients still in the ICU at that day, then 11.8\% of the death cases occurring within the next 14 days could've been prevented. This corresponds to a total number of 50 preventable ICU death cases among these patients. The $\textrm{PAF}_{LM}$ demonstrates at which time points the health impact of VAP is the strongest. In this example, the smoothed $\widehat{\textrm{PAF}}_{LM}$ leads to more efficient but less precise results. The data example demonstrates that the supermodel should be complemented by the separate models. It is a weighted average of the separate models with more weight on early landmarks with many observations.
A more detailed discussion on the supermodel and the separate models as well as alternative smoothing methods is discussed in \cite{vonCube2019lm}.
To account for potential differences between exposed and unexposed patients, we adjusted for the available baseline covariates age, gender and severity of illness score at first day of ventilation. The estimator $\widehat{\textrm{PAF}}_{LM}$ was adjusted as described in Section 4 assuming a common RR among different patient groups. Both $\widehat{\textrm{PAF}}_o(t)$ and $\widehat{\textrm{PAF}}_c(t)$ were adjusted using the weighted average based on a Cox proportional hazards model as described in \cite{coeurjolly2012attributable}. The results differed only slightly from the unadjusted analysis.
\begin{figure*}
\centering
\includegraphics[width=\textwidth]{ReaR_PAFsSwCI.png}
\caption{Four estimates ($\widehat{PAF}_{LM}$ (separate models and supermodel), $\widehat{PAF}_o(t)$, $\widehat{PAF}_c(t)$ and $\widehat{PAF}_{crude}$) of the PAF of ICU mortality due to VAP for a sample of the Rea-Raisin database.}
\label{fig:ReaR_PAFs}
\end{figure*}
\section{Discussion}
In this article, we provide a comprehensive investigation of the PAF for time-dependent exposures and competing outcomes. By reviewing existing literature on the PAF and evaluating a novel estimand, we defined, identified and estimated the PAF in four different ways. Based on a theoretical exploration and with a simulation study, we discussed the differences in interpretation of the estimands, the advantages, and disadvantages of each approach as well as the performance of the corresponding estimators. The four estimands were used to quantify the burden of VAP for ventilated patients in intensive care on a population level.
The PAF as initially proposed by Levin \cite{Levin1953PAF} defines the attributable risk due to an exposure and is -- after sufficient control for confounding -- interpretable as proportion of preventable cases. In contrast, if the exposure depends on time, the effect measures $\textrm{PAF}_{crude}$ and $\textrm{PAF}_o(t)$, which are defined with conditional probabilities based on observable random variables, have no such causal interpretation. Nevertheless, they indicate how many of the observed cases are explained by the exposure.
The $\textrm{PAF}_c(t)$ seems to be the more natural extension of the PAF to time-dependent exposures. It is defined with hypothetical probabilities and is -- after control for confounding -- interpretable as proportion of preventable cases if exposure was eliminated. However, $\textrm{PAF}_c(t)$ is based on unobservable variables complicating estimation. Moreover, it fails to describe the \textit{observable} accumulation of death cases. In contrast, the $\textrm{PAF}_{LM}$ can be interpreted as both the
population attributable risk and -- given sufficient adjustment for confounding and the Markov property -- the percentage of preventable cases.
In hospital-epidemiology, the commonly used estimand of the PAF due to an internal time-dependent exposure is $\textrm{PAF}_{crude}$. This estimand does not capture the temporal dynamics. The $\textrm{PAF}_o(t)$ is the time-dependent counterpart of $\textrm{PAF}_{crude}$. It is a more detailed description of how deaths accumulate over the course of time. At the end of follow-up in the absence of censoring $\textrm{PAF}_o(t)$ is equal to $\textrm{PAF}_{crude}$.
In a simulation study, we demonstrated that the estimands $\textrm{PAF}_o(t)$ and $\textrm{PAF}_{crude}$ can differ substantially from the causal estimand $\textrm{PAF}_c(t)$. However, under constant hazards both $\textrm{PAF}_o(t)$ and $\textrm{PAF}_c(t)$ converge to $\textrm{PAF}_{crude}$. In this specific data situation, the $\textrm{PAF}_{crude}$ can be interpreted causally as the proportion of preventable cases. The simulation study showed that due to the systematic censoring of exposed patients in the estimation procedure, estimators of $\textrm{PAF}_c(t)$ can be inaccurate if the prevalence of the exposure is high. If the exposure prevalence is rather low, as in our data example, the bias is negligible. Moreover, the difference between $\textrm{PAF}_c(t)$ and $\textrm{PAF}_o(t)$ is small in such data settings.
Interpretation of $\textrm{PAF}_{LM}$ is substantially different from that of the other estimands. Being based on patients still at risk at specific time points, the percentage of preventable death cases is in reference to a time-dependent subpopulation of the initial population. The subpopulations allow to differentiate between short stayers and long stayers that are due to their extended length of stay at higher risk of NI acquisition \cite{wolkewitz2017landmark}. In contrast, $\textrm{PAF}_o(t)$, $\textrm{PAF}_c(t)$ and $\textrm{PAF}_{crude}$ refer to the initial population.
While estimation of $\textrm{PAF}_{LM}$ and adjustment for (time-varying) confounding is straightforward, a clear drawback of this approach is the loss of precision due to the smaller sample size at the landmarks.
Finally, the choice of estimand depends on the intention of the study. To quantify the benefit of an intervention $\textrm{PAF}_c(t)$ and $\textrm{PAF}_{LM}$ are adequate measures. If the observable burden of an exposure on the population level is of main interest $\textrm{PAF}_o(t)$, $\textrm{PAF}_{crude}$ and $\textrm{PAF}_{LM}$ provide helpful insights. Decision on the estimand may be also data-driven. If the time of exposure is not available, only $\textrm{PAF}_{crude}$ can be estimated. If the no unmeasured confounding assumption is not reasonable, $\textrm{PAF}_o(t)$ and $\textrm{PAF}_{LM}$ are the preferred estimands.
We emphasize that care must be taken in the interpretation of the various estimands.
\subsection*{Acknowledgement}
The authors thank the 201 participating intensive care unit and infection control teams of the Rea-Raisin network. The Rea-Raisin network is supported by a grant from the French National Public Health Agency (Santé publique France).
\subsection*{Funding}
MvC and JFT were supported by the Innovative Medicines Initiative Joint Undertaking under grant agreement n [115737-2 – COMBACTE-MAGNET], resources of which are composed of financial contribution from the European Union's Seventh Framework Programme (FP7/2007-2013) and EFPIA companies; MW has received funding from the German Research Foundation (Deutsche Forschungsgemeinschaft) under grant no. WO 1746/1-2.
\subsection*{Potential conflicts of interest}
Conflicts of interest for all authors: none.
\subsection*{Data availability}
The R code of the simulation study is provided as ESM.
\subsection*{Abbreviations}
PAF: Population-attributable fraction\\
ICU: Intensive-care unit\\
NI: Nosocomial infection
{\footnotesize
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,377 |
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,351 |
\section{Introduction}
Software defects (bugs) that go undetected during the development process can cause software failure, resulting in financial and reputational harm to companies and a host of problems for users of buggy software. Developers often rely on static analysis tools to scan their codebases and find potential bugs. Despite their benefits, static analysis tools are not consistently used in many software projects \cite{Ayewah-MS2008}. Previous work has attributed their inconsistent usage to high false positive rates and ineffective presentation of warnings \cite{johnson-icse13}.
Developing any static analyzer is a non-trivial task due to the trade-off between precision and recall; it is challenging to report only correct bugs (precision) while covering all bugs with a similar pattern (coverage/recall). Balancing these two objectives manually is difficult and can result in analyzers with high false positive rate (low precision). Analyzers with high initial precision can also degrade in predictive performance as the nature of bugs changes over time. Continuously updating and maintaining static analyzers to handle concept drift can be costly \cite{bielik2017learning}.
Previous research has investigated various methods to improve static analysis false positive rates. In particular, researchers have explored eliminating bugs along infeasible paths using syntactic model-checking \cite{junker2012smt}; eliminating all the bugs that are similar to a false positive based on similarity of modification points \cite{muske2013review}; and using a two-staged error ranking strategy where false positive patterns are learned after manual labeling in the first stage \cite{shen-icst2011, Tripp-CCS2014}. Our work uniquely contributes to this line of prior work by leveraging state-of-the-art neural models to automatically refine the output of static analyzers.
Beyond traditional rule-based tools, there has been significant recent work leveraging machine learning for software bug and vulnerability detection in various languages, including C/C++ \cite{russell2018automated, li2018vuldeepecker}, Java \cite{pang2015predicting}, and JavaScript \cite{pradel-oopsla-2018}. However, much like rule-based analyzers, these machine learning models often suffer from low precision when applied in real world settings. Another challenge with some machine learning approaches is the need to develop new models to capture new types of vulnerabilities. Unlike this line of work, we do not use machine learning to detect bugs directly. Instead, we leverage machine learning to augment existing static analyzers. We believe this strategy yields the best of both worlds, where machine learning complements the capabilities of current static analyzers.
To augment static analyzers, we explored several models, including a feature based model and two neural models. Our feature-based model includes a set of carefully handcrafted features extracted from source code. Our neural models were inspired by the recent successes of transformer models in code search and document generation \cite{feng2020codebert} as well as code completion \cite{Svyatkovskiy-corr-2020}. One of our neural models learns from labeled data (DeepInferEnhance), while the other is applied in a zero-shot setting without the need for further training or finetuning (GPT-C \cite{Svyatkovskiy-corr-2020}). We conducted an experiment with all the models on bugs identified by Infer, an interprocedural static analyzer that detects bugs in Java, C++, and C\#. Our results show that we can improve the precision of Infer's analysis by up to 17\%.
\section{Related Work}
We describe the prior work on static analyzers and the use of machine learning for bug detection.
\subsection{Static Analysis-Based Bug Detection}
Rule-based systems and static analyzers have been widely adopted for detecting software bugs \cite{xu2010memory, viega2000its4, sonarqube, coverity}. However, one of the barriers to consistent usage of static analyzers is their high false positive rate \cite{johnson-icse13}. Previous work has explored various ways of reducing this false positive rate. For instance, Junker et al. \cite{junker2012smt} leveraged syntactic model-checking to eliminate infeasible paths (program slices). An implementation of their approach on Goanna, an static analyzer for C/C++ programs showed that they could exclude the majority of false positives. Muske, et al. \cite{muske2013review} implemented a partitioning mechanism to partition similar warnings based on the modified variables and modification points. A whole partition is then considered false positive once its leader is determined as false positive. Shen et al. \cite{shen-icst2011} developed EFindBugs, which uses a two-staged error ranking strategy to deal with the false positives issue in FindBugs \cite{Ayewah-oopsla2007}. EFindBugs first reports warnings on a sample program. Once the warnings are manually labeled, the tool learns what bug patterns to eliminate on the second run against the user application. Similarly, ALETHEIA learns users preferences from manual labeling on a smaller set \cite{Tripp-CCS2014}. Our work uniquely contributes to this line of prior work by exploring the use of state-of-the-art neural models to automatically refine the output of static analyzers by removing false positives.
\subsection{Learning-Based Bug Detection}
Beyond rule-based tools, there has been significant recent work on data-driven and machine learning approaches to detect software bugs and vulnerabilities. For instance, Russell et al. \cite{russell2018automated} proposed a machine learning method for detecting software vulnerabilities in C/C++ code bases. Similarly, Choi et al. \cite{choi-corr-2017} trained a memory neural network to detect a variety of buffer overruns in C-style code. Li et al. \cite{li2018vuldeepecker} trained a recurrent neural network (RNN) to detect two specific types of vulnerabilities related to improper use of library/API functions. Bugram \cite{wang2016bugram} leveraged n-gram language models to identify low probability token sequences in code as bugs. Pang et al. \cite{pang2015predicting} trained a machine learning model to predict static analyzer labels for Java source code. Finally, DeepBugs \cite{pradel-oopsla-2018} trained a classifier that distinguishes correct from incorrect code for three classes of bugs (swapped function arguments, wrong binary operator, and wrong operand in a binary operation) in JavaScript. However, the majority of machine learning solutions suffer from low precision when applied on real world settings. Another challenge with some machine learning approaches is the need to develop new models to capture new types of vulnerabilities. By leveraging machine learning to augment existing static analyzers, our work creates the best of both worlds, where machine learning will complement the capabilities of current static analyzers to generate more precise results.
\begin{figure}[h!]
\begin{minted}[fontsize=\footnotesize, linenos, firstnumber=8]{csharp}
static void Main(string[] args)
{
var returnNull = ReturnNull();
_ = returnNull.Value;
}
private static NullObj ReturnNull()
{
return null;
}
internal class NullObj
{
internal string Value { get; set; }
}
\end{minted}
\mintinline{vim}{/Examples/NullDeref/Program.cs:11}
\mintinline{vim}{error: NULL_DEREFERENCE} pointer 'returnNull' could be null and is dereferenced at line 11, column 13.
\caption{An example of a Null Dereference detected by Infer}
\label{fig:Infer_example}
\end{figure}
\section{Infer}
Our false positive reduction approach can work with any static analyzer for which labeled data is available. Our experiments specifically targeted Infer, an interprocedural static analyzer that is used to detect a variety of bugs in Java and C++. The recent release of Infer\# also added support for bug detection in C\# projects. Infer uses separation logic, a program logic for reasoning about memory manipulations, to prove certain memory safety conditions and create program state summaries for each method in a code base.
Infer's analysis examines multiple methods in order to identify bugs in code. When analyzing each method, Infer formulates pre- and post-conditions that describe the impact of the method on the memory state of the program. When analyzing a method invocation, Infer uses the conditions of the callee to form logical predicates for the caller. Thus, Infer analyzes the entire call stack of a program by composing logical predicates from all nested callee methods. Figure \ref{fig:Infer_example} shows an example of a null dereference bug identified by Infer.
\begin{figure*}[ht!]
\begin{minted}[fontsize=\footnotesize, linenos, firstnumber=136]{java}
private void dumpLog(File logFile, long startOffset, long endOffset, ArrayList<String> blobs) throws IOException {
Map<String, LogBlobStatus> blobIdToLogRecord = new HashMap<>();
final Timer.Context context = metrics.dumpLogTimeMs.time();
try {
dumpLog(logFile, startOffset, endOffset, blobs, blobIdToLogRecord);
long totalInConsistentBlobs = 0;
for (String blobId : blobIdToLogRecord.keySet()) {
LogBlobStatus logBlobStatus = blobIdToLogRecord.get(blobId);
if (!logBlobStatus.isConsistent) {
totalInConsistentBlobs++;
logger.error("Inconsistent blob " + blobId + " " + logBlobStatus);
}
\end{minted}
\mintinline{vim}{ambry-tools/src/main/java/com.github.ambry/store/DumpLogTool.java:144}
\mintinline{vim}{error: NULL_DEREFERENCE} object `logBlobStatus` last assigned on line 143 could be null and is dereferenced at line 144.
\caption{An example of a false positive warning from Infer. Infer warns that \mintinline{java}{logBlobStatus} can be null. This occurs if \mintinline{java}{blobId} is not a valid key of \mintinline{java}{blobIdToLogRecord}. The warning is incorrect, since \mintinline{java}{blobId} comes from \mintinline{java}{blobIdToLogRecord}'s key set.}
\label{figure:false_positive}
\end{figure*}
We decided to focus on Infer for three reasons. First, unlike the majority of common analyzers that only consider the context of a single method (i.e. intraprocedural), Infer's analysis is interprocedural and its context can stretch across several methods. Second, as opposed to many analyzers that rely on developer annotations to detect certain bugs, Infer's analysis is automated and does not rely on annotations. Finally, due to incremental change analysis, Infer can scale well on large production codebases.
Like other static analyzers, Infer is also prone to false positives. Figure \ref{figure:false_positive} shows an example, in which Infer reports that the variable \mintinline{java}{logBlobStatus} can be null, since it is assigned by calling \mintinline{java}{get()} on a map; if the key is not present in the map, \mintinline{java}{get()} will return null.
However, the key \mintinline{java}{blobId} comes from the \mintinline{java}{keySet} of the same map, meaning the value must exist in the map and \mintinline{java}{logBlobStatus} cannot be null. Infer is not able to recognize the coding convention of iterating over a map's key set and incorrectly triggers a null dereference warning. Language models, which are trained to identify patterns across a large corpus of code, can recognize such idioms. This motivated us to turn to machine learning to detect false positives reported by Infer. Indeed, our model identifies this specific warning as a false positive.
\section{False Positive Reduction}
False positive Infer warnings share common characteristics and follow patterns in coding conventions, as described in the example above. This motivated us to turn to machine learning as a means of capturing these patterns and identifying false positive warnings. We experimented with several models, including a feature-based model and two transformer-based neural models. Below, we present the data set we used for training and testing these models, as well as the details of each model.
\subsection{Data Collection}
Our data set consists of 539 \emph{null dereference} warnings generated by running Infer on seven Java repositories. Null dereference bugs occur when a pointer that can potentially be null is dereferenced. To create a diverse dataset, we chose several open source projects and two proprietary projects. The projects include back-end service components (\emph{Ambry}, \emph{Azure SDK}, and \emph{Nacos}), build plugins (\emph{Azure Maven Plugins}), and browser automation (\emph{Playwright}). Table \ref{table:repo-stats} summarizes the projects in our dataset, including the number of total warnings and true positives reported by vanilla Infer. Project A and Project B denote the proprietary projects.
\begin{table}[h!]
\centering
\caption{Summary statistics of null dereference warnings. Total warnings and true positives are as reported by vanilla Infer.}
\label{table:repo-stats}
\begin{tabular}{c c c c c}
\hline
Name & Lines of & Total & True & Precision \\
& Code & Warnings & Positives \\
\hline\hline
Project A & 35,527 & 57 & 47 & 82.4\% \\\hline
Project B & 66,346 & 33 & 30 & 90.9\% \\\hline
Ambry & 138,947 & 25 & 17 & 68.0\% \\\hline
Azure SDK & 3,555,286 & 343 & 272 & 79.3\% \\\hline
Playwright & 21,094 & 18 & 3 & 16.7\% \\\hline
Nacos & 62,443 & 37 & 13 & 35.1\% \\\hline
Azure Maven & 23,995 & 26 & 10 & 38.5\% \\
Plugins\\\hline
\textbf{Total} & \textbf{3,903,638} & \textbf{539} & \textbf{392} & \textbf{72.7\%}\\\hline
\end{tabular}
\end{table}
Each warning was investigated and labeled as valid (true positive) or invalid (false positive) by experienced developers. The need for manual labeling presents a bottleneck to scaling up to larger data sets. In the end, the developers identified 392 of the warnings as true positives (72.7\% precision) and 147 as false positives. Precision for individual repositories varied between 16\% to 90\%; the lower end of this range can correspond to poor experience for developers of those projects. There is significant opportunity for machine learning to benefit the experience by improving precision.
For each warning, we record the following information:
\begin{itemize}
\item the \emph{label}: whether the warning was legitimate or not
\item the \emph{location} of the warning: includes the file name and line number where the warning occurred
\item the \emph{code}: this is the code snippet on the line of warning
\item the error \emph{message}: the error message produced by Infer
\item the \emph{local context} around the warning: consists of all lines of code from beginning of the surrounding function to the line of the warning.
\item the \emph{non-local context}: includes the content of functions that were called in the current context.
\end{itemize}
\begin{figure*}[ht!]
\begin{minted}[fontsize=\footnotesize, linenos, firstnumber=461]{java}
Datacenter datacenterToAdd = hardwareLayout.findDatacenter(dataCenterName);
List<Disk> disksForReplicas =
allocateDisksForPartition(numberOfReplicasPerDatacenter, capacityOfReplicasInBytes, datacenterToAdd,
attemptNonRackAwareOnFailure);
partitionLayout.addNewReplicas((Partition) partitionId, disksForReplicas);
System.out.println("Added partition " + partitionId + " to datacenter " + dataCenterName);
\end{minted}
\rule{\textwidth}{0.4pt}
\begin{minted}[fontsize=\footnotesize, linenos, firstnumber=198]{java}
public Datacenter findDatacenter(String datacenterName) {
for (Datacenter datacenter : datacenters) {
if (datacenter.getName().compareToIgnoreCase(datacenterName) == 0) {
return datacenter;
}
}
return null;
}
\end{minted}
\mintinline{vim}{ambry-clustermap/src/main/java/com.github.ambry.clustermap/StaticClusterManager.java:463}
\mintinline{vim}{error: NULL_DEREFERENCE} object `datacenterToAdd' last assigned on line 461 could be null and is dereferenced by call to `allocateDisksForPartition(...)' at line 463.
\caption{An example of an interprocedural bug detected by Infer. Infer reports that \mintinline{java}{datacenterToAdd} (top, line 461) can be null. To determine if this is the case, an investigator must find the implementation of \mintinline{java}{findDataCenter()} (bottom), which is used to assign the value of \mintinline{java}{datacenterToAdd}. Since \mintinline{java}{findDataCenter()} explicitly contains the line \mintinline{java}{return null}, \mintinline{java}{datacenterToAdd} can be null and the warning is reasonable.}
\label{figure:nonlocal}
\end{figure*}
The \emph{non-local context} enables us to account for the interprocedural nature of Infer.
To obtain interprocedural information, we collect and use the content of certain methods invoked in the local context that can impact the value of the null pointer. For example, for some null dereference warnings, the null pointer originates as the return value of a method; we retrieve the body of this method as non-local context.
Figure \ref{figure:nonlocal} demonstrates the importance of non-local context. Infer reports that the variable \mintinline{java}{datacenterToAdd} assigned on line 461 (top) can be null. To investigate this, a developer must look into the \mintinline{java}{findDatacenter} method in a different file (bottom). Here, we can see that \mintinline{java}{findDatacenter} can return null on line 204 if none of the \mintinline{java}{datacenters} match the argument, meaning it is possible for \mintinline{java}{datacenterToAdd} to be null when it is dereferenced. Therefore, in order to determine whether this warning is correct, the content of the callee method (\mintinline{java}{findDatacenter}) is necessary. Although it is possible for a null pointer to originate from multiple nested method calls, we found that in most cases, collecting the immediate callee was sufficient.
\subsection{Feature-Based False Positive Reduction}
As a baseline, we extracted feature vectors from our data and trained a classifier to predict whether a warning is a false positive. Our features included:
\begin{itemize}
\item whether the non-local context explicitly contains the line \linebreak \mintinline{java}{return null;}. If this line exists in non-local context, then it is possible for the callee to return null, and the variable that holds the return value in the caller can be null.
\item whether a null-check method appears in the context of the warning. For some Infer warnings, the dereferenced variable is verified to be non-null earlier in the method using special null-check methods (e.g. \mintinline{java}{Objects.requireNonNull()}). Since these null-check methods belong to external libraries, Infer is unable to understand their behavior, resulting in false positive warnings.
\item whether a dereferenced variable is a class field. In practice, Infer's logic makes errors when tracking the state of class fields and often incorrectly treats them as nullable.
\item whether an implicit cast of a wrapper class to a primitive type occurs on the warning line. In our analysis, we realized that implicit casts can be the cause of many null pointer issues. For example, when the code includes a map object with primitive-type values (e.g. HashMap with double values), the map's values must instead be wrapper class objects (Double) instead of primitives (double), since maps in Java cannot take primitives. Values retrieved from the map are often stored in primitive-type variables, causing an implicit cast (see Figure \ref{fig:implicit_cast}). If the wrapper object is null, this cast operation causes a null dereference.
\end{itemize}
We trained a logistic regression classifier on these features. Since the limited size of our data prevents us from using a simple train-test split, we instead used 5-fold cross-validation for training and evaluation. In a realistic scenario, the model would not have access to training data from the same project for which it is making predictions. However, as shown in Table \ref{table:repo-stats}, the projects that comprise our dataset vary widely in the number of warnings, and attempting to separate repos across different folds would result in insufficient training data in several folds. To partially mitigate this issue, we ensure that all warnings from the same file appear in the same fold.
\begin{figure}[ht!]
\begin{minted}[fontsize=\footnotesize, linenos, ]{java}
HashMap<String, Double> m = new HashMap<String, Double>();
m.put("Bla", new Double(1.0));
//below line will cause an implicit cast operation
double v = m.get("Bla");
\end{minted}
\caption{Example of an implicit cast of a wrapper class (Double) to primitive type (double) in line 4. Calling \mintinline{java}{get()} on the map \mintinline{java}{m} returns a Double, which is implicitly cast to double to comply with the type of \mintinline{java}{v}.}
\label{fig:implicit_cast}
\end{figure}
\subsection{Neural False Positive Reduction}
Engineered features, while easy to understand, are inflexible and cannot automatically learn new patterns from data. Deep learning models, particularly transformers, are able to better capture the complexities of modern source code. Transformers are deep neural networks that leverage attention mechanisms to learn patterns in sequential data, such as language. They contain billions of parameters and can leverage massive datasets to learn representations of language patterns. They have achieved state-of-the-art results for applications in natural language processing (NLP) such as machine translation, question answering, and document summarization \cite{vaswani2017attention}. Transformers are usually pretrained on a large unlabeled corpus and further finetuned on task-specific labeled data to perform classification or language generation.
The wealth of open source code available on GitHub has inspired researchers to train a variety of transformers on open source code and finetune them to support many downstream tasks such as code completion\cite{Svyatkovskiy-corr-2020}, documentation generation\cite{feng2020codebert}, automated code review \cite{tufano2021autocodereview}, software traceability \cite{lin2021traceability}, and code search using natural language.
Two major categories of transformers are auto-generative models and auto-regressive models. Auto-generative models such as BERT \cite{bert} are trained to reproduce their inputs, while auto-regressive model produce the next token in the sequence. In this work, we leverage two transformers to help reduce Infer's false positive rate. The first model, DeepInferEnhance, is a customized version of CodeBERTa: an auto-generative encoder model similar to RoBERTa \cite{liu2019roberta}. The second model is GPT-C, an auto-regressive model with only decoder layers (similar to GPT-2 \cite{radford2019language} and GPT-3 \cite{gpt3}). Both models require only source code as input, rather than any intermediate code structure such as syntax trees or control flow graphs.
\subsubsection{DeepInferEnhance}
CodeBERTa is a pre-trained transformer based on the RoBERTa \cite{liu2019roberta} architecture and developed by HuggingFace \cite{wolf2020huggingfaces}. The model was pre-trained on CodeSearchNet \cite{husain2020codesearchnet}: a multilingual source code corpus of 2 million functions (with comments and docstrings) from GitHub. CodeSearchNet consists of functions from Go, Java, JavaScript, PHP, Python, and Ruby. CodeBERTa was inspired by the success of CodeBERT \cite{feng2020codebert}, an application of the BERT architecture to source code. CodeBERT was also trained on CodeSearchNet and yielded state-of-the-art results for tasks such as code search and documentation generation. Furthermore, CodeBERT's promising results in zero-shot settings showed the power of its representations.
We decided to use the more lightweight and efficient CodeBERTa architecture. However, we were interested in applying Infer to both Java and C\# code, and C\# was notably absent from CodeBERTa's training dataset. Therefore, we pretrained an identical CodeBERTa model on a corpus of 2 million Java and C\# functions that we collected from GitHub. Like the original CodeBERTa, our model is pretrained using a masked language modeling (MLM) objective.
Encoder-based transformers like CodeBERTa, which incorporate information from both sides of the current position, can learn to create efficient representations of their entire input. Through transfer learning, these representations can then be used to solve more specific tasks. We sought to transfer our pretrained model's learned representations to the task of identifying false positive Infer warnings. Therefore, we added a sequence classification head to this model in order to classify warnings as true positive or false positive. We finetuned the model on our dataset of Infer warnings by freezing all layers except for the classification head. The inputs for finetuning are strings of code context, and the labels are boolean indicators of valid or invalid warnings. Our final model consists of a 6-layer encoder and 2-layer classification head, with a total of 83 million parameters. We call this model \emph{DeepInferEnhance}.
\\\\
\subsubsection{GPT-C}
Unlike auto-generative models, which learn representations to reproduce their input, auto-regressive (generative) models learn to create new text. GPT-3 is one example of such a generative model \cite{gpt3}. Because of the scarcity of labeled Infer warnings for supervised learning, we turned to generative models and used code completion recommendations as a signal of the legitimacy of Infer warnings. Many null dereference warnings can be resolved - even if sub-optimally - by introducing a null check before the dereference. Similarly, many resource leak bugs can be fixed by explicitly releasing the leaked resource. If a generative model recommends a null check or resource release, this may indicate that the corresponding warning is indeed legitimate, since the model deemed that such a fix is necessary. Our intuition is that the model may have a fuzzy understanding that a null check or resource release is required.
To generate these code recommendations, we use GPT-C \cite{Svyatkovskiy-corr-2020}, a generative transformer based on the well-known GPT-2 \cite{radford2019language}. This model was designed and trained for code line completion and represents the state of the art in this field; it was implemented as part of the IntelliCode Compose web service. This model is also multilingual and was pretrained on C\#, Python, C++, Java, JavaScript, TypeScript, Go, PHP, Ruby, and C. GPT-C takes in a partially written method body and uses multi-headed self-attention to predict the next line. We use it in a zero-shot setting: unlike DeepInferEnhance, we do not train GPT-C ourselves, but instead rely on its pretrained parameters. We do not verify the syntactic correctness of the generated code, but rather use it as a "fuzzy" signal only to determine if a warning is valid or not. For null dereference warnings, if the model generates a null check statement at a line before a null pointer warning occurs, we consider that warning valid.
GPT-C is trained specifically for line completion, rather than whole line generation. This means that, rather than generating a full line of code from previous lines, GPT-C expects an incomplete line of code at the end of its input and generates code to complete this line. This incomplete trailing line is a \emph{prompt} and consists of several tokens at the beginning of the final line. For our objective of predicting Infer warning validity, we provide specific prompts to GPT-C for each warning type. For null dereferences, the input prompts are the prefixes of 7 different null check statements (e.g. \mintinline{java}{if} or \mintinline{java}{Debug.Assert}). For each prompt, we use GPT-C with beam search to generate line completion recommendations. With a beam size of 5, this results in 35 recommendations per warning. We also prepend non-local context to the input where possible. Figure \ref{figure:gptc_success} shows an example input.
\begin{figure*}[ht!]
\begin{minted}[fontsize=\footnotesize, linenos, firstnumber=201]{java}
for (Node dataNode : nodes) {
if (allocatedDisks.size() == numberOfReplicas) {
break;
}
Disk disk = dataNode.getDiskWithMostCapacity(replicaSize);
allocatedDisks.add(disk);
disk.freeCapacity = disk.freeCapacity - replicaSize;
\end{minted}
\rule{\textwidth}{0.4pt}
\begin{minted}[fontsize=\footnotesize]{java}
public Disk getDiskWithMostCapacity(long replicaSize) {
Disk minDisk = null;
for (Disk disk : disks) {
if ((minDisk == null || minDisk.freeCapacity < disk.freeCapacity) && disk.freeCapacity >= replicaSize) {
minDisk = disk;
}
}
return minDisk;
}
public static void Strategy3(Datacenter dc, List<Partition> partitions, int numberOfPartitions, int numberOfReplicas,
long replicaSize) {
for (int i = 0; i < numberOfPartitions; i++) {
List<Node> nodes = dc.nodes;
Collections.shuffle(nodes);
List<Disk> allocatedDisks = new ArrayList<Disk>();
for (Node dataNode : nodes) {
if (allocatedDisks.size() == numberOfReplicas) {
break;
}
Disk disk = dataNode.getDiskWithMostCapacity(replicaSize);
allocatedDisks.add(disk);
if (
\end{minted}
\caption{An example of a legitimate Infer warning (top) and the corresponding input to GPT-C (bottom). Infer reports that \mintinline{java}{disk}, which is assigned by \mintinline{java}{getDiskWithMostCapacity()} (bottom) can be null and is dereferenced on line 207. The GPT-C input is constructed by appending a prompt to the method body preceding this line, as well as prepending the non-local context method \mintinline{java}{getDiskWithMostCapacity()}. Here GPT-C correctly predicts a null check and therefore this warning is regarded as legitimate by the GPT-C based model.}
\label{figure:gptc_success}
\end{figure*}
Each Infer warning has an associated file path and line number that correspond to the method where the warning occurs; we call this the target method. For both transformer models, the input to the neural network includes the source code of the target method up to (but not including) the line of the warning. For GPT-C, we include two additional components: the non-local context method body preceding the target method and a line completion prompt immediately following the target method.
\break
\section{Experiments}
We performed two experiments to better understand how these models perform in a real-world setting. The first experiment, summarized in Table \ref{table:null_deref_results}, was focused on comparing effectiveness of our feature-based and neural models. The second experiment focused on verifying the generalizability of our neural approaches when applied to a different bug type. Since our objective is to eliminate false positives reported by Infer, our primary metric to evaluate our models is the relative precision improvement over vanilla Infer. We also measure recall with respect to Infer's true positive warnings: a recall of 100\% means that all of the true positive warnings from vanilla Infer were reported. By construction, none of the approaches in this work report new warnings beyond those originally reported by Infer.
\begin{table}[h!]
\centering
\caption{Performance of machine learning for removing false positive null dereference warnings}
\label{table:null_deref_results}
\begin{tabular}{c c c c c} \hline
Approach & Precision & $\Delta$ Precision & Recall \\
\hline\hline
Baseline & 72.7\% & - & 100\% \\\hline
Feature-Based & 78.7\% & +8.26\% & 65.1\% \\
DeepInferEnhance & 83.7\% & +15.13\% & 88.3\% \\
GPT-C & 85.4\% & +17.47\% & 83.7\% \\
\hline
\end{tabular}
\end{table}
\subsection{Experiment 1: Comparing feature-based and neural models}
\subsubsection{Feature-Based Model}
The simplest data-driven approach to identify false positive Infer warnings is to manually search for patterns in the warnings. The handcrafted features we collected for our logistic regression model capture the patterns that we discovered from manual review of our dataset. This feature-based model was able to improve Infer's precision by 8\%, but with significant reduction in recall. Since source code can be inherently complex, it is unsurprising that simple handcrafted features are insufficient to identify false positive warnings.
\subsubsection{DeepInferEnhance}
Since handcrafted features cannot adequately represent source code, we turned to deep learning to automatically learn patterns in code that indicate the legitimacy of Infer warnings. We took a traditional supervised transfer learning approach, using our dataset of labeled warnings to finetune our DeepInferEnhance model. The results show that this model greatly improved precision and recall compared to the feature-based model.
Transformers are generally finetuned on much larger datasets than the several hundred warnings we used. However, DeepInferEnhance was still able to learn patterns that provided a significant improvement in precision. One such pattern occurs when \mintinline{java}{null} is explicitly passed as an argument to a method. Even if the method handles null arguments, Infer still reports a null dereference warning, which is often a false positive. DeepInferEnhance is able to learn this pattern purely from the code itself.
\begin{figure*}[h]
\begin{minted}[fontsize=\footnotesize, linenos, firstnumber=17]{java}
public class DefaultAzureMessageHandler implements AzureMessageHandler {
@Nullable
private InvocableHandlerMethod handlerMethod;
private Class<?> messagePayloadType;
private String createMessagingErrorMessage(String description) {
InvocableHandlerMethod handlerMethod = getHandlerMethod();
StringBuilder sb =
new StringBuilder(description).append("\n").append("Endpoint handler details:\n").append("Method [")
.append(handlerMethod.getMethod()).append("]\n").append("Bean [")
.append(handlerMethod.getBean()).append("]\n");
return sb.toString();
}
\end{minted}
\rule{\textwidth}{0.4pt}
\begin{minted}[fontsize=\footnotesize, linenos, firstnumber=56]{java}
public InvocableHandlerMethod getHandlerMethod() {
return handlerMethod;
}
\end{minted}
\caption{An example of an Infer warning where non-local context does not provide enough information about the value of a class field. Infer warns that \mintinline{java}{handlerMethod} can be null (top). \mintinline{java}{getHandlerMethod()} simply returns the \mintinline{java}{handlerMethod} class field (bottom). But this is not enough to determine the legitimacy of this warning.}
\label{figure:class_field_ex}
\end{figure*}
\subsubsection{GPT-C}
DeepInferEnhance is able to boost vanilla Infer's precision, but requires labeled data. Since this data is expensive to collect, we sought a solution that could forego supervised learning altogether. Transformer models such as CodeBERT have shown promising performance in zero-shot settings for source code. Our approach is novel due to our interpretation of code completion recommendations by self-supervised generative models: recommendations for null checks are a signal that the null dereference warning is legitimate. With this approach, GPT-C had the highest precision of our models, improving on Infer by relative 17.5\%, with slightly lower recall than DeepInferEnhance.
While analyzing the results from GPT-C, we identified several patterns in the warnings that GPT-C predicts incorrectly. These patterns included:
\textbf{Insufficient or nonexistent non-local context} Our investigation revealed that when non-local context is unavailable or contains insufficient information, GPT-C does not perform well. For example, method calls belonging to an interface type cannot be resolved until runtime. Therefore, we cannot retrieve such methods as non-local context.
Similarly, non-local context can include getter methods that return a class field; however, these methods do not provide any information about the value the class field may hold. In the example in Figure \ref{figure:class_field_ex}, Infer warns that \mintinline{java}{handlerMethod}, which is assigned using \mintinline{java}{getHandlerMethod()}, can be null. \mintinline{java}{getHandlerMethod()} (middle) simply returns the \mintinline{java}{handlerMethod} class field (bottom). In order to correctly determine if the local variable \mintinline{java}{handlerMethod} can be null, we would need to collect not only the bodies of the methods \mintinline{java}{getHandlerMethod()} and \mintinline{java}{createMessagingErrorMessage()}, but also the constructors and fields of \mintinline{java}{DefaultAzureMessageHandler}.
\textbf{No reference to the target object} Null dereference warnings generally fall into two categories with respect to the target pointer. For some warnings, the null pointer is represented by a variable in the source code; for other warnings, the pointer is returned from a method with no explicit variable to hold its value. The latter case presents a problem for GPT-C recommendations: the nullable pointer has no reference in the code before the line where the warning occurs, which is not included in the input to the model. Therefore, this pointer does not appear in the input to GPT-C, reducing the chance that GPT-C recommends a null-check.
\textbf{Excessive sensitivity to the input} Several Infer warnings in a single project can refer to similar code, often with the same target variable or method. In such cases, if the instances are truly similar and legitimate, all of the instances should be reported as bugs to the end user. However, because GPT-C is very sensitive to minor differences in the input sequence, it may report only a subset of the warnings as legitimate. To enforce consistency, we group together warnings with the same target variable and label them all according to a logical OR, where all warnings are predicted as legitimate if GPT-C predicts any warning in the group as legitimate. The results in Table \ref{table:null_deref_results} include this consistency postprocessing. Alternatively, warnings could be grouped according to code similarity metrics such as edit distance.
\subsubsection{Overall Result}
DeepInferEnhance and GPT-C offer a tradeoff. Our objective is to increase precision, for which GPT-C is best. However, DeepInferEnhance has significantly better recall, capturing 88\% of legitimate bugs while still providing a 15\% boost in precision over vanilla Infer. Because of its superior recall, we would be more likely to recommend DeepInferEnhance to developers who value coverage in addition to precision. However, this model requires finetuning, whereas GPT-C offers the best precision and moderate recall without the need for additional data or further training.
\subsection{Experiment 2: Verifying the generalizability of neural approaches}\
To verify the generalizability of our neural approaches beyond the \emph{null pointer} bug, we evaluated our GPT-C model on Infer's \emph{resource leak} warnings. A resource leak happens when a program does not release resources it has acquired. The below code snippet shows an example of a resource leak warning, where an exception in \mintinline{java}{f.write(7)} will cause the program to skip the \mintinline{java}{f.close()} statement and leak the stream resource.
\begin{minted}[fontsize=\footnotesize, linenos, firstnumber=56]{java}
public static void foo () throws IOException {
FileOutputStream f = new FileOutputStream(new File("w"));
f.write(7); //an exception here will cause a leak
f.close();
}
\end{minted}
In our target Java projects, Infer detected a total of 108 resource leak warnings. Table \ref{table:rl-repo-stats} shows the summary statistics of the identified resource leaks (Infer did not detect any resource leaks in Ambry).
\begin{table}[h!]
\centering
\caption{Summary statistics of resource leak warnings.Total warnings and true positives are as reported by vanillaInfer.}
\label{table:rl-repo-stats}
\begin{tabular}{c c c c c} \hline
Name & Lines of & Total & True & Precision\\
& Code & Warnings & Positives \\
\hline\hline
Project A & 35,527 & 6 & 2 & 33.3\% \\\hline
Project B & 66,346 & 49 & 33 & 67.3\% \\\hline
Azure SDK & 3,555,286 & 33 & 16 & 48.5\% \\\hline
Playwright & 21,094 & 2 & 2 & 100 \% \\\hline
Nacos & 62,443 & 7 & 2 & 28.6\% \\\hline
Azure Maven & 23,995 & 11 & 7 & 63.6\% \\
Plugins\\\hline
\textbf{Total} & \textbf{3,764,691} & \textbf{108} & \textbf{62} & \textbf{57.4\%} \\\hline
\end{tabular}
\end{table}
Since this data set was not large enough to meaningfully finetune DeepInferEnhance, we decided to only focus on our GPT-C model, where no further training or finetuning is required. We only had to adjust our prompting logic. For resource leaks, we use prefixes (first three characters) of the method names \mintinline{java}{close()} and \mintinline{java}{release()} as the prompts. If the leaked resource is assigned to a variable, we also use this variable name as a prompt. Table \ref{table:rl_results} shows the results of using GPT-C to remove false positives in resource leak warnings.
As shown in the table, GPT-C can improve Infer's precision by 5.5\%. However, it fails to identify over a third of legitimate bugs. One pattern in the missed bugs is that some leaked resources have names or types, such as \mintinline{java}{EntityNotFoundHttpResponse} or \mintinline{java}{ChangeFeedProcessorBuilderImpl}, that do not clearly indicate that they are in fact resources, and therefore should be released. Types that clearly indicate resources, such as those that contain \mintinline{java}{File} or \mintinline{java}{Stream} in the name, are recognized more often by GPT-C.
\begin{table}[h!]
\centering
\caption{Performance of machine learning for removing false positive resource leak warnings}
\label{table:rl_results}
\begin{tabular}{c c c c c} \hline
Approach & Precision & $\Delta$ Precision & Recall \\
\hline\hline
GPT-C & 60.6\% & 5.56\% & 64.5\% \\
\hline
\end{tabular}
\end{table}
\section{Discussion}
Our GPT-C model improved Infer's precision by 17.5\% for \emph{null dereferences} and by 5.5\% for \emph{resource leaks}. However, it missed some of the correct warnings that Infer detected, with a recall of 84\% for \emph{null dereferences} and 65\% for \emph{resource leaks}. We identified several patterns of false negative predictions, which resulted in the reduced recall. One pattern occurred when the non-local context was a class field getter method. These methods are often a single return statement, which is not sufficient information for GPT-C to make the correct prediction. One way to mitigate this problem could be to include class fields and constructors as part of non-local context. However, the current GPT-C model is only trained for line completion using single method bodies. Newer transformer models for code, which use supplementary context in addition to individual method bodies, can better leverage this context to create more complete representations of the program state. Therefore, future work should explore training an extended-context model for code completion, as an evolution of the GPT-C model we used. We expect that such a model would perform better in many downstream tasks, including for verifying true positive warning from static analyzers.
Another class of warnings for which GPT-C did not perform well were chained method calls (e.g. \mintinline{java}{foo.bar().baz()}). If a warning is triggered on a method call in the middle of a chain, GPT-C cannot reasonably predict a null check. Since the intermediate method call is not stored in a variable, we cannot prompt GPT-C to predict a null check for the return value of that method call. One way to mitigate this problem is to modify the source code to insert a variable assignment for each method call in the chain. However, a developer would only break the method chain for a null check where necessary. Therefore, breaking the chain may create an abnormal code pattern that GPT-C will not recognize. Alternatively, the variable assignment could be inserted for only one method in the chain. For each method call in the chain, we could insert an assignment, generate recommendations using GPT-C, and select the recommendation with the highest confidence. However, we decided on a much simpler approach to mitigate chained method calls: simply trust Infer's decision and predict such warnings as legitimate bugs.
For any bug detection system, precision and recall have significantly different downstream impacts for developers. Low precision means that developers waste time analyzing many false positive warnings, while low recall means that some legitimate bugs are not identified. Static analyzers have typically favored coverage and recall over precision, with the objective of maximizing the number of reported legitimate bugs. However, in practice, low precision reduces developer adoption of analysis tools \cite{johnson-icse13} due to the time developers waste on investigating false positives. Prior work has found that developers mostly use analysis tools in their spare time and tend to fix warnings in short working sessions. Therefore, they are primarily driven by time constraints when addressing bugs identified by static analyzers \cite{quangdo2020developerneeds}. As a result, we chose to focus on precision rather than recall; we believe presenting developers with higher quality warnings will lead to bugs actually being addressed, rather than ignored due to a lack of confidence or time constraints. However in certain cases, where recall is more important, our models can be used to re-rank the warnings so that developers are presented with more true positives first. This allows us to present all warnings to developers while prioritizing likely legitimate bugs.
We demonstrated the effectiveness of transformer models for two bug types and one tool, but we believe this approach should generalize to other languages and tools. Our experiment on resource leaks provides evidence of this. In addition, our GPT-C approach is not tied to a particular programming language, static analyzer, or warning type. Because we use GPT-C in a zero-shot setting, no further training is required. Customization may instead be required through unique ways of prompting GPT-C and specific signals to seek in its outputs; adjusting prompts should be the only change necessary to apply GPT-C to new bug types. For example, one way to apply this technique to buffer overflow bugs in C/C++ could be to search for bounds checking recommendations. Even DeepInferEnhance, which requires labeled data for finetuning, can be expanded to additional programming languages by pretraining on a larger and more diverse corpus.
In this work we applied large-scale transformers to further verify bugs that have already been localized by static analyzers. While this means that our approach will not find bugs beyond those reported by the static analyzers, it is a cost-effective way to leverage transformers for this problem. Large-scale transformer models are expensive to train and evaluate, and using them to scan every method or every line of a project can be prohibitively expensive. By applying these models to resolve warnings that have already been localized by a static analyzer, we ensure that transformers are utilized in a cost-effective way. However, there may be other ways to localize bugs and use transformers. For example, one can leverage prior work on bug localization to determine buggy files \cite{wang2016icse} and only examine those files as opposed to the entire program.
\subsection{Threats to Validity}
\subsubsection{Dataset Size}
Static analysis warnings are time-intensive to triage, since each warning requires a detailed review of the source code involved in the warning. It is expensive to collect a large dataset of labeled warnings, which is preferred when training transformer models. This is particularly impactful for DeepInferEnhance, which requires labeled data for both finetuning and evaluation. Although we used cross validation to compensate for the limited dataset size, all of our approaches would benefit from a larger dataset. In order to scale the dataset, we must present warnings to project owners for review. Through developer engagements, we found that this raises a cold-start problem: in order to receive appropriate attention and high-quality feedback, warnings must have sufficiently high precision, or else developers may not engage with warnings shared for labeling purposes. We believe that the precision improvements of the approaches discussed here serve as a solution to this cold-start problem, and will allow us to share warnings with a wider set of projects to scale our dataset.
\subsubsection{Evidence of Generalizability}
Our approach of using machine learning to augment and complement static analysis is designed generically to benefit any analyzer. However, in this study, we focus on one analyzer (Infer) and two categories of bugs (null dereference and resource leak) for one language (Java). To gain wider adoption among developers of diverse projects, our approach must demonstrate benefits across additional languages and bug types. Our experiments with resource leaks are our first attempt to demonstrate this. We plan to apply and evaluate our approach to C\#, as well as additional languages, as the next step for expanding our approach.
\subsection{Data Release}
Our dataset consists of warnings from Infer for various open source and proprietary software projects. Source code from proprietary projects was made available to us solely for research purposes. Since we do not own this data, we cannot release it publicly. We intend to release data from open source projects after we have worked with each project owner to resolve the issues, or otherwise verify with the owners the safety of releasing bug or vulnerability data.
\section{Conclusion}
Rule-based bug detectors and static analyzers have been widely adopted for detecting security vulnerabilities, functional bugs, and even performance issues. However, building an analyzer is non-trivial because of the difficulty of balancing precision and coverage: reporting only correct bugs and ensuring that all similar bugs are reported.
The majority of existing analyzers favor higher coverage to ensure completeness, and therefore they produce more false positive warnings. However, frequent false positive warnings are one of the main barriers to wider adoption of static analyzers in the software industry; this problem cannot be solved by the analyzers themselves. To close this gap, we augmented static analyzers with a variety of machine learning models. We experimented with both feature-based and neural models for false positive reduction. Our experiments on Infer, a well-known interprocedural static analyzer, showed that leveraging GPT-C in a zero-shot setting can improve the precision of null pointer warnings by 17.5\% and resource leak warnings by 6\%.
One immediate direction for future work is to experiment with more warning types and languages to further verify the generalizability of our approach. Another direction involves training transformers with broader context. For instance, one may include the imports, constructors, class fields, and superclasses (in cases of inheritance) as part of the context while training. We expect this broader context to increase transformer effectiveness in general, and especially in zero-shot settings to augment other code analyzers. A third direction is to explore whether a generative transformer similar to GPT-C can be used in conjunction with a static analyzer to suggest fixes for some or all the bugs.
\bibliographystyle{ACM-Reference-Format}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,731 |
Brent Rydin
Brent A. Rydin, 35
Brent A. Rydin of Natick and formerly of Avon, Conn. died April 12 in a tragic fire. He was 35 and was the beloved husband of Julia Harty Rydin and son of Craig and Linda Labnon Rydin of Avon.
Born in Arlington Heights, Ill., Brent grew up primarily in Connecticut, living in Trumbull before moving to Avon. A playful and precocious child, he graduated from the Kingswood Oxford School in West Hartford where he competed in tennis and swimming, and readily began friendships that lasted throughout his lamentably short life. He was a graduate of Trinity College in Hartford, where his stage triumph was the title role in Macbeth.
He was a remarkably gifted writer and a passionate reader, and was nearing completion of a master's degree in creative writing from Emerson College with the goal of teaching creative writing in addition to his own novelistic projects. He connected easily with just about everyone on just about every topic and was eager to share his seemingly limitless knowledge.
Introduced to Martha's Vineyard in early childhood, he spent every happy summer of his life there and served as a counselor at Camp Jabberwocky, the oldest summer camp in America for people with disabilities. Julia quickly introduced him to Ocean City N.J., where the beach-and-boardwalk life delighted him and his notorious sweet tooth was easily satisfied. Christmases with relatives in the White Mountains were special family time and allowed Brent to develop strong ties to grandparents, aunts, uncles and cousins there.
He enjoyed being outdoors and especially loved the Berkshires, where he and Julia lived and formed the love of their lives. They were married on Feb. 26 of this year.
Blessed with a smile that lit up any room and a contagious laugh, Brent was gentle, patient and unconditionally kind, with a gift for ensuring those close to him always felt his loyalty, love and support. The writer in him listened very carefully, taking in not just what people said but why and how they said it. His ambition was not just to be a great writer but to be a great person.
Tragic barely describes his unexpected, painful and premature loss.
In addition to his wife and parents, Brent is survived by his grandmother, Lorraine Rydin of Berlin, N.H. and godparents Holly and Ed Rene of Rochester, N.H. In addition, he leaves uncles and aunts Randy and Kim Labnon, Scott and Paula Labnon, Lori and Mike Morin, Gary and Kathy Rydin, and John and Linda D. Rydin, along with 15 cousins. Brent was also loved deeply by his parents in law Cate and Stephen Harty, their daughters Caroline, Lily and Alice, and the extended Harty family. A devoted pet dad, he would want his beloved Juno and Kalina mentioned as well.
A mass of Christian burial was held at the Church of Saint Ann in Avon, Conn. He was interred at Elmwood Cemetery in Great Barrington.
Donations can be made to Motley Mutts Rescue in Hooksett, N.H. or the Aquinnah Cultural Center on the Vineyard.
Arrangements are under the care of the Carmon Funeral Home & Family Center in Avon. To leave condolences online, please visit www.carmonfuneralhome.com. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,039 |
The Pennsylvania Film Production Tax Credit is a tax credit program supporting the production of feature films and television programs in Pennsylvania. The tax credit was signed into law by Gov. Ed Rendell in July 2004.
The tax credit for qualifying productions equals a 25% reduction in Personal Income Tax, Corporate Net Income, Capital Stock/Foreign Franchise Tax. However, because most productions filming in Pennsylvania do not incur a tax liability in the state, the credits are fully transferable, which means they can be sold to a company or individual in the state who does have a tax liability. In order to qualify for the tax credit, the production must incur 60% of its total production expenses within Pennsylvania. The credit also applies to individual television shows that are 15 minutes or longer and intended for a national audience.
Watchdogs, including the Pennsylvania Common Cause criticized lobbyist Leslie McCombs for failing to properly register as a lobbyist for Lions Gate Entertainment while lobbying on behalf of the tax credit.
A 2009 report from the Legislative Budget and Finance Committee in the Pennsylvania General Assembly found that the tax credit supported 4,000 jobs and produced $4.5 million between 2007 and 2008.
During the 2009 Pennsylvania budget impasse, the tax credit was in danger of being repealed. Instead, its total amount was reduced from $75 million to $42 million, with that number increasing to $60 million the next year. The tax credit was expanded again during the state budget negotiations in summer 2016. $65 million will be available for fiscal year 2017-18.
The tax credit brought the production of Zack and Miri Make a Porno, The Road, Shelter, Shannon's Rainbow, Sorority Row, and She's Out of My League to the Pittsburgh region in 2008 and 2009. The majority of filming for I Am Number Four also took place in the greater Pittsburgh area in 2010 due to the tax credit.
See also
Greater Philadelphia Film Office
Pittsburgh Film Office
References
Taxation in Pennsylvania
Tax credits
Cinema of Pennsylvania | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,140 |
Agrilus goldsteini é uma espécie de inseto do género Agrilus, família Buprestidae, ordem Coleoptera.
Foi descrita cientificamente por Curletti, 2010.
Referências
goldsteini | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,922 |
\section*{This is an unnumbered first-level section head}
This is an example of an unnumbered first-level heading.
\specialsection*{THIS IS A SPECIAL SECTION HEAD}
This is an example of a special section head%
\footnote{Here is an example of a footnote. Notice that this footnote
text is running on so that it can stand as an example of how a footnote
with separate paragraphs should be written.
\par
And here is the beginning of the second paragraph.}%
.
\end{comment}
\textbf{Key words.} Monge-Amp\`{e}re, two-scale method, monotone, continuous dependence, error estimates, classical and viscosity solutions, degenerate.
\vspace{0.2cm}
\textbf{AMS subject classifications.} 65N30, 65N15, 65N12, 65N06, 35J96
\section{Introduction}
We consider the Monge-Amp\`ere equation with Dirichlet boundary condition
\begin{equation} \label{E:MA}
\left\{
\begin{aligned}
\det{D^2u}&=f & {\rm in} \ &\Omega \subset \mathbb {R}^d,
\\ u &=g & {\rm on} \ &\partial \Omega,
\end{aligned}
\right.
\end{equation}
where $f \geq 0$ is uniformly continuous, $\Omega$ is a uniformly
convex domain and $g$ is a continuous function. We seek a
\textit{convex} solution $u$ of \eqref{E:MA}, which is critical for \eqref{E:MA} to be elliptic and
have a unique viscosity solution \cite{Gut}.
The Monge-Amp\`ere equation has a wide spectrum of applications, which has led to an increasing interest
in the investigation of efficient numerical methods. There are several existing methods for
the Monge-Amp\`ere equation, as described in \cite{NoNtZh}. Error estimates in $H^1(\Omega)$ are
established in \cite{BrenNeil, BrenNeil2} for solutions with $H^3(\Omega)$ regularity or more.
Awanou \cite{Aw} also proved a linear rate of convergence for classical
solutions for the wide-stencil method, when applied to a perturbed
Monge-Amp\`ere equation with an extra lower order term $\delta u$;
the parameter $\delta > 0$ is independent of the mesh and appears in
reciprocal form in the rate.
On the other hand, Nochetto and Zhang followed an
approach based on the discrete Alexandroff estimate developed
in \cite{NoZh} and established pointwise error estimates in
\cite{NoZh2} for the method of Oliker and Prussner \cite{OlPr}.
In this paper we follow a similar approach and derive
pointwise rates of convergence for classical solutions of \eqref{E:MA} that have
H\"older or Sobolev regularity and for viscosity
solutions with bounded Hessians which may be piecewise smooth or
degenerate.
It is worth mentioning a rather strong connection between the
semi-Lagrangian method of Feng and Jensen \cite{FeJe:16} and our
two-scale approach introduced in \cite{NoNtZh}. In fact, for an appropriate choice of discretization of symmetric positive semidefinite matrices with trace one, discussed in \cite{FeJe:16} along with the implementation, one can show that the discrete solutions of both methods coincide. Therefore, the error estimates in this paper extend to the fully discrete method of \cite{FeJe:16}. This rather surprising equivalence property is fully derived in a forthcoming paper, along with optimal error estimates in special cases via enhanced techniques for pointwise error analysis.
\subsection{Our contribution}
The two-scale method was introduced in \cite{NoNtZh} and hinges on the following
formula for the determinant of the semi-positive Hessian $D^2w$ of a smooth
function $w$, first suggested by Froese and Oberman \cite{FrOb1}:
%
\begin{equation}\label{E:Det}
\det{D^2w}(x) = \min\limits_{(v_1,\ldots,v_d) \in \mathbb{S}^{\perp}} \prod_{j=1}^d v_j^TD^2w(x) \ v_j ,
\end{equation}
where $\mathbb{S}^{\perp}$ is the set of all $d-$orthonormal bases in $\mathbb{R}^d$.
To discretize this expression, we impose our discrete
solutions to lie on a space of
continuous piecewise linear functions over an unstructured quasi-uniform
mesh $\mathcal{T}_h$ of size $h$; this defines the fine scale. The
mesh also defines the computational domain $\Omega_h$, which
we describe in more detail in \Cref{S:KeyProperties}. The
coarser scale $\delta$ corresponds to the length of
directions used to approximate
the directional derivatives that appear in \eqref{E:Det}, namely
\[
\sdd w (x;v) := \frac{ w(x+\delta v) -2w(x) +w(x-\delta v) }{ \delta^2}
\quad
\text{and}
\quad
|v| = 1 ,
\]
%
for any $w\in C^0(\overline{\Omega})$;
To render the method practical, we introduce a discretization
$\mathbb{S}^{\perp}_{\theta}$ of the set $\mathbb{S}^{\perp}$ governed by the
parameter $\theta$ and denote our discrete solution by $u_{\varepsilon}$,
where $\varepsilon = (h,\delta, \theta)$ represents the scales of the method
and the parameter $\theta$. We define the discrete Monge-Amp\`{e}re operator to be
%
$$
T_{\varepsilon}[u_{\varepsilon}](x_i):=\min\limits_{\mathbf{v} \in \mathbb{S}^{\perp}_{\theta}} \left( \prod_{j=1}^d \sddp u_{\varepsilon}(x_i;v_j) - \sum_{j=1}^d \sddm u_{\varepsilon} (x_i;v_j) \right) ,
$$
where $\nabla_\delta^{2,\pm}$ are the positive and negative
parts of $\nabla_\delta^2$.
In \Cref{S:KeyProperties} we review briefly the role of each term in
the operator $T_{\varepsilon}$ and recall some key properties
of $T_{\varepsilon}$.
The merit of this definition of $T_{\varepsilon}$ is that it
leads to a clear separation of scales, which is a key theoretical advantage
over the original wide stencil method of \cite{FrOb1}. This also
yields continuous dependence of discrete solutions on data, namely
\Cref{P:ContDep}, which allows us to prove
rates of convergence in $L^{\infty}(\Omega)$ for our method
depending on the regularity of $u$;
this is not clear for the wide stencil method of \cite{FrOb1}.
Moreover, the two-scale method is formulated over
unstructured meshes $\mathcal{T}_h$, which adds flexibility to
partition arbitrary uniformly convex domains $\Omega$.
This is achieved at the expense of points
$x_i\pm\delta v_j$ no longer being nodes of $\mathcal{T}_h$, which is
responsible for an additional interpolation error in the
consistency estimate of $T_\varepsilon$. To locate such points and
evaluate $\sdd u_{\varepsilon}(x_i;v_j)$, we resort to fast search techniques
within \cite{WalkerPaper,WalkerWeb} and thus render the
two-scale method practical.
Compared with the error analysis of the Oliker-Prussner method
\cite{NoZh}, we do not require $\mathcal{T}_h$ to be cartesian.
In \cite{NoNtZh} we prove existence and uniqueness of a discrete solution
for our method, and convergence to the viscosity solution of
\eqref{E:MA}, without regularity beyond uniform continuity of $f$ and $g$. This entails dealing with the $L^\infty-$norm and using the discrete comparison principle for piecewise linear functions (monotonicity). Within this $L^\infty$ framework and under the regularity requirement $u \in W^2_\infty(\Omega)$, we now prove rates of convergence for classical solutions with either
H\"older or Sobolev regularity and for a special class of viscosity solutions. Therefore, our two-scale method \cite{NoNtZh} and the Oliker-Prussner method \cite{OlPr,NoZh2} are the only schemes known to us to converge to the viscosity solution and have provable rates of convergence.
The first important tool for proving pointwise rates of convergence is the
discrete Alexandroff estimate introduced in \cite{NoZh}:
if $w_h$ is an arbitrary continuous piecewise linear function,
$w_h\ge0$ on $\partial\Omega_h$, and
$\Gamma w_h$ stands for its convex envelope, then
%
\begin{equation*}
\max\limits_{ x_i \in \mathcal{N}_h } w_h^-(x_i) \leq C \left( \sum\limits_{x_i \in C_{-}(w_h)} \left| \partial \Gamma w_h (x_i) \right| \right)^{1/d}
\end{equation*}
%
where $\partial \Gamma w_h$ is the subdifferential of $\Gamma w_h$ and
$C_{-}(w_h)$ represents the lower contact set of $w_h$, i.e. the set
of interior nodes $x_i\in\mathcal{N}_h^0$ such that $\Gamma w_h(x_i)=w_h(x_i)$;
hereafter we write $w_h^-(x_i) := - \min\{w_h(x_i),0\}$.
%
To control the measure of the subdifferential at each node, we show the following estimate
$$
|\partial w_h(x_i)| \leq \delta^d \min\limits_{(v_1,\ldots,v_d)\in \mathbb{S}^{\perp}}
\prod_{j=1}^d \sdd w_h(x_i;v_j)
\quad\forall \, x_i\in\mathcal{N}_h^0,
$$
%
such that the ball centered
at $x_i$ and of radius $\delta$ is contained in $\Omega_h$.
Combining both estimates, we derive the following continuous dependence estimate
$$
\max_{\Omega_h} \, (u_h-w_h)^- \leq C \delta
\left( \sum\limits_{x_i \in C_{-}(u_h-w_h)} \left( T_\varepsilon[u_h](x_i)^{1/d}-T_\varepsilon[w_h](x_i)^{1/d} \right)^d \right)^{1/d}
$$
%
for all continuous piecewise linear functions $u_h$ and $w_h$ such
that $T_\varepsilon[u_h](x_i)\ge0$ and $T_\varepsilon[w_h](x_i)\ge 0$ for all $x_i\in\mathcal{N}_h^0$.
This result is instrumental and, combined with operator consistency and a
discrete barrier argument close to the boundary, eventually leads to
the following pointwise error estimates
%
$$
\|u_{\varepsilon}-u\|_{L^\infty(\Omega_h)} \leq C(d, \Omega,f,u) \ h^{\frac{\alpha+k}{\alpha+k+2}}
$$
%
provided $u\in C^{2+k,\alpha}(\overline{\Omega})$ with $0<\alpha\le1$
and $k=0,1$, as well as
%
\[
\|u_{\varepsilon}-u\|_{L^\infty(\Omega_h)} \leq C(d, \Omega,f,u) \ h^{1-\frac{2}{s}}
\]
%
provided $u\in W^s_p(\Omega)$ with $2+d/p<s\le4$ and $p > d$, and
$\delta$ is suitably chosen in terms of $h$; see Theorems
\ref{T:RatesHolder} and \ref{T:RatesSobolev}.
%
We also consider a special case of viscosity solutions with
bounded but
discontinuous Hessians, and manage to prove a rate of
convergence (see Theorem \ref{T:RatesPW}). Since these theorems
are proven under the nondegeneracy assumption $f > 0$,
we examine in \Cref{T:RatesDegen} the effect of degeneracy $f \geq 0$.
In \cite{NoNtZh} we explore numerically both classical and $W^2_\infty$ viscosity
solutions and observe linear rates with respect to $h$ for both cases, which are better
than predicted by this theory.
\subsection{Outline}
We start by briefly presenting the operator
$T_\varepsilon$ in \Cref{S:KeyProperties}
and recalling some important results from \cite{NoNtZh}.
In \Cref{S:dAle} we mention the discrete Alexandroff estimate and
combine it in \Cref{S:CoDeDa} with some geometric estimates to
obtain the continuous dependence of the discrete solution on
data. This is much stronger than stability,
and is critical to prove rates of convergence for fully nonlinear
PDEs. Lastly, in \Cref{S:RoC} we combine this result with
operator consistency and a discrete
barrier argument close to the boundary to
derive rates of convergence upon making
judicious choices of $\delta$ and $\theta$ in terms of $h$.
\section{Key Properties of the Discrete Operator}\label{S:KeyProperties}
We recall briefly some of the key properties of operator $T_\varepsilon$,
as proven in \cite{NoNtZh}.
\subsection{Definition of $T_{\varepsilon}$} \label{S:MonotoneDefinition}
Let $\mathcal{T}_h$ be a shape-regular and quasi-uniform triangulation
with meshsize $h$. The computational domain $\Omega_h$
is the union of elements of $\mathcal{T}_h$ and $\Omega_h\ne\Omega$.
If $\mathcal{N}_h$ denotes the nodes of $\mathcal{T}_h$, then
$\mathcal{N}_h^b := \{x_i \in \mathcal{N}_h: x_i \in \partial \Omega_h\}$
are the boundary nodes and
$\mathcal{N}_h^0 := \mathcal{N}_h \setminus \mathcal{N}_h^b$
are the interior nodes. We require that $\mathcal{N}_h^b \subset \partial \Omega$, which in view of the convexity of $\Omega$ implies that $\Omega_h$ is also convex and $\Omega_h \subset \Omega$.
We denote by $\mathbb{V}_h$ the space of continuous
piecewise linear functions over $\mathcal{T}_h$.
We let $\mathbb{S}^{\perp}$ be the collection of all
$d$-tuples of orthonormal bases and
$\mathbf{v} := (v_1,\ldots,v_d) \in \mathbb{S}^{\perp}$ be a generic element, whence
each component $v_i\in\mathbb{S}$, the unit sphere $\mathbb{S}$ of
$\mathbb{R}^d$. We next introduce a finite subset
$\mathbb{S}_\theta$ of $\mathbb{S}$ governed by the angular parameter $\theta>0$:
given $v \in \mathbb S$, there
exists $v^{\theta}\in\mathbb{S}_\theta$ such that
%
$$
|v-v^{\theta}| \leq \theta.
$$
%
Likewise, we let $\mathbb{S}^{\perp}_{\theta}\subset\mathbb{S}^{\perp}$
be a finite approximation of $\mathbb{S}^{\perp}$: for any
$\mathbf v = (v_j)_{j=1}^d \in \mathbb{S}^{\perp}$ there exists
$\mathbf v^{\theta} = (v_j^{\theta})_{j=1}^d \in \mathbb{S}^{\perp}_{\theta}$
such that $v_j^\theta \in \mathbb S_{\theta}$ and $|v_j - v_j^{\theta}| \leq \theta $ for all $1 \leq j \leq d$
and conversely.
For $x_i\in\mathcal{N}_h^0$, we use centered second
differences with a coarse scale $\delta$
%
\begin{equation} \label{E:2Sc2Dif}
\sdd w(x_i;v_j) := \frac{ w(x_i+ \hat\delta v_j) -2 w(x_i) +
w(x_i- \hat\delta v_j) }{ \hat\delta^2}
\end{equation}
where $\hat\delta:=\rho\delta$ with $0 < \rho \le 1$ the
biggest number such that the ball centered at $x_i$ of radius
$\hat\delta$ is contained in $\Omega_h$; we stress that
$\rho$ need not be computed exactly.
This is well defined for any
$w \in C^0(\overline{\Omega})$, in particular for $w\in\mathbb{V}_h$.
We define $\varepsilon:= (h,\delta, \theta)$ and we seek $u_{\varepsilon} \in \mathbb{V}_h$ such that $u^{\varepsilon}(x_i)=g(x_i)$ for
$x_i \in \mathcal{N}_h^b$ and for $x_i \in \mathcal{N}_h^0$
%
\begin{equation} \label{E:2ScOp}
T_{\varepsilon}[u_{\varepsilon}](x_i):=\min\limits_{\mathbf{v} \in \mathbb{S}^{\perp}_{\theta}} \left( \prod_{j=1}^d \sddp u_{\varepsilon}(x_i;v_j) - \sum_{j=1}^d \sddm u_{\varepsilon} (x_i;v_j) \right) = f(x_i),
\end{equation}
%
where we use the notation
$$
\sddp u_{\varepsilon}(x_i;v_j) = \max{(\sdd u_{\varepsilon}(x_i;v_j),0)},
\quad \sddm u_{\varepsilon}(x_i;v_j) = -\min{(\sdd u_{\varepsilon}(x_i;v_j),0)}
$$
to indicate positive and negative parts of
the centered second differences.
\subsection{Key Properties of $T_\varepsilon$} \label{S:PropertiesMonotone}
One of the critical properties of the Monge-Amp\`{e}re equation is the convexity of the solution $u$.
The following notion mimics this at the discrete level.
\begin{Definition}[discrete convexity]\label{D:discrete-convexity}
We say that $w_h \in \mathbb V_h$ is discretely convex if
$$
\sdd w_h(x_i;v_j) \geq 0 \qquad \forall x_i \in \mathcal{N}_h^0, \quad
\forall v_j \in \mathbb S_{\theta}.
$$
\end{Definition}
The following lemma guarantees the discrete convexity of
subsolutions of \eqref{E:2ScOp} \cite[Lemma 2.2]{NoNtZh}.
\begin{Lemma}[discrete convexity]\label{L:DisConv}
If $w_h \in \mathbb{V}_h$ satisfies
\begin{equation} \label{E:Oper}
T_{\varepsilon}[w_h](x_i) \geq 0 \quad \forall x_i \in \mathcal{N}_h^0,
\end{equation}
then $w_h$ is \textit{discretely convex} and as a consequence
\begin{equation}\label{E:simpler-def}
T_{\varepsilon} [w_h](x_i)= \min_{\mathbf{v} \in \mathbb{S}^{\perp}_{\theta}} \prod_{j=1}^d \sdd w_h(x_i;v_j),
\end{equation}
namely
$$
\sddp w_h(x_i;v_j) = \sdd w_h(x_i;v_j),
\quad
\sddm w_h(x_i;v_j) =0
\quad\forall x_i\in \mathcal{N}_h^0,\quad\forall v_j\in \mathbb S_{\theta}.
$$
Conversely, if $w_h$ is discretely convex, then (\ref{E:Oper}) is valid.
\end{Lemma}
Another important property of operator $T_\varepsilon$
that relies on its monotonicity is the following
discrete comparison principle \cite[Lemma 2.4]{NoNtZh}.
\begin{Lemma}[discrete comparison principle] \label{L:DCP}
Let $u_h,w_h \in \mathbb{V}_h$ with $u_h \leq w_h$ on the
discrete boundary $\partial \Omega_h$ be such that
\begin{equation}\label{E:comparison}
T_{\varepsilon}[u_h](x_i) \geq T_{\varepsilon}[w_h](x_i) \geq 0 \ \ \ \forall x_i \in \mathcal{N}_h^0.
\end{equation}
Then, $u_h \leq w_h$ everywhere.
\end{Lemma}
We now state a consistency estimate, proved in \cite[Lemma 4.1]{NoNtZh},
that leads to
pointwise rates of convergence. To this end, given a node $x_i \in \mathcal{N}_h^0$, we denote by
%
\begin{equation}\label{E:Bi}
B_i := \cup \{\overline{T}: T\in\mathcal{T}_h, \, \textrm{dist }(x_i,T) \le \hat\delta\}
\end{equation}
%
where $\hat\delta$ is defined in \eqref{E:2Sc2Dif}.
We also define the $\delta$-interior region
\begin{equation}\label{Omega-delta}
\Omega_{h,\delta} = \left\{ T \in \mathcal{T}_h \ : \ {\rm dist}
(x, \partial \Omega_h ) \geq \delta \ \forall x \in T \right\},
\end{equation}
%
and the $\delta$-boundary region:
$$
\omega_{h,\delta} = \Omega \setminus \Omega_{h,\delta}.
$$
\begin{Lemma}[{consistency of $T_{\varepsilon} [\mathcal{I}_h u]$}] \label{L:FullConsistency}
Let $x_i \in \mathcal{N}_h^0 \cap \Omega_{h,\delta}$ and $B_i$ be defined as in
\eqref{E:Bi}. If $u \in C^{2+k,\alpha}(B_i)$ with $0<\alpha\leq 1$ and
$k=0,1$ is convex, and $\mathcal I_h u $ is its piecewise linear interpolant, then
\begin{equation}\label{E:FullConsistency}
\left| \det D^2u(x_i) - T_{\varepsilon}[\mathcal I_h u] (x_i) \right| \leq C_1(d,\Omega,u) \delta^{k+\alpha} + C_2(d,\Omega,u) \left( \frac{h^2}{\delta^2} + \theta^2 \right),
\end{equation}
where
\begin{equation}\label{E:C1-C2}
C_1(d,\Omega,u)= C |u|_{C^{2+k,\alpha}(B_i)} |u|_{W^2_{\infty}(B_i)}^{d-1}, \quad C_2(d,\Omega,u) = C |u|_{W^2_{\infty}(B_i)}^d.
\end{equation}
If $x_i\in\mathcal{N}_h^0$ and $u \in W^2_{\infty}(B_i)$, then (\ref{E:FullConsistency}) remains valid with $\alpha=k=0$ and $C^{2+k,\alpha}(B_i)$ replaced by $W^2_{\infty}(B_i)$.
\end{Lemma}
\section{Discrete Alexandroff Estimate} \label{S:dAle}
In this section, we review several concepts related to convexity
as well as the discrete Alexandroff estimate of \cite{NoZh}.
We first recall several definitions.
\begin{Definition}[subdifferential] \label{D:ConvEnv} \
\begin{enumerate}[$(i)$]
\item The subdifferential of a function $w$
at a point
$x_0\in \Omega_h$ is the set
\[ \partial w(x_0) := \left\{ p \in \mathbb{R}^d: \ w(x) \geq w(x_0) + p \cdot (x-x_0), \ \ \forall x \in \Omega_h \right\}. \]
\item The subdifferential of a function $w$ on
set $E \subset
\Omega_h$ is $\partial u(E) := \cup_{x \in E} \partial w(x)$.
\end{enumerate}
\end{Definition}
%
\begin{Definition}[convex envelope and discrete lower contact set]\label{def:CEandLCS} \
\begin{enumerate}[$(i)$]
\item The convex envelope $\Gamma u$ of a function $w$ is defined to be
\[
\Gamma w (x) := \sup_{L } \{ L(x), \; L(y) \leq w(y) \text{ for all $y \in \Omega_h$ and $L$ is affine} \}.
\]
\item The discrete lower contact set $C_-(w_h)$ of a function $w_h\in\mathbb{V}_h$ is the set of nodes where the function coincides with its convex envelope, i.e.
\[
\mathcal{C}_- (w_h) := \big\{x_i \in \mathcal{N}_h^0: \Gamma w_h(x_i) = w_h(x_i) \big\}.
\]
\end{enumerate}
\end{Definition}
\begin{remark}[$w_h$ dominates $\Gamma w_h$] \label{R:2DifConvEnv}
Since $w_h\ge\Gamma w_h$, at a contact node $x_i\in\mathcal{C}_-(w_h)$ we have
$$
\sdd \Gamma w_h(x_i;v_j) \leq \sdd
w_h(x_i;v_j)(x_i)\qquad \forall v_j \in \mathbb S_{\theta}.
$$
\end{remark}
\begin{remark}[minima of $w_h$ and $\Gamma w_h$] \label{R:MinConvEnv}
A consequence of Definition
\ref{def:CEandLCS} (convex envelope and discrete lower contact set)
is that the minima of $w_h\in\mathbb{V}_h$ and $\Gamma w_h$ are attained at the same
contact nodes and are equal.
\end{remark}
We can now present the discrete Alexandroff estimate from
\cite{NoZh},
which states that the minimum of a discrete function is controlled by
the measure of the subdifferential of its convex envelope in the
discrete contact set.
\begin{Proposition} [discrete Alexandroff estimate \cite{NoZh}] \label{P:DAE}
Let $v_h$ be a continuous piecewise linear function that satisfies $v_h \geq 0$ on $\partial \Omega_h$. Then,
\begin{equation*}
\max \limits_{ x_i \in \mathcal{N}_h^0} v_h(x_i)^- \leq C \left( \sum\limits_{x_i \in \mathcal{C}_{-}(v_h)} \left| \partial \Gamma v_h (x_i) \right| \right)^{1/d}
\end{equation*}
where $C=C(d,\Omega)$ depends only on the dimension $d$ and the domain $\Omega$.
\end{Proposition}
\section{Continuous Dependence on Data} \label{S:CoDeDa}
We derive the continuous dependence of the discrete
solution on data in Section \ref{S:cont-depend}, which is essential to prove rates of
convergence. To this end, we first prove a stability estimate in the
max norm in Section \ref{S:stab} and the concavity of the discrete
operator in Section \ref{S:concavity}.
\subsection{Stability of the Two-Scale Method.}\label{S:stab}
%
We start with some geometric estimates. The
first and second lemmas connect the discrete
Alexandroff estimate with the 2-scale method. They allow us to estimate the
measure of the subdifferential of a discrete function $w_h$ in terms of our discrete
operator $T_\varepsilon[w_h]$, defined in \eqref{E:2ScOp}.
\begin{Lemma} [subdifferential vs hyper-rectangle] \label{L:SubDifBound}
Let $w \in C^0(\overline{\Omega}_h)$ be convex
and $x_i\in\mathcal{N}_h^0$ be so
that $x_i\pm\hat\delta v \in \overline{\Omega}_h$ for all
$v\in \mathbb S_{\theta}$ with $\hat\delta\le\delta$. If
$\mathbf{v}=(v_j)_{j=1}^d\in\mathbb{S}^{\perp}_{\theta}$ and
%
\[
\alpha_{i,j}^\pm := \frac{w(x_i\pm \hat\delta v_j) - w(x_i)}{\hat\delta}
\quad\forall \, 1\le j\le d,
\]
%
then
%
\[
\partial w(x_i) \subset \left\{ p \in \mathbb{R}^d: \
\alpha_{i,j}^- \le p\cdot v_j \le \alpha_{i,j}^+ \ 1\le j \le d \right\}.
\]
%
\end{Lemma}
\begin{proof}
Take $p \in \partial w(x_i)$ and write
$$
w(x) \geq w(x_i) + p \cdot (x-x_i) \ \ \forall x \in \overline{\Omega}_h.
$$
Consequently, for any $1\le j \le d$ we infer that
\[
w(x_i + \hat\delta v_j) \geq w(x_i) + \hat\delta \ p \cdot v_j,
\quad
w(x_i - \hat\delta v_j) \geq w(x_i) - \hat\delta \ p \cdot v_j,
\]
%
or equivalently
%
\[
\frac{w(x_i)-w(x_i-\hat\delta v_j)}{\hat\delta } \leq p \cdot v_j
\leq \frac{w(x_i+\hat\delta v_j)-w(x_i)}{\hat\delta}.
\]
This implies that $p$ belongs to the desired set.
\end{proof}
\begin{Lemma}[hyper-rectangle volume] \label{L:HypRectVol}
For d-tuple $\mathbf{v} = (v_j)_{j=1}^d \in \mathbb{S}^{\perp}_{\theta}$ the volume of the set
$$
K= \left\{ p \in \mathbb{R}^d: \ a_j \leq p \cdot v_j \leq b_j, \ \ j=1,\ldots,d \right\}
$$
is given by
$$
|K|=\prod_{j=1}^d (b_i-a_i).
$$
\end{Lemma}
\begin{proof}
Let $V=[v_1, \cdots,v_d]\in\mathbb{R}^{d\times d}$ be the orthogonal
matrix whose columns are the elements of $\mathbf{v}$; hence
$v_j=V e_j$ where $\left\{ e_j \right\}_{j=1}^d $ is the canonical basis in $\mathbb{R}^d$.
We now seek a more convenient representation of $K$
%
\begin{align*}
K &= \left\{ p \in \mathbb{R}^d: \ a_j \leq p \cdot (Ve_j) \leq b_j, \ \ j=1,\ldots,d \right\}
\\ &= V^{-T} \left\{ x \in \mathbb{R}^d: \ a_j \leq x \cdot e_j \leq b_j, \ \ j=1,\ldots,d \right\}
= V^{-T} \widetilde{K},
\end{align*}
whence
\[
|K| = |\det{V^{-T}} | \ |\widetilde{K}|=|\widetilde{K}|
= \prod_{j=1}^d (b_j-a_j),
\]
%
because $\widetilde{K}$ is an orthogonal hyper-rectangle.
\end{proof}
Combining Lemmas \ref{L:SubDifBound} and \ref{L:HypRectVol}
we get the following corollary.
\begin{Corollary}[subdifferential vs discrete operator] \label{C:SubDifOper}
For every $x_i \in \mathcal{N}_h^0 \cap \Omega_{h,\delta}$ and a convex function $w$ we have that
%
\[ | \partial w(x_i)| \leq \left(
\min\limits_{\mathbf{v} \in \mathbb{S}^{\perp}_{\theta}} \prod_{j=1}^d \sdd w(x_i;v_j)
\right) \delta^d .
\]
\end{Corollary}
\begin{remark} [artificial factor $\frac{\delta}{h}$]\label{R:VolumeSubopt}
The above estimate is critical in deriving \Cref{P:ContDep} (continuous dependence on data) and subsequently rates of convergence in \Cref{S:RoC}. We thus wish to provide here intuition about the reduced rates of convergence of \Cref{T:RatesHolder} (rates of convergence for classical solutions) relative to the numerical experiments in \cite{NoNtZh}. To this end, we let $w \in C^2(\overline\Omega)$ be a convex function. Then, \Cref{C:SubDifOper} implies that
$$
T_\varepsilon[\mathcal I_h w] (x_i) \geq \frac{1}{\delta^d} | \partial \mathcal I_h w(x_i)|.
$$
However, it was shown by Nochetto and Zhang in \cite[Proposition 5.4]{NoZh2} that
$$
| \partial \mathcal I_h w(x_i)| \geq C h^d \det{(D^2w(x_i))},
$$
provided the mesh $\mathcal{T}_h$ is translation invariant, whence
$$
\det{(D^2w(x_i))} \leq C \frac{\delta^d}{h^d} T_\varepsilon[\mathcal I_h w] (x_i).
$$
We can now see that using this estimate introduces an extra factor $\frac{\delta}{h} \gg 1$, which could possibly explain the suboptimal rate proved in \Cref{T:RatesHolder} (rates of convergence for classical solutions).
\end{remark}
\begin{Lemma} [stability] \label{L:Stability}
If $w_h\in\mathbb{V}_h$ is $w_h \geq 0$ on $\partial\Omega_h$, then
%
$$
\max_{x_i \in \mathcal{N}_h^0} w_h(x_i)^- \leq C \delta \left( \sum_{x_i \in \mathcal{C}_-(w_h)}
T_{\varepsilon}[w_h](x_i) \right)^{1/d} .
$$
\end{Lemma}
\begin{proof}
Since the function $w_h\ge0$ on $\partial\Omega_h$,
we invoke Proposition \ref{P:DAE} (discrete Alexandroff estimate) for $w_h$ to obtain
%
\begin{equation*} \label{E:dAe}
\max \limits_{ x_i \in \mathcal{N}_h^0} w_h(x_i)^- \leq C \left( \sum\limits_{x_i \in \mathcal{C}_-(w_h)} \left| \partial \Gamma w_h (x_i) \right| \right)^{1/d}
\end{equation*}
%
Applying \Cref{C:SubDifOper} (subdifferential vs discrete operator) to
the convex function $\Gamma w_h (x_i)$ at a contact point
$x_i \in \mathcal{C}_-(w_h)$ and recalling \Cref{R:2DifConvEnv}, we have
%
\begin{align*}
\left| \partial \Gamma w_h (x_i) \right| &\leq \delta^d \min\limits_{\mathbf{v} \in \mathbb{S}^{\perp}_{\theta}} \prod_{j=1}^d \sdd \Gamma w_h(x_i;v_j)
\leq \delta^d \min\limits_{\mathbf{v} \in \mathbb{S}^{\perp}_{\theta}} \prod_{j=1}^d \sdd w_h(x_i;v_j)
= \delta^d T_{\varepsilon}[w_h](x_i),
\end{align*}
%
where the last equality follows from \Cref{L:DisConv} (discrete convexity).
\end{proof}
\subsection{Concavity of the Discrete Operator}\label{S:concavity}
%
We recall concavity properties of $(\det A)^{1/d}$ for symmetric positive semi-definite
matrices $A$ and extend them to $T_{\varepsilon}$. The results can be traced back to \cite{Krylov,Lions}, but we present them here for completeness.
\begin{Lemma} [concavity of determinant] \label{L:Concavity} The following two statements are valid.
\begin{enumerate}[$(i)$]
\item For every symmetric positive semi-definite (SPSD) matrix $A$ we have that
\[ (\det{A})^{1/d} = \frac{1}{d} \inf{\left\{ {\rm tr}(AB) \ \Big| \ B \ { \rm is \ SPD \ and } \ \det{B}=1 \right\} } \]
\item The function $A \mapsto (\det{A})^{1/d}$ is concave on SPSD matrices.
\end{enumerate}
\end{Lemma}
%
\begin{proof}
We proceed in three steps.
\medskip
{\it Step 1: Proof of (i) for $A$ invertible.}
Let $B$ be SPD with $\det B = 1$. Then $B^{1/2}$ is well defined,
$\det(B^{1/2})=1$ and we obtain
%
\[
\det A = \det(B^{1/2} A B^{1/2}).
\]
%
Let $P$ be an orthogonal matrix that converts $B^{1/2} A B^{1/2}$ into
a diagonal matrix $D$, namely $D = PB^{1/2} A B^{1/2}P^T$. Applying
the geometric mean inequality yields
%
\[
\det(B^{1/2} A B^{1/2})^{1/d} = (\det D)^{1/d} \le \frac{1}{d} {\rm tr} D
= \frac{1}{d} {\rm tr}(B^{1/2} A B^{1/2}) = \frac{1}{d} {\rm tr}(AB),
\]
%
where we have used the invariance of the trace under cyclic
permutations of the factor to write the last two equalities. This
shows that
%
\[
(\det{A})^{1/d} \leq \frac{1}{d} \inf{\left\{ {\rm tr}(AB) \ \Big| \ B \ { \rm is \ SPD \ and } \ \det{B}=1 \right\} }
\]
%
This inequality is actually equality provided $A$ is invertible. In
fact, we can take $B = (\det A)^{1/d} A^{-1}$, which is SPD and $\det B = 1$.
This proves (i) for $A$ nonsingular.
\medskip
{\it Step 2: Proof of (i) for $A$ singular}.
Given the singular value decomposition of $A$
%
\[
A = \sum_{i=1}^d \lambda_i v_i \otimes v_i,
\quad \lambda_1 \ge \cdots \lambda_k > \lambda_{k+1} = \cdots =
\lambda_d = 0,
\]
%
with orthogonal vectors $(v_i)_{i=1}^d$, we can assume that $k>0$ for
otherwise $A=0$ and the assertion is trivial. Given a parameter
$\sigma>0$, let $B$ be defined by
%
\[
B := \sum_{i=1}^k \sigma v_i \otimes v_i + \sum_{i=k+1}^d
\sigma^{-\beta} v_i \otimes v_i
\]
%
and $\beta=k/(d-k)$ because then $\det B = \sigma^k\sigma^{-\beta(d-k)}=1$.
Therefore,
%
\[
AB = \sigma \sum_{i=1}^k
\lambda_i v_i \otimes v_i
\quad\Rightarrow\quad
{\rm tr}(AB) = \sigma \sum_{i=1}^k \lambda_i
\to 0
\quad \textrm{as } \sigma \to 0,
\]
%
which proves (i) for $A$ singular since $B$ is SPD.
\medskip
{\it Step 3: Proof of (ii)}.
Let $A$ and $B$ be SPSD matrices and $0\le \lambda \le 1$.
Then $\lambda A + (1-\lambda) B$ is also SPSD and we can apply (i) to
%
\begin{align*}
(\det{[ \lambda A + (1- \lambda) B ]})^{1/d} &= \frac{1}{d} \inf{ \left\{ {\rm tr}[( \lambda A + (1- \lambda) B)C] \Big| \ C\ \textrm{is SPD and} \det{C}=1 \right\} }
\\ &\geq \frac{\lambda}{d} \inf{ \left\{ {\rm tr}(AC) \ \Big| \ C\ { \rm is \ SPD \ and} \ \det{C}=1 \right\} }
\\&+ \frac{1- \lambda}{d} \inf{ \left\{ {\rm tr}(BC) \ \Big| \ C\ { \rm is \ SPD \ and} \ \det{C}=1 \right\} }
\\ &= \lambda (\det{A})^{1/d} + (1-\lambda) (\det{B})^{1/d}.
\end{align*}
This completes the proof.
\end{proof}
Upon relabeling $\widehat{A}=\lambda A$ and
$\widehat{B}=(1-\lambda)B$, which are still SPSD, we can write Lemma
\ref{L:Concavity} (ii) as follows:
%
\begin{equation}\label{E:concavity}
(\det \widehat{A})^{1/d} + (\det \widehat{B})^{1/d}
\le \big(\det(\widehat{A}+\widehat{B})\big)^{1/d}.
\end{equation}
%
We now show that our discrete operator $T_\varepsilon[\cdot]$
possesses a similar property.
\begin{Corollary} [concavity of discrete operator] \label{C:OperIneq}
Given two functions $u_h,w_h\in\mathbb{V}_h$, we have
%
\[
\big( T_{\epsilon} [u_h] (x_i) \big)^{1/d} +
\big( T_{\epsilon} [w_h](x_i) \big)^{1/d} \le
\big( T_{\epsilon}[u_h+w_h](x_i) \big)^{1/d},
\]
for all nodes $x_i \in \mathcal{N}_h^0$ such that
$\sdd u_h(x_i;v_j)\ge0, \ \sdd w_h(x_i;v_j)\geq 0$ for all $v_j \in \mathbb S_{\theta}$.
\end{Corollary}
\begin{proof}
We argue in two steps.
\medskip
\textit{Step 1.}
For $a=(a_j)_{j=1}^d \in \mathbb{R}^d$ with $a_j \geq 0, \ j=1,\ldots,d$ we consider
the function
\[
f(a) := \left( \prod_{j=1}^d a_j \right)^{1/d},
\]
which can be conceived as the determinant of a
diagonal (and thus symmetric)
positive semi-definite matrix with diagonal elements $(a_j)_{j=1}^d$, i.e.
\[
f(a) = \big(\det { \rm diag
}{\left\{a_1,\ldots,a_d\right\}} \big)^{1/d}.
\]
Applying \eqref{E:concavity} to $\widehat{A}={ \rm diag
}{\left\{a_1,\ldots,a_d\right\}} , \widehat{B}={ \rm diag
}{\left\{b_1,\ldots,b_d\right\}} $
with $a=(a_j)_{j=1}^d, b=(b_j)_{j=1}^d\ge0$ component wise, we deduce
%
\[
f(a) + f(b) \le f(a+b).
\]
%
{\it Step 2.}
We now apply this formula to the discrete operator. Since both
$u_h,w_h$ are discretely convex at $x_i\in\mathcal{N}_h^0$, so is $u_h+w_h$, and we
can apply Lemma \ref{L:DisConv} (discrete convexity) to write
%
\[
T_\varepsilon[u_h+w_h](x_i) = \prod_{j=1}^d \sdd[u_h+w_h](x_i;v_j)
\]
%
for a suitable $\mathbf{v}=(v_j)_{j=1}^d\in\mathbb{S}^{\perp}_{\theta}$. Making use again
of \eqref{E:simpler-def}, this time for $u_h$ and $w_h$ and for the
specific set of directions $\mathbf{v}$ just found, we obtain
%
\begin{align*}
\big( T_\varepsilon [u_h](x_i) \big)^{\frac{1}{d}} &
+ \big( T_\varepsilon [w_h](x_i) \big)^{\frac{1}{d}}
\le \left(\prod_{j=1}^d \sdd u_h(x_i;v_j)\right)^{\frac{1}{d}}
+ \left(\prod_{j=1}^d \sdd w_h(x_i;v_j)\right)^{\frac{1}{d}}
\\
& \le \left(\prod_{j=1}^d \sdd u_h(x_i;v_j) + \sdd w_h(x_i;v_j) \right)^{\frac{1}{d}}
= \big(T_\varepsilon[u_h+w_h](x_i)\big)^{\frac{1}{d}},
\end{align*}
where the second inequality is given by Step 1 for
$a = ( \sdd u_h(x_i;v_j) )_{j=1}^d$ and
$b = ( \sdd w_h(x_i;v_j) )_{j=1}^d$.
This is the asserted estimate.
\end{proof}
\subsection{Continuous Dependence of the Two-Scale Method on Data}
\label{S:cont-depend}
We are now ready to prove the continuous dependence of discrete solutions on data. This will be instrumental later for deriving rates of convergence for the two-scale method.
\begin{Proposition}[continuous dependence on data] \label{P:ContDep}
Given two functions $u_h,w_h\in\mathbb{V}_h$ such that $u_h \geq w_h$ on $\partial \Omega_h$ and
%
\[
T_{\varepsilon}[u_h](x_i) =f_1(x_i) \geq 0 \ \ {\rm and} \ \
T_{\varepsilon}[w_h](x_i) = f_2(x_i) \geq 0
\]
at all interior nodes $x_i\in\mathcal{N}_h^0$, we have that
\[
\max \limits_{ \Omega_h} (u_h-w_h)^- \leq C \ \delta \ \left(
\sum\limits_{x_i \in \mathcal{C}_{-}(u_h-w_h)} \left(
f_1(x_i)^{1/d}- f_2(x_i)^{1/d} \right)^d \right)^{1/d}. \]
\end{Proposition}
%
\begin{proof}
Since $u_h-w_h\in\mathbb{V}_h$ and $u_h -w_h \geq 0$ on $\partial \Omega_h$,
\Cref{L:Stability} (stability) yields
%
$$
\max_{x_i\in\mathcal{N}_h^0} (u_h - w_h) (x_i)^- \leq C \delta
\left( \sum_{x_i \in \mathcal{C}_-(u_h - w_h)}
T_{\epsilon} [u_h - w_h] (x_i) \right)^{1/d} .
$$
%
Since $x_i \in \mathcal{C}_-(u_h-w_h)$, we have that $\sdd (u_h-w_h)(x_i;v_j)\geq 0$, whence
$$
\sdd u_h(x_i;v_j)\geq \sdd w_h(x_i;v_j) \ge 0
\quad\forall v_j\in\mathbb S_{\theta},
$$
%
where we have made use of Lemma \ref{L:DisConv} (discrete convexity).
Invoking \Cref{C:OperIneq} (concavity of discrete operator)
for $u_h-w_h$ and $w_h$, we deduce
%
\[
\big( T_{\epsilon} [u_h-w_h] (x_i) \big)^{1/d} \le
\big( T_{\epsilon} [u_h](x_i) \big)^{1/d} -
\big( T_{\epsilon} [w_h](x_i) \big)^{1/d},
\]
%
whence
%
\begin{align*}
\max_{x_i\in\mathcal{N}_h^0} (u_h - w_h) (x_i)^- \leq &\;
C \delta \left( \sum_{x_i \in \mathcal{C}_-(u_h - w_h)}
\left( T_{\epsilon} [u_h](x_i)^{1/d} - T_{\epsilon} [w_h] (x_i)^{1/d} \right)^d
\right)^{1/d}
\\
= &\; C \delta \left( \sum_{x_i \in \mathcal{C}_-(u_h - w_h)}
\left( f_1(x_i)^{1/d} - f_2(x_i)^{1/d} \right)^d \right)^{1/d} .
\end{align*}
This completes the proof.
\end{proof}
\section{Rates of Convergence} \label {S:RoC}
We now combine the preceding estimates to prove
pointwise convergence rates for solutions with varying degree of regularity.
We first present in \Cref{T:RatesHolder} the case of a classical solution with H\"older regularity.
This allows us to introduce the main techniques employed for deriving the rates of convergence. We then build on these techniques and prove error estimates for three more cases of increasing generality. In \Cref{T:RatesSobolev} we assume a classical solution with Sobolev regularity, which requires the use of embedding estimates and accumulating the truncation error in $l^d$, rather than $l^\infty$. We next deal with a non-classical solution that is globally in $W^{2}_{\infty}(\Omega)$ but its Hessian is discontinuous across a $d-1$ dimensional Lipschitz surface. To prove rates for this case we need to take advantage of the small volume affected by this discontinuity and combine it with the techniques used in \Cref{T:RatesHolder} and \Cref{T:RatesSobolev}. Lastly, we remove the non-degeneracy assumption $f \geq f_0 >0$ used in the previous three cases to obtain rates of convergence for a piecewise smooth viscosity solution with degenerate right hand side $f$. This corresponds to one of the numerical experiments performed in \cite{NoNtZh}.
Our estimates do not require $h$ small and are
stated over the computational domain
$\Omega_h\subset\Omega$.
\subsection{Barrier Function}\label{S:Barrier}
We recall here the two discrete barrier functions
introduced in \cite[Lemmas 5.1, 5.2]{NoNtZh}.
The first one is critical in order to control the behavior of
$u_{\varepsilon}$ close to the boundary of $\Omega_h$ and prove the
convergence to the unique viscosity solution $u$ of \eqref{E:MA}. We now
use the same barrier function to control the pointwise error of $u_{\varepsilon}$ and $u$
close to the boundary. The second barrier allows us
to treat the degenerate case
$f \geq 0$, using techniques similar to the case $f >0$.
\begin{Lemma}[discrete boundary barrier] \label{L:Barrier} Let $\Omega$ be uniformly convex and $E>0$ be arbitrary. For each node $z \in \mathcal{N}_h^0$ with ${\rm dist}(z,\partial \Omega_h) \leq \delta$, there exists a function $p_h\in\mathbb{V}_h$ such that $T_{\varepsilon}[p_h](x_i) \geq E$ for all $x_i \in \mathcal{N}_h^0$, $p_h \leq 0$ on $\partial \Omega_h$ and
\[
|p_h(z)| \leq CE^{1/d} \delta
\]
with $C$ depending on $\Omega$.
\end{Lemma}
\begin{Lemma}[discrete interior barrier] \label{L:BarrierInterior}
Let $\Omega$ be contained in the ball $B(x_0,R)$ of center $x_0$ and radius
$R$. If $q(x):= \frac12\big( |x-x_0|^2 - R^2 \big)$, then its
interpolant $q_h:=\mathcal I_h q\in\mathbb{V}_h$ satisfies
%
\[
T_\varepsilon[q_h](x_i) \ge 1\quad\forall x_i\in\mathcal{N}_h^0,
\qquad
q_h(x_i) \le 0 \quad\forall x_i\in\mathcal{N}_h^b.
\]
\end{Lemma}
\subsection{Error Estimates for Solutions with H\"older Regularity}\label{S:RatesHolder}
We now deal with classical solutions $u$ of (\ref{E:MA}) of
class $C^{2+k,\alpha}(\overline{\Omega})$, with $k=0,1$ and
$0<\alpha \leq 1$, and derive pointwise error estimates.
We proceed as follows. We first use \Cref{L:Barrier}
(discrete boundary barrier) to control $u_{\varepsilon} -\mathcal I_h u$ in
the $\delta$-neighborhood $\omega_{h,\delta}$
of $\partial \Omega_h$, where the consistency error of
$T_\varepsilon[\mathcal I_h u]$ is of order one according to
\Cref{L:FullConsistency} (consistency of $T_\varepsilon[\mathcal I_h u]$).
In the $\delta$-interior region $\Omega_{h,\delta}$ we combine
the interior consistency error of
$T_\varepsilon[\mathcal I_h u]$ from \Cref{L:FullConsistency} and \Cref{P:ContDep}
(continuous dependence on data). Judicious choices of
$\delta$ and $\theta$ in terms of $h$ conclude the argument.
\begin{Theorem}[rates of convergence for classical solutions]\label{T:RatesHolder}
Let $f(x) \geq f_0 >0$ for all $x \in \Omega$. Let $u$ be the
classical solution of (\ref{E:MA}) and $u_{\varepsilon}$ be the discrete
solution of (\ref{E:2ScOp}). If $u \in C^{2,\alpha}(\overline{\Omega})$ for $0<\alpha
\leq 1$ and
\[
\delta = R_0(u) \ h^{\frac{2}{2+\alpha}},
\quad
\theta = R_0(u)^{-1} \ h^{\frac{\alpha}{2+\alpha}}
\]
with $R_0(u) = |u|_{W^2_{\infty}(\Omega)}^{\frac{1}{2+\alpha}} \ |u|_{C^{2,\alpha}(\overline{\Omega})}^{-{\frac{1}{2+\alpha}}}$, then
%
\[
\|u-u_{\varepsilon}\|_{L^{\infty}(\Omega_h)} \leq C(\Omega,d,f_0)
\Big( |u|_{C^{2,\alpha}(\overline{\Omega})}^{\frac{1}{2+\alpha}}
\ |u|_{W^2_{\infty}(\Omega)}^{d-\frac{1}{2+\alpha}} + \big(1+ R_0(u)\big) \
|u|_{W^2_{\infty}(\Omega)} \Big) \ h^{\frac{\alpha}{2+\alpha}}.
\]
Otherwise, if $u \in C^{3,\alpha}(\overline{\Omega})$ for $0 < \alpha \leq 1$ and
%
\[
\delta = R_1(u) \ h^{\frac{2}{3+\alpha}},
\quad
\theta = R_1(u)^{-1} \ h^{\frac{1+\alpha}{3+\alpha}}
\]
with $R_1(u) := |u|_{W^2_{\infty}(\Omega)}^\frac{1}{3+\alpha}|u|_{C^{3,\alpha}(\overline{\Omega})}^{-\frac{1}{3+\alpha}}$, then
\[
\|u-u_{\varepsilon}\|_{L^{\infty}(\Omega_h)} \leq C(\Omega,d,f_0)
\Big( |u|_{C^{3,\alpha}(\overline{\Omega})}^{\frac{1}{3+\alpha}}
\ |u|_{W^2_{\infty}(\Omega)}^{d-\frac{1}{3+\alpha}} +
\big(1 + R_1(u) \big) \
|u|_{W^2_{\infty}(\Omega)} \Big) \ h^{\frac{1+\alpha}{3+\alpha}}.
\]
%
\end{Theorem}
\begin{proof}
If $R_k(u) :=
|u|_{W^2_{\infty}(\Omega)}^\frac{1}{2+k+\alpha}|u|_{C^{2+k,\alpha}(\overline{\Omega})}^{-\frac{1}{2+k+\alpha}}$,
$k=0,1$, we prove below the estimate
\[
\max_{\Omega_h} \, (u_{\varepsilon} - \mathcal I_h u) \lesssim
\Big( \big(1+R_k(u)|u|_{W^2_{\infty}(\Omega)}\big)+ |u|_{C^{2+k,\alpha}(\overline{\Omega})}^{\frac{1}{2+k+\alpha}}
\ |u|_{W^2_{\infty}(\Omega)}^{d-\frac{1}{2+k+\alpha}}
\Big) \ h^{\frac{k+\alpha}{2+k+\alpha}}
\]
with a hidden constant depending on $\Omega, d, f_0$.
We proceed in three steps.
The estimates for $\max_{\Omega_h} \, (\mathcal I_h u - u_{\varepsilon})$ are similar
and thus omitted. Adding the interpolation error $\|u-\mathcal I_h
u\|_{L^{\infty}(\Omega_h)} \leq Ch^2 |u|_{W^2_{\infty}(\Omega)}$
\cite{BrenScott} readily gives the asserted estimates because
$\frac{k+\alpha}{2+k+\alpha} \le \frac{1}{2}$ for $k=0,1$ and
$0<\alpha\le 1$.
\medskip
\textit{Step 1: Boundary estimate.} We show
that for $z \in \mathcal{N}_h^0$ so that
${\rm dist}(z,\partial \Omega_h) \leq \delta$
$$
u_{\varepsilon}(z) - \mathcal I_h u(z) \leq C |u|_{W^2_{\infty}(\Omega)} \delta.
$$
Given the function $p_h$ of \Cref{L:Barrier}
(discrete boundary barrier), for $z$ fixed, we examine the behavior of $u_{\varepsilon} + p_h$. For any interior node $x_i \in \mathcal{N}_h^0$, we have
$$
\begin{aligned}
\prod_{j=1}^d \sdd (u_{\varepsilon} +p_h) (x_i;v_j) &= \prod_{j=1}^d (\sdd u_{\varepsilon} (x_i;v_j) + \sdd p_h(x_i;v_j) )\\
&\geq \prod_{j=1}^d \sdd u_{\varepsilon} (x_i;v_j) + \prod_{j=1}^d \sdd p_h (x_i;v_j) \quad \forall \mathbf{v}=(v_j)_{j=1}^d \in \mathbb{S}^{\perp}_{\theta},
\end{aligned}
$$
because $\sdd u_{\varepsilon} (x_i;v_j) \geq 0$ and $\sdd p_h(x_i;v_j)\geq 0$. We apply \Cref{L:FullConsistency} (consistency of $T_{\varepsilon}[\mathcal I_h u])$ to obtain
$$
\begin{aligned}
T_{\varepsilon} [u_{\varepsilon} + p_h] (x_i) & \geq T_{\varepsilon}[u_{\varepsilon}](x_i) + T_{\varepsilon}[p_h](x_i) \\
& \geq f(x_i) + E \\
& \geq T_{\varepsilon}[\mathcal I_h u](x_i) - C|u|_{W^2_{\infty}(\Omega)}^d + E \geq T_{\varepsilon} [\mathcal I_h u](x_i),
\end{aligned}
$$
provided $E \geq C|u|_{W^2_{\infty}(\Omega)}^d$. Since $\mathcal I_h u = u_{\varepsilon}$ and
$p_h \leq 0 $ on $\partial \Omega_h$, we deduce from
\Cref{L:DCP} (discrete comparison principle) that
%
$$
u_{\varepsilon}(z) + p_h(z) \leq \mathcal I_h u (z),
$$
whence,
$$
u_{\varepsilon}(z) - \mathcal I_h u(z) \leq C |u|_{W^2_{\infty}(\Omega)} \delta.
$$
\medskip
\textit{Step 2: Interior estimate}. We show that for
all $x_i \in \mathcal{N}_h^0$ so that
${\rm dist}(x_i,\partial \Omega_h) \geq \delta$
$$
T_{\varepsilon} [u_{\varepsilon}] (x_i)- T_{\varepsilon} [\mathcal I_h u](x_i) \leq C_1(u) \delta^{\alpha +k} + C_2(u) \left( \frac{h^2}{\delta^2}+\theta^2 \right)
$$
with $k=0,1$ and
$$
C_1(u) = C |u|_{C^{2+k,\alpha}(\overline{\Omega})} \ |u|_{W^2_{\infty}(\Omega)}^{d-1}, \quad C_2(u) = C |u|_{W^2_{\infty}(\Omega)}^d
$$
dictated by \Cref{L:FullConsistency}.
Step 1 guarantees that
$$
u_{\varepsilon} - \mathcal I_h u \leq C|u|_{W^2_{\infty}(\Omega)} \delta \quad \text{on } \partial \Omega_{h,\delta},
$$
where $\Omega_{h,\delta}$ is defined in \eqref{Omega-delta}.
Let $d_{\varepsilon}:= \mathcal I_h u-u_{\varepsilon} +C|u|_{W^2_{\infty}(\Omega)}\delta$ and note that $d_{\varepsilon} \geq 0 $ on $\partial \Omega_{h,\delta}$. We then apply \Cref{P:ContDep} (continuous dependence on data) to $d_{\varepsilon}$ in $\Omega_{h,\delta}$, in conjunction with \Cref{L:FullConsistency} (consistency of $T_{\varepsilon}[\mathcal I_h u]$), to obtain
$$
\max_{\Omega_{h,\delta}} d_{\varepsilon}^- \lesssim
\ \delta \left( \sum_{x_i \in \mathcal{C}_-(d_{\varepsilon})} \left( (f(x_i) +e)^{1/d} - f(x_i)^{1/d} \right)^d \right)^{1/d}
$$
with $e:= C_1(u) \delta^{\alpha+k} + C_2(u) \left(
\frac{h^2}{\delta^2} + \theta^2 \right)$. We now use
that the function $t \mapsto t^{1/d}$ is concave with derivative
$\frac{1}{d}t^{1/d-1}$ and $f(x_i)\geq f_0 >0$ to estimate
$$
(f(x_i)+e)^{1/d}-f(x_i)^{1/d} \leq \frac{e}{d f_0^{\frac{d-1}{d}}},
$$
whence
$$
\max_{\Omega_{h,\delta}} d_{\varepsilon}^- \lesssim \delta \left( \sum_{x_i \in \mathcal{C}_-(d_{\varepsilon})} \left(C_1(u) \delta^{\alpha +k}+C_2(u)\left(\frac{h^2}{\delta^2}+\theta^2\right) \right)^d \right)^{1/d}.
$$
Since the cardinality of $\mathcal{C}_-(d_{\varepsilon})$ is bounded by that of $\mathcal N_h$, which in turn is bounded by $Ch^{-d}$ with $C$ depending on shape regularity, we end up with
\begin{equation} \label{E:rates-factor}
\max_{\Omega_h} \, (u_{\varepsilon} -\mathcal I_h u) \lesssim
|u|_{W^2_{\infty}(\Omega)} \delta + \frac{\delta}{h} \left( C_1(u)
\delta^{\alpha+k} + C_2(u) \Big( \frac{h^2}{\delta^2}
+ \theta^2 \Big) \right).
\end{equation}
\medskip
\textit{Step 3: Choice of $\delta$ and
$\theta$.} To find an optimal choice of $\delta$
and $\theta$ in terms of $h$, we minimize the
right-hand side of the preceding estimate. We first
set $\theta^2 = \frac{h^2}{\delta^2}$ and equate
the last two terms
$$
C_1(u) \delta^{k+\alpha} = C_2(u) \frac{h^2}{\delta^2} \quad \Longrightarrow \quad \delta = R_k(u) h^{\frac{2}{2+k+\alpha}}.
$$
Writing again $C_1(u)$ and
$C_2(u)$ in terms of $|u|_{C^{2+k,\alpha}(\overline{\Omega})}$
and $|u|_{W^2_{\infty}(\Omega)}$, we thus obtain
$$
\max_{\Omega_h} \, (u_{\varepsilon} - \mathcal I_h u) \lesssim
R_k(u) |u|_{W^2_{\infty}(\Omega)} \ h^{\frac{2}{2+k+\alpha}}
+ |u|_{C^{2+k,\alpha}(\overline{\Omega})}^{\frac{1}{2+k+\alpha}}
\ |u|_{W^2_{\infty}(\Omega)}^{d-\frac{1}{2+k+\alpha}}
\ h^{\frac{k+\alpha}{2+k+\alpha}}.
$$
Finally, the desired estimate follows immediately because
$k+\alpha \leq 2$.
\end{proof}
We observe that according to \Cref{T:RatesHolder} the rate of convergence is of order $h^{1/2}$ whenever $u\in C^{3,1}(\overline{\Omega})$. However, our numerical experiments in \cite{NoNtZh} indicate linear rates of convergence, which correspond to \Cref{L:FullConsistency} (consistency of $T_\varepsilon[\mathcal I_h u_h]$). This mismatch may be attributed to the factor $\frac{\delta}{h} \gg 1$ in \eqref{E:rates-factor}, which relates to \Cref{R:VolumeSubopt} (artificial factor $\frac{\delta}{h}$). This issue will be tackled in a forthcoming paper.
\subsection{Error Estimates for Solutions with Sobolev Regularity}\label{S:RatesSobolev}
We now derive error estimates for solutions $u \in W^s_p(\Omega)$ with $s>2+\frac{d}{p}$ so that $W^s_p(\Omega)\subset C^2(\overline{\Omega})$.
We exploit the structure of the estimate of \Cref{P:ContDep} (continuous dependence on data) which shows that its right-hand side accumulates in $l^d$ rather than $l^{\infty}$.
\begin{Theorem} [convergence rate for $W_p^s$
solutions] \label{T:RatesSobolev} Let $f \geq f_0 >0$ in $\Omega$
and let the viscosity solution $u$ of (\ref{E:MA}) be of class
$W_p^s(\Omega)$ with $\frac{d}{p} < s-2-k\le 1,
\ k=0,1$. If $u_{\varepsilon}$ is the discrete solution of
(\ref{E:2ScOp}) and
%
\[
\delta = R(u) \ h^{\frac{2}{s}},
\quad
\theta = R(u)^{-1} \ h^{1-\frac{2}{s}},
\]
with $R(u) := |u|_{W^2_{\infty}(\Omega)}^{\frac{1}{s}} |u|_{W_p^s(\Omega)}^{-\frac{1}{s}}$,
then
$$
\| u - u_{\varepsilon}\|_{L^{\infty}(\Omega_h)} \leq
C(d,\Omega,f_0) \Big( |u|_{W_p^s(\Omega)}^{\frac{1}{s}}
\ |u|_{W^2_{\infty}(\Omega)}^{d-\frac{1}{s}} + \big(1 + R(u) \big)
|u|_{W^2_\infty(\Omega)} \Big) h^{1-\frac{2}{s}} .
$$
\end{Theorem}
\begin{proof}
We proceed as in \Cref{T:RatesHolder}
to show an upper bound for $u_{\varepsilon} - \mathcal I_h u$.
The boundary estimate of Step 1 remains intact, namely
$$
u_{\varepsilon}(z) - \mathcal I_h u(z) \leq C \ |u|_{W^2_{\infty}(\Omega)} \ \delta
$$
for all $z \in \mathcal{N}_h^0$ such that
${\rm dist}(z,\partial \Omega_h) \leq \delta$.
On the other hand, Step 2 yields
$$
\max_{\Omega_{h,\delta}}(u_{\varepsilon} - \mathcal I_h u)
\lesssim \delta |u|_{W^2_{\infty}(\Omega)} + \delta \left(
\sum_{x_i \in \mathcal{N}_h^0} C_1(u)^d \delta^{(k+\alpha)d} +
C_2(u)^d \left( \frac{h^2}{\delta^2} + \theta^2
\right)^d \right)^{1/d},
$$
where $C_1(u)$ and $C_2(u)$ are defined in \Cref{L:FullConsistency}
(consistency of $T_\varepsilon [\mathcal I_h u]$) and $0 <
\alpha = s-2-k-\frac{d}{p} \leq 1$ corresponds to the
Sobolev embedding $W_p^s(B_i) \subset C^{2+k,\alpha}(B_i)$.
In the following calculations we resort to the
Sobolev inequality \cite[Theorem 2.9]{Giusti}
$$
|u|_{C^{2+k,\alpha}(B_i)} \le C |u|_{W_p^s(B_i)},
$$
involving only semi-norms. We stress that $C>0$
depends on the Lipschitz constant of $B_i$ but not on
its size. The latter is due to the fact that the
Sobolev numbers of $W^{s-2-k}_p(B_i)$ and
$C^{0,\alpha}(B_i)$ coincide:
$0< s-k-2-d/p=\alpha \le 1$. We refer to \cite[Theorem
2.9]{Giusti} for a proof for $0<s<1$.
We now use the H\"older
inequality with exponent $\frac{p}{d} > 1$ to obtain
%
$$
\begin{aligned}
\left( \sum_{x_i \in \mathcal{N}_h^0} C_1(u)^d \right)^{\frac{1}{d}} &\lesssim \left( \sum_{x_i \in \mathcal{N}_h^0} |u|_{W_p^s(B_i)}^d |u|_{W^2_{\infty}(B_i)}^{d(d-1)} \right)^{\frac{1}{d}} \\
&\lesssim \left( \sum_{x_i \in \mathcal{N}_h^0} |u|_{W_p^s(B_i)}^{d\frac{p}{d}} \right)^{\frac{1}{d}\frac{d}{p}} \ \left( \sum_{x_i \in \mathcal{N}_h^0} |u|_{W^2_{\infty}(B_i)}^{d(d-1)\frac{p}{p-d}} \right)^{\frac{1}{d}\frac{p-d}{p}}.
\end{aligned}
$$
%
Since the cardinality of the set of balls $B_i$ containing an
arbitrarily given $x \in \Omega$ is proportional to $\left(
\frac{\delta}{h} \right)^d$, while the cardinality of $\mathcal{N}_h^0$ is
proportional to $h^{-d}$,
we get
\begin{align*}
\left( \sum_{x_i \in \mathcal{N}_h^0} C_1(u)^d \right)^{\frac{1}{d}}
& \lesssim \left( \frac{\delta}{h} \right)^{\frac{d}{p}} |u|_{W_p^s(\Omega)}
\ \left( h^{-d} |u|_{W^2_{\infty}(\Omega)}^{\frac{d(d-1)p}{p-d}}
\right)^{\frac{p-d}{pd}} \\
& \lesssim \frac{\delta^{\frac{d}{p}}}{h} \ |u|_{W_p^s(\Omega)} \ |u|_{W^2_{\infty}(\Omega)}^{d-1}.
\end{align*}
%
Exploiting that $\alpha + k + \frac{d}{p}+1=s-1$,
we readily arrive at
%
$$
\delta \left( \sum_{x_i \in \mathcal{N}_h^0} C_1(u)^d \ \delta^{(k+\alpha)d}
\right)^{\frac{1}{d}} \lesssim \frac{\delta^{s-1}}{h} |u|_{W_p^s(\Omega)} \ |u|_{W^2_{\infty}(\Omega)}^{d-1}.
$$
In addition, we have
$$
\left( \sum_{x_i \in \mathcal{N}_h^0} C_2(u)^d \right)^{\frac{1}{d}}
\lesssim |u|_{W^2_{\infty}(\Omega)}^d \ \frac{1}{h},
$$
whence
$$
\delta \left( \sum_{x_i \in \mathcal{N}_h^0} C_2(u)^d \left( \frac{h^2}{\delta^2} + \theta^2 \right)^d \right)^{\frac{1}{d}} \lesssim |u|_{W^2_{\infty}(\Omega)}^d \ \frac{\delta}{h} \left( \frac{h^2}{\delta^2} + \theta^2 \right).
$$
Collecting the previous estimates, we end up with
$$
\max_{\Omega_h} \, (u_{\varepsilon} - \mathcal I_h u) \lesssim
\delta |u|_{W^2_{\infty}(\Omega)} + |u|_{W^2_{\infty}(\Omega)}^{d-1}
\frac{\delta}{h} \left( |u|_{W_p^s(\Omega)} \delta^{s-2} +
|u|_{W^2_{\infty}(\Omega)} \left( \frac{h^2}{\delta^2} + \theta^2 \right) \right).
$$
To find an optimal relation among $h,\delta$ and
$\theta$, we first choose $\theta^2 =
\frac{h^2}{\delta^2}$ and next equate the two terms in
the second summand to obtain
$$
\delta = R(u) \ h^{\frac{2}{s}},
\quad
\theta = R(u)^{-1} \ h^{1-\frac{2}{s}},
$$
whence
$$
\max_{\Omega_h} \, (u_{\varepsilon} - \mathcal I_h u) \lesssim
R(u) |u|_{W^2_{\infty}(\Omega)} h^{\frac{2}{s}} +
|u|_{W_p^s(\Omega)}^{\frac{1}{s}} \ |u|_{W^2_{\infty}(\Omega)}^{d-\frac{1}{s}}
h^{1-\frac{2}{s}}.
$$
Adding the interpolation error estimate $\|u-\mathcal I_h u\|_{L^\infty(\Omega)}
\lesssim h^2 |u|_{W^2_{\infty}(\Omega)}$, and using that $2 > \frac{2}{s} \ge 1 -
\frac{2}{s}$ for $2<s\le 4$, leads to the asserted estimate.
\end{proof}
The error estimate of \Cref{T:RatesSobolev} (convergence rate for $W_p^s$-solutions) is of order $\frac{1}{2}$ for $s=4$ and $u \in W_p^4(\Omega)$ with $p > d$. This rate requires much weaker regularity than the corresponding error estimate in \Cref{T:RatesHolder}, namely $u \in C^{3,1}(\overline{\Omega}) = W^4_{\infty}(\Omega)$. In both cases, the relation between $\delta$ and $h$ is $\delta \approx h^{\frac{1}{2}}$.
\subsection{Error Estimates for Piecewise Smooth Solutions} \label{S:RatesPW}
We now derive pointwise rates of convergence for a larger class of solutions than in \Cref{S:RatesSobolev}. These are viscosity
solutions which are piecewise $W_p^s$ but have discontinuous Hessians
across a Lipschitz $(d-1)$-dimensional manifold $\mathcal{S}$;
we refer to the second numerical example in \cite{NoNtZh}.
Since $T_\varepsilon[\mathcal I_h u]$ has a
consistency error of order one in a $\delta$-region around
$\mathcal{S}$, due to the discontinuity of $D^2u$, we
exploit the fact that the measure of this region is
proportional to $\delta|\mathcal{S}|$. We are thus able to adapt the argument of
\Cref{T:RatesSobolev} (convergence rate for $W^s_p$ solutions),
and accumulate such consistency error in $l^d$,
at the expense of an extra additive term of order
$h^{-1}\delta^{1+\frac{1}{d}}$. This term is responsible for
a reduced convergence rate when $u \in W^s_p(\Omega\setminus\mathcal{S})$,
$s > 2+ \frac{1}{d}$.
%
\begin{Theorem}[convergence rate for piecewise smooth
solutions] \label{T:RatesPW}
Let $\mathcal{S}$ denote a $(d-1)$-dimensional Lipschitz manifold
that divides $\Omega$ into two disjoint subdomains $\Omega_1, \Omega_2$
so that $S = \overline{\Omega}_1 \cap \overline{\Omega}_2$.
Let $f \geq f_0>0$ in $\Omega$ and let $u \in W_p^s(\Omega_i) \cap
W^2_{\infty}(\Omega)$, for $i=1,2$ and $\frac{d}{p} < s-2-k \le 1, k=0,1$,
be the viscosity solution of (\ref{E:MA}). If $u_{\varepsilon}$ denotes the
discrete solution of (\ref{E:2ScOp}), then for $\beta = \min\{s,2+\frac{1}{d}\}$
we have
$$
\| u -u_{\varepsilon}\|_{L^{\infty}(\Omega_h)} \leq
C(d,\Omega,f_0) \left( R(u)^{-1} |u|_{W^2_{\infty}(\Omega)}^d +
\big(1+ R(u) \big) |u|_{W^2_{\infty}(\Omega)}
\right) h^{1-\frac{2}{\beta}},
$$
with
$R(u) = \Big(\frac{|u|_{W^2_{\infty}(\Omega)}}{|u|_{W_p^s(\Omega\setminus \mathcal{S})}+{|u|_{W^2_{\infty}(\Omega)}}}\Big)^{\frac{1}{\beta}}$
and $|u|_{W_p^s(\Omega \setminus \mathcal{S})}:= \max_i |u|_{W_p^s(\Omega_i)}$,
provided
%
\[
\delta = R(u) \ h^{\frac{2}{\beta}},
\quad
\theta= R(u)^{-1} \ h^{1-\frac{2}{\beta}}.
\]
%
\end{Theorem}
\begin{proof}
We proceed as in Theorems \ref{T:RatesHolder} and
\ref{T:RatesSobolev}. The
boundary layer estimate relies on the regularity $u \in W^2_{\infty}(\Omega)$ which
is still valid, whence for all $x \in \Omega_h$
such that ${\rm dist}(x,\partial \Omega_h) \leq \delta$
we obtain
$$
u_{\varepsilon}(x) - \mathcal I_h u(x) \leq C |u|_{W^2_{\infty}(\Omega)} \delta.
$$
Consider now the internal layer
\begin{equation*}
\mathcal{S}^{\delta}_h : = \left\{ x \in \Omega_h : \ {\rm dist}(x,\mathcal{S}) \leq \delta \right\},
\end{equation*}
which is the region affected by the discontinuity of
the Hessian $D^2u$. Recall the auxiliary function
$d_{\varepsilon} = \mathcal I_h u - u_{\varepsilon} + C |u|_{W^2_{\infty}(\Omega)} \delta$
of \Cref{T:RatesHolder} (rates of convergence for
classical solutions) and split the contact set $\mathcal{C}_-^\delta(d_{\varepsilon}):= \mathcal{C}_-(d_{\varepsilon}) \cap \Omega_{h,\delta}$ as follows:
\begin{equation*}
\mathcal{S}_{h,1}^{\delta} := \mathcal{C}_-^\delta(d_{\varepsilon}) \cap \mathcal{S}^{\delta}_h,
\quad \mathcal{S}_{h,2}^{\delta}:= \mathcal{C}_-^\delta(d_{\varepsilon}) \setminus \mathcal{S}^{\delta}_h.
\end{equation*}
An argument similar to Step 2 (interior estimate)
of \Cref{T:RatesHolder}, based on combining
\Cref{P:ContDep} (continuous dependence on data)
and \Cref{L:FullConsistency} (consistency of $T_\varepsilon[\mathcal I_h u]$)
with assumption $f\ge f_0>0$, yields
$$
\begin{aligned}
\max_{\Omega_{h,\delta}} \ d_{\varepsilon}^- &\lesssim
\delta \left( \sum_{x_i \in \mathcal{S}_{h,1}^{\delta}} C_2(u)^d
\right)^{1/d}
\\ & + \delta \ \left( \sum_{x_i \in \mathcal{S}_{h,2}^{\delta}} C_1(u)^d \delta^{(k+\alpha)d} + C_2(u)^d \left( \frac{h^2}{\delta^2} + \theta^2 \right)^d \right)^{1/d}
=: I_1 + I_2,
\end{aligned}
$$
because the consistency error in $\mathcal{S}_{h,1}^{\delta}$ is bounded by
$C_2(u) = C |u|_{W^2_\infty(B_i)}^d$. As in
\Cref{T:RatesSobolev} (convergence rate for $W^s_p$ solutions),
$C_1(u)$ satisfies
%
\[
C_1(u) \lesssim |u|_{W^s_p(B_i)} |u|_{W^2_\infty(B_i)}^{d-1}.
\]
%
Since the number of nodes $x_i \in \mathcal{S}_{h,1}^{\delta}$ is bounded by $C|\mathcal{S}|\delta h^{-d}$, we deduce
$$
I_1 \lesssim \delta \left( \sum_{x_i \in \mathcal{S}_{h,1}^{\delta}} C_2(u)^d \right)^{1/d} \lesssim \ |u|_{W^2_{\infty}(\Omega)}^d \frac{\delta^{1+\frac{1}{d}}}{h}.
$$
For $I_2$ we distinguish whether $x_i$ belongs to
$\Omega_1$ or $\Omega_2$ and accumulate $C_1(u)$ in
$\ell^p$, exactly as in \Cref{T:RatesSobolev}, to obtain
%
$$
I_2 \lesssim \ |u|_{W^2_{\infty}(\Omega)}^{d-1} \left( |u|_{W_p^s(\Omega \setminus \mathcal{S} ) }\frac{\delta^{s-1}}{h} + |u|_{W^2_{\infty}(\Omega)} \ \frac{\delta}{h} \ \left( \frac{h^2}{\delta^2} + \theta^2 \right) \right).
$$
%
Collecting the previous estimates and using the
definition of $\beta$ yields
%
\begin{align*}
\max_{\Omega_h} (u_{\varepsilon} &- \mathcal I_h u) \lesssim |u|_{W^2_{\infty}(\Omega)} \delta
\\
& + \ |u|_{W^2_{\infty}(\Omega)}^{d-1} \frac{\delta}{h} \left(
\Big(|u|_{W_p^s(\Omega \setminus \mathcal{S} )}
+ |u|_{W^2_{\infty}(\Omega)}\Big)\delta^{\beta-2} + |u|_{W^2_{\infty}(\Omega)}
\ \left( \frac{h^2}{\delta^2} + \theta^2 \right) \right).
\end{align*}
We finally realize that this estimate is similar
to that in the proof of \Cref{T:RatesSobolev} except for the
middle term on the right-hand side. Therefore, we
proceed as in \Cref{T:RatesSobolev} to find the
relation between $\delta, \theta$ and $h$, add the
estimate $\|u-\mathcal I_h u\|_{L^\infty(\Omega)}\lesssim h^2 |u|_{W^2_{\infty}(\Omega)}$,
and eventually derive the asserted error estimate.
\end{proof}
\subsection{Error Estimates for Piecewise Smooth Solutions with Degenerate $f$} \label{S:RatesDegen}
We observe that in all three preceding theorems we assume that $f \geq f_0 >0$.
This is an important assumption in the proofs, since it allows us to use
the concavity of $t\mapsto t^{1/d}$ and \Cref{P:ContDep} (continuous dependence on data)
to obtain
\begin{equation}\label{E:fconcavity}
(f(x_i)+e)^{1/d} -f(x_i)^{1/d} \leq \frac{e}{df_0^{\frac{d-1}{d}}},
\end{equation}
where $e$ is related to the consistency of the operator in
\Cref{L:FullConsistency} (consistency of $T_{\varepsilon}[\mathcal I_h u]$).
We see that this is only possible if $f_0 >0$.
If we allow $f$ to touch zero, then \eqref{E:fconcavity}
reduces to
\begin{equation}\label{E:fconcavitydegen}
(f(x_i)+e)^{1/d} -f(x_i)^{1/d} \leq e^{1/d},
\end{equation}
with equality for $f(x_i)=0$. This leads to a
rate of order $\big(\frac{\delta}{h}\big)^{1-\frac{2}{d}}\ge1$
for $d \geq 2$.
To circumvent this obstruction, we use \Cref{L:BarrierInterior}
(interior barrier function) which allows us
to introduce an extra parameter
$\sigma>0$ that
compensates for the lack of lower bound $f_0>0$ and yields
pointwise error estimates of reduced order.
\begin{Theorem}[degenerate forcing $f\ge0$]\label{T:RatesDegen}
Let $\mathcal{S}$ denote a $(d-1)$-dimensional
Lipschitz manifold that divides $\Omega$ into
two disjoint subdomains $\Omega_1, \Omega_2$ such that
$\mathcal{S} = \overline{\Omega}_1 \cap \overline{\Omega}_2$. Let $f \geq 0$ in
$\Omega$ and let $u \in W_p^s(\Omega_i) \cap W^2_{\infty}(\Omega)$, for $i=1,2$
and $\frac{d}{p} < s-2-k \le 1, k=0,1$, be the viscosity solution
of (\ref{E:MA}). If $u_{\varepsilon}$ denotes the discrete solution of
(\ref{E:2ScOp}), then for $\beta = \min\{ s, 2+\frac{1}{d}\}$ we have
$$
\| u -u_{\varepsilon}\|_{L^{\infty}(\Omega_h)} \leq C(d,\Omega)
|u|_{W^2_{\infty}(\Omega)} \Big( 1+ R(u) + R(u)^{-\frac{1}{d}} \Big)
\ h^{\frac{1}{d}\left(1-\frac{2}{\beta}\right)}
$$
with
$R(u) = \Big(\frac{|u|_{W^2_{\infty}(\Omega)}}{|u|_{W_p^s(\Omega\setminus \mathcal{S})}+|u|_{W^2_{\infty}(\Omega)}}\Big)^{\frac{1}{\beta}}$
and
$|u|_{W_p^s(\Omega \setminus \mathcal{S})}:= \max_i |u|_{W_p^s(\Omega_i)}$,
provided
\[
\delta = R(u) \ h^{\frac{2}{\beta}},
\quad
\theta= R(u)^{-1} \ h^{1-\frac{2}{\beta}}.
\]
\end{Theorem}
\begin{proof}
We employ the interior barrier function $q_h$
of \Cref{L:BarrierInterior} scaled by
a parameter $\sigma>0$ to control
$u_{\varepsilon}-\mathcal I_h u$ and $\mathcal I_h u -u_{\varepsilon}$ in
two steps. The parameter $\sigma$
allows us to mimic the calculation
in \eqref{E:fconcavity}. In the third step we
choose $\sigma$ optimally with respect to
the scales of our scheme.
\medskip
\textit{Step 1: Upper bound for
$u_{\varepsilon}-\mathcal I_h u$.} We let $w_h:= u_{\varepsilon} + \sigma q_h$
and $v_h:= \mathcal I_h u +C|u|_{W^2_{\infty}(\Omega)}
\delta$, observe that $T_\varepsilon[w_h](x_i)
\ge f(x_i) + \sigma^d$, and proceed as in Step
1 of \Cref{T:RatesHolder} to show
$
w_h(z) \leq v_h(z)
$
%
for all $z\in\mathcal{N}_h^0$ such that
$\textrm{dist} (z,\partial\Omega_h) \le \delta$.
We now focus on $\Omega_{h,\delta}$ and
define the auxiliary function $d_{\varepsilon}:= v_h -w_h$ and contact set
$\mathcal{C}_-^\delta(d_{\varepsilon}) := \mathcal{C}_-(d_{\varepsilon}) \cap \Omega_{h,\delta}$.
Since the previous argument guarantees that $d_{\varepsilon} \geq 0$ on $\partial \Omega_{h,\delta}$,
\Cref{P:ContDep} (continuous dependence on data) gives
$$
\max_{\Omega_{h,\delta}} d_{\varepsilon}^- \lesssim \
\delta \left( \sum_{x_i \in
\mathcal{C}_-^\delta(d_{\varepsilon})} \left(
\big(T_\varepsilon[v_h](x_i)\big)^{1/d}-
\big(T_\varepsilon[w_h](x_i)\big)^{1/d}
\right)^d \right)^{1/d} .
$$
If $e_i$ is the local
consistency error given in \Cref{L:FullConsistency}, we further note that
$$
T_\varepsilon[v_h](x_i) \le f(x_i) + e_i,
\quad
T_\varepsilon[w_h](x_i) \geq T_\varepsilon[u_{\varepsilon}](x_i) + T_\varepsilon[\sigma q_h](x_i) \geq f(x_i)+ \sigma^d
$$
for all $x_i\in\mathcal{N}_h^0$, whence
$$
\begin{aligned}
\max_{\Omega_{h,\delta}} d_{\varepsilon}^- &\lesssim \delta \left( \sum_{x_i \in \mathcal{C}_-^\delta(d_{\varepsilon})} \left( \big(f(x_i)+e_i\big)^{1/d}- \big(f(x_i)+\sigma^d\big)^{1/d}
\right)^d \right)^{1/d}.
\end{aligned}
$$
We now observe that $e_i \geq \sigma^d$ for all
$x_i \in \mathcal{C}_-^\delta(d_{\varepsilon})$
because all terms in the above sum are non-negative.
If there is no such $x_i$, then the above bound implies that $d_{\varepsilon}^-=0$
and $w_h \leq v_h$, whence $u_{\varepsilon} - \mathcal I_h u \lesssim \sigma +
|u|_{W^2_{\infty}(\Omega)} \delta$.
Otherwise, the above observation combined with \eqref{E:fconcavity}
and $f(x_i)\ge0$ implies
$$
\begin{aligned}
\big(f(x_i)+e_i \big)^{1/d} &- \big(f(x_i)+\sigma^d \big)^{1/d}
\\ &=
\big(f(x_i)+\sigma^d+(e_i-\sigma^d)\big)^{1/d}- \big(f(x_i)+\sigma^d\big)^{1/d} \\
&\leq \frac{e_i-\sigma^d}{d \sigma^{d\frac{d-1}{d}}} \leq d^{-1} \sigma^{1-d} e_i.
\end{aligned}
$$
We next proceed exactly as in \Cref{T:RatesPW}
(convergence rate for piecewise smooth solutions) to derive an upper
bound for $d_{\varepsilon}^-$, but with the additional factor $\sigma^{1-d}$.
Employing the definition of $d_{\varepsilon}$, we thereby obtain
$$
u_{\varepsilon} - \mathcal I_h u \lesssim \sigma + |u|_{W^2_{\infty}(\Omega)} \delta + \sigma^{1-d} \ \frac{\delta}{h} \left( C_1(u) \delta^{s-2} + C_2(u) \ \left( \delta^{1/d} + \frac{h^2}{\delta^2} + \theta^2 \right) \right),
$$
where $C_1(u) = C |u|_{W_p^s(\Omega \setminus \mathcal{S})} |u|_{W^2_{\infty}(\Omega)}^{d-1}$ and
$C_2(u)=C|u|_{W^2_{\infty}(\Omega)}^d$.
\medskip
\textit{Step 2: Lower bound for $u_{\varepsilon}-\mathcal I_h u$.}
To prove the reverse inequality, we
proceed as in Step 1, except that this time we
define $v_h:= u_{\varepsilon} + C |u|_{W^2_{\infty}(\Omega)} \delta$
and $w_h:= \mathcal I_h u + \sigma q_h$. An
argument similar to Step 1 yields $w_h \leq
v_h$ in $\omega_{h,\delta}$. Moreover,
recalling \Cref{L:FullConsistency}
(consistency of $T_\varepsilon[\mathcal I_h u]$) we have for all $x_i\in\mathcal{N}_h^0$
%
\[
T_\varepsilon[v_h](x_i) = f(x_i) \le
T_\varepsilon[\mathcal I_h u](x_i) + e_i,
\quad
T_\varepsilon[w_h](x_i) \ge T_\varepsilon[\mathcal I_h u](x_i) + \sigma^d,
\]
where $e_i$ is a local bound for the consistency error.
Combining this with \Cref{P:ContDep} (continuous dependence on data) in $\Omega_{h,\delta}$ gives
\[
\max_{\Omega_{h,\delta}} d_\varepsilon^- \lesssim \delta
\left( \sum_{x_i\in\mathcal{C}_-^\delta(d_\varepsilon^-)} \Big(
\big(T_\varepsilon[\mathcal I_h u](x_i) + e_i\big)^{\frac{1}{d}}
- \big( T_\varepsilon[\mathcal I_h u](x_i) + \sigma^d \big)^{\frac{1}{d}}
\Big)^d\right)^{\frac{1}{d}} ,
\]
Since $\mathcal I_h u$ is discretely convex, we apply \Cref{L:DisConv}
(discrete convexity) to deduce $T_\varepsilon[\mathcal I_h u](x_i)\ge 0$
and next argue as in Step 1 to obtain
$$
\mathcal I_h u - u_{\varepsilon} \lesssim \sigma + |u|_{W^2_{\infty}(\Omega)} \delta + \sigma^{1-d} \ \frac{\delta}{h} \left( C_1(u) \delta^{s-2} + C_2(u) \ \left( \delta^{1/d} + \frac{h^2}{\delta^2} + \theta^2 \right) \right).
$$
\medskip
\textit{Step 3: Choice of $\delta, \theta$ and $\sigma$.}
Since $\|u-\mathcal I_h u\|_{L^{\infty}(\Omega_h)}\leq
C|u|_{W^2_{\infty}(\Omega)} h^2$, combining Steps 1 and 2 yields
\begin{align*}
\|u_{\varepsilon} - u\|_{L^\infty(\Omega_h)} &\lesssim
\sigma + |u|_{W^2_{\infty}(\Omega)} (\delta + h^2) \\
& + \sigma^{1-d} \ \frac{\delta}{h} \left( C_1(u) \delta^{s-2} + C_2(u) \ \left( \delta^{1/d} + \frac{h^2}{\delta^2} + \theta^2 \right) \right) .
\end{align*}
We now minimize the right-hand side upon choosing
$\delta, \theta$ and $\sigma$ suitably with respect to $h$.
We first recall the definition of $\beta$ and
choose $\delta$ and $\theta$ as in \Cref{T:RatesPW}.
At this stage it only remains to find $\sigma$ upon solving
$$
\sigma = C_2(u) \sigma^{1-d} \frac{h}{\delta} = C \sigma^{1-d}
|u|_{W^2_{\infty}(\Omega)}^d R(u)^{-1} \ h^{1-\frac{2}{\beta}},
$$
which leads to
$$
\sigma = |u|_{W^2_{\infty}(\Omega)} R(u)^{-\frac{1}{d}} \ h^{\frac{1}{d}\left(1-\frac{2}{\beta}\right)}.
$$
Since $\beta>2$ we get $h^2 + \delta \le \big(1 +
R(u)^{-\frac{1}{\beta}}\big) h^{\frac{2}{\beta}}$ and
\[
\|u_{\varepsilon} - u\|_{L^\infty(\Omega_h)} \lesssim
|u|_{W^2_{\infty}(\Omega)} \big(1 + R(u) \big) h^{\frac{2}{\beta}}
+ |u|_{W^2_{\infty}(\Omega)} R(u)^{-\frac{1}{d}} \ h^{\frac{1}{d}\left(1-\frac{2}{\beta}\right)}.
\]
This yields the asserted estimate and finishes the proof.
\end{proof}
\Cref{T:RatesDegen} is an extension of \Cref{T:RatesPW} to the
degenerate case $f\ge0$, but the same techniques and estimates
extend as well to Theorems \ref{T:RatesHolder} and \ref{T:RatesSobolev}.
We stress that Theorems \ref{T:RatesPW} and \ref{T:RatesDegen} correspond to non-classical viscosity solutions that are of class $W^{2}_{\infty}(\Omega)$. In order to deal with discontinuous Hessians and degenerate right hand sides, we rely on techniques that give rise to reduced rates. For \Cref{T:RatesPW} we obtain rates that depend on the space dimension, whereas for \Cref{T:RatesDegen} we resort to a regularization procedure that leads to further reduction of the rates. Although the derived estimates are suboptimal with respect to the computational rates observed in \cite{NoNtZh}, we wish to emphasize that \Cref{T:RatesDegen} is, to our knowledge, the only error estimate available in the literature that deals with degenerate right hand sides.
\section{Conclusions}
In this paper we extend the analysis of the two-scale method
introduced in \cite{NoNtZh}. We derive
continuous dependence of discrete solutions on data and use it to prove rates of
convergence in the $L^{\infty}$ norm in the computational domain $\Omega_h$
for four different
cases. We first prove rates of order up to $h^{1/2}$ for
smooth classical solutions with H\"older regularity. We then
exploit the structure of the continuous dependence
estimate of discrete solutions on data to
derive error estimates for classical solutions with Sobolev regularity,
thereby achieving the same rates under weaker regularity
assumptions. In a more general scenario, we derive error estimates
for viscosity solutions with discontinuous Hessian across a
surface with appropriate smoothness, but otherwise possessing
piecewise Sobolev regularity.
Lastly, we use an
interior barrier function that allows us to remove the
nondegeneracy assumption
$f > 0$ at the cost of a reduced rate that depends
on dimension. Our theoretical
predictions are sub-optimal with respect to the linear rates
observed experimentally in
\cite{NoNtZh} for a smooth classical solution and a
piecewise smooth viscosity solution with
degenerate right-hand side $f\ge 0$. This can be
attributed to the fact that the continuous dependence estimate
of discrete solutions on data introduces a factor $\frac{\delta}{h} \gg 1$
in the error estimates. This feature is similar to the
discrete ABP estimate developed in \cite{KuoTru} and is the
result of using sets of measure $\approx \delta^d$ instead of
$\approx h^d$ to approximate subdifferentials. In a
forthcoming paper we will tackle this issue and connect our
two-scale method with that of Feng and Jensen \cite{FeJe:16}.
\bibliographystyle{amsplain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,111 |
\section{Introduction}
\label{sec:introduction}
Theory of quantum deformations based on the
$\kappa$-Poincar\'{e}-Hopf algebra has been a alternative
framework for studying relativistic and nonrelativistic quantum
systems.
The Hopf-algebraic description of $\kappa$-deformed Poincar\'{e}
symmetries, with $\kappa$ a masslike fundamental deformation
parameter, was introduced in
\cite{PLB.1991.264.331,PLB.1992.293.344}.
In this context, the space-like $\kappa$-deformed Minkowski
spacetime is the more interesting among them because its
phenomenological applications.
Such $\kappa$-deformed Poincar\'{e}-Hopf algebra established in
Refs. \cite{PLB.1991.264.331,PLB.1992.293.344,PLB.1993.302.419,
PLB.1993.318.613,PLB.1994.329.189,PLB.1994.334.348}
is defined by the following commutation relations
\begin{subequations}
\label{eq:algebra}
\begin{equation}
\left[\Pi_{\nu},\Pi_{\mu}\right]=0,
\label{eq:algebraa}
\end{equation}
\begin{equation}
\left[M_{i},\Pi_{\mu}\right]=
(1-\delta_{0\mu})i\epsilon_{ijk}\Pi_{k},
\label{eq:algebrab}
\end{equation}
\begin{equation}
\left[L_{i},\Pi_{\mu}\right]=i [\Pi_{i}]^{\delta_{0\mu}}
[\delta_{ij}\varepsilon^{-1}
\sinh \left( \varepsilon \Pi_{0}\right)]^{1-\delta_{0\mu}},
\label{eq:algebrac}
\end{equation}
\begin{equation}
\left[M_{i},M_{j}\right]=i\epsilon_{ijk} M_{k},\qquad
\left[M_{i},L_{j}\right]=i\epsilon_{ijk} L_{k},
\label{eq:algebrad}
\end{equation}
\begin{equation}
\left[L_{i},L_{j}\right]=
-i\epsilon_{ijk}
\left[
M_{k}\cosh \left(\varepsilon \Pi_{0}\right)-
\frac{\varepsilon ^{2}}{4}\Pi_{k}\Pi_{l} M_{l}
\right],
\label{eq:algebrae}
\end{equation}
\end{subequations}
where $\varepsilon$ is defined by
\begin{equation}
\varepsilon=\kappa^{-1}=
\lim_{R\rightarrow \infty }(R\ln q),
\end{equation}
with $R$ being the de Sitter curvature and $q$ is a real
deformation parameter, $\Pi_{\mu }=(\Pi_{0},\boldsymbol{\Pi})$
are the $\kappa$-deformed generators for energy and momenta.
Also, the $M_{i}$, $L_{i}$ represent the spatial rotations and
deformed boosts generators, respectively.
The coalgebra and antipode for the $\kappa$-deformed
Poincar\'{e} algebra was established in
Ref. \cite{AP.1995.243.90}.
The physical properties of $\kappa$-deformed relativistic
quantum systems can be accessed by solving the $\kappa$-deformed
Dirac equation \cite{PLB.1993.302.419,PLB.1993.318.613,
CQG.2004.21.2179,JHEP.2004.2004.28}.
The deformation parameter $\kappa$ can be usually interpreted as
being the Planck mass $M_{P}$ \cite{PLB.2012.711.122}.
The $\kappa$-deformation has implications for various properties
of physical systems as for example, vacuum energy divergent
\cite{PRD.2007.76.125005}, Landau levels \cite{PLB.1994.339.87},
spin-1/2 Aharonov-Bohm (AB) interaction creating additional
bound states \cite{PLB.1995.359.339}, Dirac oscillator
\cite{EPL.1997.39.583}, Dirac-Coulomb problem
\cite{PLB.1993.318.613} and constant magnetic interaction
\cite{MPLA.1995.10.1969}.
In Ref. \cite{PLB.1995.359.339} the spin-1/2 AB problem was
solved for the first time in connection with the theory of
quantum deformations.
The AB problem \cite{PR.1959.115.485} has been extensively
studied in different contexts in recent years
\cite{PRD.2011.84.045002,PRL.2012.108.230404,JPA.2010.43.075202,
PRD.2012.85.041701, PRA.2012.86.040101,PRL.2012.108.153901,
PRD.2011.83.125025,PRD.2012.86.125015}.
In this letter we study the scattering scenario of the model
addressed in Ref. \cite{PLB.1995.359.339} where only the bound
state problem was considered.
We solve the problem by following the self-adjoint extension
approach
\cite{CMP.1991.139.103,JMP.1985.26.2520,Book.2004.Albeverio}
and by using the general regularization prescription proposed in
\cite{PRD.2012.85.041701} we determine the self-adjoint
extension parameter in terms of the physics of the problem.
Such procedure allows discuss the problem of helicity
conservation and, as a alternative approach, we obtain the bound
states energy from the poles of $S$-matrix.
The plan of our Letter is the following.
In Section \ref{sec:k-deformed-SPE} we introduce the
$\kappa$-deformed Dirac equation to be solved and take its
nonrelativistic limit in order to study the physical
implications of $\kappa$-deformation in the spin-1/2 AB
problem.
A new contribution to the nonrelativistic Hamiltonian arises in
this approach.
These new term imply a direct correction on the anomalous
magnetic moment term.
We impose a upper bound on the magnitude of the deformation
parameter $\varepsilon$.
The Section \ref{sec:selfae} is devoted to study the
$\kappa$-deformed Hamiltonian via self-adjoint extension
approach and presented some important properties of the
$\kappa$-deformed wave function.
In Section \ref{sec:scatt-bound} are addressed the scattering and
bound states scenario within the framework of $\kappa$-deformed
Schr\"{o}dinger-Pauli equation.
Expressions for the phase shift, $S$-matrix, and bound states
are derived.
We also derive a relation between the self-adjoint extension
parameter and the physical parameters of the problem.
For last, we make a detailed analysis of the helicity
conservation problem in the present framework.
A brief conclusion in outlined in Section \ref{sec:conclusion}.
\section{$\kappa$-deformed Schr\"{o}dinger-Pauli
equation}
\label{sec:k-deformed-SPE}
In the minimal coupling prescription the (3+1)-dimensional
$\kappa$-deformed Dirac equation supported by the algebra in
Eq. \eqref{eq:algebra} up to $O(\varepsilon)$ order was derived
in Ref. \cite{PLB.1995.359.339} (see also Refs. therein).
We here analyze the (2+1)-dimensional $\kappa$-deformed Dirac
equation, which follows from the decoupling of (3+1)-dimensional
$\kappa$-deformed Dirac equation for the specialized case where
$\partial_3=0$ and $A_{3}=0$, into two uncoupled two-component
equations, such as implemented in
Refs. \cite{PRD.1978.18.2932,NPB.1988.307.909,PRL.1989.62.1071}.
This way, the planar $\kappa$-deformed Dirac equation
($\hbar=c=1$) is
\begin{equation}
\hat{H}\psi=
\left[
\beta \boldsymbol{\gamma} \cdot \boldsymbol{\Pi}
+\beta M +
\frac{\varepsilon}{2}
\left(
M \boldsymbol{\gamma} \cdot \boldsymbol{\Pi} +
e s \boldsymbol{\sigma} \cdot \boldsymbol{B}
\right)
\right]\psi= \overline{E}\psi,
\label{eq:defdirac}
\end{equation}
where $\psi$ is a two-component spinor,
$\boldsymbol{\Pi}=\boldsymbol{p}-e\boldsymbol{A}$ is the
generalized momentum, and $s$ is twice the spin value, with
$s=+1$ for spin ``up'' and $s=-1$ for spin ``down''.
The $\gamma$-matrices in $(2+1)$ are given in terms of the Pauli
matrices
\begin{equation}
\beta=\gamma_{0}=\sigma_{3}, \qquad
\gamma_{1}=i\sigma_{2}, \qquad
\gamma_{2}=-is\sigma_{1}.
\end{equation}
Here few comments are in order.
First, the $\kappa$-deformed Dirac equation is defined in the
commutative spacetime and the corresponding $\gamma$-matrices
are independent of the deformation parameter $\kappa$
\cite{MPLA.2011.26.1103}.
Second, it is important to observe that in
Ref. \cite{PLB.1995.359.339} the authors only consider the
negative value of the spin projection, here our approach considers
a more general situation.
We shall now take the nonrelativistic limit of
Eq. \eqref{eq:defdirac}.
Writing $\psi=(\chi,\phi)^{T}$, where $\chi$ and $\phi$ are the
``large'' and ``small'' components of the spinor, and
using $\overline{E}=M+E$ with $M\gg E$, after expressing the
lower component $\phi$ in terms of the upper one, $\chi$, we get
the $\kappa$-deformed Schr\"{o}dinger-Pauli equation for the
large component
\begin{equation}
H\chi=E\chi,
\end{equation}
with
\begin{equation}
H=\frac{1}{2M}
\left[
\Pi_{1}^{2}+\Pi_{2}^{2}-(1-M\varepsilon) e s B_{3}
\right],
\label{eq:nrdefdirac}
\end{equation}
where it was assumed that $\varepsilon^{2}\cong 0$.
It can be seen from \eqref{eq:nrdefdirac} that the magnetic
moment has modified by a quantity proportional to the deformation
parameter.
Another effect enclosed in Hamiltonian \eqref{eq:nrdefdirac} is
concerned with the anomalous magnetic moment of the electron.
The electron magnetic moment is
$\boldsymbol{\mu} =-\mu \boldsymbol{\sigma}$, with $\mu=e/2M$,
and $g=2$ the gyromagnetic factor.
The anomalous magnetic moment of the electron is given by
$g=2(1+a)$, with $a=\alpha /2\pi=0.00115965218279$ representing the
deviation in relation to the usual case \cite{RMP.2012.84.1527}.
In this case, the magnetic interaction is
$\bar{H}=\mu(1+a)(\boldsymbol{\sigma}\cdot\boldsymbol{B})$.
In accordance with very precise measurements and quantum
electrodynamics (QED) calculations \cite{PRL.2006.97.030802}, precision corrections to
this factor are now evaluated at the level of $1$ part in
$10^{11}$, that is, $\Delta a\leq 3\times 10^{-11}$.
In our case, the Hamiltonian \eqref{eq:nrdefdirac} provides
$\kappa$-tree-level contributions to the usual $g=2$
gyromagnetic factor, which can not be larger than $a=0.00116$
(the current experimental value for the anomalous magnetic
moment).
The total $\kappa$-deformed magnetic interaction in
Eq. \eqref{eq:nrdefdirac} is
\begin{equation}
H_{\text{magn}}=(1-M\varepsilon) s(\boldsymbol{\mu \cdot B}).
\label{eq:hmagn}
\end{equation}
For the magnetic field along the $z$-axis and a spin-polarized
configuration in the $z$-axis, this interaction assumes the form
\begin{equation}
\left( 1-M\varepsilon \right) s\mu B_{z},
\end{equation}
with $M\varepsilon$ representing the $\kappa$-tree-level
correction that should be smaller than $0.00116$.
Under such consideration, we obtain the following upper bound
for $\varepsilon $:
\begin{equation}
\varepsilon <2.27\times 10^{-9}\;(eV) ^{-1},
\label{eq:bound}
\end{equation}
where we have used $M=5.11\times 10^{5}eV$.
We now pass to study the $\kappa$-deformed Schr\"{o}dinger-Pauli
equation in the AB background potential
\cite{PR.1959.115.485}.
The vector potential of the AB interaction, in the
Coulomb gauge, is
\begin{equation}
\mathbf{A}=-
\frac{\alpha}{r}
\hat{\boldsymbol{\varphi}},
\qquad A_{0}=0,
\label{eq:vectora}
\end{equation}
where $\alpha = \Phi /\Phi_{0}$ is the flux parameter with
$\Phi_{0}=2\pi/e$.
The magnetic field is given in the usual way
\begin{equation}
e \mathbf{B}=e\nabla \times \mathbf{A}=
-\alpha \frac{\delta (r)}{r}\mathbf{\hat{z}}.
\label{eq:vectorb}
\end{equation}
So, the $\kappa$-deformed Schr\"{o}dinger-Pauli equation can be
written as
\begin{equation}
\frac{1}{2M}
\left[
H_{0}+{\eta}
\frac{\delta(r)}{r}
\right]
\chi = E\chi,
\label{eq:schor}
\end{equation}
with
\begin{equation}
H_{0}=
\left(
\frac{1}{i}\boldsymbol{\nabla}
- e \mathbf{A}
\right)^{2},
\end{equation}
and
\begin{equation}
\label{eq:dcoup}
\eta=(1-M\varepsilon)\alpha s,
\end{equation}
is the coupling constant of the $\delta(r)/r$ potential.
For the present system the total angular momentum operator in
the $z$ direction,
\begin{equation}
\hat{J}_{3}=-i\partial_{\varphi}+\frac{1}{2}\sigma_{3},
\end{equation}
commutes with the effective Hamiltonian.
So, it is possible to express the eigenfunctions of the two
dimensional Hamiltonian in terms of the eigenfunctions of
$\hat{J}_{3}$.
The eigenfunctions of this operator are
\begin{equation}
\psi=
\left(
\begin{array}{c}
\chi \\
\phi
\end{array}
\right)=
\left(
\begin{array}{c}
f_{m}(r)\; e^{i(m_{j}-1/2)\varphi} \\
g_{m}(r)\; e^{i(m_{j}+1/2)\varphi}
\end{array}
\right),
\label{eq:wavef}
\end{equation}
with $m_{j}=m+1/2=\pm 1/2,\pm 3/2, \ldots$, with
$m\in\mathbb{Z}$.
Inserting this into Eq. \eqref{eq:schor}, we can extract
the radial equation for $f_{m}(r)$ ($k^{2}= 2 M E$)
\begin{equation}
h f_{m}(r)=k^{2} f_{m}(r),
\label{eq:eigen}
\end{equation}
where
\begin{equation}
h=h_{0}+\eta \frac{\delta(r)}{r},
\label{eq:hfull}
\end{equation}
\begin{equation}
h_{0}=
-\frac{d^{2}}{dr^{2}}
-\frac{1}{r}\frac{d}{dr}
+\frac{(m+\alpha)^{2}}{r^{2}}.
\label{eq:hzero}
\end{equation}
The Hamiltonian in Eq. \eqref{eq:hfull} is singular at
the origin.
This problem can then be treated by the method of the
self-adjoint extension \cite{Book.2004.Albeverio}, which we pass
to discuss in the next Section.
\section{Self-adjoint extension analysis}
\label{sec:selfae}
The operator $h_{0}$, with domain $\mathcal{D}(h_{0})$, is
self-adjoint if $h_{0}^{\dagger}=h_{0}$ and
$\mathcal{D}(h_{0}^{\dagger})=\mathcal{D}(h_{0})$.
For smooth functions, $\xi \in C_{0}^{\infty}(\mathbb{R}^2)$ with
$\xi(0)=0$, we should have $h \xi =h_{0} \xi$, and hence it is
reasonable to interpret the Hamiltonian \eqref{eq:hfull} as a
self-adjoint extension of $h_{0}|_{C_{0}^{\infty}(\mathbb{R}^{2}/\{0\})}$
\cite{crll.1987.380.87,JMP.1998.39.47,LMP.1998.43.43}.
In order to proceed to the self-adjoint extensions of
\eqref{eq:hzero}, we decompose the Hilbert space
$\mathfrak{H}=L^{2}(\mathbb{R}^{2})$
with respect to the angular momentum
$\mathfrak{H}=\mathfrak{H}_{r}\otimes\mathfrak{H}_{\varphi}$, where
$\mathfrak{H}_{r}=L^{2}(\mathbb{R}^{+},rdr)$ and
$\mathfrak{H}_{\varphi}=L^{2}(\mathcal{S}^{1},d\varphi)$,
with $\mathcal{S}^{1}$ denoting the unit sphere in
$\mathbb{R}^{2}$.
The operator $-\partial^{2}/\partial\varphi^{2}$ is
essentially self-adjoint in
$L^{2}(\mathcal{S}^{1},d\varphi)$
\cite{Book.1975.Reed.II} and we obtain the operator $h_{0}$ in
each angular momentum sector.
Now, using the unitary operator
$U: L^{2}(\mathbb{R}^{+},rdr)
\to L^{2}(\mathbb{R}^{+}, dr)$,
given by $(U \xi)(r)=r^{1/2}\xi(r)$, the operator $h_{0}$ becomes
\begin{equation}
\tilde{h}_{0}=
U h_{0} U^{-1}=
-\frac{d^{2}}{dr^{2}}
-\left[
(m+\alpha)^{2}-
\frac{1}{4}
\right]
\frac{1}{r^{2}},
\end{equation}
which is essentially self-adjoint for $|m+\alpha| \geq 1$, while
for $|m+\alpha|< 1$ it admits a one-parameter family of
self-adjoint extensions \cite{Book.1975.Reed.II},
$h_{0,\lambda_{m}}$, where $\lambda_{m}$ is the self-adjoint
extension parameter.
To characterize this family we will use the approach in
\cite{JMP.1985.26.2520}, which is based in a boundary
conditions at the origin.
Following the approach in
Refs. \cite{JMP.1985.26.2520,Book.2004.Albeverio}, all the
self-adjoint extensions $h_{0,\lambda_{m}}$ of $h_{0}$ are
parametrized by the boundary condition at the origin
\begin{equation}
\label{eq:bc}
f_{0,\lambda_{m}}=\lambda_{m} f_{1,\lambda_{m}},
\end{equation}
with
\begin{align}
f_{0,\lambda_{m}}&=\lim_{r\rightarrow 0^{+}}r^{|m+\alpha|}f_{m}(r),
\\
f_{1,\lambda_{m}}&=\lim_{r\rightarrow 0^{+}}\frac{1}{r^{|m+\alpha|}}
\left[
f_{m}(r)-f_{0,\lambda_{m}}\frac{1}{r^{|m+\alpha|}}
\right],
\end{align}
where $\lambda_{m}\in \mathbb{R}$ is the self-adjoint extension
parameter.
The self-adjoint extension parameter $\lambda_{m}$ has a
physical interpretation, it represents the scattering length
\cite{Book.2011.Sakurai} of $h_{0,\lambda_{m}}$
\cite{Book.2004.Albeverio}.
For $\lambda_{m}=0$ we have the free Hamiltonian (without the
$\delta$ function) with regular wave functions at the origin,
and for $\lambda_{m}\neq 0$ the boundary condition in
Eq. \eqref{eq:bc}
permit a $r^{-|m+\alpha|}$ singularity in the wave functions at
the origin.
\section{Scattering and bound states analysis}
\label{sec:scatt-bound}
The general solution for Eq. \eqref{eq:eigen} in the $r\neq 0$
region can be written as
\begin{equation}
\label{eq:sol1}
f_{m}(r)=a_{m}J_{|m+\alpha|}(kr)+b_{m}Y_{|m+\alpha|}(kr),
\end{equation}
with $a_{m}$ and $b_{m}$ being constants and $J_{\nu}(z)$ and
$Y_{\nu}(z)$ are the Bessel functions of first and second kind,
respectively.
Upon replacing $f_{m}(r)$ in the boundary condition
\eqref{eq:bc},
we obtain
\begin{align}
\lambda_{m} \, a_{m} \, \upsilon \, k^{|m+\alpha|}
= {} &
b_{m}\left[\zeta k^{-|m+\alpha|}\right.
\nonumber \\
& \left. -\lambda_{m} \big(\beta k^{|m+\alpha|} +
\zeta \nu k^{-|m+\alpha|}
\lim_{r\rightarrow 0^{+}}r^{2-2|m+\alpha|}\big)\right],
\label{eq:bcf}
\end{align}
where
\begin{align}
\upsilon & = \frac{1}{2^{|m+\alpha|}\Gamma(1+|m+\alpha|)}, &
\zeta & =-\frac{2^{|m+\alpha|}\Gamma(|m+\alpha|)}{\pi},
\nonumber \\
\beta & =-\frac{\cos (\pi |m+\alpha|)
\Gamma(-|m+\alpha|)}{\pi 2^{|m+\alpha|}},&
\nu & =\frac{k^{2}}{4(1-|m+\alpha|)}.
\end{align}
In Eq. \eqref{eq:bcf}, $\lim_{r\rightarrow 0^{+}}r^{2-2|m+\alpha|}$
is divergent if $|m+\alpha|\geq 1$, hence $b_{m}$ must be zero.
On the other hand, $\lim_{r\rightarrow 0^{+}}r^{2-2|m+\alpha|}$
is finite for $|m+\alpha|<1$, it means that there arises the
contribution of the irregular solution $Y_{|m+\alpha|}(kr)$.
Here, the presence of an irregular solution contributing to the
wave function stems from the fact the Hamiltonian $h$ is not a
self-adjoint operator when $|m+\alpha|<1$ (cf., Section
\ref{sec:selfae}), hence such irregular solution must be
associated with a self-adjoint extension of the operator $h_{0}$
\cite{JPA.1995.28.2359,PRA.1992.46.6052}.
Thus, for $|m+\alpha|<1$, we have
\begin{equation}
\lambda_{m}a_{m}\upsilon k^{|m+\alpha|}=
b_{m}(\zeta k^{-|m+\alpha|}-
\lambda_{m}\beta k^{|m+\alpha|}),
\end{equation}
and by substituting the values of $\upsilon$, $\zeta$ and $\beta$
into above expression we find
\begin{equation}
b_{m}=-\mu_{m}^{\lambda_{m}}a_{m},
\end{equation}
where
\begin{equation}
\mu_{m}^{\lambda_{m}}=
\frac
{\lambda_{m}k^{2|m+\alpha|}
\Gamma(1-|m+\alpha|)\sin(\pi |m+\alpha| )}
{B_{k}},
\label{eq:mul}
\end{equation}
and
\begin{align}
B_{k}= {} & \lambda_{m}k^{2|m+\alpha|}
\Gamma{(1-|m+\alpha|)}\cos (\pi|m+\alpha|)\nonumber \\
& + 4^{|m+\alpha|}\Gamma(1+|m+\alpha|).
\end{align}
Since a $\delta$ function is a very short range potential, it
follows that the asymptotic behavior of $f_{m}(r)$ for
$r\rightarrow \infty$ is given by \cite{JPA.2010.43.354011}
\begin{equation}
f_{m}(r)\sim \sqrt{\frac{2}{\pi kr}}
\cos \left( kr-\frac{|m|\pi}{2}-
\frac{\pi}{4}+
\delta_{m}^{{\lambda_{m}}}(k,\alpha)\right) ,
\label{eq:f1asim}
\end{equation}
where $\delta_{m}^{{\lambda_{m}}}(k,\alpha)$ is a
scattering phase shift.
The phase shift is a measure of the argument difference to the
asymptotic behavior of the solution $J_{|m|}(kr)$ of the radial
free equation which is regular at the origin.
By using the asymptotic behavior of the Bessel functions
\cite{Book.1972.Abramowitz} into Eq. \eqref{eq:sol1} we obtain
\begin{align}
\label{eq:scattsol}
f_{m}(r)
\sim {} &
a_{m}\sqrt{\frac{2}{\pi kr}}
\left[
\cos\left(kr-\frac{\pi |m+\alpha|}{2}-\frac{\pi}{4}\right)
\right. \nonumber\\
&
\left.
- \mu_{m}^{{\lambda_{m}}}
\sin \left( kr-\frac{\pi |m+\alpha|}{2}-\frac{\pi}{4}\right)
\right] .
\end{align}
By comparing the above expression with Eq. \eqref{eq:f1asim}, we
found
\begin{equation}
\delta_{m}^{{\lambda_{m}}}(k,\alpha)=
\Delta_{m}^{AB}(\alpha)+\theta_{{\lambda_{m}}},
\label{eq:phaseshift}
\end{equation}
where
\begin{equation}
\Delta_{m}^{AB}(\alpha)=\frac{\pi}{2}(|m|-|m+\alpha|),
\end{equation}
is the usual phase shift of the AB scattering and
\begin{equation}
\theta_{{\lambda_{m}}}=\arctan {(\mu_{m}^{\lambda_{m}})}.
\end{equation}
Therefore, the scattering operator $S_{\alpha,m}^{\lambda_{m}}$
($S$-matrix) for the self-adjoint extension is
\begin{equation}
S_{\alpha,m}^{\lambda_{m}}=
e^{2i\delta_{m}^{{\lambda_{m}}}(k,\alpha)}=
e^{2i\Delta_{m}^{AB}(\alpha)}
\left[
\frac{1+i\mu_{m}^{\lambda_{m}}}{1-i\mu_{m}^{\lambda_{m}}}
\right].
\end{equation}
Using Eq. \eqref{eq:mul}, we have
\begin{align}
S_{\alpha,m}^{\lambda_{m}}
= {} &
e^{2i\Delta_{m}^{AB}(\alpha)} \nonumber \\
{} & \times
\bigg[
\frac
{B_{k}+i\lambda_{m}k^{2|m+\alpha|}
\Gamma(1-|m+\alpha|)\sin(\pi |m+\alpha|)}
{B_{k}-i\lambda_{m}k^{2|m+\alpha|}
\Gamma(1-|m+\alpha|)\sin(\pi |m+\alpha|)}
\bigg].
\label{eq:smatrix}
\end{align}
Hence, for any value of the self-adjoint extension parameter
$\lambda_{m}$, there is an additional scattering.
If ${\lambda_{m}}=0$, we achieve the corresponding result
for the usual AB problem with Dirichlet boundary condition; in
this case, we recover the expression for the scattering matrix
found in Ref. \cite{AP.1983.146.1},
$S_{\alpha,m}^{\lambda_{m}}=e^{2i\Delta_{m}^{AB}(\alpha)}$.
If we make ${\lambda_{m}}=\infty $, we get
$S_{\alpha,m}^{\lambda_{m}}=e^{2i\Delta_{m}^{AB}(\alpha)+2i\pi |m+\alpha|}$.
In accordance with the general theory of scattering, the poles
of the $S$-matrix in the upper half of the complex plane
\cite{PRC.1999.60.34308} determine the positions of the bound
states in the energy scale.
These poles occur in the denominator of \eqref{eq:smatrix} with
the replacement $k\rightarrow i\kappa$,
\begin{equation}
B_{i \kappa}+i\lambda_{m}(i \kappa)^{2|m+\alpha|}
\Gamma(1-|m+\alpha|)\sin(\pi |m+\alpha|)=0.
\end{equation}
Solving the above equation for $E$, we found the bound state
energy
\begin{equation}
E=-\frac{2}{M}
\left[-\frac{1}{\lambda_{m}}
\frac{\Gamma(1+|m+\alpha|)}{\Gamma(1-|m+\alpha|)}
\right]^{1/|m+\alpha|},
\label{eq:energy_BG-sc}
\end{equation}
for $\lambda_{m}<0$.
Hence, the poles of the scattering matrix only occur for
negative values of the self-adjoint extension parameter.
In this latter case, the scattering operator can be expressed in
terms of the bound state energy
\begin{equation}
S_{\alpha,m}^{\lambda_{m}}=e^{2i\Delta_{m}^{AB}(\alpha)}
\left[
\frac
{e^{2 i \pi |m+\alpha|}-(\kappa/k)^{2|m+\alpha|}}
{1-(\kappa/k)^{2|m+\alpha|}}
\right].
\end{equation}
The scattering amplitude $f_{\alpha}(k,\varphi)$
can be obtained using the standard methods of scattering theory,
namely
\begin{align}
f_{\alpha}(k,\varphi)
= {} &
\frac{1}{\sqrt{2\pi i k}}\sum_{m=-\infty}^{\infty}
\left(
e^{2 i\delta_{m}^{{\lambda_{m}}}(k,\alpha)}-1
\right)
e^{im\varphi} \nonumber \\
={} &
\frac{1}{\sqrt{2\pi i k}}\sum_{m=-\infty}^{\infty}
\left( e^{2 i \Delta_{m}(\alpha)}
\left[
\frac
{1+ i\mu_{m}^{\lambda_{m}}}
{1-i\mu_{m}^{\lambda_{m}}}
\right]
-1
\right) e^{im\varphi}.
\label{eq:scattamp}
\end{align}
In the above equation we can see that the scattering amplitude
differ from the usual AB scattering amplitude off a thin
solenoid because it is energy dependent (cf., Eq. \eqref{eq:mul}).
The only length scale in the nonrelativistic problem is set by
$1/k$, so it follows that the scattering amplitude
would be a function of the angle alone, multiplied by $1/k$
\cite{PRD.1977.16.1815}.
This statement is the manifestation of the helicity conservation
\cite{Book.1967.Sakurai}.
So, one would to expect the commutator of the Hamiltonian with
the helicity operator,
$\hat{h}=\boldsymbol{\Sigma} \cdot \boldsymbol{\Pi}$, to be
zero.
However, when calculated, one finds that
\begin{equation}
[\hat{H},\hat{h}]=e \varepsilon
\left(
\begin{array}{cc}
0 & (\boldsymbol{\sigma} \cdot \boldsymbol{B})
(\boldsymbol{\sigma} \cdot \boldsymbol{\Pi}) \\
(\boldsymbol{\sigma} \cdot \boldsymbol{B})
(\boldsymbol{\sigma} \cdot \boldsymbol{\Pi}) & 0
\end{array}
\right),
\end{equation}
which is nonzero for $\varepsilon \neq 0$.
So, the inevitable failure of helicity conservation expressed in
Eq. \eqref{eq:scattamp} follow directly from the deformation
parameter $\varepsilon$ and it must be related with the
self-adjoint extension parameter, because the scattering
amplitude depend on $\lambda_{m}$.
Indeed, as it was shown in \cite{PRD.2012.85.041701} it is
possible to find a relation between the self-adjoint extension
parameter and the coupling constant $\eta$ in \eqref{eq:dcoup}.
By direct inspection we can claim that such relation is
\begin{equation}
\frac{1}{\lambda_{m}}=
-\frac{1}{r_{0}^{2|m+\alpha|}}
\left(
\frac
{\eta + |m+\alpha|}
{\eta - |m+\alpha|}
\right),
\label{eq:lambdaj}
\end{equation}
where $r_0$ is a very small radius smaller than the Compton wave
length $\lambda_C$ of the electron \cite{PLB.1994.333.238},
which comes from the regularization of the $\delta$ function
(for detailed analysis see \cite{arXiv.quant-ph.1207.0214}).
The above relation is only valid for $\lambda_{m}<0$
(when we have scattering and bound states), consequently we
have $|\eta|\geq |m+\alpha|$ and due to $|m+\alpha|<1$ it is
sufficient to consider $|\eta|\geq 1$ to guarantee $\lambda_{m}$
to be negative.
A necessary condition for a $\delta$ function generates an
attractive potential, which is able to support bound states, is
that the coupling constant must be negative.
Thus, the existence of bound states requires
\begin{equation}
\eta \leq -1.
\end{equation}
Also, it seems from the above equation and from \eqref{eq:dcoup}
that we must have $\alpha s < 0$ and there is a minimum value
for the magnetic flux $\alpha$.
It is worthwhile observe that bound states and additional
scattering still remain inclusive when $\varepsilon=0$, i.e., no
quantum deformation case, because the condition $\lambda_m<0$ is
satisfied, as it is evident from \eqref{eq:lambdaj}.
It was shown in
Refs. \cite{JPA.1993.26.7637,PRD.2012.85.041701}.
Now, let us comeback to helicity conservation problem.
In fact, the failure of helicity conservation expressed in
Eq. \eqref{eq:scattamp}, it stems from the fact that the
$\delta$ function singularity make the Hamiltonian and the
helicity non self-adjoint operators
\cite{PRD.1977.15.2287,PRL.1983.50.464,PLB.1993.298.63,
NPB.1994.419.323}, hence their commutation must be analyzed
carefully by considering first the correspondent self-adjoint
extensions and after that compute the commutation relation, as
we explain below.
By expressing the helicity operator in terms of the variables
used in \eqref{eq:wavef}, we attain
\begin{equation}
\hat{h} =
\left(
\begin{array}{cc}
0
& \displaystyle -i\left(\partial_r
+\frac{s|m+\alpha|+1}{r}\right) \\
\displaystyle -i\left(\partial_r
-\frac{s |m+\alpha|}{r}\right) & 0
\end{array}
\right).
\end{equation}
This operator suffers from the same disease as the Hamiltonian
operator in the interval $|m+\alpha|<1$, i.e., it is not
self-adjoint \cite{PRD.1994.49.2092,JPA.2001.34.8859}.
Despite that on a finite interval $[0,L]$, $\hat{h}$ is a
self-adjoint operator with domain in the functions satisfying
$\xi(L)=e^{i\theta}\xi{(0)}$, it does not admit a self-adjoint
extension on the interval $[0,\infty)$ \cite{AJP.2001.69.322},
and consequently it can be not conserved, thus the helicity
conservation is broken due to the presence of the singularity at
the origin \cite{PRD.1977.16.1815,PRL.1983.50.464}.
\section{Conclusion}
\label{sec:conclusion}
We have studied the AB problem within the framework of
$\kappa$-deformed Schr\"{o}dinger-Pauli equation.
The new contribution to the Pauli's term is used to impose a
upper bound in the deformation parameter,
$\varepsilon < 2.27\times 10^{-9} \;(eV)^{-1}$.
It has been shown that there is an additional scattering for any
value of the self-adjoint extension parameter and for negative
values there is non-zero energy bound states.
On the other hand, the scattering amplitude show a energy
dependency, it stems from the fact that the helicity operator
and the Hamiltonian do not to commute.
These results could be compared with those obtained in Ref.
\cite{JPA.1993.26.7637} where a relation between the
self-adjoint extension parameter and the gyromagnetic ratio $g$
was obtained.
The usual Schr\"{o}dinger-Pauli equation with $g=2$ is
supersymmetric \cite{PRD.1984.29.2375} and consequently it
admits zero energy bound states \cite{PRA.1979.19.2461}.
However, in the $\kappa$-deformed Schr\"{o}dinger-Pauli equation
$g \neq 2$ and supersymmetry is broken, giving rise to non-zero
energy bound states.
Changes in the helicity in a magnetic field represent a measure
of the departure of the gyromagnetic ratio of the electron or
muon from the Dirac value of $2e/2M$ \cite{Book.1967.Sakurai}.
Hence, the helicity nonconservation is related to nonvanishing
value of $g-2$.
\section*{Acknowledgments}
The authors would like to thank R. Casana and M. M. Ferreira Jr.
for critical reading the manuscript and helpful discussions.
E. O. Silva acknowledges research grants by CNPq-(Universal)
project No. 484959/2011-5.
\bibliographystyle{model1a-num-names}
\input{abd-scatt.bbl}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,664 |
{"url":"http:\/\/math.stackexchange.com\/questions\/361315\/why-is-partial-partial-m-varnothing","text":"# Why is $\\partial\\partial M=\\varnothing$?\n\nWhy is the border of the border of an oriented differentiable $n$-dimensional Manifold $M$ empty, that is $$\\partial\\partial M = \\emptyset?$$\n\n-\nWell, what is the boundary of the boundary of a closed half-space in $\\mathbb R^n$? Since manifolds are locally like closed half-spaces of $\\mathbb R^n$ and the boundary is computed locally, this gives you the answer. \u2013\u00a0 Mariano Su\u00e1rez-Alvarez Apr 14 '13 at 14:48\n\nThis simply says that the boundary of the manifold $M$ is a manifold without boundary. Indeed, by definition, it is locally homeomorphic to $\\mathbb{R}^{n-1}$ by restriction of the atlas of $M$ to $\\partial M$. Note this has nothing to do with the differential structure.\n\nNote: I think it is worth noting that the boundary $\\partial^\\mathrm{man}$ of a manifold is a notion which is different from that of boundary in a general topological space $\\partial^\\mathrm{top}$. For instance, $\\partial^\\mathrm{man}(0,1)=\\emptyset$ while $\\partial^\\mathrm{top}(0,1)=\\{0,1\\}$. To avoid confusion, some people call $\\partial^\\mathrm{top}$ the fronteer.\n\nIt is not true that $\\partial^\\mathrm{top}\\partial^\\mathrm{top} S=\\emptyset$ in general. Precisely, in the case of a closed half-space, $\\partial^\\mathrm{top}\\partial^\\mathrm{top} S=\\partial ^\\mathrm{top}S\\neq \\emptyset$. For instance, $$\\partial^\\mathrm{top} \\{(x,y)\\in\\mathbb{R}^2\\;;\\;y\\geq 0\\}=\\partial^\\mathrm{man} \\{(x,y)\\in\\mathbb{R}^2\\;;\\;y\\geq 0\\}=\\{(x,y)\\in\\mathbb{R}^2\\;;\\;y=0\\}=B$$ and $$\\partial^\\mathrm{top}B=B\\qquad\\text{while}\\qquad \\partial^\\mathrm{man}B=\\emptyset$$ as $B$ is homeomorphic to $\\mathbb{R}$.\n\n-\nThanks a lot to whoever took the time to do the $\\rm$ edit. \u2013\u00a0 1015 Apr 14 '13 at 16:28\nCan you help me with this please ? math.stackexchange.com\/questions\/361342\/mass-of-a-rectangle\/\u2026 \u2013\u00a0 user43418 Apr 14 '13 at 16:35\n\nLet M be a manifold and $\\omega>0$ be a function. By twice use of Stokes Theorem:\n\n$$\\int_M d^2 \\omega=\\int_M d(d(\\omega))=\\int_{\\partial M}d\\omega=\\int_{\\partial{\\partial M}} \\omega$$\n\nSince $d^2 \\omega=0$ always (property of exterior derivative) then $\\int_{\\partial{\\partial M}} \\omega=0$ and because $\\omega>0$ then $\\partial\\partial M=0$.\n\n-\nYou can only integrate top-dimensional forms on a manifold. So if $\\dim(M) = n$, $\\omega$ needs to be a $(n - 2)$-form, not a function. \u2013\u00a0 Henry T. Horton Apr 14 '13 at 15:35","date":"2014-12-22 04:58:34","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9131555557250977, \"perplexity\": 166.7330576889243}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-52\/segments\/1418802773864.47\/warc\/CC-MAIN-20141217075253-00110-ip-10-231-17-201.ec2.internal.warc.gz\"}"} | null | null |
Semnocera is een geslacht van vlinders uit de familie mineermotten (Gracillariidae).
Het geslacht omvat één soort:
Semnocera procellaris (Meyrick, 1914)
Gracillariinae | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,694 |
Q: How to generate a Java Class from a database for use with Hibernate 4 I want to use Hibernate 4 to work with the database. I use this configuration to map tables in database with Java class:
<mapping class="test.table1"></mapping>
In my Java class I define compatible fields with the table. But now I want to generate the compatible fields automatically. Is there any tool to do it?
I'm using Java 1.7 and MySQL.
A: If you just want to generate some Java classes based on the schema defined in your database why don't you use a code generator designed for this kind of job?
For example you could use Telosys, it's a very handy tool that can create a "database model" in a few minutes by connecting to an relational DB and then use it to generate any kind of code and especially Java classes.
The advantage is that you can adapt the templates if necessary (and if you want you can generate more than the domain classes).
For more information see the web site http://www.telosys.org/ and read this article https://modeling-languages.com/telosys-tools-the-concept-of-lightweight-model-for-code-generation/
A: You can use Hibernate Tools Reverse Engineer, which inspects the database and generates the domain model classes from the database table definition.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,607 |
The set of UX axioms has gone through an evolution over the last year as I iterated through the concepts, refined and combined ideas. I started with 150 concepts that were combined and synthesized into an initial set of 50 axioms presented to IxDA Grand Rapids in December 2012. Over the course of 2013, I presented the UX Axioms several times and further synthesized the set down to 21 Axioms. I recently added a few more axioms to the set I felt were missing. The current set stands at 26 UX axioms. Once the axioms are finalized, I will work to produce a card deck similar to the previous Design Axioms and Health Axioms decks produced by Invo. As you go through the axioms, you may notice that several of them equally apply to how we make sense of the world and how we craft our products that are birthed into the world.
UX design starts and ends with people. It's not everything, but designing for people should be your focus. We need to stop fetishizing the objects we create. It is in their transparency that they fulfill their function.
There are lots of resources to learn user experience design and interactions design. I've compiled a few resources to get you started.
Rosenfeld Media Books. Rosenfeld has a great collection of books by on all different aspects of UX Design. I would recommend you check them out as a place to start.
Interviewing Users by Steve Portigal. With this book, Steve Portigal uses stories and examples from his 15 years of experience to show how interviewing can be incorporated into the design process, helping you learn the best and right information to inform and inspire your design.
Thoughts on Interaction Design by Jon Kolko. Some books about HCI or UX design focus on a web sites or a specific similar products. Some texts explore the aesthetic and emotional value provided by various elements of design. However, there are few texts that explore the semantic connections that live between technology, and form and people-or "interactions."
Elements of User Experience by Jesse James Garrett. From the moment it was published almost ten years ago, Elements of User Experience became a vital reference for web and interaction designers the world over, and has come to define the core principles of the practice.
A book list to help you become great at User Experience Design. Christina Wodtke put together a reading list of the go to UX books by surveying UX practitioners on twitter. There are some really great books here. Definitely worth checking out.
Erik is an independent designer. Let's work together!
He was recently the Creative Director and Principal at Involution Studios, Columbus. He founded and organizes the MidwestUX Conference, leads the local Columbus IxDA, and enjoys taking pictures of people in their side view mirrors. Erik is also on the Board of the Interaction Design Association (IxDA) and the Columbus Center for Architecture and Design. His work often explores the principles of transparency, empowerment, and cultural connections between people and technology.
For Press Inquiries, Speaking Engagements, Greetings, or Collaborations write to eadahl@gmail.com.
Photo of Erik by Paul J. Hart. Presentation title image inspired by work and code of Joshua Davis. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,294 |
\section{Introduction}
\label{sec:intro}
Single Image Super-Resolution (SISR) consists in producing a high-resolution image from its low-resolution counterpart. Image super-resolution has long been considered one of the most arduous challenges in image processing. This is yet another computer vision task that was transformed by the deep learning revolution and has potential applications including but not limited to medical imaging, security, computer graphics, and surveillance.
Deep generative models have been shown to excel at image generation. This is particularly true for autoregressive models \cite{nade,pixel_rnn,pixel_cnn,pixel_snail,image-transformer} and Generative Adversarial Networks (GAN) \cite{goodfellow2014generative,zhu2017unpaired,karras2019style,brock2018large}, whereas Variational Autoencoders (VAE) \cite{kingma2013auto,rezende2014stochastic} have long been thought to be unable to produce high-quality samples. However, recent improvements in VAE design, such as using a hierarchy of latent variables and increasing depth \cite{kingma2016improved,maaloe2019biva,vahdat2020nvae,child2020very} have demonstrated that deep VAEs can compete with both GANs and autoregressive models for high-resolution image generation.
The current state-of-the-art VAE is the Very Deep Variational Autoencoder (VDVAE) \cite{child2020very} which successfully scales to 78 stochastic layers, whereas previous work only experimented with up to 40 layers \cite{vahdat2020nvae}.
Since the VAE is an unconditional generative model, in order to perform image super-resolution it has to be turned into a \emph{conditional} generative model which generates data depending on additional conditioning data. This can be achieved by using the framework of Conditional Variational Autoencoders (CVAE) \cite{NIPS2015_8d55a249}, where the prior is conditioned on an additional random variable and parameterized by a neural network.
In this work, we introduce \textbf{VDVAE-SR}, a VDVAE conditioned on low-resolution images by adding a new component that we call LR-encoder\xspace as it resembles the encoder of the original VDVAE. This component is connected to the decoder, passing information on each layer in the top-down path both to the prior and the approximate posterior. During training, the latent distributions of the low- and high-resolution images are matched using the KL divergence term in the evidence lower bound (ELBO). The learned information is used in generative mode, where only the low-resolution image is included in the model.
A drawback of deep models such as the VDVAE is that they require a large amount of computing and training time. One way to compensate in that regard is to apply transfer learning and utilize a pre-trained model in order to speed up the process. However, this is not always straightforward in practice as presenting a pre-trained model with new data could lead to exploding gradients. This is particularly relevant for deep variational autoencoders as they are prone to unstable training and can be sensitive to hyperparameters changes. We show that using transfer learning for such a model is possible, and we describe the methods to do so, by making only certain parts of the network trainable and using gate parameters to stabilise the process.
We fine-tune a VDVAE model pretrained on FFHQ 256x256 \cite{karras2019style} using DIV2K \cite{Agustsson_2017_CVPR_Workshops}, a common dataset in the image super-resolution literature \cite{lim2017enhanced,wang2018esrgan,niu2020single,Dai_2019_CVPR}.
We evaluate the fine-tuned model on a number of common datasets in the literature of single image super-resolution: Set5 \cite{BMVC.26.135}, Set14 \cite{zeyde2010single}, Urban100 \cite{Huang_2015_CVPR}, BSD100 \cite{937655}, and Manga109 \cite{Matsui_2016}. Following previous work \cite{ledig2017photo,wang2018esrgan,niu2020single}, we test our approach both quantitatively, in terms of PSNR and SSIM metrics, and qualitatively, by visually inspecting the generated images, and compare our results against three state-of-the-art super-resolution methods: EDSR \cite{lim2017enhanced}, ESRGAN \cite{wang2018esrgan} and RFANet \cite{9156371}.
We investigate the role of the sampling temperature, which controls the variance of samples at each stochastic layer in VDVAEs, and show results generated with low and high temperatures. By sampling with a lower temperature, the model achieves quantitative scores better than ESRGAN, but slightly lower than EDSR. At the same time, qualitatively, when sampling with a higher temperature, the images look sharper and less blurred than those generated by the EDSR model. Even though, in general, ESRGAN generates sharper images, it is prone to produce more artifacts as well. We believe that our proposed method shows a good compromise between visual artifacts and image sharpness.
We summarize our contributions as follows:
\begin{enumerate}
\item We propose VDVAE-SR, an adaptation of very deep VAEs (VDVAEs) for the task of single image super-resolution. VDVAE-SR introduces an additional component that we call LR-encoder\xspace, which takes the low-resolution image as input, while its output is used to condition the prior.
\item We show how to utilize transfer learning and achieve stable training in order to take advantage of a VDVAE model already pre-trained on 32 V100 GPUs for 2.5 weeks.
\item We present competitive qualitative and quantitative results compared to state-of-the-art methods on popular test datasets for 4x upscaling.
\end{enumerate}
\section{Related Work}
One of the first successes in image super-resolution is the SR-CNN \cite{dong2015image}, which is based on a three-layer CNN structure and uses a bicubic interpolated low-resolution image as input to the network. Later, with the proposal of residual neural networks (ResNets) \cite{he2016deep}, which provide fast training and better performance for deep architectures, numerous works have adapted ResNets-based models to the task of super-resolution, such as SR-ResNet \cite{ledig2017photo} and SR-DenseNet \cite{tong2017image}. One of the frequently used CNN-based super-resolution models in comparative studies is EDSR \cite{lim2017enhanced}, where the authors use ResNets without batch normalization in the residual block, achieving impressive results and getting first place on the NTIRE2017 Super-Resolution Challenge.
In terms of GAN-based image super-resolution models, several methods have gained a lot of popularity starting with SRGAN \cite{ledig2017photo} where the authors argue that most popular metrics (PSNR, SSIM) do not necessarily reflect perceptually better SR results and that is why they use an extensive mean opinion score (MOS) for evaluating perceptual quality. With that in mind, SRGAN introduces a perceptual loss different from previous work, based on adversarial as well as content loss. Another method, ESRGAN \cite{wang2018esrgan}, builds upon SRGAN by improving the network architecture removing all batch normalization layers and introducing a new Residual in Residual Dense Block (RRDB). In addition, an enhanced discriminator is used based on Relativistic GAN \cite{jolicoeur2018relativistic} and the features before the activation loss are used to improve perceptual loss.
A recent work that uses VAEs for image super-resolution is the srVAE \cite{gatopoulos2020super}, which consists of a VAE with three latent variables, one of them being a downscaled version of the original image. This work shows impressive generative performance in terms of FID score when tested on ImageNet-32 and CIFAR-10, but no quantitative results of their super-resolution model are reported. Another recent work that uses a VAE-based model for image super-resolution is VarSR \cite{hyun2020varsr}. This work focuses on very low-resolution images (8x8) and shows better results compared to some popular super-resolution methods.
Deep VAEs such as \cite{kingma2016improved,maaloe2019biva,vahdat2020nvae,child2020very} adapt their architecture from Ladder VAEs (LVAE) \cite{sonderby2016ladder}, which introduce a novel top-down inference model and achieve stable training with multiple stochastic layers. A method that improved upon the LVAE is the Bidirectional-Inference VAE (BIVA) \cite{maaloe2019biva} adding a deterministic top-down path in the generative model and applying a bidirectional inference network. These modifications solved the variable collapse issue of the LVAE which may occur when the architecture consists of a very deep hierarchy of stochastic latent variables. Recently, NVAE \cite{vahdat2020nvae} reported further improvements by using normalizing flows in order to allow for more expressive distributions and thus outperform the state-of-the-art among non-autoregressive and VAE models. Finally, the VDVAE model \cite{child2020very} demonstrated that the number of stochastic layers matters greatly for performance, achieving better results than previous VAE-based models and some autoregressive ones, having the potential to outperform those as well.
Denoising Diffusion Probabilistic Models (DDPM) \cite{ddpm} are the latest addition to the family of probabilistic generative models. DDPMs define a diffusion process that progressively turns the input image into noise, and learn to synthesize images by inverting that process. DDPMs and variations thereof excel at high-resolution image generation \cite{nichol2021improved,dhariwal2021diffusion} and have been successfully applied to the task of single image super-resolution \cite{cascaded_ddpm,sr_diff}.
\section{Preliminaries}
In this section, we define variational autoencoders (VAEs) and conditional VAEs (CVAEs), for which we derive the evidence lower bound. We then introduce the VDVAE using the VAE framework.
\subsection{Variational Autoencoders}
The Variational Autoencoder \cite{kingma2013auto} is a generative model built on probabilistic principles. It consists of a joint model $p_\theta(\mathbf{x}, \mathbf{z}) = p_\theta(\mathbf{x}|\mathbf{z}) p_\theta(\mathbf{z})$ parameterized by $\theta$ and an approximate posterior $q_\phi(\mathbf{z}|\mathbf{x})$ parameterized by $\phi$. All models are implemented using neural networks. During generation, the latent variable $\mathbf{z}$ is sampled from the prior and the observation variable $\mathbf{x}$ is sampled from the observation model following $ \mathbf{z} \sim p_{\theta} (\mathbf{z}), \mathbf{x} \sim p_{\theta} (\mathbf{x}|\mathbf{z}) $.
VAE models are optimized with stochastic gradient ascent to maximize the marginal likelihood:
\begin{equation}
p_\theta(\mathbf{x}) = \int_{\mathbf{z}} p_\theta(\mathbf{x}|\mathbf{z}) p_\theta(\mathbf{z}) d \mathbf{z}
\end{equation}
In practice, $p_\theta(\mathbf{x})$ is intractable of the integration over $\mathbf{z}$, which makes the posterior $p_\theta(\mathbf{z}|\mathbf{x})$ also intractable. Variational Inference (VI) solves the intractability of $p_\theta(\mathbf{z}|\mathbf{x})$ using an approximate posterior $q_\phi(\mathbf{z}|\mathbf{x})$.
The resulting objective function, the evidence lower bound (ELBO), is further derived using Jensen's inequality and expressed as:
\begin{equation}
\mathcal{L}(\mathbf{x} ; \theta, \phi) = E_{q_{\phi}(\mathbf{z}|\mathbf{x})} \left[log \frac{p_{\theta}(\mathbf{x}, \mathbf{z})}{q_\phi(\mathbf{z} | \mathbf{x})} \right] \leq \log p_\theta(\mathbf{x}) \ .
\label{eq:vae_elbo}
\end{equation}
\subsection{Conditional Variational Autoencoders}
In order to generate specific data as in the case of image super-resolution, where we need to generate a high-resolution image from its low-resolution counterpart, the Conditional Variational Autoencoders (CVAE) can be used.
Similar to the VAE, the CVAE is also built on probabilistic principles. CVAE is optimized to maximize the marginal probability similar to \cref{eq:vae_elbo} but this time conditioned on a random variable which could be for example a low-resolution image $\mathbf{y}$:
\begin{equation} \label{eq:CVAE_gen}
p_\theta (\mathbf{x}|\mathbf{y}) = \int_\mathbf{z} p_\theta(\mathbf{x} | \mathbf{y},\mathbf{z}) p(\mathbf{z}|\mathbf{y}) d \mathbf{z} \
\end{equation}
The posterior of the latent variables is:
\begin{equation} \label{eq:CVAE_bayes}
p_{\theta}(\mathbf{z}|\mathbf{x},\mathbf{y}) = \frac{p_{\theta}(\mathbf{x}|\mathbf{z},\mathbf{y})p_{\theta}(\mathbf{z}|\mathbf{y})}{p_{\theta}(\mathbf{x}|\mathbf{y})}
\end{equation}
where again $p_{\theta}(\mathbf{x}|\mathbf{y})$ is intractable and needs to be approximated using a variational distribution $q_{\phi}(\mathbf{z}|\mathbf{x},\mathbf{y}) \approx p_{\theta}(\mathbf{z}|\mathbf{x},\mathbf{y})$.
The conditional ELBO for the CVAE can be derived again using Jensen's inequality, resulting in:
\begin{equation}
\mathcal{L}(\mathbf{x} , \mathbf{y}; \theta, \phi) = E_{q_{\phi}(\mathbf{z}|\mathbf{x}, \mathbf{y})} \left[\log \frac{p_{\theta}(\mathbf{x}, \mathbf{z}, \mathbf{y})}{q_\phi(\mathbf{z} | \mathbf{x}, \mathbf{y})} \right] \leq \log p_\theta(\mathbf{x} | \mathbf{y}) \ .
\label{eq:ELBO_CVAE}
\end{equation}
\subsection{Very Deep Variational Autoencoder (VDVAE)}
The VDVAE \cite{child2020very}
consists of a hierarchy of layers of latent variables conditionally dependent on each other. This results in a more flexible prior and posterior compared to a simple diagonal Gaussian prior which could be too limiting. An iterative interaction between ``bottom-up'' and ``top-down'' layers is achieved through parameter sharing between the inference and generative models in each layer. The prior and the approximate posterior for a model with $K$ stochastic layers factorize as:
\begin{align}
p_{\theta}(\mathbf{z}) &= p_{\theta}(\mathbf{z}_0)p_{\theta}(\mathbf{z}_1|\mathbf{z}_0)...p_{\theta}(\mathbf{z}_K|\mathbf{z}_{<K})\\
q_{\phi}(\mathbf{z}|\mathbf{x}) &= q_{\phi}(\mathbf{z}_0|\mathbf{x})q_{\phi}(\mathbf{z}_1|\mathbf{z}_0,\mathbf{x})...q_{\phi}(\mathbf{z}_K|\mathbf{z}_{<K},\mathbf{x})
\end{align}
where $p_{\theta}(\mathbf{z}_0)$ is a diagonal Gaussian distribution $\mathcal{N}(\mathbf{z}_0\,|\,\mathbf{0},\mathbf{I})$ and the latent variable group $\mathbf{z}_0$ is at the top layer that corresponds to small number of latent variables at low resolution. Intuitively, $\mathbf{z}_K$ is at the bottom of the network having a larger number of latent variables at high resolution.
The VDVAE architecture is composed of blocks of two types: the residual blocks (bottom-up path) and the top-down blocks (\cref{fig:VDVAE_top_down_block}). The top-down blocks are also residual and handle two tasks: processing the information flowing through the decoder and handling the stochasticity. Each top-down block of index $j > 0$ handles the distributions $q_\phi(\mathbf{z}_{j}|\mathbf{z}_{j-1}, \mathbf{x})$ and $p_\theta(\mathbf{z}_{j} | \mathbf{z}_{j-1})$. Top-down blocks are composed sequentially. Therefore, we can define $\hb_j$ as the input to the top-down block of index $j$, where $\mathbf{h}_j$ is a function of the samples $\mathbf{z}_{<j}$. This allows us to express the VDVAE model as:
\begin{equation}\label{eq:vdvae}
p_{\theta}(\mathbf{z}) = p_{\theta}(\mathbf{z}_0) \prod_{j = 1}^{K} p_{\theta}(\mathbf{z}_j| \hb_j),
\qquad q_{\phi}(\mathbf{z}|\mathbf{x}) = q_{\phi}(\mathbf{z}_0|\mathbf{x}) \prod_{j = 1}^{K} q_{\phi}(\mathbf{z}_j| \hb_j, \mathbf{x}) \ . \\
\end{equation}
\begin{figure}
\centering
\includegraphics[height=6cm]{Pictures/Block-of-VDVAE.png}
\caption{Top-down block of the VDVAE \cite{child2020very}.}
\label{fig:VDVAE_top_down_block}
\end{figure}
\section{VDVAE-SR}\label{sec:vdvae-sr}
In this section, we introduce the proposed VDVAE-SR model. We provide an overview of the model architecture, after which we detail the conditional prior network and its integration with the VDVAE model.
\begin{figure}
\centering
\includegraphics[height=11cm]{Pictures/VDVAE-SR.png}
\caption{Network Architecture of the proposed VDVAE-SR Model.}
\label{fig:VDVAE-SR_architecture}
\end{figure}
\subsection{LR-encoder\xspace}
The dependency on the lower-resolution image $\mathbf{y}$ is implemented using the encoder of a lower-resolution VDVAE of depth $K' < K$, which we call LR-encoder\xspace. The LR-encoder\xspace maps the lower-resolution image to latent space, providing one activation $\mathbf{g}_j$ for each layer $j \in [0, K']$. Each activation $\mathbf{g}_j$ is defined as the output of the bottom-up residual block of index $j$.
\subsection{Conditional Prior}
\begin{figure}
\centering
\includegraphics[height=8cm]{Pictures/Block-of-VDVAE-SR.png}
\caption{Top-down block of the VDVAE-SR.}
\label{fig:VDVAE-SR_top_down_block}
\end{figure}
The top-down path, or decoder, of the VDVAE is modified to depend on $\mathbf{y}$ using the LR-encoder\xspace activations $\mathbf{g}_0, \ldots, \mathbf{g}_{K'}$. This results in a conditional prior $p{_\theta}(\mathbf{z}|\mathbf{y})$ that maps the low-resolution image $\mathbf{y}$ to a distribution over the latent variables $\mathbf{z}$ (\cref{fig:VDVAE-SR_architecture}).
The architecture of the VDVAE-SR is identical to the one of the VDVAE, except for two alterations:
\begin{enumerate}
\item The input to each top-down block (see \cref{fig:VDVAE-SR_top_down_block}) is defined as:
%
\begin{equation}
\Tilde{\hb}_j =
\begin{cases}
\mathbf{g}_j & \text{if $j = 0 $} \\
\hb_j + \alpha_j \mathbf{g}_j & \text{if $j \in [1, K']$} \\
\hb_j & \text{otherwise}
\end{cases}
\end{equation}
%
where $\alpha_1, \ldots, \alpha_{K'}$ are scalar gate parameters initialized to zero \cite{bachlechner2020rezero}.
\item The top layer is conditioned on $\mathbf{y}$ such that
\begin{equation}
p_{\theta}(\mathbf{z}_0|\Tilde{\hb}) = \mathcal{N}\left(\mathbf{z}_0 \, | \, \mu_\theta(\Tilde{\hb}_0),\, \sigma_\theta(\Tilde{\hb}_0)\right) \ ,
\end{equation}
where $\mu_\theta$ and $\sigma_\theta$ are linear layers mapping the output of the top-most LR-encoder\xspace layer to the parameter-space of $p_\theta(\mathbf{z}_0 | \mathbf{y})$.
\end{enumerate}
\subsection{Generative model and inference network}
Because of the sharing of the top-down model between the generative model and the inference network \cite{sonderby2016ladder}, the conditional inference network naturally arises from the alteration of the prior, without further modification. Using the activations $\Tilde{\hb}_0, \ldots, \Tilde{\hb}_{K}$ and the definition of the VDVAE given in \cref{eq:vdvae}, we define the VDVAE-SR as:
\begin{equation}\label{eq:vdvae-sr}
p_{\theta}(\mathbf{z}|\mathbf{y}) = \prod_{j = 0}^{K} p_{\theta}(\mathbf{z}_j| \Tilde{\hb}_j),
\qquad q_{\phi}(\mathbf{z}|\mathbf{y},\mathbf{x}) = q_{\phi}(\mathbf{z}_0|\mathbf{x}) \prod_{j = 1}^{K} q_{\phi}(\mathbf{z}_j| \Tilde{\hb}_j, \mathbf{x}) \ . \\
\end{equation}
\section{Experiments}
\subsection{Datasets}
\subsubsection{Training Dataset.}
We train our models on the DIV2K dataset, introduced by \cite{Agustsson_2017_CVPR_Workshops}. The DIV2K dataset consists of 800 RGB high-definition high-resolution images for training, 100 images for validation, and 100 for testing. The dataset contains a variety of diverse pictures, including different types of shot such as portrait, scenery, and object shots.
\subsubsection{Test Datasets.}
We test our method on popular benchmarking datasets commonly used in single-image super resolution: Set5 \cite{BMVC.26.135}, Set14 \cite{zeyde2010single}, Urban100 \cite{Huang_2015_CVPR}, BSD100 \cite{937655}, and Manga109 \cite{Matsui_2016}. Having multiple test datasets gives a better understanding of the strengths and shortcomings of our model, since these datasets contain different types of pictures: BSD100, Set5, and Set14 mostly consist of natural images with a broad range of styles, while the focus on Urban100 is mainly on buildings and urban scenes, and Manga109 consists of drawings of Japanese manga.
\subsection{Implementation Details}
Since it takes about 2.5 weeks to train a VDVAE model on FFHQ 256x256 on 32 NVIDIA V100 GPUs, we choose to rely on pretrained VDVAEs and adapt them to the super-resolution task. We use a pretrained VDVAE with a stochastic depth of 62 layers. Our method, VDVAE-SR, includes the original VDVAE encoder and decoder, which we initialize with the weights from the pretrained model. We then freeze the encoder, allow fine-tuning of the decoder, and train the LR-encoder\xspace from scratch. We optimize the model end-to-end for 100,000 steps using the Adam optimizer \cite{kingma2014adam} with a learning rate of $5\cdot10^{-4}$ and batch size of 1 on one NVIDIA V100 GPU.
When using transfer learning, it was observed that the model suffered from exploding gradients if the new information from the LR-encoder\xspace was introduced in an uncontrolled manner. Introducing gate parameters similar to the approach in \cite{bachlechner2020rezero} significantly improved training stability.
\subsection{Evaluation}
In terms of evaluation metrics, we use the traditional PSNR and SSIM quality measures, both widely used as metrics for image restoration tasks. While PSNR (Peak Signal to Noise Ratio) is calculated based on the mean squared error of the pixel-to-pixel difference, the SSIM (Structural Similarity Method) is considered to have a closer correlation with human perception by calculating distortion levels based on comparisons of structure, luminance, and contrast. Additional to the traditional PSNR and SSIM metrics, we evaluate the produced images using the DISTS \cite{ding2020iqa} score, which has showed evidence that the metric matches closer to human perception.
We quantitatively evaluate different super-resolution methods by applying them to low-resolution images and computing the PSNR, SSIM and DISTS metrics using the super-resolution output and the reference high-resolution image.
For the PSNR and SSIM, all pictures are converted from RGB to YCbCr and the metrics are computed on the Y channel (luma component) of the pictures. The reason for this is that it has been observed (e.g., in \cite{Pisharoty}) that the results of evaluating on the luminosity channel in the YCbCr color space, rather than on the usual RGB representation, are closer to the actual perceived structural noise of the image. We thus adopt the same approach, following prior work. Finally, note that the YCbCr space is used during the testing phase exclusively, while the training and validation are still performed in the RGB color space.\looseness=-1
\subsection{Results}
\subsubsection{Quantitative Results.}
We compare our method to three other super-resolution methods, namely EDSR, ESRGAN and RFANet, based on their official implementation. The quantitative results on PSNR and SSIM are shown in \cref{tab:eval_metrics}, where EDSR performs best on both metrics, with our method ($t = 0.1$) closely following on second place.
\begin{table}
\centering
\caption{Evaluation metrics using PSNR and SSIM on the Y channel and DISTS. The number next to VDVAE-SR (our method) denotes the temperature used for sampling. The best scores are represented in \textbf{bold}, while the second best results are {\ul underlined}.}
\resizebox{\columnwidth}{!}{%
\begin{tabular}{cccccccccccclccc}
\toprule
\multicolumn{1}{l}{\multirow{2}{*}{\textbf{Dataset}}} & \multicolumn{3}{c}{\textbf{EDSR}} & \multicolumn{3}{c}{\textbf{ESRGAN}} & \multicolumn{3}{c}{\textbf{RFANet}} & \multicolumn{3}{c}{\textbf{VDVAE-SR 0.1}} & \multicolumn{3}{c}{\textbf{VDVAE-SR 0.8}} \\ \cmidrule(lr){2-4} \cmidrule(lr){5-7} \cmidrule(lr){8-10} \cmidrule(lr){11-13} \cmidrule(lr){14-16}
\multicolumn{1}{l}{} & PSNR & SSIM & \multicolumn{1}{l}{DISTS} & PSNR & SSIM & \multicolumn{1}{l}{DISTS} & PSNR & SSIM & \multicolumn{1}{l}{DISTS} & PSNR & SSIM & DISTS & PSNR & SSIM & \multicolumn{1}{l}{DISTS} \\ \midrule
Set5 & {\ul 31.97} & {\ul 0.902} & 0.121 & 30.39 & 0.864 & \textbf{0.078} & \textbf{32.53} & \textbf{0.908} & 0.119 & 31.48 & 0.886 & 0.123 & 30.51 & 0.869 & {\ul 0.108} \\
Set14 & \textbf{28.33} & \textbf{0.800} & 0.097 & 26.20 & 0.720 & \textbf{0.064} & 27.33 & 0.774 & {\ul 0.092} & {\ul 27.99} & {\ul 0.776} & 0.105 & 27.62 & 0.761 & 0.097 \\
BSDS100 & \textbf{28.46} & \textbf{0.781} & 0.158 & 25.87 & 0.690 & \textbf{0.094} & 27.04 & {\ul 0.758} & 0.154 & {\ul 28.05} & 0.752 & 0.169 & 27.69 & 0.738 & {\ul 0.152} \\
Manga109 & \textbf{30.85} & \textbf{0.918} & \textbf{0.009} & 28.77 & 0.870 & {\ul 0.010} & 21.09 & 0.739 & 0.015 & {\ul 29.92} & {\ul 0.904} & 0.013 & 29.55 & 0.896 & 0.011 \\
Urban100 & {\ul 26.02} & {\ul 0.798} & 0.029 & 24.36 & 0.748 & {\ul 0.024} & \textbf{26.89} & \textbf{0.823} & \textbf{0.023} & 25.36 & 0.759 & 0.037 & 25.15 & 0.750 & 0.034 \\ \bottomrule
\end{tabular}%
}
\label{tab:eval_metrics}
\end{table}
As first discussed in \cite{ledig2017photo}, the PSNR and SSIM scores tend to favor smoother images, this being attributed to the nature of how these metrics are calculated, which is in contrast to human visual perception. This is confirmed by the obtained scores of our method using different temperatures as decreasing the variance produces more averaged-out images and thus higher scores. Based on the DISTS metric, ESRGAN performs best on three datasets. Our method with higher temperature follows on second place on the Set5 and BSDS100 datasets.
\subsubsection{Qualitative Results.}
\cref{fig:bulls_comp,fig:soldier_comp,fig:bird_comp} show a visual comparison of two pictures from BSD100 dataset between the original HR image, Bicubic, EDSR, ESRGAN, RFANet and our method with both $0.1$ and $0.8$ temperatures.
It can be observed that the points made in the quantitative section still stand, as EDSR, having the best PSNR and SSIM scores, has a smoother and blurrier look, and our model with 0.1 temperature looks closer to it. As for the model with 0.8 temperature, it introduces more details compared to EDSR. It is still blurrier than the outputs of ESRGAN but has fewer artifacts and it is able to reproduce some details without introducing any generative noise. As for the RFANet, the images are still blurrier, but having more visual similarities with our method than EDSR. For this reason in most metrics it gets a better score, but visually it still does not generate highly detailed features.
In \cref{fig:bulls_comp,fig:soldier_comp} it can be observed that ESRGAN produces some artifacts on the bull's head and the person's hand, while our model retains the structure of the objects. In \cref{fig:bird_comp} we can again see how the eye of the bird has a different shape and a more averaged-out look in the case of the EDSR, and even more drastic shape change in the case of the ESRGAN, while our models keep the rounder shape, while not averaging out the outer colors as much.
\begin{figure}
\centering
\includegraphics[height=4.2cm]{Pictures/bsd100_bulls_comp_wRFA.png}
\caption{SR output comparison between multiple models for a picture (image 376043) of the BSD100 dataset.}
\label{fig:bulls_comp}
\end{figure}
\begin{figure}
\centering
\includegraphics[height=4.5cm]{Pictures/bsd100_soldier_comp_wRFA.png}
\caption{SR output comparison between multiple models for a picture (image 38092) of the BSD100 dataset.}
\label{fig:soldier_comp}
\end{figure}
\begin{figure}
\centering
\includegraphics[height=5.5cm]{Pictures/Set5_bird_comp_wRFA.png}
\caption{SR output comparison between multiple models for the bird picture of the Set5 DataSet.}
\label{fig:bird_comp}
\end{figure}
\subsubsection{Temperature.}
The ``temperature'' parameter $t$, taking values between 0 and 1, is used in VDVAE when sampling from prior in generative mode, often resulting in higher-quality samples when lowered as observed in previous work \cite{kingma2018glow,vahdat2020nvae}.
Reducing the temperature results in reducing the variance of the Gaussian distributions in the prior and so achieving more regularity in the generated samples. \cref{fig:temp_256} shows examples of samples with different temperatures. We can observe how samples taken with a lower temperature look smoother, whereas those taken with a higher temperature have more details but also more artifacts.
We corroborate this quantitatively in \cref{fig:temp_PSNR}, which shows that the PSNR and SSIM scores (for Set5 and Set14) both decrease as the sampling temperature is increased. This agrees with our qualitative observations, as PSNR and SSIM measures are usually higher for images that are more averaged out and contain less noise.
\begin{figure}
\centering
\includegraphics[height=5.5cm]{Pictures/Temperature.jpg}
\caption{Prior sampling difference with varying temperature values for 256x256 images (comic picture from Set14 dataset).}
\label{fig:temp_256}
\end{figure}
\begin{figure}
\centering
\includegraphics[height=4.32cm]{Pictures/psnr_temp.png}
\caption{PSNR and SSIM scores of Prior samples with varying temperature values for Set5 and Set14 datasets.}
\label{fig:temp_PSNR}
\end{figure}
\subsubsection{Patch Size.}
A crucial parameter in our super-resolution method is the size of patches to which we apply super-resolution addressed also in \cite{zhang2018residual,sajjadi2017enhancenet}. After experimenting with patches of size 16x16 and 64x64 (i.e., 64x64 and 256x256 after super-resolution), we observed that the 16x16 patch size models were generally performing worse than their counterparts with bigger patch sizes, both in terms of PSNR and SSIM, and in a perceptual sense as the models fail to recreate details that the 64x64 patch models have no problem with. This can also be seen in \cref{fig:16vs64patch}, especially on the bird's eye, as the general shape and sharpness cannot be recreated by the 16x16 patch size model.
We hypothesise that as the patch size gets smaller, the amount of details found in a patch becomes lesser, and the models will not be able to recreate those details anymore based on context, as the patches will start to look more similar to each other and generic.
\begin{figure}
\centering
\includegraphics[height=4.4cm]{Pictures/16vs64patch.jpg}
\caption{16x16 and 64x64 patch size model outputs for a Set5 bird image.}
\label{fig:16vs64patch}
\end{figure}
\subsubsection{Activations only in posterior.}
As another ablation study, we investigated the scenario where the activations from the LR-encoder\xspace are passed only in the posterior part of the top-down block as shown on \cref{fig:top_down_post}. Doing only this, the network does not get enough information during the learning phase, only being able to generate more global features of the images, without any fine details as observed in \cref{fig:acts_post}.
\begin{figure}[!h]
\centering
\includegraphics[height=2.8cm]{Pictures/acts_in_post.png}
\caption{The first three images are test samples taken during the training process, while the forth image is the reference.}
\label{fig:acts_post}
\end{figure}
\begin{figure}
\centering
\includegraphics[height=8cm]{Pictures/Block_posterior.png}
\caption{Top-down block adding activations in posterior.}
\label{fig:top_down_post}
\end{figure}
\section{Conclusions}
In this paper, we investigated the use of Very Deep Variational Autoencoders (VDVAE) for the purpose of generating super-resolution (SR) images. After the introduction of the proposed VDVAE-SR model, and based on the results presented, we conclude that the introduced model and its quantitative and qualitative results are satisfying as they are comparable to other popular methods, generating images that compensate between image sharpness and visual artifacts. As being part of the scarce family of VAE-based models for image super-resolution and the first to our knowledge that uses a deep hierarchical architecture, we believe that our proposed method still has a lot of space for building upon, to improve the results even further, as multiple modifications such as changes to training time, layer architecture, or the use of more flexible distributions can be investigated in the future.
\clearpage
\bibliographystyle{splncs04}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,496 |
using System.Collections.Generic;
using System.Linq;
using Orchard.AntiSpam.Models;
using Orchard.ContentManagement.MetaData;
using Orchard.Localization;
using Orchard.UI.Admin.Notification;
using Orchard.UI.Notify;
namespace Orchard.AntiSpam.Services {
public class MissingFilterBanner : INotificationProvider {
private readonly ISpamService _spamService;
private readonly IContentDefinitionManager _contentDefinitionManager;
public MissingFilterBanner(ISpamService spamService, IContentDefinitionManager contentDefinitionManager) {
_spamService = spamService;
_contentDefinitionManager = contentDefinitionManager;
T = NullLocalizer.Instance;
}
public Localizer T { get; set; }
public IEnumerable<NotifyEntry> GetNotifications() {
// if there is any content type with Spam Part, ensure there is a filter available
var typeHasPart = _contentDefinitionManager.ListTypeDefinitions().Any(t => t.Parts.Any(p => p.PartDefinition.Name.Equals(typeof (SpamFilterPart).Name)));
if(typeHasPart && !_spamService.GetSpamFilters().Any()) {
yield return new NotifyEntry {Message = T("Anti-spam protection requires at least one anti-spam filter to be enabled and configured."), Type = NotifyType.Warning};
}
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 29 |
Q: Show current Activity in background when launching AlertDialog from BroadcastRecevier I have a translucent AlertDialog set to show if the user receives a text message. It is being started from a Broadcast Receiver.
The user only gets this "emergency" type of message, only if the sender sets it as such a message and the user enables this type of interruption.
I have a slight problem because if my application is running, my background is what my application last left off at. The only way I get the background to show what the user is "currenty doing" is by completely closing my app.
Has anyone run into a similar issue using AlertDialogs with a translucent background?
here is how I start my activity;
Intent i = new Intent(context, LayoutStartActivity.class);
i.putExtras(intent);
i.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK);
context.startActivity(i);
and here is a stripped down version of my alert dialog
AlertDialog.Builder builder = new AlertDialog.Builder(this);
builder.setView(holder);
builder.setPositiveButton("OK", new DialogInterface.OnClickListener() {
public void onClick(DialogInterface dialog, int which) {
dialog.cancel();
finish();
}
});
Thanks
A: Set the task affinity in the AndroidManifest.xml so that it runs as a unique process on the recents stack.
Example
<activity android:name=".LayoutStartActivity"
android:theme="@style/Theme.Light"
android:taskAffinity="com.example.standAlone">
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,072 |
\section{Introduction}
The $\Lambda_c^+$ charmed baryons consist of a heavy charm quark
and two light ($ud$) quarks with the ground state
having quantum numbers $J^P = \frac{1}{2}^+$.
The $\Lambda_c(2595)^+$ and $\Lambda_c(2625)^+$ are the two
lowest-lying excited states observed, and are generally believed to have
$J^P = \frac{1}{2}^-$ and $J^P = \frac{3}{2}^-$, respectively.
The $\Lambda_c(2595)^+$ predominantly decays
to the $J^P=\frac{1}{2}^+$ $\Sigma_c(2455)^{++/0}$ states
via an $s$-wave decay.
The analogous decay for the $\Lambda_c(2625)^+$ to the
$J^P = \frac{3}{2}^-$ $\Sigma_c(2520)^{++/0}$ states
is kinematically suppressed as it can only happen
through the low-mass tail of the $\Sigma_c(2520)^{++/0}$.
The $d$-wave decay to the $J^P=\frac{1}{2}^+$
$\Sigma_c(2455)^{++/0}$ states
is allowed, but its contribution is known to be small.
Thus, the $\Lambda_c(2625)^+$ decay is thought to proceed
primarily via the
direct three-body, $p$-wave decay
$\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^+ \pi^-$.
The $\Lambda_c(2625)^+$ was first observed in 1993~\cite{ARGUS:1993}.
The CDF collaboration reported the most recent measurements of
$\Lambda_c(2625)^+$ properties in 2011 using a data sample of 6.2k events~\cite{CDF:2011}.
Their measurement for the $\Lambda_c(2625)^+$ mass with respect to
the $\Lambda_c^+$ mass is much more precise compared with previous
measurements, and an upper limit on the $\Lambda_c(2625)^+$ width
was reported. The limited decay phase space of
$\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^+ \pi^-$ makes it difficult
to extract the $\Sigma_c(2455)^{++/0}$ yields by fitting the
$\Lambda_c^+\pi^{\pm}$ invariant mass due to the presence of
reflection peaks formed by the combination of the $\Lambda_c^+$ and
the other final state pion.
The large data sample collected by Belle, together with the use of an
amplitude model~\cite{Arifi:2018prd} to describe the decay, allows
us to use a full Dalitz
fit that naturally includes the reflections.
The mass of the $\Lambda_c(2625)^+$, relative to the $\Lambda_c^+$ mass,
is already relatively well known, but the large Belle data sample
allows for a more precise measurement.
No intrinsic width of the $\Lambda_c(2625)^+$ has yet been measured,
and the current upper limit
$\Gamma < 0.97\ \ensuremath{\textrm{MeV}/\textit{c}^2}$ at 90\% credibility level
by the Particle Data Group (PDG)~\cite{PDG:2020} is based on the CDF measurement.
Theoretical predictions for the width vary
for this narrow state~\cite{Arifi:2018prd, Arifi:2021prd, Kawakami:2018prd, Guo:2019prd}.
An improved limit on the width of the $\Lambda_c(2625)^+$
will help to constrain these predictions,
and provide insights into other charmed baryons since
their widths are related through common coupling constants~\cite{Cheng:2015}.
\section{Detector and dataset}
The measurement presented here is based on the entire dataset collected by the
Belle detector~\cite{Belle, Belle:achievments} operating at the KEKB
asymmetric-energy $e^+ e^-$ collider~\cite{KEKB, KEKB:achievements}.
The total integrated luminosity of the dataset is $980\ \textrm{fb}^{-1}$,
which is mostly collected at or near the $\Upsilon(4S)$ resonance.
The Belle detector is a large-solid-angle magnetic
spectrometer that consists of a silicon vertex detector (SVD),
a 50-layer central drift chamber (CDC), an array of
aerogel threshold Cherenkov counters (ACC),
a barrel-like arrangement of time-of-flight
scintillation counters (TOF), and an electromagnetic calorimeter
comprised of CsI(Tl) crystals (ECL) located inside
a super-conducting solenoid coil that provides a 1.5~T
magnetic field. An iron flux-return located outside of
the coil is instrumented to detect $K_L^0$ mesons and to identify
muons (KLM). The detector
is described in detail elsewhere~\cite{Belle}.
Two inner detector configurations were used.
The first consisted of a 2.0 cm radius beampipe
and a 3-layer silicon vertex detector,
while the second used a 1.5 cm radius beampipe, a 4-layer
silicon detector and a small-cell inner drift chamber.
Monte Carlo (MC) events are generated using EVTGEN~\cite{Evtgen}
to optimize selection criteria and to be used in the Dalitz plot fit.
The $\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^+ \pi^-$ and
$\Lambda_c^+ \to p K^- \pi^+$ samples are generated using a phase space model.
A $D^{*+} \to D^0 \pi^+$, with $D^0 \to K^- \pi^+$, sample is also generated
to compare the mass-resolution function in the MC sample and the experimental data, and thus to estimate
the systematic uncertainties on the measurements.
The detector response is simulated with GEANT3~\cite{Geant3}
and the event reconstruction is performed using
data converted with the Belle-to-Belle-II (B2BII)
software package~\cite{B2BII}
and then analyzed using Belle II software~\cite{BASF2, basf2-zenodo}.
\section{Analysis}
The candidate $\Lambda_c(2625)^+$ baryons are reconstructed
from the decay chain
$\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^+ \pi^-$, $\Lambda_c^+ \to p K^- \pi^+$
~\cite{charge_conjugates}.
The final-state charged particles, $\pi^\pm$, $K^-$ and $p$, are selected
based on the likelihood information from the tracking (SVD, CDC) and
particle identification (CDC, ACC, TOF) systems into a combined likelihood,
$\mathcal{L}(h_1 {:} h_2) = \mathcal{L}(h_1) / (\mathcal{L}(h_1) + \mathcal{L}(h_2))$,
where $h_1$ and $h_2$ are $p$, $K$ or $\pi$~\cite{BellePID}.
We require the proton candidates to have
$\mathcal{L}(p{:}K) > 0.6$ and $\mathcal{L}(p{:}\pi) > 0.6$,
kaon candidates to have $\mathcal{L}(K{:}p) > 0.6$ and $\mathcal{L}(K{:}\pi) > 0.6$,
and pion candidates to have $\mathcal{L}(\pi{:}K) > 0.6$ and $\mathcal{L}(\pi{:}p) > 0.6$.
Electrons are suppressed by requiring
$\mathcal{L}(e^-)/(\mathcal{L}(e^-) + \mathcal{L}(\mathrm{hadrons})) < 0.1$
for all candidates; the likelihoods $\mathcal{L}(e^-)$ and
$\mathcal{L}(\mathrm{hadrons})$ include information from the ECL
in addition to the tracking and particle identification systems~\cite{BellePID}.
The particle identification efficiency is approximately
87\% for proton, 85\% for kaons and
96\% for pions.
Charged tracks are also required to have a
point of closest approach
with respect to the interaction point
less than 3 cm in the $e^{+}$ beam direction
and less than 1 cm in the plane perpendicular to it.
A vertex fit is applied to the daughter particles of
the $\Lambda_c^+$ candidates and
the resultant $\chi^2$ probability of the fit
is required to be greater than 0.001.
Candidates within $\pm 7.0\ \ensuremath{\textrm{MeV}/\textit{c}^2}\ (\approx 1.6\sigma)$
are selected and mass-constrained
to the $\Lambda_c^+$ PDG mass of $2286.46\,\ensuremath{\textrm{MeV}/\textit{c}^2}$ ~\cite{PDG:2020}.
Two pions of opposite charge are then combined
with the constrained $\Lambda_c^+$ candidate to form a $\Lambda_c(2625)^+$
candidate. The $\Lambda_c(2625)^+$ daughters are then kinematically fitted to come from
a common vertex, with a constraint that the vertex has to be within the beamspot since the $\Lambda_c(2625)^+$ is short-lived.
The $\chi^2$ probability of this fit is required to be
greater than 0.001 to ensure the quality of the fit.
As excited charmed baryons including the $\Lambda_c(2625)^+$ typically have
a hard momentum distribution, we only keep $\Lambda_c(2625)^+$ candidates
with $x_p > 0.7$, where
$x_p = p^{*} / \sqrt{E_{\mathrm{beam}}^2/\mathit{c}^2 - M^2\mathit{c}^2}$ and
$p^*$ is momentum of the $\Lambda_c(2625)^+$
in the $e^+e^-$ center of mass frame.
As the mass of the $\Lambda_c^+$ is constrained to its PDG
value, the reconstructed mass $M(\Lambda_c^+\pi^+\pi^-)$
has the resolution of the
mass difference $M(\Lambda_c(2625)^+) - M(\Lambda_c^+)$.
Correctly calibrating the momentum scale for low momentum pions
is critical for this analysis.
We calibrate the momentum
scale using copious $K^0_S\to\pi^+\pi^-$ events in the experimental data.
Low-momentum tracks are iteratively calibrated as a
function of the curvature,
polar angle, and momentum of each track in the laboratory frame
by comparing the reconstructed and world-average mass of the $K^0_S$
meson as a function of the $K^0_S$ momentum.
This correction has been used in a previous $\Sigma_c^{++/0}$
study using Belle data~\cite{SLee:2014PRD}.
Since the mass-resolution function is
crucial for the precise measurement of
the $\Lambda_c(2625)^+$ mass and width,
the MC tracks are smeared using
the analysis software during reconstruction,
as otherwise the MC mass resolution is known
to be better than that of the experimental data.
This track smearing affects
the width of the mass-resolution function but not
its central value.
The mass-resolution function of the $\Lambda_c(2625)^+$ mass is parameterized
as a sum of two Gaussian functions with parameters fixed according to
a signal MC sample with both corrections as detailed above.
The consistency between the MC sample and the experimental data
is checked by comparing the mass resolution of $D^{*+}$ events,
which have similar
kinematics to the events under study.
The low-momentum track correction ensures that the
measured $D^{*+}$ mass in data and MC are independent of the
momentum of the soft pion~\cite{SLee:2014PRD}.
The resolution of the $D^{*+}$ mass relative to the $D^{0}$ mass
in the experimental data is found by fitting the $M(D^0\pi^+) - M(D^0)$
mass distribution in the experimental data with a Breit-Wigner distribution
convoluted with a double-Gaussian mass-resolution function,
where the width
of the Breit-Wigner is fixed to the PDG value of $83.4\ \ensuremath{\textrm{keV}/\textit{c}^2}$~\cite{PDG:2020}.
In this study, without track smearing, the mass resolution
in the experimental data is measured to be 114\% of the value obtained from the
MC sample.
However, with track smearing,
the mass resolution
in the experimental data is measured to be
86\% of the value obtained from the MC sample.
In all other narrow signals studied, for instance the $\Lambda_c^+$, the track smearing
ensures that the MC and data agrees reasonably.
The track smearing has negligible effect on the mass
measurement.
The results of these consistency checks are used in the estimation of the systematic
uncertainties described below.
The reconstructed $M(\Lambda_c^+\pi^+\pi^-)$ mass distribution
in the experimental is fitted using RooFit~\cite{Roofit}.
Figure~\ref{mass_fit1} shows the $M(\Lambda_c^+\pi^+\pi^-)$ mass distribution
in the experimental data overlaid with the fit result.
The signal function is a Breit-Wigner distribution
convolved with a double-Gaussian mass-resolution function, and
the background function is a second-order Chebychev polynomial.
The resolution function for the invariant mass distribution
is obtained from the MC sample, without track smearing, and
scaled by 114\% in accordance with the $D^{*+}$ study.
The solid line shows the overall fit and the dashed lines
show the individual signal and background components of the fit.
The fitted mass is $2628.025 \pm 0.006 \,\ensuremath{\textrm{MeV}/\textit{c}^2}$, independent of
which version of the mass-resolution function we use.
If we use the track-smearing correction without any rescaling,
the fitted width is found to be zero, so we have no definitive
evidence of a non-zero width and will present only an upper limit
for the measurement of the intrinsic width of the $\Lambda_c^+(2625)$.
If we use the mass resolution without track smearing, scaled by 114\%,
the fitted width is $0.490 \pm 0.025 \,\ensuremath{\textrm{MeV}/\textit{c}^2}$.
With the mass-resolution function with track smearing scaled by 86\%,
the fitted width is $0.293 \pm 0.026 \,\ensuremath{\textrm{MeV}/\textit{c}^2}$.
These finite values for the fitted width after scaling the mass resolution
are only used to find the limit on the intrinsic width including
systematic uncertainties.
The fitted mass of $\Lambda_c(2625)^+$ in the signal
MC sample is slightly different from the generated value.
Applying a bias correction, determined by the mass shift observed
in the signal MC sample,
the mass of the $\Lambda_c(2625)^+$ is measured to be
$2627.978 \pm 0.007 \,\ensuremath{\textrm{MeV}/\textit{c}^2}$,
where the uncertainty is statistical.
Two upper limits on the width are calculated
based on the two fit methods described in the previous section
and the larger upper limit
is reported as the final answer.
Using the mass-resolution function determined from MC
scaled by 114\% without
track smearing, the upper limit
is determined to be
\begin{equation}
\Gamma(\Lambda_c(2625)^+) < 0.52 \,\ensuremath{\textrm{MeV}/\textit{c}^2}
\end{equation}
at 90\% credibility level by integrating the likelihood function
to find the value for which the integral contains
90\% of the total area.
Using the mass-resolution function scaled by
86\% with track smearing
would yield a tighter upper limit.
Therefore, we conservatively report the former as
the upper limit on the width of $\Lambda_c(2625)^+$.
\begin{figure}[htb]
\includegraphics[width=\linewidth]{figs/lamc2625_mass.pdf}
\caption{Distribution of the invariant mass $M(\Lambda_c^+\pi^+\pi^-)$
where the $\Lambda_c^+$ mass is fixed to the PDG value.
The solid line shows the overall distribution and the dashed lines
show the individual signal and background components.
}
\label{mass_fit1}
\end{figure}
\section{Dalitz plot fit}
A Dalitz plot fit is made in order to determine the relative branching
ratios of $\Lambda_c(2625)^+$ with respect to the mode
$\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^+ \pi^-$.
For the Dalitz plot fit, only $\Lambda_c(2625)^+$ candidates
within $\pm 2\,\ensuremath{\textrm{MeV}/\textit{c}^2}$ of the $\Lambda_c(2625)^+$ PDG mass are accepted~\cite{PDG:2020}.
The invariant mass of the $\Lambda_c(2625)^+$ candidates
is then constrained to the $\Lambda_c(2625)^+$ PDG mass of $2628.11\,\ensuremath{\textrm{MeV}/\textit{c}^2}$,
and the four-vectors of
the daughter particles are updated accordingly.
A fit is made to the Dalitz plot using an amplitude model
as presented by Arifi {\em et al.}~\cite{Arifi:2018prd}
using the AmpTools software package~\cite{AMPTOOLS}.
The $\Lambda_c(2625)^+$ signal distribution is calculated
from the squared amplitude with spin sum of final states and
spin average of the initial states
\begin{equation}
\sum |\mathcal{T}_1 + \mathcal{T}_2 + \mathcal{T}_3 +
\mathcal{T}_4 + \mathcal{T}_5|^2
\end{equation}
where $\mathcal{T}_1$ through $\mathcal{T}_5$ are the decay
amplitudes through the intermediate states
$\Sigma_c^0$, $\Sigma_c(2520)^0$,
$\Sigma_c^{++}$, $\Sigma_c(2520)^{++}$, and the
direct three-body decay, respectively.
Each amplitude is modeled as a Breit-Wigner function multiplied
by a form factor specific to each decay channel.
A constant amplitude is used to model the background
$\Lambda_c^+\pi^+\pi^-$ combinations, which are not decay products
of $\Lambda_c(2625)^+$. The yield of each decay channel is calculated
using AmpTools by an integration of the individual component
over the Dalitz plot.
The contribution of the three-body decay in the signal model
is different from the background phasespace decay in that
the former is not flat across the Dalitz plot.
During the fit,
the masses and widths of these intermediate particles are constrained
to their respective PDG values to facilitate the convergence.
The small variations of the detector acceptance across the Dalitz plot
are taken into account by using the output of a phasespace
MC sample passed through the GEANT3 detector simulation
as input to the AmpTools fitting package.
Figure~\ref{data_dalitz} shows the Dalitz plots for
candidates in the signal region.
On the left subplot, the contributions
from $\Sigma_c^{++}$ and the reflection
from $\Sigma_c^0$ constitute
the two horizontal stripes. The upper and lower parts
of the Dalitz plot show slight excesses
due to $\Sigma_c(2520)^{++/0}$ decays. There is also
a clear excess on the left side of the Dalitz plot compared to
the right in agreement with the three-body decay taking into account the spin,
as predicted in the amplitude
model~\cite{Arifi:2018prd}.
On the right subplot, the horizontal and vertical stripes
indicate the $\Sigma_c^{++}$ and $\Sigma_c^0$ decays
respectively. It is straightforward to see the origin of
the reflection peaks on the $M(\Lambda_c^+\pi^+)$ mass projection
from this 2D Dalitz plot.
Figure~\ref{data_dalitz_projection} shows the projections
of the fitted results with each component labeled on the plot.
The $\Sigma_c^{++}$ peak and the reflection peak
from $\Sigma_c^0$ are evident on the $M(\Lambda_c^+\pi^+)$ mass
projection.
The shoulders on the left and right side of the mass region
are mostly formed by the decays from
the off-shell $\Sigma_c(2520)^{++/0}$.
The three-body $p$-wave decay in the signal model shows up
in the $M(\pi^+\pi^-)$ mass projection as
an assymetric distribution, in contrast to
the symmetric distribution from the background
phasespace decay.
The $\Lambda_c(2625)^+$ yield in the signal region is
$N_{\mathrm{sig}}(\Lambda_c(2625)^+)) = 30319 \pm 371$.
The $\Sigma_c^{0}$ yield is
$N_{\mathrm{sig}}(\Sigma_c^{0}) = 1964 \pm 66$
and the $\Sigma_c^{++}$ yield is
$N_{\mathrm{sig}}(\Sigma_c^{++}) = 2022 \pm 76$.
\begin{figure*}[htb]
\begin{subfigure}[b]{0.49\linewidth}
\includegraphics[width=\linewidth]{figs/data_dalitz.pdf}
\end{subfigure}
\begin{subfigure}[b]{0.49\linewidth}
\includegraphics[width=\linewidth]{figs/data_dalitz_lamcpip_lamcpim.pdf}
\end{subfigure}
\caption{Dalitz plot for $\Lambda_c(2625)^+$ candidates in the signal region. Explanations of the patterns in the text.}
\label{data_dalitz}
\end{figure*}
\begin{figure*}[htb]
\begin{subfigure}[b]{0.49\linewidth}
\includegraphics[width=\linewidth]{figs/data_dalitz_lamcpi.pdf}
\end{subfigure}
\begin{subfigure}[b]{0.49\linewidth}
\includegraphics[width=\linewidth]{figs/data_dalitz_pipi.pdf}
\end{subfigure}
\caption{Dalitz plot fit result plotted as projections.
Solid lines shows the overall fitted distribution and its
individual components as indicated in the legend.
More explanations in the text.}
\label{data_dalitz_projection}
\end{figure*}
To account for $\Sigma_c(2455)^{++/0}$ candidates that
are not decay products of the $\Lambda_c(2625)^+$,
the $\Sigma_c(2455)^{++/0}$ yields from the
$M(\Lambda_c^+\pi^+\pi^-)$ sidebands are subtracted from
the $\Sigma_c(2455)^{++/0}$ yields found from the amplitude fit.
The sidebands are six $4\,\ensuremath{\textrm{MeV}/\textit{c}^2}$ regions near the
$\Lambda_c(2625)^+$ signal region,
as shown in Fig.~\ref{fig:region_def}.
Each sideband region is fitted as
an incoherent sum of the contributions from
the $\Sigma_c(2455)^0$, the $\Sigma_c(2455)^{++}$,
and the three-body phasespace decay.
Figures~\ref{fig:sideband_dalitz_left} and
\ref{fig:sideband_dalitz_right}
show the projections of the fit results for each
sideband region with each component labeled on the
plot.
The $\Sigma_c(2455)^{++/0}$ yields in the signal
region are determined by extrapolating the yields
from the sidebands according to a linear fit, as shown
in Fig.~\ref{fig:simgac_yields} and tabulated in
Table~\ref{tab:subtractedYields}.
The background yields to be subtracted
are $N_{\mathrm{bkg}}(\Sigma_c^{0}) = 391 \pm 11$ and
$N_{\mathrm{bkg}}(\Sigma_c^{++}) = 467 \pm 12$.
The branching ratio of
$\Lambda_c(2625)^+ \to \Sigma_c^{0} \pi^{+}$
relative to the reference mode
$\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-}$
is calculated using
\begin{equation} \label{eq:br_calc}
\begin{split}
\frac{\mathcal{B}(\Lambda_c(2625)^+ \to \Sigma_c^{0} \pi^{+})}
{\mathcal{B}(\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-})}
= \frac{N_{\mathrm{sig}}(\Sigma_c^{0}) -
N_{\mathrm{bkg}}(\Sigma_c^{0})}{N_{\mathrm{sig}}(\Lambda_c(2625)^+)}
\end{split}
\end{equation}
and similarly for the $\Sigma_c^{++}\pi^-$ mode.
\begin{figure}[htb]
\includegraphics[width=\linewidth]{figs/mass_regions.pdf}
\caption{Signal region and the six sideband regions on either
side of the signal region used for sideband subtraction.}
\label{fig:region_def}
\end{figure}
\begin{figure*}[htb]
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_a_lamcpi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_a_pipi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_b_lamcpi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_b_pipi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_c_lamcpi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_c_pipi.pdf}
\caption{Projections of the Dalitz plot fits of the 3 sidebands on the left side of the signal region. Overall fitted distribution and the individual fitted components are shown alongside the experimental data.}
\label{fig:sideband_dalitz_left}
\end{figure*}
\begin{figure*}[htb]
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_d_lamcpi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_d_pipi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_e_lamcpi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_e_pipi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_f_lamcpi.pdf}
\includegraphics[width=0.48\linewidth]{figs/sideband_dalitz_f_pipi.pdf}
\caption{Projections of the Dalitz plot fits of the 3 sidebands on the right side of the signal region. Overall fitted distribution and the individual fitted components are shown alongside the experimental data.}
\label{fig:sideband_dalitz_right}
\end{figure*}
\begin{figure*}[htb]
\begin{subfigure}[b]{0.49\linewidth}
\includegraphics[width=\linewidth]{figs/sigmac0_yields.pdf}
\end{subfigure}
\begin{subfigure}[b]{0.49\linewidth}
\includegraphics[width=\linewidth]{figs/sigmacpp_yields.pdf}
\end{subfigure}
\caption{$\Sigma_c^0$ and $\Sigma_c^{++}$ yields from the
sideband Dalitz plot fits, overlaid with linear and quadratic extrapolations.}
\label{fig:simgac_yields}
\end{figure*}
We measure relative branching ratios to be
\begin{equation}
\begin{aligned}
\frac{\mathcal{B}(\Lambda_c(2625)^+ \to \Sigma_c^{0} \pi^{+})}
{\mathcal{B}(\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-})}
= (5.19 \pm 0.23)\% \\
\frac{\mathcal{B}(\Lambda_c(2625)^+ \to \Sigma_c^{++} \pi^{-})}
{\mathcal{B}(\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-})}
= (5.13 \pm 0.26)\%
\end{aligned}
\end{equation}
where the errors are statistical only.
\section{Systematic uncertainties}
The primary source of systematic uncertainty on the
$\Lambda_c(2625)^+$ width is the inconsistency of the mass-resolution
function between the MC sample and the experimental data.
We use the $D^{*+}\to D^0\pi^+$ decay
as a control sample to determine the
under- or over-estimation of the mass resolution in the MC sample
relative to the experimental data.
The mass resolution in the experimental data is found to
be 86\% of that in the MC sample with track smearing,
114\% without track smearing.
Both mass-resolution functions are used to determine the
upper limit on the $\Lambda_c(2625)^+$ width in the
experimental data.
When applied to the experimental data,
the mass resolution without track smearing scaled by 114\%
results in a more conservative upper limit on the
$\Lambda_c(2625)^+$ width, thus reported as the
final result.
The systematic uncertainty on the $\Lambda_c(2625)^+$ mass
is not greatly affected by the uncertainty on the
$M(\Lambda_c^+\pi^+\pi^-)$ mass resolution,
but is limited by the precision with which the Belle detector
can measure the mass in this range.
Studies with $D^{*+} \to D^0\pi^+$ decays show that the
measured $D^{*+}$ mass difference with respect to the
world-average value is $0.004 \,\ensuremath{\textrm{MeV}/\textit{c}^2}$.
Any imperfection in the soft pion momentum calibration
changes the measured mass of the $\Lambda_c(2625)^+$
more than that of the $D^{*+}$.
We determine the scale factor required to correct
the soft pion momentum such that the $D^{*+}$ mass
matches its PDG value, then apply the same scale
factor to the daughter pions from $\Lambda_c(2625)^+$ candidates.
The $\Lambda_c(2625)^+$ mass changed by $0.042 \,\ensuremath{\textrm{MeV}/\textit{c}^2}$,
which we assign as the systematic uncertainty due to
the mass scale.
The track smearing correction applied to
tracks in the MC sample
has a negligible effect on the mass measurement.
The systematic uncertainty due to the low momentum
correction is $0.025 \,\ensuremath{\textrm{MeV}/\textit{c}^2}$, which is found
by comparing the measured $\Lambda_c(2625)^+$ mass
with and without the low momentum correction.
Summing the contributions from the mass scale and
low momentum track correction in quadrature,
the total systematic uncertainty
on the mass measurement is $0.049 \,\ensuremath{\textrm{MeV}/\textit{c}^2}$.
The systematic uncertainties on the relative branching ratios,
which are calculated from Eq.~(\ref{eq:br_calc}),
are derived from the uncertainty of the $\Lambda_c(2625)^+$
yield in the signal region, the $\Sigma_c^{++/0}$ yields
fitted in the signal Dalitz plot fit, and the $\Sigma_c^{++/0}$
subtracted yields extrapolated from the sideband fits.
The systematic uncertainty associated with each is
tabulated in Table~\ref{tab:yields_uncertainty}.
The $\Lambda_c(2625)^+$ signal yield is most affected
by the mass-resolution function. We fit the experimental data
with a mass-resolution function determined with and without
track smearing. The difference in the yields is taken as
the systematic uncertainty on the
$\Lambda_c(2625)^+$ signal yield.
The $\Sigma_c^{++/0}$ signal yields are determined
from the Dalitz plot fit, with their masses and widths
fixed to PDG values. The masses, widths, and mass resolutions
are systematically varied within the PDG uncertainties, and
the maximum change in the fitted $\Sigma_c^{++/0}$ yield
is taken as the systematic uncertainty.
In order to determine the sideband subtracted
yield, the six sidebands are fitted individually
to determine the $\Sigma_c^{++/0}$ yields,
with the yield and uncertainty in each sideband region
shown in Fig.~\ref{fig:simgac_yields}. The extrapolated
yield at the nominal $\Lambda_c(2625)^+$ mass
is a weighted average of
the yields of the six sidebands.
We take the difference
between the linear and quadratic extrapolation
as shown in Table~\ref{tab:subtractedYields}
as the systematic uncertainty due to the extrapolation.
To account for the statistical fluctuation due
the finite MC sample sizes in the Dalitz plot fits,
we compare the fitted results using two statistically
independent MC samples of the same size. The difference
is taken as the systematic uncertainty due to the
MC sample size.
With systematic uncertainties on the yields in
Eq.~(\ref{eq:br_calc}) listed in Table~\ref{tab:yields_uncertainty},
the total systematic uncertainties on the ratio
of branching fractions are calculated from
the propagation of error and are listed in
Table~\ref{tab:br_uncertainty}.
the total systematic uncertainty on the
ratio of branching fractions
is found to be 0.40\% for the
$\Sigma_c^0 \pi^+$ channel, and
0.32\% for the $\Sigma_c^{++}\pi^-$ channel.
\begin{table}[htb]
\caption{Subtracted yields for $\Sigma_c^{++/0}$}
\label{tab:subtractedYields}
\begin{tabular}{@{\hspace{0.5cm}}l@{\hspace{0.5cm}} @{\hspace{0.5cm}}c@{\hspace{0.5cm}}
@{\hspace{0.5cm}}c@{\hspace{0.5cm}}}
\hline \hline
Method & $\Sigma_c^{0}$ yield
& $\Sigma_c^{++}$ yield \\
\hline
Linear & $391 \pm 11$ & $467 \pm 12$ \\
Quadratic & $348 \pm 26$ & $436 \pm 28$ \\
\hline
Difference & 11.00\% & 6.64\% \\
\hline \hline
\end{tabular}
\end{table}
\begin{table*}[htb]
\caption{The percentage systematic uncertainties of the signal yields used for the
branching ratio calculation.}
\label{tab:yields_uncertainty}
\begin{tabular}{@{\hspace{0.5cm}}l@{\hspace{0.5cm}}
@{\hspace{0.5cm}}c@{\hspace{0.5cm}}
@{\hspace{0.5cm}}c@{\hspace{0.5cm}}
@{\hspace{0.5cm}}c@{\hspace{0.5cm}}
@{\hspace{0.5cm}}c@{\hspace{0.5cm}}
@{\hspace{0.5cm}}c@{\hspace{0.5cm}}}
\hline \hline
Source & $\Sigma_c^{0}$ signal & $\Sigma_c^{++}$ signal
& $\Sigma_c^{0}$ sideband & $\Sigma_c^{++}$ sideband
& $\Lambda_c(2625)^+$ signal \\
\hline
Resolution & 1.97\% & 1.42\% & 2.74\% & 1.08\% & 3.64\%\\
$\Sigma_c^{0/++}$ width & 4.00\% & 2.26\% & 2.52\% & 2.38\% & -\\
$\Sigma_c^{0/++}$ mass & 1.25\% & 1.11\% & 0.08\% & 0.08\% & -\\
Extrapolation & - & - & 11.00\% & 6.64\% & - \\
MC sample size & 1.91\% & 2.09\% & 0.71\% & 0.22\% & - \\
\hline
Total & 5.01\% & 3.57\% & 11.63\% & 7.14\% & 3.64\% \\
\hline \hline
\end{tabular}
\end{table*}
\begin{table*}[htb]
\caption{Systematic uncertainties on the ratio of branching fractions.}
\label{tab:br_uncertainty}
\begin{tabular}{@{\hspace{0.5cm}}l@{\hspace{0.5cm}}
@{\hspace{0.5cm}}c@{\hspace{0.5cm}}
@{\hspace{0.5cm}}c@{\hspace{0.5cm}}
}
\hline \hline
Source &
$\frac{\mathcal{B}(\Lambda_c(2625)^+ \to \Sigma_c^{0} \pi^{+})}
{\mathcal{B}(\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-})}$ &
$\frac{\mathcal{B}(\Lambda_c(2625)^+ \to \Sigma_c^{++} \pi^{-})}
{\mathcal{B}(\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-})}$ \\
\hline
$\Sigma_c^{0/++}$ resolution & 0.13\% & 0.10\% \\
$\Sigma_c^{0/++}$ width & 0.26\% & 0.16\% \\
$\Sigma_c^{0/++}$ mass & 0.08\% & 0.07\% \\
Extrapolation & 0.14\% & 0.10\% \\
MC sample size & 0.12\% & 0.14\% \\
$\Lambda_c^+(2625)$ resolution & 0.19\% & 0.19\% \\
\hline
Total & 0.40\% & 0.32\% \\
\hline \hline
\end{tabular}
\end{table*}
\section{Discussion}
We report the most precise $\Lambda_c(2625)^+$ mass,
width, and branching
ratio measurements to date.
The measured mass is consistent with previous results.
The measured upper limit on $\Lambda_c(2625)^+$ width
is $\Gamma(\Lambda_c(2625)^+) < 0.52\,\ensuremath{\textrm{MeV}/\textit{c}^2}$
at the 90\% credibility level.
Theoretical predictions for the $\Lambda_c(2625)^+$ width vary.
Arifi {\em et al.} predict the width to be 0.570 MeV/$\textrm{c}^2$ based on
chiral and heavy quark symmetry~\cite{Arifi:2018prd}.
The width is revised to be between 0.09 and 0.26 MeV/$\textrm{c}^2$
in a subsequent publication with the inclusion of
relativistic corrections~\cite{Arifi:2021prd}.
Kawakami {\em et al.} predict a width in the range of
0.11 - 0.73 MeV/$\textrm{c}^2$ based on chiral symmetry~\cite{Kawakami:2018prd}.
Guo {\em et al.} predict a much smaller width of
$1.13\times10^{-2}$ MeV/$\textrm{c}^2$,
based on the $^3P_0$ model~\cite{Guo:2019prd}.
The relative branching ratios of
$\Lambda_c(2625)^+ \to \Sigma_c^0 \pi^+$ and
$\Lambda_c(2625)^+ \to \Sigma_c^{++} \pi^-$
relative to the reference mode
$\Lambda_c(2625)^+ \to \Lambda_c^{++} \pi^+ \pi^-$
are extracted from a full Dalitz plot fit.
Backgrounds from non-$\Lambda_c(2625)^+$ decays are
subtracted from the $\Sigma_c^{++/0}$ yields.
Our measurements align with the prediction
by Arifi {\em et al.}, who assume $\Lambda_c(2625)^+$
is a $\lambda$ mode excitation~\cite{Arifi:2018prd}.
Kawakami {\em et al.} predicted
a wide range~\cite{Kawakami:2018prd} and
Guo {\em et al.}'s predicted the ratio
$\Gamma(\Sigma_c^{++} \pi^{-})/\Gamma_{\mathrm{total}}$
to be
29.9\%~\cite{Guo:2019prd},
which is already in contradiction with the previous measurement.
Our measurements of the properties of the $\Lambda_c(2625)^+$ charmed
baryon will be useful to further constrain the parameter
space of the quark models and can be applied to other heavy quark systems.
\section{Conclusions}
We measure the mass of the $\Lambda_c(2625)^+$ to be
$2627.978 \pm 0.006 \pm 0.049\,\ensuremath{\textrm{MeV}/\textit{c}^2}$, where
the uncertainty on the $\Lambda_c^+$ mass is not included
since it is constrained to the PDG value during reconstruction.
This is equivalent to
\begin{equation}
M(\Lambda_c(2625)^+) - M(\Lambda_c^+) =
341.518 \pm 0.006 \pm 0.049 \,\ensuremath{\textrm{MeV}/\textit{c}^2}
\end{equation}
The mass measurement is consistent with
the previous CDF measurement but with approximately
half the uncertainty
\cite{CDF:2011}.
An upper limit on the $\Lambda_c(2625)^+$ width is determined to be
\begin{equation}
\Gamma(\Lambda_c(2625)^+) < 0.52 \,\ensuremath{\textrm{MeV}/\textit{c}^2}\
\end{equation}
at 90\% credibility level
which is around a factor of two more stringent than the previous
limit.
Based on a full Dalitz plot fit and with sideband subtraction
of the $\Sigma_c^{++/0}$ yields,
the branching ratios
relative to the mode $\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^+ \pi^-$
are obtained:
\begin{equation}
\begin{aligned}
\frac{\mathcal{B}(\Lambda_c(2625)^+ \to \Sigma_c^{0} \pi^{+})}
{\mathcal{B}(\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-})} =
(5.19 \pm 0.23 \pm 0.40)\% \\
\frac{\mathcal{B}(\Lambda_c(2625)^+ \to \Sigma_c^{++} \pi^{-})}
{\mathcal{B}(\Lambda_c(2625)^+ \to \Lambda_c^+ \pi^{+} \pi^{-})}
= (5.13 \pm 0.26 \pm 0.32) \%
\end{aligned}
\end{equation}
This is the first measurement made of
these branching fractions as previously only limits have been presented.
These measurements can be used as inputs to theoretical models
to generate predictions for other heavy quark baryons.
\section{Acknowledgements}
\input{ack}
| {
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Navajo blanket nets man on welfare more than $1 million
1 Jan, 2018 09:40 PM 3 minutes to read
A man who was down on his luck and living in a shack in California got a new lease on life when he discovered a ratty old blanket that belonged to his grandmother was worth NZ$1.8 million.
Loren Krytzer, who lost his foot in a car crash, was living off paltry disability checks when he walked into a California auction room and came out a millionaire, thanks to the rare Navajo blanket that was almost thrown out after his grandmother died.
Krytzer was watching Antiques Roadshow when a blanket that looked identical to his appeared on the screen.
The blanket Loren Krytzer had stashed in his closet was made by Navajo people. Photo / John Moran Auctions
He then tried various auction houses to sell the blanket before John Moran Auctioneers in Monrovia, California, agreed to put it under the hammer, according to CNBC.
Krytzer also provided a photograph of his great-great-grandfather at his North Dakota trading post, which helped boost interest.
The blanket became the most expensive item Moran's company had ever sold.
The sale of the blanket "gave me a new lease on life", Krytzer said. "It truly did."
He was living off just US$200 a month from his disability checks after the crash, which left him unable to work as a carpenter.
A photo Loren Krytzer provided of his great-great-grandfather John Chantland, right, at his trading post boosted interest in the blanket. Photo / Loren Krytzer
He has told US media that he went to his grandmother's house after she died to collect books she had promised him. The last bag in the house held two blankets handed down from his great-grandmother. The Navajo blanket was once put to use when his great-grandmother's cat had kittens, he said.
He put the blanket in the cupboard, where it stayed for seven years.
Loren Krytzer bought himself a new car and a custom motorbike. Photo / Loren Krytzer
But now, he is finding that the unexpected windfall has brought its own challenges along with it, including high property taxes.
"It's not like it was 40 or 50 years ago," he says. "If I'd have gotten $1 million 50 years ago, I'd be rich right now. I would literally be rich."
He bought two homes in Central California, but he is out about $10,000 a year in insurance and property taxes alone.
Krytzer also bought a new car and a custom motorcycle.
"I never had nothing like that, so I wanted a nice car, and I did, I bought one," he says.
He also lost his disability eligibility, so he has no income. Krytzer says he is looking to sell
his home and move to Idaho where life is more affordable.
"We're getting taxed to death here. I can't afford it," he says. "I'm from California, I grew up here, but without working, it's just hard to survive."
Family members have come out of the woodwork asking for a piece of the pie. He says his sister even threatened to sue him.
"I had people calling me and bugging me and stuff," Krytzer says. "People you haven't seen in years, family members that don't talk to you. . . . You get some money and they're like 'where's mine?'"
He also has a hard time explaining to his children that the US$1.3million he received isn't enough to buy them whatever they want.
'When I first got the money, I helped them out,' Krytzer said. "But now it's like I can't do it, I don't have it, and they are like 'you have millions of dollars, you're being selfish'."
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} | 4,845 |
The Debut Album from Whethan is an Electronic 'Fantasy'
By Hayden McGuiganOctober 17, 20202 Comments
Whethan has finally released his highly anticipated debut album, Fantasy and we are BUZZING over it. Take a ride with us over this 14 track masterpiece filled with lush soundscapes, party starters, and serotonin boosters. Out now on Atlantic/Big Beat Records.
First, I want to start this article with a little story. My first experience with a Whethan live set came from a little place I call home, Electric Forest. It was Day 1 at Ranch Arena. Me and the homies were getting loose to SNBRN, and in a state of bliss. The Knocks were up next, and after them, our boy Whethan was set to take the stage. This was one of our group's most highly anticipated sets of the entire weekend, and there wasn't a thing on this planet that could get in our way.
But Mother Nature is a fickle one. As we were gearing up to get down, myself, as well as my surrounding forest family, got a notification from the Forest app that filled our hearts with dread. There was a dangerous weather cell approaching the venue, and we were advised to take shelter.
Gnarly storm approaching
That storm looked unlike anything I've ever seen. Stress and anxiety almost consumed me as I pictured a canceled Whethan set. However, in true Forest fashion, we decided to stay put. Ignoring the signs, and investing in Whethan no matter the imminent threat of severe weather. What happened next I will never forget. Whethan took the stage. And with some level of wook wizardry, mixed with a little Forest magic, the storm completely dispersed without a drop of rain. We were safe, and Whethan's set proved to be one of the best performances all weekend.
Whethan has racked up over 800 MILLION streams and shows no sign of slowing down.
Ethan Snoreck is the mastermind behind the Whethan project. At the ripe age of only 16 years old, Snoreck began his metamorphosis into the artist that we know and love today. If you've taken the time out of your day to listen to literally anything this man has produced, you wouldn't be surprised with the amount of support he's gained from the electronic community. Whether it be earning nods from OWSLA, befriending Skrillex, or touring with The Chainsmokers while finishing his senior year of high school — Whethan has carved his name in the industry as a pillar of dance music.
The amazing Abby Price compiled a list of every unreleased Whethan song known to date in a previous write-up. Check it out here.
https://www.instagram.com/p/CDArn2JB6-Z/
Fantasy is the perfect representation of what makes Whethan great.
Teasing six singles from the album, Fantasy was a three-year process that in my personal opinion, highlights his best work yet. Those six singles alone have amassed over 961,000 streams combined. "All In My Head" feat. grandson was met with extremely positive critical acclaim. SPIN named it "one of the best songs of 2020 thus far." And Billboard rightfully categorized it as "an alt-bop explosion good enough to leave on repeat…"
Whethan · All In My Head (feat. grandson)
"Freefall," feat. frequent collaborator Oliver Tree, is one of those summertime anthems that proves to be an instant party starter. Paired with the music video with over 800k views, this track is just an all-around good time.
The rest of Fantasy is an absolute conglomerate of amazing production. Boasting collaborations with Chrome Sparks, bülow, The Front Bottoms, STRFKR, and the trap lord himself RL GRIME — Fantasy quite literally can't miss. Whethan's style is self-described as "overall euphoric, uplifting, and distorted." And that style is something we can all come to appreciate. The diversity in his work is something to marvel over. Whether it be trap anthems like "Outta Here" feat. RL GRIME, or dancefloor fillers like "Sunshine" feat. The Knocks; Whethan checks every box with his debut album.
Listen to Fantasy, the debut album from Whethan below, and support your favorite creatives:
Keep Up with Whethan:
Soundcloud | Twitter | Instagram | Facebook | Spotify | Youtube | Official Site
And if you're looking for a solid playlist to follow, keep up with our weekly Spotify playlist, Fresh Hunts. Whether it's new Whethan, all your other favorite artists, some old-school, or underground…we just want you to hear it.
And don't forget to use your voice this November. Head over to Headcount to check your status and find other resources. Vote, and while your sharing new music, encourage your friends to vote too!
Hayden McGuigan
It's always about the music.
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"redpajama_set_name": "RedPajamaCommonCrawl"
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{"url":"https:\/\/www.chemeurope.com\/en\/encyclopedia\/Maximum_entropy_spectral_estimation.html","text":"My watch list\nmy.chemeurope.com\n\n# Maximum entropy spectral estimation\n\nThe maximum entropy method applied to spectral density estimation. The overall idea is that the maximum entropy rate stochastic process that satisfies the given constant autocorrelation and variance constraints, is a linear Gauss-Markov process with i.i.d. zero-mean, Gaussian input.\n\n## Method description\n\nThe maximum entropy rate, strongly stationary stochastic process xi with autocorrelation sequence $R_{xx}(k), k = 0,1, \\dots P$ satisfying the constraints:\n\nRxx(k) = \u03b1k\n\nfor arbitrary constants \u03b1k is the P-th order, linear Markov chain of the form:\n\n$x_i = -\\sum_{k=1}^P a_k x_{i-k} + y_i$\n\nwhere the yi are zero mean, i.i.d. and normally-distributed of finite variance \u03c32.\n\n## Spectral estimation\n\nGiven the ak, the square of the absolute value of the transfer function of the linear Markov chain model can be evaluated at any required frequency in order to find the power spectrum of xi.\n\n## References\n\n\u2022 Cover, T. and Thomas, J. (1991) Elements of Information Theory, John Wiley and Sons, Inc.","date":"2023-01-30 15:31:53","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 2, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9300159811973572, \"perplexity\": 1155.4647315053546}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764499819.32\/warc\/CC-MAIN-20230130133622-20230130163622-00815.warc.gz\"}"} | null | null |
{"url":"https:\/\/worksheets.tutorvista.com\/factor-special-products-worksheet.html","text":"To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)\n\n# Factor Special Products Worksheet\n\nFactor Special Products Worksheet\n\u2022 Page 1\n1.\nFactor completely.\n196$t$$m$2 - 448$t$$m$ + 256$t$\n a. $t$(4$m$ - 7)2 b. 4$t$(7$m$ - 8)2 c. 4$m$(7$m$ - 8)(7$m$ + 8) d. 4$m$($t$ - 7)2\n\n#### Solution:\n\n196tm2 - 448tm + 256t\n\n= 4t(49m2 - 112m + 64)\n[GCF is 4t.]\n\n= 4t(7m - 8)2\n[(a - b)2= a2 - 2ab + b2.]\n\nCorrect answer : (2)\n2.\nExpress as a perfect square.\n$t$2 + 14$t$ + 49\n a. b. c. d. $t$($t$ + 7)\n\n#### Solution:\n\nt2\u00a0+\u00a014t\u00a0+\u00a049\n[Given expression.]\n\n= t2\u00a0+\u00a02(t)(7)\u00a0+72\n[Write as (t2\u00a0+\u00a02\u00a0t\u00a0m\u00a0+m2).]\n\n= (t\u00a0+\u00a07)2\n[Write as (t\u00a0+\u00a0m)2.]\n\nCorrect answer : (3)\n3.\nExpress as a perfect square.\n$\\frac{{r}^{2}}{{y}^{2}}$ + $\\frac{6r}{y}$ + 9\n a. b. c. d.\n\n#### Solution:\n\nr2y2\u00a0+6ry\u00a0+\u00a09\n[Given expression.]\n\n= (ry)2\u00a0+\u00a02(ry)(3)\u00a0+(3)2\n[Write as (a2\u00a0+\u00a02ab\u00a0+b2).]\n\n= (ry\u00a0+\u00a03)2\n[Write as (a\u00a0+\u00a0b)2.]\n\nCorrect answer : (4)\n4.\nExpress as a perfect square.\n a. b. c. d.\n\n#### Solution:\n\nb2\u00a0-\u00a010b\u00a0+\u00a025\n[Given expression.]\n\n= b2\u00a0-\u00a02(b)(5)\u00a0+52\n[Write as (a2\u00a0-\u00a02ab\u00a0+b2).]\n\n= (b\u00a0-\u00a05)2\n[Write as (a\u00a0-\u00a0b)2.]\n\nCorrect answer : (1)\n5.\nExpress as a perfect square.\n\n a. b. c. d.\n\n#### Solution:\n\nz2\u00a0-\u00a02.4z\u00a0+\u00a01.44\n[Given expression.]\n\n= z2-2(z)(1.2)+1.22\n[Write as (a2-2ab+b2).]\n\n= (z\u00a0-\u00a01.2)2\n[Write as (a\u00a0-\u00a0b)2.]\n\nCorrect answer : (4)\n6.\nExpress as a perfect square.\n${s}^{2}-\\frac{14s}{6}+\\frac{49}{36}$\n a. b. c. d.\n\n#### Solution:\n\ns2-14s6+4936\n[Given expression.]\n\n= s2-2(s)(7)6+(76)2\n[Write as (a2-2ab+b2).]\n\n= (s\u00a0-76)2\n[Write as (a\u00a0-\u00a0b)2.]\n\nCorrect answer : (1)\n7.\nExpress as a perfect square.\n$\\frac{1}{{r}^{2}}+\\frac{88}{r}+1936$\n a. b. c. d.\n\n#### Solution:\n\n1r2\u00a0+88r\u00a0+\u00a01936\n[Original expression.]\n\nLet 1r\u00a0=\u00a0h then 1r2\u00a0+88r\u00a0+\u00a01936 = h2 + 88h + 1936\n\n= h2+2(h)(44)+442\n[Write as (a2+2ab+b2).]\n\n= (h\u00a0+\u00a044)2\n[Write as (a\u00a0+\u00a0b)2.]\n\n= (1r\u00a0+\u00a044)2\n[Replace h with 1r.]\n\nCorrect answer : (3)\n8.\nExpress as a perfect square.\n a. b. c. d.\n\n#### Solution:\n\np2\u00a0-\u00a016p\u00a0+\u00a064\n[Original expression.]\n\n= p2-2(p)(8)+82\n[Write as (a2-2ab+b2).]\n\n= (p\u00a0-\u00a08)2\n[Write as (a\u00a0-\u00a0b)2.]\n\nCorrect answer : (3)\n9.\nExpress as a perfect square.\n${t}^{2}$ - 16ta + 64${a}^{2}$\n a. b. c. d.\n\n#### Solution:\n\nt2 - 16ta + 64a2\n[Original expression.]\n\n= t2\u00a0-\u00a02(t)(8a)+(8a)2\n[Write as (a2\u00a0-\u00a02ab\u00a0+b2).]\n\n= (t\u00a0-\u00a08a)2\n[Write as (a\u00a0-\u00a0b)2.]\n\nCorrect answer : (2)\n10.\nExpress as a perfect square: ${0.25q}^{2}$ - 5q + 25\n a. b. c. d.\n\n#### Solution:\n\n0.25q2 - 5q + 25\n[Original expression.]\n\n= (0.5q)2\u00a0-\u00a02(0.5q)(5)+(5)2\n[Write as (a2\u00a0-\u00a02ab\u00a0+b2).]\n\n= (0.5q\u00a0-\u00a05)2\n[Write as (a\u00a0-\u00a0b)2.]\n\nCorrect answer : (2)\n\n*AP and SAT are registered trademarks of the College Board.","date":"2019-05-24 14:02:33","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 25, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2201770395040512, \"perplexity\": 3577.8346509887624}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-22\/segments\/1558232257624.9\/warc\/CC-MAIN-20190524124534-20190524150534-00494.warc.gz\"}"} | null | null |
Cherry Professional are currently supporting a leading Nottingham based business in their search for a Senior Strategic Finance Manager. This is a high profile and challenging role that's far from traditional reporting - you'll help shape the direction of the organisation. As your insight takes the business to new and exciting places, your career will follow.
The Strategic Finance Manager will be joining to advise senior management on the financial impacts of major decisions on the group's funding strategy, funding requirements, including M&A activity, financing initiatives and changes to financing strategy.
The business will consider a number of backgrounds including, a candidate straight from the Big 4 (Senior Manager/Assistant Director who has trained within Corporate Finance/Deals) or a Practice trained candidate with experience within a commercial finance position in industry. The successful candidate must be bright, commercially astute and hungry to succeed in a fast paced, high growth entrepreneurial business.
An ambitious and confident candidate will exceed in this dynamic, rapidly expanding company. Your role will evolve dramatically within year one, from a hands-on role on day one, to a more strategic and operationally focused role after 6 months. This is a fantastic opportunity for an individual who is keen to make an impact within an evolving business that has embarked on significant period of change. | {
"redpajama_set_name": "RedPajamaC4"
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{"url":"https:\/\/www.cfm.brown.edu\/people\/dobrush\/am33\/Mathematica\/ch6\/nonconstant.html","text":"}\n\n# Preface\n\nThe Laplace transform helps also to solve variable coefficient linear differential equations.\n\n# Nonconstant coefficient IVP\u2019s\n\nExample: Consider the initial value problem\n\n$\\left( t +1\\right) \\ddot{y} - \\dot{y} -t\\,y(t) = 0, \\qquad y(0) =1, \\quad \\dot{y} = -1.$\nwhere overdot stands for the derivative with respect to t. \u00a0\u00a0\u00a0\u25a0\n\nExample: Consider the initial value problem\n\n$t\\,\\ddot{y} - \\dot{y} -t\\,y(t) = 0, \\qquad y(0) =1, \\tag{Example2.1}$\nwhere overdot stands for the derivative with respect to t. Note that this IVP has only one initial condition because the differential equation has a regular singular point at t = 0. The given differential equation has two linearly independent solution, but only one of them is of exponential order and admits Laplace transformation. Another linearly independent solution is underfined at the origin and is not suitable for our technique. So we have to disregard this solution and work only with one of them. Therefore, only one initial condition is relevant in our case.\n\nFirst, we ask Mathematica whether it knows its general solution.\n\nDSolve[t*y''[t] - y'[t] - t*y[t] == 0, y[t], t]\n{{y[t] -> -t BesselJ[1, I t] C[1] + t BesselY[1, -I t] C[2]}}\nIt turns out that the general solution is expressed through modified Bessel functions I1 and K1:\n$y(t) = C_1 t\\,I_1 (t) + C_2 t\\,K_1 (t) ,$\nwhere C1 and C1 are arbitrary constants. Next, we find the limits when the argument tends to zero (in order to verify the initial condition):\nLimit[x*BesselI[1, x], x -> 0]\n0\nLimit[x*BesselK[1, x], x -> 0]\n1\nAt infinity, the modified Bessel function of the first kind is growing exponentially:\n$t\\,I_1 (t) \\sim \\sqrt{\\frac{t}{2\\pi}} \\,e^t \\qquad\\mbox{as} \\quad t \\to \\infty .$\nSo it is of exponential order and its Laplace transform exists and equals\n${\\cal L}_{t\\to\\lambda} \\left[ t\\,I_1 (t) \\right] = \\left( \\lambda^2 -1 \\right)^{-3\/2} .$\nAnother function involving the Kelvin function is bounded ($$\\left\\vert t\\,K_1 (t) \\right\\vert \\le 1$$ for 0 \u2264 t <\u221e) and its Laplace transform exists, but the corresponding explicit formula is unknown yet.\n\nThe initial condition is\n$y(0) = C_1 \\cdot 0 + C_2 \\cdot 1 = C_2 ,$\nbut the first derivative\n$\\dot{y}(0) = C_2 \\lim_{t\\to 0} \\left[ K_1 (t) - t\\,K_2 (t) \\right] \\qquad \\mbox{undetermined}.$\nTherefore, we cannot specify the second initial condition for the given singular differential equation. Now we can make a conclusion that the given inital value problem has a solution only when the initial condition is homogeneous:\n$t\\,\\ddot{y} - \\dot{y} -t\\,y(t) = 0, \\qquad y(0) =0. \\tag{Example2.2}$\nIts solution is not unique:\n$y(t) = C_1 t\\, I_1 (t) , \\tag{Example2.3}$\nand depends on an arbitrary constant C1. On the other hand, the formulkated initially the problem (Example2.1) has no solution. Now we verify this conclusion with the aid of the Laplace transform.\n\nWe need to determine the Laplace transforms of each term in the given differential equation. So we have\n\n\\begin{align*} {\\cal L}\\left[ y(t) \\right] &= y^L (\\lambda ) = \\int_0^{\\infty} y(t) \\,e^{-\\lambda t} {\\text d} t , \\\\ {\\cal L}\\left[ t\\,y(t) \\right] &= \\int_0^{\\infty} t\\,y(t) \\,e^{-\\lambda t} {\\text d} t = - \\frac{\\text d}{{\\text d}\\lambda} \\, y^L (\\lambda ) , \\\\ {\\cal L}\\left[ \\dot{y}(t) \\right] &= \\lambda\\,y^L - y(0) = \\lambda\\,y^L -1. \\end{align*}\nIntegrating by parts, we get\n\\begin{align*} {\\cal L}\\left[ t\\ddot{y}(t) \\right] &= \\int_0^{\\infty} t\\ddot{y}(t) \\, e^{-\\lambda t} {\\text d} t = - \\int_0^{\\infty} \\dot{y} \\left[ e^{-\\lambda t} - \\lambda t\\,e^{-\\lambda t} \\right] {\\text d} t \\\\ &= y(0) \\left[ e^{-\\lambda t} - \\lambda t\\,e^{-\\lambda t} \\right]_{t=0} + \\int_0^{\\infty} y(t) \\left[ -2\\lambda\\, e^{-\\lambda t} + \\lambda^2 t \\,e^{-\\lambda t} \\right] {\\text d} t \\\\ &= y(0) -2\\lambda\\,y^L + \\lambda^2 {\\cal L} \\left[ t\\,y(t) \\right] . \\end{align*}\nPutting all terms together, we obtain the equation for the Laplace transform of the required function:\n$1 - 2\\lambda\\,y^L -\\lambda^2 \\frac{\\text d}{{\\text d}\\lambda} \\, y^L (\\lambda ) -\\lambda\\,y^L + 1 + \\frac{\\text d}{{\\text d}\\lambda} \\, y^L (\\lambda ) =0,$\nor upon simplification,\n$\\left( 1 - \\lambda^2 \\right) \\frac{\\text d}{{\\text d}\\lambda} \\, y^L (\\lambda ) - 3\\lambda\\,y^L = -2 .$\nIts solution is\nDSolve[(x^2 - 1)*y'[x] + 3*y[x] == 2, y, x]\n{{y -> Function[{x}, ( 2 E^(-3 (1\/2 Log[1 - x] - 1\/2 Log[1 + x])) (1 - x)^(3\/2))\/( 3 (1 + x)^(3\/2)) + E^(-3 (1\/2 Log[1 - x] - 1\/2 Log[1 + x])) C[1]]}}\n$y^L (\\lambda ) = \\frac{c}{\\left( \\lambda^2 -1 \\right)^{3\/2}} + \\frac{2}{3} \\left( 1 - \\lambda \\right)^{-3\/2} ,$\nwhere c is a constant of integration. Taking the inverse Laplac e transform, we obtain\n$y(t) = ct\\,I_1 (t) + \\frac{1}{3\\sqrt{2}}\\,\\delta (t) ,$\nwhere I1(t) is the modofied Bessel function of order 1 and \u03b4 is the delta Dirac function.\nInverseLaplaceTransform[(p - 1)^(-3\/2) , p, t]\nDiracDelta[t]\/(2 Sqrt[2])\n\u25a0","date":"2023-03-29 12:12:42","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9992408752441406, \"perplexity\": 1255.357223268167}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296948976.45\/warc\/CC-MAIN-20230329120545-20230329150545-00144.warc.gz\"}"} | null | null |
Blended essential oil based on the 2nd (Sacral) Chakra. Refreshes lower abdomen area and relieves constipation.
A natural & organically blended oil formulated based on the chakra system, targeting the 2nd (Sacral) chakra.
Refreshes lower abdomen area and relieves constipation.
Targets rejuvenation of kidneys, uterus/ testes, bladder & stomach skin.
Can be used for Menstrual cramps, PMS and sexual issues.
Use five (5) drops of INTO WELLNESS, and mix it with one (1) pump of BEST WATER.
Massage it on to the area between your navel and hips in clockwise motion. Massage staring from hips to below the belly, in downwards motion. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,466 |
Q: ValueError: invalid literal for int() with base 10: '01234SS' I'll like to know, why I'm getting "invalid literal for int() with base 10 error" but works pretty well in the interactive mode?
fees = {u'nid':u'179', u'type':u'fees', u'jamb_no': u'01234SS'}
for fee in fees:
# Transaction model
try:
txn = Transaction()
txn.nid = int(fee.get(u'nid'))
txn.type = options.get(u'type')
txn.jamb_no = fee.get(u'jamb_no') # invalid literal for int() with base 10
txn.save()
Models.py
class Transaction(models.Model):
id = models.AutoField(primary_key=True)
type = models.CharField(max_length=50)
nid = models.IntegerField()
jamb_no = models.CharField(max_length=20, blank=False)
Traceback:
Traceback (most recent call last):
File "C:\Python27\lib\site-packages\celery-2.3.2-py2.7.egg\celery\execute\trace.py"
, line 36, in trace
return cls(states.SUCCESS, retval=fun(*args, **kwargs))
File "C:\Python27\lib\site-packages\celery-2.3.2-py2.7.egg\celery\app\task\__init__
.py", line 232, in __call__
return self.run(*args, **kwargs)
File "C:\Python27\lib\site-packages\celery-2.3.2-py2.7.egg\celery\app\__init__.py",
line 172, in run
return fun(*args, **kwargs)
File "C:\Python27\lib\site-packages\django-1.3-py2.7.egg\django\db\transaction.py",
line 217, in inner
res = func(*args, **kwargs)
File "api\tasks.py", line 142, in queue_transaction
ValueError: invalid literal for int() with base 10: '01234SS'
on the interactive prompt, this works pretty well
>>> fees = {u'jamb_no': u'01234SS'}
>>> fees.get(u'jamb_no')
u'01234SS'
>>>
>>> jamb_no = u'01234SS'
>>> str(jamb_no)
'01234SS'
Please help me. I've been on this for 2 days.
A: The problem has to do with celery. When I make changes to tasks.py, celery need to be restarted. This I didn't do, which obviously is causing a repetitive error messages even when the state has changed.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 96 |
Weird coincidences keep happening to me. My buddy, who is a math teacher, says it is all just the mathematical odds playing out.
I'm not always so sure.
Do you think the universe reveals things to us serendipitously, or are the things that happen to us just due to mathematical chance?
I was talking to my buddy as we often do (Not the math teacher buddy, but a different guy). We talk about all things, big and small.
On one particular day, he was telling me about a time when he was younger. He had picked up a pizza. He had carried it home under his arm like you would carry a book. Of course, the toppings all slid off the pizza. He folded it in half and made a panzerotti.
Until now, I had only ever seen a pizza carried this way once in my life. I saw a boy on his bike pick up a Little Caesar's pizza and sling it under his arm. Vertically.
So at this point in the story, I had encountered a pizza being carried vertically or heard a story about it, twice in my entire life (that I can remember).
The very next day after I heard the story, my family and I drove to a microbrewery/restaurant that was about an hour and a half drive from our house. After we paid the bill my wife laughed an pointed out a grown man holding his takeout pizza under his arm vertically.
Okay, math people, what are the odds? The odds I would see this the day after my friend's story? The odds I would even be in this town in the first place? The odds that a grown man wouldn't know how to properly hold a pizza?
I can't believe this was a coincidence, but I also can't imagine why the universe would want me to take notice of something so seemingly insignificant.
It goes way deeper than mathematical odd or chance, it's a rare Earthly event called "the leaning slice of Pizza".
Ha ha. I knew I had heard of it before.
This sort of thing happens to me fairly often. It's not always as striking as your pizza example, though. Sometimes it just seems to be a matter of life organizing itself thematically.
For example, you and I started talking about the nature of reality right around the same time that one of the characters in my current work in progress was wrestling with the question of how to know what is real. In fact, that's an emerging theme of the WIP … but, I swear, it was *already* emerging before our online conversation.
What causes this is an interesting question. I think I could write 1,000 – 2,000 words about it. Would it be OK with you if I did so and linked back to this post?
Yes, please feel free. These happen to me all the time, so I'm going to make it a series.
Awesome. Maybe I can have it up by next week.
Synchronicities. They happen to me all the time. I suppose a room full of mathematicians could come up with odds or even an algorithm. You see John Nash trying to formulate an algorithmic approach to pigeons gathering in A Beautiful Mind.
I could answer you using CT's material but, you probably wouldn't believe me.
Doesn't John Nash turn out to be nuts in the end?
I'd love to hear the CT explanation.
He was schizophrenic but, learned how to distinguish between real & fantasy.
CT's investigations into the human condition via his healing practice & research into the Akashic revealed that there are no accidents or coincidences. Everything in your life is planned out (it's where the predestination thing comes from in some religious texts). Murder isn't random. It's pre-planned between two souls. One soul agrees to 'murder' the other one for the experience for both. And, as this is a free will Universe, said plan to murder can be stopped or re-negotiated. All 'meetings' are planned in advance & can be changed at the last minute.
The only seemingly random things that can happen are when a soul deviates from a life path. The ultimate wake-up call that you aren't doing what you should for yourself is cancer. Cancer can be caused by external factors such as nuclear accidents but, that would be a planned event and a soul's choice for experience or…a group of souls will agree to go thru an accident like that to call attention to all the other souls that, maybe, nuclear power is not such a good thing. Either way, cancer, out of the blue, is the soul's last ditch effort to 'get your attention' and follow your intended path.
Thanks for sharing. It's interesting. Based on what I currently think I know, it doesn't make sense, but that doesn't mean it's wrong. I really need to invest some time in looking at the material.
The explanation that I've heard before is that you're "looking for it". You probably saw 1 person carry it vertically and thought it was strange, but then the next time you saw it, you didn't pay too much attention. Your brain normalized it and didn't store it in its memory. It was nothing special. However, now that you've been talking about carrying a pizza vertically, your brain was on alert.
I considered that, but I think I would've noticed a pizza being carried that way no matter what. It is so unusual. It would be like seeing someone carry an umbrella upside-down.
An umbrella upside-down? What's wrong with that?
Only if it is indoors. | {
"redpajama_set_name": "RedPajamaC4"
} | 416 |
Q: Балансировка ASP.NET MVC приложения. Слетает авторизация, если более одного бекенда Опишу ситуацию.
Имеется ASP.NET MVC приложение, достаточно старое, для авторизации используется form authentication.
Пытаюсь решить проблему деплоя кода на prod окружение. Сейчас при публикации ASP.NET MVC приложения оно становится недоступным от 10 секунд до нескольких минут (не очень понимаю, почему так долго, если честно).
Вопрос не по теме, может быть есть решения для этой проблемы от Microsoft?
Поэтому перед IIS сервером (перед тестовым окружением, для начала) поставил nginx, настроил на нем upstream и указал текущий сервер в качестве бекенда.
Протестировал - все работает.
Далее, развернул еще одно окружение с ASP.NET MVC приложением на другой виртуальной машине и добавил его адрес в upstream.
То есть, dns всегда ведет на nginx, а он уже проксирует запросы то на один, то на другой север обычным round robin. Все заработало корректно, авторизовавшись, на адресе v2.domain.ru, все корректно работает, даже если мы заменяем/включаем/отключаем backend'ы, прописанные в upstream.
Далее, настроил все это в teamcity и заменил домен v2.domain.ru на dev.domain.ru, поскольку это "официальное" тестовое окружение. Естественно, перед этим создал приложения 1.dev и 2.dev для публикации двух экземпляров.
Запускаю deploy - все работает, запросы чередуются, но после авторизации на сайте, начинает грузиться правильная страница, а вот контент в нее загружается уже такой, будто мы не авторизованы.
Тесты показали, что если настроить, что dev.domain.ru всегда ведет на 1.dev.domain.ru - все работает корректно. Если меняем, чтобы запросы шли на 2.dev.domain.ru - авторизация сразу слетает. Аналогично, если наоборот.
Путем изучения логики авторизации понял, что токен .ASPXAUTH в куках - это зашифрованный UserName при помощи ключа, которым является machineKey, который по умолчанию генерируется автоматически для каждого приложения в iis.
Тогда логично, почему слетает аутентификация на dev окружении и не понятно, почему она не слетает до сих пор на v2 окружении.
Сгенерировал machineKey вручную, отключил автогенерацию, добавил его в web.config и переопубликовал 1.dev и 2.dev приложения.
При этом, ничего не изменилось.
Далее, чтобы убедиться, что токен действительно корректный и может работать с обоими приложениями, сделал следующее:
*
*Открыл оба приложения 1.dev.domain.ru и 2.dev.domain.ru и авторизовался в обоих
*Взял куку .ASPXAUTH первого приложения и перезаписал через консоль браузера ее во второе приложение вместе с датой окончания. Авторизация сохранилась и продолжила работать. При этом, если изменить, например, один символ, авторизация, естественно, слетает.
И теперь вопрос - что я делаю не так и почему не работает dev окружение и каким вообще образом работает v2 окружение?
PS: проекты 1.v2 и 1.dev расположены на VM1, а 2.v2 и 2.dev - на VM2. То есть окружения у них идентичные.
В каждом IIS приложении в Bindings прописаны адреса:
*
*X.dev.domain.ru
*dev.domain.ru
где X - 1 или 2 в зависимости от машины.
Конфиг nginx настроен как proxy_pass на upstream и содержит следующие настройки:
location / {
proxy_pass http://dev;
proxy_set_header Host $host;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-For $remote_addr;
proxy_set_header X-Forwarded-Proto $scheme;
proxy_set_header X-Forwarded-Host $host;
}
A: Проблема решена.
У меня в некоторых местах кода была операция WebSecurity.Logout(), если User.UserInRole(..) выполнялся, генерируя исключение.
То есть сам создал себе проблему)
Просто закомментировал строку и все заработало.
Вопрос только в том, почему оно там падает и почему не падало на v2 окружении.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,272 |
import DxfArrayScanner, { IGroup } from '../DxfArrayScanner.js';
import * as helpers from '../ParseHelpers.js';
import IGeometry, { IEntity, IPoint } from './geomtry.js';
export interface ILineEntity extends IEntity{
vertices: IPoint[];
extrusionDirection: IPoint;
}
export default class Line implements IGeometry{
public ForEntityName= 'LINE' as const;
public parseEntity(scanner: DxfArrayScanner, curr: IGroup) {
const entity = { type: curr.value, vertices: [] as IPoint[] } as ILineEntity;
curr = scanner.next();
while(!scanner.isEOF()) {
if(curr.code === 0) break;
switch(curr.code) {
case 10: // X coordinate of point
entity.vertices.unshift(helpers.parsePoint(scanner));
break;
case 11:
entity.vertices.push(helpers.parsePoint(scanner));
break;
case 210:
entity.extrusionDirection = helpers.parsePoint(scanner);
break;
case 100:
break;
default:
helpers.checkCommonEntityProperties(entity, curr, scanner);
break;
}
curr = scanner.next();
}
return entity;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,021 |
\section{Introduction} \label{intro}
The tippe top is a spinning top, consisting of a section of a sphere
fitted with a short, cylindrical rod (\emph{the stem}). One typically sets off the top by making it spin with the stem upwards, which we call, from now on the {\em initial spin} of the top. When the top is spun on a table, it will turn the stem down towards the table. When the stem touches the table, the top overturns and starts
spinning on the stem. The overturning motion as
we shall see is a transition from an unstable (relative) equilibrium
to a stable one. Experimentally, it is known that such a transition only occurs when the spin speed exceeds a certain critical value.
Let us make things more precise and first describe in some detail the model used throughout this paper. The tippe top is assumed to be a spherical rigid body with its center of mass $\epsilon$ off the geometrical center of the sphere with radius $R$. In addition, we assume that this eccentric sphere has a mass distribution which is axially symmetric about the axis through the center of mass $O$ and the geometrical center $\cal C$ of the sphere. The tippe top is subject to a holonomic constraint since we only consider motions of the tippe top on a horizontal plane. An important observation is that the system has an integral of motion, regardless of the model of the friction force that is used. This integral is called the {\em Jellet} $J$ and is proportional to the initial spin $n_0$ (equation~\eqref{Jellet}). For the sake of completeness we mention here that a nonholonomic model (rolling without slipping) for the tippe top is not appropriate, since the equations of motion then allow two more integrals of motion (the energy and the Routh-integral) that prohibit the typical turning motion, cf.\ eg.\ \cite{CBJB,Gray}. We will choose the friction force to be linearly dependent on the slip velocity of the contact point $Q$ of the top and the horizontal plane.
In earlier works \cite{scheck,RW} conditions of stability for asymptotic states of the tippe top were retrieved by the Lyapunov function method starting with the Newton equations of motion. We take a different approach to the problem.
Our goal is to describe the behaviour of the tippe top in terms of Lagrangian variables and thereby classify its asymptotic motions as function of non-dimensional (physical) parameters $A/C$, the \emph{inertia ratio} and $\epsilon/R$, the \emph{eccentricity} of the sphere and of the value the Jellet $J$. As main novelty, we show that by ignoring the translational velocity of the center of mass in the friction law, the Lagrangian formulation of the dynamics of the tippe top allows a restriction to a system on $SO(3)$ which is amenable to Routhian reduction~\cite{pars}. The reduced system allows a rather simple stability analysis of the relative equilibria based on the relationship of the value of the Jellet's integral $J$ and the tumbling angle $\theta$, see below.
Through the Routhian reduction we retrieve a simple stability criterium which leads to the same conclusions as in \cite{scheck,RW}.
The hypothesis of neglecting translational effects is similar to the one made by Bou-Rabee et al.~\cite{Romero}. They motivated it by reasoning that for all possible asymptotic states (the relative equilibria of the system) the velocity of the center of mass is zero \cite{scheck}, and, for this reason, in a neighborhood of these solutions the translational friction can be neglected.
In~\cite{RW} the dynamics of the spherical tippe top with small friction has been studied without such an approximation and a full analysis of the asymptotic long term dynamics of the system is given in terms of the Jellet and the eccentricity of the sphere and inertia ratio. Remarkable is the fact that the stability results obtained by means of the Routhian reduction procedure fully coincides with the results of~\cite{RW}. This justifies a-posteriori the approximation assumption in the friction force and shows that it accurately describes the behavior of the tippe top.
The main result of this paper is summarized in the following theorem, also compare with \cite{CBJB,RW}.
\begin{theorem}\label{mainthm}
In the approximation of negligible translational effects, a spinning eccentric sphere on an horizontal (perfectly hard) surface subject to a sliding friction is reducible with a Routhian reduction procedure~\cite{pars}. The relative equilibria of the reduced system are precisely the steady states of the original system. They are purely rolling solutions and except for the trivial state of rest, they are of three types:
\begin{itemize}
\item[(i)] (non-inverted) vertically spinning top with center of mass straight below the geometric center;
\item[(ii)] (inverted) vertically spinning top with center of mass straight above the geometric center;
\item[(iii)] intermediate spinning top, the top precesses about a vertical while spinning about its axle and rolling over the plane without gliding.
\end{itemize}
The existence and stability type of these relative equilibria only depend on the inertia ratio $\frac{A}{C}$, the eccentricity of the sphere $\frac{\epsilon}{R}$ and the Jellet invariant $J$. In particular, six regimes are identified in terms of the Jellet invariant and only three exhibit the `tipping' behavior.
\end{theorem}
It turns out that the vertical states always exist, and intermediate states may branch off from them. Qualitative bifurcation diagrams corresponding to the possible different regimes are sketched in Fig.~\ref{fig:bifdia}.
\newcommand{.5}{.5}
\begin{figure}[ht]
\centering \includegraphics[scale=.5]{group1a.eps}\hspace{.5cm}
\includegraphics[scale=.5]{group1b.eps}\\
\centering \includegraphics[scale=.5]{group2a.eps}\hspace{.5cm}
\includegraphics[scale=.5]{group2b.eps}\\
\centering \includegraphics[scale=.5]{group2c.eps}\hspace{.5cm}
\includegraphics[scale=.5]{group3.eps}
\caption{\footnotesize Bifurcation diagrams of relative equilibria in function of the Jellet invariant $J$. Solid black branches correspond to stable relative equilibria, while dashed black branches correspond to unstable ones. The vertical states
$\theta=0$ and $\theta=\pi$ always exist, from which intermediate states (with $0<\theta<\pi$) may branch off.}
\label{fig:bifdia}
\end{figure}
The reader is referred to Sec.~\ref{Sec:Stability} -- Sec.~\ref{Sec:stability} for the
details and specification of the parameter ranges. There are three main groups Group I, II and III determined by existence properties of intermediate equilibrium states (similar to the subdivision from~\cite{watanabe}). Tippe tops of Group I may admit intermediate states for $\theta>\theta_c$, where $\theta$ denotes the angle between the vertical and the symmetry axis of the top. Two subgroups are distinguished according to change in stability type of the intermediate states.
Relevant is that for tippe tops belonging to this class the
non-inverted position is always stable, so they never flip however
large the initial spin when launched under an angle $\theta$ close
to $0$.
Tippe tops of Group II may admit intermediate states for all
$\theta$, and they show complete inversion when the initial spin is large enough. Tops of Group III tend to flip over up to a certain angle
$\theta_c<\pi$ when spun rapidly enough. Since stability results are often
in the literature expressed using the `initial' spin $n_0$ of the
tippe top, one can read the $J^2$ in the figures as $n_0^2$. We anticipate to further results by noting that the instability inequalities are independent of the friction coefficient unless it is zero.
\medskip
\noindent
The structure of the paper is as follows. In
Section~\ref{sec:equat} our model is described and the equation of motion are given according to the Lagrangian formalism. After introducing the Jellet integral of motion, the Routhian reduction is performed in Section~\ref{sec:Routhreduction}. The steady states of the system are then calculated and their stability type is determined, yielding a tippe top classification in six groups which is summarized in Section~\ref{classifi}.
\section{Equations of motion}\label{sec:equat}
As is mentioned in the introduction, we consider the \emph{eccentric sphere} model of such a top, see Fig.~\ref{tiptopgeometry}. That is, we consider a sphere with radius $R$ whose mass
distribution is axially symmetric but not spherically symmetric, so
that the center of mass and the geometric center do not coincide.
The line joining the center of mass and the geometrical center is an
axis of inertial symmetry, that is, in the plane perpendicular to
this axis the inertia tensor of the sphere has two equal
principal moments of inertia $A=B$. The inertia moment along the axis of symmetry is denoted by $C$ and the total mass of the sphere is $m$.
The eccentricity $\epsilon$ is the distance between the center of mass $O$ and the geometric center
$\cal C$ of the sphere, with $0<\epsilon<R$. The point $Q$ is the
point of contact with the plane of support.
\begin{figure}[htb]
\begin{center}
\scalebox{.5}{ \psfrag{t_1}{$z$} \psfrag{t_2}{$x$} \psfrag{t_3}{}
\psfrag{t_4}{${\mathsf z}$} \psfrag{t_5}{$\psi$} \psfrag{t_6}{$\varphi$}
\psfrag{t_7}{$\theta$} \psfrag{t_8}{$\mathcal C$} \psfrag{t_9}{$O$}
\psfrag{e}{$\epsilon$} \psfrag{R}{$R$} \psfrag{t_10}{$Q$}
\psfrag{t_11}{$h(\theta)=R-\epsilon \cos(\theta)$} \psfrag{t_12}{$\bf G$} \psfrag{t_13}{$\bf{R}_f$}
\psfrag{t_14}{$\Pi$}
\includegraphics[width=11cm]{ec_ball.eps}}
\caption{\footnotesize Eccentric sphere version of the tippe top. $R$ is the
radius of the sphere, the center of mass $O$ is off center by
$\epsilon$. The top spins on a horizontal table with point of
contact $Q$. The axis of symmetry is $Oz$ and the vertical axis is
$O{\mathsf z}$, they define a plane $\Pi$ (containing $\vec{OQ}$) which
precesses about $O{\mathsf z}$ with angular velocity $\dot \varphi$. The
height of $O$ above the table is $h(\theta)$.
\label{tiptopgeometry}}
\end{center}
\end{figure}
We assume that an inertial (laboratory) frame $M{\mathsf x}{\mathsf y}{\mathsf z}$ is chosen, where $M$ is some point on
the table and the ${\mathsf z}$-axis is the vertical. Let us denote the unit vectors along the axis of the reference frame
$O{\mathsf x},O{\mathsf y},O{\mathsf z}$ fixed to the body by respectively $e_{\mathsf x},e_{\mathsf y},e_{\mathsf z}$. The coordinates of the center of mass are denoted by ${\bf r}_O=({\mathsf x},{\mathsf y},{\mathsf z})_{M{\mathsf x}{\mathsf y}{\mathsf z}}$. A second reference frame is denoted by $Oxyz$, and is defined in such a way that its third axis is precisely the symmetry axis of the top and the $y$-axis is perpendicular to the plane $\Pi$ through the ${\mathsf z}$- and $z$-axes (see Fig.~\ref{tiptopgeometry}). Again we denote the unit vectors along the axis of this reference frame by $e_x,e_y,e_z$\footnote{In~\cite{Romero} the origin of the reference system attached to the body is in
the center of the sphere $\cal C$, and not in the center of mass $O$.}.
Let $(\theta,\varphi,\psi)$ be the Euler angles of the
body with respect to the inertial frame, Fig.~\ref{tiptopgeometry}, chosen in such a way that (i) the vertical plane $\Pi$ is
inclined at $\varphi$ to the fixed vertical plane ${\mathsf x}{\mathsf z}$ and
precesses with angular velocity $\dot \varphi$ around the vertical
$O{\mathsf z}$; (ii) the angle $\theta$ is the angle between the vertical
$O{\mathsf z}$ and the axle $O{\mathsf z}$ of the top; $\dot{\theta}$ causes the nodding
(nutation) of the axle in the vertical plane $\Pi$; and (iii) the angle $\psi$
orients the body with respect to the fixed-body frame, $\dot
\psi$ is the spin about the axle.
As it was pointed out before, the tippe top is constrained to move
on a horizontal plane. This holonomic constraint is expressed by
${\mathsf z}=R-\epsilon\cos\theta=h(\theta)$. We assume throughout the paper that the only forces acting on the sphere are gravity ${\bf G}=-mg e_{\mathsf z}$ and a friction force ${\bf{F}}$ exerted at the point of contact $Q$ of the sphere with the plane. It is now immediate to write down the Lagrangian for the tippe top:
\begin{multline}
L=\mbox{$\frac{1}{2}$} \left(m(\dot {\mathsf x}^2 + \dot {\mathsf y}^2)+ (\epsilon^2m\sin^2\theta+A)\dot
\theta^2 + A\sin^2\theta\dot\varphi^2+ C(\dot\psi
+\dot\varphi\cos\theta)^2\right) \\ - mg(R-\epsilon\cos\theta),
\end{multline}
where $g$ is earth acceleration.
This function is defined on the tangent space of the configuration manifold $M={\rm I\kern-.20em R}^2\times
SO(3)$. In order to obtain the equations of motion, it only remains to define a suitable friction force ${\bf{F}}$. The Lagrangian equations of motion for the tippe top then read:
\begin{equation}\label{thesystem}
\frac{d}{dt}\left(\frac{\partial L}{\partial \dot q^i}
\right)-\frac{\partial L}{\partial q^i}=Q^{F}_i,
\end{equation}where $q^i$ represents one of the coordinates $({\mathsf x},{\mathsf y},\varphi,\theta,\psi)$, and $Q^{F}=Q^{F}_idq^i$ is a one-form on $M$ representing the generalized force moment of the friction force at the point of contact. It is defined by, with ${\bf F}={\bf R}_f+R_n e_{\mathsf z}$ the orthogonal decomposition of ${\bf F}$:
\[
Q^{F}={\bf{R}}_f\cdot e_{\mathsf x} d{\mathsf x} + {\bf{R}}_f\cdot e_{\mathsf y} d{\mathsf y}+ ({\bf{q}}
\times {\bf{R}}_f)\cdot (e_y d\theta + e_{\mathsf z} d\varphi +
e_zd\psi).
\]
\paragraph{Modeling the friction force
One typically models the friction force ${\bf F}={\bf R}_f+R_ne_{\mathsf z}$ to be proportional to the slip velocity of the point of contact ${\bf v}_Q$. We denote by
${{\bf{R}}_n}=R_n {e}_{\mathsf z}$ the normal reaction of the floor at
$Q$, which is of order $mg$, and ${\bf R}_f= F_X {e}_{\mathsf x}+F_Y
{e}_{\mathsf y}$ is the (sliding) friction which opposes the slipping
motion of the body. The fact that the sliding friction opposes the slipping motion is
expressed by ${\bf R}_{f}\cdot {\bf{v}}_Q \leq 0$.
We adopt a viscous friction law~\cite{CBJB,Levi,MofShi,watanabe} and assume that
\begin{equation}\label{viscfric}
{\mathbf R}_f=-\mu R_n {\bf{v}}_Q.
\end{equation}
Here $\mu$ is a coefficient of friction with the dimension of
(velocity)$^{-1}$. It now takes a few tedious computations to arrive to the coordinate expressions for the force moments of the friction force.
The coordinates of the point of contact $\vec{OQ}:={\bf q}$ are $Q =(x_Q,0,z_Q)_{Oxyz}=(R\sin\theta,0,\epsilon-R\cos\theta)_{Oxyz}.$
The velocity of the point of contact $Q$ equals
\begin{equation}
{\mathbf{v}}_Q={{\bf{v}}_O} + {\boldsymbol{\omega}}\times {\mathbf{q}},
\end{equation}
${{\mathbf{v}}_O}=(\dot {\mathsf x},\dot {\mathsf y},h^\prime(\theta)\dot\theta)_{M{\mathsf x}{\mathsf y}{\mathsf z}}$ is the velocity of the
center of mass. A coordinate expression for the angular velocity is given by
\begin{equation} \label{omega}
{\boldsymbol{\omega}}= -\dot{\varphi} \sin(\theta) e_x \; + \; \dot{\theta} e_y \; + \; {n} e_z, \quad \mbox{where} \quad {n}:=\dot{\psi}+\dot{\varphi}\cos(\theta)
\end{equation}
$n$ is the spin (that is, the component of $\boldsymbol{\omega}$ about $Oz$). The generalized force moments now read:
\begin{eqnarray*}
Q_{\mathsf x}&=& -\mu R_n (\dot {\mathsf x}-\sin\varphi\ \dot
\theta(R-\epsilon\cos\theta)+\cos\varphi\sin\theta(R\dot\psi+\epsilon\dot
\varphi))\\ Q_{\mathsf y}&=&-\mu R_n(\dot {\mathsf y}+\cos\varphi\ \dot
\theta(R-\epsilon\cos\theta)+\sin\varphi\sin\theta(R\dot\psi+\epsilon\dot \varphi))\\
Q_\theta&=& -\mu R_n(R-\epsilon\cos\theta)(\cos\varphi\dot {\mathsf y} -\sin\varphi
\dot {\mathsf x}
+(R-\epsilon\cos\theta)\dot\theta)\\
Q_\varphi&=& -\mu R_n\epsilon \sin\theta(\cos\varphi\dot {\mathsf x}+\sin\varphi\dot {\mathsf y}+\sin\theta (\epsilon\dot \varphi+R\dot\psi))\\
Q_\psi&=& -\mu R_n R\sin\theta(\cos\varphi\dot {\mathsf x}+ \sin\varphi \dot
{\mathsf y} +\sin\theta(R\dot \psi +\epsilon\dot\varphi)).
\end{eqnarray*}
For the sake of completeness we write an explicit expression for the normal component of the reaction force $R_n$, which can be determined from Newton's law for the center of mass of the sphere:
\begin{equation}\label{reactie}
R_n(\theta,\varphi,\dot\theta,\dot\varphi,\dot\psi,\dot{\mathsf x},\dot{\mathsf y})=\frac{g+\dot
\theta^2 h^{\prime
\prime}+h^{\prime}\dot\varphi\sin(\theta)(\dot\varphi\cos(\theta)-C
({\dot\psi
+\dot\varphi\cos\theta})/A)}{1/m+h^{\prime}/A[-h\mu(\sin\varphi\dot{\mathsf x}-\cos\varphi\dot{\mathsf y}-\dot\theta
h)+ h^{\prime}]}
\end{equation}
\noindent To conclude this section, we briefly discuss other models for the tippe top. The eccentric sphere model does not accurately model the contact effects of the tippe top stem. However,
it does describe the fundamental phenomenon of the over-turning. For the sake of
completeness we remark that as soon as the top rises to spin on its
stem, it behaves as a `normal' spinning top with rounded peg, we
refer to~\cite[Chapter 6]{book} for a satisfactory introduction
to this topic. Note that our model also does not describe the peculiar `Hycaro'
tippe tops by Prof.\ T.\ Tokieda~\cite{T^2}, which need a non-axisymmetric asymmetric mass distribution. These tippe tops have a
`preferred direction' meaning that the top would flip over only if
spun in the preferred direction with a certain initial spin, and, no
matter what the initial spin is, it would just continue rotating
around the rest position when spun the other way round. We refer to~\cite{Duitsers} for a detailed analysis when elasticity
properties of the horizontal surface and tippe top are taken into account. Their model allows for jumps of the tippe top on the horizontal surface (that we assumed to be rigid). Finally, we mention that we do not debate over the issue of whether transitions sliding-rolling and rolling-sliding occur in the motion of an eccentric sphere on a flat surface. We chose to concentrate on the sliding model only, because we were interested in capturing the `overturning' phenomenon which cannot occur under the non-holonomic constraint of pure rolling. We refer the interested reader to \cite{CBJB,Gray,Levi} for a discussion of the topic and to \cite{cush,mamaev,Tor} for an analysis of the motion of the rolling eccentric sphere also called the Routh's sphere.
\subsection{Constants of motion: the Jellet invariant }
It was first shown by Jellet~\cite{Jellet} by an approximate argument, and later proved by Routh~\cite{routh} that the system, even if dissipative, has a conserved quantity:
\begin{equation}\label{Jellet}
J=-{\bf{L}}\cdot {\bf{q}}= {\rm const},
\end{equation}
where ${\bf L}$ is the angular momentum of the tippe top about the center of mass. We prove this by using Euler equations which govern the evolution of the angular momentum $\dot{{\bf {L}}}={\bf{q}}\times {\bf{F}}.$
The total time derivative of $J$ then becomes:
\begin{align*}
\dot J&=-\dot{\mathbf L}\cdot {\bf q} -{\mathbf L}\cdot \dot {\mathbf q}\\
&=0-\left(A{\boldsymbol{\omega}}-(A-C)({\boldsymbol{\omega}}\cdot e_z)e_z\right)\cdot (\epsilon {\boldsymbol{\omega}}\times e_z)=0\ .
\end{align*}
Straightforward calculations show that Jellet's constant can be written as
\begin{equation}
J=C{n}(R \cos(\theta)-\epsilon)+A \dot{\varphi} R
\sin^2(\theta)\ .\label{jello}
\end{equation}
We emphasize once more that the Jellet's constant is an
exact constant of motion for the tippe top whether or not there is
slipping and independent of the expression for $\bf F$. As we will explain later, it is this constant that to some
extent controls the motion of the spinning top. Indeed, it allows a
Routhian reduction procedure (see Sec.~\ref{sec:Routhreduction}),
resulting in relatively simple reduced equations from which we are
able to recover in full detail the stability properties of the
steady states. In the specific case that $\theta=0$, the Jellet is proportional to $n_0=n|_{\theta=0}$, the spin about the $z$-axis. Since one typically sets off the tippe top at an angle $\theta\approx 0$, one can say that the Jellet is proportional to the initial spin $n_0$. Note that the spin at $\theta=\pi$ has an opposite sign to the initial spin $n_0$, meaning that, relative to a body fixed frame, the spin is reversed when the tippe top fulfills a complete inversion.
\medskip
\noindent There is a rotational symmetry for
which the Jellet is the associated first integral. The action of
$S^1$ on ${\rm I\kern-.20em R}^2\times SO(3)$ can be defined as a simultaneous
rotation about $\hat e_3$ over the angle $R\xi$ and about $\hat k$
over the angle $-\epsilon \xi$, where $\xi \in S^1$ (see also~\cite{Romero}). Noether's theorem is applicable in this situation
since the work of the friction force at the point of contact
vanishes under this action.
\medskip
\noindent Note that the total energy of the spinning top is $E=T+V$ is in
general not conserved. Here $T$ is the kinetic energy
with its rotational and translational part, $V=m gh(\theta)$ is the
potential energy. The orbital derivative of $E$ is
\begin{equation}\label{derE}
\frac{d}{dt}E={\bf v}_Q\cdot {\bf R}_{f} \leq 0,
\end{equation}
which is negative semi-definite and vanishes if and only if
${\bf v}_Q$ vanishes. Observe that $E(t)$ decreases monotonically
and hence is a suitable Lyapunov function\footnote{$E(t)$ is
analytical, therefore it is either strictly monotone or a constant.
The energy $E$ is constant only if ${\bf v}_Q=0$. Note that $E$
being Lyapunov~\cite{scheck} implies that the limiting solutions for $t\rightarrow
\infty$ are solutions of constant energy.}, see~\cite{scheck}. From (\ref{derE}) it
follows that dissipation is due to friction.
\subsection{Routhian reduction}\label{sec:Routhreduction}
\newcommand{et al.}{et al.}
It turns out that, if we consider an approximation of the
friction law, the resulting generalized force moments assume a form
that allows us to apply a Routhian reduction procedure, see~\cite{pars} and appendix~\ref{app:routh}. In turn,
using the reduced equations we are able to study in full detail the
stability properties of the tippe top which confirm the results
obtained in~\cite{RW}, and also
recover those of~\cite{Romero,watanabe}.
We now ignore
translational effects in the friction force, i.e. we assume
that all terms in $Q_{\theta}, Q_{\varphi}, Q_{\psi}$ containing
$\dot {\mathsf x}$ and $\dot {\mathsf y}$ are neglected. Typically this approximation is
justified by noting that for all steady states the velocity of the
center of mass is zero, and that in a neighborhood of the steady
states it can be neglected. In our situation, it allows to restrict
ourselves to a system on $SO(3)$ which is reducible using Routh's
procedure. It is easily seen that within this
approximation, if we study the Lagrangian system on $SO(3)$
determined by
\begin{eqnarray*}
L'&=&\mbox{$\frac{1}{2}$} \left( (\epsilon^2m\sin^2\theta+A)\dot \theta^2 +
A\sin^2\theta\dot\varphi^2+ C(\dot\psi
+\dot\varphi\cos\theta)^2\right) \\ && \qquad \quad
-mg(R-\epsilon\cos\theta),\\
Q'&=& -\mu R'_n(R-\epsilon\cos\theta)^2\dot\theta d\theta
-\mu R'_n\epsilon \sin^2\theta(\epsilon\dot \varphi+R\dot\psi)d\varphi\\ &&\qquad \quad
-\mu R'_n R\sin^2\theta(R\dot \psi +\epsilon\dot\varphi)d\psi,
\end{eqnarray*}
with $R'_n(\theta,\dot \theta,\dot\varphi,\dot\psi) =
R_n(\theta,\varphi,\dot \theta,\dot\varphi,\dot\psi,\dot{\mathsf x}=0,\dot{\mathsf y}=0)$, then we essentially study the entire approximated system. Indeed, any
solution $(\varphi(t),\theta(t),\psi(t))$ to this Lagrangian system
will determine the remaining unknowns $({\mathsf x}(t),{\mathsf y}(t))$ as solutions
to the following system of time-dependent second order differential
equations:
\begin{equation}
m\ddot {\mathsf x} = Q_{\mathsf x}(\dot{\mathsf x},\theta(t),\varphi(t),\psi(t)), \quad m\ddot
{\mathsf y} = Q_{\mathsf y}(\dot{\mathsf y},\theta(t),\varphi(t),\psi(t)).
\end{equation}
Our next step in the reduction procedure is to consider the Lagrangian system $L'$ on $SO(3)$ with generalized
force form $Q'$ and perform a simple coordinate transformation,
determined by
\[
(\theta,\varphi,\psi)\mapsto(\theta,\ovl\varphi=\epsilon\varphi
+R\psi,c=R\varphi-\epsilon\psi).
\]
The Lagrangian $L'$ and the force $Q'$ then become
\begin{align*}
L'&=\textstyle\mbox{$\frac{1}{2}$} \bigg( (\epsilon^2m\sin^2\theta+A)\dot \theta^2 +
\frac{A\sin^2\theta}{(\epsilon^2+R^2)^2}(\epsilon\dot{\ovl \varphi}+R\dot c)^2+\\
& \qquad \textstyle \frac{C}{(\epsilon^2+R^2)^2}\big((R+\epsilon\cos\theta)\dot{\ovl\varphi} +
(R\cos\theta-\epsilon)\dot c\big)^2\bigg)- mg(R-\epsilon\cos\theta)\\
Q'&=
\textstyle -\mu R'_n\big((R-\epsilon\cos\theta)^2\dot\theta d\theta
+\sin^2\theta\dot{\ovl\varphi} d\ovl\varphi\big),\\
\end{align*}
where it is understood that $R'_n$ is a function of
$\theta,\dot\theta,\dot{\ovl\varphi}$ and $\dot c$. The main reason
for writing $L'$ and $Q'$ in this form is the fact that $c$ is a
cyclic coordinate and that $Q'_c=0$. Indeed, recall that Jellet
integral was associated to the symmetry determined by the vector
field $R\partial_\varphi -\epsilon\partial_\psi$, or in the above
introduced coordinate system by the vector field $\partial_c$. In
particular, we have made the symmetry generator into a coordinate
vector field, and this ensures that we can apply the Routhian
reduction procedure~(\cite{pars} and appendix~\ref{app:routh}), provided the coefficients of $Q'$
do not depend on $c$. This is the case since we neglected the terms
in the velocity of the center of mass. The conserved quantity
associated with the cyclic coordinate is precisely the Jellet
integral:
\begin{align*}
\fpd{L'}{\dot c} &=\textstyle \frac{R A\sin^2\theta}{(\epsilon^2+R^2)^2}(\epsilon\dot{\ovl
\varphi}+R\dot c)+
\frac{C(R\cos\theta-\epsilon)}{(\epsilon^2+R^2)^2}\big((R+\epsilon\cos\theta)\dot{\ovl\varphi}
+ (R\cos\theta-\epsilon)\dot c\big) \\ & \textstyle = J/(\epsilon^2+R^2).
\end{align*}
The latter equality implies that
\begin{eqnarray}
\dot c &=& \frac{J(\epsilon^2+R^2)-(RA\epsilon\sin^2\theta
+C(R\cos\theta-\epsilon)(R+\epsilon\cos\theta))\dot{\ovl\varphi}}{R^2
A\sin^2\theta + C(R\cos\theta-\epsilon)^2}\label{routh1}
\end{eqnarray}
The Routhian reduction procedure defines a Lagrangian system
$${\cal R} = L'-J\dot c/(\epsilon^2+R^2)$$ with two degrees of freedom
$(\theta,\ovl\varphi)$ (here every instance of $\dot c$ in ${\cal
R}$ is replaced using~\eqref{routh1}). The reduced equations of
motion are then given by
\begin{eqnarray}
\label{reducedeqs} \frac{d}{dt}\left(\fpd{{\cal R}}{\dot
\theta}\right)-\fpd{{\cal R}}{\theta} &=& Q'_\theta =-\mu
R'_n(R-\epsilon\cos\theta)^2\dot\theta \\
\label{reducedeqs2} \frac{d}{dt}\left(\fpd{{\cal
R}}{\dot{\ovl\varphi}}\right)-\fpd{{\cal R}}{\ovl\varphi} &=&
Q'_{\ovl\varphi} =-\mu R'_n\sin^2\theta\dot{\ovl\varphi},
\end{eqnarray}
where it is understood that~\eqref{routh1} is used to eliminate
$\dot c$ in $R'_n$. It takes rather tedious but straightforward
computations to show that $\cal R$ can be written as
$${\cal R} = T_2 + T_1 - W,$$
where
\begin{eqnarray*}
T_2 &=&\textstyle T_{\theta\theta}(\theta) \dot\theta^2 +
T_{\ovl\varphi\ovl\varphi}(\theta) \dot{\ovl\varphi}^2\\ &=&
\frac12(\epsilon^2m\sin^2\theta +A)\dot\theta^2 + \frac12\frac{AC
\sin^2\theta }{(R^2 A\sin^2\theta +
C(R\cos\theta-\epsilon)^2)}\dot{\ovl\varphi}^2, \\
T_1&=&\textstyle \frac{J}{(R^2+\epsilon^2)}\frac{( R\epsilon
A\sin^2\theta+C(R+\epsilon\cos\theta)(R\cos\theta-\epsilon))}{R^2
A\sin^2\theta + C(R\cos\theta-\epsilon)^2}\dot{\ovl\varphi},\\
W&=&\textstyle \frac12\frac{J^2}{R^2 A\sin^2\theta +
C(R\cos\theta-\epsilon)^2}-mg\epsilon\cos\theta .
\end{eqnarray*}
The function $W$ is also called the effective potential.
\begin{remark}
The above defined Routhian function $\cal R$ is not globally defined
on the sphere. In order to provide a globally defined system of
differential equations for the reduced system, we need to extract
the term $T_1$ from the Routhian and consider it as a gyroscopic
force (see e.g.\ \cite{marsdenrouth}).
\end{remark}
\begin{remark}
Observe that the effective potential $W$, obtained through reduction, coincides with the effective energy on a Jellet's level surface as it has been used in \cite{RW}, Sec.~3.
\end{remark}
\medskip
\noindent Note that $\mathcal R$ and $Q'$ are independent of
$\ovl\varphi$. This residual symmetry does not lead to a conserved
quantity (the friction does not vanish for
$\partial_{\ovl\varphi}$). This symmetry is due to the approximation
we carried out in the previous section; it is not present in the
original system $(L,Q)$ or~\eqref{thesystem}. It leads however to a
zero eigenvalue of the linearized system at equilibrium points, see
Section~\ref{Sec:stability}.
\section{Steady states }\label{Sec:Stability}
The equilibria of the reduced Routhian system \eqref{reducedeqs} and \eqref{reducedeqs2} are determined by
\begin{equation}
\dot \theta=0, \dot{\ovl\varphi}=0 \quad \rm{and} \quad
\partial W/\partial \theta =0, \label{crit_amendedpot}
\end{equation}
i.e. they are the critical points of the effective potential (note that if $\dot \theta=\dot{\ovl\varphi}=0$ the components of the force vanish).
Equation (\ref{crit_amendedpot}) is satisfied if (i) $\sin\theta =0 $ or, if (ii)
\begin{multline}\label{define_intstates}
f(J^2,\cos\theta) =\textstyle
\frac{J^2}{mgCR^2\epsilon}\left(\left(\frac{A}{C}-1\right)\cos\theta+\frac{\epsilon}{R}\right)-
\left(\frac{A}{C}\sin^2\theta +
\left(\cos\theta-\frac{\epsilon}{R}\right)^2\right)^2= 0.
\end{multline}
Solutions to (i) are $\theta=0,\pi$ and give the vertical spinning states. Solutions to (ii) only occur if
\begin{equation}\label{Exist}
\left( \frac{A}{C}-1\right)\cos(\theta)+\frac{\epsilon}{R}>0.
\end{equation}
If this condition is satisfied, solutions to (ii) are the so-called intermediate states. The existence condition only depends on $A/C$ and $\epsilon/R$, and will determine in our classification the three main groups I, II and III, as it was proposed in~\cite{watanabe}. The values for $\theta$ for which (ii) is satisfied will depend on the Jellet, $A/C$ and $\epsilon/R$.
The vertical spinning states correspond to the periodic motion of the tippe top spinning about its axle (which is in vertical position) either in the non-inverted position ($\theta=0$) or inverted position ($\theta=\pi$).
The intermediate states correspond to those relative equilibria in which the tippe top shows in general quasi-periodic motion precessing about a vertical while spinning about its inclined axle rolling over the plane without gliding
(observe that the intermediate states correspond to the tumbling solution of~\cite{scheck}).
\medskip
The condition (\ref{Exist}) for existence of intermediate states leads to a first classification of tippe tops into three groups.\\
- Group I $[(A/C-1)<-\epsilon/R]$: the tippe tops belonging to this group do not admit
intermediate states in an interval of the form $[0,\theta_c[$, where $\theta_c$ is determined by $(A/C-1)\cos\theta_c
+\epsilon/R =0$.\\
- Group II $[-\epsilon/R<(A/C-1)<\epsilon/R]$: intermediate states may exist for all $\theta\in ]0,\pi[$.\\
- Group III $[(A/C-1)>\epsilon/R]$: tippe tops belonging to this group do not admit intermediate
state in an interval of the form $]\theta_c,\pi[$, where
$\cos\theta_c= (\epsilon/R)/(1-A/C)$.
\medskip \noindent
In the following section we refine this first classification taking into account the stability type of the steady states and their bifurcations, explaining and giving the details of the $J^2$ versus $\theta$ diagrams in Fig.~\ref{fig:bifdia} from the introduction.
We anticipate that the subdivision in subgroups according to a change in stability type of the intermediate states is based on the simple observation that they lie on a curve $f(J^2,\cos\theta) =0$ in the $(J^2,\theta)$-plane, and, denoting by $\partial_2f$ the partial derivative to the second
argument of $f$, a bifurcation point for intermediate states is characterized as the point where
\begin{eqnarray*}
f(J^2,\cos\theta)&=&0,\\
\partial_2 f(J^2,\cos\theta)&=& 0.
\end{eqnarray*}
Note that the relation $\partial_2 f(J^2,\cos\theta)= 0$ is essentially the same basic relation (4.27) in \cite{RW}, however its derivation is different. As a consequence we expect the stability results for intermediate states to confirm earlier known facts.
\section{Stability analysis via the reduced equations}\label{Sec:stability}
Determining the (linear) stability of the steady states as given above is an extremely simple task in the reduced setting. Indeed,
let $(\theta_0,\ovl\varphi_0)$ be an equilibrium. The linearized
equations of motion at this relative equilibrium read as
\begin{eqnarray*}
T_{\theta\theta}(\theta_0)\ddot\theta &=& \fpdt{T_1}{\dot{\ovl\varphi}}{\theta}(\theta_0)\dot{\ovl\varphi}
-\fpd{^2W}{\theta^2}(\theta_0)(\theta-\theta_0)
-\mu mg(R-\epsilon\cos\theta_0)^2\dot\theta\\
T_{\ovl\varphi\ovl\varphi}(\theta_0)\ddot{\ovl\varphi} &=&
-\fpdt{T_1}{\dot{\ovl\varphi}}{\theta}(\theta_0)\dot\theta -\mu mg
\sin^2\theta_0\dot{\ovl\varphi},
\end{eqnarray*}
where we used that $R'_n$ equals $mg$~\eqref{reactie} at the relative
equilibria. It is not hard to show that the
characteristic polynomial of this system is
\begin{eqnarray*} &&p(\lambda)= \lambda\Bigg[\lambda^3 +\mu mg\left(\frac{(R-\epsilon\cos\theta_0)^2}{T_{\theta\theta}(\theta_0)}+ \frac{\sin^2\theta_0}{T_{\ovl\varphi\ovl\varphi}(\theta_0)}\right)\lambda^2 \\ && + \left(\frac{\big(\mu mg(R-\epsilon\cos\theta_0)\sin\theta_0\big)^2 + \left(\fpdt{T_1}{\dot{\ovl\varphi}}{\theta}(\theta_0)\right)^2}{T_{\theta\theta}(\theta_0)T_{\ovl\varphi\ovl\varphi}(\theta_0)} + \frac{\fpd{^2W}{\theta^2}(\theta_0)}{T_{\theta\theta}(\theta_0)}\right)\lambda
\\ && +\frac{\big(\mu mg \sin^2\theta_0\big) \fpd{^2W}{\theta^2}(\theta_0)}{T_{\theta\theta}(\theta_0)T_{\ovl\varphi\ovl\varphi}(\theta_0)} \Bigg].\end{eqnarray*} Due to the translational
symmetry in $\ovl\varphi$, one eigenvalue is zero. In Appendix~\ref{app:roots} we show that all remaining eigenvalues have a negative real part, if and
only if $\partial^2W/\partial \theta^2 (\theta_0)
>0$, or if
\begin{multline}\label{stabilityba}
\textstyle mg\epsilon\cos\theta_0 > \textstyle \frac{J^2 R^2 C}{(R^2 A\sin^2\theta_0
+ C(R\cos\theta_0-\epsilon)^2)^2}\textstyle\bigg(-(A/C-1)\sin^2\theta_0\\
\textstyle + \frac{\mathcal{B}}{C}\cos\theta_0
-4\frac{\mathcal{B}^2}{C^2}\frac{\sin^2\theta_0}{(A/C)\sin^2\theta_0
+ (\cos\theta_0-\epsilon/R)^2}\bigg),
\end{multline}
with $\mathcal{B}$ given by
$\mathcal{B}:=(A-C)\cos(\theta_0)+C\frac{\epsilon}{R}.$
We will further manipulate
this equation to retrieve the stability results, compare also with~\cite{watanabe}. We will retrieve six groups depending on how the inertia ratio $A/C$ relates to the eccentricity $\epsilon/R$. Since in the literature results have been expressed in terms of the spin of an initial condition at a vertical state, we introduce $n_0:=\frac{J}{C(R-\epsilon)}$, which is the value of the spin $n$ at $\theta=0$ for a given Jellet $J$. Similarly, $n_{\pi}:=-\frac{J}{C(R+\epsilon)}$ is the spin of the solution with Jellet J at $\theta= \pi$. Note that for a fixed $J$ these spins are related by $n_0=-n_{\pi}\frac{R+\epsilon}{R-\epsilon}$.
\paragraph{Vertical spinning state: $\theta=0$.}
For the vertical
spinning state $\theta=0$, the relation
\eqref{stabilityba} yields
\begin{equation}\label{cond_n1}
n^2_0\left[\frac{A}{C}-(1-\frac{\epsilon}{R})\right]<
{\frac{mg\epsilon}{C}}\left(1-\frac{\epsilon}{R}\right)^2.
\end{equation}
It follows that in Group I, the vertical state
$\theta=0$ is always stable, while for Group II and Group III stability requires that
\begin{equation}\label{n1}
|n_0|<\textstyle n_1:=\sqrt{\frac{mg\epsilon}{C\left[\frac{A}{C}-(1-\frac{\epsilon}{R})\right]}}\left(1-\frac{\epsilon}{R}\right).
\end{equation}
\paragraph{Vertical spinning state: $\theta=\pi$.}
For the vertical
spinning state $\theta=\pi$, the relation
\eqref{stabilityba} yields
\begin{equation}\label{stabpi_muniet0}
n^2_\pi\left[(1+\frac{\epsilon}{R})-\frac{A}{C}\right]>{\frac{mg\epsilon}{C}}\left(1+\frac{\epsilon}{R}\right)^2.
\end{equation}
This condition is never satisfied for Group III, so $\theta=\pi$ is unstable; in the case of Group I and II, when $\frac{A}{C}< (1+\frac{\epsilon}{R})$, stability requires
\begin{equation}\label{n2}
|n_\pi|>\textstyle n_2=:\sqrt{{\frac{mg\epsilon}{C\left[(1+\frac{\epsilon}{R})-\frac{A}{C}\right]}}}\left(1+\frac{\epsilon}{R}\right)
.
\end{equation}
Note that for tippe tops of Group I and II $n_2^2\geq n_*^2$, with $n_*:=2 \frac{\sqrt{Amg\epsilon}}{C}$. The equality holds when
$\frac{A}{C}=\frac{1}{2}\left(1+\frac{\epsilon}{R}\right).$
\paragraph{Intermediate states.}
Recall that intermediate states are determined by
(\ref{define_intstates}): $f(J^2,\cos\theta_0)=0$. Using this
condition, the requirement~\eqref{stabilityba} becomes
$0<g(\cos\theta_0)$
where we set
\begin{equation}\label{eq:defg}
g(\cos\theta_0):=\textstyle \left(\frac{A}{C}-1\right)+\frac{4\left[(\frac{A}{C}-1)\cos\theta+\frac{\epsilon}{R}\right]^2}
{\frac{A}{C}\sin^2\theta+(\cos\theta-\frac{\epsilon}{R})^2}.
\end{equation}
We now prove that $g(\cos\theta_0)$ is strictly increasing and
changes sign at a bifurcation point for intermediate states. As we already mentioned, a bifurcation point along the curve in the
$(J^2,\cos\theta)$-plane of intermediate states is determined by the conditions
\begin{eqnarray*}
f(J^2,\cos\theta)=&& 0,\\
\partial_2 f(J^2,\cos\theta)=&& \textstyle \frac{J^2}{mg\epsilon R^2C}(\frac{A}{C}-1) + \\
&& \textstyle
4((\frac{A}{C}-1)\cos\theta+\frac{\epsilon}{R})(\frac{A}{C}(1-\cos^2\theta)
+(\cos\theta-\frac{\epsilon}{R})^2)= 0.
\end{eqnarray*}
An elementary substitution of the first equation into the second
shows that the function $\partial_2 f(J^2,\cos\theta)$ along the
intermediate states can also be written as \[\partial_2
f(J^2,\cos\theta)=g(\cos\theta)\frac{J^2}{mg\epsilon R^2 C}.\] Hence, bifurcation
points are given by those $\theta$ such that
$g(\cos\theta_0)=0.$
Solving for $\cos\theta$ gives the two solutions:
\begin{equation}\label{eqbif}
\frac{\epsilon/R}{1-A/C} \pm \frac{1}{1-A/C} \frac{\sqrt3}{3}\sqrt{A/C}
\sqrt{1-A/C-(\epsilon/R)^2}.
\end{equation}
Note that $1-A/C-(\epsilon/R)^2>0$ only for tippe tops in Groups I and II.
Moreover, the solution $\cos\theta_b = \frac{\epsilon/R}{1-A/C}+\ldots$
leads to a contradiction since, for tippe tops of Group I, it is
incident with the interval $]0,\theta_c[$ where no intermediate
states exist and for tippe tops in Group II satisfying
$1-A/C-(\epsilon/R)^2>0$, the number $\frac{\epsilon/R}{1-A/C}$ is greater than
$1$, implying that the $+$ solution of \eqref{eqbif} can not equal a
cosine. We denote the $-$ solution by $x_b$, i.e.
$$x_b : =\textstyle
\frac{\epsilon/R}{1-A/C} -\frac{1}{1-A/C} \frac{\sqrt3}{3}\sqrt{A/C}
\sqrt{1-A/C-(\epsilon/R)^2}.$$ We conclude that a bifurcation point for
intermediate states exists if $1-A/C-(\epsilon/R)^2>0$ and
$\left|x_b\right|<1$.
Before studying in further detail these two conditions, we first
show that the function $g(\cos\theta)$ is strictly increasing for
increasing $\theta$. This result implies that, if a bifurcation
exists (i.e. a point $\theta$ with $g(\cos\theta)=0$) then stability
will change. On the other hand, if no bifurcation occurs, the entire
branch of intermediate states is either stable or unstable.
Let us assume that $x=\cos\theta$. If we consider $\partial_2
f(J^2,x)$ as a function on the submanifold $f(J^2,x)=0$ and if we
compute its derivative w.r.t $x$, i.e. $\partial_{2,2}f
-(\partial_{1,2} f)(\partial_2 f/\partial_1 f)$, then after some
tedious computations we may conclude that the sign of this
derivative is opposite to the sign of
\[\textstyle
8((A/C-1)x+\epsilon/R)^2+(A/C-1)^2\frac{(A/C(1-x^2)+(x-\epsilon/R)^2)^2}{((A/C-1)x+\epsilon/R)^2}>0
\]
Hence, if there is a bifurcation at a certain $x=\cos(\theta_b)$ in
the set of intermediate states, then we know that the intermediate
states for which $\theta>\theta_b$ are stable, while the other
branch is unstable.
It now remains to study the conditions for the bifurcation point to
exist. The first condition says that $1-A/C-(\epsilon/R)^2>0$, implying
that we only have to consider Groups I and II. We start with Group
I.
\paragraph{Group I} From $(A/C-1) < -\epsilon/R$, it follows that $1-A/C-(\epsilon/R)^2>0$ and $x_b< 1$. We have to distinguish between two subgroups: $x_b < -1$ (Group Ia) and $x_b>-1$ (Group Ib). From the previous paragraph it should be clear that if $x_b<-1$ then the
value of the function $g(x)$ on the intermediate states $-1<x<1$ is
negative, i.e. the entire branch is unstable.
\paragraph{Group II} We define three subgroups:
Group IIa is the group for which $1-A/C-(\epsilon/R)^2>0$ and $|x_b|<1$, Group IIc is defined by $1-A/C-(\epsilon/R)^2>0$ and $x_b< -1$ and thirdly Group IIb as the group containing the remaining tippe tops in II. Again from the previous, we
immediately conclude that the entire branch of intermediate states
is unstable in Group IIc. Group IIb can alternatively be
defined as the group containing all tippe tops for which the branch
of intermediate state is entirely stable. To show this, we first remark that the remaining tippe tops in II are characterized by $1-A/C-(\epsilon/R)^2>0$ and $x_b>1$ or $1-A/C-(\epsilon/R)^2\le 0$. If $1-A/C-(\epsilon/R)^2>0$ and $x_b> 1$ then the intermediate branch is entirely stable. If $1-A/C-(\epsilon/R)^2=0$ then $x_b>1$ and the intermediate branch is stable. The remaining tippe tops we have to consider are characterized by the condition $1-A/C-(\epsilon/R)^2< 0$. To show that $g(x)>0$, we consider two subcases: (i) if $1-A/C<0$ then from~\eqref{eq:defg} it is clear that $g(x) >0$, (ii) if $(\epsilon/R)^2>1-A/C>0$ then it suffices to compute $g(0)$ ($g(x)$ will not change sign since there is no bifurcation point $x_b$): from $1-A/C-(\epsilon/R)^2<0$,
$A/C<1$ and $(\epsilon/R)^2<1$ we find
\[\textstyle
g(0)= (A/C-1) + 4\frac{(\epsilon/R)^2} {A/C+(\epsilon/R)^2}>
(\epsilon/R)^2
>0.
\] The above argument also proves
stability for intermediate states in Group III.
\medskip
Note that tippe tops in Group II are real `tippe tops' since they
admit tipping from a position near $\theta=0$ to the inverted
state near $\theta=\pi$. Tipping never occur for tops of Group III, though they may rise up to a (stable) intermediate state. Tippe tops of group I never flip over since the position $\theta=0$ is always stable.
\subsection{Tippe Top Classification}\label{classifi}
The following schematic classification summarizes the previous analysis, and presented in Fig.~\ref{fig:bifdia}. Compare also with Fig.~3 in \cite{RW}.
\medskip \noindent
\textbf{Group I:} $A/C-1<-\epsilon/R$ \\
- The non-inverted vertical position
$\theta=0$ is stable for any value of $J$.
\\
- The inverted
vertical position $\theta=\pi$ is stable for $|n_\pi|>n_2$, unstable otherwise, with $n_2$ given by (\ref{n2}).\\
- Intermediate states do not exist for all values of $\theta$, but only for
$\theta>\theta_c=\arccos((\frac{\epsilon}{R})/(1-\frac{A}{C}))$. \\
{\bf Group Ia}: $\textstyle\frac{\epsilon/R}{1-A/C} -\frac{1}{1-A/C} \frac{\sqrt3}{3}\sqrt{A/C}
\sqrt{1-A/C-(\epsilon/R)^2} <-1 \ .$ \\
\indent The entire branch of intermediate states
is unstable.
\\ {\bf Group Ib}: if $\textstyle -1<\frac{\epsilon/R}{1-A/C} - \frac{1}{1-A/C} \frac{\sqrt3}{3}\sqrt{A/C}
\sqrt{1-A/C-(\epsilon/R)^2}:=\cos\theta_b\ .$ \\
\indent There is a bifurcation: intermediate state are stable if $\theta>\theta_b$ and unstable if $\theta<\theta_b$.
\medskip \noindent
\textbf{Group II:} $-\epsilon/R<(A/C-1)<\epsilon/R$.\\
- If $|n_0| > n_1$ the equilibria $\theta=0$ become unstable,
with $n_1$ as in (\ref{n1}).\\
- If $|n_\pi| > n_2$ the equilibria $\theta=\pi$ become
stable.\\
- There are intermediate states for any $\theta$.
We distinguish the following three subgroups. \\
{\bf Group IIa}: $(A/C-1)<-(\epsilon/R)^2$ and
\[\textstyle\left|\frac{\epsilon/R}{1-A/C} -\frac{1}{1-A/C} \frac{\sqrt3}{3}\sqrt{A/C}
\sqrt{1-A/C-(\epsilon/R)^2}\right|<1\ .\]
\indent There is a bifurcation of intermediate
states. \\
{\bf Group IIb}: either $(A/C-1)\ge-(\epsilon/R)^2$ or
\[\textstyle \frac{\epsilon/R}{1-A/C} -\frac{1}{1-A/C} \frac{\sqrt3}{3}\sqrt{A/C}
\sqrt{1-A/C-(\epsilon/R)^2} >1 \ .\]
\indent The branch of intermediate states is
entirely stable.\\
{\bf Group IIc}: $(A/C-1)<-(\epsilon/R)^2$ and
\[\textstyle \frac{\epsilon/R}{1-A/C} -\frac{1}{1-A/C} \frac{\sqrt3}{3}\sqrt{A/C}
\sqrt{1-A/C-(\epsilon/R)^2}<-1 \ .\]
\indent The branch of intermediate states is entirely unstable.
\medskip \noindent
\textbf{Group III:} $(A/C-1)>\epsilon/R$.\\
- The equilibria with $\theta=0$ become unstable for $|n_0|>n_1$.\\
- The equilibria with $\theta=\pi$ are always unstable.\\
- For these tippe tops intermediate states do not exist for
$\theta\in ]\theta_c,\pi[$. Bifurcations in intermediate states do
not occur and the intermediate states are stable.
\medskip
\noindent
Tippe tops in Group II exhibit `tipping' behavior: if the initial spin satisfies $|n_0| > \max(n_1,n_2\frac{R+\epsilon}{R -\epsilon})$\footnote{About the relation between $n_1$ and
$n_2$: in Group IIb $n_2^2/n_1^2>1$ holds and in Group IIc $n_2^2/n_1^2<1$.}, then tipping is possible from $\theta=0$ to
$\theta=\pi$.
\section{Remarks and Conclusions}
We would like to remark that the results on the linear stability for the tippe top presented here are equivalent to the stability properties for the model of the tippe top without the assumption that the translational friction terms can be neglected. In fact, the function $g(\cos\theta)$ which fully determines the stability of the intermediate states can be retrieved in the expressions for the eigenvalues of the linearized equations of motion about the relative equilibria of the full system. It is also remarkable that the presented stability analysis does {\em not} depend on the friction coefficient $\mu$, which suggests that the above stability analysis is valid for a rather large class of possible dissipative friction forces at the point of contact as was pointed out in~\cite{RW}. Up until now, a {\em linear stability} analysis for the intermediate states was not available upon our knowledge in the literature.
Most recently Ueda et al.~\cite{watanabe} analyzed the motion of the
tippe top under the gyroscopic balance condition ({\sc{gbc}}) and
approached the stability problem by perturbing the system around a
steady state and obtained under linear approximation a first order
{\sc{ode}} for the perturbation of the variable $\theta$. They
derive stability criteria in terms of the initial spin $n$ given at
the non-inverted position $\theta=0$. Possible intermediate states
for tippe tops of Group I were not considered. Our approach is based on a complete different technique, namely Routhian reduction and we obtain a more refined and exhaustive classification of tippe tops in six groups (instead of three). Moreover,
our analysis does not exclude the possibility of launching the top
with its stem down (i.e. $\theta$ near $\pi$).
\medskip
\section*{Acknowledgments}
The results presented here were obtained while the first author had financial support by the European Community's 6th Framework Programme, Marie Curie Intraeuropean Fellowship EC contract Ref.\ MEIF-CT-2005-515291, award Nr.\ MATH P00286 and the second author was Postdoctoral Fellow of the Research Foundation -- Flanders (FWO) at the Department of Mathematical Physics and Astronomy, Ghent University, Belgium.
\\ The authors wish to thank Dr.\ B.\ Malengier,~Prof.\ F.\ Cantrijn, and Prof.\ J.\ Lamb for stimulating discussions and the anonymous referee for pointing out reference~\cite{RW}.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,286 |
XPO Logistics adds capacity near Chicago amid intermodal congestion
Sarah Zimmerman Associate Editor
Permission granted by XPO Logistics
XPO Logistics opened a 150,000-square-foot LTL service center in the Chicago-area Sunday to expand capacity as demand skyrockets from the growth of e-commerce and a rebound in manufacturing, the company announced during the facility's opening.
The center in Chicago Heights, about 30 miles southeast of the city, has 264 dock doors and will largely handle industrial parts, bulk goods and other types of palletized freight, according to service center manager Mark Curcio.
The facility is a "massively important part of the plan to expand our capacity," XPO's CIO and acting LTL President Mario Harik said at the event, adding it will more than double the amount of space available to service customers in the area.
XPO's new service center is its 14th in Illinois, a critical logistics hub as Chicago is a one-day truck drive away from 30% of consumers in North America according to World Business Chicago.
"We really are in the focal point of the country, almost everything flows through Chicago," said Curcio, who will lead the facility in Chicago Heights.
The Chicago area has emerged as a choke point within the last few months as carriers struggle to keep up with a deluge of freight coming from the coasts. The average unload dwell time for Schneider's intermodal customers jumped 70% from pre-pandemic levels, Schneider President and CEO Mark Rourke said in August.
Dwell times in Chicago hit an average of 9.3 days, according to a Hapag Llyod analysis of its own boxes. Congestion at inland rail container ramps has slowed the flow of goods and contributed to major backlogs, pushing railroads to temporarily suspend service over the summer.
XPO's new center also comes as the company expects industrial demand to rebound, which would add to the demand. The manufacturing industry has been working to overcome supply chain bottlenecks and ramp up production.
The company wrote in a September investor presentation that it's been steadily working to build up "the massive capacity needed to serve this increased demand" in manufacturing and in e-commerce.
While e-commerce has been a major driver of growth among LTL carriers, XPO said the resurgence of manufacturing has also boosted demand for its services. XPO's LTL business posted its "strongest growth rates" since it began in 2015 with the acquisitions of Con-way and Norbert Dentressangle, Chief Strategy Officer Matt Fassler said in a Q2 earnings call.
"The acceleration in growth for our largest vertical, industrial and manufacturing, outpaced the pickup in retail and e-commerce," said Fassler.
Over 200 employees will work at XPO's new site, including drivers, dockworkers, shop technicians and customer service representatives. The center will also host one of the company's driving schools, a program that's recently been overhauled to attract more workers during a national labor constraint.
The rise of LTL: How e-commerce changed the middle mile By S.L. Fuller • Oct. 6, 2021
From sapling to pure-play LTL: The story of XPO Logistics under Jacobs Transport Dive
Follow Sarah Zimmerman on Twitter
Kenny Holston via Getty Images
8 industry reactions: How the infrastructure deal could change supply chains
Biden's signature paves the way for $17 billion in port infrastructure and $25 billion for airports. Here's what trade associations are saying.
By Alejandra Salgado • Nov. 19, 2021 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,546 |
Superfoods! A new buzzword. This reading worksheet is designed for the 13-15 non-native speakers in the early stages of IELTS or another similar kind of exam. After they finish the reading you can carry on to have a discussion about the topic.
This downloadable printable is meant for high school students, elementary school students and adults at Pre-intermediate (A2) and Intermediate (B1) level. It can be used for improving your students' Reading skills. It focuses on the vocabulary topic of Food. There is an answer key provided with the exercises. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,288 |
\section{Introduction}
Modern society increasingly relies on the Internet for a wide range of tasks, including gathering, sharing, and commenting on content, events, and discussions.
Alas, the Web has also enabled anti-social and toxic behavior to occur at an unprecedented scale.
Malevolent actors routinely exploit social networks to target other users via hate speech and abusive behavior, or spread extremist ideologies~\cite{allison2018social,chetty2018hate,cresci2018fake,waseem2016you}.
A non-negligible portion of these nefarious activities often originate on ``fringe'' online platforms, e.g., 4chan, 8chan, Gab.
In fact, research has shown how influential 4chan is in spreading disinformation~\cite{kang2016fake,zannettou2017web}, hateful memes~\cite{zannettou2018origins}, and coordinating harassment campaigns on other platforms~\cite{hine2017kek,mariconti2018you,snyder2017fifteen}.
These platforms are also linked to various real-world violent events, including the radicalization of users who committed mass shootings~\cite{christchurch,8chanmanifesto,4chanbellingcat}.
4chan is an imageboard where
users (aka Original Posters, or OPs) can create a thread by posting an image and a message to a board; others can post in the OP's thread, with a message and/or an image.
Among 4chan's key features are anonymity and ephemerality; users do not need to register to post content, and in fact the overwhelming majority of posts are anonymous.
At most, threads are archived after they become inactive and deleted within 7 days.
Overall, 4chan is widely known for the large amount of content, memes, slang, and Internet culture it has generated over the years~\cite{wp2014understand4chan}.
For example, 4chan popularized the ``lolcat'' meme on the early Web.
More recently, politically charged memes, e.g., ``God Emperor Trump''~\cite{kym2019geotus} have also originated on the platform.
\descr{Data Release.} In this work, we focus on the {\em ``Politically Incorrect'' board} ({{\selectfont /pol/}}\xspace),\footnote{\url{http://boards.4chan.org/pol/}} given the interest it has generated in prior research and the influential role it seems to play on the rest of the Web~\cite{pettisambiguity,hine2017kek,zannettou2017web,snyder2017fifteen,zannettou2018origins,tuters2019they}.
Along with the paper, we release a dataset~\cite{zenodo} including 134.5M posts from over 3.3M {{\selectfont /pol/}}\xspace conversation threads, made over a period of approximately 3.5 years (June 2016--November 2019).
Each post in our dataset has the text provided by the poster, along with various post metadata (e.g., post id, time, etc.).
We also {\em augment} the dataset by attaching additional set of labels to each post, including: 1) the named entities mentioned in the post, and 2) the toxicity scores of the post.
For the former, we use the spaCy library~\cite{spacy.io}, and for the latter, Google's Perspective API~\cite{jigsaw2018perspective}.
We also wish to warn the readers that some of the content in our dataset, as well as in this paper, is highly toxic, racist, and hateful, and can be rather disturbing.
\descr{Relevance.} We are confident that our dataset will be useful to the research community in several ways.
First, {{\selectfont /pol/}}\xspace contains a large amount of hate speech and coded language that can be leveraged to establish baseline comparisons, as well as to train classifiers.
Second, due to 4chan's outsized influence on other platforms, our dataset is also useful for understanding flows of information across the greater Web.
Third, our dataset contains numerous events, including highly controversial elections around the world (e.g., the 2016 US Presidential Election, the 2017 French Presidential Election, and the Charlottesville Unite the Right Rally), thus the data can be useful in retrospective analyses of these events.
Fourth, we are releasing this dataset also due to the relatively high bar needed to build a data collection system for 4chan and a desire to increase data accessibility in the community.
Recall that, given 4chan's ephemerality, it is impossible to retrieve old threads.
While there are other, third party archives that maintain deleted 4chan threads, they are either no longer maintained (e.g., \url{chanarchive.org}), are focused around front-end uses (e.g., \url{4plebs}), or are not fully publicly available (e.g., \url{4archive.org}).
\descr{Paper Organization.} The rest of the paper is organized as follows.
First, we provide a high-level explanation on how 4chan works in Section~\ref{sec:whatis4chan}.
Then, we describe our data collection infrastructure (Section~\ref{sec:datacollection}) and
present the structure of our dataset in Section~\ref{sec:datastructure}.
Next, we provide a statistical analysis of the dataset (Section~\ref{sec:analysis}), followed by a topic detection, entity recognition, and toxicity assessment of the posts in Section~\ref{sec:contentanalysis}.
Finally, after reviewing related work (Section~\ref{sec:relatedwork}), the paper concludes with Section~\ref{sec:conclusion}.
\section{What is 4chan?}\label{sec:whatis4chan}
\begin{figure}[t]
\centering
\includegraphics[width=0.99\columnwidth]{figure01.png}
\caption{Example of a typical {{\selectfont /pol/}}\xspace thread.}
\label{fig:pol-example-threads}
\end{figure}
\url{4chan.org} is an imageboard launched on October 2003 by Christopher Poole, a then-15-year-old student.
An OP can create a new thread by posting an image and a message to a board. Then, others can post on the OP's thread with a message and/or an image.
Users can also ``reply'' to other posts in a thread by referring to the post ID in their comment.
Figure~\ref{fig:pol-example-threads} shows a typical {{\selectfont /pol/}}\xspace thread:
(0) shows the original post, while (1), (2), and (3) are other posts on that thread.
\descr{Boards.}
As of January 2020, 4chan features 70 different boards, which are categorized into 7 high level categories, namely, Japanese Culture, Video Games, Interests, Creative, Other, Misc (NSFW), and Adult (NSFW).
This paper presents a dataset of posts on {{\selectfont /pol/}}\xspace, the ``Politically Incorrect'' board, which falls under the Misc category.
\descr{Anonymity.} Users do not need an account to post on 4chan.
When posting, users have the \emph{option} to enter a name along with their post,
but anonymous posting is the default and by far preferred way of posting on 4chan (see `a' in Figure~\ref{fig:pol-example-threads}).
Note that anonymity in 4chan is meant to be towards other users and not towards the service, as 4chan maintains IP logs and actually makes them available in response to subpoenas~\cite{vice2019arrested}.
Users also have the option to use \emph{Tripcodes}, i.e., adding a password along with a name while posting: the hash of the password will be the unique tripcode of the user, thus making their posts identifiable across threads.
In addition, some boards, including {{\selectfont /pol/}}\xspace, attach a \emph{poster ID} to each post (d in the figure); this is a unique ID linking posts by the same user in the same thread.
\descr{Flags.} Posts on {{\selectfont /pol/}}\xspace also include the flag of the country the user posted from, based on IP geo-location.
Obviously, geo-location may be manipulated using VPNs and proxies, however, popular VPNs as well as Tor are blacklisted~\cite{torwiki}.
Note that {{\selectfont /pol/}}\xspace is only one of four boards using flags.
Figure~\ref{fig:pol-example-threads} also shows the use of flags on {{\selectfont /pol/}}\xspace: the author of post (2) appears to be posting from the US (f).
In addition, users on {{\selectfont /pol/}}\xspace can choose \emph{troll flags} when posting, rather than the default geo-localization based country.
As of January 2020 the troll flags options are Anarcho-Capitalist, Anarchist,
Black Nationalist, Confederate, Communist, Catalonia, Democrat, European, Fascist, Gadsden, Gay, Jihadi, Kekistani, Muslim, National Bolshevik, Nazi, Hippie, Pirate,
Republican, Templar, Tree Hugger, United Nations, and White Supremacist.
For instance, the OP (post (0)) selected the ``European'' troll flag (b).
\descr{Ephemerality.} Ephemerality is one of the key features of 4chan.
Each board has a limited number of active threads called the \emph{catalog}.
When a user posts to a thread, that thread will be \emph{bumped} to the top of the catalog.
When a new thread is created, the thread at the bottom of the catalog, i.e., the one with the least recent post, is removed.
After the thread is removed from the catalog it is placed into an archive, and then, after 7 days, it is permanently deleted.
That is, popular threads are kept alive by new posts, while less popular threads die off as new threads are created.
However, threads are also limited in the number of times they can be bumped.
When a thread reaches the {\em bump limit} (300 for {{\selectfont /pol/}}\xspace), it can no longer be bumped, but does remain active until it falls off the bottom of the catalog.
\descr{Replies.}
Figure~\ref{fig:pol-example-threads} also illustrates the {\em reply} feature of 4chan.
A user can click on the post ID (c) to generate a post including ``\textgreater \textgreater {\em post ID}'' (see, e.g., e in post (1)).
\descr{Moderation.} 4chan has very little moderation, especially on {{\selectfont /pol/}}\xspace.
Users can volunteer to be moderators, aka ``janitors.''
Janitors have the ability to delete posts and threads, and also recommend users to be banned.
These recommendations go to 4chan employees who are responsible for reviewing user activity before applying a ban.
Overall, {{\selectfont /pol/}}\xspace is considered a containment board, allowing generally distasteful content, even by 4chan standards, to be discussed without disturbing the operations of other boards~\cite{hine2017kek}.
\descr{Slang.} Over the years, 4chan has been the de-facto incubator for a huge number of memes and behaviors that we now consider central to mainstream Internet culture, including lolcats, Rickrolling, and rage comics~\cite{wp2014understand4chan}.
It has also served as a platform for activist movements (e.g., Anonymous) and broad political ideologies like the Alt-Right.
In particular, {{\selectfont /pol/}}\xspace discourse is strongly characterized by a rather ``original'' slang, with popular words appearing in our dataset including expressions like
``Goy'' (a somewhat derogatory term originally used by Jews to denote non-Jews, used on 4chan primarily in reference to anti-Semitic conspiracy theories where Jews act as ``malevolent puppet-masters''~\cite{goyim}), ``Kek'' (which originated as a variant of LOL and became the God of memes, via which they influence reality), ``anon'' (abbreviated for anonymous, describing another 4chan poster), etc.
\section{Data Collection}\label{sec:datacollection}
\begin{table}[t]
\centering
\resizebox{1.0\columnwidth}{!}{
\smallskip\begin{tabular}{l r r r r r}
\toprule
& \textbf{2016} & \textbf{2017} & \textbf{2018} & \textbf{2019} & \textbf{Total} \\
\midrule
\textbf{Threads} & 643,535 & 1,123,341 & 922,103 & 708,932 & 3,397,911\\
\textbf{Posts} & 21,892,815 & 44,573,337 & 39,413,548 & 28,649,533 & 134,529,233 \\
\toprule
\end{tabular}}
\caption{Number of threads and posts in the dataset.}\label{tbl:threadsposts_crawled}
\end{table}
We now discuss our methodology to collect the dataset released along with this paper.
We started crawling {{\selectfont /pol/}}\xspace, in June 2016, using 4chan's JSON API.\footnote{\url{https://github.com/4chan/4chan-API}}
(This was done as part of our first academic study of 4chan~\cite{hine2017kek}.)
Given 4chan's ephemeral nature, we devised the following methodology to ensure we obtained the full/final contents of all threads.
Every 5 minutes, we retrieve {{\selectfont /pol/}}\xspace's thread catalog and compare the list of the currently active threads to the ones obtained earlier.
Once a thread is no longer active, we obtain the full copy of that thread from 4chan's archive.
For each post in a thread, the 4chan API returns, among other things, the post's number, its author, UNIX timestamp, and content of the post.
We explain in detail our dataset and what it contains in the
next section.
Note that while we do not provide posted images, posts do include image metadata, e.g., filename, dimensions (width and height), file size, and an MD5 hash of the image.
Table~\ref{tbl:threadsposts_crawled} provides an overview of our dataset.
Note that for, about $6\%$ of the threads, the crawler gets a 404 error: from a manual inspection, it seems that this is due to ``janitors'' (i.e., volunteer moderators) removing threads for violating rules.
The data released with this paper, as well as the analysis presented in later sections, spans from June 29, 2016 to November 1, 2019.
Alas, our dataset has some (minor) gaps due to failure of our data collection infrastructure; specifically, we are missing 10, 4, and 8 days worth of posts during 2016 (October 15 and December 16--24), 2017 (January 10--12 and May 13), and 2019 (April 13 and July 21--27).
\descr{Ethical considerations.} 4chan posts are typically anonymous, however, analysis of the activity generated by links on 4chan to other services could be potentially used to de-anonymize users.
Overall, we followed standard ethical guidelines~\cite{rivers2014ethical} and made no attempt to de-anonymize users.
Also note that the collection and release of this data does not violate 4chan's API Terms of Service.
\section{Data Structure}\label{sec:datastructure}
\begin{figure}[t]
\centering
\includegraphics[width=0.95\columnwidth]{figure02.png}
\caption{Schematic representation of the JSON structure of the threads in our dataset. (Some keys are omitted to ease presentation.)}
\label{fig:json_structure}
\end{figure}
In this section, we present the structure of our dataset, available from~\cite{zenodo}.
The dataset is released as a single newline-delimited JSON\footnote{\url{http://ndjson.org/}} file (\texttt{.ndjson}), with each line consisting of a full thread.
More specifically, each line is a JSON object which contains a list of posts from a single thread.
Each post is a JSON object containing all the key/values returned by the 4chan API, along with three additional ones ({\em entities}, {\em perspectives}, and {\em extracted\_poster\_id}); see below.
Note that the poster ID (d in Figure~\ref{fig:pol-example-threads}) is not always available from the 4chan API.
As of this writing, the API does not return poster IDs for archived threads, but at certain points of our collection period, it did.
To ensure that our dataset includes the poster ID our data collection infrastructure parses the HTML catalog of the 4chan threads to capture it and store it with the key {\em extracted\_poster\_id}: $95\%$ of the posts have an extracted\_poster\_id.
In Figure~\ref{fig:json_structure}, we report the JSON structure of a thread with two posts: the original post and the second post, with index 0 and 1, respectively.
Due to space limitations, we only list some of the keys, i.e., the most relevant to the analysis presented in the rest of the paper.
The complete list of keys, along with the type of values they hold and any related documentation, is available at~\cite{zenodo}.
\descr{Keys/Values from the API.} Each post includes the following key/values:
\begin{compactitem}[--]
\item \emph{extracted\_poster\_id}: the poster ID.
\item \emph{com}: the post text in HTML escaped format.
\item \emph{no}: the numeric (unique) post ID.
\item \emph{time}: UNIX timestamp of the post.
\item \emph{now}: human-readable format of the UNIX timestamp.
\item \emph{name}: the name of the poster (default to ``Anonymous'').
\item \emph{trip}: a unique ID to the poster, a hash computed based on the password provided by the user, if any.
\item \emph{country\_name}: full name of the country the user posts from.
\item \emph{country}: country code in Alpha ISO-2 format.
\item \emph{troll\_country}: the troll flag selected by the poster, if any.
\item \emph{bumplimit} (only in the original post): flag indicating whether a thread reached the board's bump limit.
\item \emph{archived\_on} (only in the original post): UNIX timestamp of the time the thread is archived.
\item \emph{replies} (only in the original post): the number of posts the thread has, without counting the original post.
\end{compactitem}
\smallskip\noindent As mentioned, we do not crawl images, however, the 4chan API returns some image metadata, e.g.;
\begin{compactitem}[--]
\item \emph{filename}: image name as stored on poster's device.
\item \emph{tim}: the time the image is uploaded as a UNIX timestamp.
\item \emph{md5}: the MD5 hash of the image. Note that the image can be found, using the MD5 hash, in unofficial 4chan archives like 4plebs.\footnote{\url{https://4plebs.org/}}
\end{compactitem}
\descr{Named Entities.}
For each JSON object, we complement the data with the list of the named entities we detect for each post, using the spaCy (v2.2+) Python library~\cite{spacy.io}.
For each entity, we include a dictionary with four different characteristics of the named entity, namely:
\begin{compactitem}[--]
\item \emph{entity\_text}: the name of the detected entity.
\item \emph{entity\_label}: the type of the named entity. %
\item \emph{entity\_start}: character index in \emph{com} in which the named entity starts.
\item \emph{entity\_end}: character index in \emph{com} in which the named entity ends.
\end{compactitem}
\descr{Perspective Scores.} We also add scores returned by the Google's Perspective API~\cite{jigsaw2018perspective}, and more specifically seven scores in the $[0,1]$ interval:
\begin{compactitem}[--]
\item {\sc toxicity} (v6)
\item {\sc severe\_toxicity} (v2)
\item {\sc inflammatory} (v2)
\item {\sc profanity} (v2)
\item {\sc insult} (v2)
\item {\sc obscene} (v2)
\item {\sc spam} (v1)
\end{compactitem}
The process of augmenting every post in our dataset with the named entities and the perspective scores took place between January 2--9, 2020.
\descr{FAIR Principles.} The data released along with this paper aligns with the FAIR guiding principles for scientific data.\footnote{\url{https://www.go-fair.org/fair-principles/}}
First, we make our data \emph{Findable} by assigning a unique and persistent digital object identifier (DOI): 10.5281/zenodo.3606810.\footnote{\url{https://doi.org/10.5281/zenodo.3606810}}
Second, our dataset is \emph{Accessible} as it can be downloaded, for free, and is in the standard JSON format.
JSON is widely used for storing data and has an extensive and detailed documentation for all of the computer programming languages that support it, thus enabling our data to be \emph{Interoperable}.
Finally, our dataset comes with rich metadata that are extensively documented and described in this paper, in~\cite{zenodo}, and in the 4chan API documentation as well.
The data is released in full and hence is \emph{Reusable}.
\section{General Characterization}\label{sec:analysis}
\begin{figure}[t!]
\centering
\subfigure[Threads]{\includegraphics[width=1\columnwidth]{figure03.pdf}\label{fig:oneline_threads_per_day}}
\subfigure[Posts]{\includegraphics[width=1\columnwidth]{figure04.pdf}\label{fig:oneline_posts_per_day}}
\caption{Number of threads and posts shared per day.}
\label{fig:oneline_threads_posts_per_day}
\end{figure}
In this section, we provide a general characterization of the dataset that we release.
Our dataset spans 3.5 years, and this prompts the need to shed light on the temporal evolution of {{\selectfont /pol/}}\xspace.
Moreover, we analyze the use of tripcodes, images, and flags within the board, aiming to showcase some of the peculiar features that characterize 4chan.
\descr{Posting Activity.} We start by looking at how {{\selectfont /pol/}}\xspace's posts are shared over time.
Figure~\ref{fig:oneline_threads_per_day} and Figure~\ref{fig:oneline_posts_per_day} show the number of threads and posts created per day, respectively.
On average, throughout our dataset, over 2.8K threads and 112.3K posts are posted every day on the board.
We observe a peak in posting activity on November 5-13, 2016 (around the US Presidential Election) with 390K posts just on November 8 (Election Day), followed by another peak that lasts from January 20 (Donald Trump's inauguration: 195K posts) until February 3, 2017. Notably, the highest number of posts between these two weeks is observed on January 29 with 204K posts when Donald Trump issued a 90-day travel ban for certain nationals~\cite{dailymail2017bans}.
Additional peaks can be observed close to other world events:
(1) on April 7, 2017 (184K posts) when Donald Trump ordered missile strikes in Syria~\cite{missile2017nytimes};
(2) on April 1, 2018 (225K posts), possibly due to Donald Trump criticizing California's Governor Jerry Brown's decision to grant 56 pardons~\cite{theweek2019things}; (3) on November 6, 2018 (192K posts), when the US Midterm Election took place;
and (4) March 15, 2019 (189K posts), when
51 people died in a terrorist attack in a New Zealand mosque~\cite{terrorist2019guardian}.
Overall, posting activity on {{\selectfont /pol/}}\xspace is strongly related to important events worldwide and is known to spread conspiracy theories after catastrophic events take place.
Notably, numerous mainstream news outlets point to 4chan as the conspiracy theory originator; for instance, about the phrase ``cheese pizza'' referring to a pedophilic code in Hilary Clinton's leaked emails~\cite{newstatesman2019pizzagate}, the ``deep state'' organization against Donald Trump's administration~\cite{guardian2018qanon}, or about the Notre Dame fire~\cite{newstatesman2019notredame}.
Therefore, we are confident our dataset will be useful for further research analyzing conversations on 4chan, as well as activity within and spilling off the platform in response to important events and breaking news.
\begin{figure}[t!]
\centering
\hspace{-0.25cm}
\subfigure[Threads -- Hour of the week]{\includegraphics[width=0.24\textwidth]{figure05.pdf}\label{fig:threads_per_hour_week_per_year}}\hspace{-0.25cm}
\subfigure[Posts -- Hour of the week]{\includegraphics[width=0.24\textwidth]{figure06.pdf}\label{fig:posts_per_hour_week_per_year}}\\
\hspace{-0.25cm}
\subfigure[Threads -- Hour of the day]{\includegraphics[width=0.24\textwidth]{figure07.pdf}\label{fig:threads_per_hour_day_per_year}}
\hspace{-0.25cm}
\subfigure[Posts -- Hour of the day]{\includegraphics[width=0.24\textwidth]{figure08.pdf}\label{fig:posts_per_hour_day_per_year}}
\caption{Temporal characteristics of threads/posts per hour of week and day. (UTC time zone, week starts on Monday.)}
\label{fig:hour_day_week}
\end{figure}
\descr{Temporal Patterns.} We also look for temporal patterns throughout the day/week.
In Figure~\ref{fig:hour_day_week}, we report the percentage of threads and posts, as per hour of day as well as hour of week.
We do so comparing across the years, finding a very similar behavior throughout.
Overall, we observe that the activity seems to peak during what appear to be the hours of the day in Western countries and more or less weekdays.
\begin{figure}[t!]
\centering
\hspace{-0.25cm}
\subfigure[\#threads created per flag]{\includegraphics[width=0.24\textwidth]{figure09.pdf}\label{fig:threads_per_flag}}
\hspace{-0.25cm}
\subfigure[\#posts per flag]{\includegraphics[width=0.24\textwidth]{figure10.pdf}\label{fig:posts_per_flag}}\\
\hspace{-0.25cm}
\subfigure[\#threads created per troll flag]{\includegraphics[width=0.24\textwidth]{figure11.pdf}\label{fig:threads_per_trollflag}}
\hspace{-0.25cm}
\subfigure[\#posts per troll flag]{\includegraphics[width=0.24\textwidth]{figure12.pdf}\label{fig:posts_per_trollflag}}
\caption{Number of threads created and posts per flag and troll flag.}
\label{fig:threads_posts_flags}
\end{figure}
\descr{Flags.} We then look at the countries where posts originate, using the flags displayed on {{\selectfont /pol/}}\xspace.
Recall that these are based on IP geo-localization so at best they provide a {\em signal} for general trends and should not be taken at face value.
In Figure~\ref{fig:threads_posts_flags}, we report the top 10 countries, along with the number of threads (Figure~\ref{fig:threads_per_flag}) and overall posts (Figure~\ref{fig:posts_per_flag}) they created.
The most active countries are the US (1.6M threads and 68M posts), followed by the UK (200K threads and 9.7M posts), Canada (210K threads and 8.1M posts), Australia (121K threads and 5.1M posts), and Germany (83.3K threads and 3.7M posts).
We also report the top 15 ``troll flags'' with ``Nazi'' being the most popular with over 50K threads (Figure~\ref{fig:threads_per_trollflag}) and 1.2M posts (Figure~\ref{fig:posts_per_trollflag}).
Figure~\ref{fig:threads_choropleth} and~\ref{fig:posts_choropleth}, depict the choropleths of the number of threads and posts created per country worldwide, respectively, this time {\em normalized} using each country's estimated Internet-using population.\footnote{\url{https://www.internetlivestats.com/internet-users-by-country/}}
While the US dominates in terms of sheer volume of threads created (Figure~\ref{fig:threads_per_flag}), when taking into account the number of Internet users, the top 5 countries actually are Canada (0.0066), Australia (0.0059), US (0.0058), Ireland (0.0058), and Croatia (0.0054).
As for posts, the top 5 countries are Monaco (0.35), Finland (0.26), Canada (0.25), Australia (0.25), and Iceland (0.24).
Overall,
besides Croatia, Monaco, and Finland, we find a number of North and East European countries being relatively active.
\begin{figure}[t!]
\centering
\subfigure[threads]{\includegraphics[width=0.99\columnwidth]{figure13.png}\label{fig:threads_choropleth}}
\subfigure[posts]{\includegraphics[width=\columnwidth]{figure14.png}\label{fig:posts_choropleth}}
\caption{Choropleth of the number of threads created/posts per country, normalized by Internet-using population. }
\label{fig:thread_post_choropleth}
\end{figure}
\begin{figure}[t!]
\centering
\subfigure[]{\includegraphics[width=0.49\columnwidth]{figure15.pdf}\label{fig:cdf_posts_per_thread_per_year}}
\subfigure[]{\includegraphics[width=0.49\columnwidth]{figure16.pdf}\label{fig:ccdf_posts_per_thread_per_year}}
\caption{CDF and CCDF of the number of posts per thread.}
\label{fig:cdf_ccdf_posts_per_thread}
\end{figure}
\descr{Thread Engagement.} Next, we look at how many posts threads tend to get.
On average, there are 39.6 posts per thread throughout our dataset, with this number increasing over the years, and specifically 34, 39.7, 42.7, and 40.4 for 2016, 2017, 2018, 2019, respectively.
To capture the distribution of posts per threads we plot the Cumulative Distribution Function (CDF) and the Complementary Cumulative Distribution Function (CCDF) for each year in Figure~\ref{fig:cdf_ccdf_posts_per_thread}.
The figure highlights that, overall, more {{\selectfont /pol/}}\xspace threads tend to get more posts over time.
Specifically, $37\%$, $41\%$, $43\%$, and $44\%$ of the threads in 2016, 2017, 2018, and 2019, respectively, have over 100 posts.
We also test for statistically significant differences between the distributions, using a two-sample Kolmogorov-Smirnov (KS) test, finding them on each pair ($p<0.01$).
Thus, this suggests that the change over the year is indeed significant.
\descr{Tripcodes.} Next, we study the use of tripcodes by {{\selectfont /pol/}}\xspace users to see whether this is negligible or relatively widespread.
Recall that tripcodes are the only way a user can ``sign'' their posts on 4chan, letting others recognize posts made by the same user across different threads.
For instance, the QAnon far-right conspiracy theory (built around alleged efforts by the ``deep state'' against US President Donald Trump) started with a post on 4chan in October 2017 by someone using the name Q~\cite{guardian2018qanon}; Q has reportedly used tripcodes on 4chan and 8chan to ``authenticate'' themselves.
In Figure~\ref{fig:cdf_ccdf_posts_per_tripcode}, we plot the CDF and the CCDF of the number of posts with unique tripcode.
Overall, we find that the use of tripcodes goes down over the years.
\begin{compactitem}[--]
\item 2016: 311K posts ($0.23\%$) with unique tripcode from 5.7K different posters;
\item 2017: 365.6K posts ($0.27\%$) from 7.1K posters;
\item 2018: 206K posts ($0.15\%$) from 3.6K posters;
\item 2019: 117K posts ($0.09\%$) from 2.3K posters.
\end{compactitem}
\begin{figure}[t!]
\centering
\subfigure[]{\includegraphics[width=0.49\columnwidth]{figure17.pdf}\label{fig:cdf_post_per_year_tripcode.pdf}}
\subfigure[]{\includegraphics[width=0.49\columnwidth]{figure18.pdf}\label{fig:ccdf_post_per_year_tripcode.pdf}}
\caption{CDF and CCDF of the number of posts with unique tripcode.}
\label{fig:cdf_ccdf_posts_per_tripcode}
\end{figure}
\descr{Images.} Sharing images is very common on 4chan, in fact, OPs need to post an image when creating new threads.
Specifically, 4chan is mentioned by popular press and academic studies about the amount of original content (e.g., memes) it creates and disseminates across the Web~\cite{nyt2018meme,zannettou2018origins,vice2015meme}.
We aim to provide an overview of how many image metadata are included in our dataset.
To shed light on the use of images on {{\selectfont /pol/}}\xspace over the years, we plot the CDF and CCDF of the number of images per thread in Figure~\ref{fig:cdf_ccdf_pictures_per_thread}.
We find that around $27\%$ of posts (36.9M) in our dataset include an image.
On average, 9.2, 10.8, 11.9, and 11 images appear, per thread, in 2016, 2017, 2018, and 2019, respectively.
Overall, 2017 was the year with the highest number of images shared: 12.1M.
Specifically, $17\%$ of the threads in 2016 have over 10 images, rising to $19\%$ in 2017, and eventually around $20\%$ in 2018 and 2019.
We test for statistically significant differences between the distributions using a two-sample KS test, and find them on each pair ($p<0.01$).
\begin{figure}[t!]
\centering
\subfigure[]{\includegraphics[width=0.49\columnwidth]{figure19.pdf}\label{fig:cdf_pictures_per_thread_per_year}}
\subfigure[]{\includegraphics[width=0.49\columnwidth]{figure20.pdf}\label{fig:ccdf_pictures_per_thread_per_year}}
\caption{CDF and CCDF of the number of images per thread.}
\label{fig:cdf_ccdf_pictures_per_thread}
\end{figure}
\section{Content Analysis}\label{sec:contentanalysis}
In this section, we provide an analysis of the content of the posts in our dataset.
More specifically, we detect the most popular topics discussed over the years, the named entities mentioned in each post, and how toxic a post is.
While the latter two are included in our data release, the first is not because topic extraction is done over {\em sets} of posts.
Nonetheless, we present it here to give an overview of what is discussed on {{\selectfont /pol/}}\xspace, and thus is in the dataset.
\begin{table*}[t]
\centering
\resizebox{1.0\textwidth}{!}{
\begin{tabular}{r l}
\toprule
\textbf{Topic} & \textbf{Year 2016} \\
\midrule
1 & people (0.007), like (0.005), think (0.005), right (0.004), thing (0.004), know (0.004),
polite (0.004), need (0.003), want (0.003), human (0.003) \\
2 & Trump (0.03), vote (0.021), elect (0.013), leaf (0.012), president (0.012), Hillary (0.011), fuck (0.01), shit (0.01), lose (0.009), happen (0.009) \\
3 & white (0.023), bump (0.013), nigger (0.013), country (0.009), praise (0.009),
black (0.009), check (0.008), race (0.008), fuck (0.008), people (0.007) \\
4 & thread (0.022), Jew (0.014), fuck (0.014), faggot (0.014), good (0.011), kike (0.010),
wrong (0.009), kill (0.009), shill (0.009), retard (0.009)\\
5 & fuck (0.009), girl (0.009), women (0.009), like (0.008), dick (0.007), cuck (0.007),
love (0.006), look (0.006), woman (0.006), lmao (0.006)\\
\toprule
\textbf{Topic} & \textbf{Year 2017} \\
\midrule
1 & post (0.021), shit (0.012), know (0.011), fuck (0.01), think (0.009), meme (0.009),
retard (0.009), fake (0.008), mean (0.007), leaf (0.007) \\
2 & good (0.009), moor (0.008), lmao (0.006), base (0.006), go (0.006), kill (0.005),
movie (0.004), fuck (0.004), like (0.004), roll (0.004) \\
3 & people (0.006), like (0.005), think (0.004), thing (0.004), work (0.003), want (0.003),
know (0.003), right (0.003), social (0.003), human (0.003) \\
4 & nigger (0.012), fuck (0.007), money (0.006), like (0.006), people (0.006), year (0.005),
work (0.005), want (0.005), live (0.005), shoot (0.005) \\
5 & thank (0.027), anon (0.021), kike (0.012), love (0.01), remind (0.008), fuck (0.008),
maga (0.007), delete (0.007), sorry (0.007), time (0.007) \\
\toprule
\textbf{Topic} & \textbf{Year 2018} \\
\midrule
1 & bump (0.025), good (0.018), thank (0.017), anon (0.015), happen (0.01), Christmas (0.009),
suck (0.007), dick (0.006), feel (0.006), hope (0.006) \\
2 & white (0.016), Jew (0.01), country (0.009), American (0.006), German (0.006),
fuck (0.006), people (0.006), America (0.006), Europe (0.006), European (0.006) \\
3 & kike (0.024), right (0.014), fuck (0.012), mean (0.011), Israel (0.011), wall (0.01),
btfo (0.01), boomer (0.009), go (0.008), haha (0.007) \\
4 & money (0.007), work (0.007), year (0.006), people (0.006), live (0.005), like (0.004),
fuck (0.004), need (0.004), go (0.004), want (0.004) \\
5 & fuck (0.027), post (0.02), thread (0.019), faggot (0.013), shit (0.012), retard (0.01),
know (0.01), shill (0.009), flag (0.009), meme (0.008) \\
\toprule
\textbf{Topic} & \textbf{Year 2019} \\
\midrule
1 & people (0.006), christian (0.006), believe (0.005), Jew (0.005), like (0.005),
think (0.005), Jewish (0.004), know (0.004), read (0.004), white (0.004) \\
2 & white (0.015), country (0.009), Jew (0.009), America (0.007), American (0.007),
china (0.006), people (0.006), Israel (0.006), fuck (0.006), Europe (0.005) \\
3 & fpbp (0.007), sage (0.007), drink (0.007), glow (0.006), nigga (0.006), like (0.005),
fuck (0.005), tulsi (0.005), water (0.005), meat (0.005) \\
4 & base (0.089), bump (0.05), post (0.022), true (0.016), incel (0.015), cringe (0.014),
redpill (0.014), know (0.012), seethe (0.011), btfo (0.01) \\
5 & kike (0.025), flag (0.024), nice (0.022), leaf (0.015), shill (0.015), meme (0.013),
fuck (0.013), cope (0.011), memeflag (0.009), forget (0.008) \\
\toprule
\end{tabular}
}
\caption{Topics discussed on {{\selectfont /pol/}}\xspace per year.}\label{tbl:yeartopics}
\end{table*}
\subsection{Topics}
Looking at topics frequently mentioned on {{\selectfont /pol/}}\xspace over the years provides a high-level reflection of the nature of discussions taking place on the board.
Importantly, researchers interested in studying discussions around specific topics included in this analysis can find our dataset useful.
We use Latent Dirichlet Allocation (LDA), which is used for basic topic modeling~\cite{blei2003latent}.
First, for each year, we collect the escaped HTML text provided for each post by the 4chan API.
Then, before tokenizing every post, we remove any stopwords, URLs, and HTML code.
Last, we create a term frequency-inverse document frequency (TF-IDF) array that is used to fit our LDA model.
TF-IDF statistically measures how important a word is to a collection of words; previous work shows it yields more accurate topics~\cite{mehrotra2013improving}.
In Table~\ref{tbl:yeartopics}, we list the top five topics discussed on {{\selectfont /pol/}}\xspace for each year, along with the weights of each word for that topic.
We find that, during 2016, {{\selectfont /pol/}}\xspace users were discussing political matters in a significant manner, and in particular the 2016 US Presidential Elections (topic 2).
We also find several topics with racist connotations, like \emph{kike} (derogatory term to denote Jews) and \emph{nigger}.
Other racist topics appear in other years as well, which highlights that controversial and racist words are used frequently on {{\selectfont /pol/}}\xspace.
Overall, our topic analysis shows that discussions in {{\selectfont /pol/}}\xspace feature political matters, hate, misogyny, and racism over the course of our dataset.
\subsection{Toxicity}
Next, we set to score the content of the posts according to how toxic, inflammatory, profane, insulting, obscene, or spammy the text is.
To this end, we use Google's Perspective API~\cite{jigsaw2018perspective}, which offers several models for scoring text trained over crowdsourced annotations.
We choose Google's Perspective API as other available methods mostly use short texts (tweets) for their training samples~\cite{davidson2017automated}.
Perspective API should perform better for our dataset as it was trained using comments with no restriction in character length~\cite{wired2017api}, similar to the comments of our dataset.
We focus on the following 7 models:
\begin{compactitem}[--]
\item {\sc toxicity} and {\sc severe\_toxicity}: quantify how rude or disrespectful a comment is; note that the latter is less sensitive to messages that include positive uses of curse words compared to the former.
\item {\sc inflammatory}: how likely it is for a message to ``inflame'' discussion.
\item {\sc profanity}: how likely a message is to contain swear or curse words.
\item {\sc insult}: how likely a message is to contain insulting or negative content towards an individual or group of individuals.
\item {\sc obscene}: how likely a message is to contain obscene language.
\item {\sc spam}: how likely a message is to be spam.
\end{compactitem}
We score each post in our dataset using the API and include the results in the final dataset.
We only obtain results for posts that include text, since scores are computed only over text.
That is, we do not score $2.3\%$ (3.1M) of the posts in our dataset that have no text.
In Figure~\ref{fig:cdf_perspective_scores}, we plot the CDF of the scores for each of the models.
We observe that {{\selectfont /pol/}}\xspace exhibits a high degree of toxic content: $37\%$ and $27\%$ of the posts have, respectively, {\sc toxicity} and {\sc severe\_toxicity} scores greater than 0.5 (see Figure~\ref{fig:cdf_perspective_toxicity}).
These results are in line with previous research findings~\cite{hine2017kek}.
For the other models, we observe similar trends: $36\%$ of the posts have an {\sc inflammatory} score greater than 0.5 (Figure~\ref{fig:cdf_perspective_insult}), $33\%$ for {\sc profanity} (Figure~\ref{fig:cdf_perspective_insult}), $35\%$ for {\sc insult} (Figure~\ref{fig:cdf_perspective_insult}), $30\%$ for {\sc obscene} (Figure~\ref{fig:cdf_perspective_insult}), but only $16\%$ for {\sc spam} (Figure~\ref{fig:cdf_perspective_spam}).
We also test for statistically significant differences between the distributions in Figure~\ref{fig:cdf_perspective_scores}, using two-sample KS test, and find them on each pair ($p<0.01$).
Overall, we are confident that this additional set of labels can be extremely useful for researchers studying hate speech, bullying, and aggression on the Web.
\begin{figure*}[t!]
\center
\subfigure[]{\includegraphics[width=0.27\textwidth]{figure21.pdf}\label{fig:cdf_perspective_toxicity}}
\subfigure[]{\includegraphics[width=0.27\textwidth]{figure22.pdf}\label{fig:cdf_perspective_insult}}
\subfigure[]{\includegraphics[width=0.27\textwidth]{figure23.pdf}\label{fig:cdf_perspective_spam}}
\caption{CDF of the Perspective Scores related to how toxic, inflammatory, obscene, profane, insulting, or spammy is a post. }
\label{fig:cdf_perspective_scores}
\end{figure*}
\subsection{Named Entity Recognition}
\begin{table}[t]
\centering
\resizebox{0.9\columnwidth}{!}{
\begin{tabular}{ l r r | l r r}
\toprule
\textbf{Named Entity} & \textbf{\#Posts} & \textbf{($\%$)} &\textbf{Entity Label} & \textbf{\#Posts} & \textbf{($\%$)}\\
\midrule
Trump & 2,461,452 & 1.83 & DATE & 92,945,374 & 69.06 \\
one & 1,811,983 & 1.35 & CARDINAL & 20,069,995 & 14.92 \\
first & 1,584,686 & 1.18 & PERSON & 17,532,857 & 13.03 \\
US & 1,066,408 & 0.79 & ORG & 17,145,386 & 12.74 \\
Jews & 963,398 & 0.72 & NORP & 16,820,469 & 12.50 \\
America & 831,007 & 0.62 & GPE & 14,813,739 & 11.01 \\
Europe & 719,873 & 0.54 & TIME & 4,498,824 & 3.34 \\
two & 703,767 & 0.52 & ORDINAL & 2,923,765 & 2.17 \\
American & 676,332 & 0.50 & LOC & 2,676,504 & 1.99 \\
Israel & 589,718 & 0.44 & PERCENT & 2,189,227 & 1.68 \\
\toprule
\end{tabular}
}
\caption{Top 10 named entity and entity label that appear in {{\selectfont /pol/}}\xspace posts.}
\label{tbl:label_entity_occurrunces}
\end{table}
Finally, we extract the ``named entities'' mentioned in {{\selectfont /pol/}}\xspace posts, as we hope this will allow the research community to study discussions around specific entities, e.g., individuals, countries, etc.
To obtain the named entities, we use the \emph{en\_core\_web\_lg} model publicly available via the SpaCy library~\cite{spacy.io}.
We choose this specific model over other alternatives since it was trained with the largest available dataset.
In addition, previous work~\cite{jiang2016evaluating} ranked it among the top two most accurate methods for named entity recognition.
It uses millions of Web entries consisting of news articles, blogs, and comments to detect and extract a variety of entities from text.
Entities range from specific popular individuals to nationalities, countries, and even events.\footnote{See \url{https://spacy.io/api/annotation\#named-entities} for the full list of labels.}
We run the entity detection model against all the posts in our dataset and include the extracted entities in the final dataset.
Note that the model did not return any entities for 18M posts ($13\%$); this is expected since a lot of posts do not reference any entities and due to the fact that a considerable number of posts do not have any text.
In Table~\ref{tbl:label_entity_occurrunces}, we list the ten most popular named entities in our dataset.
Note that a post can mention a popular entity more than once.
We report the number of posts in our dataset that mention an entity {\em at least} once.
We find that Donald Trump is the most popular named entity on {{\selectfont /pol/}}\xspace with over 2.46M posts ($1.83\%$) mentioning him.
Other popular named entities include ``US'' ($0.79\%$), ``Jews'' ($0.72\%$), ``America'' ($0.62\%$), ``Europe'' ($0.54\%$), ``American'' ($0.50\%$), and ``Israel'' ($0.44\%$).
We also report the top ten entity {\em labels} in our dataset.
The entity labels specify the category of the entity mentioned in each post (e.g., ``PERSON'' for Donald Trump).
The most popular label is date ($69.06\%$), followed by cardinal numbers ($14.92\%$), and real or imaginary people ($13.03\%$).
Other popular labels include organizations ($12.74\%$), nationalities, religious, or political groups ($12.50\%$), and times smaller than a day ($3.34\%$).
Reviewing the most popular named entities and labels of our dataset suggests that discussions on {{\selectfont /pol/}}\xspace are related to discussions about world happenings and events.
Overall, we hope that augmenting our dataset with the named entities will be valuable to researchers working on Computational Social Sciences who wish to study discussions around specific individuals, nationalities, etc.
\section{Related Work}\label{sec:relatedwork}
In this section, we review relevant related work.
Over the past couple of years, a number of research papers have used data collected from 4chan; some also mention that data is available upon request.
Overall, our 4chan dataset is, to the best of our knowledge, 1) the only one to be freely and publicly available online, and 2) the largest and most comprehensive one, including 3.5 years worth of data.
\descr{Studies focusing on 4chan.} Bernstein et al.~\cite{bernstein20114chan} crawl 5.5M posts from 500K threads posted on the ``Random'' (/b/) board between July 19 and August 2, 2010, and present a content analysis showing how posts are dominated by images and posting of external URLs.
Their dataset is not openly accessible.
Hine et al.~\cite{hine2017kek} collect 11M posts from June 30 to September 12, 2016 from 3 different boards, namely, ``Politically Incorrect'' ({{\selectfont /pol/}}\xspace), ``Sports'' (/sp/), and ``International'' (/int/), presenting a general characterization of the former while mostly using the latter two for comparison.
Overall, they study the effect of ephemerality and bump limits, and show that {{\selectfont /pol/}}\xspace is characterized by a high degree of hate speech.
Moreover, they find that the board serves as an aggregation point for {\em coordinated} harassment campaigns on other platforms such as YouTube.
Given the timeline of the data (Summer 2016), a lot of the content is related to the 2016 US Presidential Election, with 4chan users exhibiting unconventional support, often in terms of memes and novel image content, to Donald Trump's 2016 presidential campaign.
The dataset of this study is only available upon request and, more importantly, only includes 2.5 months rather than 3.5 years worth of data.
Tuters and Hagen~\cite{tuters2019they} analyze 1M posts from 4chan's {{\selectfont /pol/}}\xspace that contained words enclosed in triple parenthesis, i.e., ((())).
They find that such posts often feature anti-Semitic nature and that {{\selectfont /pol/}}\xspace posters tend to create and use political and racist memes.
This dataset is not openly accessible.
Finally, Pettis~\cite{pettisambiguity} collect 2.7K and 1.1K threads from {{\selectfont /pol/}}\xspace and the ``Technology'' board (/g/), respectively and focus on qualitatively studying whether anonymity lets individuals be more open to reveal their emotions and beliefs online.
Again, this dataset is not available online.
\descr{Multi-platform studies.} Zannettou et al.~\cite{zannettou2017web} study how mainstream and fringe Web communities (4chan, Reddit, and Twitter) share mainstream and alternative news sources to influence each other.
Between June 30, 2016 and February 28, 2017 they collected: a) 487K tweets; b) 42M posts, 390M comments, and 300K subreddits; and c) 97K posts made on {{\selectfont /pol/}}\xspace, /sp/, /int/, and the ``Science'' board (/sci/).
They find that, before a story is made popular, it was often posted on 4chan for the first time, and use a statistical method called Hawkes Process to quantify the influence of 4chan with respect to news dissemination.
This dataset is available upon request.
Snyder et al.~\cite{snyder2017fifteen} collect more than 1.45M posts from paste-bin.com, 282K posts from {{\selectfont /pol/}}\xspace and /b/, and 4K posts from 8ch's {{\selectfont /pol/}}\xspace and /baphomet/ to detect doxing.
This dataset is not publicly available.
Then, Zannettou et al.~\cite{zannettou2018origins} present a large-scale measurement study of the meme ecosystem, using 160M images obtained from {{\selectfont /pol/}}\xspace, Reddit, Twitter, and Gab.
They collect 74M unique images from Twitter, 30M from Reddit, 193K from Gab, and 3.6M from {{\selectfont /pol/}}\xspace.
The study shows that Reddit and Twitter tend to post memes for ``fun,'' while Gab and {{\selectfont /pol/}}\xspace users post racist and political memes targeting specific audiences.
Importantly, they find that {{\selectfont /pol/}}\xspace is the leading creator of racist and political memes, and the subreddit "The\_Donald" is very successful in disseminating memes to both fringe and mainstream Web communities.
The authors created an openly accessible dataset, however, it only consists of the URLs and the hashes of the images collected.
Finally, Mittos et al.~\cite{mittos2020and} gather 1.9M threads from {{\selectfont /pol/}}\xspace, along with the pictures posted, and 2B comments from 473K subreddits.
They extract posts that might be related to genetic testing, showing the context in which genetic testing is discussed and finding that it often yields high user engagement.
In addition, the discussion of this topic often includes hateful, racist, and misogynistic comments.
Specifically, {{\selectfont /pol/}}\xspace conversations about genetic testing involves several alt-right personalities, antisemitism, and hateful memes.
The authors did not make their dataset openly accessible.
\descr{Dataset Papers.} Here we list other dataset papers that are also somewhat related to the motivations behind our work, in that they release data associated with social network content as well as potentially nefarious activities.
Brena et al.~\cite{brena2019news} present a data collection pipeline and a dataset with news articles along with their associated sharing activity on Twitter, which is relevant in studying the involvement of Twitter users in news dissemination.
The pipeline can also be used to classify the political party supported by Twitter users, based on the news outlets they share along with the hashtags they post on their tweets.
Fair and Wesslen~\cite{fair2019shouting} present a dataset of 37M posts, 24.5M comments, and 819K user profiles collected from the social network Gab, which, like 4chan, is often associated to alt-right and hateful content.
Their dataset includes user account data, along with friends and follower information, and edited posts and comments in case a user made an edit.
Garimella and Tyson~\cite{garimella2018whatapp} present a methodology for collecting large-scale data from WhatsApp public groups and release an anonymized version of the collected data.
They scrape data from 200 public groups and obtain 454K messages from 45K users.
They analyze the topics discussed, as well as the frequency and topics of the messages to characterize the communication patterns in WhatsApp groups.
Finally, Founta et al.~\cite{founta2018crowdsourcing} use crowdsourcing to label a dataset of 80K tweets as normal, spam, abusive, or hateful.
More specifically, they release the tweet IDs (not the actual tweet) along with the majority label received from the crowdworkers.
\section{Conclusion}\label{sec:conclusion}
This paper presented our 4chan dataset; to the best of our knowledge, the largest publicly available dataset of its kind.
The dataset includes over 3.3M threads and 134.5M posts from 4chan's Politically Incorrect board collected between June 2016 and November 2019.
We also augmented the dataset with a set of labels measuring the toxicity of each post, as well as the named entities mentioned in each post.
Overall, we are confident that our work will further motivate and assist researchers in studying and understanding 4chan as well as its role on the greater Web.
Access to the dataset could also help answer numerous questions about {{\selectfont /pol/}}\xspace,
e.g., what is the nature of discussion on the board following sharing of news articles?
what is the role played by 4chan in alternative and fake news dissemination?
what is 4chan's role in coordinated aggression campaigns, doxing, trolling, etc.?
Moreover, using this dataset in conjunction with data from other social networks could also help researchers understand the similarities and differences of users of different communities.
Also, our dataset is an invaluable resource for training algorithms in natural language processing, modeling of slang words, or detecting hate speech, fake news dissemination, conspiracy theories, etc.
Finally, we hope that the data can be used in qualitative work to present in-depth case studies of specific narratives, events, or social theories.
\descr{Acknowledgments.}
This work was funded by the EU Horizon 2020 Research and Innovation program under the Marie Skłodowska Curie ENCASE project (GA No.~691025),
the US National Science Foundation (Grant No.~CNS-1942610),
and the UK EPSRC grant EP/S022503/1 that supports the
Centre for Doctoral Training in Cybersecurity.
\small
\bibliographystyle{abbrv}
| {
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Q: Is this assembly code sorting numbers in ascending order? I am trying to figure out what this assembly code is performing.
.equ SIZE =128
.equ TABLE_L =$60
.equ TABLE_H =$00
.def A =r13
.def B =r14
.def cnt2 =r15
.def cnt1 =r16
.def endL =r17
.def endH =r18
Outer:
mov ZL, endL
mov ZH, endH
mov cnt2, cnt1
inner_loop: ld A, Z
ld B, -Z
cp A, B
brlo L1
st Z, A
std Z+1, B
L1: dec cnt2
brne inner_loop
dec cnt1
brne Outer
ret
table:
I believe it may be sorting numbers in ascending order, but I am not sure. The table is left blank as I am not sure what values are stored there. I am trying to figure out what the code does based only on the code.
A: Yeah, looks like a simple Bubble Sort (without the "early out" optimization that bloats the code by checking if any swaps have happened; if you want better almost-sorted-input performance, use InsertionSort). See Bubble Sort: An Archaeological Algorithmic Analysis for a look at different forms of Bubble Sort, including this where the range of elements scanned decreases by 1 each outer iteration.
It has an interesting advantage for code-size on AVR vs. other simple sort, which is that the accesses are all local so they can all use the Z register, and don't have to do add-with-carry for address calculation. (Although Insertion Sort should be similar.)
A is loaded from the higher address.
cp A,B / brlo skips the swap if the unsigned lower element is already at the higher address, so it's sorting the lowest (unsigned) elements to the end of the array. That's descending order.
The stores (if they happen) are to the same two locations the loads were from, so this is indeed a swap, not some buggy nonsense.
| {
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Home Dispute digest Using US discovery for proceedings in Asia
Using US discovery for proceedings in Asia
Often, the discovery a party really needs is found in the US. Multinational companies trade with US counterparties. Financial transactions clear through Wall Street. Electronic data traverse servers in Silicon Valley. Parties to US litigation can obtain all of this information to further their cases.
Participants in disputes outside the US can access this information, too. Under a little-known US law, 28 USC, section 1782, parties to "foreign proceedings" can obtain documents and testimony from third parties in the US.
The statute can give an informed party a decisive advantage. Take, for example, the recent dispute in Hong Kong between casino magnate Sheldon Adelson and a reporter from The Wall Street Journal who described him unflatteringly in an article.
Adelson sued the reporter for libel. To defend the suit, the reporter brought section 1782 applications to take discovery from a rabbi whom Adelson had allegedly berated and "reduced to tears", and from the director of the Brookings Institute, whom Adelson allegedly yelled at for "hosting terrorists" at its events. The Hong Kong libel case settled earlier this year with no payment from either party.
Using Hong Kong as an example, this article explains how parties to disputes outside the US can use the powerful US discovery system, what elements parties must show under section 1782, and practical considerations for executing an effective cross-border discovery plan.
Unique scope of US system
The US discovery system is unique in terms of its breadth and invasiveness. It allows parties to take extensive party and third-party discovery before trial. In complex cases involving large amounts in dispute, the scope of discovery can appear virtually limitless.
Parties can command documents and testimony from parties and third parties without prior court permission. The US system prioritizes exhaustiveness over efficiency, based on a belief that the truth is more likely to be found if no stone is left unturned. Parties can meticulously test evidence to eliminate any risk of "trial by surprise".
This is not the case in civil law jurisdictions, where parties typically must only produce helpful evidence that they intend to use in the proceedings. Further discovery is extremely limited and at the court's discretion.
Discovery in private commercial arbitrations is typically similarly limited. Hong Kong and other former English common law jurisdictions strike a middle ground. Pretrial discovery is available but tempered by the interests of achieving efficient resolution of disputes.
After exchange of "lists of documents" at the start of a litigation, further discovery is subject to court screening for "necessity". This curtails the "fishing expeditions" common in US litigation. Practically speaking, the scope of the discovery is dramatically more limited than in the US.
Using section 1782 and cross-border discovery
The English common law system can leave material evidence undiscovered by relying (unrealistically) on good-faith self-disclosure between litigation adversaries. Litigants can use the US discovery system to turn this flaw into a strategic advantage.
Section 1782 allows "any interested person" in a "proceeding in a foreign or international tribunal" to bring an application in US district court where "a person resides or is found" to give evidence for use in the foreign proceedings. Through section 1782, Hong Kong litigants can "obtain as much discovery as it could if the lawsuit had been brought in [the US] court rather than abroad".
Obtaining discovery using section 1782
Litigants can use section 1782 to compel a third party to "give his testimony or statement or to produce a document or thing".
Once a section 1782 application is granted, the applicant serves a subpoena on the third party under the Federal Rules of Civil Procedure. The subpoena can compel document production as long as the documents: (1) bear "some relevance" to the subject matter of the foreign dispute; (2) are not protected by the attorney-client privilege or by another privilege; and (3) are within the respondent's "possession, custody or control". The information requested need not be "admissible" or "discoverable" in the foreign proceedings to be discovered. Courts have interpreted "possession, custody or control" broadly to include any document that a party has the "legal right to obtain on demand". Thus, some courts have ordered respondents to produce documents kept outside of the jurisdiction (including, in some instances, documents maintained outside of the US entirely).
The subpoena can also be used to compel the recipient to testify, under oath and on the record, for up to seven hours. The deposition duration can be lengthened or shortened by application to the court. Because the testimony is under oath, witnesses can be punished for perjury if they do not tell the truth.
Elements required to obtain discovery under section 1782
Section 1782 discovery is discretionary. Even if an applicant meets every criteria within the statute and case authorities, the court may still deny the application for any reason.
An applicant must show three mandatory requirements to be eligible to take section 1782 discovery. If the elements are met, the court will consider four discretionary factors to decide whether discovery should be granted.
The mandatory factors
The statute provides that the application must show that the discovery is sought: (1) by an "interested person" in the foreign dispute; (2) from a "person" who "resides" or is "found" in the district where the court sits; and (3) that the discovery is "for use" in a proceedings before a "foreign or international tribunal".
The discovery is requested by an "interested person". Those with "participation rights" in foreign proceedings are "interested persons". Parties to the foreign proceedings obviously meet this definition. But others who are, for example, entitled to submit evidence or to appeal the decision in the foreign case (such as the victim in a criminal case) also constitute interested persons who can take discovery in the US. Someone with only a financial interest in the outcome of the case, however, is not an interested person who can bring an application.
The discovery is requested from a person "found" in the district. The person must "reside" or be "found" in the district the court sits in. A person is found in a district where he or she is physically present, even temporarily. So a person can be tagged with a subpoena while passing through a district with which he or she otherwise has no connection. The person must then respond, or risk contempt of court. In addition, the application can be taken against a human being or a corporation, but not a government. Thus, courts have rejected applications to collect evidence from the US Central Intelligence Agency or the Federal Bureau of Investigation to identify confidential informants who testified against them in a non-US trial.
The discovery is for use in a "foreign or international tribunal". These foreign or international tribunals include "investigating magistrates, administrative tribunals and arbitral tribunals, and quasi-judicial agencies, as well as conventional civil, commercial, criminal and administrative courts". Some courts have held previously that private commercial arbitral tribunals also qualify as foreign tribunals. Section 1782 can also be used to take discovery for use in proceedings within "reasonable contemplation". Practically, the courts will only grant discovery for proceedings in "contemplation" if the possible claim is very clearly spelled out in the application.
The discretionary factors
If an applicant proves these elements, the court will consider four factors in determining whether to grant the application:
Whether the discovery is also within the foreign tribunal's jurisdiction. US courts are less willing to grant assistance with tasks the foreign tribunal can do itself, such as compel discovery from parties over whom it has
personal jurisdiction.
The foreign tribunal's "receptivity" to assistance. US courts will reject the discovery if there is "authoritative proof" that the foreign tribunal would not be "receptive" to it, for example, a letter from a legal body saying the discovery would compromise the foreign proceedings. (The risk of this would not be high in Hong Kong, for example, where courts routinely welcome section 1782 assistance.)
Whether the discovery attempts to "circumvent" the foreign tribunal's policies. US courts ask whether the application is brought in "bad faith". Accordingly, courts have rejected applications when the foreign tribunal has already repeatedly denied identical requests. The applicant is not required to show, however, that the same evidence is discoverable or admissible in the foreign tribunal.
Whether the discovery would be unduly burdensome. Finally, the discovery should not place an "undue burden" on the respondent. So a court may reject a request for thousands of documents, some of which date back 30 years. It is more likely to grant an application targeting a set of documents limited by date and subject matter. The court will typically abide by these factors and grant discovery when they are met. However, it still has the discretion to deny the application and will do so if it perceives the application or the applicant as bullying or unfair.
Taking cross-border discovery
Litigants should comply with a number of additional tacit criteria when designing and executing an effective cross-border discovery plan:
Document requests should be laser-focused. Even though litigants bring section 1782 applications ex parte in the first instance, courts regularly reject unfocused applications that request nebulous categories of documents, or that are not solidly anchored to the facts of the foreign dispute. Applications should carefully spell out how the discovery will advance the foreign case. It is not enough to say that the documents are relevant.
Use emotion to win over the court. The key to section 1782 is that the court has ultimate discretion. Craft a narrative that shows the application is "just" and "equitable". Judges do not want to grant section 1782 applications to bullies. Even if you meet the legal test, you must show upfront that your client is the "good guy".
Assemble a legal team that understands the nuances of both jurisdictions. Your US legal team must understand the nuance of the tribunal and proceedings in Asia to execute an effective cross-border discovery plan. US lawyers without an understanding of the non-US tribunal can alienate decision-makers and get counter-productive results. Plan and execute the two cases in close concert so the discovery is collected at the right time and in the right way.
John Han is a principal and Jason Kang is an associate at Kobre & Kim in Hong Kong
Jason Kang
Kobre & Kim
US Discovery system
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Gujarat elections are far from over, BJP is eyeing a 2nd round
Prime Minister Narendra Modi will fly to Delhi after voting in Gandhinagar.
Prime Minister Narendra Modi and Union Home Minister Amit Shah will hold a strategy session with BJP office-bearers and senior leaders after the second phase of elections. Assembly Elections in Gujarat Ends Monday. Sources said the session will be for the next round of assembly elections in 2023 and the general election — a crucial home stretch ahead of 2024.
The BJP-ruled states of Madhya Pradesh and Rajasthan are also expected to wrest control from the Congress in the states that will go to polls next year.
The Prime Minister will soon leave for Delhi after voting in Gandhinagar to inaugurate the two-day office staff meeting. Sources said that party in-charge, joint in-charge, in-charges of fronts and organizations and all state ministers will attend the meeting.
Polling for the second phase of Assembly elections in Gujarat tomorrow – Voting will be held tomorrow for 93 constituencies covering the central and northern parts of the state, including the largest city Ahmedabad and the capital Gandhinagar.
Ahead of the 2024 elections, a seventh straight win in Gujarat is crucial for the BJP, which has ruled the state since 1995. The party ran a high-pressure campaign in the state led by Prime Minister Modi. Mr Shah, the party's chief strategist, has set a target of 140 seats — a steep rise from the 99 it currently rules.
Congress, which won 77 seats in the last election, campaigned less this time. Rahul Gandhi, who led from the front in the 2018 elections, is busy with Bharat Jodo Yatra and can spare only one day to campaign in Gujarat.
Arvind Kejriwal's Aam Aadmi Party has positioned itself as the main opposition party to the BJP, with a high-decibel campaign based on its model of governance in Delhi and Punjab.
Biden attends Kennedy Center Honors for Gladys Knight, George Clooney, U2 and more.
FX swap debt $80 trillion 'blind spot' global regulator says | {
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} | 7,250 |
0.000 seconds (0.000); 51.87 MB (51.868) - beforeSearch
Mosaïek acquires first grandMA3 in SA
Schalk Botha (DWR), Mduduzi Msibi and Estian Els of Mosaïek Theatre and Jannie de Jager (DWR)
South Africa - The Mosaïek Church and Theatre in Fairland has invested in the first grandMA3 console in South Africa, they had a bigger plan in mind.
Estian Els, head of technical at Mosaïek Theatre, works closely with colleague Mduduzi Msibi. While the pair may be audio technicians, first and foremost, they provide technical support in every ministry of the church, including lighting, audio, LED screens and AV. Every sermon is broadcast on KykNET where there is a remarkable viewership between 75,000 and 80,000 each Sunday.
The theatre is not only used for church events but is hired out as a venue with some headline productions under the belt including Idols and the upcoming The Voice finale. The income generated is then planted back into various outreach programs hosted by the church.
"The biggest fulfilment is being part of working in the changing lives," said Mduduzi. "You are an instrument in God's hands in bringing the ministry to life."
The church, initially running off a PC based lighting console, decided on a grandMA3. "When we started the upgrade process we looked at all the available options on the market the MA definitely stood out as the market leader in lighting control," Estian explained. "That made it the obvious choice as we push to be a world-class venue, and the fact that MA appears as the number one requested lighting console on all international riders."
A couple of years ago, Mosaïek had a dream to be energy efficient. "To give you some background, the entire theatre is run on solar power; we have a UPS system in the background and we also have a generator, so the solar powers our batteries which in turn constantly powers the theatre," said Estian. "This meant we had to change to LED lighting fixtures."
Ten years ago, the theatre ran on a PC based software control system and then reached a point where they had to finalize an upgrade. "We constantly have productions in the theatre, and repeatedly grandMA consoles are hired in to run the shows. We started looking at consoles. Then we went back to our roots to see what we were trying to achieve. We knew the grandMA3 would meet technical riders, and as a result, is already booked out to go on The Voice for eight weeks, to be operated by Joshua Cutts and Andre Siebrits."
The grandMA3 has been set up over ArtNet, running into the controller. Fibre runs all the way down to the stage where it breaks out into nodes which is all run through DMXking ArtNet.
"It's quite easy especially now as we don't have to physically run DMX lines to the back," commented Mduduzi "The upgrade from PC bases has simplified the workflow. Now it's more about getting to know the technicalities and how to operate in depth."
Estian and Mduduzi have also enrolled on the MA e-learning platform. "It's phenomenal," said Estian. "I'm considering going for extensive training on the console because I've found a love for it and the online course has helped so much. A big shout out also goes to DWR's Duncan Riley, Jannie de Jager, Bruce Riley and Robert Izzett. They have really made the experience amazing and the customer support has been really good."
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\section{Introduction}\label{sec:intro}
\vspace{-0.2em}
Named Entity Recognition (NER) is an
NLP task that involves identifying key entities in text such as person, location, time or organisation. Research around NER has grown rapidly with the adoption of deep learning techniques and has been an integral step to many NLP pipelines \citep{sun2018overview} such as information retrieval, knowledge base completion, and question answering. As NER models have matured to involve deep Transformer \citep{vaswani2017attention} models and achieve greater performance, the demand for more human labelled strong data has followed. This has become a common bottleneck as attaining more strongly labelled data is expensive and time consuming.
\begin{figure}
\centering
\includegraphics[width=0.96\linewidth]{figures/weak_strong_ner_main_fig_v2.pdf}
\caption{We consider a realistic setup, combining machine-generated noisy weak labels and a small amount of human-generated strong labels for tackling NER in an emerging domain. \scriptsize{(Real name replaced with a fictitious name: \url{https://en.wikipedia.org/wiki/John_Doe}.)}}
\label{fig:main_fig}
\vspace{-1.5em}
\end{figure}
To work around the limited amount of strongly labelled data, many have experimented with using lower quality weak data generated by weakly supervised methods. Popular techniques to generate weak data include using knowledge bases and heuristic rule based methods while leveraging multiple sources \citep{multilabel, multibert, labeltool}. All techniques can be applied to any suitable text allowing the methods to generate weak data for any topic. Generating weak labels is especially promising for the medical domain where labelling may require experts to accurately label text and common vocabulary is constantly evolving as seen due to the COVID-19 pandemic. COVID-19 is thus a perfect real-world use case for weakly supervised models.
\begin{figure*}[t]
\centering
\includegraphics[width=0.8\textwidth]{figures/modelsfinal.png}
\caption{\textsc{Controster}\xspace: a double-backboned weak-strong data finetuning architecture.}
\label{fig:modelarchs}
\vspace{-1.3em}
\end{figure*}
However, weakly supervised methods are mostly tested on general-domain datasets rather than an emerging domain or topic.
The inability of current state-of-the-art NER models to perform when given new biomedical topics such as COVID-19 preprints has been previously stated as a major gap in current NER applications \citep{arenotready}.
This was explained by a propensity for models to overfit to currently available training data and a lack of data in the target domain for models to learn such a complex emerging topic like COVID-19. We bridge this gap by proposing a domain-specific NER dataset called \textsc{CovidNews-NER}\xspace to evaluate these weakly supervised methods and providing suggestions of combining weak and strong data to address this issue (for a real example of weak and strong labels, see \Cref{fig:main_fig}). We expect that the data we publish will drive research around techniques to better adapt to new topics and the strong data we publish to unlock NER applications about COVID-19 and in the medical domain. We plan for our paper to specifically contribute to the relaunched and currently being improved ontology-based text mining tool BioCaster \citep{biocaster2021} for automatic monitoring and surveillance of disease outbreaks.
For our analysis of mixing weak and strong data, we build upon the recent weakly labelled NER model RoSTER \citep{Roster}. The model uses a noise robust loss function with noisy label removal, ensemble training and self training without the use of strong data to achieve best performance out of other distantly labelled methods.
We propose \textsc{Controster}\xspace, which improves upon RoSTER by performing cross-domain transfer learning over 3 training stages: The first two stages progressively train the model on out-of-domain and in-domain weak data; Afterwards, we finetune the model on in-domain strong data in the last stage (\Cref{fig:modelarchs}).
To summarise, this paper has the following contributions: \textbf{(1)} We propose a novel COVID-19 NER dataset with 13000 weakly labelled sentences generated by rule based methods and 3000 manually annotated sentences. To our knowledge, this is the first COVID-19 orientated NER dataset in English.
\textbf{(2)} We experiment with the data and provide insight into the effect from training with weak and strong data individually and when combined. \textbf{(3)} We propose \textsc{Controster}\xspace, a cross-domain continual training framework, to best leverage strong data and multi-source weak data, and achieve state-of-the-art performance on \textsc{CovidNews-NER}\xspace.
\section{Dataset: \textsc{CovidNews-NER}\xspace} \label{sec:dataset}
\vspace{-0.2em}
\paragraph{Data generation and filtering.}
The data consists of 13000 sentences gathered and weakly labelled using the BioCaster ontology-based text mining tool \citep{biocaster} with 3000 of the sentences also being manually annotated. BioCaster first generated the text for the dataset by scraping news articles from multiple local news providers and RSS feeds covering pandemic related topics between approximately January to August 2021. Once BioCaster collected sentences from its news sources, the entries were passed through a text classifer to further refine that selections were oriented towards disease outbreaks \citep{conway2009classifying}. The classifer selected was recently updated to use the pretrained PubMedBERT \citep{gu2021domain} as a backbone classifier with further finetuning on a binary document classification dataset made of alternating pandemic and normal type news. BioCaster generated part of the dataset from native English texts with additional entries translated from French, Indonesian and Mandarin to English using Language Weaver's Edge MT engine\footnote{\url{https://www.rws.com/language-weaver/edge/}}. The system finally filtered entries by removing entries from duplicate sources from the randomly sampled variety of articles chosen during selection. The weak labels of the dataset were then generated using BioCaster's rule-based method \citep{collier-etal-2010-ontology}. The method is made up of regular expression patterns in simple rule language (SRL), a tool built on top of DIAL \citep{dial}.
To ensure a high quality of final dataset entries, multiple filtering methods were implemented after this procedure to further prune text with errors. All candidate text was filtered out based on insufficient text lengths, non-ASCII characters involved and text duplicates. Additionally, texts were pruned based on number of grammatical mistakes per entry and finally through manual examination. Manually annotated strong data was labelled by a recent graduate working in the NLP domain. Challenging entries such as differentiating between virus and disease entities were flagged and resolved by discussion with a PhD student and Professor who served as experts in the biomedical NLP domain.\footnote{See \Cref{sec:data_filtering_details} for more details.}
\vspace{-0.6em}
\paragraph{Dataset entities and content.}
We employ 10 entity types: \texttt{Animal}, \texttt{Bacterium}, \texttt{Disease}, \texttt{Location}, \texttt{Organisation}, \texttt{Person}, \texttt{Product}, \texttt{Symptom}, \texttt{Time}, \texttt{Virus}.\footnote{See \Cref{sec:entity_defs} for definitions of the entity types.} The \texttt{Person} entity has been expanded to label human cases of a disease as a group of people and the \texttt{Product} entity refers to manufactured articles in the medical domain used during the COVID-19 pandemic (eg. vaccines, face masks). The \texttt{Virus} entity is an especially useful common emerging label since the neighbouring text referencing COVID-19 changes whether it is a \texttt{Virus} or \texttt{Disease}, a common mislabel in weak data. In addition to this, the context developed as a result of the COVID-19 pandemic has produced emerging entities that current rule or knowledge-based labelling systems do not capture. These are however clear to the general public and human annotators which we demonstrate through examples found in \mbox{\textsc{CovidNews-NER}\xspace} in \mbox{\Cref{fig:additional_fig}}. Because the dataset has a heavy focus on the COVID-19 virus, new terminology is also featured surrounding vaccination, testing, variants, etc. Other viruses that gained exposure to the public due to the pandemic are also included in the dataset such as the Zika virus, MERS coronavirus and influenza virus. In general, emerging entities and unique text make \mbox{\textsc{CovidNews-NER}\xspace} tailored to pandemics and the medical domain while still providing some useful entities for general NER applications.
\vspace{-0.6em}
\paragraph{Inter-Annotator Agreement (IAA).}
To demonstrate the quality of the strong data when compared to the weak data we preform an inter-annotator agreement test. The method of Cohen's Kappa for inter-annotator agreement has been considered inaccurate for NER due to the task not having negative cases to fulfil the methods calculation \mbox{\citep{inter_ref}}. In our case, we recruited four additional validators with relevant background to re-annotate 100 randomly selected entries from our dataset. Annotators were given a comprehensive guideline on the labelling strategy and spent on average 90 minutes to read the guideline and complete the labels. We then computed pairwise F1 scores between each of the annotators and the original human annotated 100 strong labels from the dataset. We show this score along with the annotators score when compared to the weak data and the original strong data when compared to the weak data in \mbox{\Cref{tab:intertable}}. The human-labelled strong data has shown high agreement with the validators' labels, achieving >90\% F1 score, demonstrating that the human labelled strong data have high quality.
\begin{table}[htb]
\centering
\small
\begin{tabular}{lcc}
\toprule
\textbf{Test} & \textbf{F1} & \textbf{Std. Dev}\\
\midrule
Strong vs Weak & 46.2 & - \\
Weak vs Validators & 49.8 & 2.35 \\
Strong vs Validators & 92.3 & 3.08 \\
\bottomrule
\end{tabular}
\caption{\label{tab:intertable} Dataset Inter-Annotator Agreement}
\vspace{-0.1cm}
\end{table}
\paragraph{Data statistics.}
\Cref{tab:datasetstats} summarises multiple metrics that describe the \textsc{CovidNews-NER}\xspace dataset. Of the 13000 weak data entries, 3000 of the same text have been manually annotated to provide the parallel strong labels with the equivalent 3000 weak labels also evaluated for fair comparison. We provide the total number of words, labelled words and entities for both strong and weak data. There is a noticeable difference in entity length with the average number of words in an entity being 1.489 and 1.890 for the respective 3000 weak and strong data entries. Longer entities are more challenging to fully label and explains how the weak labelling scheme tends to produce shorter labelled entities. This is especially noticable in types \texttt{Organisation} and \texttt{Bacterium} seen in \Cref{tab:weakdataperf} where weak data is evaluated directly against strong data. The weak data also had a lower number of entities per entry than the strong data which infers that the weak labelling scheme misses more ambiguous entities and that it is in general under labelled. We provide more analysis on weak vs. strong data in \Cref{sec:weak_against_strong} and data split generation in \Cref{sec:data_split}.
\begin{table}
\centering
\small
\scalebox{0.92}{
\begin{tabular}{lrrr}
\toprule
\textbf{Metric} & \textbf{Weak} & \textbf{Weak-3k} & \textbf{Strong} \\
\midrule
Total Entries (Sentences) & 13000 & 3000 & 3000 \\
Total Words & 349913 & 80539 & 80539 \\
Total Labelled Words & 42692 & 9327 & 14786 \\
Total Entities & 28431 & 6263 & 7823 \\
Mean Entity Length & 1.50 & 1.50 & 1.89 \\
Percent Labelled Words & 12.2\% & 11.6\% & 18.4\% \\
Mean Entities Per Entry & 2.19 & 2.09 & 2.61 \\
\bottomrule
\end{tabular}
}
\caption{\label{tab:datasetstats} Generic statistics of \textsc{CovidNews-NER}\xspace}
\vspace{-0.4cm}
\end{table}
\section{Model} \label{sec:model}
\vspace{-0.2em}
We build upon RoSTER \citep{Roster} which achieves the best performance among distantly-supervised methods. The model contains multiple stages to handle the weak data and its inherent noise. Starting with RoBERTa \citep{liu2019roberta} weights, the first step is noise robust training using generalised cross entropy ($\mathcal{L}_{\text{GCE}}$) with tunable parameters dictating noise robustness and noisy label removal. The second step uses ensemble training to improve model stability and the third step introduces contextualised augmentations and self-training with pre-trained RoBERTa embeddings.\footnote{See \Cref{sec:roster_details} for details of RoSTER.}
\vspace{-0.5em}
\paragraph{\textsc{Controster}\xspace: \underline{Cont}inually-learned \underline{RoSTER}.}
While RoSTER achieves strong performance on noisy data, it remains unclear what is the optimal strategy when both strong and weak data are presented. Additionally, in a real-world use case, we can also assume access to weak labels in other domains. We propose a continual learning approach called \textsc{Controster}\xspace to adapt RoSTER for learning from out of domain weak data and in domain weak and strong data (\Cref{fig:modelarchs} represents the fine-tuning pipeline). The pipeline has three training stages: \textbf{(1)} We initially train a RoSTER model on out-of-domain weak data (grey box in \Cref{fig:modelarchs}). The out-of-domain data are from weak labels generated onto the Wikigold or OntoNotes dataset via knowledge bases (details explained in \Cref{sec:compared_models}). \textbf{(2)} Then we repeat RoSTER training on in-domain COVIDNews weak data (yellow box) and \textbf{(3)} finally finetuning on strong data with only the noise-robust loss.
\section{Experiments}\label{sec:exp}
\vspace{-0.2em}
\paragraph{Compared models.}\label{sec:compared_models} We train four models and evaluate them on the \textsc{CovidNews-NER}\xspace test set.
\textbf{(1)} We train the original RoSTER model with no backbone (initialised with original RoBERTa weights) on strong data. As the data are clean, the model is only trained with the noise robust loss with ensemble learning and self-training stages removed.
\textbf{(2)} We train the model on 6000 lines of weak COVIDNews data (this creates a weak COVIDNews backbone) and then finetune on strong COVIDNews data the same as (1). \textbf{(3)} \& \textbf{(4)} In the double backbone approach (i.e., our full \textsc{Controster}\xspace model), we first train RoSTER on either the weak labels from the Wikigold dataset \citep{wikigold} or the OntoNotes5.0 dataset \citep{onto} followed by training on weak COVIDNews data and finally fine-tuning on strong COVIDNews data. This approach is visualised in \mbox{\Cref{fig:modelarchs}} in which \textbf{(1)} is made up of only the \texttt{Strong COVIDNews} box and \textbf{(2)} is made up of the \texttt{Weak COVIDNews} and \texttt{Strong COVIDNews} boxes. The Wikigold dataset contains 13041 lines of training data and 3 overlapping entity categories with COVIDNews out of 4 total entity categories. The OntoNotes5.0 dataset contains 59924 lines of training data and 5 overlapping entity categories with COVIDNews out of 18 total entity categories\footnote{Wikigold/OntoNotes weak data are from \citet{Roster}.}.
\vspace{-0.5em}
\paragraph{Main results.}\label{sec:main_res}
\Cref{fig:multidata} shows the four model's F1-score performance.\footnote{Precision \& Recall follow the same trend (see \Cref{tab:multidata}).} The double backbone approach, i.e. \textsc{Controster}\xspace, performs best for all quantities of strong data used for finetuning. Additionally, using a weak COVIDNews backbone performs noticeably better than the baseline without a backbone for all four amounts of finetuning strong data. The improvement in performance with using either a single or double backbone approach is greatest for experiments with 100 and 500 entries of strong data when compared to using 1000 or 2100. An example of this can be seen by looking at the improvement of 11.0 in F1 score (56.7 to 66.7) when the weak Wiki+COV. backbone was paired with 100 entries of strong data in comparison to an increase of 2.2 in F1 score (74.6 to 76.8) in the same scenario when 2100 entries of strong data were used.
\begin{figure}[htb]
\centering
\includegraphics[width=\linewidth]{figures/different_backbone_strong_data_v5.png}
\caption{Main weak and strong data results. When using different number of strong data points, having the COVIDNews backbone (COV.) has always helped. Adding the Wiki/Onto backbone on top of COV. has also almost universally helped.}
\label{fig:multidata}
\vspace{-1.2em}
\end{figure}
These findings support the use of combining weak data with strong data through the method of transfer learning for research and NER applications. We provide insight into the amounts of strong data necessary for effective combination of the two types of data. We recommend using a weak data generated backbone in general NER models with the potential for profound impact in few-shot learning models that have a limited number of strong data. Similarly, in scenarios where only weak data is available we advise manually annotating a minimum of 100 sentences can lead to large improvements in NER model performance.
\begin{figure}[htb]
\centering
\vspace{-0.1cm}
\includegraphics[width=0.8\linewidth]{figures/different_weak_data_roster.png}
\vspace{-0.2em}
\caption{Weak data performance of RoSTER.}
\label{fig:indivdata}
\vspace{-1.3em}
\end{figure}
\vspace{-0.5em}
\paragraph{Weak data study.}\label{sec:weak_data_study}
We investigate the magnitude of weak data for the models trained to be effective on the \textsc{CovidNews-NER}\xspace dataset.
\Cref{fig:indivdata} shows the improvement in precision, recall and F1 scores as weak data scales with the RoSTER model. After surpassing the 6k entry mark, the weak data saturates and does not lead to improved performance for each additional entry. Alternatively, the strong data in \Cref{tab:multidata} demonstrates how the higher quality strong labels continue to scale with additional data. Varying amounts of weak data were also evaluated for the COVIDNews backbone prior to finetuning on strong data. \Cref{tab:combineddata} in Appendix shows tests with 2000, 6000 and 10000 weak entries paired with 100, 500, 1000 and 2100 strong entries. Although using a weak data backbone was clearly beneficial, the amount of weak data to train the backbone was fairly insignificant.
\section{Further Discussion} \label{sec:furthur_discussion}
\vspace{-0.3em}
\paragraph{Combining weak \& strong data.}
We believe a wide and deep strategy should be used when combining weak \& strong data. This means training on weak data to embed the model with an expansive breadth of knowledge over all entities and then fine-tuning on strong data to overwrite noise in the weak data and generate more sophisticated ability in NER. We suggest two avenues for further research to maximise utility of weak data when paired with strong data. An improvement in noise reduction techniques via improved loss functions or model architecture will serve beneficial in allowing model performance to continue to scale with increases in weak data. Additionally, investigation into how weak data generated from specific rules saturates individually and after fine-tuning with strong data will also lead to improved knowledge on mixing the different forms of labels.
\vspace{-0.6em}
\paragraph{Out-of-domain weak data.}
We observed that using the two stage backbone pipeline of first training on a different NER dataset and then following through with training on \textsc{CovidNews-NER}\xspace weak and strong data led to a further improvement in performance across varying \textsc{CovidNews-NER}\xspace weak and strong data lengths. Even though the Wikigold dataset had only three overlapping entity categories with \textsc{CovidNews-NER}\xspace and OntoNotes5.0, the performance still improved in part due to the overlapping categories being the prominent ones in \textsc{CovidNews-NER}\xspace (eg. organisation, person, location, date). The additional variety of labels in the crossover entities led to improved precision, recall and F1 scores in those categories and overall scores. We implore future works to evaluate the impact of overlapping and non-overlapping categories from cross-domain weak data backbones while considering overlapping category definition similarities and differences. Overall, similar to how \citet{multibert} determined the importance of using multiple sources for text to be distantly labelled, we conclude it is also beneficial to use different weak labelling techniques to create a diverse collection of weak data. We implore future work to investigate the diversity necessary for optimal combination of weak data from different sources.
In Appendix, we include a dedicated related work section (\Cref{sec:RW}) for interested readers.
\vspace{-0.1em}
\section{Conclusion}
\vspace{-0.3em}
We presented \textsc{CovidNews-NER}\xspace, an English COVID-19 Named Entity Recognition dataset in the pandemic news domain, addressing current NER models' lack of ability to tackle new and out-of-domain topics.
We labelled 13000 entries using a rule-based system to generate weak labels and 3000 entries using hand annotation to generate strong labels.
We further proposed a continual learning approach called \textsc{Controster}\xspace that transfers knowledge learned in both out-of-domain and in-domain weak data. After finetuning on strong in-domain data, \textsc{Controster}\xspace achieved state-of-the-art performance on our proposed dataset. We further provide detailed and thorough analysis into how to successfully combine both types of data and suggest promising avenues for future research. We think that the dataset we provide and the findings we conclude will be beneficial to other NER applications, such as improving the evaluation and ability of the BioCaster pandemic surveilling tool. We hope that our work drives more research in leveraging a combination of weak and strong data to improve performance on new topics such as the COVID-19 pandemic.
\section{More Dataset Details}\label{sec:data_details}
\subsection{Data Generation and Filtering Details}\label{sec:data_filtering_details}
The text used in the dataset and the corresponding manually annotated strong labels had some deviation in metrics depending on the original language translated from. Additional statistics of the dataset for each text language origin can be seen in \Cref{tab:extralanguagemetrics}. The metrics suggest that Mandarin was an especially useful and unique language to generate data from as it introduced many longer entities due to person titles and location addresses being more verbose. Other languages like French introduced text with fewer entities per sentence than others.
\begin{table}[htb]
\centering
\small
\scalebox{0.8}{
\begin{tabular}{lrrrrr}
\toprule
\textbf{Metric} & \textbf{Total} & \textbf{Eng.} & \textbf{Fre.} & \textbf{Ind.} & \textbf{Man.} \\
\midrule
Total Entries & 3000 & 1500 & 505 & 500 & 495 \\
Mean Entity Length & 1.89 & 1.79 & 1.80 & 1.68 & 2.46 \\
Percent Labelled Words & 18.4\% & 17.5\% & 15.4\% & 18.9\% & 22.9\% \\
Mean Entities Per Entry & 2.61 & 2.71 & 2.09 & 2.70 & 2.74 \\
\bottomrule
\end{tabular}
}
\caption{\label{tab:extralanguagemetrics} Generic statistics of \textsc{CovidNews-NER}\xspace strong data separated by language}
\end{table}
For filtering, texts that were less than 4 words, less than 15 characters or greater than 500 characters were removed. Duplicate sentences were also filtered out and poorly structured entries were identified using the LanguageTool grammar checking API\footnote{\url{https://languagetool.org/}}. This checked and removed entries with grammar, punctuation and syntactical mistakes.
\subsection{Entity Definitions}\label{sec:entity_defs}
The exact definitions of the 10 entity types included in \textsc{CovidNews-NER}\xspace can be found in \Cref{tab:entitydefs}.
\begin{table*}
\small
\centering
\begin{tabular}{rl}
\toprule
\textbf{Entity Type} & \textbf{Definition} \\
\midrule
\texttt{Animal} & Multi-cell organisms that are eukaryotes of the kingdom Animalia, other than humans. \\
\texttt{Bacterium} & Single-celled prokaryotic microorganisms of the bacteria domain. \\
\texttt{Disease} & A disorder of a structure or function that affects an organism, associated with specific phenotypes. \\
\texttt{Location} & A politically or geographically defined location for example a region, a province, a town. \\
\texttt{Organisation} & Named corporate, governmental, or other organisational entity. \\
\texttt{Person} & A person or group of persons. \\
\texttt{Product} & Medical articles or substances manufactured and used throughout pandemics. \\
\texttt{Symptom} & Phenotypic descriptions of any abnormal morphology, physiology or behaviour. \\
\texttt{Time} & Temporal expressions that can be anchored on a timeline. \\
\texttt{Virus} & A disease causing infectious agent that is non-living. \\
\bottomrule
\end{tabular}
\caption{\label{tab:entitydefs} Entity Type Definitions}
\vspace{-0.2cm}
\end{table*}
\subsection{Weak vs. Strong Data}\label{sec:weak_against_strong}
\begin{table}[t]
\centering
\small
\begin{tabular}{lcc}
\toprule
\textbf{Entity Type} & Strong & Weak \\
\midrule
\texttt{Animal} & 177 & 201 \\
\texttt{Bacterium} & 25 & 12 \\
\texttt{Disease} & 641 & 612 \\
\texttt{Location} & 1703 & 1568 \\
\texttt{Organisation} & 1076 & 270\\
\texttt{Person} & 2652 & 2370 \\
\texttt{Product} & 233 & 203 \\
\texttt{Symptom} & 121 & 146 \\
\texttt{Time} & 799 & 697 \\
\texttt{Virus} & 396 & 184 \\
\midrule
Total & 7823 & 6263 \\
\bottomrule
\end{tabular}
\caption{Entity counts in \textsc{CovidNews-NER}\xspace}
\vspace{-0.7cm}
\label{tab:entity_stats}
\end{table}
We further investigate the differences in performance and style between the rule based weak data generation method and human annotated strong data.
\Cref{tab:entity_stats} shows the difference in entity count for each category between the two types of data. \texttt{Organisation} is noticeably out numbered in the strong data case which can be explained by the category requiring more in depth understanding of contextual knowledge as that can change it being classified as a \texttt{Location} or \texttt{Organisation} (eg. ``The White House'').
Another notable difference is that larger groups of words are categorised as entities in the strong labels when compared to the weak. The strong data contains 2.5 times more entities containing greater than three words due to the difficulty in labelling longer entities.
The \texttt{Symptom}, \texttt{Disease} and \texttt{Virus} entity categories in the dataset significantly orient the dataset towards the COVID-19 pandemic. The difference between the three categories are challenging to distinguish, examples of which are shown in \Cref{fig:additional_fig}. \Cref{tab:weakdataperf} shows a detailed breakdown of the performance of weak data when evaluated directly against strong data and \Cref{tab:langaugeperf} shows the performance across the different languages the text was translated from.
\begin{table}[t]
\centering
\small
\begin{tabular}{llllr}
\toprule
\textbf{Entity Type} & \textbf{Pre.} & \textbf{Rec.} & \textbf{F1} & \textbf{Support} \\
\midrule
\texttt{Animal} & 62.2 & 70.6 & 66.1 & 177 \\
\texttt{Bacterium} & 33.3 & 16.0 & 21.6 & 25 \\
\texttt{Disease} & 66.2 & 63.2 & 64.6 & 641 \\
\texttt{Location} & 57.0 & 52.4 & 54.6 & 1703 \\
\texttt{Organisation} & 33.3 & 8.4 & 13.4 & 1076 \\
\texttt{Person} & 46.7 & 41.7 & 44.0 & 2652 \\
\texttt{Product} & 63.1 & 54.9 & 58.7 & 233 \\
\texttt{Symptom} & 46.6 & 56.2 & 50.9 & 121 \\
\texttt{Time} & 68.4 & 59.7 & 63.8 & 799 \\
\texttt{Virus} & 49.5 & 23.0 & 31.4 & 396 \\
\midrule
Weighted Avg & 51.8 & 43.3 & 46.2 & 7823 \\
\bottomrule
\end{tabular}
\caption{\label{tab:weakdataperf} Weak Data Performance}
\vspace{-0.2cm}
\end{table}
\begin{figure*}[t]
\centering
\includegraphics[width=\linewidth]{figures/additional_examplesv3.png}
\caption{Additional examples from the \textsc{CovidNews-NER}\xspace dataset}
\label{fig:additional_fig}
\vspace{-0.2cm}
\end{figure*}
\begin{table}[t]
\centering
\small
\begin{tabular}{llllr}
\toprule
\textbf{Entry Language} & \textbf{Entries} & \textbf{Pre.} & \textbf{Rec.} & \textbf{F1} \\
\midrule
Combined & 3000 & 59.4 & 44.3 & 49.7 \\
English & 1500 & 60.3 & 41.0 & 47.5 \\
French & 505 & 62.3 & 53.3 & 56.5 \\
Indonesian & 500 & 62.6 & 49.4 & 54.1 \\
Mandarin & 495 & 53.9 & 42.6 & 46.1 \\
\bottomrule
\end{tabular}
\caption{\label{tab:langaugeperf} Weak Data Performance Across Languages}
\vspace{-0.5cm}
\end{table}
\subsection{Data Split}\label{sec:data_split}
To best split the data into training, validation and test sets, a unique Monte Carlo technique was implemented to insure entities with limited labels such as \texttt{Bacterium} were allocated in proper amounts to each partition. An optimal distribution of all entities was generated and 10000 random iterations of the input data was split and scored based on fractional proximity to the optimal distribution. The split dataset partitions had 2100/300/600 entries in train, validation and test sets respectively.
\section{RoSTER Details}\label{sec:roster_details}
\vspace{-0.5cm}
Here we explain the RoSTER methodology in greater detail. The first stage is known as the noise-robust learning stage and introduces two hyperparameters for adjusting to noisy labels. \citep{Roster} uncovers that cross entropy loss is useful for model convergence but is sensitive to noise while mean absolute error (MAE) loss is robust to noise at the cost of convergence. The generalised cross entropy loss uses a \emph{q} parameter to adjust cross entropy towards CE loss by lowering and towards MAE loss by raising. A thersholding parameter is introduced to remove incorrect labels during the training process. The parameter $\uptau$ is used as a threshold for comparing model predictions with distant labels. If there are differences between model predictions and distant labels greater than the threshold, the model omits those labels when updating weights.
\vspace{0.5cm}
\begin{equation}
\mathcal{L}_{\text{GCE}} = \sum_{i=1}^{n} w_{i}\frac{1-f_{i,y_{i}}(x;\theta)^{q}}{q}
\end{equation}
RoSTER also implements ensemble and self training stages to improve results on distantly labelled data. The ensemble stage uses a \emph{K} parameter to determine the number of models trained using different seeds and a final model is employed to approximate the performance of trained models by minimising Kullback–Leibler (KL) divergence loss. Prior to self-training, contextualised augmentations are generated using PLM's like RoBERTa. Then the model trains on an unlabelled version of the corpus to leverage knowledge embedded in the selected PLM while generalising model predictions to tokens removed by noisy label removal. Self-training is done by polarising predictions during iterations by squaring high-confidence predictions and normalising low-confidence predictions.
\section{More Experimental Details}\label{sec:more_exp_details}
\paragraph{Weak-strong main results full table (\Cref{tab:multidata}).} In the main text we showed performance of \textsc{Controster}\xspace and its ablated versions' in \Cref{fig:multidata}. Here, we provide a more detailed view of the same data, listing also Precision and Recall scores in \Cref{tab:multidata}.
\begin{table}[htb]
\centering
\small
\begin{tabular}{lclll}
\toprule
\textbf{W. Backbone} & \textbf{S. Tuning} & \textbf{Pre.} & \textbf{Rec.} & \textbf{F1} \\
\midrule
None & 100 & 50.9 & 65.2 & 56.7 \\
COV. & 100 & 59.9 & 71.7 & 65.2 \\
Wiki. + COV. & 100 & \textbf{62.1} & \textbf{72.5} & \textbf{66.7} \\
Onto. + COV. & 100 & 60.2 & 69.9 & 64.6 \\
\midrule
None & 500 & 62.8 & 73.0 & 67.3 \\
COV. & 500 & 66.3 & 73.9 & 69.7 \\
Wiki. + COV. & 500 & 68.0 & 75.7 & 71.6 \\
Onto. + COV. & 500 & \textbf{68.5} & \textbf{76.7} & \textbf{72.2} \\
\midrule
None & 1000 & 66.7 & 75.8 & 70.9 \\
COV. & 1000 & 69.1 & 76.1 & 72.3 \\
Wiki. + COV. & 1000 & 69.6 & 76.6 & 72.8 \\
Onto. + COV. & 1000 & \textbf{70.2} & \textbf{77.3} & \textbf{73.5} \\
\midrule
None & 2100 & 71.7 & 77.9 & 74.6 \\
COV. & 2100 & 72.9 & 78.2 & 75.4 \\
Wiki. + COV. & 2100 & 73.9 & \textbf{79.9} & 76.7 \\
Onto. + COV. & 2100 & \textbf{74.2} & 79.7 & \textbf{76.8} \\
\bottomrule
\end{tabular}
\caption{\label{tab:multidata} Main weak and strong data results
}
\vspace{-0.5cm}
\end{table}
\paragraph{Weak backbone saturation data (\Cref{tab:indivdata}).} Since we have an in-domain rule-based weak labeller, why not generate as much in-domain weak data as possible? As mentioned in the main text \Cref{fig:indivdata}, we found that in-domain weak data only helps up to a certain point. Here we list the exact precision, recall and F1 results used for plotting the figure of reference in the main text (\Cref{tab:indivdata}).
\begin{table}[htb]
\centering
\small
\begin{tabular}{llll}
\toprule
\textbf{Weak Data} & \textbf{Pre.} & \textbf{Rec.} & \textbf{F1} \\
\midrule
1000 entries & 46.4 & \textbf{52.7} & 47.7 \\
2000 entries & 47.1 & 52.4 & 48.7 \\
4000 entries & 48.9 & 52.4 & 49.8 \\
6000 entries & \textbf{52.2} & 52.2 & \textbf{51.2} \\
10000 entries & 51.8 & 50.5 & 50.3 \\
13000 entries & 49.7 & 49.4 & 48.7 \\
\bottomrule
\end{tabular}
\caption{\label{tab:indivdata} Performance of RoSTER when varying number of weak data }
\vspace{-0.5cm}
\end{table}
\paragraph{Weak data study (\Cref{sec:weak_data_study}) full table (\Cref{tab:combineddata}).} In the main text we discussed varying amounts of weak data when pretraining on \textsc{CovidNews-NER}\xspace. Here we attach the full table (\Cref{tab:combineddata}) for reference.
\begin{table}[htb]
\centering
\small
\begin{tabular}{lclll}
\toprule
\textbf{W. Backbone} & \textbf{S. Tuning} & \textbf{Pre.} & \textbf{Rec.} & \textbf{F1} \\
\midrule
None & 100 & 50.9 & 65.2 & 56.7 \\
Weak 2000 & 100 & 59.9 & 69.2 & 64.1 \\
Weak 6000 & 100 & 60.4 & 70.6 & 65.0 \\
Weak 10000 & 100 & \textbf{61.5} & \textbf{70.9} & \textbf{65.7} \\
\midrule
None & 500 & 62.8 & 73.0 & 67.3 \\
Weak 2000 & 500 & \textbf{67.1} & 74.2 & \textbf{70.3} \\
Weak 6000 & 500 & 66.3 & 73.9 & 69.7 \\
Weak 10000 & 500 & 66.9 & \textbf{74.3} & 70.2 \\
\midrule
None & 1000 & 66.7 & 75.8 & 70.9 \\
Weak 2000 & 1000 & 69.6 & 76.1 & 72.6 \\
Weak 6000 & 1000 & 69.1 & 76.1 & 72.3 \\
Weak 10000 & 1000 & \textbf{70.2} & \textbf{76.7} & \textbf{73.2} \\
\midrule
None & 2100 & 71.7 & 77.9 & 74.6 \\
Weak 2000 & 2100 & 72.7 & 77.2 & 74.7 \\
Weak 6000 & 2100 & \textbf{72.9} & \textbf{78.2} & \textbf{75.4} \\
Weak 10000 & 2100 & 72.6 & 77.5 & 74.9 \\
\bottomrule
\end{tabular}
\caption{\label{tab:combineddata} Weak data quantities with strong data results
}
\vspace{-0.5cm}
\end{table}
\section{Related Work}\label{sec:RW}
Our work is related to other COVID-19 datasets in the NER domain. \citet{vietcovid} introduced a COVID-19 NER dataset for the low resource language of Vietnamese and \citet{italiancovid} provided a NER dataset based on medical records in Italian. \citet{englishcovid} scraped and annotated COVID-19 related tweets, generating a knowledge base but labelling events (eg. tested positive, can not test) as opposed to entities necessary for NER. Our dataset provides the first COVID-19 NER dataset in English with distantly supervised weak data and human annotated strong data.
Our analysis of combining weak and strong data is related to previous methods which successfully utilise either types of data to improve performance. \citet{bond2020} implemented the use of pre-trained language models with subsequent self-training with weak labels generated through knowledge bases to improve model performance. \citet{Jiang2021} architected a multistage pipeline involving pre-training on unlabelled data, weak label completion, a noise robust loss function and fine tuning on strong data to effectively null the impact of noise. We build upon these works and provide insight into using the two forms of data together in addition to using cross-domain datasets on an emerging topic such as COVID-19.
\section*{Acknowledgements}
We are grateful to RWS Language Weaver for use of their neural MT engine. We also thank Qianchu Liu, Parth Shah, Chandni Bhatt and Marko Popovic for contributing to the inter-annotator agreement.
\section*{Limitations}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,408 |
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,981 |
Link Global Management can provide a full range of payroll services in Finland. The individual will be engaged on our payroll and income is paid in the form of salary, allowances and expenses, the proportion of each part depending on individual circumstances.
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Income is managed tax efficiently, not just in Finland but also in any other country where there may be a liability. A tax return is filed each year in Finland with advice and assistance from Link Global Management who will also provide help with filing tax returns elsewhere, if required.
Individuals resident in Finland are taxed on their worldwide income. However, salary earned abroad is exempt from tax in Finland if a Finnish resident works abroad continuously for at least six months and satisfies certain other requirements. Nonresident individuals are subject to income tax on income from Finnish sources only.
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In the case of emigration, foreign citizens become nonresidents for Finnish tax purposes at the time they leave the country and surrender their permanent home in Finland. With respect to a Finnish citizen, he or she is still considered to be resident in Finland until three years have passed from the end of the year when the individual left the country, unless he or she can establish that no essential connections with Finland have been maintained.
Under a special expatriate tax regime, qualifying expatriates may elect to be taxed on their salary income at a rate of 35% for a period of up to 48 months, instead of at the normal progressive income tax rates.
Thinking of contracting in Finland? | {
"redpajama_set_name": "RedPajamaC4"
} | 33 |
import {AsyncStorage} from '../jobPersistence'
import {AsyncStorage as AsyncStorageReactNative} from 'react-native'
export default (
asyncStorage: AsyncStorageReactNative
): AsyncStorage => {
const serializeItem = (item: any) => {
if (typeof item === 'object') {
return JSON.stringify(item)
} else {
return item + ''
}
}
// public
async function getItem(key: string) {
const serializedData = <string> await asyncStorage.getItem(key)
try {
return JSON.parse(serializedData)
} catch (e) {
return parseInt(serializedData) || serializedData
}
}
// public
async function setItem(key: string, value: any) {
asyncStorage.setItem(key, serializeItem(value))
}
// public
async function multiSet(keyValuePairs: {key: string, value: any}[]) {
if (keyValuePairs.length === 0) return;
const pairsAsArray = keyValuePairs.map(({key, value}) => [key, serializeItem(value)])
await asyncStorage.multiSet(pairsAsArray)
}
// public
async function multiRemove(keys: string[]) {
if (keys.length === 0) return;
await asyncStorage.multiRemove(keys)
}
return {
removeItem: asyncStorage.removeItem,
multiRemove,
getItem,
setItem,
multiSet
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 8,645 |
package com.sdl.selenium.extjs6.panel;
import com.sdl.selenium.web.SearchType;
import com.sdl.selenium.web.WebLocator;
import org.testng.annotations.DataProvider;
import org.testng.annotations.Test;
import static org.hamcrest.MatcherAssert.assertThat;
import static org.hamcrest.Matchers.equalTo;
public class PanelTest {
private static final WebLocator container = new WebLocator("container");
private static final WebLocator title = new WebLocator().setClasses("x-title").setText("Title");
@DataProvider
public static Object[][] testConstructorPathDataProvider() {
return new Object[][]{
{new Panel(), "//*[contains(concat(' ', @class, ' '), ' x-panel ')]"},
{new Panel(new Panel()), "//*[contains(concat(' ', @class, ' '), ' x-panel ')]//*[contains(concat(' ', @class, ' '), ' x-panel ')]"},
{new Panel(container), "//*[contains(concat(' ', @class, ' '), ' container ')]//*[contains(concat(' ', @class, ' '), ' x-panel ')]"},
{new Panel(container, "PanelTest"), "//*[contains(concat(' ', @class, ' '), ' container ')]//*[contains(concat(' ', @class, ' '), ' x-panel ') and count(./*[contains(concat(' ', @class, ' '), ' x-panel-header ')]//*[contains(concat(' ', @class, ' '), ' x-title ')]//*[text()='PanelTest']) > 0]"},
{new Panel().setTemplateTitle(title), "//*[contains(concat(' ', @class, ' '), ' x-panel ') and count(.//*[contains(concat(' ', @class, ' '), ' x-title ') and contains(text(),'Title')]) > 0]"},
{new Panel().setTemplateTitle(title).setSearchTitleType(SearchType.EQUALS), "//*[contains(concat(' ', @class, ' '), ' x-panel ') and count(.//*[contains(concat(' ', @class, ' '), ' x-title ') and contains(text(),'Title')]) > 0]"},
{new Panel(null, "TitlePanel").setTemplateTitle(title).setSearchTitleType(SearchType.EQUALS), "//*[contains(concat(' ', @class, ' '), ' x-panel ') and count(.//*[contains(concat(' ', @class, ' '), ' x-title ') and text()='TitlePanel']) > 0]"},
};
}
@Test(dataProvider = "testConstructorPathDataProvider")
public void getPathSelectorCorrectlyFromConstructors(Panel panel, String expectedXpath) {
assertThat(panel.getXPath(), equalTo(expectedXpath));
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,249 |
\section{Introduction}
Deep neural networks have demonstrated their potential to reach human-level performance for image classification, however, their performance generally correlates with the amount of available samples \cite{domingos2012few}. When focusing on rare medical conditions, the limited availability of pathological (positive) training images can cause severe class imbalance that limits the accuracy of these models. In contrast, the collection of normal (negative) cases is often substantially simpler. One example of a pathology that is both of high interest but also rare are bone lesions \cite{franchi2012epidemiology}. The classification of the presence of bone lesion pathology in X-ray images is the subject of our work.
Traditional methods to handle class-imbalance, such as image transformations \citep{hussain2017differential} and different sampling strategies \citep{li2010learning, dubey2014analysis}, are often of limited benefit as they do not address the inherent problem of dealing with a small training set not fully representing the underlying data distribution. Recent works have proposed the use of synthetic data in order to augment and increase diversity in the training set \citep{antoniou2017data, mariani2018bagan}. However, learning to generate high-resolution images from random noise requires an often prohibitively large training dataset.
In this work, we aim to synthesize bone lesions by translating spatially-constrained patches extracted from non-pathological X-ray images rather than generating from scratch. The lesion-generation pipeline is illustrated in \figurename~\ref{pipeline}. The model is trained on patches to ensure localized generation of pathology. A blending approach merges the translated patches back into those full-images. A subset of the generated images is filtered to form the augmented training set by performing pseudo-labelling. We observed non-trivial performance gains in the task of bone lesion detection for individual body parts (humerus, tibia, femur) when trained using this augmented set. We further show that transfer learning can be a viable option to enhance the training set of body parts for which a powerful image-translation model cannot be trained due to insufficient or noisy samples.
\begin{figure}
\includegraphics[width=13cm]{fig/lesion_inference.png}
\centering
\caption{Pipeline of the lesion generation process on non-lesion images. $x_h$ is non-lesion patch; $E_h$, $z$ and $G_l$ are non-lesion encoder, latent representation and lesion generator respectively. $x_{h \rightarrow l}$ is the generated lesion and $x_{h \rightarrow l}^{blended}$ is the result after alpha-blending.}
\label{pipeline}
\end{figure}
\section{Related Work}
Data augmentation is a well-studied problem in machine learning. Employing transformation-based augmentation techniques \citep{rajkomar2017high, kohli2017medical} or transfer learning by using pretrained weights, are common approaches \citep{rajkomar2017high}, which are used in this work as well.
Generative Adversarial Networks (GANs) \citep{goodfellow2014generative} have been used successfully in the medical imaging domain to accomplish tasks such as image translation \citep{wolterink2017deep, nie2017medical}, segmentation \citep{xue2018segan, kamnitsas2017unsupervised} and data augmentation. \citet{shin2018medical} generate brain tumors for data augmentation by translating segmentation masks to multi-parameteric magnetic resonance (MR) images, using a multi-modal dataset with uniform view. \citet{frid2018gan} use a small dataset of regions of interest of liver lesions in CT images to train a DCGAN \citep{radford2015unsupervised} and generate an augmented set. In comparison, our method focuses on generative data augmentation using a small number of high-resolution X-ray images often varying in positional view even within a single body part.
\citet{salehinejad2017generalization} use DCGAN to generate chest X-rays for multiple pathologies. Plausible samples are filtered out by a team of radiologists to create an augmented set. In our work we perform filtering in an automated manner to mine for hard positives. Recent work by \citet{lau2018scargan} generate scars on cardiac MR scans and employ a blending mask to remove unwanted artifacts. To the best of our knowledge, there is no existing literature that addresses the problem of bone lesion classification by automatically generating pathology in normal radiographs to enhance the training set.
\section{Methodology}
\subsection{Unsupervised Image-to-Image Translation Model}
The generation of bone lesions is posed as an unsupervised image to image translation task \cite{liu2017unsupervised}. In this task, $P{\chi_l}(x_l)$ and $P{\chi_h}(x_h)$ are two marginal distributions from which X-ray patches of bones with lesion $x_l$, and non-lesion $x_h$ are drawn respectively. The model maps these samples to a shared latent representation, using encoders for respective distributions: $E_l(x_l) = E_h(x_h) = z \in \mathcal{Z}$. The generators respective to each distribution decode back the input sample from this latent vector: $G_l(z) = x_l, G_h(z) = x_h$. Lesion-like properties are generated in a normal bone X-ray with the following translation operation: $G_l(E_h(x_h)) = x_{h \rightarrow l}$. This framework is based on the assumption that there exists an unknown but finite joint distribution $P_{\chi_l, \chi_h}$, which the shared latent space can learn to represent.
In order to find the optimal hypothesis for this problem, the lesion encoder-generator is a variational autoencoder (VAE) \cite{kingma2013auto}, whose loss function maximizes the Evidence Lower Bound (ELBO) by minimizing the following objective:
\begin{equation}
\mathcal{L}_{\text{\tiny VAE}_l} = \lambda_1\text{KL}(q_l(z_l|x_l)||\mathcal{N}(z|0, I)) - \lambda_2 \mathbb{E}_{z_l \sim q_l(z_l|x_l)}[\log p_{G_l}(x_l|z_l)]
\end{equation}
where $q_l(z_l|x_l)$ is the distribution from which $z_l$ (encoding of $x_l$) is sampled. In the first term, the KL divergence between this distribution and the prior is minimized, which encourages $q_l(z_l|x_l)$ to follow a normal (zero-mean, unit-covariance) distribution. The second term aims to maximize the log-likelihood of $p_G$. The same formulation is followed to train a second VAE for normal, non-lesion samples. This would ensure each generator is able to reconstruct images of the respective distribution.
An adversarial objective \cite{goodfellow2014generative} is employed to help in learning to translate from one domain to another. In this setting, the lesion generator $G_l$ is conditioned on the latent encoding of a healthy patch $z_h$ and the generated sample is evaluated by the discriminator $D_l$ to classify whether the sample was drawn from $P{\chi_l}(x_l)$ or not. This encourages the generator to create lesion-like image features while constructing an image sample. The GAN objective is defined as:
\begin{equation}
\mathcal{L}_{\text{\tiny GAN}_l} = \lambda_0[\mathbb{E}_{x_l \sim P_{\chi_1}}[\log D_l(x_l)] + \mathbb{E}_{z_h \sim q_h(z_h|x_h)}[\log (1 - D_l(G_l(z_h)))]]
\end{equation}
The conceptual shared latent space is implemented in practice by weight-sharing across the two VAEs. The shared latent space implies a cycle-consistency constraint \cite{zhu2017unpaired} that ensures successful circular back and forth mapping between domains:
\begin{align}
\mathcal{L}_{\text{\tiny CC}_l} = &\lambda_3[\text{KL}(q_l(z_l|x_l)||\mathcal{N}(z|0, I)) + \text{KL}(q_h(z_h|x_{l \rightarrow h})||\mathcal{N}(z|0, I))] \nonumber \\
&- \lambda_4 \mathbb{E}_{z_h \sim q_h(z_h|x_{l \rightarrow h})}[\log p_{G_l}(x_l|z_h)]
\end{align}
This objective aims at preserving the original information of the input image and prevents mode collapse by translating all images to a single output image. Similar loss objectives are minimized for $\text{VAE}_h$, $\text{GAN}_h$ and $\text{CC}_h$. The hyperparameters ($\lambda$) control the contribution of each respective loss function. The network is jointly trained to optimize the following objective:
\begin{align}
\min_{E_l,E_h,G_l,G_h} \max_{D_l,D_h}
\mathcal{L}_{\text{\tiny VAE}_l} + \mathcal{L}_{\text{\tiny GAN}_l} + \mathcal{L}_{\text{\tiny CC}_l} +
\mathcal{L}_{\text{\tiny VAE}_h} + \mathcal{L}_{\text{\tiny GAN}_h} + \mathcal{L}_{\text{\tiny CC}_h}
\end{align}
\subsection{Patch-making}
\label{subsec:patches}
Bone lesions tend to cause local alterations in bone anatomy without substantially affecting the global visual appearance of the image. We therefore aim to translate localized image patches rather than training a translation model for the complete images. This technique has the following advantages: i) computationally cheaper, ii) multiple patches can be created from a single image, iii) lesion-like features are more prominent on the localized patch, which supports efficient training of the translation model.
Lesion patches are created by randomly cropping a square area (if image size permits) by a factor $s\in\{1,2\}$ larger than the larger side of the bounding box around the area containing the pathology. This area is marked with a manually annotated bounding box (c.f. \figurename~\ref{fig:patch}). We employ an heuristic to automate cropping of normal patches. We identify potential `crop-areas' in a two step process. First we randomly choose $n$ similar non-lesion images for each lesion image. Second we crop each non-lesion image based on the lesion annotations of the matched lesion image. All non-lesion patches with a mean, normalized ([0,1]) pixel intensity of less than 0.15 are assumed to not contain bone structure and are dropped from the dataset.
\subsection{Blending}
The translated patches also exhibit subtle changes in the overall image characteristics, such as contrast and brightness. This leads to the patch being visibly distinct when placed back in the full-image after translation. We employ alpha-blending to smoothly blend the translated patch in the original image: $x_{h \rightarrow l}^{blended} = \alpha x_{h \rightarrow l} + (1 - \alpha) x_h$. Specifically, we define a locally varying blending factor $\alpha$ as: $\alpha = \cos(|i|^n * \frac{\pi}{2}) \cos(|j|^n * \frac{\pi}{2})$, where $i$ and $j$ are the normalized ([-1,1]) coordinates of a pixel in the patch and $n$ is a hyper-parameter.
\subsection{Pseudo-Labelling}
We aim to augment the training set with images containing a prominent lesion after the blending operation. We perform hard positive mining \cite{lee2013pseudo} on the generated set using a classifier trained on the available empirical training data (baseline). Based on a threshold parameter $t$, the baseline classifier segregates the generated samples into two disjoint sets: samples with extreme lesion-like properties, and noisy samples. The former is used for augmentation and added to the training set.
\begin{figure}
\subfigure[Humerus]{\label{fig:humerus}%
\includegraphics[width=2.5cm,height=3.1cm]{fig/new_cropped_lesions/h_f1_cropped.png}
\includegraphics[width=2.5cm,height=3.1cm]{fig/new_cropped_lesions/h_f2_cropped.png}}
\hspace{1mm}
\subfigure[Tibia]{\label{fig:tibia}%
\includegraphics[width=2.5cm,height=3.1cm]{fig/new_cropped_lesions/t_f1.png}
\includegraphics[width=2.5cm,height=3.1cm]{fig/new_cropped_lesions/t_f2_cropped.png}}
\hspace{1mm}
\subfigure[Femur]{\label{fig:femur}%
\includegraphics[width=2.5cm,height=3.1cm]{fig/new_cropped_lesions/f_f1_cropped.png}
\includegraphics[width=1.8cm,height=3.1cm]{fig/new_cropped_lesions/f_f6.png}}
\caption{\label{fig:patch}Bone lesion with expert-annotated bounding box (red). Random sized patches (white), cropped around lesions, used for training the generative model.}
\end{figure}
\section{Experimental Setup}
\subsection{Dataset}
A set of adult X-ray images showing bone anatomy with and without lesion are sourced from various U.S. hospitals and assessed by expert, board-certified radiologists by drawing bounding boxes around the target pathology (bone lesions) of concern (c.f. \figurename~\ref{fig:patch}). A test dataset is held out containing sufficient positive samples for evaluation and used at no point to train or fine-tune any model. The remaining dataset is then used for training and validating both the classifiers and the translation models.
\textbf{Classification Task:} Images with presence of confounding features (e.g., congenital deformity, fixation hardware) negatively impacted the model's classification performance. We thus removed those images from all datasets when training classification models. A summary of the data split, excluding augmented samples, is provided for the three investigated body parts in Table \ref{datasplit} (left). The generated images used for augmentation are only added to the training set but not the validation set.
\textbf{Translation Task:}
We do not remove images from the lesion set when training the generative model, as it is trained on cropped image patches that are less affected by the confounding features. However, we remove images with confounding features from the non-lesion set to ensure that the augmented training set does not contain confounding images. The class split is kept balanced to facilitate training of the models. The images from the negative class in the training set that are not used to train the generative model are used for creating the augmented training set. Image patches are cropped from those images as described in Section~\ref{subsec:patches}. Table \ref{datasplit} (right) reports the distribution of the patch dataset and the configuration settings.
\begin{table}
\caption{Datasets for each model (ratio denotes lesion:non-lesion class split). Left: images used for classification. Right: Extracted patches used for generation. Source samples are only non-lesion and used for creating the augmented sets. $s$ is the factor by which the patch is larger than the larger side of the bounding box. $n$ is the number of non-lesion images chosen against each lesion image.}
\label{datasplit}
\begin{minipage}{.5\linewidth}
\centering
\small
\begin{tabular}{lrrr}
\\
\toprule
\multicolumn{4}{c}{\bf Classification Task}\\
\bf Body part & \bf Train & \bf Val & \bf Test \\
\midrule
Humerus & 268:2295 & 41:305 & 50:500 \\
Tibia & 214:14482 & 22:1628 & 50:500 \\
Femur & 32:4558 & 14:573 & 50:500 \\
\bottomrule
\end{tabular}
\end{minipage}%
\quad
\begin{minipage}{.4\linewidth}
\centering
\small
\begin{tabular}{lrrrr}
\\
\toprule
\multicolumn{5}{c}{\bf Translation Task}\\
\bf Body part & \bf Train & \bf Source & \bf $s$ & \bf $n$\\
\midrule
Humerus & 536:536 & 4643 & 2 & 10\\
Tibia & 515:515 & 4680 & 1 & 7\\
Femur & 285:285 & 9171 & 2 & 10\\
\bottomrule
\end{tabular}
\end{minipage}
\end{table}
\begin{figure}[t]
\subfigure[]{
\includegraphics[width=0.45\linewidth]{fig/lesion_stages3_1.png}}
\qquad
\subfigure[]{
\includegraphics[width=0.45\linewidth]{fig/lesion_stages3_2.png}}
\caption{Stages of patch translation for full-image (top) and selected patch, highlighted with white box (bottom): i) original, ii) translated and iii) blended.}
\label{fig-blend}
\end{figure}
\subsection{Model Architecture and Optimization}
The classifier is a dilated residual net (DRN) \cite{yu2017dilated}. Dilated convolutional filters increase the receptive field of view and help capture finer details in high-resolution images. Images are downsampled to 1024x512 pixels in our experiments. To avoid overfitting on our comparatively small training set, our model was pretrained on a larger corpus of X-ray images for the auxiliary task of fracture detection. Training the classifier in this work involves fine-tuning of the last two convolutional blocks and the fully-connected layer of the model. Regularization is performed through augmentation procedures including linear transformations, along with weight decay. The model is optimized using Adam with an initial learning rate of 0.0001 which decays by a factor of 0.9 when the performance on the validation set plateaus.
The variability of the body part specific bone anatomy influenced our ability to train the translation model. Models on more diverse datasets like tibia could only be trained if the patch sizes were not larger than the bounding box ($s=1$). On the other hand, a comparably uniform anatomical view among humerus images allowed training with larger patch sizes ($s=2$). The adversarial loss weight influenced the qualitative results. Setting $\lambda_0=1$ resulted in a change in texture of the bone, rather than synthesis of a circular lesion. The default architecture and loss weighting as specified in \cite{liu2017unsupervised} proved to yield the best results. We found residual connections in the encoder and generator beneficial and hypothesize that copying the common features in the patch helps in training on such a small dataset. Figure \ref{fig-blend} demonstrates the blending process after translation using the default mask.
\subsection{Transfer Learning}
\begin{figure}[t]
\subfigure[Tibia]{
\includegraphics[width=2.4cm,height=3.42cm]{fig/tl_marked/tl_tibia_1.png}
\includegraphics[width=2.4cm,height=3.42cm]{fig/tl_marked/tl_tibia_2.png}
\includegraphics[width=2.4cm,height=3.42cm]{fig/tl_marked/tl_tibia_4.png}}
\hspace{1mm}
\subfigure[Femur]{
\includegraphics[width=2.4cm,height=3.42cm]{fig/tl_marked/tl1.png}
\includegraphics[width=2.4cm,height=3.42cm]{fig/tl_marked/tl2.png}
\includegraphics[width=2.4cm,height=3.42cm]{fig/tl_marked/tl3.png}}
\caption{\label{femur-tl}Bone lesion generated using transfer learning techniques. The variation in positional views within each body part makes it challenging to train a generative model.}
\end{figure}
In comparison to the available humerus X-rays, the available tibia and femur datasets were highly heterogeneous. We observed highly variable radiographic views and frequent confounding image content (e.g. external objects) in the not excluded positives. This made it particularly challenging to train a valuable generative model for tibia and unfeasible for femur, regardless of the patch size. We explored the potential of using transfer learning by i) employing the translation model trained on humerus to generate lesions on other body parts, ii) doing pseudo-labelling based on the humerus baseline classifier. For tibia we set $s=1$ to kept it consistent with the tibia-specific generative model. For femur we set $s=2$ to keep it consistent with the humerus configuration.
\subsection{Performance Measures}
We report the Area Under the ROC-Curve (AUC) and the bootstrapped 95\% Confidence Interval (CI). It was ensured that all models are compared on the same set of bootstrap samples. This allows us to examine the bootstrap-wise difference in AUC scores of models against the baseline. We consider a model to be significantly different to the baseline if the 95\% CI of those bootstrapped difference scores does not contain zero. We report Sensitivity (Sens) and Specificity (Spec) by defining an Operating Point (OP) over the validation set as the point which minimizes $(1-\text{true positive rate})^2 + (\text{false positive rate})^2$ over the ROC curve. We focus on AUC scores since the operating point is, due to the low sample size of our validation set, highly variable and does not generalize well across experiments.
\begin{table}
\caption{Ablation study of $t$ (threshold score of pseudo-labeller) reporting classifier performance on humerus test-set. Sensitivity and Specificity are calculated at the OP. Significantly different AUC with respect to baseline indicated with $^{*}$.}
\label{threshold}
\centering
\small
\begin{tabular}{lrrrrrrr}
\toprule
\bf Type & \bf $t$ & \bf Augmented Samples & \bf ROC AUC (CI 95\%) & \bf Sens. & \bf Spec. & \bf OP\\
\midrule
Baseline & 0 & 0 & 0.876 (0.817-0.926) & 0.9 & 0.776 & 0.455 \\
\midrule
Augmented & 0.70 & 1412 & 0.882 (0.829-0.928) & 0.80 & 0.842 & 0.390 \\
& 0.85 & 577 & 0.899 (0.854-0.939) & 0.82 & 0.802 & 0.086 \\
& 0.90 & 401 & \bf 0.924 (0.889-0.955)$^*$ & 0.84 & 0.798 & 0.058 \\
& 0.95 & 257 & 0.877 (0.820-0.926) & 0.90 & 0.766 & 0.273 \\
\bottomrule
\end{tabular}
\end{table}
\begin{table}[t]
\caption{Comparison of classifier model performance on tibia and femur test-sets. A translation model couldn't be trained for femur due to high diversity of radiographic view and insufficient samples. $\text{TL}_\text{G}$=Inference with humerus translation model, $\text{TL}_{\text{PL}}$=Pseudo-labelling with humerus baseline model.\label{tl-scores}}
\subtable[Tibia]{
\small
\centering
\begin{tabular}{lrrrrr}
\toprule
\bf Augment Type & \bf Augmented Samples & \bf ROC AUC (CI 95\%) & \bf Sens. & \bf Spec. & \bf OP \\
\midrule
Baseline & 0 & 0.618 (0.532-0.705) & 0.54 & 0.652 & 0.300 \\
Augmented & 124 & 0.640 (0.547-0.732) & 0.6 & 0.542 & 0.244 \\
$\text{TL}_\text{G}$ & 118 & 0.642 (0.550-0.735) & 0.52 & 0.66 & 0.290 \\
$\text{TL}_\text{G} + \text{TL}_{\text{PL}}$ & 1264 & \bf 0.698 (0.610-0.785)$^{*}$ & 0.74 & 0.464 & 0.066 \\
\bottomrule
\end{tabular}
}\medbreak
\subtable[Femur]{
\small
\centering
\begin{tabular}{lrrrrrr}
\toprule
\bf Augment Type & \bf Augmented Samples & \bf ROC AUC (CI 95\%) & \bf
Sens. & \bf Spec. & \bf OP \\
\midrule
Baseline & 0 & 0.533 (0.441-0.627) & 0.64 & 0.376 & 0.010 \\
$\text{TL}_\text{G}$ & 579 & 0.601 (0.504-0.695)$^{*}$ & 0.56 & 0.61 & 0.012 \\
$\text{TL}_\text{G} + \text{TL}_{\text{PL}}$ & 1342 & \bf 0.682 (0.594-0.764)$^{*}$ & 0.66 & 0.67 & 0.008 \\
\bottomrule
\end{tabular}
}
\end{table}
\section{Results}
The augmentation set is composed of generated images that the baseline classifier assigns a confidence score of $t$ or higher. In the transfer learning setting, the humerus baseline classifier is used to select generated images for tibia and femur respectively. A grid search is performed on the validation set and $t$ is chosen to be the value that gives the highest validation set AUC ($t_\textrm{humerus}=0.9$, $t_\textrm{tibia}=0.9$, $t_\textrm{femur}=0.95$). To assess the influence of this parameter we report AUCs on the humerus test set for different values of $t$ in Table \ref{threshold}. We observe that the approach is sensitive to the choice of $t$ which, however, can be successfully chosen on the validation set. Adding either insufficient number of samples (larger $t$) or excessive low-quality samples (smaller $t$) reduces the benefit of data augmentation. We observed a significant increase in AUC of around 5\% over the humerus baseline model at $t=0.9$, as determined on the validation set.
For tibia we observed similar minor improvements ($\approx$2\%) when using either the humerus or tibia generative model. However, when further relying on the humerus baseline classifier for sample selection we observed a more substantial performance gain of around 8\% that was borderline to significant in the conducted test. For femur we observed significant gains in AUC when employing transferring knowledge from the humerus models. In particular, we observed an substantial improvement of around 15\% over the barely discriminative femur baseline classifier. See Table \ref{tl-scores} for the full quantitative analysis for tibia and femur when using transfer learning.
Figure \ref{femur-tl} illustrates some of the generated samples for tibia and femur obtained using transfer-learning based on the humerus model.
\section{Conclusion}
We trained a generative model that can represent some properties of the target pathology (bone lesions in X-ray) and synthesize those into sample patches drawn from another distribution (normal anatomy). When employing generative models for augmenting medical datasets, great care needs to be taken to avoid and control for possibly introduced bias. Future work should be concerned with the exploration of those limitations and explore the method's potential on both a more diverse set of disease pathology and other modalities.
\section*{Acknowledgements}
The project is funded by Imagen Technologies. The work presented in this manuscript is for research purposes only and is not for sale within the United States.
\bibliographystyle{unsrt}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 543 |
\section{Introduction}
Language models play an important role in many applications like speech recognition, machine translation, information retrieval and nature language understanding. Traditionally, the back-off n-gram models \cite{Katz.1987,Kneser.1995} are the standard approach to language modeling. Recently, neural networks have been successfully applied to language modeling and have achieved the state-of-the-art performance in many tasks. In neural network language models (NNLM), the feedforward neural networks (FNN) and recurrent neural networks (RNN) \cite{Elman1990} are two popular architectures. The basic idea of NNLMs is to use a projection layer to project discrete words into a continuous space and estimate word conditional probabilities in this space, which may be smoother to better generalize to unseen contexts. FNN language models (FNN-LM) \cite{Bengio2001,Bengio2003} usually use a limited history within a fixed-size context window to predict the next word. RNN language models (RNN-LM) \cite{Mikolov2010recurrent,Mikolov2012} adopt a time-delayed recursive architecture for the hidden layers to memorize the long-term dependency in language. Therefore, it is widely reported that RNN-LMs usually outperform FNN-LMs in language modeling. While RNNs are theoretically powerful, the learning of RNNs needs to use the so-called back-propagation through time (BPTT) \cite{Werbos1990} due to the internal recurrent feedback cycles. The BPTT significantly increases the computational complexity of the learning algorithms and it may cause many problems in learning, such as gradient vanishing and exploding \cite{Bengio1994}. More recently, some new architectures have been proposed to solve these problems. For example, the long short term memory (LSTM) RNN \cite{Hochreiter1997} is an enhanced architecture to implement the recurrent feedbacks using various learnable gates, and it has obtained promising results on handwriting recognition \cite{Graves2009} and sequence modeling \cite{Graves2013}.
Moreover, the so-called temporal-kernel recurrent neural networks (TKRNN) \cite{Sutskever2010} have been proposed to handle the gradient vanishing problem. The main idea of TKRNN is to add direct connections between units in all time steps and every unit is implemented as an efficient leaky integrator, which makes it easier to learn the long-term dependency. Along this line, a temporal-kernel model has been successfully used for language modeling in \cite{Shi2013}.
Comparing with RNN-LMs, FNN-LMs can be learned in a simpler and more efficient way. However, FNN-LMs can not model the long-term dependency in language due to the fixed-size input window. In this paper, we propose a novel encoding method for discrete sequences, named {\em fixed-size ordinally-forgetting encoding} (FOFE), which can almost uniquely encode any variable-length word sequence into a fixed-size code. Relying on a constant forgetting factor, FOFE can model the word order in a sequence based on a simple ordinally-forgetting mechanism, which uses the position of each word in the sequence. Both the theoretical analysis and the experimental simulation have shown that FOFE can provide {\em almost} unique codes for variable-length word sequences as long as the forgetting factor is properly selected. In this work, we apply FOFE to neural network language models, where the fixed-size FOFE codes are fed to FNNs as input to predict next word, enabling FNN-LMs to model long-term dependency in language. Experiments on two benchmark tasks, Penn Treebank Corpus (PTB) and Large Text Compression Benchmark (LTCB), have shown that FOFE-based FNN-LMs can not only significantly outperform the standard fixed-input FNN-LMs but also achieve better performance than the popular RNN-LMs with or without using LSTM. Moreover, our implementation also shows that FOFE based FNN-LMs can be learned very efficiently on GPUs without the complex BPTT procedure.
\section{Our Approach: FOFE}
\label{sec.fofe}
Assume vocabulary size is $K$, NNLMs adopt the 1-of-K encoding vectors as input. In this case, each word in vocabulary is represented as a one-hot vector ${\mathbf e} \in \mathbb{R}^{K}$. The 1-of-K representation is a context independent encoding method. When the 1-of-K representation is used to model a word in a sequence, it can not model its history or context.
\subsection{Fixed-size Ordinally Forgetting Encoding}
We propose a simple context-dependent encoding method for any sequence consisting of discrete symbols, namely {\em fixed-size ordinally-forgetting encoding} (FOFE).
Given a sequence of words (or any discrete symbols), $S=\{ w_1, w_2, \cdots, w_T \}$, each word $w_t$ is first represented by a 1-of-K representation ${\bf e}_t$, from the first word $t=1$ to the end of the sequence $t=T$, FOFE encodes each partial sequence (history) based on a simple recursive formula (with $ {\bf z}_0 = {\bf 0}$) as:
\begin{equation}\label{eq-fofe-coding}
{\bf z}_t = \alpha \cdot {\bf z}_{t-1} + {\bf e}_{t} \;\;\; (1 \leq t \leq T)
\end{equation}
where ${\bf z}_t$ denotes the FOFE code for the partial sequence up to $w_t$, and $\alpha$ ($0<\alpha<1$) is a constant forgetting factor to control the influence of the history on the current position.
Let's take a simple example here, assume we have three symbols in vocabulary, e.g., {\em A}, {\em B}, {\em C}, whose 1-of-K codes are $[1,0,0]$, $[0,1,0]$ and $[0,0,1]$ respectively. In this case, the FOFE code for the sequence {\em \{ABC\}} is $[\alpha^2, \alpha ,1]$, and that of {\em \{ABCBC\}} is $[\alpha^4, \alpha+\alpha^3 ,1+\alpha^2]$.
Obviously, FOFE can encode any variable-length discrete sequence into a fixed-size code. Moreover, it is a recursive context dependent encoding method that smartly models the order information by various powers of the forgetting factor. Furthermore, FOFE has an appealing property in modeling natural languages that the far-away context will be gradually forgotten due to $\alpha<1$ and the nearby contexts play much larger role in the resultant FOFE codes.
\begin{figure}[t]
\centering
\includegraphics[width=0.9\linewidth]{FOFE_bigram.png}
\caption{The FOFE-based FNN language model.}
\label{fig:FOFE_bigram}
\end{figure}
\subsection{Uniqueness of FOFE codes}
Given the vocabulary (of $K$ symbols), for any sequence $S$ with a length of $T$, based on the FOFE code ${\bf z}_T$ computed as above, if we can always decode the original sequence $S$ unambiguously (perfectly recovering $S$ from ${\bf z}_T$), we say FOFE is unique.
\begin{theorem}
\label{theorem-FOFE-alpha-less-half}
If the forgetting factor $\alpha$ satisfies $0<\alpha \leq 0.5$, {\em FOFE} is unique for any $K$ and $T$.
\end{theorem}
The proof is simple because if the FOFE code has a value $\alpha^t$ in its $i$-th element, we may determine the word $w_i$ occurs in the position $t$ of $S$ without ambiguity since no matter how many times $w_i$ occurs in the far-away contexts ($<t$), they do not sum to $\alpha^t$ (due to $\alpha \leq 0.5$). If $w_i$ appears in any closer context ($>t$), the $i$-th element must be larger than $\alpha^t$.
For $0.5 < \alpha <1$, we have the following theorem:
\begin{theorem}
\label{theorem-FOFE-alpha-less-one}
For $0.5 < \alpha <1$, given any finite values of $K$ and $T$, {\em FOFE} is almost unique everywhere for $\alpha \in (0.5, 1.0)$, except only a finite set of countable choices of $\alpha$.
\end{theorem}
\begin{figure}[t]
\centering
\includegraphics[width=0.9\linewidth]{collision.png}
\caption{Numbers of collisions in simulation.}
\label{fig:collisions}
\end{figure}
The complete proof \cite{Oguz2015} is given in Appendix A. Based on Theorem \ref{theorem-FOFE-alpha-less-one}, FOFE is unique almost everywhere between $(0.5, 1.0)$ only except a countable set of isolated choices of $\alpha$. In practice, the chance to exactly choose these isolated values between $(0.5, 1.0)$ is extremely slim, realistically almost impossible due to quantization errors in the system. To verify this,
we have run simulation experiments for all possible sequences up to $T=20$ symbols to count the number of collisions. Each collision is defined as the maximum element-wise difference between two FOFE codes (generated from two different sequences) is less than a small threshold $\epsilon$.
In Figure \ref{fig:collisions}, we have shown the number of collisions (out of the total $2^{20}$ tested cases) for various $\alpha$ values when $\epsilon=0.01$, $0.001$ and $0.0001$.\footnote{When we use a bigger value for $\alpha$, the magnitudes of the resultant FOFE codes become much larger. As a result, the number of collisions (as measured by a fixed absolute threshold $\epsilon$) becomes smaller.}
The simulation experiments have shown that the chance of collision is extremely small even when we allow a word to appear any times in the context. Obviously, in a natural language, a word normally does not appear repeatedly within a near context. Moreover, we have run the simulation to examine whether collisions actually occur in two real text corpora, namely PTB (1M words) and LTCB (160M words), using $\epsilon=0.01$, we have not observed a single collision for nine different $\alpha$ values between $[0.55, 1.0]$ (incremental $0.05$).
\subsection{Implement FOFE for FNN-LMs}
The architecture of a FOFE based neural network language model (FOFE-FNNLM) is as shown in Figure \ref{fig:FOFE_bigram}. It is similar to standard bigram FNN-LMs except that it uses a FOFE code
to feed into neural network LM at each time instance.
Moreover, the FOFE can be easily scaled to other n-gram based neural network LMs.
For example,
Figure \ref{fig:FOFE_trigram} is an illustration of fixed-size ordinally forgetting encoding based tri-gram neural network language model.
FOFE is a simple recursive encoding method but a direct sequential implementation may not be efficient for the parallel computation platform like GPUs.
Here, we will show that the FOFE computation can be efficiently implemented as sentence-by-sentence matrix multiplications, which are particularly suitable for the mini-batch based stochastic gradient descent (SGD) method running on GPUs.
Given a sentence, $S = \{ {w}_1, {w}_2, \cdots, {w}_T \} $, where each word is represented by a 1-of-K code as ${\bf e}_t$ $(1\leq t \leq T)$. The FOFE codes for all partial sequences in $S$ can be computed based on the following matrix multiplication:
\begin{equation}\nonumber
{\bf S} = \left[ \begin{gathered}
1 \hfill \\
\alpha \quad 1 \hfill \\
{\alpha ^2}\;\;\alpha \quad 1 \hfill \\
\vdots \quad \;\;\quad \ddots \quad 1 \hfill \\
{\alpha ^{T - 1}}\; \cdots \quad \alpha \quad 1 \hfill \\
\end{gathered} \right] \left[ \begin{gathered}
{\bf e}_1 \hfill \\
{\bf e}_2 \hfill \\
{\bf e}_3 \hfill \\
\hspace{0.1cm} \vdots \hfill \\
{\bf e}_T \hfill \\
\end{gathered} \right] = {\bf M} {\bf V}
\end{equation}
where ${\bf V}$ is a matrix arranging all 1-of-K codes of the words in the sentence row by row, and ${\bf M}$ is a $T$-th order lower triangular matrix. Each row vector of ${\bf S}$ represents a FOFE code of the partial sequence up to each position in the sentence.
This matrix formulation can be easily extended to a mini-batch consisting of several sentences.
Assume that a mini-batch is composed of N sequences, ${\cal L}=\{ S_1 \; S_2 \cdots S_N\}$, we can compute the FOFE codes for all sentences in the mini-batch as follows:
\begin{equation}\nonumber
{\bf \bar{S}} =\left[ \begin{gathered}
{\bf M}_1 \hfill \\
\qquad {\bf M}_2 \hfill \\
\qquad \qquad \ddots \hfill \\
\qquad \qquad \qquad {\bf M}_N\hfill \\
\end{gathered} \right] \left[ \begin{gathered}
{\bf V}_1 \hfill \\
{\bf V}_2\hfill \\
\quad \vdots \hfill \\
{\bf V}_N \hfill \\
\end{gathered} \right] = {\bf \bar{M}} {\bf \bar{V}}
\end{equation}
\begin{figure}[t]
\centering
\includegraphics[width=0.9\linewidth]{FOFE_trigram.png}
\caption{Illustration of a 2nd-order FOFE based FNN-LM.}
\label{fig:FOFE_trigram}
\end{figure}
When feeding the FOFE codes to FNN as shown in Figure \ref{fig:FOFE_bigram}, we can compute the activation signals (assume $f$ is the activation function) in the first hidden layer for all histories in $S$ as follows:
\begin{equation}
\label{eq.FOFE_forward}
{\bf H} = f\Big(({\bf M} {\bf V}) {\bf U} {\bf W} + {\bf b}\Big)
= f\Big({\bf M} ({\bf V} {\bf U}) {\bf W} + {\bf b}\Big) \nonumber
\end{equation}
where ${\bf U}$ denotes the word embedding matrix that projects the word indices onto a continuous low-dimensional continuous space.
As above, ${\bf V} {\bf U}$ can be done efficiently by looking up the embedding matrix. Therefore,
for the computational efficiency purpose, we may apply FOFE to the word embedding vectors instead of the original high-dimensional one-hot vectors. In the backward pass, we can calculate the gradients with the standard back-propagation (BP) algorithm rather than BPTT. As a result, FOFE based FNN-LMs are the same as the standard FNN-LMs
in terms of computational complexity in training, which is much more efficient than RNN-LMs.
\section{Experiments}
\label{sec.Experiments}
We have evaluated the FOFE method for NNLMs on two benchmark tasks: i) the Penn Treebank (PTB) corpus of about 1M words, following the same setup as \cite{Mikolov2011Extension}.
The vocabulary size is limited to 10k. The preprocessing method and the way to split data into training/validation/test sets are the same as \cite{Mikolov2011Extension}.
ii) The Large Text Compression Benchmark (LTCB) \cite{Mahoney2011}. In LTCB, we use the {\em enwik9} dataset, which is composed of the first $10^9$ bytes of enwiki-20060303-pages-articles.xml. We
split it into three parts: training (153M), validation (8.9M) and testing (8.9M) sets.
We limit the vocabulary size to 80k for LTCB and replace all out-of-vocabulary words by a $<$UNK$>$ token.
Details of the two datasets can be found in Table \ref{tab:datasets}. \footnote{Matlab codes are available at \url{https://wiki.eecs.yorku.ca/lab/MLL/projects:fofe:start} for readers to reproduce all results reported in this paper.}
\begin{table}[t]
\centering
\caption{The size of PTB and LTCB corpora in words. }
\begin{tabular}{|c|c|c|c|}
\hline
Corpus & train & valid & test \\ \hline
PTB & 930k & 74k & 82k \\ \hline
LTC & 153M & 8.9M & 8.9M \\
\hline
\end{tabular}
\label{tab:datasets}
\end{table}
\subsection{Experimental results on PTB }
We have first evaluated the performance of the traditional FNN-LMs, taking the previous several words as input, denoted as n-gram FNN-LMs here. We have trained neural networks with a linear projection layer (of 200 hidden nodes) and two hidden layers (of 400 nodes per layer). All hidden units in networks use the rectified linear activation function, i.e., $f(x)=\max(0,x)$. The nets are initialized based on the normalized initialization in \cite{Glorot2010}, without using any pre-training.
We use SGD with a mini-batch size of 200 and an initial learning rate of 0.4. The learning rate is kept fixed as long as the perplexity on the validation set decreases by at least 1. After that, we continue six more epochs of training, where the learning rate is halved after each epoch. The performance (in perplexity) of various n-gram FNN-LMs is shown in Table \ref{tab:PTB_summary}.
For the FOFE-FNNLMs, the net architecture and the parameter setting are the same as above. The mini-batch size is also 200 and each mini-batch is composed of several sentences up to 200 words (the last sentence may be truncated). All sentences in the corpus are randomly shuffled at the beginning of each epoch. In this experiment, we first investigate how the forgetting factor $\alpha$ may affect the performance of LMs. We have trained two FOFE-FNNLMs: i) 1st-order (using ${\bf z}_t$ as input to FNN for each time $t$; ii) 2nd-order (using both ${\bf z}_t$ and ${\bf z}_{t-1}$ as input for each time $t$, with a forgetting factor varying between $[0.0,1.0]$. Experimental results in Figure \ref{fig:Dif_factor} have shown that
a good choice of $\alpha$ lies between $[0.5,0.8]$.
Using a too large or too small forgetting factor will hurt the performance. A too small forgetting factor may limit the memory of the encoding while a too large $\alpha$ may confuse LM with a far-away history.
In the following experiments, we set $\alpha=0.7$ for the rest experiments in this paper.
\begin{figure}[t]
\centering
\includegraphics[width=0.9\linewidth]{Dif_factor}
\caption{Perplexities of FOFE FNNLMs as a function of the forgetting factor.}
\label{fig:Dif_factor}
\end{figure}
In Table \ref{tab:PTB_summary}, we have summarized the perplexities on the PTB test set for various models. The proposed FOFE-FNNLMs can significantly outperform the baseline FNN-LMs using the same architecture.
For example, the perplexity of the baseline bigram FNNLM is 176, while the FOFE-FNNLM can improve to 116.
Moreover, the FOFE-FNNLMs can even overtake a well-trained RNNLM (400 hidden units) in \cite{Mikolov2011Extension} and an LSTM in \cite{Graves2013}. It indicates FOFE-FNNLMs can effectively model the long-term dependency in language without using any recurrent feedback.
At last, the 2nd-order FOFE-FNNLM can provide further improvement, yielding the perplexity of 108 on PTB. It also outperforms all higher-order FNN-LMs (4-gram, 5-gram and 6-gram), which are bigger in model size. To our knowledge, this is one of the best reported results on PTB without model combination.
\begin{table}[t]
\centering
\caption{Perplexities on PTB for various LMs.}
\begin{tabular}{|c|c|}
\hline
Model & Test PPL \\\hline \hline
KN 5-gram \cite{Mikolov2011Extension} & 141 \\
FNNLM \cite{Mikolov2012} & 140 \\
RNNLM \cite{Mikolov2011Extension} & 123 \\
LSTM \cite{Graves2013} & 117 \\ \hline
bigram FNNLM & 176 \\
trigram FNNLM & 131 \\
4-gram FNNLM & 118 \\
5-gram FNNLM & 114 \\
6-gram FNNLM & 113 \\ \hline
1st-order FOFE-FNNLM & 116 \\
2nd-order FOFE-FNNLM & \textbf{108} \\ \hline
\end{tabular}
\label{tab:PTB_summary}
\end{table}
\subsection{Experimental results on LTCB}
\begin{table}[t]
\centering
\caption{Perplexities on LTCB for various language models. [M*N] denotes the sizes of the input context window and projection layer.}
\begin{tabular}{|c|c|c|}
\hline
Model & Architecture & Test PPL \\\hline
KN 3-gram & - & 156 \\
KN 5-gram & - & 132 \\\hline
& [1*200]-400-400-80k & 241 \\
& [2*200]-400-400-80k & 155\\
FNN-LM & [2*200]-600-600-80k & 150 \\
& [3*200]-400-400-80k & 131 \\
& [4*200]-400-400-80k & 125 \\ \hline
RNN-LM & [1*600]-600-80k & 112 \\\hline
& [1*200]-400-400-80k & 120 \\
FOFE & [1*200]-600-600-80k & 115\\
FNN-LM & [2*200]-400-400-80k & 112\\
& [2*200]-600-600-80k & {\bf 107} \\\hline
\end{tabular}
\label{tab:WIKI_summary}
\end{table}
We have further examined the FOFE based FNN-LMs on a much larger text corpus, i.e. LTCB, which contains articles from Wikipedia. We have trained several baseline systems: i) two n-gram LMs (3-gram and 5-gram) using the modified Kneser-Ney smoothing without count cutoffs; ii) several traditional FNN-LMs with different model sizes and input context windows (bigram, trigram, 4-gram and 5-gram ones); iii) an RNN-LM with one hidden layer of 600 nodes using the toolkit in \cite{Mikolov2010recurrent}, in which we have further used a spliced sentence bunch in \cite{Chen2014} to speed up the training on GPUs. Moreover, we have examined four FOFE based FNN-LMs with various model sizes and input window sizes (two 1st-order FOFE models and two 2nd-order ones). For all NNLMs, we have used an output layer of the full vocabulary (80k words). In these experiments, we have used an initial learning rate of 0.01, and a bigger mini-batch of 500 for FNN-LMMs and of 256 sentences for the RNN and FOFE models.
Experimental results in Table \ref{tab:WIKI_summary} have shown that the FOFE-based FNN-LMs can significantly outperform the baseline FNN-LMs (including some larger higher-order models) and also slightly overtake the popular RNN-based LM, yielding the best result (perplexity of 107) on the test set.
\section{Conclusions}
\label{sec.conclusion}
In this paper, we propose the fixed-size ordinally-forgetting encoding (FOFE) method to {\em almost} uniquely encode any variable-length sequence into a fixed-size code. In this work, FOFE has been successfully applied to neural network language modeling.
Next, FOFE may be combined with neural networks \cite{Zhang2015a,Zhang2015b} for other NLP tasks, such as sentence modeling/matching, paraphrase detection, machine translation, question and answer and etc.
\section*{Acknowledgments}
This work was supported in part by the Science and Technology Development of Anhui Province, China (Grants No. 2014z02006) and the Fundamental Research Funds for the Central Universities from China, as well as an NSERC Discovery grant from Canadian federal govenment. We appreciate Dr. Barlas Oguz at Microsoft for his insightful comments and constructive suggestions on Theorem \ref{theorem-FOFE-alpha-less-one}.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,833 |
Contents
_Contributors_
_Preface_
**Volume 1: BASIC CONCEPTS**
**Part 1: Anatomy**
**1 The Anatomy of Periodontal Tissues**
Introduction
Gingiva
Periodontal ligament
Root cementum
Alveolar bone
Blood supply of the periodontium
Lymphatic system of the periodontium
Nerves of the periodontium
**2 The Edentulous Alveolar Ridge**
Clinical considerations
Topography of the alveolar process
Alterations of the alveolar process following tooth extraction
Topography of the edentulous ridge
**3 The Mucosa at Teeth and Implants**
The gingiva
The peri-implant mucosa
Probing gingiva and peri-implant mucosa
Dimensions of the buccal soft tissue at implants
Dimensions of the papilla between teeth and implants
Dimensions of the "papilla" between adjacent implants
**4 Bone as a Tissue**
Basic bone biology
Local and systemic factors affecting bone volume and healing
Bone healing
**5 Osseointegration**
The edentulous site
Osseointegration
Implant installation
Cutting and non-cutting implants
The process of osseointegration
**6 Periodontal Tactile Perception and Peri-implant Osseoperception**
Introduction
Neurophysiological background
Trigeminal neurophysiology
Periodontal innervation
Testing tactile function
Periodontal tactile function
Functional testing of the oral somatosensory system
From periodontal tactile function to peri-implant osseoperception
Conclusions
**Part 2: Epidemiology**
**7 Epidemiology of Periodontal Diseases**
Introduction
Methodological issues
Prevalence of periodontal diseases
Risk factors for periodontitis
Periodontal infections and risk for systemic disease
**Part 3: Microbiology**
**8 Oral Biofilms and Calculus**
Microbial considerations
General introduction to plaque formation
Dental plaque as a biofilm
Structure of dental plaque
Dental calculus
**9 Periodontal Infections**
Introduction
Historical perspective
Current suspected pathogens of destructive periodontal diseases
The nature of dental plaque – the biofilm way of life
Prerequisites for periodontal disease initiation and progression
Mechanisms of pathogenicity
Effect of therapy on subgingival biofilms
**10 Peri-implant Infections**
Introduction
Early biofilm development on implant surfaces
Time of implant exposure and climax community complexity
The microbiota on implants in edentulous subjects
The microbiota on implants in partially edentulous subjects
The microbiota on implants in subjects with a history of periodontal disease
The microbiota of peri-implantitis sites
**Part 4: Host–Parasite Interactions**
**11 Pathogenesis of Periodontitis**
Introduction
Clinically healthy gingiva
Gingival inflammation
Different lesions in gingivitis/periodontitis
Host–parasite interactions
Host defense processes
**12 Modifying Factors**
Diabetes mellitus
Puberty, pregnancy, and the menopause
Tobacco smoking
**13 Susceptibility**
Introduction
Evidence for the role of genetics in periodontitis
A gene mutation with major effect on human disease and its association with periodontitis
Disease-modifying genes in relation to periodontitis
Disease-modifying genes in relation to implant failures and peri-implantitis
Conclusions and future developments
**Part 5: Trauma from Occlusion**
**14 Trauma from Occlusion: Periodontal Tissues**
Definition and terminology
Trauma from occlusion and plaque-associated periodontal disease
Analysis of human autopsy material
Clinical trials
Animal experiments
**15 Trauma from Occlusion: Peri-implant Tissues**
Introduction
Orthodontic loading and alveolar bone
Bone reactions to functional loading
Excessive occlusal load on implants
Static and cyclic loads on implants
Load and loss of osseointegration
Masticatory occlusal forces on implants
Tooth–implant supported reconstructions
**Part 6: Periodontal Pathology**
**16 Non-Plaque Induced Inflammatory Gingival Lesions**
Gingival diseases of specific bacterial origin
Gingival diseases of viral origin
Gingival diseases of fungal origin
Gingival lesions of genetic origin
Gingival diseases of systemic origin
Traumatic lesions
**17 Plaque-Induced Gingival Diseases**
Classification criteria for gingival diseases
Plaque-induced gingivitis
Gingival diseases associated with endogenous hormones
Gingival diseases associated with medications
Gingival diseases associated with systemic diseases
Gingival diseases associated with malnutrition
Gingival diseases associated with heredity
Gingival diseases associated with ulcerative lesions
Treatment of plaque-induced gingival diseases
The significance of gingivitis
**18 Chronic Periodontitis**
Clinical features of chronic periodontitis
Overall characteristics of chronic periodontitis
Gingivitis as a risk for chronic periodontitis
Susceptibility to chronic periodontitis
Prevalence of chronic periodontitis
Progression of chronic periodontitis
Risk factors for chronic periodontitis
Scientific basis for treatment of chronic periodontitis
**19 Aggressive Periodontitis**
Classification and clinical syndromes
Epidemiology
Etiology and pathogenesis
Diagnosis
Principles of therapeutic intervention
**20 Necrotizing Periodontal Disease**
Nomenclature
Prevalence
Clinical characteristics
Diagnosis
Histopathology
Microbiology
Host response and predisposing factors
Treatment
**21 Periodontal Disease as a Risk for Systemic Disease**
Early twentieth century concepts
Periodontitis as a risk for cardiovascular disease
Periodontitis as a risk for adverse pregnancy outcomes
Periodontitis as a risk for diabetic complications
Periodontitis as a risk for respiratory infections
Effects of treatment of periodontitis on systemic diseases
**22 The Periodontal Abscess**
Introduction
Classification
Prevalence
Pathogenesis and histopathology
Microbiology
Diagnosis
Treatment
Complications
**23 Lesions of Endodontic Origin**
Introduction
Disease processes of the dental pulp
Effects of periodontal disease and periodontal therapy on the condition of the pulp
**Part 7: Peri-implant Pathology**
**24 Peri-implant Mucositis and Peri-implantitis**
Definitions
Ridge mucosa
Peri-implant mucosa
Peri-implant mucositis
Peri-implantitis
**Part 8: Tissue Regeneration**
**25 Concepts in Periodontal Tissue Regeneration**
Introduction
Regenerative periodontal surgery
Periodontal wound healing
Regenerative concepts
Assessment of periodontal regeneration
**Volume 2: CLINICAL CONCEPTS**
**Part 9: Examination Protocols**
**26 Examination of Patients with Periodontal Diseases**
History of periodontal patients
Signs and symptoms of periodontal diseases
Diagnosis of periodontal lesions
Oral hygiene status
Additional dental examinations
**27 Examination of the Candidate for Implant Therapy**
Dental implants in periodontally compromised patients
Patient history
Local examination
Patient-specific risk assessment
**28 Radiographic Examination of the Implant Patient**
Introduction
Radiographic examination for implant planning purposes – general aspects
Radiographic examination for implant planning purposes – upper jaw examination
Radiographic examination for implant planning purposes – lower jaw examination
Radiographic monitoring of implant treatment
Image-guided surgery
**29 Examination of Patients with Implant-Supported Restorations**
Identification of the presence of implants and implant systems
Clinical inspection and examination
Technical failures/complications
Function
Implant
Soft tissues
Esthetics
**30 Risk Assessment of the Implant Patient**
Principles of risk assessment
Local risk factors and conditions
Systemic risk factors
Importance of behavioral considerations in risk assessment
Interest and commitment to post-treatment care and maintenance program
**Part 10: Treatment Planning Protocols**
**31 Treatment Planning of Patients with Periodontal Diseases**
Screening for periodontal disease
Diagnosis
Treatment planning
Case report
**32 Treatment Planning for Implant Therapy in the Periodontally Compromised Patient**
Prognosis of implant therapy in the periodontally compromised patient
Strategies in treatment planning
Treatment decisions – case reports
**33 Systemic Phase of Therapy**
Introduction
Protection of the dental team and other patients against infectious diseases
Protection of the patient's health
Prevention of complications
Systemic diseases, disorders or conditions influencing pathogenesis and healing potential
Control of anxiety and pain
Smoking counseling
**Part 11: Initial Periodontal Therapy (Infection Control)**
**34 Motivational Interviewing**
The importance of behavioral change counseling in periodontal care
Development of motivational interviewing
Evidence for motivational interviewing
Implementation of motivational interviewing into the periodontal treatment plan
Case examples for oral hygiene motivation
Case example for tobacco use cessation
**35 Mechanical Supragingival Plaque Control**
Importance of supragingival plaque removal
Self-performed plaque control
Importance of instruction and motivation in mechanical plaque control
**36 Chemical Supragingival Plaque Control**
Classification and terminology of agents
The concept of chemical supragingival plaque control
Chemical plaque control agents
Chlorhexidine
Evaluation of chemical agents and products
**37 Non-surgical Therapy**
Introduction
Detection and removal of dental calculus
Methods used for non-surgical root surface debridement
The influence of mechanical debridement on subgingival biofilms
Implication of furcation involvement
Pain and discomfort following non-surgical therapy
Re-evaluation
Prediction of outcome and evaluation of treatment
Full-mouth disinfection
**Part 12: Additional Therapy**
**38 Periodontal Surgery: Access Therapy**
Introduction
Techniques in periodontal pocket surgery
Distal wedge procedures
Osseous surgery
General guidelines for periodontal surgery
Outcome of surgical periodontal therapy
**39 Treatment of Furcation-Involved Teeth**
Terminology
Anatomy
Diagnosis
Differential diagnosis
Therapy
Prognosis
**40 Endodontics and Periodontics**
Introduction
Infectious processes in the periodontium of endodontic origin
Iatrogenic root perforations
Vertical root fractures
External root resorptions
**41 Treatment of Peri-implant Lesions**
Introduction
The diagnostic process
Treatment strategies
Cumulative Interceptive Supportive Therapy (CIST)
**42 Antibiotics in Periodontal Therapy**
Principles of antibiotic therapy
Evaluation of antibiotics for periodontal therapy
**Part 13: Reconstructive Therapy**
**43 Regenerative Periodontal Therapy**
Introduction
Classification and diagnosis of periodontal osseous defects
Clinical indications
Long-term effects and benefits of regeneration
Evidence for clinical efficacy and effectiveness
Patient and defect prognostic factors
The relevance of the surgical approach
Barrier materials for regenerative surgery
Bone replacement grafts
Biologically active regenerative materials
Membranes combined with other regenerative procedures
Root surface biomodification
Clinical strategies
**44 Mucogingival Therapy – Periodontal Plastic Surgery**
Introduction
Gingival augmentation
Root coverage
Interdental papilla reconstruction
Crown-lengthening procedures
The deformed edentulous ridge
**45 Periodontal Plastic Microsurgery**
Microsurgical techniques in dentistry (development of concepts)
Concepts in microsurgery
Clinical indications and limitations
Comparison to conventional mucogingival interventions
**46 Re-osseointegration**
Introduction
Is it possible to resolve a marginal hard tissue defect adjacent to an oral implant?
Is re-osseointegration a feasible outcome of regenerative therapy?
Is the quality of the implant surface important in a healing process that may lead to re-osseointegration?
**Part 14: Surgery for Implant Installation**
**47 Timing of Implant Placement**
Introduction
Type 1: placement of an implant as part of the same surgical procedure and immediately following tooth extraction
Type 2: completed soft tissue coverage of the tooth socket
Type 3: substantial bone fill has occurred in the extraction socket
Type 4: the alveolar ridge is healed following tooth loss
Clinical concepts
**48 The Surgical Site**
Bone: shape and quality
Implant placement
Anatomic landmarks with potential risk
Implant position
Implant direction
Healing time
**Part 15: Reconstructive Ridge Therapy**
**49 Ridge Augmentation Procedures**
Introduction
Patient situation
Bone morphology
Soft tissue morphology
Augmentation materials
Long-term results
Clinical concepts
Future developments
**50 Elevation of the Maxillary Sinus Floor**
Introduction
Treatment options in the posterior maxilla
Sinus floor elevation with a lateral approach
Sinus floor elevation with the crestal approach (osteotome technique)
Short implants
Conclusions and clinical suggestions
**Part 16: Occlusal and Prosthetic Therapy**
**51 Tooth-Supported Fixed Partial Dentures**
Clinical symptoms of trauma from occlusion
Tooth mobility crown excursion/root displacement
Treatment of increased tooth mobility
**52 Implants in Restorative Dentistry**
Introduction
Treatment concepts
Indications for implants
Increase the subjective chewing comfort
Preservation of natural tooth substance and existing functional, satisfactory reconstructions
Replacement of strategically important missing teeth
**53 Implants in the Esthetic Zone**
Basic concepts
Anterior single-tooth replacement
Multiple-unit anterior fixed implant restorations
Conclusions and perspectives
**54 Implants in the Posterior Dentition**
Basic concepts
Restoration of the distally shortened arch with fixed implant-supported prostheses
Multiple-unit tooth-bound posterior implant restorations
Posterior single-tooth replacement
Clinical applications
Concluding remarks and perspectives
**55 Implant–Implant and Tooth–Implant Supported Fixed Partial Dentures**
Introduction
Initial patient assessment
Implant treatment planning for the edentulous arch
Prosthesis design and partially edentulous tooth replacement therapy
Tooth–implant fixed partial dentures
**56 Complications Related to Implant-Supported Restorations**
Introduction
Clinical complications in conventional fixed restorations
Clinical complications in implant-supported restorations
Other issues related to prosthetic complications
**Part 17: Orthodontics and Periodontics**
**57 Tooth Movements in the Periodontally Compromised Patient**
Orthodontic tooth movement in adults with periodontal tissue breakdown
Specific factors associated with orthodontic tooth movement in adults
Gingival recession
Minor surgery associated with orthodontic therapy
**58 Implants Used for Orthodontic Anchorage**
Introduction
Evolution of implants for orthodontic anchorage
Prosthetic implants for orthodontic anchorage
Orthodontic implants as temporary anchorage devices
**Part 18: Supportive Care**
**59 Supportive Periodontal Therapy (SPT)**
Definitions
Basic paradigms for the prevention of periodontal disease
Patients at risk for periodontitis without SPT
SPT for patients with gingivitis
SPT for patients with periodontitis
Continuous multi-level risk assessment
Objectives for SPT
SPT in daily practice
**Part 19: Halitosis**
**60 Halitosis Control**
Introduction
Diagnosis
Therapy
© 2008 by Blackwell Munksgaard, a Blackwell Publishing company
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First published 1983 by Munksgaard
Second edition published 1989
Third edition published 1997
Fourth edition published by Blackwell Munksgaard 2003
Reprinted 2003, 2005, 2006
Fifth edition 2008 by Blackwell Publishing Ltd
ISBN: 978-1-4051-6099-5
Library of Congress Cataloging-in-Publication Data
Clinical periodontology and implant dentistry / edited by Jan Lindhe,
Niklaus P. Lang, Thorkild Karring. — 5th ed.
p. ; cm.
Includes bibliographical references and index.
ISBN: 978-1-4051-6099-5 (hardback : alk. paper)
1. Periodontics. 2. Periodontal disease. 3. Dental implants. I. Lindhe, Jan.
II. Lang, Niklaus Peter. III. Karring, Thorkild.
[DNLM: 1. Periodontal Diseases. 2. Dental Implantation. 3. Dental Implants.
WU 240 C6415 2008]
RK361.C54 2008
617.6′32—dc22
2007037124
A catalogue record for this title is available from the British Library
For further information on Blackwell Publishing, visit our website:
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**Contributors**
**Martin Addy**
Division of Restorative Dentistry (Periodontology)
Department of Oral and Dental Science
Bristol Dental School and Hospital
Bristol
UK
**Maurício Araújo**
Department of Dentistry
State University of Maringá
Maringá
Paraná
Brazil
**Gary C. Armitage**
Division of Periodontology
School of Dentistry
University of California San Francisco
San Francisco
CA
USA
**Rolf Attström**
Department of Periodontology
Centre for Oral Health Sciences
Malmö University
Malmö
Sweden
**Robert A. Bagramian**
Department of Periodontics and Oral Medicine
University of Michigan School of Dentistry
Ann Arbor
MI
USA
**Hans-Rudolf Baur**
Department of Internal Medicine
Spital Bern Tiefenau
Berne
Switzerland
**Urs C. Belser**
Department of Prosthetic Dentistry
School of Dental Medicine
University of Geneva
Geneva
Switzerland
**Gunnar Bergenholtz**
Department of Endodontology
Institute of Odontology
The Sahlgrenska Academy at Göteborg University
Göteborg
Sweden
**Tord Berglundh**
Department of Periodontology
Institute of Odontology
The Sahlgrenska Academy at Göteborg University
Göteborg
Sweden
**Jean-Pierre Bernard**
Department of Oral Surgery and Stomatology
School of Dental Medicine
University of Geneva
Geneva
Switzerland
**Urs Brägger**
Department of Periodontology and Fixed Prosthodontics
School of Dental Medicine
University of Berne
Berne
Switzerland
**Rino Burkhardt**
Private Practice
Zürich
Switzerland
**Daniel Buser**
Department of Oral Surgery and Stomatology
School of Dental Medicine
University of Berne
Berne
Switzerland
**Gianfranco Carnevale**
Private Practice
Rome
Italy
**Delwyn Catley**
Department of Psychology
University of Missouri – Kansas City
Kansas City
MO
USA
**Noel Claffey**
Dublin Dental School and Hospital
Trinity College
Dublin
Ireland
**Lyndon F. Cooper**
Department of Prosthodontics
University of North Carolina
Chapel Hill
NC
USA
**Pierpaolo Cortellini**
Private Practice
Florence
Italy
**José J. Echeverría**
Department of Periodontics
School of Dentistry
University of Barcelona
Barcelona
Spain
**Ingvar Ericsson**
Department of Prosthetic Dentistry
Faculty of Odontology
Malmö University
Malmö
Sweden
**William V. Giannobile**
Michigan Center for Oral Health Research
University of Michigan Clinical Center
Ann Arbor
MI
USA
**Hans-Göran Gröndahl**
Department of Oral and Maxillofacial Radiology
Institute of Odontology
The Sahlgrenska Academy at Göteborg University
Göteborg
Sweden
**Kerstin Gröndahl**
Department of Oral and Maxillofacial Radiology
Institute of Odontology
The Sahlgrenska Academy at Göteborg University
Göteborg
Sweden
**Anne D. Haffajee**
Department of Periodontology
The Forsyth Institute
Boston
MA
USA
**Christoph H.F. Hämmerle**
Clinic for Fixed and Removable Prosthodontics
Center for Dental and Oral Medicine and Cranio-Maxillofacial Surgery
University of Zürich
Zürich
Switzerland
**Gunnar Hasselgren**
Division of Endodontics
School of Dental and Oral Surgery
Columbia University College of Dental Medicine
New York
NY
USA
**Lars Heijl**
Department of Periodontology
Institute of Odontology
The Sahlgrenska Academy at Göteborg University
Göteborg
Sweden
**David Herrera**
Faculty of Odontology
University Complutense
Madrid
Spain
**Palle Holmstrup**
Department of Periodontology
School of Dentistry
University of Copenhagen
Copenhagen
Denmark
**Reinhilde Jacobs**
Oral Imaging Center
School of Dentistry, Oral Pathology and Maxillofacial Surgery
Catholic University of Leuven
Leuven
Belgium
**Ronald E. Jung**
Clinic for Fixed and Removable Prosthodontics
Center for Dental and Oral Medicine and Cranio-Maxillofacial Surgery
University of Zürich
Zürich
Switzerland
**Thorkild Karring**
Department of Periodontology and Oral Gerontology
Royal Dental College
University of Aarhus
Aarhus
Denmark
**Denis F. Kinane**
Oral Health and Systemic Disease Research Facility
School of Dentistry
University of Louisville
Louisville
KY
USA
**Y. Joon Ko**
Department of Prosthodontics
University of Iowa
Iowa City
IA
USA
**Susan Krigel**
Department of Psychology
University of Missouri – Kansas City
Kansas City
MO
USA
**Marja L. Laine**
Department of Oral Microbiology
Academic Centre for Dentistry Amsterdam (ACTA)
Amsterdam
The Netherlands
**Niklaus P. Lang**
Department of Periodontology and Fixed Prosthodontics
School of Dental Medicine
University of Berne
Berne
Switzerland
**Ulf Lekholm**
Department of Oral and Maxillofacial Surgery
Institute of Odontology
The Sahlgrenska Academy at Göteborg University
Göteborg
Sweden
**Jan Lindhe**
Department of Periodontology
Institute of Odontology
The Sahlgrenska Academy at Göteborg University
Göteborg
Sweden
**Bruno G. Loos**
Department of Periodontology
Academic Centre for Dentistry Amsterdam (ACTA)
Amsterdam
The Netherlands
**Tord Lundgren**
Department of Periodontics
School of Dentistry
Loma Linda University
Loma Linda
CA
USA
**Angelo Mariotti**
Section of Periodontology
Ohio State University College of Dentistry
Columbus
OH
USA
**Andrea Mombelli**
Department of Periodontology and Oral Pathophysiology
School of Dental Medicine
University of Geneva
Geneva
Switzerland
**John Moran**
Division of Restorative Dentistry (Periodontology)
Department of Oral and Dental Science
Bristol Dental School and Hospital
Bristol
UK
**Sture Nyman**
Deceased
**Richard Palmer**
Restorative Dentistry
King's College London Dental Institute
Guy's, King's and St Thomas' Hospitals
London
UK
**Panos N. Papapanou**
Division of Periodontics
Section of Oral and Diagnostic Sciences
Columbia University College of Dental Medicine
New York
NY
USA
**David W. Paquette**
Department of Periodontology
University of North Carolina School of Dentistry
Chapel Hill
NC
USA
**Giovan P. Pini Prato**
Department of Periodontology
University of Florence
Florence
Italy
**Bjarni E. Pjetursson**
Department of Periodontology and Fixed Prosthodontics
School of Dental Medicine
University of Berne
Berne
Switzerland
**Ioannis Polyzois**
Dublin Dental School and Hospital
Trinity College
Dublin
Ireland
**Roberto Pontoriero**
Private Practice
Milan
Italy
**Marc Quirynen**
Department of Periodontology
School of Dentistry
Catholic University of Leuven
Leuven
Belgium
**Christoph A. Ramseier**
Michigan Center for Oral Health Research
Department of Periodontics and Oral Medicine
University of Michigan School of Dentistry
Ann Arbor
MI
USA
**Domenico Ricucci**
Private Practice
Rome
Italy
**Hector F. Rios**
Department of Periodontics and Oral Medicine
University of Michigan School of Dentistry
Ann Arbor
MI
USA
**Giovanni E. Salvi**
Department of Periodontology
School of Dental Medicine
University of Berne
Berne
Switzerland
**Mariano Sanz**
Faculty of Odontology
University Complutense
Madrid
Spain
**Marc A. Schätzle**
Department of Orthodontics and Pediatric Dentistry
University of Zürich
Zürich
Switzerland
**Sigmund S. Socransky**
Department of Periodontology
The Forsyth Institute
Boston
MA
USA
**Mena Soory**
Restorative Dentistry
King's College London Dental Institute
Guy's, King's and St Thomas' Hospitals
London
UK
**Clark M. Stanford**
Dows Institute for Dental Research
University of Iowa
Iowa City
IA
USA
**Ricardo P. Teles**
Department of Periodontology
The Forsyth Institute
Boston
MA
USA
**Maurizio S. Tonetti**
Private Practice
Genoa
Italy
**Leonardo Trombelli**
Research Center for the Study of Periodontal Diseases
University of Ferrara
Ferrara
Italy
**Ubele van der Velden**
Department of Periodontology
Academic Centre for Dentistry Amsterdam (ACTA)
Amsterdam
The Netherlands
**Fridus van der Weijden**
Department of Periodontology
Academic Centre for Dentistry Amsterdam (ACTA)
Amsterdam
The Netherlands
**Arie J. van Winkelhoff**
Department of Oral Microbiology
Academic Centre for Dentistry Amsterdam (ACTA)
Amsterdam
The Netherlands
**Hans-Peter Weber**
Department of Restorative Dentistry and Biomaterials Science
Harvard School of Dental Medicine
Boston
MA
USA
**Jan L. Wennström**
Department of Periodontology
Institute of Odontology
The Sahlgrenska Academy at Göteborg University
Göteborg
Sweden
**Jytte Westergaard**
Department of Periodontology
School of Dentistry
University of Copenhagen
Copenhagen
Denmark
**Ray C. Williams**
Department of Periodontology
University of North Carolina School of Dentistry
Chapel Hill
NC
USA
**Edwin G. Winkel**
Department of Periodontology
Academic Centre for Oral Health
University Medical Centre Groningen
Groningen
The Netherlands
**Björn U. Zachrisson**
Department of Orthodontics
Dental Faculty
University of Oslo
Oslo
Norway
**Giovanni Zucchelli**
Department of Periodontology
Bologna University
Bologna
Italy
Preface
When the groundwork for the fifth edition of _Clinical Periodontology and Implant Dentistry_ began in early 2007, it became clear that we had reached a fork in the road. It has always been my intention that each successive edition of this work should reflect the state of the art of clinical periodontology and, in doing such, should run the gamut of topics within this subject area. However, thorough coverage of an already large and now rapidly expanding specialty has resulted in a book of commensurate size and therefore for the fifth edition, the decision was taken to divide the book into two volumes: basic concepts and clinical concepts. The decision to make the split a purely physical one, and not an intellectual one, reflects the realization that over the past decade, implant dentistry has become a basic part of periodontology. The integrated structure of this latest edition of the textbook mirrors this merger.
In order for the student of dentistry, whatever his or her level, to learn how teeth and implants may function together as separate or connected units in the same dentition, a sound knowledge of the tissues that surround the natural tooth and the dental implant, as well as an understanding of the various lesions that may occur in the supporting tissues, is imperative. Hence, in both volumes of the textbook, chapters dealing with traditional periodontal issues, such as anatomy, pathology and treatment, are followed by similar topics related to tissues surrounding dental implants. In the first volume of the fifth edition, "basic concepts" as they relate to anatomy, microbiology and pathology, for example, are presented, while in the second volume ("clinical concepts"), various aspects of often evidence-based periodontal and restorative examination and treatment procedures are outlined.
It is my hope that the fifth edition of _Clinical Periodontology and Implant Dentistry_ will challenge the reader intellectually, provide elucidation and clarity of information, and also impart an understanding of how the information presented in the text can, and should, be used in the practice of contemporary dentistry.
Jan Lindhe
# Volume 1
# BASIC CONCEPTS
_Edited by_
Jan Lindhe
Niklaus P. Lang
Thorkild Karring
# Part 1: Anatomy
1 The Anatomy of Periodontal Tissues
_Jan Lindhe, Thorkild Karring, and Maurício Araújo_
2 The Edentulous Alveolar Ridge
_Maurício Araújo and Jan Lindhe_
3 The Mucosa at Teeth and Implants
_Jan Lindhe, Jan L. Wennström, and Tord Berglundh_
4 Bone as a Tissue
_William V. Giannobile, Hector F. Rios, and Niklaus P. Lang_
5 Osseointegration
_Jan Lindhe, Tord Berglundh, and Niklaus P. Lang_
6 Periodontal Tactile Perception and Peri-implant Osseoperception
_Reinhilde Jacobs_
# Chapter 1
# The Anatomy of Periodontal Tissues
Jan Lindhe, Thorkild Karring, and Maurício Araújo
* * *
Introduction
Gingiva
Macroscopic anatomy
Microscopic anatomy
Periodontal ligament
Root cementum
Alveolar bone
Blood supply of the periodontium
Lymphatic system of the periodontium
Nerves of the periodontium
* * *
# Introduction
This chapter includes a brief description of the characteristics of the normal periodontium. It is assumed that the reader has prior knowledge of oral embryology and histology. The periodontium (peri = around, odontos = tooth) comprises the following tissues (Fig. 1-1): (1) the _gingiva_ (G), (2) the _periodontal ligament_ (PL), (3) the _root cementum_ (RC), and (4) the _alveolar bone_ (AP). The alveolar bone consists of two components, the _alveolar bone proper_ (ABP) and the alveolar process. The alveolar bone proper, also called "bundle bone", is continuous with the alveolar process and forms the thin bone plate that lines the alveolus of the tooth.
The main function of the periodontium is to attach the tooth to the bone tissue of the jaws and to maintain the integrity of the surface of the masticatory mucosa of the oral cavity. The periodontium, also called "the attachment apparatus" or "the supporting tissues of the teeth", constitutes a developmental, biologic, and functional unit which undergoes certain changes with age and is, in addition, subjected to morphologic changes related to functional alterations and alterations in the oral environment.
The development of the periodontal tissues occurs during the development and formation of teeth. This process starts early in the embryonic phase when cells from the neural crest (from the neural tube of the embryo) migrate into the first branchial arch. In this position the neural crest cells form a band of _ectomesenchyme_ beneath the epithelium of the stomatodeum (the primitive oral cavity). After the uncommitted neural crest cells have reached their location in the jaw space, the epithelium of the stomatodeum releases factors which initiate epithelial–ectomesenchymal interactions. Once these interactions have occurred, the ectomesenchyme takes the dominant role in the further development. Following the formation of the _dental lamina_ , a series of processes are initiated (bud stage, cap stage, bell stage with root development) which result in the formation of a tooth and its surrounding periodontal tissues, including the alveolar bone proper. During the cap stage, condensation of ectomesenchymal cells appears in relation to the dental epithelium (the dental organ (DO) ), forming the _dental papilla_ (DP) that gives rise to the dentin and the pulp, and the _dental follicle_ (DF) that gives rise to the periodontal supporting tissues (Fig. 1-2). The decisive role played by the ectomesenchyme in this process is further established by the fact that the tissue of the dental papilla apparently also determines the shape and form of the tooth.
**Fig. 1-1**
**Fig. 1-2**
If a tooth germ in the bell stage of development is dissected and transplanted to an ectopic site (e.g. the connective tissue or the anterior chamber of the eye), the tooth formation process continues. The crown and the root are formed, and the supporting structures, i.e. cementum, periodontal ligament, and a thin lamina of alveolar bone proper, also develop. Such experiments document that all information necessary for the formation of a tooth and its attachment apparatus obviously resides within the tissues of the dental organ and the surrounding ectomesenchyme. The dental organ is the formative organ of enamel, the dental papilla is the formative organ of the dentin–pulp complex, and the dental follicle is the formative organ of the attachment apparatus (the cementum, the periodontal ligament, and the alveolar bone proper).
The development of the root and the periodontal supporting tissues follows that of the crown. Epithelial cells of the external and internal dental epithelium (the dental organ) proliferate in an apical direction forming a double layer of cells named _Hertwig's epithelial root sheath_ (RS). The odontoblasts (OB) forming the dentin of the root differentiate from ectomesenchymal cells in the dental papilla under inductive influence of the inner epithelial cells (Fig. 1-3). The dentin (D) continues to form in an apical direction producing the framework of the root. During formation of the root, the periodontal supporting tissues, including acellular cementum, develop. Some of the events in the cementogenesis are still unclear, but the following concept is gradually emerging.
**Fig. 1-3**
At the start of dentin formation, the inner cells of Hertwig's epithelial root sheath synthesize and secrete enamel-related proteins, probably belonging to the amelogenin family. At the end of this period, the epithelial root sheath becomes fenestrated and ectomesenchymal cells from the dental follicle penetrate through these fenestrations and contact the root surface. The ectomesenchymal cells in contact with the enamel-related proteins differentiate into cementoblasts and start to form cementoid. This cementoid represents the organic matrix of the cementum and consists of a ground substance and collagen fibers, which intermingle with collagen fibers in the not yet fully mineralized outer layer of the dentin. It is assumed that the cementum becomes firmly attached to the dentin through these fiber interactions. The formation of the cellular cementum, which covers the apical third of the dental roots, differs from that of acellular cementum in that some of the cementoblasts become embedded in the cementum.
**Fig. 1-4**
**Fig. 1-5**
The remaining parts of the periodontium are formed by ectomesenchymal cells from the dental follicle lateral to the cementum. Some of them differentiate into periodontal fibroblasts and form the fibers of the periodontal ligament while others become osteoblasts producing the alveolar bone proper in which the periodontal fibers are anchored. In other words, the primary alveolar wall is also an ectomesenchymal product. It is likely, but still not conclusively documented, that ectomesenchymal cells remain in the mature periodontium and take part in the turnover of this tissue.
# Gingiva
## Macroscopic anatomy
The oral mucosa (mucous membrane) is continuous with the skin of the lips and the mucosa of the soft palate and pharynx. The oral mucosa consists of (1) the _masticatory mucosa_ , which includes the gingiva and the covering of the hard palate, (2) the _specialized mucosa_ , which covers the dorsum of the tongue, and (3) the remaining part, called the _lining mucosa_.
**Fig. 1-4** The gingiva is that part of the masticatory mucosa which covers the alveolar process and surrounds the cervical portion of the teeth. It consists of an epithelial layer and an underlying connective tissue layer called the _lamina propria_. The gingiva obtains its final shape and texture in conjunction with eruption of the teeth.
In the coronal direction the coral pink gingiva terminates in the _free gingival margin_ , which has a scalloped outline. In the apical direction the gingiva is continuous with the loose, darker red _alveolar mucosa_ (lining mucosa) from which the gingiva is separated by a usually easily recognizable borderline called either the mucogingival junction (arrows) or the mucogingival line.
**Fig. 1-6**
**Fig. 1-7**
**Fig. 1-5** There is no mucogingival line present in the palate since the hard palate and the maxillary alveolar process are covered by the same type of masticatory mucosa.
**Fig. 1-6** Two parts of the gingiva can be differentiated:
1. The free gingiva (FG)
2. The attached gingiva (AG).
The free gingiva is coral pink, has a dull surface and firm consistency. It comprises the gingival tissue at the vestibular and lingual/palatal aspects of the teeth, and the _interdental gingiva_ or the _interdental papillae_. On the vestibular and lingual side of the teeth, the free gingiva extends from the gingival margin in apical direction to the _free gingival groove_ which is positioned at a level corresponding to the level of the _cemento-enamel junction_ (CEJ). The attached gingiva is demarcated by the mucogingival junction (MGJ) in the apical direction.
**Fig. 1-8**
**Fig. 1-7** The free gingival margin is often rounded in such a way that a small invagination or sulcus is formed between the tooth and the gingiva (Fig. 1-7a).
When a periodontal probe is inserted into this invagination and, further apically, towards the cemento-enamel junction, the gingival tissue is separated from the tooth, and a " _gingival pocket_ " or " _gingival crevice_ " is artificially opened. Thus, in normal or clinically healthy gingiva there is in fact no "gingival pocket" or "gingival crevice" present but the gingiva is in close contact with the enamel surface. In the illustration to the right (Fig. 1-7b), a periodontal probe has been inserted in the tooth/gingiva interface and a "gingival crevice" artificially opened approximately to the level of the cemento-enamel junction.
After completed tooth eruption, the free gingival margin is located on the enamel surface approximately 1.5–2 mm coronal to the cemento-enamel junction.
**Fig. 1-8** The shape of the interdental gingiva (the interdental papilla) is determined by the contact relationships between the teeth, the width of the approximal tooth surfaces, and the course of the cemento-enamel junction. In anterior regions of the dentition, the interdental papilla is of pyramidal form (Fig. 1-8b) while in the molar regions, the papillae are more flattened in the buccolingual direction (Fig. 18a). Due to the presence of interdental papillae, the free gingival margin follows a more or less accentuated, scalloped course through the dentition.
**Fig. 1-9**
**Fig. 1-9c**
**Fig. 1-10**
**Fig. 1-9** In the premolar/molar regions of the dentition, the teeth have approximal contact surfaces (Fig. 1-9a) rather than contact points. Since the interdental papilla has a shape in conformity with the outline of the interdental contact surfaces, a concavity – _a col_ – is established in the premolar and molar regions, as demonstrated in Fig. 1-9b, where the distal tooth has been removed. Thus, the interdental papillae in these areas often have one vestibular (VP) and one lingual/ palatal portion (LP) separated by the col region. The col region, as demonstrated in the histological section (Fig. 1-9c), is covered by a thin non-keratinized epithelium (arrows). This epithelium has many features in common with the junctional epithelium (see Fig. 1-34).
**Fig. 1-10** The attached gingiva is demarcated in the coronal direction, by the free gingival groove (GG) or, when such a groove is not present, by a horizontal plane placed at the level of the cemento-enamel junction. In clinical examinations it was observed that a free gingival groove is only present in about 30–40% of adults.
**Fig. 1-11**
The free gingival groove is often most pronounced on the vestibular aspect of the teeth, occurring most frequently in the incisor and premolar regions of the mandible, and least frequently in the mandibular molar and maxillary premolar regions.
The attached gingiva extends in the apical direction to the mucogingival junction (arrows), where it becomes continuous with the alveolar (lining) mucosa (AM). It is of firm texture, coral pink in color, and often shows small depressions on the surface. The depressions, named "stippling", give the appearance of orange peel. It is firmly attached to the underlying alveolar bone and cementum by connective tissue fibers, and is, therefore, comparatively immobile in relation to the underlying tissue. The darker red alveolar mucosa (AM) located apical to the mucogingival junction, on the other hand, is loosely bound to the underlying bone. Therefore, in contrast to the attached gingiva, the alveolar mucosa is mobile in relation to the underlying tissue.
**Fig. 1-12**
**Fig. 1-11** describes how the width of the gingiva varies in different parts of the mouth. In the maxilla (Fig. 1-11a) the vestibular gingiva is generally widest in the area of the incisors and most narrow adjacent to the premolars. In the mandible (Fig. 1-11b) the gingiva on the lingual aspect is particularly narrow in the area of the incisors and wide in the molar region. The range of variation is 1–9 mm.
**Fig. 1-12** illustrates an area in the mandibular premolar region where the gingiva is extremely narrow. The arrows indicate the location of the mucogingival junction. The mucosa has been stained with an iodine solution in order to distinguish more accurately between the gingiva and the alveolar mucosa.
**Fig. 1-13** depicts the result of a study in which the width of the attached gingiva was assessed and related to the age of the patients examined. It was found that the gingiva in 40–50-year-olds was significantly wider than that in 20–30-year-olds. This observation indicates that the width of the gingiva tends to increase with age. Since the mucogingival junction remains stable throughout life in relation to the lower border of the mandible, the increasing width of the gingiva may suggest that the teeth, as a result of occlusal wear, erupt slowly throughout life.
## Microscopic anatomy
### Oral epithelium
**Fig. 1-14a** A schematic drawing of a histologic section (see Fig. 1-14b) describing the composition of the gingiva and the contact area between the gingiva and the enamel (E).
**Fig. 1-13**
**Fig 1-14b** The free gingiva comprises all epithelial and connective tissue structures (CT) located coronal to a horizontal line placed at the level of the cemento-enamel junction (CEJ). The epithelium covering the free gingiva may be differentiated as follows:
* _Oral epithelium_ (OE), which faces the oral cavity
* _Oral sulcular epithelium_ (OSE), which faces the tooth without being in contact with the tooth surface
* _Junctional epithelium_ (JE), which provides the contact between the gingiva and the tooth.
**Fig. 1-14a**
**Fig. 1-14c** The boundary between the oral epithelium (OE) and underlying connective tissue (CT) has a wavy course. The connective tissue portions which project into the epithelium are called _connective tissue papillae_ (CTP) and are separated from each other by _epithelial ridges_ – so-called _rete pegs_ (ER). In normal, non-inflamed gingiva, rete pegs and connective tissue papillae are lacking at the boundary between the junctional epithelium and its underlying connective tissue (Fig. 1-14b). Thus, a characteristic morphologic feature of the oral epithelium and the oral sulcular epithelium is the presence of rete pegs, while these structures are lacking in the junctional epithelium.
**Fig. 1-14b**
**Fig. 1-14c**
**Fig. 1-15**
**Fig. 1-16**
**Fig. 1-17**
**Fig. 1-15** presents a model, constructed on the basis of magnified serial histologic sections, showing the subsurface of the oral epithelium of the gingiva after the connective tissue has been removed. The subsurface of the oral epithelium (i.e. the surface of the epithelium facing the connective tissue) exhibits several depressions corresponding to the connective tissue papillae (in Fig. 1-16) which project into the epithelium. It can be seen that the epithelial projections, which in histologic sections separate the connective tissue papillae, constitute a continuous system of epithelial ridges.
**Fig. 1-16** presents a model of the connective tissue, corresponding to the model of the epithelium shown in Fig. 1-15. The epithelium has been removed, thereby making the vestibular aspect of the gingival connective tissue visible. Notice the connective tissue papillae which project into the space that was occupied by the oral epithelium (OE) in Fig. 1-15 and by the oral sulcular epithelium (OSE) on the back of the model.
**Fig. 1-17a** In 40% of adults the attached gingiva shows a stippling on the surface. The photograph shows a case where this stippling is conspicuous (see also Fig. 1-10).
**Fig. 1-18**
**Fig. 1-17b** presents a magnified model of the outer surface of the oral epithelium of the attached gingiva. The surface exhibits the minute depressions (1–3) which, when present, give the gingiva its characteristic stippled appearance.
**Fig. 1-17c** shows a photograph of the subsurface (i.e. the surface of the epithelium facing the connective tissue) of the same model as that shown in Fig. 1-17b. The subsurface of the epithelium is characterized by the presence of epithelial ridges which merge at various locations (1–3). The depressions (1–3) seen on the outer surface of the epithelium (shown in Fig. 117b) correspond with the fusion sites (1–3) between epithelial ridges. Thus, the depressions on the surface of the gingiva occur in the areas of fusion between various epithelial ridges.
**Fig. 1-18** (a) A portion of the oral epithelium covering the free gingiva is illustrated in this photomicrograph. The oral epithelium is a _keratinized_ , _stratified_ , _squamous epithelium_ which, on the basis of the degree to which the keratin-producing cells are differentiated, can be divided into the following cell layers:
1. _Basal layer_ (stratum basale or stratum germinativum)
2. _Prickle cell layer_ (stratum spinosum)
3. _Granular cell layer_ (stratum granulosum)
4. _Keratinized cell layer_ (stratum corneum).
It should be observed that in this section, cell nuclei are lacking in the outer cell layers. Such an epithelium is denoted _orthokeratinized_. Often, however, the cells of the stratum corneum of the epithelium of human gingiva contain remnants of the nuclei (arrows) as seen in Fig. 1-18b. In such a case, the epithelium is denoted _parakeratinized_.
**Fig. 1-19** In addition to the keratin-producing cells which comprise about 90% of the total cell population, the oral epithelium contains the following types of cell:
* _Melanocytes_
* _Langerhans cells_
* _Merkel's cells_
* _Inflammatory cells._
**Fig. 1-19**
These cell types are often stellate and have cytoplasmic extensions of various size and appearance. They are also called "clear cells" since in histologic sections, the zone around their nuclei appears lighter than that in the surrounding keratin-producing cells.
The photomicrograph shows "clear cells" (arrows) located in or near the stratum basale of the oral epithelium. Except the Merkel's cells, these "clear cells", which do not produce keratin, lack desmosomal attachment to adjacent cells. The melanocytes are pigment-synthesizing cells and are responsible for the melanin pigmentation occasionally seen on the gingiva. However, both lightly and darkly pigmented individuals present melanocytes in the epithelium.
**Fig. 1-20**
**Fig. 1-21**
The Langerhans cells are believed to play a role in the defense mechanism of the oral mucosa. It has been suggested that the Langerhans cells react with antigens which are in the process of penetrating the epithelium. An early immunologic response is thereby initiated, inhibiting or preventing further antigen penetration of the tissue. The Merkel's cells have been suggested to have a sensory function.
**Fig. 1-20** The cells in the basal layer are either cylindric or cuboid, and are in contact with the _basement membrane_ that separates the epithelium and the connective tissue. The basal cells possess the ability to divide, i.e. undergo mitotic cell division. The cells marked with arrows in the photomicrograph are in the process of dividing. It is in the basal layer that the epithelium is renewed. Therefore, this layer is also termed _stratum germinativum_ , and can be considered the _progenitor cell compartment_ of the epithelium.
**Fig. 1-21** When two daughter cells (D) have been formed by cell division, an adjacent "older" basal cell (OB) is pushed into the spinous cell layer and starts, as a _keratinocyte_ , to traverse the epithelium. It takes approximately 1 month for a keratinocyte to reach the outer epithelial surface, where it becomes shed from the stratum corneum. Within a given time, the number of cells which divide in the basal layer equals the number of cells which become shed from the surface. Thus, under normal conditions there is complete equilibrium between cell renewal and cell loss so that the epithelium maintains a constant thickness. As the basal cell migrates through the epithelium, it becomes flattened with its long axis parallel to the epithelial surface.
**Fig. 1-22** The basal cells are found immediately adjacent to the connective tissue and are separated from this tissue by the basement membrane, probably produced by the basal cells. Under the light microscope this membrane appears as a structureless zone approximately 1–2 μm wide (arrows) which reacts positively to a PAS stain (periodic acid-Schiff stain). This positive reaction demonstrates that the basement membrane contains carbohydrate (glycoproteins). The epithelial cells are surrounded by an extracellular substance which also contains protein–Polysaccharide complexes. At the ultrastructural level, the basement membrane has a complex composition.
**Fig. 1-23** is an electronmicrograph (magnification ×70 000) of an area including part of a basal cell, the basement membrane, and part of the adjacent connective tissue. The basal cell (BC) occupies the upper portion of the picture. Immediately beneath the basal cell an approximately 400 Å wide electron-lucent zone can be seen which is called _lamina lucida_ (LL). Beneath the lamina lucida an electron-dense zone of approximately the same thickness can be observed. This zone is called _lamina densa_ (LD). From the lamina densa so-called _anchoring fibers_ (AF) project in a fan-shaped fashion into the connective tissue. The anchoring fibers are approximately 1 μm in length and terminate freely in the connective tissue. The basement membrane, which appeared as an entity under the light microscope, thus, in the electronmicrograph, appears to comprise one lamina lucida and one lamina densa with adjacent connective tissue fibers (anchoring fibers). The cell membrane of the epithelial cells facing the lamina lucida harbors a number of electron-dense, thicker zones appearing at various intervals along the cell membrane. These structures are called _hemidesmosomes_ (HD). The cytoplasmic _tonofilaments_ (CT) in the cell converge towards the hemidesmosomes. The hemidesmosomes are involved in the attachment of the epithelium to the underlying basement membrane.
**Fig. 1-22**
**Fig. 1-23**
**Fig. 1-24** illustrates an area of stratum spinosum in the gingival oral epithelium. Stratum spinosum consists of 10–20 layers of relatively large, polyhedral cells, equipped with short cytoplasmic processes resembling spines. The cytoplasmic processes (arrows) occur at regular intervals and give the cells a prickly appearance. Together with intercellular protein–carbohydrate complexes, cohesion between the cells is provided by numerous "desmosomes" (pairs of hemidesmosomes) which are located between the cytoplasmic processes of adjacent cells.
**Fig. 1-24**
**Fig. 1-25** shows an area of stratum spinosum in an electronmicrograph. The dark-stained structures between the individual epithelial cells represent the _desmosomes_ (arrows). A desmosome may be considered to be two hemidesmosomes facing one another. The presence of a large number of desmosomes indicates that the cohesion between the epithelial cells is solid. The light cell (LC) in the center of the illustration harbors no hemidesmosomes and is, therefore, not a keratinocyte but rather a "clear cell" (see also Fig. 1-19).
**Fig. 1-26** is a schematic drawing describing the composition of a desmosome. A desmosome can be considered to consist of two adjoining hemidesmosomes separated by a zone containing electron-dense granulated material (GM). Thus, a desmosome comprises the following structural components: (1) the _outer leaflets_ (OL) of the cell membrane of two adjoining cells, (2) the thick _inner leaflets_ (IL) of the cell membranes and (3) the _attachment plaques_ (AP), which represent granular and fibrillar material in the cytoplasm.
**Fig. 1-25**
**Fig. 1-26**
**Fig. 1-27** As mentioned previously, the oral epithelium also contains melanocytes, which are responsible for the production of the pigment melanin. Melanocytes are present in individuals with marked pigmentation of the oral mucosa as well as in individuals where no clinical signs of pigmentation can be seen. In this electronmicrograph a melanocyte (MC) is present in the lower portion of the stratum spinosum. In contrast to the keratinocytes, this cell contains melanin granules (MG) and has no tonofilaments or hemidesmosomes. Note the large amount of tonofilaments in the cytoplasm of the adjacent keratinocytes.
**Fig. 1-28** When traversing the epithelium from the basal layer to the epithelial surface, the keratinocytes undergo continuous differentiation and specialization. The many changes which occur during this process are indicated in this diagram of a keratinized stratified squamous epithelium. From the basal layer (stratum basale) to the granular layer (stratum granulosum) both the number of tonofilaments (F) in the cytoplasm and the number of desmosomes (D) increase. In contrast, the number of organelles, such as mitochondria (M), lamellae of rough endoplasmic reticulum (E) and Golgi complexes (G), decrease in the keratinocytes on their way from the basal layer towards the surface. In the stratum granulosum, electron-dense _keratohyalin bodies_ (K) and clusters of glycogen-containing granules start to occur. Such granules are believed to be related to the synthesis of keratin.
**Fig. 1-27**
**Fig. 1-28**
**Fig. 1-29** is a photomicrograph of the stratum granulosum and stratum corneum. Keratohyalin granules (arrows) are seen in the stratum granulosum. There is an abrupt transition of the cells from the stratum granulosum to the stratum corneum. This is indicative of a very sudden keratinization of the cytoplasm of the keratinocyte and its conversion into a horny squame. The cytoplasm of the cells in the stratum corneum (SC) is filled with keratin and the entire apparatus for protein synthesis and energy production, i.e. the nucleus, the mitochondria, the endoplasmic reticulum, and the Golgi complex, is lost. In a parakeratinized epithelium, however, the cells of the stratum corneum contain remnants of nuclei. Keratinization is considered a process of differentiation rather than degeneration. It is a process of protein synthesis which requires energy and is dependent on functional cells, i.e. cells containing a nucleus and a normal set of organelles.
_Summary:_ The keratinocyte undergoes continuous differentiation on its way from the basal layer to the surface of the epithelium. Thus, once the keratinocyte has left the basement membrane it can no longer divide but maintains a capacity for production of protein (tonofilaments and keratohyalin granules). In the granular layer, the keratinocyte is deprived of its energy- and protein-producing apparatus (probably by enzymatic breakdown) and is abruptly converted into a keratin-filled cell which, via the stratum corneum, is shed from the epithelial surface.
**Fig. 1-30** illustrates a portion of the epithelium of the alveolar (lining) mucosa. In contrast to the epithelium of the gingiva, the lining mucosa has no stratum corneum. Notice that cells containing nuclei can be identified in all layers, from the basal layer to the surface of the epithelium.
**Fig. 1-29**
**Fig. 1-30**
**Fig. 1-31**
### Dento-gingival epithelium
The tissue components of the dento-gingival region achieve their final structural characteristics in conjunction with the eruption of the teeth. This is illustrated in Fig. 1-31a–d.
**Fig. 1-31a** When the enamel of the tooth is fully developed, the enamel-producing cells (ameloblasts) become reduced in height, produce a basal lamina and form, together with cells from the outer enamel epithelium, the so-called reduced dental epithelium (RE). The basal lamina (epithelial attachment lamina: EAL) lies in direct contact with the enamel. The contact between this lamina and the epithelial cells is maintained by hemidesmosomes. The reduced enamel epithelium surrounds the crown of the tooth from the moment the enamel is properly mineralized until the tooth starts to erupt.
**Fig. 1-31b** As the erupting tooth approaches the oral epithelium, the cells of the outer layer of the reduced dental epithelium (RE), as well as the cells of the basal layer of the oral epithelium (OE), show increased mitotic activity (arrows) and start to migrate into the underlying connective tissue. The migrating epithelium produces an epithelial mass between the oral epithelium and the reduced dental epithelium so that the tooth can erupt without bleeding. The former ameloblasts do not divide.
**Fig. 1-31c** When the tooth has penetrated into the oral cavity, large portions immediately apical to the incisal area of the enamel are covered by a junctional epithelium (JE) containing only a few layers of cells. The cervical region of the enamel, however, is still covered by ameloblasts (AB) and outer cells of the reduced dental epithelium.
**Fig. 1-32**
**Fig. 1-31d** During the later phases of tooth eruption, all cells of the reduced enamel epithelium are replaced by a junctional epithelium. This epithelium is continuous with the oral epithelium and provides the attachment between the tooth and the gingiva. If the free gingiva is excised after the tooth has fully erupted, a new junctional epithelium, indistinguishable from that found following tooth eruption, will develop during healing. The fact that this new junctional epithelium has developed from the oral epithelium indicates that the cells of the oral epithelium possess the ability to differentiate into cells of junctional epithelium.
**Fig. 1-32** is a histologic section cut through the border area between the tooth and the gingiva, i.e. the _dentogingival region_. The enamel (E) is to the left. To the right are the _junctional epithelium_ (JE), the _oral sulcular epithelium_ (OSE), and the _oral epithelium_ (OE). The oral sulcular epithelium covers the shallow groove, the gingival sulcus, located between the enamel and the top of the free gingiva. The junctional epithelium differs morphologically from the oral sulcular epithelium and oral epithelium, while the two latter are structurally very similar. Although individual variation may occur, the junctional epithelium is usually widest in its coronal portion (about 15–20 cell layers), but becomes thinner (3–4 cells) towards the cemento-enamel junction (CEJ). The borderline between the junctional epithelium and the underlying connective tissue does not present epithelial rete pegs except when inflamed.
**Fig. 1-33**
**Fig. 1-33** The junctional epithelium has a free surface at the bottom of the _gingival sulcus_ (GS). Like the oral sulcular epithelium and the oral epithelium, the junctional epithelium is continuously renewed through cell division in the basal layer. The cells migrate to the base of the gingival sulcus from where they are shed. The border between the junctional epithelium (JE) and the oral sulcular epithelium (OSE) is indicated by arrows. The cells of the oral sulcular epithelium are cuboidal and the surface of this epithelium is keratinized.
**Fig. 1-34**
**Fig. 1-34** illustrates different characteristics of the junctional epithelium. As can be seen in Fig. 1-34a, the cells of the junctional epithelium (JE) are arranged into one basal layer (BL) and several suprabasal layers (SBL).Fig. 1-34b demonstrates that the basal cells as well as the suprabasal cells are flattened with their long axis parallel to the tooth surface. (CT= connective tissue, E = enamel space.)
There are distinct differences between the oral sulcular epithelium, the oral epithelium and the junctional epithelium:
1. The size of the cells in the junctional epithelium is, relative to the tissue volume, larger than in the oral epithelium.
2. The intercellular space in the junctional epithelium is, relative to the tissue volume, comparatively wider than in the oral epithelium.
3. The number of desmosomes is smaller in the junctional epithelium than in the oral epithelium.
Note the comparatively wide intercellular spaces between the oblong cells of the junctional epithelium, and the presence of two neutrophilic granulocytes (PMN) which are traversing the epithelium.
The framed area (A) is shown in a higher magnification in Fig. 1-34c, from which it can be seen that the basal cells of the junctional epithelium are not in direct contact with the enamel (E). Between the enamel and the epithelium (JE) one electron-dense zone (1) and one electron-lucent zone (2) can be seen. The electron-lucent zone is in contact with the cells of the junctional epithelium (JE). These two zones have a structure very similar to that of the lamina densa (LD) and lamina lucida (LL) in the basement membrane area (i.e. the epithelium (JE) –connective tissue (CT) interface) described in Fig. 1-23. Furthermore, as seen in Fig. 1-34d, the cell membrane of the junctional epithelial cells harbors hemidesmosomes (HD) towards the enamel as it does towards the connective tissue. Thus, the interface between the enamel and the junctional epithelium is similar to the interface between the epithelium and the connective tissue.
**Fig. 1-35** is a schematic drawing of the most apically positioned cell in the junctional epithelium. The enamel (E) is depicted to the left in the drawing. It can be seen that the electron-dense zone (1) between the junctional epithelium and the enamel can be considered a continuation of the lamina densa (LD) in the basement membrane of the connective tissue side. Similarly, the electron-lucent zone (2) can be considered a continuation of the lamina lucida (LL). It should be noted, however, that at variance with the epithelium–connective tissue interface, there are no anchoring fibers (AF) attached to the lamina densa-like structure (1) adjacent to the enamel. On the other hand, like the basal cells adjacent to the basement membrane (at the connective tissue interface), the cells of the junctional epithelium facing the lamina lucida-like structure (2) harbor hemidesmosomes. Thus, the interface between the junctional epithelium and the enamel is structurally very similar to the epithelium–connective tissue interface, which means that the junctional epithelium is not only in contact with the enamel but is actually physically attached to the tooth via hemidesmosomes.
**Fig. 1-35**
### Lamina propria
The predominant tissue component of the gingiva is the connective tissue (lamina propria). The major components of the connective tissue are _collagen fibers_ (around 60% of connective tissue volume), _fibroblasts_ (around 5%), _vessels and nerves_ (around 35%) which are embedded in an amorphous ground substance (matrix).
**Fig. 1-36** The drawing illustrates a fibroblast (F) residing in a network of connective tissue fibers (CF). The intervening space is filled with matrix (M), which constitutes the 'environment' for the cell.
#### _Cells_
The different types of cell present in the connective tissue are: (1) _fibroblasts_ , (2) _mast cells_ , (3) _macrophages_ , and (4) _inflammatory cells_.
**Fig. 1-37** The _fibroblast_ is the predominant connective tissue cell (65% of the total cell population). The fibroblast is engaged in the production of various types of fibers found in the connective tissue, but is also instrumental in the synthesis of the connective tissue matrix. The fibroblast is a spindle-shaped or stellate cell with an oval-shaped nucleus containing one or more nucleoli. A part of a fibroblast is shown in electron microscopic magnification. The cytoplasm contains a well developed granular endoplasmic reticulum (E) with ribosomes. The Golgi complex (G) is usually of considerable size and the mitochondria (M) are large and numerous. Furthermore, the cytoplasm contains many fine tonofilaments (F). Adjacent to the cell membrane, all along the periphery of the cell, a large number of vesicles (V) can be found.
**Fig. 1-36**
**Fig. 1-38** The _mast cell_ is responsible for the production of certain components of the matrix. This cell also produces vasoactive substances, which can affect the function of the microvascular system and control the flow of blood through the tissue. A mast cell is presented in electron microscopic magnification. The cytoplasm is characterized by the presence of a large number of vesicles (V) of varying size. These vesicles contain biologically active substances such as proteolytic enzymes, histamine and heparin. The Golgi complex (G) is well developed, while granular endoplasmic reticulum structures are scarce. A large number of small cytoplasmic projections, i.e. microvilli (MV), can be seen along the periphery of the cell.
**Fig. 1-37**
**Fig. 1-38**
**Fig. 1-39**
**Fig. 1-40**
**Fig. 1-39** The _macrophage_ has a number of different phagocytic and synthetic functions in the tissue. A macrophage is shown in electron microscopic magnification. The nucleus is characterized by numerous invaginations of varying size. A zone of electron-dense chromatin condensations can be seen along the periphery of the nucleus. The Golgi complex (G) is well developed and numerous vesicles (V) of varying size are present in the cytoplasm. Granular endoplasmic reticulum (E) is scarce, but a certain number of free ribosomes (R) are evenly distributed in the cytoplasm. Remnants of phagocytosed material are often found in lysosomal vesicles: phagosomes (PH). In the periphery of the cell, a large number of microvilli of varying size can be seen. Macrophages are particularly numerous in inflamed tissue. They are derived from circulating blood monocytes which migrate into the tissue.
**Fig. 1-41**
**Fig. 1-40** Besides fibroblasts, mast cells and macrophages, the connective tissue also harbors inflammatory cells of various types, for example neutrophilic granulocytes, lymphocytes, and plasma cells.
The _neutrophilic granulocytes_ , also called _polymorphonuclear leukocytes_ , have a characteristic appearance (Fig. 1-40a). The nucleus is lobulate and numerous lysosomes (L), containing lysosomal enzymes, are found in the cytoplasm.
The _lymphocytes_ (Fig. 1-40b) are characterized by an oval to spherical nucleus containing localized areas of electron-dense chromatin. The narrow border of cytoplasm surrounding the nucleus contains numerous free ribosomes, a few mitochondria (M), and, in localized areas, endoplasmic reticulum with fixed ribosomes. Lysosomes are also present in the cytoplasm.
The _plasma cells_ (Fig. 1-40c) contain an eccentrically located spherical nucleus with radially deployed electron-dense chromatin. Endoplasmic reticulum (E) with numerous ribosomes is found randomly distributed in the cytoplasm. In addition, the cytoplasm contains numerous mitochondria (M) and a well developed Golgi complex.
#### _Fibers_
The connective tissue fibers are produced by the fibroblasts and can be divided into: (1) _collagen fibers_ , (2) _reticulin fibers_ , (3) _oxytalan fibers_ , and (4) _elastic fibers_.
**Fig. 1-41** The _collagen fibers_ predominate in the gingival connective tissue and constitute the most essential components of the periodontium. The electronmicrograph shows cross sections and longitudinal sections of collagen fibers. The collagen fibers have a characteristic cross-banding with a periodicity of 700 Å between the individual dark bands.
**Fig. 1-42**
**Fig. 1-42** illustrates some important features of the synthesis and the composition of collagen fibers produced by fibroblasts (F). The smallest unit, the collagen molecule, is often referred to as _tropocollagen_. A tropocollagen molecule (TC) which is seen in the upper portion of the drawing is approximately 3000 Å long and has a diameter of 15 Å. It consists of three polypeptide chains intertwined to form a helix. Each chain contains about 1000 amino acids. One third of these are glycine and about 20% proline and hydroxyproline, the latter being found practically only in collagen. Tropocollagen synthesis takes place inside the fibroblast from which the tropocollagen molecule is secreted into the extracellular space. Thus, the polymerization of tropocollagen molecules to collagen fibers takes place in the extracellular compartment. First, tropocollagen molecules are aggregated longitudinally to _protofibrils_ (PF), which are subsequently laterally aggregated parallel to _collagen fibrils_ (CFR), with an overlapping of the tropocollagen molecules by about 25% of their length. Due to the fact that special refraction conditions develop after staining at the sites where the tropocollagen molecules adjoin, a cross-banding with a periodicity of approximately 700 Å occurs under light microscopy. The _collagen fibers_ (CF) are bundles of collagen fibrils, aligned in such a way that the fibers also exhibit a cross-banding with a periodicity of 700 Å. In the tissue, the fibers are usually arranged in bundles. As the collagen fibers mature, covalent crosslinks are formed between the tropocollagen molecules, resulting in an age-related reduction in collagen solubility.
_Cementoblasts_ and _osteoblasts_ are cells which also possess the ability to produce collagen.
**Fig. 1-43**
**Fig. 1-44**
**Fig. 1-43** _Reticulin fibers_ , as seen in this photomicrograph, exhibit argyrophilic staining properties and are numerous in the tissue adjacent to the basement membrane (arrows). However, reticulin fibers also occur in large numbers in the loose connective tissue surrounding the blood vessels. Thus, reticulin fibers are present at the epithelium–connective tissue and the endothelium–connective tissue interfaces.
**Fig 1-44** _Oxytalan fibers_ are scarce in the gingiva but numerous in the periodontal ligament. They are composed of long thin fibrils with a diameter of approximately 150 Å. These connective tissue fibers can be demonstrated light microscopically only after previous oxidation with peracetic acid. The photomicrograph illustrates oxytalan fibers (arrows) in the periodontal ligament, where they have a course mainly parallel to the long axis of the tooth. The function of these fibers is as yet unknown. The cementum is seen to the left and the alveolar bone to the right.
**Fig. 1-45** _Elastic fibers_ in the connective tissue of the gingiva and periodontal ligament are only present in association with blood vessels. However, as seen in this photomicrograph, the lamina propria and submucosa of the alveolar (lining) mucosa contain numerous elastic fibers (arrows). The gingiva (G) seen coronal to the mucogingival junction (MGJ) contains no elastic fibers except in association with the blood vessels.
**Fig. 1-46** Although many of the collagen fibers in the gingiva and the periodontal ligament are irregularly or randomly distributed, most tend to be arranged in groups of bundles with a distinct orientation. According to their insertion and course in the tissue, the oriented bundles in the gingiva can be divided into the following groups:
1. _Circular fibers_ (CF) are fiber bundles which run their course in the free gingiva and encircle the tooth in a cuff- or ring-like fashion.
2. _Dento-gingival fibers_ (DGF) are embedded in the cementum of the supra-alveolar portion of the root and project from the cementum in a fan-like configuration out into the free gingival tissue of the facial, lingual and interproximal surfaces.
3. _Dento-periosteal fibers_ (DPF) are embedded in the same portion of the cementum as the dento-gingival fibers, but run their course apically over the vestibular and lingual bone crest and terminate in the tissue of the attached gingiva. In the border area between the free and attached gingiva, the epithelium often lacks support by underlying oriented collagen fiber bundles. In this area the free gingival groove (GG) is often present.
4. _Trans-septal fibers_ (TF), seen on the drawing to the right, extend between the supra-alveolar cementum of approximating teeth. The trans-septal fibers run straight across the interdental septum and are embedded in the cementum of adjacent teeth.
**Fig. 1-47** illustrates in a histologic section the orientation of the trans-septal fiber bundles (arrows) in the supra-alveolar portion of the interdental area. It should be observed that, besides connecting the cementum (C) of adjacent teeth, the trans-septal fibers also connect the supra-alveolar cementum (C) with the crest of the alveolar bone (AB). The four groups of collagen fiber bundles presented in Fig. 1-46 reinforce the gingiva and provide the resilience and tone which is necessary for maintaining its architectural form and the integrity of the dento-gingival attachment.
**Fig. 1-45**
#### _Matrix_
The _matrix_ of the connective tissue is produced mainly by the fibroblasts, although some constituents are produced by mast cells, and other components are derived from the blood. The matrix is the medium in which the connective tissue cells are embedded and it is essential for the maintenance of the normal function of the connective tissue. Thus, the transportation of water, electrolytes, nutrients, metabolites, etc., to and from the individual connective tissue cells occurs within the matrix. The main constituents of the connective tissue matrix are protein–carbohydrate macromolecules. These complexes are normally divided into _proteoglycans_ and _glycoproteins_. The proteoglycans contain _glycosaminoglycans_ as the carbohydrate units (hyaluronan sulfate, heparan sulfate, etc.), which are attached to one or more protein chains via covalent bonds. The carbohydrate component is always predominant in the proteoglycans. The glycosaminoglycan called hyaluronan or "hyaluronic acid" is probably not bound to protein. The glycoproteins (fibronectin, osteonectin, etc.) also contain polysaccharides, but these macromolecules are different from glycosaminoglycans. The protein component is predominating in glycoproteins. In the macromolecules, mono- or oligosaccharides are connected to one or more protein chains via covalent bonds.
**Fig. 1-46**
**Fig. 1-47**
**Fig. 1-48** Normal function of the connective tissue depends on the presence of proteoglycans and glycosaminoglycans. The carbohydrate moiety of the proteoglycans, the glycosaminoglycans , are large, flexible, chain formed, negatively charged molecules, each of which occupies a rather large space (Fig. 1-48a). In such a space, smaller molecules, e.g. water and electrolytes, can be incorporated while larger molecules are prevented from entering (Fig. 1-48b). The proteoglycans thereby regulate diffusion and fluid flow through the matrix and are important determinants for the fluid content of the tissue and the maintenance of the osmotic pressure. In other words, the proteoglycans act as a molecule filter and, in addition, play an important role in the regulation of cell migration (movements) in the tissue. Due to their structure and hydration, the macromolecules exert resistance towards deformation, thereby serving as regulators of the consistency of the connective tissue (Fig. 1-48c). If the gingiva is suppressed, the macromolecules become deformed. When the pressure is eliminated, the macromolecules regain their original form. Thus, the macromolecules are important for the resilience of the gingiva.
**Fig. 1-48**
**Fig. 1-49**
### Epithelial mesenchymal interaction
There are many examples of the fact that during the embryonic development of various organs, a mutual inductive influence occurs between the epithelium and the connective tissue. The development of the teeth is a characteristic example of such phenomena. The connective tissue is, on the one hand, a determining factor for normal development of the tooth bud while, on the other, the enamel epithelia exert a definite influence on the development of the mesenchymal components of the teeth.
It has been suggested that tissue differentiation in the adult organism can be influenced by environmental factors. The skin and mucous membranes, for instance, often display increased keratinization and hyperplasia of the epithelium in areas which are exposed to mechanical stimulation. Thus, the tissues seem to adapt to environmental stimuli. The presence of keratinized epithelium on the masticatory mucosa has been considered to represent an adaptation to mechanical irritation released by mastication. However, research has demonstrated that the characteristic features of the epithelium in such areas are genetically determined. Some pertinent observations are reported in the following:
**Fig. 1-50**
**Fig. 1-51**
**Fig. 1-49** shows an area in a monkey where the gingiva (G) and the alveolar mucosa (AM) have been transposed by a surgical procedure. The alveolar mucosa is placed in close contact with the teeth while the gingiva is positioned in the area of the alveolar mucosa.
**Fig. 1-50** shows the same area, as seen in Fig. 1-49, 4 months later. Despite the fact that the transplanted gingiva (G) is mobile in relation to the underlying bone, like the alveolar mucosa, it has retained its characteristic, morphologic features of a masticatory mucosa. However, a narrow zone of new keratinized gingiva (NG) has regenerated between the transplanted alveolar mucosa (AM) and the teeth.
**Fig. 1-51** presents a histologic section cut through the transplanted gingiva seen in Fig. 1-50. Since elastic fibers are lacking in the gingival connective tissue (G), but are numerous (small arrows) in the connective tissue of the alveolar mucosa (AM), the transplanted gingival tissue can readily be identified. The epithelium covering the transplanted gingival tissue exhibits a distinct keratin layer (between large arrows) on the surface, and also the configuration of the epithelium–connective tissue interface (i.e. rete pegs and connective tissue papillae) is similar to that of normal non-transplanted gingiva. Thus, the heterotopically located gingival tissue has maintained its original specificity. This observation demonstrates that the characteristics of the gingiva are genetically determined rather than being the result of functional adaptation to environmental stimuli.
**Fig. 1-52**
**Fig. 1-52** shows a histologic section cut through the coronal portion of the area of transplantation (shown in Fig. 1-50). The transplanted gingival tissue (G) shown in Fig. 1-51 can be seen in the lower portion of the photomicrograph. The alveolar mucosa transplant (AM) is seen between the large arrows in the middle of the illustration. After surgery, the alveolar mucosa transplant was positioned in close contact with the teeth as seen in Fig. 1-49. After healing, a narrow zone of keratinized gingiva (NG) developed coronal to the alveolar mucosa transplant (see Fig. 150). This new zone of gingiva (NG), which can be seen in the upper portion of the histologic section, is covered by keratinized epithelium and the connective tissue contains no purple-stained elastic fibers. In addition, it is important to notice that the junction between keratinized and non-keratinized epithelium (large arrows) corresponds exactly to the junction between "elastic" and "inelastic" connective tissue (small arrows). The connective tissue of the new gingiva has regenerated from the connective tissue of the supra-alveolar and periodontal ligament compartments and has separated the alveolar mucosal transplant (AM) from the tooth (see Fig. 1-53). However, it is most likely that the epithelium which covers the new gingiva has migrated from the adjacent epithelium of the alveolar mucosa.
**Fig. 1-53**
Fig. 1-53 presents a schematic drawing of the development of the new, narrow zone of keratinized gingiva (NG) seen in Figs. 1-50 and 1-52.
**Fig. 1-53a** Granulation tissue has proliferated coronally along the root surface (arrow) and has separated the alveolar mucosa transplant (AM) from its original contact with the tooth surface.
**Fig. 1-53b** Epithelial cells have migrated from the alveolar mucosal transplant (AM) on to the newly formed gingival connective tissue (NG). Thus, the newly formed gingiva has become covered with a keratinized epithelium (KE) which originated from the non-keratinized epithelium of the alveolar mucosa (AM). This implies that the newly formed gingival connective tissue (NG) possesses the ability to induce changes in the differentiation of the epithelium originating from the alveolar mucosa. This epithelium, which is normally non-keratinized, apparently differentiates to keratinized epithelium because of stimuli arising from the newly formed gingival connective tissue (NG). (GT: gingival transplant.)
**Fig. 1-54** illustrates a portion of gingival connective tissue (G) and alveolar mucosal connective tissue (AM) which, after transplantation, has healed into wound areas in the alveolar mucosa. Epithelialization of these transplants can only occur through migration of epithelial cells from the surrounding alveolar mucosa.
**Fig. 1-55** shows the transplanted gingival connective tissue (G) after re-epithelialization. This tissue portion has attained an appearance similar to that of the normal gingiva, indicating that this connective tissue is now covered by keratinized epithelium. The transplanted connective tissue from the alveolar mucosa (AM) is covered by non-keratinized epithelium, and has the same appearance as the surrounding alveolar mucosa.
**Fig. 1-54**
**Fig. 1-55**
**Fig. 1-56** presents two histologic sections through the area of the transplanted gingival connective tissue. The section shown in Fig. 1-56a is stained for elastic fibers (arrows). The tissue in the middle without elastic fibers is the transplanted gingival connective tissue (G).Fig. 1-56b shows an adjacent section stained with hematoxylin and eosin. By comparing Figs. 1-56a and Figs. 1-56a it can be seen that:
1. The transplanted gingival connective tissue is covered by keratinized epithelium (between arrowheads)
2. The epithelium–connective tissue interface has the same wavy course (i.e. rete pegs and connective tissue papillae) as seen in normal gingiva.
The photomicrographs seen in Figs. 1-56c and 1-56d illustrate, at a higher magnification, the border area between the alveolar mucosa (AM) and the transplanted gingival connective tissue (G). Note the distinct relationship between keratinized epithelium (arrow) and "inelastic" connective tissue (arrowheads), and between non-keratinized epithelium and "elastic" connective tissue. The establishment of such a close relationship during healing implies that the transplanted gingival connective tissue possesses the ability to alter the differentiation of epithelial cells as previously suggested (Fig. 1-53). From being non-keratinizing cells, the cells of the epithelium of the alveolar mucosa have evidently become keratinizing cells. This means that the specificity of the gingival epithelium is determined by genetic factors inherent in the connective tissue.
**Fig. 1-56**
# Periodontal ligament
The periodontal ligament is the soft, richly vascular and cellular connective tissue which surrounds the roots of the teeth and joins the root cementum with the socket wall. In the coronal direction, the periodontal ligament is continuous with the lamina propria of the gingiva and is demarcated from the gingiva by the collagen fiber bundles which connect the alveolar bone crest with the root (the alveolar crest fibers).
**Fig. 1-57** is a radiograph of a mandibular premolar-molar region. In radiographs two types of alveolar bone can be distinguished:
1. The part of the alveolar bone which covers the alveolus, called "lamina dura" (arrows)
2. The portion of the alveolar process which, in the radiograph, has the appearance of a meshwork. This is called the "spongy bone".
**Fig. 1-57**
The periodontal ligament is situated in the space between the roots (R) of the teeth and the lamina dura or the alveolar bone proper (arrows). The alveolar bone (AB) surrounds the tooth to a level approximately 1 mm apical to the cemento-enamel junction (CEJ). The coronal border of the bone is called the _alveolar crest_ (arrows).
The periodontal ligament space has the shape of an hourglass and is narrowest at the mid-root level. The width of the periodontal ligament is approximately 0.25 mm (range 0.2–0.4 mm). The presence of a periodontal ligament permits forces, elicited during masticatory function and other tooth contacts, to be distributed to and resorbed by the alveolar process via the alveolar bone proper. The periodontal ligament is also essential for the mobility of the teeth. Tooth mobility is to a large extent determined by the width, height, and quality of the periodontal ligament (see Chapters 14 and 51).
**Fig. 1-58** illustrates in a schematic drawing how the periodontal ligament is situated between the alveolar bone proper (ABP) and the root cementum (RC). The tooth is joined to the bone by bundles of collagen fibers which can be divided into the following main groups according to their arrangement:
1. _Alveolar crest fibers_ (ACF)
2. _Horizontal fibers_ (HF)
3. _Oblique fibers_ (OF)
4. _Apical fibers_ (APF).
**Fig. 1-59** The periodontal ligament and the root cementum develop from the loose connective tissue (the follicle) which surrounds the tooth bud. The schematic drawing depicts the various stages in the organization of the periodontal ligament which forms concomitantly with the development of the root and the eruption of the tooth.
**Fig. 1-58**
**Fig. 1-59a** The tooth bud is formed in a crypt of the bone. The collagen fibers produced by the fibroblasts in the loose connective tissue around the tooth bud are embedded, during the process of their maturation, into the newly formed cementum immediately apical to the cemento-enamel junction (CEJ). These fiber bundles oriented towards the coronal portion of the bone crypt will later form the dento-gingival fiber group, the dento-periosteal fiber group and the trans-septal fiber group which belong to the oriented fibers of the gingiva (see Fig. 1-46).
**Fig. 1-59b** The true periodontal ligament fibers, the _principal fibers_ , develop in conjunction with the eruption of the tooth. First, fibers can be identified entering the most marginal portion of the alveolar bone.
**Fig. 1-59c** Later, more apically positioned bundles of oriented collagen fibers are seen.
**Fig. 1-59d** The orientation of the collagen fiber bundles alters continuously during the phase of tooth eruption. First, when the tooth has reached contact in occlusion and is functioning properly, the fibers of the periodontal ligament associate into groups of well oriented dentoalveolar collagen fibers demonstrated in Fig. 1-58. These collagen structures undergo constant remodeling (i.e. resorption of old fibers and formation of new ones).
**Fig. 1-59**
**Fig. 1-60**
**Fig. 1-60** This schematic drawing illustrates the development of the principal fibers of the periodontal ligament. The alveolar bone proper (ABP) is seen to the left, the periodontal ligament (PL) is depicted in the center and the root cementum (RC) is seen to the right.
**Fig. 1-60a** First, small, fine, brush-like fibrils are detected arising from the root cementum and projecting into the PL space. At this stage the surface of the bone is covered by osteoblasts. From the surface of the bone only a small number of radiating, thin collagen fibrils can be seen.
**Fig. 1-60b** Later on, the number and thickness of fibers entering the bone increase. These fibers radiate towards the loose connective tissue in the mid-portion of the periodontal ligament area (PL), which contains more or less randomly oriented collagen fibrils. The fibers originating from the cementum are still short while those entering the bone gradually become longer. The terminal portions of these fibers carry finger-like projections.
**Fig. 1-60c** The fibers originating from the cementum subsequently increase in length and thickness and fuse in the periodontal ligament space with the fibers originating from the alveolar bone. When the tooth, following eruption, reaches contact in occlusion and starts to function, the principal fibers become organized in bundles and run continuously from the bone to the cementum.
**Fig. 1-61a**
**Fig. 1-61b**
**Fig. 1-62a**
**Fig. 1-62b**
Fig. 1-61a illustrates how the principal fibers of the periodontal ligament (PDL) run continuously from the root cementum to the alveolar bone proper (ABP). The principal fibers embedded in the cementum (Sharpey's fibers) have a smaller diameter but are more numerous than those embedded in the alveolar bone proper (Sharpey's fibers).
**Fig. 1-61b** presents a polarized version of Fig. 1-61 a. In this illustration the Sharpey's fibers (SF) can be seen penetrating not only the cementum (C) but also the entire width of the alveolar bone proper (ABP). The periodontal ligament also contains a few elastic fibers associated with the blood vessels. Oxytalan fibers (see Fig. 1-44) are also present in the periodontal ligament. They have a mainly apico-occlusal orientation and are located in the ligament closer to the tooth than to the alveolar bone. Very often they insert into the cementum. Their function has not been determined.
The cells of the periodontal ligament are: _fibroblasts_ , _osteoblasts_ , _cementoblasts_ , _osteoclasts_ , as well as _epithelial cells_ and _nerve fibers_. The fibroblasts are aligned along the principal fibers, while cementoblasts line the surface of the cementum, and the osteoblasts line the bone surface.
**Fig. 1-62a** shows the presence of clusters of epithelial cells (ER) in the periodontal ligament (PDL). These cells, called the _epithelial cell rests of Mallassez_ , represent remnants of the Hertwig's epithelial root sheath. The epithelial cell rests are situated in the periodontal ligament at a distance of 15–75 μm from the cementum (C) on the root surface. A group of such epithelial cell rests is seen in a higher magnification in Fig. 1-62b.
Fig. 1-63 Electron microscopically it can be seen that the epithelial cell rests are surrounded by a basement membrane (BM) and that the cell membranes of the epithelial cells exhibit the presence of desmosomes (D) as well as hemidesmosomes (HD). The epithelial cells contain only few mitochondria and have a poorly developed endoplasmic reticulum. This means that they are vital, but resting, cells with minute metabolism.
**Fig. 1-64** is a photomicrograph of a periodontal ligament removed from an extracted tooth. This specimen, prepared tangential to the root surface, shows that the epithelial cell rests of Mallassez, which in ordinary histologic sections appear as isolated groups of epithelial cells, in fact form a continuous network of epithelial cells surrounding the root. Their function is unknown at present.
**Fig. 1-63**
**Fig. 1-64**
# Root cementum
The cementum is a specialized mineralized tissue covering the root surfaces and, occasionally, small portions of the crown of the teeth. It has many features in common with bone tissue. However, the cementum contains no blood or lymph vessels, has no innervation, does not undergo physiologic resorption or remodeling, but is characterized by continuing deposition throughout life. Like other mineralized tissues, it contains collagen fibers embedded in an organic matrix. Its mineral content, which is mainly hydroxyapatite, is about 65% by weight; a little more than that of bone (i.e. 60%). Cementum serves different functions. It attaches the periodontal ligament fibers to the root and contributes to the process of repair after damage to the root surface.
Different forms of cementum have been described:
1. _Acellular, extrinsic fiber cementum_ (AEFC) is found in the coronal and middle portions of the root and contains mainly bundles of Sharpey's fibers. This type of cementum is an important part of the attachment apparatus and connects the tooth with the alveolar bone proper.
2. _Cellular, mixed stratified cementum_ (CMSC) occurs in the apical third of the roots and in the furcations. It contains both extrinsic and intrinsic fibers as well as cementocytes.
3. _Cellular, intrinsic fiber cementum_ (CIFC) is found mainly in resorption lacunae and it contains intrinsic fibers and cementocytes.
**Fig. 1-65a** shows a portion of a root with adjacent periodontal ligament (PDL). A thin layer of acellular, extrinsic fiber cementum (AEFC) with densely packed extrinsic fibers covers the peripheral dentin. Cementoblasts and fibroblasts can be observed adjacent to the cementum.
**Fig. 1-65b** represents a scanning electron micrograph of AEFC. Note that the extrinsic fibers attach to the dentin (left) and are continous with the collagen fiber bundles (CB) of the periodontal ligament (PDL). The AEFC is formed concomitantly with the formation of the root dentin. At a certain stage during tooth formation, the epithelial sheath of Hertwig, which lines the newly formed predentin, is fragmented. Cells from the dental follicle then penetrate the epithelial sheath of Hertwig and occupy the area next to the predentin. In this position, the ectomesenchymal cells from the dental follicle differentiate into cementoblasts and begin to produce collagen fibers at right angles to the surface. The first cementum is deposited on the highly mineralized superficial layer of the mantle dentin called the "hyaline layer" which contains enamel matrix proteins and the initial collagen fibers of the cementum. Subsequently, cementoblasts drift away from the surface resulting in increased thickness of the cementum and incorporation of principal fibers.
**Fig. 1-65a**
**Fig. 1-65b**
**Fig. 1-66**
**Fig. 1-67**
**Fig. 1-66** demonstrates the structure of cellular, mixed stratified cementum (CMSC) which, in contrast to AEFC, contains cells and intrinsic fibers. The CMSC is laid down throughout the functional period of the tooth. The various types of cementum are produced by cementoblasts or periodontal ligament (PDL) cells lining the cementum surface. Some of these cells become incorporated into the cementoid, which subsequently mineralizes to form cementum. The cells which are incorporated in the cementum are called _cementocytes_ (CC).
**Fig. 1-67** illustrates how cementocytes (blue cell) reside in lacunae in CMSC or CIFC. They communicate with each other through a network of cytoplasmic processes (arrows) running in canaliculi in the cementum. The cementocytes also communicate with the cementoblasts on the surface through cytoplasmic processes. The presence of cementocytes allows transportation of nutrients through the cementum, and contributes to the maintenance of the vitality of this mineralized tissue.
**Fig. 1-68a**
**Fig. 1-68a** is a photomicrograph of a section through the periodontal ligament (PDL) in an area where the root is covered with acellular, extrinsic fiber cementum (AEFC). The portions of the principal fibers of the periodontal ligament which are embedded in the root cementum (arrows) and in the alveolar bone proper (ABP) are called _Sharpey's fibers_. The arrows to the right indicate the border between ABP and the alveolar bone (AB). In AEFC the Sharpey's fibers have a smaller diameter and are more densely packed than their counterparts in the alveolar bone. During the continuous formation of AEFC, portions of the periodontal ligament fibers (principal fibers) adjacent to the root become embedded in the mineralized tissue. Thus, the Sharpey's fibers in the cementum are a direct continuation of the principal fibers in the periodontal ligament and the supra-alveolar connective tissue.
**Fig. 1-68b** The Sharpey's fibers constitute the _extrinsic fiber system_ (E) of the cementum and are produced by fibroblasts in the periodontal ligament. The _intrinsic fiber system_ (I) is produced by cementoblasts and is composed of fibers oriented more or less parallel to the long axis of the root.
**Fig. 1-68b**
**Fig. 1-69**
**Fig. 1-69** shows extrinsic fibers penetrating acellular, extrinsic fiber cementum (AEFC). The characteristic cross-banding of the collagen fibers is masked in the cementum because apatite crystals have become deposited in the fiber bundles during the process of mineralization.
Fig. 1-70 In contrast to the bone, the cementum (C) does not exhibit alternating periods of resorption and apposition, but increases in thickness throughout life by deposition of successive new layers. During this process of gradual apposition, the particular portion of the principal fibers which resides immediately adjacent to the root surface becomes mineralized. Mineralization occurs by the deposition of hydroxyapatite crystals, first within the collagen fibers, later upon the fiber surface, and finally in the interfibrillar matrix. The electronphotomicrograph shows a cementoblast (CB) located near the surface of the cementum (C) and between two inserting principal fiber bundles. Generally, the AEFC is more mineralized than CMSC and CIFC. Sometimes only the periphery of the Sharpey's fibers of the CMSC is mineralized, leaving an unmineralized core within the fiber.
**Fig. 1-70**
**Fig. 1-71**
**Fig. 1-71** is a photomicrograph of the periodontal ligament (PDL) which resides between the cementum (CMSC) and the alveolar bone proper (ABP). The CMSC is densely packed with collagen fibers oriented parallel to the root surface (intrinsic fibers) and Sharpey's fibers (extrinsic fibers), oriented more or less perpendicularly to the cementum–dentin junction (predentin (PD) ). The various types of cementum increase in thickness by gradual apposition throughout life. The cementum becomes considerably wider in the apical portion of the root than in the cervical portion, where the thickness is only 20– 50 μm. In the apical root portion the cementum is often 150–250 μm wide. The cementum often contains incremental lines indicating alternating periods of formation. The CMSC is formed after the termination of tooth eruption, and after a response to functional demands.
# Alveolar bone
The alveolar process is defined as the parts of the maxilla and the mandible that form and support the sockets of the teeth. The alveolar process develops in conjunction with the development and eruption of the teeth. The alveolar process consists of bone which is formed both by cells from the dental follicle (alveolar bone proper) and cells which are independent of tooth development. Together with the root cementum and the periodontal membrane, the alveolar bone constitutes the attachment apparatus of the teeth, the main function of which is to distribute and resorb forces generated by, for example, mastication and other tooth contacts.
**Fig. 1-72** illustrates a cross section through the alveolar process (pars alveolaris) of the maxilla at the mid-root level of the teeth. Note that the bone which covers the root surfaces is considerably thicker at the palatal than at the buccal aspect of the jaw. The walls of the sockets are lined by _cortical bone_ (arrows), and the area between the sockets and between the compact jaw bone walls is occupied by _cancellous bone_. The cancellous bone occupies most of the interdental septa but only a relatively small portion of the buccal and palatal bone plates. The cancellous bone contains _bone trabeculae_ , the architecture and size of which are partly genetically determined and partly the result of the forces to which the teeth are exposed during function. Note how the bone on the buccal and palatal aspects of the alveolar process varies in thickness from one region to another. The bone plate is thick at the palatal aspect and on the buccal aspect of the molars but thin in the buccal anterior region.
**Fig. 1-73** shows cross sections through the mandibular alveolar process at levels corresponding to the coronal (Fig. 1-73a) and apical (Fig. 1-73b) thirds of the roots. The bone lining the wall of the sockets (alveolar bone proper) is often continuous with the compact or cortical bone at the lingual (L) and buccal (B) aspects of the alveolar process (arrows). Note how the bone on the buccal and lingual aspects of the alveolar process varies in thickness from one region to another. In the incisor and premolar regions, the bone plate at the buccal aspects of the teeth is considerably thinner than at the lingual aspect. In the molar region, the bone is thicker at the buccal than at the lingual surfaces.
**Fig. 1-72**
**Fig. 1-73**
**Fig. 1-74**
**Fig. 1-75**
**Fig. 1-76**
**Fig. 1-74** At the buccal aspect of the jaws, the bone coverage is sometimes missing at the coronal portion of the roots, forming a so-called _dehiscence_ (D). If some bone is present in the most coronal portion of such an area the defect is called a _fenestration_ (F). These defects often occur where a tooth is displaced out of the arch and are more frequent over anterior than posterior teeth. The root in such defects is covered only by periodontal ligament and the overlying gingiva.
**Fig. 1-75** presents vertical sections through various regions of the mandibular dentition. The bone wall at the buccal (B) and lingual (L) aspects of the teeth varies considerably in thickness, e.g. from the premolar to the molar region. Note, for instance, how the presence of the oblique line ( _linea obliqua_ ) results in a shelf-like bone process (arrows) at the buccal aspect of the second and third molars.
**Fig. 1-76** shows a section through the periodontal ligament (PL), tooth (T), and the alveolar bone (AB). The blood vessels in the periodontal ligament and the alveolar bone appear black because the blood system was perfused with ink. The compact bone (alveolar bone proper) which lines the tooth socket, and in a radiograph (Fig. 1-57) appears as "lamina dura" (LD), is perforated by numerous _Volkmann's canals_ (arrows) through which blood vessels, lymphatics, and nerve fibers pass from the alveolar bone (AB) to the periodontal ligament (PL). This layer of bone into which the principal fibers are inserted (Sharpey's fibers) is sometimes called "bundle bone". From a functional and structural point of view, this "bundle bone" has many features in common with the cementum layer on the root surfaces.
**Fig. 1-77**
**Fig. 1-78**
**Fig. 1-77** The alveolar process starts to form early in fetal life, with mineral deposition at small foci in the mesenchymal matrix surrounding the tooth buds. These small mineralized areas increase in size, fuse, and become resorbed and remodeled until a continuous mass of bone has formed around the fully erupted teeth. The mineral content of bone, which is mainly hydroxyapatite, is about 60% on a weight basis. The photomicrograph illustrates the bone tissue within the furcation area of a mandibular molar. The bone tissue can be divided into two compartments: mineralized bone (MB) and bone marrow (BM). The mineralized bone is made up of lamellae – lamellar bone – while the bone marrow contains adipocytes (ad), vascular structures (v), and undifferentiated mesenchymal cells (see insertion).
**Fig. 1-78** The mineralized, lamellar bone includes two types of bone tissue: the bone of the alveolar process (AB) and the alveolar bone proper (ABP), which covers the alveolus. The ABP or the bundle bone has a varying width and is indicated with white arrows. The alveolar bone (AB) is a tissue of mesenchymal origin and it is not considered as part of the genuine attachment apparatus. The alveolar bone proper (ABP), on the other hand, together with the periodontal ligament (PDL) and the cementum (C), is responsible for the attachment between the tooth and the skeleton. AB and ABP may, as a result of altered functional demands, undergo adaptive changes.
**Fig. 1-79** describes a portion of lamellar bone. The lamellar bone at this site contains _osteons_ (white circles) each of which harbors a blood vessel located in a Haversian canal (HC). The blood vessel is surrounded by concentric, mineralized lamellae to form the osteon. The space between the different osteons is filled with so-called interstitial lamellae. The osteons in the lamellar bone are not only structural units but also metabolic units. Thus, the nutrition of the bone is secured by the blood vessels in the Haversian canals and connecting vessels in the Volkmann canals.
**Fig. 1-79**
**Fig. 1-80a**
**Fig. 1-80** The histologic section (Fig. 1-80a) shows the borderline between the alveolar bone proper (ABP) and lamellar bone with an osteon. Note the presence of the Haversian canal (HC) in the center of the osteon. The alveolar bone proper (ABP) includes circumferential lamellae and contains Sharpey's fibers which extend into the periodontal ligament. The schematic drawing (Fig. 1-80b) is illustrating three active osteons (brown) with a blood vessel (red) in the Haversian canal (HC). Interstitial lamella (green) is located between the osteons (O) and represents an old and partly remodelled osteon. The alveolar bone proper (ABP) is presented by the dark lines into which the Sharpey's fibers (SF) insert.
**Fig. 1-80b**
**Fig. 1-81** illustrates an osteon with osteocytes (OC) residing in osteocyte lacunae in the lamellar bone. The osteocytes connect via canaliculi (can) which contain cytoplasmatic projections of the osteocytes. A Haversian canal (HC) is seen in the middle of the osteon.
**Fig. 1-81**
**Fig. 1-82**
**Fig. 1-83**
**Fig. 1-82** illustrates an area of the alveolar bone in which bone formation occurs. The osteoblasts (arrows), the bone-forming cells, are producing bone matrix (osteoid) consisting of collagen fibers, glycoproteins, and proteoglycans. The bone matrix or the osteoid undergoes mineralization by the deposition of minerals such as calcium and phosphate, which are subsequently transformed into hydroxyapatite.
**Fig. 1-83** The drawing illustrates how osteocytes, present in the mineralized bone, communicate with osteoblasts on the bone surface through canaliculi.
**Fig. 1-84**
**Fig. 1-84** All active bone-forming sites harbor osteoblasts. The outer surface of the bone is lined by a layer of such osteoblasts which, in turn, are organized in a periosteum (P) that contains densely packed collagen fibers. On the "inner surface" of the bone, i.e. in the bone marrow space, there is an endosteum (E), which presents similar features as the periosteum.
**Fig. 1-85** illustrates an osteocyte residing in a lacuna in the bone. It can be seen that cytoplasmic processes radiate in different directions.
**Fig. 1-86** illustrates an osteocytes (OC) and how their long and delicate cytoplasmic processes communicate through the canaliculi (CAN) in the bone. The resulting canalicular–lacunar system is essential for cell metabolism by allowing diffusion of nutrients and waste products. The surface between the osteocytes with their cytoplasmic processes on the one side, and the mineralized matrix on the other, is very large. It has been calculated that the interface between cells and matrix in a cube of bone, 10 × 10 × 10 cm, amounts to approximately 250 m2. This enormous surface of exchange serves as a regulator, e.g. for serum calcium and serum phosphate levels via hormonal control mechanisms.
**Fig. 1-85**
**Fig. 1-86**
**Fig. 1-87**
**Fig. 1-88**
**Fig. 1-87** The alveolar bone is constantly renewed in response to functional demands. The teeth erupt and migrate in a mesial direction throughout life to compensate for attrition. Such movement of the teeth implies remodeling of the alveolar bone. During the process of remodeling, the bone trabeculae are continuously resorbed and reformed and the cortical bone mass is dissolved and replaced by new bone. During breakdown of the cortical bone, resorption canals are formed by proliferating blood vessels. Such canals, which contain a blood vessel in the center, are subsequently refilled with new bone by the formation of lamellae arranged in concentric layers around the blood vessel. A new Haversian system (O) is seen in the photomicrograph of a horizontal section through the alveolar bone (AB), periodontal ligament (PL), and tooth (T).
**Fig. 1-88** The resorption of bone is always associated with _osteoclasts_ (Ocl). These cells are giant cells specialized in the breakdown of mineralized matrix (bone, dentin, cementum) and are probably developed from blood monocytes. The resorption occurs by the release of acid substances (lactic acid, etc.) which form an acidic environment in which the mineral salts of the bone tissue become dissolved. Remaining organic substances are eliminated by enzymes and osteoclastic phagocytosis. Actively resorbing osteoclasts adhere to the bone surface and produce lacunar pits called _Howship's lacunae_ (dotted line). They are mobile and capable of migrating over the bone surface. The photomicrograph demonstrates osteoclastic activity at the surface of alveolar bone (AB).
**Fig. 1-89**
**Fig. 1-89** illustrates a so-called bone multicellular unit (BMU), which is present in bone tissue undergoing active remodeling. The reversal line, indicated by red arrows, demonstrates the level to which bone resorption has occurred. From the reversal line new bone has started to form and has the character of osteoid. Note the presence of osteoblasts (ob) and vascular structures (v). The osteoclasts resorb organic as well as inorganic substances.
**Fig. 1-90**
**Fig. 1-91**
**Fig. 1-90** Both the cortical and cancellous alveolar bone are constantly undergoing remodeling (i.e. resorption followed by formation) in response to tooth drifting and changes in functional forces acting on the teeth. Remodeling of the trabecular bone starts with resorption of the bone surface by osteoclasts (OCL) as seen in Fig. 1-90a. After a short period, osteoblasts (OB) start depositing new bone (Fig. 1-90b) and finally a new bone multicellular unit is formed, clearly delineated by a reversal line (arrows) as seen in Fig. 1-90c.
**Fig. 1-91** Collagen fibers of the periodontal ligament (PL) insert in the mineralized bone which lines the wall of the tooth socket. This bone, called alveolar bone proper or bundle bone (BB), has a high turnover rate. The portions of the collagen fibers which are inserted inside the bundle bone are called Sharpey's fibers (SF). These fibers are mineralized at their periphery, but often have a non-mineralized central core. The collagen fiber bundles inserting in the bundle bone generally have a larger diameter and are less numerous than the corresponding fiber bundles in the cementum on the opposite side of the periodontal ligament. Individual bundles of fibers can be followed all the way from the alveolar bone to the cementum. However, despite being in the same bundle of fibers, the collagen adjacent to the bone is always less mature than that adjacent to the cementum. The collagen on the tooth side has a low turnover rate. Thus, while the collagen adjacent to the bone is renewed relatively rapidly, the collagen adjacent to the root surface is renewed slowly or not at all. Note the occurrence of osteoblasts (OB) and osteocytes (OC).
**Fig. 1-92**
**Fig. 1-93**
**Fig. 1-94**
**Fig. 1-95**
# Blood supply of the periodontium
**Fig. 1-92** The schematic drawing depicts the blood supply to the teeth and the periodontal tissues. The _dental artery_ (a.d.), which is a branch of the _superior_ or _inferior_ alveolar artery (a.a.i.), dismisses the _intra-septal artery_ (a.i.) before it enters the tooth socket. The terminal branches of the _intraseptal artery_ ( _rami perforantes_ , rr.p.) penetrate the alveolar bone proper in canals at all levels of the socket (see Fig. 1-76). They anastomose in the periodontal ligament space, together with blood vessels originating from the apical portion of the periodontal ligament and with other terminal branches, from the intraseptal artery (a.i.). Before the dental artery (a.d.) enters the root canal it puts out branches which supply the apical portion of the periodontal ligament.
**Fig. 1-93** The gingiva receives its blood supply mainly through _supraperiosteal_ blood vessels which are terminal branches of the _sublingual artery_ (a.s.), the _mental artery_ (a.m.), the _buccal artery_ (a.b.), the _facial artery_ (a.f.), the _greater palatine artery_ (a.p.), the _infra orbital artery_ (a.i.), and the _posterior superior dental artery_ (a.ap.).
**Fig. 1-94** depicts the course of the greater palatine artery (a.p.) in a specimen of a monkey which was perfused with plastic at sacrifice. Subsequently, the soft tissue was dissolved. The greater palatine artery (a.p.), which is a terminal branch of the _ascending palatine artery_ (from the _maxillary_ , "internal maxillary", artery), runs through the _greater palatine canal_ (arrow) to the palate. As this artery runs in a frontal direction it puts out branches which supply the gingiva and the masticatory mucosa of the palate.
**Fig. 1-95** The various arteries are often considered to supply certain well defined regions of the dentition. In reality, however, there are numerous anastomoses present between the different arteries. Thus, the _entire system of blood vessels_ , rather than individual groups of vessels, should be regarded as the unit supplying the soft and hard tissue of the maxilla and the mandible, e.g. in this figure there is an anastomosis (arrow) between the _facial artery_ (a.f.) and the blood vessels of the mandible.
**Fig. 1-96**
**Fig. 1-97**
**Fig. 1-96** illustrates a vestibular segment of the maxilla and mandible from a monkey which was perfused with plastic at sacrifice. Notice that the vestibular gingiva is supplied with blood mainly through _supraperiosteal_ blood vessels (arrows).
**Fig. 1-98**
**Fig. 1-97** As can be seen, blood vessels (arrows) originating from vessels in the periodontal ligament pass the alveolar bone crest and contribute to the blood supply of the free gingiva.
**Fig. 1-98** shows a specimen from a monkey which was perfused with ink at the time of sacrifice. Subsequently, the specimen was treated to make the tissue transparent (cleared specimen). To the right, the supraperiosteal blood vessels (sv) can be seen. During their course towards the free gingiva they put forth numerous branches to the _subepithelial plexus_ (sp), located immediately beneath the oral epithelium of the free and attached gingiva. This subepithelial plexus in turn yields thin _capillary loops_ to each of the connective tissue papillae projecting into the oral epithelium (OE). The number of such capillary loops is constant over a very long time and is not altered by application of epinephrine or histamine to the gingival margin. This implies that the blood vessels of the lateral portions of the gingiva, even under normal circumstances, are fully utilized and that the blood flow to the free gingiva is regulated entirely by velocity alterations. In the free gingiva, the supraperiosteal blood vessels (sv) anastomose with blood vessels from the periodontal ligament and the bone. Beneath the junctional epithelium (JE) seen to the left, is a plexus of blood vessels termed the _dento-gingival plexus_ (dp). The blood vessels in this plexus have a thickness of approximately 40 μm, which means that they are mainly venules. In healthy gingiva, no capillary loops occur in the dento-gingival plexus.
**Fig. 1-99**
**Fig. 1-99** This specimen illustrates how the subepithelial plexus (sp), beneath the oral epithelium of the free and attached gingiva, yields thin capillary loops to each connective tissue papilla. These capillary loops have a diameter of approximately 7 μm, which means they are the size of true capillaries.
**Fig. 1-100** illustrates the dento-gingival plexus in a section cut parallel to the subsurface of the junctional epithelium. As can be seen, the dento-gingival plexus consists of a fine-meshed network of blood vessels. In the upper portion of the picture, capillary loops can be detected belonging to the subepithelial plexus beneath the oral sulcular epithelium.
**Fig. 1-101** is a schematic drawing of the blood supply to the free gingiva. As stated above, the main blood supply of the free gingiva derives from the _supraperiosteal_ blood vessels (SV) which, in the gingiva, anastomose with blood vessels from the _alveolar bone_ (ab) and _periodontal ligament_ (pl). To the right in the drawing, the oral epithelium (OE) is depicted with its underlying subepithelial plexus of vessels (sp). To the left beneath the junctional epithelium (JE), the dento-gingival plexus (dp) can be seen, which, under normal conditions, comprises a fine-meshed network without capillary loops.
**Fig. 1-100**
**Fig. 1-101**
**Fig. 1-102**
**Fig. 1-102** shows a section prepared through a tooth (T) with its periodontium. Blood vessels (perforating rami; arrows) arising from the intraseptal artery in the alveolar bone run through canals (Volkmann's canals) in the socket wall (VC) into the periodontal ligament (PL), where they anastomose.
**Fig. 1-103** shows blood vessels in the periodontal ligament in a section cut parallel to the root surface. After entering the periodontal ligament, the blood vessels (perforating rami; arrows) anastomose and form a polyhedral network which surrounds the root like a stocking. The majority of the blood vessels in the periodontal ligament are found close to the alveolar bone. In the coronal portion of the periodontal ligament, blood vessels run in coronal direction, passing the alveolar bone crest, into the free gingiva (see Fig. 1-97).
**Fig. 1-104** is a schematic drawing of the blood supply of the periodontium. The blood vessels in the periodontal ligament form a polyhedral network surrounding the root. Note that the free gingiva receives its blood supply from (1) supraperiosteal blood vessels, (2) the blood vessels of the periodontal ligament, and (3) the blood vessels of the alveolar bone.
**Fig. 1-103**
**Fig. 1-105** illustrates schematically the so-called _extravascular_ circulation through which nutrients and other substances are carried to the individual cells and metabolic waste products are removed from the tissue. In the arterial (A) end of the capillary, to the left in the drawing, a hydraulic pressure of approximately 35 mmHg is maintained as a result of the pumping function of the heart. Since the hydraulic pressure is higher than the osmotic pressure (OP) in the tissue (which is approximately 30 mmHg), transportation of substances will occur from the blood vessels to the extravascular space (ES). In the venous (V) end of the capillary system, to the right in the drawing, the hydraulic pressure has decreased to approximately 25 mmHg (i.e. 5 mmHg lower than the osmotic pressure in the tissue). This allows transportation of substances from the extravascular space to the blood vessels. Thus, the difference between the hydraulic pressure and the osmotic pressure (OP) results in transportation of substances from the blood vessels to the extravascular space in the arterial part of the capillary while, in the venous part, transportation of substances occurs from the extravascular space to the blood vessels. An extravascular circulation is hereby established (small arrows).
**Fig. 1-104**
# Lymphatic system of the periodontium
**Fig. 1-106** The smallest lymph vessels, the _lymph capillaries_ , form an extensive network in the connective tissue. The wall of the lymph capillary consists of a single layer of endothelial cells. For this reason such capillaries are difficult to identify in an ordinary histologic section. The lymph is absorbed from the tissue fluid through the thin walls into the lymph capillaries. From the capillaries, the lymph passes into larger lymph vessels which are often in the vicinity of corresponding blood vessels. Before the lymph enters the blood stream it passes through one or more _lymph nodes_ in which the lymph is filtered and supplied with lymphocytes. The lymph vessels are like veins provided with valves. The lymph from the periodontal tissues drains to the lymph nodes of the head and the neck. The labial and lingual gingiva of the mandibular incisor region is drained to the _submental lymph nodes_ (sme). The palatal gingiva of the maxilla is drained to the _deep cervical lymph nodes_ (cp). The buccal gingiva of the maxilla and the buccal and lingual gingiva in the mandibular premolar–molar region are drained to _submandibular lymph nodes_ (sma). Except for the third molars and mandibular incisors, all teeth with their adjacent periodontal tissues are drained to the submandibular lymph nodes (sma). The third molars are drained to the _jugulodigastric lymph node_ (jd) and the mandibular incisors to the _submental lymph nodes_ (sme).
**Fig. 1-105**
**Fig. 1-106**
**Fig. 1-107**
# Nerves of the periodontium
Like other tissues in the body, the periodontium contains receptors which record pain, touch, and pressure ( _nociceptors_ and _mechanoreceptors_ ). In addition to the different types of sensory receptors, nerve components are found innervating the blood vessels of the periodontium. Nerves recording pain, touch, and pressure have their trophic center in the _semilunar ganglion_ and are brought to the periodontium via the _trigeminal nerve_ and its end branches. Owing to the presence of receptors in the periodontal ligament, small forces applied on the teeth may be identified. For example, the presence of a very thin (10–30 μm) metal foil strip placed between the teeth during occlusion can readily be identified. It is also well known that a movement which brings the teeth of the mandible in contact with the occlusal surfaces of the maxillary teeth is arrested reflexively and altered into an opening movement if a hard object is detected in the chew. Thus, the receptors in the periodontal ligament, together with the proprioceptors in muscles and tendons, play an essential role in the regulation of chewing movements and chewing forces.
**Fig. 1-107** shows the various regions of the gingiva which are innervated by end branches of the trigeminal nerve. The gingiva on the labial aspect of maxillary incisors, canines, and premolars is innervated by _superior labial branches_ from the _infraorbital nerve_ (n. infraorbitalis) (Fig. 1-107a). The buccal gingiva in the maxillary molar region is innervated by branches from the _posterior superior dental nerve_ (rr. alv. sup. post) (Fig. 1-107a). The palatal gingiva is innervated by the _greater palatal nerve_ (n. palatinus major) (Fig. 1-107b), except for the area of the incisors, which is innervated by the _long sphenopalatine nerve_ (n. pterygopalatini). The lingual gingiva in the mandible is innervated by the _sublingual nerve_ (n. sublingualis) (Fig. 1-107c), which is an end branch of the _lingual nerve_. The gingiva at the labial aspect of mandibular incisors and canines is innervated by the _mental nerve_ (n. mentalis), and the gingiva at the buccal aspect of the molars by the _buccal nerve_ (n. buccalis) (Fig. 1-107a). The innervation areas of these two nerves frequently overlap in the premolar region. The teeth in the mandible, including their periodontal ligament, are innervated by the _inferior alveolar nerve_ (n. alveolaris inf.), while the teeth in the maxilla are innervated by the _superior alveolar plexus_ (n. alveolares sup).
**Fig. 1-108**
**Fig. 1-108** The small nerves of the periodontium follow almost the same course as the blood vessels. The nerves to the gingiva run in the tissue superficial to the periosteum and put out several branches to the oral epithelium on their way towards the free gingiva. The nerves enter the periodontal ligament through the perforations (Volkmann's canals) in the socket wall (see Fig. 1-102). In the periodontal ligament, the nerves join larger bundles which take a course parallel to the long axis of the tooth. The photomicrograph illustrates small nerves (arrows) which have emerged from larger bundles of ascending nerves in order to supply certain parts of the periodontal ligament tissue. Various types of neural terminations such as free nerve endings and Ruffini's corpuscles have been identified in the periodontal ligament.
### **Acknowledgment**
We thank the following for contributing to the illustrations in Chapter 1: M. Listgarten, R.K. Schenk, H.E. Schroeder, K.A. Selvig, and K. Josephsen.
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Selvig, K.A. (1965). The fine structure of human cementum. _Acta Odontologica Scandinavica_ **23** , 423–441.
Valderhaug, J.R. & Nylen, M.U. (1966). Function of epithelial rests as suggested by their ultrastructure. _Journal of Periodontal Research_ **1** , 67–78.
# Chapter 2
# The Edentulous Alveolar Ridge
Maurício Araújo and Jan Lindhe
* * *
Clinical considerations
Remaining bone in the edentulous ridge
Classification of remaining bone
Topography of the alveolar process
Alterations of the alveolar process following tooth extraction
Intra-alveolar processes
Extra-alveolar processes
Topography of the edentulous ridge
* * *
# Clinical considerations
The alveolar process forms in harmony with the development and eruption of the teeth and it gradually regresses when the teeth are lost. In other words, the formation as well as the continued preservation of the alveolar process is dependent on the continued presence of teeth. Furthermore, the morphologic characteristics of the alveolar process are related to the size and shape of the teeth, events occurring during tooth eruption as well as the inclination of the erupted teeth. Thus, subjects with long and narrow teeth, compared with subjects who have short and wide teeth, appear to have a more delicate alveolar process and, in particular, a thin, sometimes fenestrated buccal bone plate (Fig. 2-1).
The tooth and its surrounding attachment tissues – the root cementum, the periodontal ligament and the bundle bone – establish a functional unit (Fig. 2-2) . Hence, forces elicited, for example during mastication, are transmitted from the crown of the tooth via the root and the attachment tissues to the load-carrying hard tissue structures in the alveolar process, where they are dispersed. The loss of teeth, and the loss or change of function within and around the socket will result in a series of adaptive alterations of the now edentulous portion of the ridge. Thus, it is well documented that following _multiple tooth_ extractions and the subsequent restoration with removable dentures, the size of the alveolar ridge will become markedly reduced, not only in the horizontal but also in the vertical dimension (Figs. 2-3, 2-4) ; in addition, the arch will be shortened (Atwood 1962, 1963; Johnson 1963, 1969; Carlsson _et al_. 1967).
Also following the removal of _single_ teeth the alveolar ridge will be markedly diminished (Fig. 2-5) . The magnitude of this change was studied and reported in a publication by Pietrokovski and Massler (1967) . The authors had access to 149 dental cast models (72 maxillary and 77 mandibular) in which one tooth was missing (and not replaced) on one side of the jaw. The outer contours of the buccal and lingual (palatal) portions of the ridge at a tooth site and at the contralateral edentulous site were determined by the use of a profile stylus and an imaging technique. Their findings are reported in Table 2-1.
**Fig. 2-1** Buccal aspect of adult skull preparations illustrating a dentate maxilla of one subject with a thick (a) and another subject with a thin (b) periodontal biotype.
**Fig. 2-2** Buccal–lingual section of a dentate portion of the alveolar process. B = buccal aspect; L = lingual aspect. (a) The tooth is surrounded by its attachment tissues. (b) Larger magnification of the attachment tissues. Note that the dentin is connected to the alveolar bone via the root cementum, the periodontal ligament and the alveolar bone. The inner portion of the alveolar bone (dotted line) is called the alveolar bone proper or the bundle bone.
**Fig. 2-3** (a) Clinical view of a partially edentulous maxilla. Note that the crest of the edentulous portions of the ridge is narrow in the buccal–palatal direction. (b) Clinical view of a fully edentulous and markedly resorbed maxilla. Note that papilla incisiva is located in the center of the ridge. This indicates that the entire buccal but also a substantial portion of the palatal ridge are missing.
**Fig. 2-4** Buccal aspect of a skull preparation illustrating a fully edentulous maxilla (a) and mandible (b) . The small segments of the alveolar ridge that still remain are extremely thin in the buccal–palatal/lingual direction.
**Fig. 2-5** Clinical view of an edentulous ridge in the maxillary premolar region. The premolar was extracted several years before the clinical documentation was made. (a) Note the presence of a buccal invagination of the ridge. (b) Following flap elevation, the crest region of the severely resorbed buccal portion of alveolar process is disclosed.
It was concluded that the amount of tissue resorption (hard and soft tissues combined) following the loss of a single tooth was substantial and that the reduction of the ridge was greater along the buccal surface than along the lingual and palatal surfaces in every specimen examined, although the absolute amounts and differences varied from one group of teeth to the next. As a result of this tissue modeling, the center of the edentulous site shifted toward the lingual or palatal aspect of the ridge. The observations made by Pietrokovski and Massler (1967) were supported by recent findings presented by Schropp _et al_. (2003) . They studied bone and soft tissue volume changes that took place during a 12-month period following the extraction of single premolars and molars. Clinical as well as cast model measurements were made immediately after tooth extraction and subsequently after 3, 6, and 12 months of healing. It was observed that the buccal–lingual/palatal dimension during the first 3 months was reduced about 30%, and after 12 months the edentulous site had lost at least 50% of its original width. Furthermore, the height of the buccal bone plate was reduced and after 12 months of healing the buccal prominence was located 1.2 mm apical of its lingual/palatal counterpart.
_Conclusion:_ The extraction of single as well as multiple teeth induces a series of adaptive changes in the soft and hard tissues that result in an overall regress of the edentulous site (s) . Resorption appears to be more pronounced at the buccal than at lingual/ palatal aspects of the ridge.
In this context it should be observed that the alveolar process might also undergo change as the result of tooth-related disease processes, such as aggressive, chronic and necrotizing forms of marginal periodontitis as well as periapical periodontitis. Furthermore, traumatic injuries may cause marked alterations of the maxilla and mandible including their alveolar processes.
**Table 2-1** Average amount of resorption of tooth extraction in different tooth areas*
## Remaining bone in the edentulous ridge
In the publication by Schropp _et al_. (2003) bone tissue formation in extraction sockets was studied by means of subtraction radiography. Thus, radiographs of the study sites were obtained using a standardized technique immediately after tooth extraction and then after 3, 6, and 12 months of healing (Fig. 2-6) _._ It was observed that in the first few months some bone loss (height) took place in the alveolar crest region. Most of the bone gain in the socket occurred in the first 3 months. There was additional gain of bone in the socket between 3 and 6 months. In the interval between 6 and 12 months, the newly formed bone obviously remodeled and the amount of mineralized tissue was reduced. In other words, towards the end of socket healing small amounts of mineralized tissue may have remained in the center of the edentulous site.
**Fig. 2-6** Radiographic (subtraction radiography) images of an extraction site obtained after (a) 3 months, (b) 6 months, and (c) 12 months of healing. The blue color represents areas of new bone formation. During the first 6 months, the deposition of new bone was intense. Between 6 and 12 months, some of the newly formed bone was remodeled. (Courtesy of Dr. L. Schropp.)
### Classification of remaining bone
Based on the volume of remaining mineralized bone, the edentulous sites may, according to Lekhom and Zarb (1985) , be classified into five different groups (Fig. 2-7) . In groups A and B substantial amounts of the alveolar process still remain, whereas in groups C, D, and E, there are only minute remnants of the alveolar process present. Lekholm and Zarb (1985) also classified the "quality" of the bone in the edentulous site. Class 1 and class 2 characterized a location in which the walls – the cortical plates – of the site are thick and the volume of bone marrow is small. Sites that belong to class 3 and class 4, however, are bordered by relatively thin walls of cortical bone, while the amount of cancellous bone (spongiosa) , including trabeculae of lamellar bone and marrow, is large.
# Topography of the alveolar process
The dentate alveolar process is defined as the portion of the mandible or maxilla that contains the sockets of the teeth (Fig. 2-8) _._ There is, however, no distinct boundary between the alveolar process and the basal bone of the jaws.
The alveolar process (Fig. 2-9) is comprised of the outer walls – buccal and lingual/palatal cortical plates – and a central portion of spongy bone (anatomic term) – or trabecular bone (radiographic term) or cancellous bone (histologic term) – that contains bone trabeculae as well as marrow. The cortical plates are continuous with the bone that lines the sockets, i.e. the alveolar bone proper (Fig. 2-10) . The alveolar bone proper can also be identified as the cribriform plate (anatomic term;Fig. 2-11) , or the lamina dura dentes (radiographic term;Fig. 2-12) or the bundle bone (histologic term; Fig. 2-2b) . The bundle bone is the tissue in which the extrinsic collagen fiber bundles of the periodontal ligament are embedded.
**Fig. 2-7** Schematic drawings showing (a) a classification of residual jaw shape, and (b) jaw bone quality, according to Lekholm and Zarb (1985).
The cortical plates (the outer walls) of the alveolar process meet the alveolar bone proper at the crest of the interdental septum (Fig. 2-10) ; at sites with a normal periodontium this is located about 1–2 mm apical of the cemento-enamel junction of adjacent teeth. In some portions of the anterior dentition, the spongy bone of the alveolar process may be absent. The cortical plates in such locations are continuous with the alveolar bone proper of the socket.
**Fig. 2-8** Buccal aspect of the maxillary incisor region of a skull preparation illustrating one subject with a thick (a) and another subject with a thin (b) periodontal biotype. Arrows indicate the presence of fenestrations in the buccal bone.
**Fig. 2-9** A buccal–lingual section from a human skull preparation illustrating the outer buccal and lingual cortical plates of the alveolar process, as well as the spongy bone in the center of the ridge.
The cortical plate is made up of lamellar bone. Lamellar bone contains both concentric and interstitial lamellae (see Chapter 1) . The spongy bone contains trabeculae of lamellar bone; in the adult these are surrounded by a marrow that is rich in adipocytes and pluripotent, mesenchymal stroma cells (Fig. 2-13) . Such cells may be induced to form bone, but also to support the differentiation of hemapoietic cells and thereby the differentiation of osteoclasts. The trabeculae of the spongy bone are orientated in directions that allow them to take up and distribute stress that occurs during mastication and other tooth contacts.
**Fig. 2-10** The empty alveolus of a second maxillary premolar is illustrated in the skull preparation. The buccal and palatal cortical plates are continuous with the alveolar bone proper and the bone tissue of the interdental septum. The perforations in the crest region represent the Volkman's canals.
# Alterations of the alveolar process following tooth extraction
The alterations that occur in the alveolar ridge following the extraction of single teeth can, for didactic reasons, be divided in two interrelated series of events, namely _intra-alveolar processes_ and _extra-alveolar processes._
## Intra-alveolar processes
The healing of extraction sockets in human volunteers was studied by e.g. Amler (1969) and Evian _et al_. (1982) . Although the biopsy technique used by Amler only allowed the study of healing in the marginal portions of the empty socket, his findings are often referred to. A copy of the drawing included in Amler's publication "The time sequence of tissue regeneration in human extraction wounds" is presented in Fig. 2-14.
**Fig. 2-11** A mandibular molar region of a human skull preparation. The second molar was removed in the skull preparation. In such an anatomic section, the alveolar bone proper (on the inside of the alveolus) is often termed the cribriform plate. This is due to the numerous perforations (Volkman's canals) that are present on the bone surface.
**Fig. 2-12** Radiograph obtained from the specimen illustrated in Fig. 2-11. In the radiograph the alveolar bone proper is often identified as lamina dura (dentes).
**Fig. 2-13** Histologic section presenting the mesio-distal aspect of a fresh extraction socket bordered by two neighboring roots. Note that the alveolar bone from the tooth sites is continuous with the walls of the empty socket. The interdental septum contains cancellous bone including trabeculae of lamellar bone and marrow.
Amler stated that following tooth extraction, the first 24 hours are characterized by the formation of a _blood clot_ in the socket _._ Within 2–3 days the blood clot is gradually being replaced with _granulation tissue._ After 4–5 days, the _epithelium_ from the margins of the soft tissue starts to proliferate to cover the granulation tissue in the socket. One week after extraction, the socket contains granulation tissue, _young connective tissue_ , and _osteoid_ formation is ongoing in the apical portion of the socket. After 3 weeks, the socket contains connective tissue and there are signs of mineralization of the osteoid. The _epithelium_ covers the wound. After 6 weeks of healing, bone formation in the socket is pronounced and trabeculae of newly formed bone can be seen.
Amler's study was of short duration, so it could only evaluate events that took place in the marginal portion of the healing socket. His experimental data did not include the important later phase of socket healing that involves the processes of modeling and remodeling of the newly formed tissue in various parts of the alveolus. Thus, the tissue composition of the fully healed extraction site was not documented in the study.
The results from a recent, long-term experiment in the dog (Cardaropoli _et al_. 2003) will therefore be used to describe more in detail the various phases of socket healing including processes of both modeling and remodeling. Following the elevation of buccal and lingual full-thickness flaps, the distal roots of mandibular premolars were extracted (Fig. 2-15a) . The mucosal flaps were managed to provide soft tissue coverage of the fresh extraction wound (Fig. 2-15b) . Healing of the extraction sites was monitored in biopsy specimens obtained at time intervals between 1 day and 6 months (Fig. 2-15c).
**Fig. 2-14** Healing of the alveolar socket after tooth extraction according to Amler (1969). (a) Bleeding and formation of a blood clot immediately after tooth extraction. Blood vessels are closed by trombi and a fibrin network is formed. (b) Already, during the first 48 hours, neutrophilic granulocytes, monocytes and fibroblasts begin to migrate within the fibrin network. (c) The blood clot is slowly replaced by granulation tissue. (d) Granulation tissue forms predominantly in the apical third of the alveolus. There is increased density of fibroblasts. After 4 days, contraction of the clot and proliferation of the oral epithelium is seen. Osteoclasts are visible at the margin of the alveolus. Osteoblasts and osteoids seem to appear in the bottom of the alveolus. (e) Reorganization of the granulation tissue through formation of osteoid trabeculae. Epithelial proliferation from the wound margins on the top of the young connective tissue. Again, the formation of osteoid trabeculae is evident from the wall of the alveolus in a coronal direction. After 3 weeks some of the trabeculae start to mineralize. (f) Radiographically, bone formation may be visible. The soft tissue wound is closed and epithelialized after 6 weeks. However, bone fill in the alveolus takes up to 4 months and does not seem to reach the level of the neighboring teeth.
**Fig. 2-15** (a) Photograph illustrating a mandibular premolar site (from a dog experiment) from which the distal root of the 4th premolar was removed. (b) The mucosal, full-thickness flaps were replaced and sutured to close the entrance of the socket. (c) The site after 6 months of healing. Note the saddle-shaped outline (loss of tissue) of the alveolar crest region.
### Overall pattern of socket healing
Figure 2-13 presents a mesio-distal section of a fresh extraction socket bordered by adjacent roots. The socket is filled with a coagulum. The socket walls are continuous with the alveolar bone proper of the neighboring teeth. The tissue inside the interdental (interradicular) septa is made up of cancellous bone and includes trabeculae of lamellar bone within bone marrow.
The empty socket is first filled with blood and a _coagulum_ (clot) forms (Fig. 2-16a). Inflammatory cells (polymorphonuclear leukocytes and monocytes/ macrophages) migrate into the coagulum and start to phagocytose elements of necrotic tissue. The process of wound cleansing is initiated (Fig. 2-16b). Sprouts of newly formed vessels and mesenchymal cells (from the severed periodontal ligament) enter the coagulum and _granulation tissue_ is formed. The granulation tissue is gradually replaced with _provisional connective tissue_ (Fig. 2-16c) and subsequently immature bone ( _woven bone_ ) is laid down (Fig. 2-16d). The hard tissue walls of the socket – the alveolar bone proper or the bundle bone – are resorbed and the socket wound becomes filled with woven bone (Fig. 2-16e). The initial phases of the healing process are now completed. In subsequent phases the woven bone in the socket is gradually remodeled into lamellar bone and marrow (Fig. 2-16f, g, h).
## Important events in socket healing
#### _Blood clotting_
Immediately after tooth extraction, blood from the severed blood vessels will fill the cavity. Proteins derived from vessels and damaged cells initiate a series of events that lead to the formation of a fibrin network (Fig. 2-17). _Platelets_ form aggregates and interact with the fibrin network to produce a _blood clot_ (a coagulum) that effectively plugs the severed vessels and stops bleeding. The blood clot acts as a physical matrix that directs cellular movements and it contains substances that are of importance for the forthcoming healing process. Thus, the clot contains substances that (1) influence mesenchymal cells (i.e. _growth factors_ ) and (2) enhance the activity of inflammatory cells. Such substances will thus induce and amplify the migration of various types of cells into the socket wound, as well as their proliferation, differentiation and synthetic activity within the coagulum.
Although the blood clot is crucial in the initial phase of wound healing, its removal is mandatory to allow the formation of new tissue. Thus, within a few days after the tooth extraction, the blood clot will start to break down, i.e. the process of "fibrinolysis" is initiated (Fig. 2-18).
**Fig. 2-16** Overall pattern of bone formation in an extraction socket. For details see text.
**Fig. 2-17** Histologic section (mesio-distal aspect) representing 1 day of healing (a). The socket is occupied with a blood clot that contains large numbers of erythrocytes (b) entrapped in a fibrin network, as well as platelets (blue in (c)).
**Fig. 2-18** (a) Histologic section (mesio-distal aspect) representing 3 days of healing. (b) Note the presence of neutrophils and macrophages that are engaged in wound cleansing and the break down of the blood clot. (c) Osteoclastic activity occurs on the surface of the old bone in the socket walls.
#### _Wound cleansing_
Neutrophils and macrophages migrate into the wound, engulf bacteria and damaged tissue (Fig. 2-18) and clean the site before the formation of new tissue can start. The neutrophils enter the wound early while macrophages appear somewhat later. The macrophages are not only involved in the cleaning of the wound but they also release growth factors and cytokines that further promote the migration, proliferation and differentiation of mesenchymal cells. Once the debris has been removed and the wound has become "sterilized", the neutrophils undergo a programmed cell death ( _apoptosis_ ) and are removed from the site through the action of macrophages. The macrophages subsequently withdraw from the wound.
#### _Tissue formation_
Sprouts of vascular structures (from the severed periodontal ligament) as well as mesenchymal, fibroblast-like cells (from the periodontal ligament and from adjacent bone marrow regions) enter the socket. The mesenchymal cells start to proliferate and deposit matrix components in an extracellular location (Fig. 2-19a,b,c); a new tissue, i.e. _granulation tissue_ , will gradually replace the blood clot. The granulation tissue eventually contains macrophages, and a large number of fibroblast-like cells as well as numerous newly formed blood vessels. The fibroblast-like cells continue (1) to release growth factors, (2) to proliferate, and (3) to deposit a new extra cellular matrix that guides the ingrowth of additional cells and allows the further differentiation of the tissue. The newly formed vessels provide the oxygen and nutrients that are needed for the increasing number of cells that occur in the new tissue. The intense synthesis of matrix components exhibited by the mesenchymal cells is called _fibroplasia_ , while the formation of new vessels is called _angiogenesis_ . A _provisional connective tissue_ is established through the combination of fibroplasia and angiogenesis (Fig. 2-20).
The transition of the provisional connective tissue into bone tissue occurs along the vascular structures. Thus, osteoprogenitor cells (e.g. pericytes) migrate and gather in the vicinity of the vessels. They differentiate into osteoblasts that produce a matrix of collagen fibers, which takes on a woven pattern. The _osteoid_ is formed. The process of mineralization is initiated within the osteoid. The osteoblasts continue to lay down osteoid and occasionally such cells are trapped in the matrix and become osteocytes. This newly formed bone is called _woven bone_ (Fig. 2-21).
The woven bone is the first type of bone to be formed and is characterized by (1) its rapid deposition as fingerlike projections along the route of vessels, (2) the poorly organized collagen matrix, (3) the large number of osteoblasts that are trapped in its mineralized matrix, and (4) its low load-bearing capacity. Trabeculae of woven bone are shaped around and encircle the vessel. The trabeculae become thicker through the deposition of additional woven bone. Cells (osteocytes) become entrapped in the bone tissue and the first set of osteons, the _primary osteons_ , are organized. The woven bone is occasionally reinforced by the deposition of so called _parallelfibered bone_ , that has its collagen fibers organized not in a woven but in a concentric pattern.
**Fig. 2-19** (a) Histologic section (mesio-distal aspect) representing 7 days of healing. (b) Note the presence of a richly vascularized early granulation tissue with large numbers of inflammatory cells in the upper portion of the socket. (c) In more apical areas, a tissue including large numbers of fibroblast-like cells is present, i.e. late granulation tissue.
**Fig. 2-20** (a) Histologic section (mesio-distal aspect) representing 14 days of healing. (b) In the marginal portion of the wound, a provisional connective tissue rich in fibroblast-like cells is present. (c) The formation of woven bone has at this time interval already begun in apical and lateral regions of the socket.
**Fig. 2-21** (a) Histologic section (mesio-distal aspect) representing 30 days of healing. The socket is filled with woven bone. (b) This woven bone contains a large number of cells and primary osteons (PO). (c) The woven pattern of the collagen fibers of this type of bone is illustrated (polarized light).
It is important to realize that during this early phase of healing the bone tissue in the walls of the socket (the bundle bone) is removed and replaced with woven bone.
### Tissue modeling and remodeling
The initial bone formation is a fast process. Within a few weeks, the entire extraction socket will become filled with woven bone or, as this tissue is also called, _primary bone spongiosa_ . The woven bone offers (1) a stable scaffold, (2) a solid surface, (3) a source of osteoprogenitor cells, and (4) ample blood supply for cell function and matrix mineralization.
The woven bone with its primary osteons is gradually replaced with lamellar bone and bone marrow (Fig. 2-22). In this process, the primary osteons are replaced with _secondary osteons_ . The woven bone is first resorbed to a certain level. This level of the resorption front will establish a so-called _reversal line_ , which is also the level from which new bone with secondary osteons will form (Fig. 2-23). Although this remodeling may start early during socket healing it will take several months until all woven bone in the extraction socket has been replaced with lamellar bone and marrow.
**Fig. 2-22** (a) Histologic section (mesio-distal aspect) representing 60 days of healing. (b) A large portion of the woven bone has been replaced with bone marrow. (c) Note the presence of a large number of adipocytes residing in a tissue that still contains woven bone.
An important part of socket healing involves the formation of a _hard tissue cap_ that will close the marginal entrance to the socket. This cap is initially comprised of woven bone (Fig. 2-24a) but is subsequently remodeled and replaced with lamellar bone that becomes continuous with the cortical plate at the periphery of the edentulous site (Fig. 2-24b). This process is called corticalization.
The wound is now healed, but the tissues in the site will continue to adapt to functional demands. Since there is no stress from forces elicited during mastication and other occlusal contacts there is no demand on mineralized bone in the areas previously occupied by the tooth. Thus, the socket apical of the hard tissue cap will remodel mainly into marrow. Indeed, in many edentulous patients the entire alveolar ridge will regress as a result of continuous adaptation to lack of function.
### Extra-alveolar processes
In an experiment in the dog (Araújo & Lindhe 2005) alterations in the profile of the edentulous ridge that occurred following tooth extraction were carefully examined. In this study the 3rd and 4th mandibular premolars were hemi-sected. Buccal and lingual full-thickness flaps were raised; the distal roots were carefully removed. The flaps were replaced and sutured to cover the fresh extraction socket (Fig. 2-25). Biopsy specimens, including an individual extraction socket and adjacent roots, were obtained after 1, 2, 4, and 8 weeks of healing. The blocks were sectioned in the _buccal–lingual_ plane.
**Fig. 2-23** Schematic drawing that describes how woven bone is replaced by lamellar bone. Woven bone with primary osteons is substituted by lamellar bone in a process that involves the presence of bone multicellular units (BMUs). The BMU contains osteoclasts (OC) , as well as vascular structures (V) and osteoblasts (OB). Thus, the osteoblasts in the BMU produce bone tissue in a concentric fashion around the vessel, and lamellar bone with secondary osteons is formed.
**Fig. 2-24** Histologic sections (mesio-distal aspect) describing the hard tissue that has formed at the entrance of a healing extraction socket and the process of corticalization. (a) Woven bone with primary osteons occupies the socket entrance after 60 days of healing. (b) After 180 days the woven bone has been replaced with mainly lamellar bone.
Figure 2-26 illustrates a buccal–lingual section of the distal root of an intact 3rd premolar with surrounding soft and hard tissues. The lingual hard tissue wall is substantially wider than its buccal counterpart. The marginal portion of the lingual wall is presented in a higher magnification in Fig. 2-26a. A layer of bundle bone occupies the inner portion of the lingual bone wall. A thin layer of bundle bone is also present at the top of the ridge. Figure 2-26b illustrates the corresponding portion of the buccal bone wall. Note that all the mineralized tissue in the marginal 1–2 mm of the buccal ridge is comprised of bundle bone. In this context, it must be remembered that bundle bone is part of the attachment tissues for the tooth; this tissue has no obvious function following the removal of the tooth and will thus eventually be resorbed and disappear.
* _1 week after tooth extraction_ (Fig. 2-27). At this interval the socket is occupied by a coagulum. Furthermore, a large number of osteoclasts can be seen on the outside as well as on the inside of the buccal and lingual bone walls. The presence of osteoclasts on the inner surface of the socket walls indicates that the bundle bone is being resorbed.
* _2 weeks after tooth extraction_ (Fig. 2-28). Newly formed immature bone (woven bone) resides in the apical and lateral parts of the socket, while more central and marginal portions are occupied by a provisional connective tissue. In the marginal and outer portions of the socket walls numerous osteoclasts can be seen. In several parts of the socket walls the bundle bone has been replaced with woven bone.
* _4 weeks after tooth extraction_ (Fig. 2-29). The entire socket is occupied with woven bone at this stage of healing. Large numbers of osteoclasts are present in the outer and marginal portions of the hard tissue walls. Osteoclasts also line the trabeculae of woven bone present in the central and lateral aspects of the socket. In other words the newly formed woven bone is being replaced with a more mature type of bone.
* _8 weeks after tooth extraction_ (Fig. 2-30). A layer of cortical bone covers the entrance to the extraction site. Corticalization has occurred. The woven bone that was present in the socket at the 4-week interval is replaced with bone marrow and some trabeculae of lamellar bone in the 8-week specimens. On the outside and on the top of the buccal and lingual bone wall there are signs of ongoing hard tissue resorption. The crest of the buccal bone wall is located apical of its lingual counterpart.
**Fig. 2-25** (a) Photograph illustrating mandibular premolar sites (from a dog experiment) from which the distal roots of the 4th and 3rd premolars were extracted. (b) The mucosal, full-thickness flaps were replaced and sutured to close the entrance of the socket.
**Fig. 2-26** Histologic section (buccal–lingual aspect) of the distal root of an intact 3rd premolar in the dog. Note the wide lingual and thinner buccal bone wall. Higher magnification of the crestal bone of the lingual wall (a) and buccal wall (b). B = buccal bone; L = lingual bone.
The relative change in the location of the crest of the buccal and lingual bone walls that took place during the 8 weeks of healing is illustrated in Fig. 2-31. While the level of the margin of the lingual wall remained reasonably unchanged, the margin of the buccal wall shifted several millimeters in an apical direction.
There are at least two reasons why, in this animal model, more bone loss occurred in the buccal than in the lingual wall during socket healing. First, prior to tooth extraction, the marginal 1–2 mm of the crest of the buccal bone wall was occupied by bundle bone. Only a minor fraction of the crest of the lingual wall contained bundle bone. Bundle bone, as stated above, is a tooth-dependent tissue and will gradually disappear after tooth extraction. Thus, since there is relatively more bundle bone in the crest region of the buccal than of the lingual wall, hard tissue loss will become most pronounced in the buccal wall. Secondly, the lingual bone wall of the socket is markedly wider than that of the buccal wall. It is well known from the periodontal literature (e.g. Wilderman _et al_. 1960; Wilderman 1963; Tavtigian 1970; Wood _et al_. 1972; Araújo _et al_. 2005) that flap elevation and the separation of the periosteum from the bone tissue will result in surface resorption; this will result in more vertical height reduction of the thin buccal than of the wider lingual bone wall.
**Fig. 2-27** (a) Histologic section (buccal–lingual aspect) of the socket after 1 week of healing. Note the presence of a large number of osteoclasts on the crestal portion (b) and inner portion (c) of the buccal wall. B = buccal bone; L = lingual bone.
**Fig. 2-28** (a) Histologic section (buccal–lingual aspect) of the socket after 2 weeks of healing. (b) Note that the bundle bone in the lingual aspect of the socket is being replaced with woven bone. B = buccal bone; L = lingual bone.
# Topography of the edentulous ridge
As described previously in this chapter, the processes of modeling and remodeling that occur following tooth extraction (loss) result in pronounced resorption of the various components of the alveolar ridge. The resorption of the buccal bone wall is more pronounced than the resorption of the lingual/palatal wall and hence the center of the ridge will move in lingual/palatal direction. In the extreme case, the entire alveolar process may be lost following tooth loss and in such situations only the bone of the base of the mandible and the base of the maxilla remains.
Figure 2-32 presents a buccal–lingual section of an edentulous site prepared from a biopsy of a dog obtained 2–3 years after tooth extraction. The ridge is covered by a mucosa (Fig. 2-33) that in this particular case is about 2–3 mm high and is comprised of keratinized epithelium and dense connective tissue that is attached via the periosteum to the cortical bone. Depending on factors such as the biotype, the jaw (maxilla or mandible) , the location (anterior, posterior) in the jaw, location of the muco-gingival junction, depth of the buccal and lingual vestibule, and the amount of hard tissue resorption, the edentulous site may be lined with either masticatory, keratinized mucosa or lining, non-keratinized mucosa.
**Fig. 2-29** Histologic section (buccal–lingual aspect) of the socket after 4 weeks of healing. The extraction socket is filled with woven bone. On the top of the buccal wall the old bone in the crest region is being resorbed and replaced with either connective tissue or woven bone. B = buccal bone; L = lingual bone.
**Fig. 2-30** Histologic section (buccal–lingual aspect) of the socket after 8 weeks of healing. The entrance of the socket is sealed with a cap of newly formed mineralized bone. Note that the crest of the buccal wall is located apical of the crest of the lingual wall. B = buccal bone; L = lingual bone.
**Fig. 2-31** Histologic sections (buccal–lingual aspects) describing the profile of the edentulous region in the dog after (a) 1, (b) 2, (c) 4, and (d) 8 weeks of healing following tooth extraction. While the marginal level of the lingual wall was maintained during the process of healing (solid line) , the crest of the buccal wall was replaced >2 mm in the apical direction (dotted line).
**Fig. 2-32** Histologic section (buccal–lingual aspect) describing an edentulous mandibular site (from a dog experiment) 2 years after the extraction of the tooth. Note that the crest is higher at the lingual than at the buccal aspect of the site. B = buccal bone; L = lingual bone.
**Fig. 2-33** Histologic section illustrating the mucosa residing over the bone crest. The mucosa has a well keratinized epithelium and a connective tissue densely packed with collagen fibers.
The outer walls of the remaining portion of the alveolar process are comprised of lamellar bone. The buccal bone plate is comparatively thin and the lingual/palatal plate comparatively thick. The cortical plates enclose the cancellous bone that harbors trabeculae of lamellar bone and marrow. The bone marrow contains numerous vascular structures as well as adipocytes and pluripotent mesenchymal cells. As a rule the ridge of the edentulous site in the maxilla contains comparatively more cancellous bone than a site in the mandible.
References
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Araújo, M.G. & Lindhe, J. (2005). Dimensional ridge alterations following tooth extraction. An experimental study in the dog. _Journal of Clinical Periodontology_ **32** , 212–218.
Araújo, M.G., Sukekava, F., Wennström, J.L. & Lindhe, J. (2005). Ridge alterations following implant placement in fresh extraction sockets; an experimental study in the dog. _Journal of Clinical Periodontology_ **32** , 645–652.
Atwood, D.A. (1962). Some clinical factors related to the rate of resorption of residual ridges. _Journal of Prosthetic Dentistry_ **12** , 441–450.
Atwood, D.A. (1963). Postextraction changes in the adult mandible as illustrated by microradiographs of midsagittal section and serial cephalometric roentgenograms. _Journal of Prosthetic Dentistry_ **13** , 810–816.
Cardaropoli, G., Araújo, M. & Lindhe, J. (2003). Dynamics of bone tissue formation in tooth extraction sites. An experimental study in dogs. _Journal of Clinical Periodontology_ **30** , 809–818.
Carlsson, G.E., Thilander, H. & Hedegård, B. (1967). Histological changes in the upper alveolar process after extraction with or without insertion of an immediate full denture. _Acta Odontologica Scandinavica_ **25** , 21–43.
Evian, C.I., Rosenberg, E.S., Cosslet, J.G. & Corn, H. (1982). The osteogenic activity of bone removed from healing extraction sockets in human. _Journal of Periodontology_ **53** , 81–85.
Friedenstein, A.G. (1973). Determined and inducible osteogenic precursor cells. In: _Hand Tissue Growth Repair and Remineralization_. Aba Foundation Symposium 11, pp. 169–181.
Johnson, K. (1963). A study of the dimensional changes occurring in the maxilla after tooth extraction. Part I. Normal healing. _Australian Dental Journal_ **8** , 241–244.
Johnson, K. (1969). A study of the dimensional changes occurring in the maxilla following tooth extraction. _Australian Dental Journal_ **14** , 428–433.
Lekholm, U. & Zarb, G.A. (1985). Patient selection. In: Brånemark, P-I., Zarb, G.A. & Albreksson, T., eds. _Tissue Integrated Prostheses. Osseointegrationin Clinical Dentistry_. Chicago: Quintessence, pp. 199–209.
Pietrokovski, J. & Massler, M. (1967). Alveolar ridge resorption following tooth extraction. _Journal of Prosthetic Dentistry_ **17** , 21–27.
Schropp, L., Wenzel, A., Kostopoulos, L. & Karring, T. (2003). Bone healing and soft tissue contour changes following single-tooth extraction: a clinical and radiograhic 12-month prospective study. _International Journal of Periodontics & Restorative Dentistry_ **23** , 313–323.
Tavtigian, R. (1970). The height of the facial radicular alveolar crest following apically positioned flap operations. _Journal of Periodontology_ **41** , 412–418.
Wilderman, M.N. (1963). Repair after a periosteal retention procedure. _Journal of Periodontology_ **34** , 487–503.
Wilderman, M.N., Wentz, F. & Orban, B.J. (1960). Histogenesis of repair after mucogingival surgery. _Journal of Periodontol-_ 141–144. _ogy_ **31** , 283–299.
Wood, D.L., Hoag, P.M., Donnenfeld, W.O. & Rosenfeld, L.D. (1972). Alveolar crest reduction following full and partial thickness flaps. _Journal of Periodontology_ **42** , 141–144.
# Chapter 3
# The Mucosa at Teeth and Implants
Jan Lindhe, Jan L. Wennström, and Tord Berglundh
* * *
The gingiva
Biologic width
Dimensions of the buccal tissue
Dimensions of the interdental papilla
The peri-implant mucosa
Biologic width
Quality
Vascular supply
Probing gingiva and peri-implant mucosa
Dimensions of the buccal soft tissue at implants
Dimensions of the papilla between teeth and implants
Dimensions of the "papilla" between adjacent implants
* * *
# The gingiva
## Biologic width
A term frequently used to describe the dimensions of the soft tissues that face the teeth is _the biologic width of the soft tissue attachment_. The development of the _biologic width concept_ was based on studies and analyses by, among others, Gottlieb (1921), Orban and Köhler (1924), and Sicher (1959), who documented that the soft tissue attached to the teeth was comprised of two parts, one fibrous tissue and one attachment of epithelium. In a publication by Gargiulo _et al_. (1961) called "Dimensions and relations of the dentogingival junction in humans", sections from autopsy block specimens that exhibited different degree of "passive tooth eruption" (i.e. periodontal tissue breakdown) were examined. Histometric assessments were made to describe the length of the sulcus (not part of the attachment), the epithelial attachment (today called junctional epithelium), and of the connective tissue attachment (Fig. 3-1). It was observed that the length of the connective tissue attachment varied within narrow limits (1.06–1.08 mm) while the length of the attached epithelium was about 1.4 mm at sites with normal periodontium, 0.8 mm at sites with moderate and 0.7 mm at sites with advanced periodontal tissue breakdown. In other words, (1) the biologic width of the attachment varied between about 2.5 mm in the normal case and 1.8 mm in the advanced disease case, and (2) the most variable part of the attachment was the length of the epithelial attachment (junctional epithelium).
**Fig. 3-1** Drawing describing the "biologic width" of the soft tissue attachment at the buccal surface of a tooth with healthy periodontium. The combined length of the junctional epithelium (epithelial attachment) and the connective tissue attachment is considered to represent the "biologic width" of the soft tissue attachment. Note the gingival sulcus is NOT part of the attachment.
## Dimensions of the buccal tissue
The morphologic characteristics of the gingiva are related to the dimension of the alveolar process, the form (anatomy) of the teeth, events that occur during tooth eruption, and the eventual inclination and position of the fully erupted teeth (Wheeler 1961; O'Connor & Biggs 1964; Weisgold 1977). Ochenbein and Ross (1969) and Becker _et al_. (1997) proposed (1) that the anatomy of the gingiva is related to the contour of the osseous crest, and (2) that two basic types of gingival architecture may exist, namely the " _pronounced scalloped_ " and the " _flat_ " biotype.
**Fig. 3-2** Clinical photograph of a subject that belongs to the "pronounced scalloped" gingival biotype. The crowns of the teeth are comparatively long and slender. The papillae are comparatively long, the gingival margin is thin and the zone of attached gingiva is short.
Subjects who belong to the " _pronounced scalloped_ " biotype have long and slender teeth with tapered crown form, delicate cervical convexity and minute interdental contact areas that are located close to the incisal edge (Fig. 3-2). The maxillary front teeth of such individuals are surrounded with a thin free gingiva, the buccal margin of which is located at or apical of the cemento-enamel junction. The zone of gingiva is narrow, and the outline of the gingival margin is highly scalloped (Olsson _et al_. 1993). On the other hand, subjects who belong to the " _flat_ " gingival biotype have incisors with squared crown form with pronounced cervical convexity (Fig. 3-3). The gingiva of such individuals is wider and more voluminous, the contact areas between the teeth are large and more apically located, and the interdental papillae are short. It was reported that subjects with pronounced scalloped gingiva often exhibited more advanced soft tissue recession in the anterior maxilla than subjects with a flat gingiva (Olsson & Lindhe 1991).
Kan _et al_. (2003) measured the dimension of the gingiva – as determined by bone sounding – at the buccal-mesial and buccal-distal aspects of maxillary anterior teeth. Bone sounding determines the distance between the soft tissue margin and the crest of the bone and, hence, provides an estimate that is about 1 mm greater than that obtained in a regular probing pocket depth measurement. The authors reported that the thickness of the gingiva varied between subjects of different gingival biotypes. Thus, the height of the gingiva at the buccal-approximal surfaces in subjects who belonged to the flat biotype was, on average, 4.5 mm, while in subjects belonging to the pronounced scalloped biotype the corresponding dimension (3.8 mm) was significantly smaller. This indicates that subjects who belong to the flat biotype have more voluminous soft buccal/ appro ximal tissues than subjects who belong to the pronounced scalloped biotype _._
**Fig. 3-3** Clinical photograph of a subject that belongs to the "flat" gingival biotype. The crowns of the teeth are comparatively short but wide. The papillae are comparatively short but voluminous and the zone of attached gingiva is wide.
Pontoriero and Carnevale (2001) performed evaluations of the reformation of the gingival unit at the buccal aspect of teeth exposed to crown lengthening procedures using a denudation technique. At the 1- year follow-up examination after surgery the regain of soft tissue – measured from the level of the denuded osseous crest – was greater in patients with a thick (flat) biotype than in those with a thin (pronounced scalloped) biotype (3.1 mm versus 2.5 mm). No assessment was made of the bone level change that had occurred between the baseline and the follow-up examination. It must, however, be anticipated that some bone resorption had taken place during healing and that the biologic width of the new connective tissue attachment had been re-established coronal to the level of the resected osseous crest.
The dimensions of the buccal gingiva may also be affected by the buccal–lingual position of the tooth within the alveolar process. A change of the tooth position in buccal direction results in reduced dimensions of the buccal gingiva, while an increase is observed following a lingual tooth movement (Coatoam _et al_. 1981; Andlin-Sobocki & Brodin 1993). In fact, Müller and Könönen (2005) demonstrated in a study of the variability of the thickness of the buccal gingiva of young adults that most of the variation in gingival thickness was due to the tooth position and that the contribution of subject variability (i.e. flat and pronounced scalloped) was minimal.
**Fig. 3-4** Tarnow _et al_. (1992) measured the distance between the contact point (P) between the crowns of the teeth and the bone crest (B) using sounding (transgingival probing).
## Dimensions of the interdental papilla
The interdental papilla in a normal, healthy dentition has one buccal and one lingual/palatal component that are joined in the col region (Chapter 1; Figs. 1-1–1-9). Experiments performed in the 1960s (Kohl & Zander 1961; Matherson & Zander 1963) revealed that the shape of the papilla in the col region was not determined by the outline of the bone crest but by the shape of the contact relationship that existed between adjacent teeth.
Tarnow _et al_. (1992) studied whether the distance between the contact point (area) between teeth and the crest of the corresponding inter-proximal bone could influence the degree of papilla fill that occurred at the site. Presence or absence of a papilla was determined visually in periodontally healthy subjects. If there was no space visible apical of the contact point, the papilla was considered complete. If a "black space" was visible at the site, the papilla was considered incomplete. The distance between the facial level of the contact point and the bone crest (Fig. 3-4) was measured by sounding. The measurement thus included not only the epithelium and connective tissue of the papilla but in addition the entire supra-alveolar connective tissue in the inter-proximal area (Fig. 3-5). The authors reported that the papilla was always complete when the distance from the contact point to the crest of the bone was ≤5 mm. When this distance was 6 mm, papilla fill occurred in about 50% of cases and at sites where the distance was ≥7 mm, the papilla fill was incomplete in about 75% of cases. Considering that the supracrestal connective tissue attachment is about 1 mm high, the above data indicate that the papilla height may be limited to about 4 mm in most cases. Interestingly, papillae of similar height (3.2–4.3 mm) were found to reform following surgical denudation procedures (van der Velden 1982; Pontoriero & Carnevale 2001), but to a greater height in patients with a thick (flat) than in those with a thin (pronounced scalloped) biotype.
**Fig. 3-5** Mesio-distal section of the interproximal area between the two central incisors. Arrows indicate the location of the cemento-enamel junction. Dotted line indicates the outline of the marginal bone crest. The distance between the contact point (P) between the crowns of the teeth and the bone crest (B) indicates the height of the papilla.
### Summary
* _Flat gingival (periodontal) biotype_ : the buccal marginal gingiva is comparatively thick, the papillae are often short, the bone of the buccal cortical wall is thick, and the vertical distance between the interdental bone crest and the buccal bone is short (about 2 mm).
* _Pronounced scalloped gingival (periodontal) biotype_ : the buccal marginal gingiva is delicate and may often be located apical of the cemento-enamel junction (receded), the papillae are high and slender, the buccal bone wall is often thin and the vertical distance between the interdental bone crest and the buccal bone is long (>4 mm).
# The peri-implant mucosa
The soft tissue that surrounds dental implants is termed _peri-implant mucosa_. Features of the periimplant mucosa are established during the process of wound healing that occurs subsequent to the closure of mucoperiosteal flaps following implant installation (one-stage procedure) or following abutment connection (two-stage procedure) surgery. Healing of the mucosa results in the establishment of a soft tissue attachment (transmucosal attachment) to the implant. This attachment serves as a seal that prevents products from the oral cavity reaching the bone tissue, and thus ensures osseointegration and the rigid fixation of the implant.
The peri-implant mucosa and the gingiva have several clinical and histological characteristics in common. Some important differences, however, also exist between the gingiva and the peri-implant mucosa.
## Biologic width
The structure of the mucosa that surrounds implants made of titanium has been examined in man and several animal models (for review see Berglundh 1999). In an early study in the dog, Berglundh _et al_. (1991) compared some anatomic features of the gingiva (at teeth) and the mucosa at implants. Since the research protocol from this study was used in subsequent experiments that will be described in this chapter, details regarding the protocol are briefly outlined here.
The mandibular premolars in one side of the mandible were extracted, leaving the corresponding teeth in the contralateral jaw quadrant. After 3 months of healing following tooth extraction (Fig. 3-6) the fixture part of implants (Brånemark system®, Nobel Biocare, Gothenburg, Sweden) were installed (Fig. 3-7) and submerged according to the guidelines given in the manual for the system. Another 3 months later, abutment connection was performed (Fig. 3-8) in a second-stage procedure, and the animals were placed in a carefully monitored plaque-control program. Four months subsequent to abutment connection, the dogs were exposed to a clinical examination following which biopsy specimens of several tooth and all implant sites were harvested.
The clinically healthy gingiva and peri-implant mucosa had a pink color and a firm consistency (Fig. 3-9). In radiographs obtained from the tooth sites it was observed that the alveolar bone crest was located about 1 mm apical of a line connecting the cementoenamel junction of neighboring premolars (Fig. 3-10). The radiographs from the implant sites disclosed that the bone crest was close to the junction between the abutment and the fixture part of the implant (Fig. 3-11).
**Fig. 3-6** The edentulous mandibular right premolar region 3 months following tooth extraction (from Berglundh et al. 1991).
**Fig. 3-7** Three titanium implants (i.e. the fixture part and cover screw; Brånemark System®) are installed.
**Fig. 3-8** Abutment connection is performed and the mucosa sutured with interrupted sutures.
**Fig. 3-9** After 4 months of careful plaque control the gingiva (a) and the peri-implant mucosa (b) are clinically healthy.
**Fig. 3-10** Radiograph obtained from the premolars in the left side of the mandible.
**Fig. 3-11** Radiograph obtained from the implants in the right side of the mandible.
Histological examination of the sections revealed that the two soft tissue units, the gingiva and the peri-implant mucosa, had several features in common. The oral epithelium of the gingiva was well keratinized and continuous with the thin junctional epithelium that faced the enamel and that ended at the cemento-enamel junction (Fig. 3-12). The supra-alveolar connective tissue was about 1 mm high and the periodontal ligament about 0.2–0.3 mm wide. The principal fibers were observed to extend from the root cementum in a fan-shaped pattern into the soft and hard tissues of the marginal periodontium (Fig. 3-13).
The outer surface of the peri-implant mucosa was also covered by a keratinized oral epithelium, which in the marginal border connected with a thin barrier epithelium (similar to the junctional epithelium at the teeth) that faced the abutment part of the implant (Fig. 3-14). It was observed that the barrier epithelium was only a few cell layers thick (Fig. 3-15) and that the epithelial structure terminated about 2 mm apical of the soft tissue margin (Fig. 3-14) and 1– 1.5 mm from the bone crest. The connective tissue in the compartment above the bone appeared to be in direct contact with the surface (TiO2) of the implant (Figs. 3-14, 3-15, 3-16). The collagen fibers in this connective tissue apparently originated from the periosteum of the bone crest and extend towards the margin of the soft tissue in directions parallel to the surface of the abutment.
**Fig. 3-12** Microphotograph of a cross section of the buccal and coronal part of the periodontium of a mandibular premolar. Note the position of the soft tissue margin (top arrow), the apical cells of the junctional epithelium (center arrow) and the crest of the alveolar bone (bottom arrow). The junctional epithelium is about 2 mm long and the supracrestal connective tissue portion about 1 mm high.
**Fig. 3-13** Higher magnification of the supracrestal connective tissue portion seen in Fig. 3-12. Note the direction of the principal fibers (arrows).
**Fig. 3-14** Microphotograph of a buccal–lingual section of the peri-implant mucosa. Note the position of the soft tissue margin (top arrow), the apical cells of the junctional epithelium (center arrow), and the crest of the marginal bone (bottom arrow). The junctional epithelium is about 2 mm long and the implant–connective tissue interface about 1.5 mm high.
**Fig. 3-15** Higher magnification of the apical portion of the barrier epithelium (arrow) in Fig. 3-14.
**Fig. 3-16** Microphotograph of a section (buccal–lingual) of the implant–connective tissue interface of the peri-implant mucosa. The collagen fibers invest in the periosteum of the bone and project in directions parallel to the implant surface towards the margin of the soft tissue.
**Fig. 3-17** Implants of three systems installed in the mandible of a beagle dog. Astra Tech Implants® Dental System (left), Brånemark System® (center) and ITI® Dental Implant System (right).
The observation that the barrier epithelium of the healthy mucosa consistently ended at a certain distance (1–1.5 mm) from the bone is important. During healing following implant installation surgery, fibroblasts of the connective tissue of the mucosa apparently formed a biological attachment to the TiO2 layer of the "apical" portion of the abutment portion of the implant. This attachment zone was evidently not recognized as a wound and was therefore not covered with an epithelial lining.
In further dog experiments (Abrahamsson _et al_. 1996, 2002) it was observed that a similar mucosal attachment formed when different types of implant systems were used (e.g. Astra Tech Implant System, Astra Tech Dental, Mölndal, Sweden; Brånemark System®, Nobel Biocare, Göteborg, Sweden; Straumann® Dental Implant System, Straumann AG, Basel, Switzerland; 3i® Implant System, Implant Innovation Inc., West Palm Beach, FL, USA). In addition, the formation of the attachment appeared to be independent of whether the implants were initially submerged or not (Figs. 3-17, 3-18.
**Fig. 3-18** Microphotographs illustrating the mucosa (buccal–lingual view) facing the three implant systems. (a) Astra. (b) Brånemark. (c) ITI.
In another study (Abrahamsson _et al_. 1998), it was demonstrated that the material used in the abutment part of the implant was of decisive importance for the location of the connective tissue portion of the transmucosal attachment. Abutments made of aluminum-based sintered ceramic (Al2O3) allowed for the establishment of a mucosal attachment similar to that which occurred at titanium abutments. Abutments made of a gold alloy or dental porcelain, however, provided conditions for inferior mucosal healing. When such materials were used, the connective tissue attachment failed to develop at the abutment level. Instead, the connective tissue attachment occurred in a more apical location. Thus, during healing following the abutment connection surgery, some resorption of the marginal peri-implant bone took place to expose the titanium portion of the fixture (Brånemark System®) to which the connective tissue attachment was eventually formed.
The location and dimensions of the transmucosal attachment were examined in a dog experiment by Berglundh and Lindhe (1996). Implants (fixtures) of the Brånemark System® were installed in edentulous premolar sites and submerged. After 3 months of healing, abutment connection was performed. In the left side of the mandible the volume of the ridge mucosa was maintained while in the right side the vertical dimension of the mucosa was reduced to ≤2 mm (Fig. 3.19) before the flaps were replaced and sutured. In biopsy specimens obtained after another 6 months, it was observed that the transmucosal attachment at all implants included one barrier epithelium that was about 2 mm long and one zone of connective tissue attachment that was about 1.3–1.8 mm high.
**Fig. 3-19** Schematic drawing illustrating that the mucosa at the test site was reduced to about 2 mm. From Berglundh & Lindhe (1996).
A further examination disclosed that at sites with a thin mucosa, wound healing consistently had included marginal bone resorption to establish space for a mucosa that eventually could harbor both the epithelial and the connective tissue components of the transmucosal attachment (Figs. 3-20, 3-21).
The dimensions of the epithelial and connective tissue components of the transmucosal attachment at implants are established during wound healing following implant surgery. As is the case for bone healing after implant placement (see Chapter 5), the wound healing in the mucosa around implants is a delicate process that requires several weeks of tissue remodeling.
In a recent animal experiment, Berglundh _et al_. (2007) described the morphogenesis of the mucosa attachment to implants made of c.p. titanium. A non-submerged implant installation technique was used and the mucosal tissues were secured to the conical marginal portion of the implants (Straumann® Dental Implant System) with interrupted sutures. The sutures were removed after 2 weeks and a plaque-control program was initiated. Biopsies were performed at various intervals to provide healing periods extending from day 0 (2 hours) to 12 weeks. It was reported that large numbers of neutrophils infiltrated and degraded the coagulum that occupied the compartment between the mucosa and the implant during the initial phase of healing. The first signs of epithelial proliferation were observed in specimens representing 1–2 weeks of healing and a mature barrier epithelium was seen after 6–8 weeks. It was also demonstrated that the collagen fibers of the mucosa were organized after 4–6 weeks of healing. Thus, prior to this time interval, the connective tissue is not properly arranged.
**Fig. 3-20** Schematic drawing illustrating that the peri-implant mucosa at both control and test sites contained a 2 mm long barrier epithelium and a zone of connective tissue that was about 1.3–1.8 mm high. Bone resorption occurred in order to accommodate the soft tissue attachment at sites with a thin mucosa. From Berglundh & Lindhe (1996).
**Fig. 3-21** Microphotograph illustrating the peri-implant mucosa of a normal dimension (left) and reduced dimension (right). Note the angular bone loss that had occurred at the site with the thin mucosa.
### Conclusion
The junctional and barrier epithelia are about 2 mm long and the zones of supra-alveolar connective tissue are between 1 and 1.5 mm high. Both epithelia are attached via hemi-desmosomes to the tooth/ implant surface (Gould _et al_. 1984). The main attachment fibers (the principal fibers) invest in the root cementum of the tooth, but at the implant site the equivalent fibers run in a direction parallel with the implant and fail to attach to the metal body. The soft tissue attachment to implants is properly established several weeks following surgery.
## Quality
The quality of the connective tissue in the supra-alveolar compartments at teeth and implants was examined by Berglundh _et al_. (1991). The authors observed that the main difference between the mesenchymal tissue present at a tooth and at an implant site was the occurrence of a cementum on the root surface. From this cementum (Fig. 3-22), coarse dento-gingival and dento-alveolar collagen fiber bundles projected in lateral, coronal, and apical directions (Fig. 3-13). At the implant site, the collagen fiber bundles were orientated in an entirely different manner. Thus, the fibers invested in the periosteum at the bone crest and projected in directions parallel with the implant surface (Fig. 3-23). Some of the fibers became aligned as coarse bundles in areas distant from the implant (Buser _et al_. 1992).
**Fig. 3-22** Microphotograph of a tooth with marginal periodontal tissues (buccal–lingual section). Note on the tooth side the presence of an acellular root cementum with inserting collagen fibers. The fibers are orientated more or less perpendicular to the root surface.
The connective tissue in the supra-crestal area at implants was found to contain more collagen fibers, but fewer fibroblasts and vascular structures, than the tissue in the corresponding location at teeth. Moon _et al_. (1999), in a dog experiment, reported that the attachment tissue close to the implant (Fig. 3-24) contained only few blood vessels but a large number of fibroblasts that were orientated with their long axes parallel with the implant surface (Fig. 3-25). In more lateral compartments, there were fewer fibroblasts but more collagen fibers and more vascular structures. From these and other similar findings it may be concluded that the connective tissue attachment between the titanium surface and the connective tissue is established and maintained by fibroblasts.
## Vascular supply
The vascular supply to the gingiva comes from two different sources (Fig. 3-26). The first source is represented by the large _supraperiosteal blood vessels_ , that put forth branches to form (1) the capillaries of the connective tissue papillae under the oral epithelium and (2) the vascular plexus lateral to the junctional epithelium. The second source is the _vascular plexus of the periodontal ligament_ , from which branches run in a coronal direction and terminate in the supra-alveolar portion of the free gingiva. Thus, the blood supply to the zone of supra-alveolar connective tissue attachment in the periodontium is derived from two apparently independent sources (see also Chapter 1).
**Fig. 3-23** Microphotograph of the peri-implant mucosa and the bone at the tissue/titanium interface. Note that the orientation of the collagen fibers is more or less parallel (not perpendicular) to the titanium surface.
**Fig. 3-24** Microphotograph of the implant/connective tissue interface of the peri-implant mucosa. A large number of fibroblasts reside in the tissue next to the implant.
**Fig. 3-25** Electron micrograph of the implant–connective tissue interface. Elongated fibroblasts are interposed between thin collagen fibrils (magnification × 24 000).
Berglundh _et al._ (1994) observed that the vascular system of the peri-implant mucosa of dogs (Fig. 3-27) originated _solely_ from the large _supra-periosteal blood vessel_ on the outside of the alveolar ridge. This vessel that gave off branches to the supra-alveolar mucosa and formed (1) the capillaries beneath the oral epithelium and (2) the vascular plexus located immediately lateral to the barrier epithelium. The connective tissue part of the transmucosal attachment to titanium implants contained only few vessels, all of which could be identified as terminal branches of the _supra-periosteal blood vessels._
**Fig. 3-26** A buccal–lingual section of a beagle dog gingiva. Cleared section. The vessels have been filled with carbon. Note the presence of a supraperiosteal vessel on the outside of the alveolar bone, the presence of a plexus of vessels within the periodontal ligament, as well as vascular structures in the very marginal portion of the gingiva.
**Fig. 3-27** (a) A buccal–lingual cleared section of a beagle dog mucosa facing an implant (the implant was positioned to the right). Note the presence of a supraperiosteal vessel on the outside of the alveolar bone, but also that there is no vasculature that corresponds to the periodontal ligament plexus. (b) Higher magnification (of a) of the peri-implant soft tissue and the bone implant interface. Note the presence of a vascular plexus lateral to the junctional epithelium, but the absence of vessels in the more apical portions of the soft tissue facing the implant and the bone.
### Summary
The gingiva at teeth and the mucosa at dental implants have some characteristics in common, but differ in the composition of the connective tissue, the alignment of the collagen fiber bundles, and the distribution of vascular structures in the compartment apical of the barrier epithelium.
# Probing gingiva and peri-implant mucosa
It was assumed for many years that the tip of the probe in a pocket depth measurement identified the most apical cells of the junctional (pocket) epithelium or the marginal level of the connective tissue attachment. This assumption was based on findings by, for example, Waerhaug (1952), who reported that the "epithelial attachment" (e.g. Gottlieb 1921; Orban & Köhler 1924) offered no resistance to probing. Waerhaug (1952) inserted, "with the greatest caution", thin blades of steel or acrylic in the gingival pocket of various teeth of >100 young subjects without signs of periodontal pathology. In several sites the blades were placed in approximal pockets, "in which position radiograms were taken of them". It was concluded that the insertion of the blades could be performed without a resulting bleeding and that the device consistently reached to the cemento-enamel junction (Fig. 3.28). Thus, the epithelium or the epithelial attachment offered no resistance to the insertion of the device.
**Fig. 3-28** An acrylic strip with a blue zone located 2 mm from the strip margin (a) prior to and (b) after its insertion into a buccal "pocket". The strip could with a light force be inserted 2 mm into the "pocket". (c) Thin blades of steel were inserted in pockets at approximal sites of teeth with healthy periodontal conditions. In radiographs, Waerhaug (1952) could observe that the blades consistently reached the cemento-enamel junction.
In subsequent studies it was observed, however, that the tip of a periodontal probe in a pocket depth measurement only identified the base of the dentogingival epithelium by chance. In the absence of an inflammatory lesion the probe frequently failed to reach the apical part of the junctional epithelium (e.g. Armitage _et al_. 1977; Magnusson & Listgarten 1980). If an inflammatory lesion, rich in leukocytes and poor in collagen, was present in the gingival connective tissue, however, the probe penetrated beyond the epithelium to reach the apical–lateral border of the infiltrate.
The outcome of probing depth measurements at _implant sites_ was examined in various animal models. Ericsson and Lindhe (1993) used the model by Berglundh _et al_. (1991) referred to above and, hence, had both teeth and implants available for examination. The gingiva at mandibular premolars and the mucosa at correspondingly positioned implants (Brånemark System®) were, after extended periods of plaque control, considered clinically healthy. A probe with a tip diameter of 0.5 mm was inserted into the buccal "pocket" using a standardized force of 0.5 N. The probe was anchored to the tooth or to the implant and biopsies from the various sites were performed. The histologic examination of the biopsy material revealed that probing the dento-gingival interface had resulted in a slight compression of the gingival tissue. The tip of the probe was located coronal to the apical cells of the junctional epithelium. At the implant sites, probing caused both compression and a lateral dislocation of the peri-implant mucosa, and the average "histologic" probing depth was markedly deeper than at the tooth site: 2.0 mm versus 0.7 mm. The tip of the probe was consistently positioned deep in the connective tissue/abutment interface and apical of the barrier epithelium. The distance between the probe tip and the bone crest at the tooth sites was about 1.2 mm. The corresponding distance at the implant site was 0.2 mm. The findings presented by Ericsson and Lindhe (1993) regarding the difference in probe penetration in healthy gingiva and peri-implant mucosa are not in agreement with data reported in subsequent animal experiments.
Lang _et al_. (1994) used beagle dogs and prepared the implant (Straumann® Dental Implant System) sites in such a way that at probing some regions were healthy, a few sites exhibited signs of mucositis, and some sites exhibited peri-implantitis. Probes with different geometry were inserted into the pockets using a standardized probing procedure and a force of only 0.2 N. The probes were anchored and block biopsy specimens were harvested. The probe locations were studied in histologic ground sections. The authors reported that the mean "histologic" probing depth at healthy sites was about 1.8 mm, i.e. similar to the depth (about 2 mm) recorded by Ericsson and Lindhe (1993). The corresponding depth at sites with mucositis and peri-implantitis was about 1.6 mm and 3.8 mm respectively. Lang _et al_. (1994) further stated that at healthy and mucositis sites, the probe tip identified "the connective tissue adhesion level" (i.e. the base of the barrier epithelium) while at periimplantitis sites, the probe exceeded the base of the ulcerated pocket epithelium by a mean distance of 0.5 mm. At such peri-implantitis sites the probe reached the base of the inflammatory cell infiltrate.
Schou _et al_. (2002) compared probing measurements at implants and teeth in eight cynomolgus monkeys. Ground sections were produced from tooth and implant sites that were (1) clinically healthy, (2) slightly inflamed (mucositis/gingivitis), and (3) severely inflamed (peri-implantitis/periodontitis) and in which probes had been inserted. An electronic probe (Peri-Probe®) with a tip diameter 0.5 mm and a standardized probing force of 0.3–0.4 N was used. It was demonstrated that the probe tip was located at a similar distance from the bone in healthy tooth sites and implant sites. On the other hand, at implants exhibiting mucositis and peri-implantitis, the probe tip was consistently identified at a more apical position than at corresponding sites at teeth (gingivitis and periodontitis). The authors concluded that (1) probing depth measurements at implant and teeth yielded different information, and (2) small alterations in probing depth at implants may reflect changes in soft tissue inflammation rather than loss of supporting tissues.
Recently, Abrahamsson and Soldini (2006) evaluated the location of the probe tip in healthy periodontal and peri-implant tissues in dogs. It was reported that probing with a force of 0.2 N resulted in a probe penetration that was similar at implants and teeth. Furthermore, the tip of the probe was often at or close to the apical cells of the junctional/barrier epithelium. The distance between the tip of the probe and the bone crest was about 1 mm at both teeth and implants (Figs. 3-29, 3-30). Similar observations were reported from clinical studies in which different implant systems were used (Buser _et al_. 1990; Quirynen _et al_. 1991; Mombelli _et al_. 1997). In these studies the distance between the probe tip and the bone was assessed in radiographs and was found to vary between 0.75 and 1.4 mm when a probing force of 0.25–0.45 N was used.
By comparing the findings from the studies reported above, it becomes apparent that probing depth and probing attachment level measurements are also meaningful at implant sites. When a "normal" probing force is applied in healthy tissues the probe seems to reach similar levels at implant and tooth sites. Probing inflamed tissues both at tooth and implant sites will, however, result in a more advanced probe penetration and the tip of the probe may come closer to the bone crest.
**Fig. 3-29** Buccal–lingual ground section from a tooth site illustrating the probe tip position in relation to the bone crest (from Abrahamsson & Soldini 2006).
**Fig. 3-30** Buccal–lingual ground section from an implant site illustrating the probe tip position in relation to the bone crest (from Abrahamsson & Soldini 2006).
# Dimensions of the buccal soft tissue at implants
Chang _et al_. (1999) compared the dimensions of the periodontal and peri-implant soft tissues of 20 subjects who had been treated with an implant-supported single-tooth restoration in the esthetic zone of the maxilla and had a non-restored natural tooth in the contralateral position (Fig. 3-31). In comparison to the natural tooth, the implant-supported crown was bordered by a thicker buccal mucosa (2.0 mm versus 1.1 mm), as assessed at a level corresponding to the bottom of the probeable pocket, and had a greater probing pocket depth (2.9 mm versus 2.5 mm) (Fig. 3-32). It was further observed that the soft tissue margin at the implant was more apically located (about 1 mm) than the gingival margin at the contralateral tooth.
**Fig. 3-31** Clinical photographs of (a) an implant-supported single tooth replacement in position 12 and (b) the natural tooth in the contralateral position (from Chang _et al_. 1999).
**Fig. 3-32** Comparison of mucosa thickness and probing depth at the facial aspect of single-implant restorations and the natural tooth in the contralateral position (from Chang _et al_. 1999).
Kan _et al_. (2003) studied the dimensions of the peri-implant mucosa at 45 single implants placed in the anterior maxilla that had been in function for an average of 33 months. Bone sounding measurements performed at the buccal aspect of the implants showed that the height of the mucosa was 3–4 mm in the majority of the cases. Less than 3 mm of mucosa height was found at only 9% of the implants. It was suggested that implants in this category were (1) found in subjects that belonged to a _thin periodontal biotype_ , (2) had been placed too labially, and/ or (3) had an overcontoured facial prosthetic emergence. A peri-implant soft tissue dimension of >4 mm was usually associated with a _thick periodontal biotype._
# Dimensions of the papilla between teeth and implants
In a study by Schropp _et al_. (2003) it was demonstrated that following single tooth extraction the height of the papilla at the adjacent teeth was reduced about 1 mm. Concomitant with this reduction (recession) of the papilla height the pocket depth was reduced and some loss of clinical attachment occurred.
Following single tooth extraction and subsequent implant installation, the height of the papilla in the tooth–implant site will be dependent on the attachment level of the tooth. Choquet _et al_. (2001) studied the papilla level adjacent to single-tooth dental implants in 26 patients and in total 27 implant sites. The distance between the apical extension of the contact point between the crowns and the bone crest, as well as the distance between the soft tissue level and the bone crest, was measured in radiographs. The examinations were made 6–75 months after the insertion of the crown restoration. The authors observed that the papilla height consistently was about 4 mm, and, depending on the location of the contact point between adjacent crowns papilla, fill was either complete or incomplete (Fig. 3-33). The closer the contact point was located to the incisal edge of the crowns (restorations) the less complete was the papilla fill.
Chang _et al_. (1999) studied the dimensions of the papillae at implant-supported single-tooth restorations in the anterior region of the maxilla and at non-restored contralateral natural teeth. They found that the papilla height at the implant-supported crown was significantly shorter and showed less fill of the embrasure space than the papillae at the natural tooth (Fig. 3-34). This was particularly evident for the distal papilla of implant-supported restorations in the central incisor position, both in comparison to the distal papilla at the contralateral tooth and to the papilla at the mesial aspect of the implant crown. This indicates that the anatomy of the adjacent natural teeth (e.g. the diameter of the root, the proximal outline/curvature of the cementoenamel junction/connective tissue attachment level) may have a profound influence on the dimension of the papilla lateral to an implant. Hence, the wider facial–lingual root diameter and the higher proximal curvature of the cemento-enamel junction of the maxillary central incisor – in comparison to corresponding dimensions of the lateral incisor (Wheeler 1966) – may favor the maintenance of the height of the mesial papilla at the single-implant supported restoration.
**Fig. 3-33** Soft tissue height adjacent to single-tooth dental implants in relation to the degree of papilla fill (from Choquet et al. 2001).
**Fig. 3-34** Comparison of papilla height and papilla fill adjacent to single-implant restorations and the natural tooth in the contralateral position (from Chang et al. 1999).
Kan _et al_. (2003) assessed the dimensions of the peri-implant mucosa lateral to 45 single implants placed in the anterior maxilla and the 90 adjacent teeth using bone sounding measurements. The bone sounding measurements were performed at the mesial and distal aspects of the implants and at the mesial and distal aspects of the teeth. The authors reported that the thickness of the mucosa at the mesial/distal surfaces of the implant sites was on the average 6 mm while the corresponding dimension at the adjacent tooth sites was about 4 mm. It was further observed that the dimensions of the peri-implant mucosa of subjects who belonged to the _thick periodontal biotype_ were significantly greater than that of subjects of a _thin biotype_.
The level of the connective tissue attachment on the adjacent tooth surface and the position of the contact point between the crowns are obviously key factors that determine whether or not a complete papilla fill will be obtained at the single-tooth implant-supported restoration (Fig. 3.35). Although there are indications that the dimensions of the approximal soft tissue may vary between individuals having thin and thick periodontal biotypes, the height of the papilla at the single-implant restoration seems to have a biological limit of about 4 mm (compare the dimension of the interdental papilla). Hence, to achieve a complete papilla fill of the embrasure space, a proper location of the contact area between the implant crown and the tooth crown is mandatory. In this respect it must also be recognized that the papilla fill at single-tooth implant restorations is unrelated to whether the implant is inserted according to a one-or two-stage protocol and whether a crown restoration is inserted immediately following surgery or delayed until the soft tissues have healed (Jemt 1999; Ryser _et al_. 2005).
# Dimensions of the "papilla" between adjacent implants
When two neighboring teeth are extracted, the papilla at the site will be lost (Fig. 3-36). Hence, at replacement of the extracted teeth with implant-supported restorations the topography of the bone crest and the thickness of the supracrestal soft tissue portion are the factors that determine the position of the soft tissue margin in the inter-implant area ("implant papilla"). Tarnow _et al_. (2003) assessed the height above the bone crest of the inter-implant soft tissue ("implant papilla") by transmucosal probing at 136 anterior and posterior sites in 33 patients who had maintained implant-supported prostheses for at least 2 months. It was found that the mean height of the "papillae" was 3.4 mm, with 90% of the measurements in the range of 2–4 mm.
**Fig. 3-35** See text for details.
**Fig. 3-36** See text for details.
The dimension of the soft tissues between adjacent implants seems to be independent of the implant design. Lee _et al._ (2006) examined the soft tissue height between implants of two different systems (Brånemark Implant® and Astra Tech Implant® systems) as well as the potential influence of the horizontal distance between implants. The height of the inter-implant "papilla", i.e. the height of soft tissue coronal to the bone crest measured in radiographs, was about 3.1 mm for both implant systems. No difference was found regarding the "papilla" height for any of the implant systems with regard to sites with <3 mm and ≥3 mm in horizontal distance between the implants. Gastaldo _et al._ (2004) evaluated the presence or absence of "papilla" at 96 inter-implant sites in 58 patients. It was reported that the "papilla" filled the entire space between the implants only when the distance from the bone crest to the base of the contact point between the crown restorations, assessed by sounding, was <4 mm. Thus, taken together these observations indicate that the soft tissue between two implants will have a maximum height of 3–4 mm, and that the location of the contact point between the crown restorations in relation to the bone crest level determines whether a complete soft tissue fill will be obtained in the embrasure space between two implants (Fig. 3-37).
**Fig. 3-37** See text for details.
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# Chapter 4
# Bone as a Tissue
William V. Giannobile, Hector F. Rios, and Niklaus P. Lang
* * *
Basic bone biology
Bone cells
Modeling and remodeling
Growth factors and alveolar bone healing
Local and systemic factors affecting bone volume and healing
Metabolic disorders affecting bone metabolism
Bone healing
Bone grafting
Human experimental studies on alveolar bone repair
* * *
During embryogenesis, in the alveolar process of the maxilla and the mandible, bone is formed within a primary connective tissue. This process is termed _intramembranous_ bone formation and also occurs at the cranial vault and in the midshaft or diaphysis of the long bones. In contrast, bone formation in the remaining parts of the skeleton occurs via an initial deposition of a cartilage template that is subsequently replaced by bone. This process is called _endochondral_ bone formation.
Alveolar bone lost as a result of disease, trauma or extensive post-extraction bone modeling may pose therapeutic problems in periodontal reconstructive and/or implant dentistry. Thus, implant placement both in the maxilla and in the mandible may be hampered by the lack of sufficient volume of alveolar bone at the recipient sites. _De novo_ formation of alveolar bone in such compromised sites may be necessary and different regenerative therapies need to be considered to promote new bone. They all, however, have one aspect in common: the compliance with the principles of bone biology. There are several reconstructive modalities for restoration of the alveolar process, such as bone graft replacements and guided bone regeneration (GBR).
# Basic bone biology
Bone is a specialized connective tissue that is mainly characterized by its mineralized organic matrix. The bone organic matrix is comprised of collagenous and non-collagenous proteins. Within this matrix, ions of calcium and phosphate are laid down in the ultimate form of hydroxyapatite. This composition allows the bone tissue to: (1) resist load, (2) protect highly sensitive organs (e.g. the central nervous system) from external forces, and (3) participate as a reservoir of minerals that contribute to systemic homeostasis of the body.
## Bone cells
_Osteoblasts_ are the primary cells responsible for the formation of bone; they synthesize the organic extra-cellular matrix (ECM) components and control the mineralization of the matrix. Osteoblasts are located on bone surfaces exhibiting active matrix deposition and may eventually differentiate into two different types of cells: _bone lining cells_ and _osteocytes_. Bone lining cells are elongated cells that cover a surface of bone tissue and exhibit no synthetic activity. Osteocytes are stellate-shaped cells that are trapped within the mineralized bone matrix but remain in contact with other bone cells by thin cellular processes. The osteocytes are organized as a syncytium that provides a very large contact area between the cells (and their processes) and the non-cellular part of the bone tissue. This arrangement allows osteocytes to: (1) participate in the regulation of the blood-calcium homeostasis, and (2) sense mechanical loading and to signal this information to other cells within the bone.
The osteoblasts are fully differentiated cells and lack the capacity for migration and proliferation. Thus, in order to allow bone formation to occur at a given site, undifferentiated mesenchymal progenitor cells ( _osteoprogenitor cells_ ) must migrate to the site and proliferate to become osteoblasts. Friedenstein (1973) divided osteoprogenitor cells into _determined_ and _inducible osteogenic precursor cells_. The determined osteoprogenitor cells are present in the bone marrow, in the endosteum and in the periosteum that covers the bone surface. Such cells possess an intrinsic capacity to proliferate and differentiate into osteoblasts. Inducible osteogenic precursor cells, on the other hand, represent mesenchymal cells present in other organs and tissues (e.g. myoblasts or adipocytes) that may differentiate into bone-forming cells when exposed to specific stimuli. As osteogenesis is generally closely related to the ingrowth of vascular tissue, the stellate-shaped perivascular cell (the _pericyte_ ) is considered to be the main osteoprogenitor cell. The differentiation and development of osteoblasts from osteoprogenitor cells are dependent on the release of osteoinductive or osteopromotive growth factors (GFs) such as bone morphogenetic proteins (BMP) and other growth factors such as insulin-like growth factor (IGF), platelet-derived growth factor (PDGF) and fibroblast growth factor (FGF) (Table 4-1).
**Table 4-1** Effects of growth factors in bone wound healing
The bone formation activity is consistently coupled to bone resorption that is initiated and maintained by _osteoclasts_. Osteoclasts are multinucleated cells that originate from hematopoietic precursor cells.
## Modeling and remodeling
Once bone has formed, the new mineralized tissue starts to be reshaped and renewed by processes of resorption and apposition, i.e. through _modeling_ and _remodeling_. Modeling represents a process that allows a change in the initial bone architecture. It has been suggested that external demands (such as load) on bone tissue may initiate modeling. Remodeling, on the other hand, represents a change that occurs within the mineralized bone without a concomitant alteration of the architecture of the tissue. The process of remodeling is important (1) during bone formation, and (2) when old bone is replaced with new bone. During bone formation, remodeling enables the substitution of the primary bone (woven bone), which has low load-bearing capacity, with lamellar bone that is more resistant to load.
The bone remodeling that occurs in order to allow replacement of old bone with new bone involves two processes: bone resorption and bone apposition (formation). These processes are coupled in time and are characterized by the presence of so called _bone multicellular units_ (BMUs). A BMU (Fig. 4-1) is comprised of (1) a front osteoclast residing on a surface of newly resorbed bone (the resorption front), (2) a compartment containing vessels and pericytes, and (3) a layer of osteoblasts present on a newly formed organic matrix (the deposition front). The process of the bone remodeling cycle is shown in Figs. 4-2 and 4-3. Local stimuli and release of hormones, such as parathyroid hormone (PTH), growth hormone, leptin, and calcitonin, are involved in the control of bone remodeling. Modeling and remodeling occur throughout life to allow bone to adapt to external and internal demands.
**Fig. 4-1** Histological section illustrating a bone multicellular unit (BMU). Note the presence of a resorption front with osteoclast (OC) and a deposition front that contains osteoblasts (OB), and osteoid (OS). Vascular structures (V) occupy the central area of the BMU. RL = reversal line; LB = lamellar bone.
**Fig. 4-2** The bone remodeling cycle. Preosteoblasts are recruited to sites of resorption, induced to differentiate into active osteoclasts, and form resoption pits. After their period of active resorption, transient mononuclear cells replace them. Through the process of coupling, preosteoblasts are recruited, differentiate into active matrix-secreting cells, and form bone. Some osteoblasts become entrapped in the matrix and become osteocytes. Adapted from McCauley, L.K. & Nohutcu, R.M. (2002) Mediators of periodontal osseous destruction and remodeling: principles and implications for diagnosis and therapy. _Journal of Periodontology_ **73** , 1377–1391, with permission.
## Growth factors and alveolar bone healing
Understanding the complex processes of wound healing has been a challenge for researchers for many years. Recently, advances in the areas of cellular and molecular biology have allowed the elucidation of functions of GFs and their participation in the different phases of wound healing. Restoration of normal form and function is the ultimate goal of regenerative approaches of alveolar bone disrupted by trauma, surgical resection or infectious disease. However, if the functional integrity of the tissue is not achieved, the process of repair will take place and a fibrous tissue will replace the original tissue (Le _et al._ 2005). Recent studies have confirmed that GFs can improve the capacity of alveolar bone to regenerate, improving cellular chemoattraction, differentiation, and proliferation. GFs are natural biological mediators that regulate important cellular events involved in tissue repair by binding to specific cell surface receptors (Giannobile 1996). After reaching specific target cells, GFs induce intracellular signaling pathways, which result in the activation of genes that change cellular activity and phenotype (Anusaksathien & Giannobile 2002). However, the effect of each GF is regulated through a complex system of feedback loops, which involve other GFs, enzymes, and binding proteins (Schilephake 2002; Ripamonti _et al._ 2005). Recent studies have taken place with the target of defining the proper application for therapeutic purposes of many different growth factors and other cytokines, each of which has several functions during the different phases of wound healing (Schilephake 2002; Ripamonti _et al._ 2005).
**Fig. 4-3** Schematic drawing describing the transition between woven bone and lamellar bone, i.e. remodeling. Woven bone with primary osteons (PO) is transformed into lamellar bone in a process that involves the presence of BMUs. The BMU contains osteoclasts (OC), as well as vascular structures (V) and osteoblasts (OB). Thus, the osteoblasts in the BMU produce bone tissue that has a concentric orientation around the vessel, and secondary osteons (SO) are formed within lamellar bone.
Healing of osseous tissue is regulated by GFs and other cytokines in a sequence of overlapping events similar to cutaneous wound repair. In ideal circumstances, this process mimics embryonic bone development allowing replacement of damaged bone with new bone, rather than with fibrous scar tissue. This process is driven by cellular and molecular mechanisms controlled by the TGF-β superfamily of genes, which encode a large number of extracellular signaling molecules (Blair _et al._ 2002). Bone morphogenetic proteins (BMPs) are a well studied group of these GFs involved in the processes of bone healing; the human genome encodes at least 20 of these multifunctional polypeptides (Blumenthal _et al_. 2002). Among several functions, BMPs induce the formation of both bone and cartilage by stimulating the cellular events of mesenchymal progenitor cells. However, only a subset of BMPs, most notably BMP-2, -4, -6, -7, and -9, has osteoinductive activity, a property of inducing _de novo_ bone formation by themselves (Cheng _et al._ 2003). Studies involving mutations of BMP ligands, receptors, and signaling proteins have shown important roles of BMPs in embryonic and postnatal development. Severe skeletal deformation, development of osteoporosis, reduction in bone mineral density and bone volume are all aberrations associated with disrupted and dysregulated BMP signaling (Chen _et al._ 2004).
Several other GFs produced by osteogenic cells, platelets and inflammatory cells participate in bone healing, including IGF-I and -II, TGFβ-1, PDGF, and FGF-2 (Sykaras & Opperman, 2003). The bone matrix serves as a reservoir for these GFs and BMPs and they are activated during matrix resorption by matrix metalloproteinases (Baylink _et al._ 1993; Janssens _et al_. 2005). Additionally, the acidic environment that develops during the inflammatory process leads to activation of latent GFs (Linkhart _et al._ 1996), which assist in the chemoattraction, migration, proliferation, and differentiation of mesenchymal cells into osteoblasts (Linkhart _et al._ 1996). All of these functions are driven by a complex mechanism of interaction among GFs and other cytokines, which is influenced by several regulatory factors (King & Cochran, 2002).
# Local and systemic factors affecting bone volume and healing
## Metabolic disorders affecting bone metabolism
A variety of systemic situations can affect local bone density, ultimately influencing tooth support or available bone volume for dental implant installation. Such diseases affecting bone mass include osteopenia, osteoporosis, and diabetes mellitus. The later two will be discussed in detail given their overall prevalence and implications to alveolar bone reconstruction.
### Osteoporosis
Osteoporosis is a systemic skeletal disease characterized by low bone mass and microarchitectural deterioration of the bone scaffold that result in increased bone fragility and susceptibility to fracture. In osteoporosis, the _bone mineral density_ (BMD) is reduced, bone microarchitecture is disrupted, and the amount and variety of non-collagenous proteins in bone is altered. _Dual energy X-ray absorptiometry_ (DXA, formerly DEXA) is considered the gold standard for diagnosis of osteoporosis. Diagnosis is made when the BMD is less than or equal to 2.5 standard deviations below that of a young adult reference population. This is translated as a T-score. The World Health Organization has established diagnostic guidelines as T-score −1.0 or greater is "normal", T-score between −1.0 and −2.5 is osteopenia, and −2.5 or below as osteoporosis (WHO Study Group 1994).
Oral bone loss has been shown to be associated with osteoporosis and low skeletal BMD. In their search for oral radiographic changes associated with osteoporosis, most investigators have focused on measures of jaw bone mass or morphology. The commonly used assessment of oral bone status include radiographic measures of loss of alveolar crestal height (ACH), measures of resorption of the residual ridge after tooth loss (RRR), and assessment of oral BMD. Tools used to measure bone mass include single and dual photon absorptiometry, DXA, quantitative computed tomography (QCT), and film densitometry.
Periodontitis results from pathogenic bacterial infection, which produces factors that destroy collagenous support of the tooth, as well as loss of alveolar bone. Systemic factors can lead to loss of BMD throughout the body, including bone loss in the maxilla and mandible. The resulting local reduction of BMD in the jaw bones could set the stage for more rapid ACH loss because a comparable challenge of bacterial bone-resorbing factors could be expected to result in greater alveolar crestal bone loss than in an individual with good bone mass. In addition to this, there are systemic risk factors such as smoking, diabetes, diet, and hormone levels that affect systemic bone level and may also affect periodontitis (discussed in Chapters 12 and 13). Although periodontal disease has historically been thought to be the result of a local infectious process, others have suggested that periodontal disease may be an early manifestation of generalized osteopenia (Whalen & Krook 1996), which would classify osteoporosis as a risk indicator, rather than a risk factor, for periodontal disease.
Mandibular mineral content is reduced in subjects with osteoporotic fractures (von Wowern _et al._ 1994). Further, the BMD of buccal mandibular bone correlates with osteoporosis (low skeletal BMD) (Klemetti _et al_. 1993; Taguchi _et al_. 1996). Mandibular density also correlates with skeletal BMD (Horner _et al_. 1996). Using film densitometry, the optical density of the mandible has been found to be increased in subjects with osteoporosis compared with controls. Further, mandibular radiographic optical density correlates with vertebral BMD in osteoporotic women (Kribbs 1990), control women (Kribbs 1990), and in women with a history of vertebral fracture (Kribbs _et al_. 1990; Law _et al._ 1996). Reduction in cortical and subcortical alveolar bone density has also been reported to correlate with osteoporosis in longitudinal studies (Payne _et al_. 1997, 1999; Civitelli _et al_. 2002). As concluded by Hildebolt (1997), the preponderance of the evidence indicates that the jaws of subjects with osteoporosis show reduced bone mass with potential implications on dental implant installation.
Several potential mechanisms by which osteoporosis or systemic bone loss may be associated with periodontal attachment loss, loss of alveolar bone height or density, and tooth loss have been proposed. One of these mechanisms states that low BMD or loss of BMD may lead to more rapid resorption of alveolar bone after insult by periodontal bacteria. With less dense oral bone to start with, loss of bone surrounding the teeth may occur more rapidly. Another mechanism proposes that systemic factors affecting bone remodeling may also modify local tissue response to periodontal infection. Persons with systemic bone loss are known to have increased production of cytokines (i.e. interleukin-1, interleukin-6) that may have effects on bone throughout the body, including the bones of the oral cavity. Periodontal infection has been shown to increase local cytokine production that, in turn, increases local osteoclast activity resulting in increased bone resorption. A third mechanism would be related to genetic factors that predispose an individual to systemic bone loss and also influence or predispose an individual to periodontal destruction. Also, certain lifestyle factors such as cigarette smoking and suboptimal calcium intake, among others, may put individuals at risk for development of both systemic osteopenia and oral bone loss (Oh _et al._ 2007).
Recently, long-term use of bone anti-resorptive agents, specifically bisphosphonates, has been associated with osteonecrosis of the jaw (ONJ) (Marx 2003; Ruggiero _et al_. 2004). According to a web-based survey conducted by the International Myeloma Foundation (Durie _et al._ 2005), an increased incidence of ONJ has been observed after 36 months from the start of therapy in patients receiving zoledronic acid or pamidronate for the treatment of myeloma or breast cancer. This data also indicated that patients with prior dental problems might have a higher risk of ONJ. As the bisphosphonates are potent osteoclast inhibitors, their long-term use may suppress bone turnover and compromise healing of even physiological micro-injuries within bone (Odvina _et al_. 2005). Despite the encouraging therapeutic results, further long-term studies are warranted to determine the relative risk : benefit ratio of bisphosphonate therapy. See Fig. 4-4 for therapies used to treat bone loss.
With regard to osseointegration, preclinical animal studies note the influence of osteoporosis on bone–implant contact as suggesting a negative effect (Mori _et al_. 1997; Duarte _et al_. 2003; Cho _et al_. 2004). For instance, Cho _et al_. (2004), using an osteoporotic animal model, found a bone contact reduction of 50%. Lugero _et al_. (2000), using an induced osteoporosis rabbit model, also found that integration was impaired, although they pointed out that cortical thickness was decreased as well.
Some early clinical reports have difficulties demonstrating an increased loss of implants during early stages of implant therapy (Becker _et al_. 2000; Friberg _et al_. 2001), mostly because osteopenia is treated at the time of placement. Yet early implant failure is often correlated with local lack of bone density or volume (van Steenberghe _et al_. 2002). For instance, Esposito _et al_. (2005) in a recent systematic review, reported that implant failure is three times greater in the posterior maxilla, where bone density is less, than in the mandible. On the other hand, clinical evaluation or resistance during surgical osteotomy creation for implant installation may be indicative of osteopenia or osteoporosis (Friberg _et al_. 2001). It has also been reported that dental radiography and clinical evaluation at the time of surgery can suggest the presence of osteopenia, but early implant survival is not affected (Becker _et al._ 2000). Although the influence of bone density on early failure is unclear, mostly because bone volume is often a confounding factor, this suggests that it is more critical to study long-term consequences. There is, however, little information available on long-term maintenance of implants in the presence of osteoporosis. Thus, based on the available data, there is evidence to interpret an association between osteoporosis and bone density that exists around teeth and dental implant fixtures. There is also some information to suggest that decreased bone mass may place dental implants at a greater risk to failure or to decreased ability to handle load over the long term.
**Fig. 4-4** Potential therapeutic strategies to treat bone resorption: agents that block the differentiation or activity of osteoclasts are potential therapeutic agents. Osteoprotegrin (OPG) inhibits the differentiation of osteoclasts through its action as a decoy receptor that blocks RANK (receptor activator of nuclear factor-kappa beta) and RANKL (RANK ligand) juxtacrine interaction. Non-steroidal anti-inflammatory drugs (NSAIDs) and other anti-inflammatory type molecules can inhibit the formation of hematoprogenitor cells to pre-osteoclasts. Antibodies to RANKL can also block this interaction. Estrogen and selective estrogen receptor modulators (SERMs) may inhibit the activity of osteoclasts but also promote apoptosis of osteoclasts, thus reducing their active lifespan. Bisphosphonates also promote osteoclast apoptosis. Chemically modified tetracylines reduce the protease degradation of the organic matrix, and anti-integrins block the initial osteoclast adhesion to the matrix. Adapted with permission from Kirkwood, K.L., Taba, M. Jr., Rossa, C., Preshaw, P. & Giannobile, W.V. (2006). Molecular biology concepts in host-microbe interaction in periodontal diseases. In: Newman M.G. _et al_. (eds). _Carranza's Clinical Periodontology_ , 10th Edn. Elsevier Publishing, St. Louis, MO, pp. 259–274.
### Diabetes mellitus
Diabetes mellitus is associated with a variety of metabolic sequlae including effects on bone maintenance and healing. There are three main types of diabetes mellitus. Type 1 is caused by damage or destruction of the beta cells of the pancreas which leads to production of insufficient amounts of insulin. Type 2 is caused by resistance to insulin with failure to produce enough additional insulin to compensate for the insulin resistance (see also Chapter 12). Type 2 diabetes constitutes 90–95% of the individuals suffering from diabetes mellitus in the US (Kahn & Flier 2000). There is a third type of diabetes that is gestational and occurs when there is a glucose intolerance of variable severity that starts or is first recognized during pregnancy (Novak _et al_. 2006).
The liver, the skeletal muscles, and the adipose tissue are the main insulin-responsive tissues, yet insulin also influences the physiology of other tissues, including bone and cartilage. In conditions of hypoinsulinemia (e.g. type 1 diabetes) or hyperinsulinemia with or without glucose intolerance or fasting hyperglycemia (type 2 diabetes), endochondral bone growth and bone remodeling show significant alterations.
#### _Type 1 diabetes_
Although bone histomorphometry data are lacking, results from biochemical markers of bone formation studies reveal unequivocal evidence that bone formation is decreased in diabetes mellitus. Serum osteocalcin concentrations are about 25% lower in diabetic children, adolescents and adults (Bouillon _et al_. 1995). Several relatively small studies that have investigated the effect of type 1 diabetes on axial bone density have found that the BMD Z score (age-matched BMD) from the lumbar spine or the femoral neck of diabetic patients is either not significantly different from that of the control groups or that there is a small decrease in cortical bone density but no difference in trabecular bone density (Roe _et al_. 1991; Ponder _et al_. 1992; Gallacher _et al_. 1993; Olmos _et al_. 1994). The conclusion from these studies is that type 1 diabetic subjects have a mean Z score below, but generally within 1 SD of, reference values (Lunt _et al_. 1998; Miazgowski & Czekalski 1998; Rix _et al._ 1999). This effect can be seen within a few years after diagnosis and is not progressive.
Although bone histomorphometry data are lacking, results from biochemical markers of bone formation studies reveal unequivocal evidence that bone formation is decreased in diabetes mellitus. Serum osteocalcin concentrations are about 25% lower in diabetic children, adolescents and adults (Bouillon _et al_. 1995). Several relatively small studies that have investigated the effect of type 1 diabetes on axial bone density have found that the BMD Z score (age-matched BMD) from the lumbar spine or the femoral neck of diabetic patients is either not significantly different from that of the control groups or that there is a small decrease in cortical bone density but no difference in trabecular bone density (Roe _et al_. 1991; Ponder _et al_. 1992; Gallacher _et al_. 1993; Olmos _et al_. 1994). The conclusion from these studies is that type 1 diabetic subjects have a mean Z score below, but generally within 1 SD of, reference values (Lunt _et al_. 1998; Miazgowski & Czekalski 1998; Rix _et al._ 1999). This effect can be seen within a few years after diagnosis and is not progressive.
#### _Type 2 diabetes_
Bone formation and bone mineralization are also decreased in type 2 diabetes. Histomorphometry results showed a significant decrease in the osteoid thickness and in the dynamic bone formation rate of a human bone biopsy specimen of a type 2 diabetic patient with a low BMD Z score at the radius. However, low bone turnover in type 2 diabetes does not cause bone loss (Krakauer _et al_. 1995).
In support of these data, hyperinsulinemia, which is a marker of insulin resistance and the central mechanism in the pathogenesis of type 2 diabetes, has been found to be linked with higher cortical thickness and a small but significant increase in BMD (Wakasugi _et al_. 1993; Rishaug _et al_. 1995; Bauer _et al._ 2002).
Insulin stimulates endochondral bone growth and osteoblast proliferation and function _in vitro_ and _in vivo_ at physiological concentrations. Severe diabetes in animal models typically induces reduction in bone blood flow, bone growth, periosteal bone apposition, and bone remodeling (both resorption and formation). Consequently, bone size and bone mass are reduced. However, no effect on bone mineral density has been identified when adjusted for bone size. Less apparent changes are observed in (insulin-treated) human type 1 diabetes, although many studies report a mild reduction in growth velocity in pubertal children with this condition, a mild deficit in BMD area (maximum 10%) which does not deteriorate with longer diabetes duration, and significantly reduced bone remodeling parameters. On the other hand, individuals with hyperinsulinemia and/or type 2 diabetes have a mild increase (3–5%) in BMD area.
Apart from insulin deficiency, there are likely to be other causative factors in the development of diabetes bone disease such as alterations in the IGFIGFBP system and hypercorticolism. The cellular and molecular mechanisms by which diabetes affects chondrocyte, (pre)osteoblast, and (pre) osteoclast proliferation and function still need to be elucidated.
In conclusion, diabetes is associated with an increased risk of periodontitis and progressive bone loss of the alveolus; however, this risk may vary depending on differences in susceptibility to periodontitis among populations (Kinane _et al._ 2006).
#### _Diabetes as a risk factor for alveolar bone loss around implants_
Studies investigating dental implants in the presence of diabetes mellitus are limited, but there is evidence that this disease is not a contra-indication for placement (Shernoff _et al._ 1994). In fact, there is evidence that early implant survival in well controlled patients is similar to that in non-diabetic patients. It is also noticeable that this may be true for all indications (Abdulwassie & Dhanrajani 2002), as well as for more advanced surgical techniques, such as bone grafting (Farzad _et al._ 2002). However, animal experiments have shown that bone–implant contact is affected (Nevins _et al_. 1998), suggesting that clinical consequences in long-term maintenance may arise. In a large prospective 5-year clinical study, Olson _et al_. (2000) found that duration of diabetes was an important factor in implant survival. Other retrospective or observational studies have also concluded that diabetes contributes to an increase in failure rates (Moy _et al_. 2005). In a 4-year retrospective clinical analysis of 215 implants of controlled diabetes mellitus patients, Fiorellini _et al_. (2000) reported an overall success rate of 85.6%, with some variation with regard to implant location and cumulative time in function. They concluded that the implant failure rate was significantly greater than in non-diabetic patients. However, there is controversy as to whether this is due to initial failure (Fiorellini _et al_. 2000).
In contrast to the previous studies where early implant loss was greater in diagnosed patients, Peled _et al_. (2003), in a clinical evaluation of well controlled edentulous patients who had received two implants, found that there was no difference in initial osseointegration. Van Steenberghe _et al_. (2002), in a large clinical evaluation exploring various systemic parameters, found that diabetes was not a detrimental factor during initial phases of integration and prosthesis fabrication, again supporting the importance of long-term studies. The influence of underlying elevated glucose levels on osseointegration is also supported by animal studies (Ottoni & Chopard 2004). For instance, using a diabetic rat model, Siqueira _et al_. (2003) reported a 50% decrease of osseointegration when animals did not receive insulin therapy, suggesting that an association exists. Kopman _et al_. (2005), using a similar model, also reported that bone–implant contact was significantly reduced. Interestingly, these previous studies also found that treatment of the condition did not improve osseointegration, when compared to uncontrolled diabetic animals, suggesting that treated individuals may have impaired implant healing regardless of their disease stability. Furthermore, there are suggestions that poorly controlled conditions could lead to loss of bone–implant contact, resulting in a weaker bone–implant interface (Kwon _et al_. 1997). Therefore, it is likely that long-term risks for complications are greater in the presence of diabetes mellitus. This hypothesis can only be reinforced when diabetes is poorly controlled or undiagnosed.
Diabetes has been reported to adversely affect bone repair by decreasing expression of genes that induce osteoblast differentiation, and diminishing growth factor and ECM production (Bouillon 1991; Kawaguchi _et al_. 1994; Lu _et al_. 2003). One proposed mechanism for these adverse effects is through the contribution of advanced glycation end-products (AGEs) to decreased extracellular matrix production and inhibition of osteoblast differentiation (McCarthy _et al_. 2001; Cortizo _et al_. 2003; Santana _et al_. 2003). AGEs may also delay wound healing by inducing apoptosis of ECM-producing cells. This enhanced apoptosis would reduce the number of osteoblastic and fibroblastic cells available for the repair of resorbed alveolar bone (Graves _et al_. 2006). In addition to promoting apoptosis, AGEs could affect oral tissue healing by reducing expression of collagen and promoting inflammation. The mechanisms suggested for AGE-enhanced apoptosis include the direct activation of caspase activity, and indirect pathways that increase oxidative stress or the expression of pro-apoptotic genes that regulate apoptosis (Graves _et al_. 2006).
# Bone healing
Healing of an injured tissue usually leads to the formation of a tissue that differs in morphology or function from the original tissue. This type of healing is termed _repair_. Tissue _regeneration_ , on the other hand, is a term used to describe a healing that leads to complete restoration of morphology and function.
The healing of bone tissue includes both regeneration and repair phenomena depending on the nature of the injury. For example, a properly stabililized, narrow bone fracture (e.g. greenstick fracture) will heal by regeneration, while a larger defect (e.g. segmental bone defect) will often heal with repair. There are certain factors that may interfere with the bone tissue formation following injury, such as:
1. Failure of vessels to proliferate into the wound
2. Improper stabilization of the coagulum and granulation tissue in the defect
3. Ingrowth of "non-osseous" or fibrous tissues with a high proliferative activity
4. Bacterial contamination.
The healing of a wound includes four phases:
1. Blood clotting
2. Wound cleansing
3. Tissue formation
4. Tissue modeling and remodeling.
These phases occur in an orderly sequence but, in a given site, may overlap in such a way that in some areas of the wound, tissue formation may be in progress, while in other areas tissue modeling is the dominating event. Examples of bone remodeling can be also seen in Chapter 2 on the edentulous ridge and Chapter 49 on ridge augmentation procedures.
## Bone grafting
Although bone tissue exhibits a large regeneration potential and may restore its original structure and function completely, bony defects may often fail to heal with bone tissue. In order to facilitate and/or promote healing, bone grafting materials have been placed into bony defects. It is generally accepted that the biologic mechanisms forming the basis for bone grafting include three basic processes: _osteogenesis_ , _osteoconduction_ , and _osteoinduction_.
_Osteogenesis_ occurs when viable osteoblasts and precursor osteoblasts are transplanted with the grafting material into the defects, where they may establish centers of bone formation. Autogenous iliac bone and marrow grafts are examples of transplants with osteogenic properties (see Chapter 49).
_Osteoconduction_ occurs when non-vital implant material serves as a scaffold for the ingrowth of precursor osteoblasts into the defect. This process is usually followed by a gradual resorption of the implant material. Autogenous cortical bone or banked bone allografts may be examples of grafting materials with osteoconductive properties (Fig. 4-5). Such grafting materials, as well as bone-derived or synthetic bone substitutes, have similar osteoconductive properties. However, degradation and substitution by viable bone is often poor. If the implanted material is not resorbable, which is the case for most porous hydroxylapatite implants, the incorporation is restricted to bone apposition to the material surface, but no substitution occurs during the remodeling phase.
_Osteoinduction_ involves new bone formation by the differentiation of local uncommitted connective tissue cells into bone-forming cells under the influence of one or more inducing agents. _Demineralized bone matrix_ (DMB) or _bone morphogenetic proteins_ (BMP) are examples of such grafting materials (Giannobile & Somerman 2003; Reynolds _et al_. 2003).
It often occurs that all three basic bone-forming mechanisms are involved in bone regeneration. In fact, osteogenesis without osteoconduction and osteoinduction is unlikely to occur, since almost none of the transmitted cells of autogenous cancellous bone grafts survive the transplantation. Thus, the grafting material predominantly functions as a scaffold for invading cells of the host. In addition, the osteoblasts and osteocytes of the surrounding bone lack the ability to migrate and divide which, in turn, means that the transplant is invaded by uncommitted mesenchymal cells that later differentiate into osteoblasts.
On that basis, it is appropriate to define three basic conditions as prerequisites for bone regeneration:
1. The _supply of bone-forming cells_ or cells with the capacity to differentiate into bone-forming cells
2. The presence of _osteoinductive stimuli_ to initiate the differentiation of mesenchymal cells into osteoblasts
3. The presence of an _osteoconductive environment_ forming a scaffold upon which invading tissue can proliferate and in which the stimulated osteoprogenitor cells can differentiate into osteoblasts and form bone.
**Fig. 4-5** (a) Microphotograph demonstrating bifurcation defect 3 weeks after grafting with autogenous cancellous jaw bone (G). New bone has invaded the defect, and the bone grafts have exerted an osteoconductive function. Epithelium (arrows) has migrated into one side of the defect. (b) Higher magnification of (a) showing that new bone has formed around the bone grafts (G), which have lost their vitality, indicated by the empty osteocyte lacunae.
The placement of bone-grafting materials to favor healing in osseous defects or to augment atrophic alveolar ridges has been evaluated in a number of experimental and clinical studies (Boyne 1970; Thompson & Casson 1970; Steinhauser & Hardt 1977; Fazili _et al_. 1978; Baker _et al_. 1979; Mulliken & Glowacki 1980; Swart & Allard 1985; Block _et al_. 1987; Cullum _et al_. 1988; Hupp & McKenna 1988) (also see Chapter 49). However, there are several reports indicating that this type of treatment fails predictably to produce bone fill and augment alveolar ridges (Korlof _et al._ 1973; Curtis & Ware 1977; Steinhauser & Hardt 1977; Taylor 1983; Davis _et al._ 1984; Jackson _et al._ 1986; Hupp & McKenna 1988). Often the bone grafts do not attach to the graft site through bony attachment and there is bone resorption and bone loss associated with grafting procedures. As a consequence, much of the intended volume is lost, and frequently the defects heal with a fibrous connective tissue instead of bone.
## Human experimental studies on alveolar bone repair
At present, most of the information regarding the biologic events which lead to new bone formation is derived from animal studies. Results regarding bone formation collected in animal studies have to be applied with proper caution in humans. In particular, the time sequence of the various steps ultimately leading to the formation of mineralized mature bone in man is different from that in all experimental animal systems known. A few human specimens, often harvested under poorly controlled conditions, contribute relatively little to the understanding of the biologic events of bone regeneration in humans.
A model system was designed to obtain human specimens of regenerated and also newly generated alveolar bone for the study of the biologic events under a variety of conditions (Hämmerle _et al_. 1996). A mucoperiosteal flap was raised in the retromolar area of the mandible of nine healthy volunteers. Following flap reflection, a standardized hole was drilled through the cortical bone into the bone marrow. Congruent test cylinders were firmly placed into the prepared bony bed, yielding primary stability; 1.5–2 mm of the test device were submerged below the level of the surrounding bone, leaving 2–3 mm above the bone surface. The bone-facing end of the cylinder was left open, while the coronal soft tissue-facing end was closed by an expanded polytetrafluoroethylene (ePTFE) membrane. The flap was sutured to obtain primary wound closure. In order to prevent infection, penicillin was prescribed systemically and oral rinses of chlorhexidine were administered. After 2, 7, and 12 weeks, one test device, including the regenerated tissue, was surgically harvested, while after 16, 24, and 36 weeks, respectively, two devices were harvested and processed for soft or hard tissue histology or immunohistochemistry. The tissue generated after 2 and 7 weeks (Fig. 4-6) presented with a cylindrical shape, whereas the specimens harvested at 12 weeks and thereafter resembled the form of an hourglass.
Specimens of 12 weeks and less regeneration time were almost entirely composed of soft tissue, while specimens with a regeneration time of 4 months and more were composed of both soft and increasing amounts of mineralized tissue (Fig. 4-7). It was concluded that the model system is suitable for studying temporal dynamics and tissue physiology of bone regeneration in humans with minimal risk of complications or adverse effects for the volunteers.
**Fig. 4-6** Histological section of a 7-week specimen, comprising non-mineralized connective tissue in the shape of an hourglass. Note the covering e-PTFE membrane.
In a retrospective re-entry study (Lang _et al_. 1994), the bone volume regenerated using nonbioresorbable membrane barriers was assessed. Nineteen patients with jaw bone defects of various sizes and configurations were included. Combined split-thickness/full-thickness mucosal flaps were elevated in the area of missing bone. The size of the defects was assessed geometrically. Following the placement of Gore-Tex® augmentation material as a barrier, the maximum possible volume for bone regeneration was calculated. At the time of membrane removal (3–8 months later), the same measurements were performed and the percentages of regenerated bone in relation to the possible volume for regeneration determined. In six patients in whom the membranes had to be removed early, between 3 and 5 months, due to an increased risk of infection, bone regeneration varied between 0 and 60%. In 13 patients in whom the membranes were left for 6–8 months, regenerated bone filled 90–100% of the possible volume. It was concluded that successful bone regeneration consistently occurred with an undisturbed healing period of at least 6 months.
**Fig. 4-7** Histological section of a 9-month specimen. The height of the mineralized tissue has reached the top 20% of the cylinder space area.
_Conclusion_ : In summary, the bone of the alveolar process is of critical importance to maintain the structure and function of the jaws and subsequently the housing of teeth or tooth replacements. The physiological and biomechanical influences on bone by local and systemic mediators of bone homeostasis are important in the maintenance of alveolus. Reconstructive modalities aimed at the repair of bone tissues as a result of disease or injury utilize fundamental principles of bone biology. These regenerative biology approaches have been exploited in implant dentistry and periodontology with the use of bone grafting biomaterials, guided bone regeneration approaches, and more recently with polypeptide growth factors. Future work in this area will focus on the implications of systemic disease on bone maintenance during function as well as more predictable modalities for alveolar bone reconstruction.
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# Chapter 5
# Osseointegration
Jan Lindhe, Tord Berglundh, and Niklaus P. Lang
* * *
The edentulous site
Osseointegration
Implant installation
Tissue injury
Wound healing
Cutting and non-cutting implants
The process of osseointegration
* * *
# **The edentulous site**
The fully healed, edentulous site of the alveolar ridge (see Fig. 2-23 and Chapter 2) is most often covered by a masticatory mucosa that is about 2–3 mm thick. This type of mucosa is covered by a keratinized epithelium and includes a connective tissue, rich in collagen fibers and fibroblasts, that is firmly attached to the bone via the periosteum. The outer walls of the alveolar process, the cortical plates, are comprised of lamellar bone and enclose the spongy or cancellous bone that contains bone trabeculae (lamellar bone) embedded in marrow. The bone marrow contains numerous vascular structures as well as adipocytes and pluripotent mesenchymal cells.
# Osseointegration
Different types of implant systems have been used to replace missing teeth, including subperiosteal implants, endosseous implants with fibrous encapsulation, and endosseous implants with direct bone contact ( _osseointegrated_ ). One definition of _osseointegration_ (a term originally proposed by Brånemark _et al_. 1969) was provided by Albrektsson _et al_. (1981) who suggested that this was "a direct functional and structural connection between living bone and the surface of a load carrying implant". Another, clinical definition was provided by Zarb and Albrektsson (1991) who proposed that _osseointegration_ was "a process whereby clinically asymptomatic rigid fixation of alloplastic materials is achieved and maintained in bone during functional loading".
Schroeder _et al_. (1976, 1981, 1995) used the term " _functional ankylosis_ " to describe the rigid fixation of the implant to the jaw bone, and stated that "new bone is laid down directly upon the implant surface, provided that the rules for atraumatic implant placement are followed (rotation of the cutting instrument and less than 800 rpm, cooling with sterile physiologic saline solution) and the implant exhibits primary stability".
Thus, in order to acquire proper conditions for osseointegration (or functional ankylosis), the implant must exhibit proper initial fixation (stability) following installation in the recipient site. This initial (primary) stability is the result of the contact relationship or friction that is established following insertion of the implant, between mineralized bone (often the cortical bone) at the recipient site and the metal device.
# Implant installation
## Tissue injury
Basic rule: the less traumatic the surgical procedure is and the smaller the tissue injury (the damage) becomes in the recipient site during implant installation, the more expeditious is the process through which new bone is formed and laid down on the implant surface.
The various steps used in the implant installation procedure, such as (1) _incision_ of the mucosa, often but not always followed by (2) the elevation of _mucosal flaps_ and the separation of the periosteum from the cortical plates, (3) the preparation of the _canal_ in the cortical and spongy bone of the recipient site, and (4) the insertion of the titanium device (the implant) in this canal, bring to bear a series of mechanical insults and injury to both the mucosa and the bone tissue. The host responds to this injury with an inflammatory reaction, the main objective of which is to eliminate the damaged portions of the tissues and prepare the site for regeneration or repair. To the above described hard tissue injury must be added the effect of the so-called "press fit", i.e. when the inserted implant is slightly wider than the canal prepared in the host bone at the recipient site. In such situations, (1) the mineralized bone tissue in the periphery of the implant is compressed, (2) the blood vessels particularly in the cortical portion of the canal are collapsed, (3) the nutrition to this portion of the bone compromised, and (4) the affected tissues most often become non-vital.
The damage or injury to the soft and hard tissues of the recipient site initiates the process of wound healing that ultimately ensures that (1) the implant becomes "ankylotic" with the bone, i.e. osseointegrated, and (2) a delicate mucosal attachment (see Chapter 3) is established and a soft tissue seal formed that protects the bone tissue from substances in the oral cavity.
## Wound healing
The healing of the severed bone following implant installation is a complex process that apparently involves different events in the cortical and in the spongy (cancellous) compartments of the surgical site.
In the _cortical bone compartment_ , the non-vital mineralized tissue must first be removed (resorbed) before new bone can form. In the _spongy compartment_ of the recipient site, on the other hand, the surgically inflicted damage (preparation of the canal and the installation of the implant) results mainly in soft tissue (marrow) injury that initially is characterized by localized bleeding and clot (coagulum) formation. The coagulum is gradually resorbed and the compartment thus becomes occupied by proliferating blood vessels and mesenchymal cells; granulation tissue. As result of the continuous migration of mesenchymal cells from the surrounding marrow, the young granulation tissue becomes replaced with provisional connective tissue and eventually with osteoid. In the osteoid, deposition of hydroxyapatite will occur around the newly formed vascular structures. Hereby, immature bone, most often woven bone, is formed (for detail see Chapter 2) and sequentially osseointegration, a direct connection between the newly formed bone and the metal device, takes place.
_In summary_ : in the initial phase of the process that results in osseointegration, the non-vital lamellar bone in the cortical compartment is of importance for the initial fixation of the implant. Osseointegration, however, is often first established in areas occupied by cancellous bone.
# Cutting and non-cutting implants
In this chapter only screw-shaped implants made of c.p. titanium will be discussed. The design of the metal device and the installation protocol followed may influence the speed of the process that leads to osseointegration.
" _Non-cutting_ " implants (Fig. 5-1) require meticulous handling of the recipient site including the preparation of a standardized track (thread) on the inside of the hard tissue canal. This preparation (precutting) of the track (thread) is made by the use of a thread-tap that is fitted with cutting edges (Fig. 5-2).
**Fig. 5-1** A 'non-cutting' implant (solid screw: Straumann® Implant System).
**Fig. 5-2** A thread-tap (Straumann® Implant System) that is used to cut a track in the walls of the hard tissue canal. Following this preparation the cavity in the host tissue and the implant are congruent.
Figure 5.1 illustrates a "non-cutting" implant (solid screw, 4.1 mm: Straumann® implant system) that is designed as a cylinder with a rounded "apical" base. The diameter of the cylinder is 3.5 mm. Pilot and twist drills of gradually increasing dimension are used to prepare the hard tissue canal of the recipient site to a final diameter of 3.5 mm. On the surface of the cylinder the implant is designed with a helix-shaped pitch that is 0.3 mm high. The diameter of the entire screw shaped device therefore becomes 4.1 mm.
In sites with a high bone density a thread-tap (Fig. 5-2) is used to cut a 4.1 mm wide helix-shaped track in the walls of the hard tissue canal. The implant and the cavity prepared in the hard tissues of the recipient site are now congruent. When the implant is installed, the pitch on the device will capture and follow the helix-shaped track on the walls of the hard tissue canal and hereby guide the implant with a minimum of force into the pre-prepared position (Fig. 5-3).
**Fig. 5-3** Ground section with a "non-cutting" implant and surrounding tissues obtained from a biopsy performed 24 hours after implant installation.
**Fig. 5-4** Detail from the apical region of the implant described in Fig. 5-3. Note the presence of a coagulum in the bone marrow.
Figure 5-3 illustrates a "non-cutting" Straumann® solid screw with surrounding tissues in a biopsy sampled 24 hours after implant installation. The implant had proper initial fixation (stability) obtained by the large contact area that was achieved between the metal screw and the buccal and lingual bone walls in the cortical compartment of the recipient site. During site preparation and placement of the implant, bone trabeculae in the spongy compartment of the site were obviously dislocated into the bone marrow. Blood vessels in the marrow compartment were severed, bleeding provoked and a coagulum formed (Fig. 5-4).
After 16 weeks of healing (Fig. 5-5) the marginal portions of the "non-cutting" implant are surrounded by dense lamellar bone that is in direct contact with the rough surface of the metal device. Also in the apical portion of the implant, a thin coat of mature bone can be seen to contact the implant surface and to separate the titanium screw from the bone marrow.
**Fig. 5-5** (a) Ground section illustrating a "non-cutting" implant and surrounding bone after 16 weeks of healing. In the cortical portion of the recipient site, the bone density is high. (b) Detail of (a). In more apical areas a thin coat of bone is present on the implant surface. Note also the presence of trabeculae of lamellar bone that extend from the implant into the bone marrow.
Fig. 5-6 A "cutting" implant (Astra Tech® Implant System). Note the presence of cutting edges in the "apical" portion of the implant. During insertion this implant will cut a 0.3 mm wide chip from the lateral border of the canal prepared in the recipient site.
_Cutting or self-tapping implants_ (e.g. Astra Tech® implants, diameter 4.0 mm) (Fig. 5-6) are designed with cutting edges placed in the "apical" portion of the screw-shaped device. The threads of the screw are prepared during manufacturing by cutting a continuous groove into the body of the titanium cylinder. When a self-tapping 4.0 mm wide implant is to be placed, the recipient site is first prepared with pilot and twist drills to establish a hard tissue canal that most often has a final diameter of 3.7 mm. During the insertion the cutting edges in the "apical" portion of the implant create a 0.15 mm wide track in the walls of the canal and thereby establish the final 4.0 mm dimension. When the implant has reached its insertion depth, contact has been established between the outer portions of the threads and the mineralized bone in the cortical compartment (initial or primary fixation is hereby secured) and with the severed bone marrow tissue in the spongy compartment.
**Fig. 5-7** (a) Ground section of an implant (Astra Tech®) site from a biopsy sampled after 2 weeks of healing. In the apical area large amounts of woven bone has formed. (b) Detail of (a). In the threaded region, newly formed bone can be seen to reach contact with the implant surface. (c) Higher magnification of (b). Newly formed bone extends from the old bone and reaches the titanium surface in the invagination between two consecutive "threads".
Figure 5-7 illustrates a recipient site with a self-tapping implant (Astra Tech® implant). This implant is designed with a TiOblast® surface modification. The biopsy was harvested 2 weeks after installation surgery. The outer portion of the thread is in contact with the parent "old" bone, while bone formation is the dominant feature in the invaginations between the threads and in areas lateral to the "apical" portions of the implant. Thus, discrete areas of newly formed bone can be seen also in direct contact with the implant surface. In sections representing 6 weeks of healing (Fig. 5-8), it was observed that a continuous layer of newly formed bone covers most of the TiOblast® surface. This newly formed bone is also in contact with the old, mature bone that is present in the periphery of the recipient site. After 16 months of healing (Fig. 5-9), the bone tissue in the zone of osseointegration has remodeled and the entire hard tissue bed for the implant is comprised of lamellar bone including both concentric and interstitial lamella.
**Fig. 5-8** Ground section of an implant site (Astra Tech® self-tapping implant) from a biopsy specimen obtained after 6 weeks of healing. (a) In the marginal area a continuous layer of bone covers most of the TiOblast® surface. (b) Higher magnification. Note the zone of newly formed (darker stained) bone that is in direct contact with the implant surface.
Fig. 5-9 Ground section of an implant site representing 16 months of healing. (a) The implant is surrounded by dense lamellar bone. (b) Higher magnification.
**Fig. 5-10** The device used in the dog experiment. The implant is a modification of a solid screw (Straumann® Implant System). The distance between two consecutive threads is 1.25 mm. The depth of the trough is 0.4 mm.
# The process of osseointegration
_De novo_ bone formation in the severed alveolar ridge following implant placement was studied in experiments in various experimental animal models (for review see Schroeder _et al_. 1995).
Recently Berglundh _et al_. (2003) and Abrahamsson _et al_. (2004) described various steps involved in bone formation and osseointegration to implants placed in the mandible of dogs.
_The device_ : Custom-made implants that had the shape of a solid screw (Straumann® implant), that were made of c.p. titanium and configured with a rough surface topography (SLA®; Straumann) were utilized (Fig. 5-10). In the implant device the distance between two consecutive profiles of the pitch (i.e. the threads in a vertical cross section) was 1.25 mm. A 0.4 mm deep U-shaped circumferential trough had been prepared within the thread region during manufacturing (Fig. 5-11). The tip of the pitch was left untouched. Following the installation of the nona cutting device (Fig. 5-12) the pitch was engaged in the hard tissue walls prepared by the cutting tapping device. This provided intitial or primary fixation of the device. The void between the pitch and the body of the implant established a geometrically well defi ned wound chamber (Fig. 5-13). Biopsies were performed to provide healing periods extending from 2 hours following implant insertion to 12 weeks of healing. The biopsy specimens were prepared for ground sectioning as well as for decalcification and embedding in epon.
**Fig. 5-11** The device. Schematic drawing illustrating the dimensions of the "wound chamber".
_The wound chamber_ : Figure 5.13 illustrates a cross section (ground section) of an implant with surrounding soft and hard tissues from a biopsy specimen sampled 2 hours after installation of the metal device. The peripheral portions of the pitch were in contact with the invaginations of the track prepared by the tap in the cortical bone. The wound chambers (Fig. 5-14a) were occupied with a blood clot in which erythrocytes, neutrophils, and monocytes/macrophages occurred in a network of fibrin (Fig. 5-14b). The leukocytes were apparently engaged in the wound cleansing process.
_Fibroplasia_ : Figure 5-15a illustrates a device with surrounding tissues after 4 days of healing. The coagulum had in part been replaced with granulation tissue that contained numerous mesenchymal cells, matrix components, and newly formed vascular structures (angiogenesis) (Fig. 5-15b). A _provisional connective tissue_ had been established.
**Fig. 5-12** Ground section showing the implant and adjacent tissues immediately after implant installation. The pitch region is engaged in the hard tissue walls. The void between two consecutive pitch profiles includes the wound chamber.
**Fig. 5-13** Detail of Fig. 5-12. The wound chamber was filled with blood and a coagulum has formed.
**Fig. 5-14** The wound chamber 2 hours after implant installation. Decalcified sections. (a) The wound chamber is filled with blood. (b) Erythrocytes, neutrophils, and macrophages are trapped in a fibrin network.
_Bone modeling_ : After 1 week of healing the wound chambers were occupied by a provisional connective tissue that was rich in vascular structures and contained numerous mesenchymal cells (Fig 5-16a). The number of remaining inflammatory cells was relatively small. In large compartments of the chamber, a cell-rich immature bone (woven bone) was seen in the mesenchymal tissues that surrounded the blood vessels. Such areas of woven bone formation occurred in the center of the chamber as well as in discrete locations that apparently were in direct contact with the surface of the titanium device (Fig. 5-16b). This was considered to represent the very first phase of osseointegration; contact between the implant surface and newly formed woven bone.
**Fig. 5-15** The wound chamber after 4 days of healing (decalcified sctions). (a) Most portions of the wound chamber are occupied by granulation tissue (fibroplasia). (b) In some areas of the chamber provisional connective tissue (matrix) is present. This tissue includes large numbers of mesenchymal cells.
**Fig. 5-16** (a) Ground section representing 1 week of healing. Note the presence of newly formed woven bone in the wound chamber. (b) Decalcified section. The woven bone is in direct contact with the implant surface.
After 2 weeks of healing, woven bone formation appeared to be pronounced in all compartments, apical as well as lateral, surrounding the implant (Fig. 5-17a). Large areas of woven bone were found in the bone marrow regions "apical" of the implant. In the wound chamber, portions of the newly formed woven bone apparently extended from the parent bone into the provisional connective tissue (Fig. 5-17b) and had in many regions reached the surface of the titanium device. At this interval most of the implant surface was occupied by newly formed bone and a more comprehensive and mature osseointegration had been established (Fig. 5-17c). In the pitch regions there were signs of ongoing new bone formation (Fig. 5-17d). Thus, areas of the recipient site located lateral to the device, that were in direct contact with the host bone immediately following installation surgery and provided initial fixation for the implant, had undergone tissue resorption and were also involved in new bone formation after 2 weeks of healing.
At 4 weeks (Fig. 5-18a), the newly formed mineralized bone extended from the cut bone surface into the chamber and a continuous layer of cell-rich, woven bone covered most of the titanium wall of the chamber. The central portion of the chamber was filled with a primary spongiosa (Fig. 5-18b), rich in vascular structures and a multitude of mesenchymal cells.
**Fig. 5-17** Ground sections illustrating, in various magnifications, the tissues in the wound chamber after 2 weeks of healing. (a) Darker stained woven bone is observed in the apical area of the metal device. (b, c, d) Most portions of the implant surface are coated with bone.
**Fig. 5-18** Ground sections representing 4 weeks of healing. (a) The newly formed bone (dark blue) extends from the "old" bone into the wound chamber. (b) Appositional growth. Note the presence of primary osteons.
_Remodeling_ : After 6–12 weeks of healing most of the wound chambers were filled with mineralized bone (Fig. 5-19). Bone tissue, including primary and secondary osteons, could be seen in the newly formed tissue and in the mineralized bone that made contact with the implant surface. Bone marrow that contained blood vessels, adipocytes, and mesenchymal cells was observed to surround the trabeculae of mineralized bone.
_Summary_ : The wound chambers were first occupied with a coagulum. With the ingrowth of vessels and migration of leukocytes and mesenchymal cells, the coagulum was replaced with granulation tissue. The migration of mesenchymal cells continued and the granulation tissue was replaced with a provisional matrix, rich in vessels, mesenchymal cells, and fibers. The process of _fibroplasia_ and angiogenesis had started. Formations of newly formed bone could be recognized already during the first week of healing; the newly formed woven bone projected from the lateral wall of the cut bony bed (appositional bone formation; distance osteogenesis) (Davies 1998) but _de novo_ formation of new bone could also be seen on the implant surface, i.e. at a distance from the parent bone (contact osteogenesis) (Davies 1998). During subsequent weeks the trabeculae of woven bone were replaced with mature bone, i.e. lamellar bone and marrow (bone remodeling).
References
Abrahamsson, I., Berglundh, T., Linder, E., Lang, N.P. & Lindhe, J. (2004). Early bone formation adjacent to rough and turned endosseous implant surfaces. An experimental study in the dog. _Clinical Oral Implants Research_ **15** , 381–392.
Albrektsson, T., Brånemark, P-I., Hansson, H-A. & Lindström, J. (1981). Osseointegrated titanium implants. Requirements for ensuring a long-lasting, direct bone anchorage in man. _Acta Orthopaedica Scandinavica_ **52** , 155–170.
Berglundh, T., Abrahamsson, I., Lang, N.P. & Lindhe, J. (2003). De novo alveolar bone formation adjacent to endosseous implants. a model study in the dog. _Clinical Oral Implants Research_ **14** , 251–262.
Brånemark, P.I., Adell, R., Breine, U., Hansson, B.O., Lindström, J. & Ohlsson, Å. (1969). Intra-osseous anchorage of dental prostheses I. Experimental studies. _Scandinavian Journal of Plastic Reconstructive Surgery_ **3** , 81–100.
Davies, J.E. (1998). Mechanisms of endosseous integration. _International Journal of Prosthodontics_ **11** , 391–401.
Schroeder, A., Pohler, O. & Sutter, F. (1976). Gewebsreaktion auf ein Titan-Hohlzylinderimplant mit Titan-Spritzschichtoberfläche. _Schweizerisches Monatsschrift für Zahnheilkunde_ **86** , 713–727.
Schroeder, A., van der Zypen, E., Stich, H. & Sutter, F. (1981). The reactions of bone, connective tissue, and epithelium to endosteal implants with titanium-sprayed surfaces. _Journal of Maxillofacial Surgery_ **9** , 15–25.
Schroeder, A., Buser, D. & Stich, H. (1995) Tissue response. In: Schroeder, A., Sutter, F., Buser, D. & Krekeler, G., eds. _Oral Implantology. Basics, ITI Hollow Cylinder System_. New York: Thieme, pp. 80–111.
Zarb, G.A. & Albrektsson, T. (1991). Osseointegration – a requiem for the periodontal ligament? Editorial. _International Journal of Periodontology and Restorative Dentistry_ **11** , 88–91.
# Chapter 6
# Periodontal Tactile Perception and Peri-implant Osseoperception
Reinhilde Jacobs
* * *
Introduction
Neurophysiological background
Afferent nerve fibres and receptors
Trigeminal neurophysiology
Trigeminal neurosensory pathway
Neurovascularization of the jaw bones
Mandibular neuroanatomy
Maxillary neuroanatomy
Periodontal innervation
Testing tactile function
Neurophysiological assessment
Psychophysical assessment
Periodontal tactile function
Active threshold determination
Passive threshold determination
Influence of dental status on tactile function
Activation of oral mechanoreceptors during oral tactile function
Functional testing of the oral somatosensory system
Oral stereognosis
Influence of dental status on stereognostic ability
Other compromising factors for oral stereognosis
Receptor activation during oral stereognosis
From periodontal tactile function to peri-implant osseoperception
Tooth extraction considered as sensory amputation
Histological background of peri-implant osseoperception
Cortical plasticity after tooth extraction
From osseoperception to implant-mediated sensory motor interactions
Clinical implications of implant-deviated sensory motor interaction
Conclusions
* * *
# **Introduction**
Perception is the ability to detect external stimuli. In man, several kinds of sensory systems enable perception (vision, audition, balance, somatic function, taste, and smell) (Martin 1991). In all sensory systems, the initial contact with the external world is made through special neural structures called sensory receptors, endings or organs. A distinction is needed between nociceptors, chemo-, photo-, thermo-, and mechanoreceptors, each responding to a particular stimulus. In the oral cavity, taste and somatic sensory systems predominate. The former are sensitive to chemical stimuli while the latter respond to mechanical, thermal, and nociceptive stimuli. In this chapter, only the somatic sensory system is explored. The preponderance of the oral somatosensory system is illustrated by its major representation, besides that of the hand, on the sensory homunculus proposed by Penfield (Penfield and Rasmussen 1950). In general, the somatosensory function is essential for fine-tuning of limb movements. In analogy with the rest of the skeleton, the tactile function of teeth plays a crucial role in refinement of jaw motor control. Periodontal mechanoreceptors, especially those located in the periodontal ligament, are extremely sensitive to external mechanical stimuli. The periodontal ligament can thus be considered as a keystone for masticatory and other oral motor behaviours. Any condition that may influence periodontal mechanoreceptors, may alter the sensory feedback pathway and thus affect tactile function and fine-tuning of jaw motor control (e.g. periodontal breakdown, bruxism, re-implantation, anesthesia).
The most dramatic change may occur after extraction of teeth, as this eliminates all periodontal ligament receptors. This condition may persist after implant placement as functional re-innervation has not yet been proven in humans. Surprisingly enough, patients with implant-supported prostheses often seem to function quite well. The underlying mechanism of this so-called "osseoperception" phenomenon remains a matter of debate, but the response of assumed peri-implant receptors might help to restore the proper peripheral feedback pathway. This hypothesized physiological integration might thus lead to better acceptance, improved psychological integration, and more natural functioning.
This chapter will unravel periodontal tactile function and guide the reader through the mysteries of peri-implant osseoperception in order to find neuroanatomical, histological, physiological, and psychophysical evidence to confirm the hypothesis.
# Neurophysiological background
## Afferent nerve fibres and receptors
When considering the human somatic sensory system, four types of afferent nerve fibers can be distinguished in association with sensation: Aα, Aβ, Aδ and C. Some types of afferent nerve fibers exist in specific tissues only, while others are widely distributed throughout the body. Based on the structure or signalling properties, receptors may be divided into several classes or categories (Birder & Perl 1994). Three different groups of receptors are associated with thermal and (vibro) tactile sensation: thermoreceptors, nociceptors and mechanoreceptors.
### Thermoreceptors and nociceptors
Thermal sensations are divided into warm and cold and are perceived by specific receptors. There are indeed separate spots on skin and mucosal surface where thermal stimulation elicits either warm or cold sensation. Cold-sensitive spots are more numerous than warm-sensitive with the highest density of both cold and warm spots on the face (Bradley 1995). Unmyelinated neurite complexes are responsible for cold sensation and some free nerve endings for warm sensation (Bradley 1995). Receptors which can induce pain feeling are referred to as nociceptors and mostly supplied by Aδ and C fibers. In the periodontal ligament, one can identify free nerve endings which may be responsive to pain, but not thermal receptors. The majority of the receptors located within the periodontal ligament are of the mechanoreceptive type.
### Mechanoreceptors
Mechanoreceptors are responsive to mechanical stimuli. These can be classified on the basis of their morphology, receptive field, and adaptation characteristics. In man, four receptor structures have been associated with mechanoperception: Meissner corpuscles, Pacinian corpuscles, Merkel cells, and Ruffini endings (Martin & Jessell 1991). These structural elements do determine, to some extent, the physiological characteristics of the peripheral receptors. On the basis of their receptive field, two subgroups of mechanoreceptors have been identified: receptors with small and distinct receptive fields (type I) and receptors with large and diffuse receptive fields (type II). Mechanoreceptors can also be subdivided based on their adaptation properties: rapidly adapting (RA) and slowly adapting (SA) receptors. The RA receptors, also called fast adapting receptors, only respond during the dynamic phase of stimulus application. In contrast, the SA receptors respond to both dynamic and static force applications (Iggo 1985). A relationship has been established between the aforementioned receptor morphologies and their adaptation characteristics. Rapidly adapting receptors include Meissner corpuscles (RA I) and Pacinian corpuscles (RA II) while SA receptors include Merkel cells (SA I) and Ruffini endings (SA II).
# Trigeminal neurophysiology
## Trigeminal neurosensory pathway
The trigeminal nerve is the largest cranial nerve, including a motor root supplying the masticatory muscles, and a predominant sensory root supplying the oral cavity, head, and face. The trigeminal nerve has three divisions (ophthalmic, maxillary, mandibular). The ophthalmic nerve is a sensory nerve and the smallest division. The maxillary nerve is a sensory nerve and intermediate, both in position and size, between ophthalmic and mandibular divisions. The mandibular nerve is the largest and made up of two roots: a large, sensory root and a small motor root.
The sensory inputs of the oral region are carried by the mandibular and maxillary divisions of the trigeminal nerve via the trigeminal ganglion to the brainstem. This is part of an important sensory feedback pathway, involved in refinement of jaw movements. The afferent signals are transmitted either to the main sensory nucleus of the trigeminal nerve (responsive to discriminate tactile senses, light touch and pressure) or to the descending spinal tract nuclei, including: (1) nucleus oralis, responsive to cutaneous sensation of oral mucosa; (2) nucleus interpolaris, responsive to tooth pulp pain; and (3) nucleus caudalis, responsive to pain, temperature, and crude touch.
From there, signals are transferred across the midline and sent to the thalamus and, via thalamocortical projections, to the respective cortical areas involved in orofacial sensation where they can result in conscious perception.
### Neurovascularization of the jaw bones
The jaws are richly supplied by neurovascular structures, and it is thus of utmost important to identify vital anatomic structures before carrying out a surgical procedure. During a radiographic preoperative planning procedure, neurovascular structures need to be precisely localized to attempt avoiding interference. Particular attention should be paid to the anterior jaw bones, which are often considered as relatively safe surgical areas. The increasing rate of surgical interventions in the anterior jaw bone, such as oral implant placement and bone grafting, has indeed highlighted potential risks and raised the number of reported complications. Recent studies reveal that edentulous and dentate anterior jaws present significant variation in the occurrence of the mandibular incisive canal and genial spinal foramina as well as the maxillary nasopalatine canal (for review see Jacobs _et al_. 2007). All these canal structures contain a neurovascular bundle, whose diameter may be large enough to cause clinically significant trauma. While surgeons need to avoid the nervous structures, these critical structures may afterwards become essential to potentially reinnervate periimplant bone. Indeed, the existence of remaining neurovascular bundles in the edentulous jaw bone may support the idea that nerves may regenerate after tooth extraction and implant placement. This particular assumption is the basis of the so-called osseoperception phenomenon and will be further outlined below.
Fig. 6-1 These human dry mandibular bone sections illustrate the presence and dimensional importance of the mandibular incisive nerve, even in edentulism. The middle section is actually visualizing the mandibular midline, confirming that there is no true connection between the left and right sections.
### Mandibular neuroanatomy
The mandibular nerve is the largest of the three divisions of the fifth cranial nerve and gives off the inferior alveolar nerve. The latter enters the mandible through the mandibular foramen and continues to run forward through the mandibular canal. At the mental foramen it gives off an important branch, called the mental nerve. It should not be considered as the only terminal branch of the inferior alveolar nerve. The mandibular incisive nerve is often detected as a second terminal branch with an intraosseous course in a so-called mandibular incisive canal, located anterior to the mental foramen (Mraiwa _et al_. 2003a,b) (Fig. 6-1). Conventional intraoral and panoramic radiographs often fail to show this canal (Jacobs _et al_. 2004). Cross-sectional imaging may however be used to locate the canal and as such avoid any risk for neurovascular damage (Jacobs _et al_. 2002a) The mandibular incisive canal contains a true neurovascular bundle with nervous sensory structures (Fig. 6-2). Its existence in edentulous patients is underlined by reported surgical complications. Indeed, sensory disturbances, caused by direct trauma to the mandibular incisive canal bundle have been reported after implant placement in the interforaminal region (Jacobs & van Steenberghe 2006; Jacobs _et al_. 2007) (Fig. 6-3).
**Fig. 6-2** Single cross-sectional slice of an high resolution MRI dataset localized at the incisor region of a dentate anterior human mandible, with the fatty marrow colored white. A black root-form structure corresponds to the root of an incisor tooth. It is surrounded by a small band of intermediate signal intensity, representing the periodontal ligament. The dental neurovascular supply is seen as a line of intermediate signal intensity in the middle of the root. The latter descends to the level of a larger structure of intermediate signal intensity (incisive nerve) with a black oval area on top (vascular structure). (Reprinted from Jacobs _et al_. 2007, Copyright 2006, with permission from Elsevier.)
A sensory disorder might also be related to indirect trauma caused by a hematoma in the canal, which acts as a closed chamber; this will affect the mandibular incisive canal bundle and spread to the main mental branch (Mraiwa _et al_. 2003b).
Other anatomic landmarks to be noted are superior and inferior genial spinal foramina and their bony canals, situated in the midline of the mandible in 85–99% of people (Liang _et al_. 2005a,b; Jacobs _et al_. 2007). The superior one is at the level of, or superior to, the genial spine; the inferior one is below the genial spine (Fig. 6-4). The superior genial spinal foramen has been found to contain a branch of the lingual artery, vein and nerve. Furthermore, a branch of the mylohyoid nerve together with branches or anastomoses of sublingual and/or submental arteries and veins have been identified upon entering the inferior genial spinal foramen. This artery could be of sufficient size to provoke hemorrhage intraosseously or in the connective soft tissue, which might be difficult to control (Darriba & Mendonca-Cardad 1997; Liang _et al_. 2005a,b) (Fig. 6-5).
**Fig. 6-3** Cross-sectional slice of a cone beam dataset showing an osseointegrated implant placed in an edentulous lateral incisor region, on top of a prominent incisive canal lumen. Chronic pressure on the incisive nerve resulted in a neuropathic pain problem. (Reprinted from Jacobs & van Steenberghe 2006, Copyright 2006, with permission from Blackwell Publishing.)
Fig. 6-4 (a) A macroanatomical view of a human anterior mandible showing a clear neurovascular bundle entering the superior genial spinal foramen. (b) A matching horizontal slice acquired through high-resolution MRI confirms the entry of a neurovascular bundle into the superior genial spinal foramen. (Courtesy of Professor I. Lambrichts, University of Hasselt.)
The observation that immediate loading of implants in the anterior mandible results in a significant reduction of tactile function using the Brånemark Novum® concept rather than a conventional implant-supported overdenture might be explained by contact with the aforementioned neurovascular bundles in the anterior mandible (Abarca _et al_. 2006).
### Maxillary neuroanatomy
The maxillary nerve is a sensory nerve, with its superior nasal and alveolar branches supplying the maxilla, including the palate, nasal and maxillary sinus mucosa, upper teeth and their periodontium. One of the superior nasal branches is named the nasopalatine nerve. It descends to the roof of the mouth through the nasopalatine canal and communicates with the corresponding nerve of the opposite side and with the anterior palatine nerve. The nasopalatine foramen and canals are situated at the maxillary midline, posterior to the central incisor teeth (Mraiwa _et al_. 2004). Typically, it has been described as having a Y-shape with the orifices of two lateral canals, terminating at the nasal floor level in the foramina of Stenson (Fig. 6-6). The nasopalatine nerve and the terminal branch of the descending palatine artery pass through these canals. Occasionally, two additional minor canals are seen (foramina of Scarpa), which may carry the nasopalatine nerves (Fig. 6-7). Mraiwa _et al_. (2004) point out a significant variability both regarding dimensions and morphological appearance of the nasopalatine canal.
To avoid disturbing neurovascular bundles and further complications, this important variability should be taken into account when dealing with surgical procedures such as implant placement in the maxillary incisor region.
Fig. 6-5 Stereomicroscopic images. (a) A single genial spinal foramen. (b) A section of the canal. (c) The neurovascular content of the canal is confirmed histologically. In this particular image, the artery has a width of about 0.5 mm (red and green lines for inner and outer wall dimensions).
Fig. 6-6 Outline of the common Y-morphology of the nasopalatine canal (seen in black oval) on a three-dimensional reconstruction of the palate and the floor of the nose, seen from a posterior viewing angle (a) and a side view (b).
# Periodontal innervation
Periodontal receptors are located within the gingiva, jaw bone, periosteum, and periodontal ligament. Most receptors seem to have mechanoreceptive characteristics, contributing to a sophisticated exteroceptive tactile function. This tactile information is not primarily used for protective purposes, but rather applied by the human brain to improve oral motor behavior and fine-tuning of biting and chewing (Trulsson 2006).
It is clear that the periodontal ligament plays a predominant role in this dedicated mechanoreceptive function. It has an extremely rich sensory nerve supply, especially in those locations that are more prone to displacement (peri-apical, buccal, and lingual periodontal ligament). It contains three types of nerve endings: free nerve endings, Ruffini-like endings, and lamellated corpuscles (Lambrichts _et al_. 1992). Free nerve endings stem from both unmyelinated and myelinated nerve fibers. Lamellated corpuscules are found in close contact to each other. Most mechanoreceptive endings are, however, Ruffinilike, and are predominantly present in the apical part of the periodontal ligament. Morphologic studies indicate that these endings are in close contact with collagen fibres of the surrounding tissues (Lambrichts _et al_. 1992) (Fig. 6-8). This particular association may explain their extremely high sensitivity upon loading a tooth. This results in low threshold levels for periodontal tactile function, and is considered as the basis of an elaborate sensory apparatus that may be linked to a number of clinical phenomena.
**Fig. 6-7** View from the palate of an edentulous dry skull, showing the nasopalatine foramen, formed at the articulation of both maxillae, behind the incisor teeth. In the depth of the canal, the orifices of two lateral canals are seen. As an anatomic variant, two minor canals can be observed on the midline, one anterior and one posterior to the major nasopalatine canals.
Fig. 6-8 Electron microscope image at the level of the human periodontal ligament, showing collagen fibrils inserted into the basal lamina of an ensheating cell in a Ruffini-like receptor. (Reprinted from Lambrichts et al. 1992, Copyright 2006, with permission from Ivo Lambrichts, University of Hasselt and Blackwell Publishing.)
Recordings from the inferior alveolar nerve reveal that human periodontal mechanoreceptors discharge continuously during sustained loading of teeth (Trulsson _et al_., 1992). Like the slowly adapting type II receptors in the human skin, most periodontal ligament mechanoreceptors are spontaneously active with a regular discharge in response to forces applied to teeth.
The mechanoreceptive function of the periodontal ligament allows it to signal differential information about the mechanical events that occur when manipulating and biting food with anterior teeth and chewing food with the posterior teeth (Trulsson 2006). The detailed differential signalling allows the brain to analyze and characterize the specific mechanical events enabling further processing for fine-tuning, resulting in an optimized masticatory sequence (Trulsson 2006). Considering this crucial role, it is clear that some sensory–motor interactions are impaired or even lost when altering or damaging the periodontal ligament. When teeth are extracted and thus ligament receptors eliminated, tactile functioning may be hampered. Indeed, Haraldson (1983) describes a similar muscle activity during the entire masticatory sequence in patients with implant-supported fixed prosthesis. This finding contrasts to subjects with natural teeth, having a chewing pattern that gradually changes with altering food bolus properties. Jacobs and van Steenberghe (1994) identify a silent period in muscle activity (reflex response) when tapping teeth or implanting neighboring teeth. A reflex response remains absent, however, when tapping implants in a fully edentulous jaw bone. Both findings may illustrate the modulatory role of periodontal ligament input in jaw muscle activity.
# Testing tactile function
### Neurophysiological assessment
Information on the exteroceptive function can be examined by neurophysiological as well as psychophysical methods. Neurophysiological investigations on the sensory function of the human trigeminal system are scarce. Afferent nerve recordings of the human trigeminal nerve require skilful performance. Only few studies have been performed so far (Johansson _et al_. 1988a,b; Trulsson _et al_. 1992). Alternatively, non-invasive approaches may be considered to evaluate oral tactile function. The first approach is the recording of the so-called trigeminal somatosensory evoked potentials (TSEP) after stimulation of receptors in the oral cavity (Van Loven _et al_. 2000, 2001). This set-up has the advantage of obtaining information on the cortical response of the trigeminal afferent system upon non-invasive stimulation of oral receptors. Unfortunately, SEPs from the trigeminal branches are, in contrast to those recorded from limbs, weak and difficult to discriminate from the background noise; advanced signal analysis is required to gain reliable information (Swinnen _et al_. 2000; van Loven _et al_. 2000, 2001). Another non-invasive method to assess sensory function is to visualize brain activity by functional magnetic resonance imaging (fMRI) (Borsook _et al_. 2004, 2006). This is a complex but most promising method, which has received hardly any attention in relation to tactile function of teeth and implants (Lundborg _et al_. 2006; Miyamoto _et al_. 2006).
The main drawbacks of fMRI include complexity of the signal, relatively long imaging time, potential hazard imposed by the presence of ferromagnetic material in the vicinity of the imaging magnet, potential risk for claustrophobia, and costs. The technique is most promising, however. When combined with other techniques, such as psychophysics and TSEPs, it may offer a new non-invasive approach to evaluate how the human oral somatosensory system functions (Ducreux _et al_. 2006; Lundborg _et al_. 2006).
### Psychophysical assessment
Sensory function can also be evaluated by psychophysical testing, relying on the patient's response. This technique has often been applied for testing oral tactile function (Jacobs & van Steenberghe 1994; Jacobs _et al_. 2002b,c,d). When carried out in a strictly standardized condition, the psychophysical response can be directly linked to the neural receptor activation (Vallbo & Johansson 1984).
Psychophysical studies on the oral sensory function are numerous. A major advantage of this type of study is that they are simple non-invasive techniques that can be performed in a clinical environment. Psychophysics include a series of well defined methodologies to help determine the threshold level of sensory receptors in man. Psychophysical methods allow connection between the psychological response of the patient to the physiological functions of the receptors involved. The methods should be carried out in a standardized and accurate manner, to enable one to draw conclusions about their outcome with regard to sensory function (Jacobs _et al_. 2002b,c,d).
Regardless of the tests used, one must keep in mind that many variables contribute to the subjective nature of psychophysical sensory testing. Some variables are manageable, others are more difficult to deal with. Influencing factors exist in various components of the experiment set-up (environmental influence, psychophysical approach, patient-related factors) (Jacobs _et al_. 2002b).
Environmental factors should be well controlled, as background noise is distracting to patient and examiner. To minimize the effect of noise, testing should be done in a quiet room with stable background illumination.
Patient-related variables may contribute greatly to the outcome of the testing. Psychological and/or physical factors may lead to an inter and intra-subject variability, making the expression of a threshold level more obvious than assessment of an absolute value. Psychological factors include motivation, level of concentration, and anxiety level. The psychophysical approach may attempt to control such variability.
Different psychophysical procedures have been described in order to assess tactile function reliably (Falmagne 1985). Adaptive methods are generally recommended for threshold level determination, as these seem very effective and consistent. Such approaches are termed adaptive, as the subsequent stimulus value depends on the subject's response in preceding trials. In the staircase method, the stimulus value is changed by a constant amount. When the response shifts from one answer to another, the stimulus direction is reversed. Afterwards, the threshold is determined by averaging peaks and valleys throughout all runs. Some patients may imagine a stimulus when there is none. Others admit feeling a sensation, only if they are absolutely positive that it was felt. The inclusion of false alarms (implying that no stimulus is presented in the specified time interval) may exclude response bias and a guessing strategy of the subject. A thorough and standardized instruction to all subjects is important in this respect.
Other patient-related factors that should be considered are of physical origin and include age, gender, dental status and dexterity. Age is an important variable with respect to implant physiology, considering the fact that edentulous patients are usually found amongst the elderly. Age-related impairment is seen, both of motor function and most sensory modalities in the extremities (Masoro 1986). A decline in oral sensory function is also established. After the age of 80, the ability to differentiate tactile and vibratory stimuli on the lip decreases and two-point discrimination deteriorates on the upper lip, on the cheeks, and on the lower lip, but not on the tongue and the palate (Calhoun _et al_. 1992). Stereognostic ability also declines with age (Müller _et al_. 1995). It is clear that this age effect should be considered in experimental studies.
In contrast to age, the influence of gender on tactile function remains a matter of debate. Taking into account the important interindividual variability, clear-cut gender differences are not easily discerned with regard to oral sensory function. There is no marked gender effect on stereognostic ability or vibrotactile function (Jacobs _et al_. 1992, 2002b). The tactile sensory systems of men and women seem to operate similarly at both threshold and suprathreshold levels of stimulation (Chen _et al_. 1995). However, females seem to have greater ability to discern subtle changes in lip, cheek, and chin position than males (Chen _et al_. 1995). Dexterity is another patient-related variable. Although there is some relation between masticatory performance and dexterity (Hoogmartens & Caubergh 1987), this is not the case for either tactile function or stereognosis (Jacobs _et al_. 1992, 2002b).
# Periodontal tactile function
A variety of psychophysical tests has been used to evaluate oral exteroceptive function by assessment of threshold levels. Although some of the methods designed for functional psychophysical testing are unable to identify the specific receptor groups involved in the mechanisms of oral sensation, the tests may clearly reflect periodontal tactile function. Assessing light touch or the tactile function of teeth is performed by determination of the threshold levels for active and passive detection and discrimination tasks (Jacobs _et al_. 1992, 2002b,d). The distinction between detection and discrimination is based on the fact that, in a detection task, the subject has to indicate the presence or absence of a stimulus ("yes" or "no" strategy) while in a discrimination task, the subject has to compare two stimuli ("smaller" or "larger" strategy). A further division is made between active and passive tasks. In the passive task, forces are applied to a tooth in the upper jaw. The active tactile function of teeth is evaluated by inserting an object, mostly a foil of a certain thickness, in between two antagonistic teeth. The latter rather reflects daily functioning and automatically involves other than periodontal receptors (e.g. joint, muscle and inner ear receptors), while the passive test involves solely activation of periodontal ligament mechanoreceptors.
### Active threshold determination
The active absolute threshold level is determined by the interocclusal detection of small objects such as foils of varying thicknesses (Fig. 6-9). This may involve the activation of mechanoreceptors, mainly originating from the periodontium but also from the muscles, inner ear, and temporomandibular joints (TMJs). It should, however, be realized that the foil materials used may have different thermal and mechanical properties, resulting in conflicting results (Jacobs _et al_. 1992). Foil materials with high thermal conductivity (e.g. steel, aluminium) may lower the threshold level by activation of thermal receptors.
Fig. 6-9 Active threshold determination by interocclusal thickness perception yields superior results for teeth than for implant-supported prostheses, with fixed prostheses being more sensitive than removable ones.
Another factor that may affect the active tactile function is chewing activity, because this involves progressive intrusion of the tooth after each chewing cycle. The latter leads to adaptation of the periodontal mechanoreceptive inputs. Chewing or bruxism may thus lead to an increase in threshold levels up to 60 times the normal values (Kiliaridis _et al_. 1990). An interocclusal discrimination task of small objects determines the differential threshold level. The active threshold level varies according to the experiment set-up, but the most important variable is test stick dimension (Jacobs & van Steenberghe 1994). For size discrimination with a mouth opening of less than 5 mm, periodontal mechanoreceptive input plays the primary role. For increased mouth opening, the response of muscle spindles predominates.
### Passive threshold determination
The most common device used in clinical neurology to measure light touch sensation is a set of Semmes-Weinstein monofilaments (Semmes-Weinstein Aesthesiometer®, Stoelting, Illinois, USA). The original idea dates back from the nineteenth century when von Frey suggested testing cutaneous light touch by using calibrated hairs of different stiffness by changing their length and hardness. Later on, the so-called von Frey hairs were replaced by nylon monofilaments mounted into a plastic handle (Fig. 6-10). This technique has also been applied intraorally for assessment of light touch thresholds for teeth, implants or oral mucosa (Jacobs & van Steenberghe 1994; Jacobs _et al_. 2002d). The drawback remains the variation caused by the hand-held and thus variable nature of stimulation application. Other stimulators have therefore been developed, enabling a controlled force level under more standardized stimulation conditions for measuring both manual and oral light touch (Jacobs _et al_. 2002b,d).
The passive discrimination task allows testing of the ability to differentiate between intensities of forces applied to a tooth. It depends on the force characteristics such as the rate of force application and the range of forces presented. When comparing teeth and implants, passive threshold levels are much lower for teeth but at suprathreshold force levels, implants and teeth become equally sensitive. For the passive detection of forces applied to a tooth, different stimulating devices have been developed. In order to avoid tapping and subsequent transmission of the waves through the jaw bone with activation of other receptors, such as in the inner ear, pushing forces are recommended (Fig. 6-11). This is done by placement of the stimulating rod in contact with the tissue under investigation (Jacobs & van Steenberghe 1993).
Fig. 6-10 Passive threshold determination. (a) Using a kit of pressure esthesiometers of increasing loads. (b) From determination of the absolute detection threshold upon tooth loading. (c) Using the individual hand-held stimulation rod.
Fig. 6-11 Set-up of passive threshold determination of a maxillary front tooth by applying axial pushing forces against the tooth.
### Influence of dental status on tactile function
From several psychophysical studies, it has been established that the oral tactile function is influenced by tooth position and dental status (Jacobs _et al_. 2002b). The tactile function of teeth is primarily determined by the presence of periodontal ligament receptors. Vital or non-vital teeth may show a comparable tactile function. However, when periodontal ligament receptors are reduced or eliminated (e.g. periodontitis, bruxism, chewing, extraction, anesthesia, etc.), tactile function is impaired (Table 6-1). This clinically implies that a patient's ability to detect occlusal inaccuracies (e.g. induced by restorative treatment) is decreased in these situations. Indeed, exteroceptors inform the nervous system on the characteristics of the stimulus, which then allows modulation of the motoneuron pool to optimize jaw motor activity and avoid overloading. Elimination of these exteroceptors by tooth extraction may reduce the tactile function to an important extent (Jacobs _et al_. 2001; Jacobs & van Steenberghe 1991, 1994, 2006; Mericske-Stern 1994; Mericske-Stern _et al_. 1995; Jacobs 1998). Even after rehabilitation with a prosthesis, tactile function remains impaired and inappropriate exteroceptive feedback may thus present a risk for overloading the prosthesis (Jacobs & van Steenberghe 2006). In comparison to the tactile function of a natural dentition, the active threshold is seven to eight times higher for dentures but only three to five times higher for implants (see Table 6-1). For the passive detection of forces applied to upper teeth, thresholds are increased 75 times for dentures and 50 times for implants (see Table 6-1). The large discrepancies between active and passive thresholds can be explained by the fact that several receptor groups may respond to active testing, while the passive method selectively activates periodontal ligament receptors. The latter are eliminated after extraction, which may explain the reduced tactile function in edentulous patients.
**Table 6-1** Factors influencing the tactile function of teeth (for review see Jacobs _et al_. 2002b; Jacobs & van Steenberghe 2006)
Influencing factors| Active threshold (thickness detection)| Passive threshold (force detection)
---|---|---
Vital tooth| 20 μm| 2 g
Non-vital tooth| 20 μm| 2 g
Anesthesia| ↑| ↑
Periodontitis| ↑| ↑ (> 5 g)
Chewing| ↑| ↑
Bruxism| ↑| ↑
Extraction| ↑| ↑
Reimplantation| ↑| ↑
Denture| 150 μm| 150 g
Implant-supported prosthesis| 50 μm| 100 g
Ageing| ↑| ↑
Polyneuropathy| ↑| ↑
↑: increase in threshold level implying a decrease in tactile function and hampered feedback.
After rehabilitation with a bone-anchored prosthesis, however, edentulous patients seem to function quite well. These patients perceive mechanical stimuli exerted on osseointegrated implants in the jaw bone. Some of them even note a special sensory awareness with the bone-anchored prosthesis, coined "osseoperception". It can be defined as a perception of external stimuli transmitted via the implant through the bone by activation of receptors located in peri-implant environment, periosteum, skin, muscles, and/or joints (Jacobs 1998). The existence of this phenomenon could imply that the feedback pathway to the sensory cortex is partly restored with a hypothetical representation of the prosthesis in the sensory cortex; this may allow an adjusted modulation of the motoneuron pool leading to more natural functioning and avoiding overload.
### Activation of oral mechanoreceptors during oral tactile function
When performing psychophysical testing, various types of oral mechanoreceptors may be activated. Mechanoreceptors in the oral region may be located in the periodontal ligament, oral mucosa, gingiva, bone, periosteum, and tongue. Mechanoreceptors in the periodontal ligament contribute to the very high sensitivity of teeth to mechanical stimuli (Jacobs & van Steenberghe 1994). The periodontal ligament is richly supplied with mechanoreceptors, with the majority being identified histologically as Ruffini-like endings (Lambrichts _et al_. 1992). During passive threshold determination, these receptors will be activated. The assessment of the active tactile threshold level is, however, not solely based on activation of periodontal mechanoreceptors. Temporomandibular joint receptors are found to only play a minor role, but muscular receptors are important in the discriminatory ability for mouth openings of 5 mm and more (Broekhuijsen & Van Willigen 1983).
Considering that mechanoreceptors in the periodontal ligament largely contribute to tactile function, one can question what happens after tooth extraction. It can be assumed that remaining receptors in the peri-implant environment (gingiva, alveolar mucosa, periosteum, and bone) may take over part of the normal exteroceptive function.
In the oral mucosa, different types of mechanoreceptors can be identified including lamellar organs, Ruffini-like endings, and free nerve endings (Lambrichts _et al_. 1992). The number of nerve fibers per unit area is greater in the anterior areas of the oral cavity, making this region the most sensitive part of the oral mucosa (Mason 1967).
The gingiva contains round and oval lamellar corpuscles. These receptors respond to mechanical stimuli for coordination of the lip and buccal muscles during mastication (Johansson _et al_. 1988a,b). Cutaneous mechanoreceptors in the facial skin are activated by skin stretching or contraction of facial muscles and may operate as proprioceptors involved in facial kinesthesia and motor control (Nordin & Hagbarth 1989).
The periosteum contains free nerve endings, complex unencapsulated, and encapsulated endings. The free nerve endings are activated by pressure or stretching of the periosteum through the action of masticatory muscles and the skin (Sakada 1974). Periosteal innervation has been suggested to play a role in peri-implant tactile function (Jacobs 1998). Indeed, when applying forces to osseointegrated implants in the jaw bone, pressure build-up in the bone is sometimes large enough to allow deformation of the bone and its surrounding periosteum (Jacobs 1998). The involvement of bone innervation in mechanoreception and peri-implant osseoperception remains a matter of debate, however (Jacobs & van Steenberghe 2006).
# Functional testing of the oral somatosensory system
Functional testing of the oral somatosensory system may include two-point and size discrimination as well as stereognosis. Two-point discrimination is the ability to differentiate between two points of simultaneous contact. A traditional disk for two-point discrimination is divided into equal triangles containing two points placed at standard distances, usually between 2 and 25 mm (Fig. 6-12). This kind of test can be applied on different areas of the skin or the oral mucosa (Jacobs _et al_. 2002b,c,d). Size discrimination consists in holding a stick between two antagonistic teeth or fingers. This discriminatory ability is better for antagonistic teeth than for fingers (Morimoto 1990). The most documented and relevant test for the oral cavity is, however, stereognosis, which is considered as a complex functional test, evaluating the ability to recognize and discriminate different forms (Jacobs _et al_. 1997).
### Oral stereognosis
While touch may obtain information on the mechanoreceptors activated by simple detection or discrimination of mechanical stimuli, stereognosis is a more complex process. It is a function of both peripheral receptors (touch and kinesthetic) and central integrating processes (Jacobs _et al_. 1998). It may give an idea on daily functioning and may be applied to measure sensory impairment due to the presence of general or local pathology (speech pathology, blindness, deafness, cleft lip and palate, temporary sensory ablations, etc.).
Fig. 6-12 Intraoral two-point discrimination testing device based on a constant pressure probe to compensate for the variability induced by hand-held equipment.
Fig. 6-13 (a) Stereognostic detection of objects in between teeth is better than for implant-supported prostheses. (b) The use of toothpicks to which the forms are attached and manipulated may avoid direct lip and tongue contact.
### Influence of dental status on stereognostic ability
A change in the oral cavity by means of partial or complete loss of the dentition certainly creates certain changes to the oral sensory function. The roles of periodontal neural receptors and of the tongue seem essential in dentate subjects. After bilateral mandibular block, the stereognostic ability decreases by about 20% (Mason 1967). When comparing teeth with full dentures, a far better stereognostic ability is noted for natural teeth when freely manipulating the test pieces (Litvak _et al_. 1971). When removing the denture (s) in complete denture wearers, a considerable reduction in stereognostic ability is noted (Jacobs _et al_. 1998).
Lundqvist (1993) demonstrated that stereognostic ability improved after rehabilitation with oral implants. Jacobs _et al_. (1997) compared different prosthetic superstructures and noted no significantly different stereognostic ability with implant-supported fixed or removable prostheses, even when eliminating the involvement of tongue and lip receptors (Fig. 6-13).
### Other compromising factors for oral stereognosis
Stutterers and speakers with articulation problems have an impaired stereognostic ability in comparison to normal speakers (Moser _et al_. 1967). They require more time to identify objects than normal speakers. Speakers with cerebral palsy also have an impaired stereognostic ability (Moser _et al_. 1967). Hemiplegic subjects make approximately three times as many errors as normal subjects in oral stereognosis tests. A surgical reduction of the tongue in case of macroglossia has a minor influence on the subject's performance in the test for oral stereognosis (Ingervall & Schmoker 1990). Other pathological conditions in the perioral area have no direct influence on the stereognostic ability (Jacobs _et al_. 1998). Cleft lip and palate is not accompanied by a sensory deficit of the oral area. There is also no overall sensory impairment following tissue manipulation in cleft lip and palate surgery. Furthermore, the stereognostic ability and oral size perception of patients with burning mouth syndrome is not significantly different from normal subjects (Jacobs _et al_. 1998).
### Receptor activation during oral stereognosis
To assess the stereognostic ability, test pieces are inserted in the oral cavity and in most experimental set-ups, free manipulation of the test pieces is allowed. The latter implies activation of a large number of receptor groups (periodontal, mucosal, muscular, articular, etc.). Since the tip of the tongue is one of the most densely innervated areas of the human body, it plays an important role in stereognosis of objects inserted in the mouth (Jacobs _et al_. 1998). Based on studies involving anesthesia of the tongue, the palate or the absence of teeth, it could be stated that oral stereognostic ability is determined mostly by receptors in the tongue mucosa, the palate, and to a lesser extent the periodontal ligament (Jacobs _et al_. 1998). A major modification to the experimental setup is the insertion of a toothpick in each test piece to eliminate the involvement of lip and tongue receptors, to allow easy handling and standardized placement in between two antagonistic teeth (Jacobs _et al_. 1997) (see Fig. 6-13).
The role of the TMJ receptors is less clear. In fact, in studies on tactile function, an interocclusal thickness of 5 mm and more seems able to activate receptors in the TMJ and the jaw muscles (Jacobs _et al_. 1998, 2002b). In the stereognostic ability tests, pieces are mostly manipulated inside the mouth and seldom kept between two antagonistic teeth, which frequently excludes the need for a mouth opening of 5 mm or even more.
Stereognostic ability testing is not designed to detect specific receptor groups, it rather reflects an overall sensory ability. A good result in a stereognosis test should indicate that the subject receives full and accurate information about what is going on in the mouth. Even if manipulation is allowed to identify the test piece, identification itself is a sensory rather than a motor accomplishment (Jacobs _et al_. 1998). It is an indicator of functional sensibility including synthesis of numerous sensory inputs in higher brain centers.
# From periodontal tactile function to peri-implant osseoperception
## Tooth extraction considered as sensory amputation
Sensory feedback plays an essential role in fine tuning of limb motor control. Thus, it is clear that amputation of a limb will not only involve destruction of an important part of the peripheral feedback pathways, but also hamper fine motor control. Conventional socket prostheses do not carry enough sensory information to restore the necessary natural feedback pathways for motor function (Jacobs _et al_. 2000). Comparable observations can be made after extraction of teeth. The periodontal ligament harbors a very rich innervation, carrying refined mechanoreceptive properties by an intimate contact between collagen fibres and Ruffini-like endings (Lambrichts _et al_. 1992) (see Fig. 6-8). The role of periodontal neural feedback is well known (Jacobs & van Steenberghe 1994, 2006). After extraction of teeth, however, the periodontal neural feedback pathway may be damaged as periodontal ligament receptors are eliminated. Dentures can be compared to socket prostheses and are not able to fully compensate for normal tooth loading and force transfer. The peripheral feedback mechanisms are more limited since the mucosal mechanoreceptor function is less efficient than the periodontal ligament function. Consequently, oral function remains impaired (Jacobs & van Steenberghe 1991, 1994, 2006; Jacobs _et al_. 1992; Mericske-Stern 1994; Mericske-Stern _et al_. 1995).
It has been assumed that by anchoring prosthetic limbs directly to the bone via osseointegrated implants, partial sensory substitution can be realized (Jacobs 1998; Jacobs _et al_. 2000). If the feedback pathway can be restored, such concept of bone-anchored limb prostheses would signify an important step towards global integration of a prosthesis in the body. Amputees and edentulous patients, rehabilitated with a bone-anchored prosthesis, report a specific feeling around endosseous implants. Psychophysical threshold determination studies confirm that patients may perceive mechanical stimuli exerted on osseointegrated implants in the bone. This phenomenon introduces discussion of which receptor groups are responsible for this perception phenomenon. New insights and more objective non-invasive approaches may help to clarify this question. It seems attractive to explain the observed tactile sensitivity of endosseous implants, coined osseoperception, by the surrounding endosseous and periosteal neural endings. Neurophysiological evidence can be found in some experiments evoking TSEPs upon implant stimulation. By triggering sweeps in the electroencephalogram by means of an implant-stimulation device and by cumulating and advanced analysis of the sweeps, one can observe significant waves (Fig. 6-14). The experiments indicate that endosseous and/or periosteal receptors around the implants convey the sensation (Van Loven _et al_. 2000). These mechanisms could be the basis of implant-mediated sensory–motor control, which may have important clinical implications, because more natural functioning with implant-supported prostheses can be attempted. It may thus open the gate for global integration of implants in the human body.
Fig. 6-14 (a) Electrical stimulation of an osseointegrated implant using a ring-shaped stimulation electrode fixed by a coverscrew. (b) Trigeminal evoked potential elicited by electrical stimulation of an osseointegrated implant in the mandible. A similar potential could be maintained after topical anesthesia of the peri-implant soft tissues indicating that the trigeminal potentials originated from other peri-implant structures such as bone and periosteal receptors.
## Histological background of peri-implant osseoperception
Tooth extraction results in damage to a large number of sensory nerve fibres and corresponds to an amputation, where the target organ and peripheral nervous structures have been destroyed (Mason & Holland 1993). After extraction of teeth, the myelinated fibre content of the inferior alveolar nerve is reduced by 20% (Heasman 1984). This finding indicates that fibers originally innervating the tooth and periodontal ligament are still present in the inferior alveolar nerve. Linden and Scott (1989) succeeded in stimulating nerves of periodontal origin in healed extraction sockets, which implies that some nerve endings remain functional. Nevertheless, most of the surviving mechanoreceptive neurons represented in the mesencephalic nucleus may lose some functionality (Linden & Scott 1989). These experiments have been the basis for a further and long-lasting debate on the presence and potential function of sensory nerve fibers in the bone and peri-implant environment. Histologic evidence indicates that there may be some re-innervation around osseointegrated implants (Wang _et al_. 1998; Lambrichts 1998) Figs. 6-15, 6-16. Indeed, it has been shown that endosseous implants may lead to degeneration of surrounding neural fibers by surgical trauma. Soon however, sprouting of new fibers is observed and the number of free nerve endings close to the bone–implant interface gradually increases during the first weeks of healing (Wada _et al_. 2001). A more recent study in the dog has succeeded in partially regenerating the periodontal ligament on an implant surface (Jahangiri _et al_. 2005). Whether such regeneration might also induce restoration of the peripheral feedback pathway needs further verification.
**Fig. 6-15** A reconstruction of histologic slices indicating the regeneration of nerve tissue 3 months after implantation of a cylindrical oral implant in a dog's jaw bone. M = mesial; D = distal. (Reprinted from Wang _et al_. 1998, Copyright 2006, with permission from R. Jacobs, editor-publisher of _Osseoperception_ , Dept of Periodontology, KU Leuven.)
**Fig. 6-16** Bone–implant specimen, obtained from a cat model, subjected to a light microscopic and immunohistochemical detection of neural structures. Elaborate neural structures in the bone trabeculae are seen surrounding the titanium implant. This histologic slice visualizes the titanium implant–bone tissue, with a bundle of myelinated nerve fibers in the bone trabeculum. (Reprinted from Lambrichts _et al_. 1998, Copyright 2006, with permission from Ivo Lambrichts, University of Hasselt and R. Jacobs, editor-publisher of _Osseoperception_ , Dept of Periodontology, KU Leuven.)
On the other hand, existing mechanoreceptors in the periosteum may also play a role in tactile function upon implant stimulation. It is evident that oral implants offer another type of loading and force transfer than teeth, considering an intimate bone–implant contact with elastic bone properties instead of the characteristic viscoelasticity of the periodontal ligament. Thus, forces applied to osseointegrated implants are directly transferred to the bone and bone deformation may lead to receptor activation in the peri-implant bone and the neighboring periosteum.
### Cortical plasticity after tooth extraction
The cortex of the brain reveals a somatotopically ordered representational map with the teeth, gingiva, and jaws (Penfield & Rasmussen 1950). In this so-called sensory homunculus by Penfield, the representation of teeth in the postcentral gyrus of the primary somatosensory cortex is located superior to that of the tongue and inferior to that of the lip. This could be confirmed in a recent fMRI study, although this clear distinction between representation of tongue, lip, and teeth disappeared in the more caudal portions of the postcentral gyrus (Miyamoto _et al_. 2006). This established overlap of sensory representations might assume converging input from various oral structures including teeth. This finding could be relevant to the dedicated but intricate sensory information processing for modulation and coordination of oral motor function.
Recent findings on neuroplasticity of somatosensory and motor processes are also applicable in the orofacial region (Sessle 2006). After limb amputation or extraction, the regions of the cortex deprived of a target acquire new targets. Remodeling takes place at a (sub) cortical level. The potential cortical adaptation and/or plasticity that might occur after tooth extraction and implant placement has not yet been fully explored. A most interesting study was recently carried out on mole-rats, in which lower incisors were extracted (Henry _et al_. 2005). Five to eight months afterwards, functional MRI analysis yielded that the orofacial representation in S1 was considerably reorganized. Neurons in the cortical lower tooth representation were responsive to tactile inputs from surrounding orofacial structures. This study may indicate that cortical representation of teeth may significantly restructure after tooth loss. Unfortunately, until now, similar evidence in humans has not yet been produced. However, a very recent fMRI study by Lundborg _et al_. (2006) demonstrates that upon tactile stimulation of an osseointegrated prosthetic thumb, the primary somatosensory cortex is bilaterally activated in an area corresponding to that of the hand. As one would only expect activation of the contralateral cortex for healthy thumb stimulation, the presence of bilateral cortical activation may be explained by some compensatory mechanism, recruiting additional sensory areas after amputation (Lundborg _et al_. 2006). This recent finding confirms once more that osseoperception and cortical plasticity may truly exist. At present, the central neural pathways and neural characteristics contributing to implant-mediated sensory motor control remain unclear. Future research should therefore try to visualize cortical plasticity after tooth extraction and further functional rehabilitation with implants in man. It should be considered that an immediate extraction and implant rehabilitation protocol might induce different cortical remodeling than a traditional two-stage implant rehabilitation protocol. An interesting phenomenon with respect to sensory–motor integration of osseointegrated implants, may be the so-called phantom tooth (after extraction) or phantom limb (after amputation), allowing perception of lost body parts (Jacobs _et al_. 2002c). In fact, it could be assumed that such a phantom feeling of the lost limb may overlap with or enforce the feeling of a bone-anchored prosthetic limb (Jacobs 1998). In this way, phantom sensations might contribute to physiological integration of a bone-anchored prosthesis in the human body.
If neuroplasticity after amputation and osseointegration could be fully unravelled, it might be considered during treatment to optimize adaptation to oral rehabilitation and implant placement (Feine _et al_.2006).
### From osseoperception to implant-mediated sensory motor interactions
During the last few decades, millions of patients have been rehabilitated by means of osseointegrated implants. Even though part of the peripheral feedback mechanism is lost after tooth extraction, edentulous patients seem to function quite well, especially when rehabilitated with a prosthesis retained by or anchored to osseointegrated implants (Jacobs 1998). These findings correspond well to the observation in amputees rehabilitated with a bone-anchored prosthesis rather than a socket prosthesis. During skeletal reconstruction, psychophysical testing reveals an improved tactile and vibrotactile capacity with an osseointegrated implant and a bone-anchored prosthetic limb (Fig. 6-17). Furthermore, both edentulous patients and amputees seem to report an improved awareness and special feeling with the implant-supported prosthesis, allowing a partial restoration of the peripheral feedback pathway with a hypothesized potential representation of the artifical limb feeling in the sensory cortex (Lundborg _et al_. 2006). If that could be confirmed, osseointegrated implants in the jaw or other skeletal bones might contribute to implant-mediated sensory–motor control allowing physiological integration of the implant in the human body, resulting in more natural functioning (Jacobs & van Steenberghe 2006).
Fig. 6-17 Psychophysical test set-up using a patient-controlled remote control for a vibrotactile stimulator fixed to a radial (a) and femoral (b) osseointegrated implant. This particular test set-up yields superior perception for implants and bone-anchored prosthetic limbs compared to socket prostheses (Jacobs _et al_. 2000).
## Clinical implications of implant-deviated sensory motor interaction
Psychophysical testing on various bone-anchored prostheses confirms an improved tactile function leading to a better physiological integration of the limb. If perception upon implant stimulation is working well, peripheral feedback mechanisms may be restored and help fine tuning of motor control. This implant-mediated sensory–motor interaction may thus help to achieve a more natural function with the bone-anchored prosthesis (Jacobs 1998; Jacobs _et al_. 2000). Osseointegrated thumb prostheses even allow patients to perform the activities of daily life without any problem, which can be attributed to bone anchorage and bilateral cortical representation after prosthesis stimulation (Lundborg _et al_. 1996, 2006).
Considering the increased tactile threshold level for oral implant stimulation, one should, however, consider a few clinical implications. During rehabilitation by means of implant-supported prostheses, dentists should not rely on the patient's perception of occlusion. In this respect, one should also be aware of gradually increasing tactile function during the healing period after implant placement. This may be of particular importance when dealing with immediate loading protocols. To avoid any overloading related to suboptimal feedback mechanisms, patients should be encouraged to limit chewing forces by soft food intake during the healing period. Furthermore, parafunctional habits, such as grinding or clenching, might have a negative impact during the implant healing phase, but more research is needed to confirm this assumption (Lobbezoo _et al_. 2006). Until further evidence is collected, bruxism may be considered as a relative contraindication for immediate loading protocols (Glauser _et al_. 2001).
# Conclusions
Sensory feedback plays an essential role in fine tuning of jaw and limb motor control. Periodontal mechanoreceptors, and more specifically those located in the periodontal ligament, are extremely sensitive to external mechanical stimuli. These receptors play the key role in tactile function of teeth, yielding detection thresholds of about 20 μm of thickness in between antagonistic teeth and 1–2 g upon tooth loading. Their sensory characteristics and the related peripheral feedback make the periodontal ligament receptors dedicated for fine tuning of masticatory and other oral motor behaviors.
It is clear that any condition that influences periodontal mechanoreceptors may also alter the sensory feedback pathway, and thus influence tactile function and modulation of jaw motor control (e.g. periodontal breakdown, bruxism, re-implantation, anesthesia). After extraction of teeth, the periodontal ligament has disappeared and so have its mechanoreceptors. After placement of oral implants, detection thresholds are increased to at least 50–100 μm of thickness and 50–100 g upon tooth loading.
Surprisingly enough, patients rehabilitated by means of osseointegrated implants seem to function quite well and/or sense better. In accordance with this, amputees rehabilitated with a lower limb prosthesis anchored to the bone by means of an osseointegrated implant, have reported that they could recognize the type of soil they were walking on, while patients with a bone-anchored thumb prosthesis have a cortical representation and thus conscious perception of their digit.
The underlying mechanism of this so-called "osseoperception" phenomenon remains a matter of debate, but is assumed that mechanoreceptors in the peri-implant bone and neighboring periosteum may be activated upon implant loading. Histological, neurophysiological and psychophysical evidence of osseoperception has been collected, making the assumption more likely that a proper peripheral feedback pathway can be restored when using osseointegrated implants. This implant-mediated sensory–motor control may have important clinical implications, because a more natural functioning with implant-supported prostheses can be attempted. It may open doors for physiological and psychophysical integration of implants in the human body.
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# Part 2: Epidemiology
7 Epidemiology of Periodontal Diseases,
_Panos N. Papapanou and Jan Lindhe_
# Chapter 7
# Epidemiology of Periodontal Diseases
Panos N. Papapanou and Jan Lindhe
* * *
Introduction
Methodological issues
Examination methods – index systems
Critical evaluation
Prevalence of periodontal diseases
Introduction
Periodontitis in adults
Periodontal disease in children and adolescents
Periodontitis and tooth loss
Risk factors for periodontitis
Introduction – definitions
Non-modifiable background factors
Environmental, acquired, and behavioral factors
Periodontal infections and risk for systemic disease
Atherosclerosis – cardiovascular/cerebrovascular disease
Pregnancy complications
Diabetes mellitus
* * *
# Introduction
The term epidemiology is of Hellenic origin; it consists of the preposition "epi", which means "among" or "against", and the noun "demos" which means "people". As denoted by its etymology, epidemiology is defined as "the study of the distribution of disease or a physiological condition in human populations and of the factors that influence this distribution" (Lilienfeld 1978). A more inclusive description by Frost (1941) emphasizes that "epidemiology is essentially an inductive science, concerned not merely with describing the distribution of disease, but equally or more with fitting it into a consistent philosophy". Thus, the information obtained from an epidemiologic investigation should extend beyond a mere description of the distribution of the disease in different populations ( _descriptive_ epidemiology). It should be further expanded to (1) elucidate the etiology of a specific disease by combining epidemiologic data with information from other disciplines such as genetics, biochemistry, microbiology, sociology, etc. ( _etiologic_ epidemiology); (2) evaluate the consistency of epidemiologic data with hypotheses developed clinically or experimentally ( _analytical_ epidemiology); and (3) provide the basis for developing and evaluating preventive procedures and public health practices ( _experimental/intervention_ epidemiology).
Based on the above, epidemiological research in periodontology must (1) fulfill the task of providing data on the _prevalence_ of periodontal diseases in different populations, i.e. the frequency of their occurrence, as well as on the _severity_ of such conditions, i.e. the level of occurring pathologic changes; (2) elucidate aspects related to the _etiology_ and the _determinants of development_ of these diseases ( _causative_ and _risk_ factors); and (3) provide documentation concerning the effectiveness of preventive and therapeutic measures aimed against these diseases on a population basis.
# Methodological issues
## Examination methods – index systems
Examination of the periodontal status of a given individual includes clinical assessments of inflammation in the periodontal tissues, recording of probing depths and clinical attachment levels and radiographic assessments of supporting alveolar bone. A variety of index systems for the scoring of these parameters has been developed over the years. Some of these systems were designed exclusively for examination of patients in a dental practice set-up, while others were developed in order to be utilized in epidemiologic research. The design of the index systems and the definition of the various scores inevitably reflects the knowledge of the etiology and pathogenesis of periodontal disease at the time these systems were introduced, as well as concepts related to the current therapeutic approaches and strategies. This section will not provide a complete list of all available scoring systems, but rather give a brief description of a limited number of indices that are either currently used or are likely to be encountered in the recent literature. For description of earlier scoring systems and a historical perspective of their development, the reader is referred to Ainamo (1989).
### Assessment of inflammation of the periodontal tissues
Presence of inflammation in the marginal portion of the gingiva is usually recorded by means of probing assessments, according to the principles of the Gingival Index outlined in the publication by Löe (1967). According to this system, entire absence of visual signs of inflammation in the gingival unit is scored as 0, while a slight change in color and texture is scored as 1. Visual inflammation and bleeding tendency from the gingival margin right after a periodontal probe is briefly run along the gingival margin is scored as 2, while overt inflammation with tendency for spontaneous bleeding is scored as 3. A parallel index for scoring plaque deposits (Plaque Index) in a scale from 0 to 3 (Silness & Löe 1964) was introduced, according to which absence of plaque deposits is scored as 0, plaque disclosed after running the periodontal probe along the gingival margin as 1, visible plaque as 2 and abundant plaque as 3. Simplified variants of both the Gingival and the Plaque Index (Ainamo & Bay 1975) have been extensively used, assessing presence/absence of inflammation or plaque, respectively, in a binomial fashion ( _dichotomous scoring_ ). In such systems, bleeding from the gingival margin and visible plaque score 1, while absence of bleeding and no visible plaque score 0.
Bleeding after probing to the base of the probeable pocket (Gingival Sulcus Bleeding Index) has been a common way of assessing presence of subgingival inflammation (Mühlemann & Son 1971). In this dichotomous registration, 1 is scored in cases where bleeding emerges within 15 seconds after probing. Presence/absence of bleeding on probing to the base of the pocket is increasingly tending to substitute the use of the Gingival Index in epidemiologic studies.
### Assessment of loss of periodontal tissue support
One of the early indices providing indirect information on the loss of periodontal tissue support was the Periodontal Index (PI) developed in the 1950s by Russell (1956), and until the 1980s it was the most widely used index in epidemiologic studies of periodontal disease. Its criteria are applied to each tooth and the scoring is as follows: a tooth with healthy periodontium scores 0, a tooth with gingivitis around only part of the tooth circumference scores 1, a tooth with gingivitis encircling the tooth scores 2, pocket formation scores 6, and loss of function due to excessive tooth mobility scores 8. Due to the nature of the criteria used, the PI is a reversible scoring system, i.e. after treatment a tooth or an individual can have the score lowered or reduced to 0.
In contrast to the PI system, the Periodontal Disease Index (PDI), developed by Ramfjord (1959), is a system designed to assess _destructive_ disease; it measures _loss of attachment_ instead of _pocket depth_ and is, therefore, an irreversible index. The scores, ranging from 0–6, denote periodontal health or gingivitis (scores 0–3) and various levels of attachment loss (scores 4–6).
In contemporary epidemiologic studies, loss of periodontal tissue support is assessed by measurements of pocket depth and attachment level. Probing pocket depth (PPD) is defined as the distance from the gingival margin to the location of the tip of a periodontal probe inserted in the pocket with moderate probing force. Likewise, probing attachment level (PAL) or clinical attachment level (CAL) is defined as the distance from the cemento-enamel junction (CEJ) to the location of the inserted probe tip. Probing assessments may be carried out at different locations of the tooth circumference (buccal, lingual, mesial or distal sites). The number of probing assessments per tooth has varied in epidemiologic studies from two to six, while the examination may either include all present teeth ( _full-mouth_ ) or a subset of _index_ teeth ( _partial-mouth_ examination).
Carlos _et al_. (1986) proposed an index system which records loss of periodontal tissue support. The index was denoted the Extent and Severity Index (ESI) and consists of two components ( _bivariate_ index) : (1) the _Extent_ , describing the proportion of tooth sites of a subject examined showing signs of destructive periodontitis, and (2) the _Severity_ , describing the amount of attachment loss at the diseased sites, expressed as a mean value. An attachment loss threshold of >1 mm was set as the criterion for a tooth site to qualify as affected by the disease. Although arbitrary, the introduction of a threshold value serves a dual purpose: (1) it readily distinguishes the fraction of the dentition affected by disease at levels exceeding the error inherent in the clinical measurement of attachment loss, and (2) it prevents unaffected tooth sites from contributing to the individual subject's mean attachment loss value. In order to limit the assessments to be performed, a partial examination comprising the mid-buccal and mesiobuccal aspects of the upper right and lower left quadrants was recommended. It has to be emphasized that the system was designed to assess the cumulative effect of destructive periodontal disease rather than the presence of the disease itself. The bivariate nature of the index facilitates a rather detailed description of attachment loss patterns: for example an ESI of (90, 2.5) suggests a generalized but rather mild form of destructive disease, in which 90% of the tooth sites are affected by an average attachment loss of 2.5 mm. In contrast, an ESI of (20, 7.0) describes a severe, localized form of disease. Validation of various partial extent and severity scoring systems against the full-mouth estimates has been also performed (Papapanou _et al_. 1993).
### Radiographic assessment of alveolar bone loss
The potential and limitations of intraoral radiography to describe loss of supporting periodontal tissues were reviewed by Lang and Hill (1977) and Benn (1990). Radiographs have been commonly employed in cross-sectional epidemiologic studies to evaluate the result of periodontal disease on the supporting tissues rather than the presence of the disease itself and are thought to provide valid estimates of the extent and severity of destructive periodontitis (Pitiphat _et al_. 2004). Radiographic assessments have been particularly common as screening methods for detecting subjects suffering from juvenile periodontitis as well as a means for monitoring periodontal disease progression in longitudinal studies. Assessments of bone loss in intraoral radiographs are usually performed by evaluating a multitude of qualitative and quantitative features of the visualized interproximal bone, e.g. (1) presence of an intact lamina dura, (2) the width of the periodontal ligament space, (3) the morphology of the bone crest ("even" or "angular" appearance), and (4) the distance between the CEJ and the most coronal level at which the periodontal ligament space is considered to retain a normal width. The threshold for bone loss, i.e. the CEJ – bone crest distance considered to indicate that bone loss has occurred, varies between 1 and 3 mm in different studies. Radiographic data are usually presented as (1) mean bone loss scores per subject (or group of subjects), and (2) number or percentage of tooth surfaces per subject (or group of subjects) exhibiting bone loss exceeding certain thresholds. In early studies, bone loss was frequently recorded using "ruler" devices, describing the amount of lost or remaining bone as a percentage of the length of the root or the tooth (Schei _et al_. 1959; Lavstedt _et al_. 1975).
### Assessment of periodontal treatment needs
An index system aimed at assessing the need for periodontal treatment in large population groups was developed, at the initiative of the World Health Organization (WHO), by Ainamo _et al_. (1982). The principles of the Community Periodontal Index for Treatment Needs (CPITN) can be summarized as follows:
1. The dentition is divided into six _sextants_ (one anterior and two posterior tooth regions in each dental arch). The treatment need in a sextant is recorded when two or more teeth, not intended for extraction, are present. If only one tooth remains in the sextant, the tooth is included in the adjoining sextant.
2. Probing assessments are performed either around all teeth in a sextant or around certain index teeth (the latter approach has been recommended for epidemiologic surveys). However, only the most severe measure in the sextant is chosen to represent the sextant.
3. The periodontal conditions are scored as follows:
* _Code 1_ is given to a sextant with no pockets, calculus or overhangs of fillings but in which bleeding occurs after gentle probing in one or several gingival units.
* _Code 2_ is assigned to a sextant if there are no pockets exceeding 3 mm, but in which dental calculus and plaque-retaining factors are seen or recognized subgingivally.
* _Code 3_ is given to a sextant that harbors 4–5 mm deep pockets.
* _Code 4_ is given to a sextant that harbors pockets 6 mm deep or deeper.
4. The treatment needs are scores based on the most severe code in the dentition as TN 0, in case of gingival health, TN 1 indicating need for improved oral hygiene if code 1 has been recorded, TN 2 indicating need for scaling, removal of overhangs, and improved oral hygiene (codes 2 + 3) and TN 3 indicating complex treatment (code 4).
Although not designed for epidemiological purposes, this index system has been extensively used worldwide, and CPITN-based studies have often been the exclusive source of epidemiologic information on periodontal conditions, particularly from developing countries. A later modification of the index, termed Community Periodontal Index (CPI; WHO 1997), places more emphasis on the assessment of periodontal conditions rather than the assessment of periodontal treatment needs. A substantial amount of data generated by the use of CPITN/CPI have been accumulated in the WHO Global Oral Data Bank (Miyazaki _et al_. 1992; Pilot & Miyazaki 1994 Petersen _et al_. 2005; Petersen & Ogawa 2005) and are accessible electronically through servers maintained at the Niigata University, Japan (WHO Collaborating Centre) and University of Malmö, Sweden (WHO Collaborating Centre).
### Critical evaluation
A fundamental prerequisite for any meaningful comparative assessment of prevalence is a valid and accurate definition of the disease under investigation. Unfortunately, no uniform criteria have been established in periodontal research for this purpose. Epidemiologic studies have employed a wide array of symptoms, including gingivitis, probing depth, clinical attachment level, and radiographically assessed alveolar bone loss, in an inconsistent manner. Considerable variation characterizes the threshold values employed for defining periodontal pockets as "deep" or "pathologic", or the clinical attachment level and alveolar bone scores required for assuming that "true" loss of periodontal tissue support has, in fact, occurred. In addition, the number of "affected" tooth surfaces required for assigning an individual subject as a "case", i.e. as suffering from periodontal disease, has varied. These inconsistencies in the definitions inevitably affect the figures describing the distribution of the disease (Papapanou 1996; Kingman & Albandar 2002) and, consequently, the identification of risk factors (Borrell & Papapanou 2005). A review of the literature charged with the task of comparing disease prevalence or incidence in different populations or at different time periods must first be confronted with the interpretation of the figures reported and literally "decode" the published data in order to extract relevant information that is amenable to interstudy comparisons. These problems have been addressed in the literature and two specific aspects have attracted special attention, namely (1) the ability of partial recording methodologies to reflect full-mouth conditions, and (2) the use of the CPITN system in epidemiological studies of periodontal disease.
There is little doubt that an optimal examination of periodontal conditions should include circumferential probing assessments around all teeth. Nevertheless, the majority of epidemiological studies have, for practical reasons, employed partial recording methodologies. The rationale for the use of partial examinations has been the assumption that (1) the time required for the performance of a partial survey, and consequently its cost, is significantly decreased, and (2) the amount of information lost is kept to a minimum, provided that the examined segments adequately reflect the periodontal condition of the entire dentition. However, attempts to quantify accurately the amount of information lost through the different partial recording systems made by several investigators (Hunt 1987; Kingman _et al_. 1988; Hunt & Fann 1991; Stoltenberg _et al_. 1993a; Diamanti-Kipioti _et al_. 1993; Eaton _et al_. 2001; Susin _et al_. 2005a) have revealed that the discrepancy between the findings obtained by means of partial and full-mouth surveys may be substantial. These studies have typically employed full-mouth data for a series of periodontal parameters and compared them with the values obtained by assessments performed at a subset of teeth or tooth surfaces. Their results suggest that:
1. High correlations between full-mouth and half-mouth attachment loss scores should be expected in adult populations, due to the apparent symmetry of periodontal conditions around the midline.
2. The performance of a partial recording system is directly dependent on the actual prevalence of periodontal disease in the population in question and, consequently, on the age of the subjects examined; the less frequent the disease in the population and the lower the number of sites that are affected in each individual mouth, the more difficult it becomes for the partial examination to detect the periodontal lesions.
3. A full-mouth examination provides the best means of accurately assessing the prevalence and severity of periodontal disease in a population.
The use of the CPITN system in epidemiological studies of periodontal disease was critically evaluated in a number of publications (Grytten & Mubarak 1989; Holmgren & Corbet 1990; Schürch _et al_. 1990; Butterworth & Sheiham 1991; Baelum _et al_. 1993a,b, 1995; Benigeri _et al_. 2000). At the time the system was designed, the conversion of periodontal health to disease was thought to include a continuum of conditions, ranging from an inflammation-free state developing through gingivitis (bleeding), calculus deposition, shallow and deep pocket formation to progressive, destructive disease. The treatment concepts were based on the assumption that probing depths determined the choice between non-surgical and more complicated, surgical periodontal therapy. It should also be remembered that this particular index was clearly intended for screening large population groups in order to determine treatment needs and to facilitate preventive and therapeutic strategies and not for describing prevalence and severity of periodontal disease. In view of the revised, contemporary views on the pathogenesis and treatment of the periodontal diseases, studies have questioned the suitability of the CPITN for such purposes. For example, Butterworth and Sheiham (1991) addressed the suitability of CPITN to record changes in periodontal conditions and examined patients of a general dental practice before and after periodontal therapy. Despite a substantial improvement in the state of health of the periodontal tissues, assessed through gingivitis, calculus, and pocketing scores, the CPITN scores were only marginally improved. In a rural Kenyan subject sample, Baelum _et al_. (1993b) examined and refuted the validity of the hierarchical principle of the CPITN, i.e. the assumptions that a tooth with calculus is assumed to be positive also for bleeding on probing, and that a tooth with moderately deep or deep pockets is assumed to be positive for both calculus and bleeding. In a companion paper, results from a full-mouth examination were compared with those generated by the use of the ten index teeth recommended by the WHO for surveys of adults (Baelum _et al_. 1993a). The study revealed that the partial CPITN methodology seriously underestimates the more severe periodontal conditions both in terms of prevalence and severity, since it fails to detect a substantial proportion of subjects with periodontal pockets. Finally, an examination of the relationship between CPITN findings and the prevalence and severity of clinical attachment loss, demonstrated that the CPITN scores do not consistently correlate with attachment loss measures, but tend to overestimate prevalence and severity among younger subjects while they underestimate such parameters in elderly populations (Baelum _et al_. 1995). The above data call for caution in the interpretation of epidemiologic studies based on the CPITN/CPI systems.
# Prevalence of periodontal diseases
## Introduction
The currently used classification of periodontal diseases was introduced by the 1999 International Workshop for a Classification of Periodontal Diseases and Conditions (Anon 1999) and encompasses eight main categories, namely:
I| Gingival diseases
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II| Chronic periodontitis
III| Aggressive periodontitis
IV| Periodontitis as a manifestation of systemic diseases
V| Necrotizing periodontal diseases
VI| Abscesses of the periodontium
VII| Periodontitis associated with endodontic lesions
VIII| Developmental or acquired deformities and conditions.
Since the current nomenclature has been in use for less than a decade, a substantial part of the existing literature on the prevalence and extent of periodontal diseases in various populations is still based on earlier classification systems. Inevitably, the following review of epidemiologic studies uses data stemming from publications employing both the earlier and the current diagnostic systems. Although the current classification no longer employs the individual subject's age as a primary determinant of diagnosis, the descriptive epidemiologic findings have still been grouped in the text below according to age, in order to facilitate data extraction from studies using inconsistent terminologies.
### Periodontitis in adults
An epidemiologic survey performed during the 1950s in India used assessments of alveolar bone height to distinguish between gingivitis and destructive periodontal disease in a sample involving 1187 dentate subjects (Marshall-Day _et al_. 1955). The authors reported (1) a decrease in the percentage of subjects with "gingival disease without any bone involvement" with increasing age concomitant with an increase in the percentage of subjects with "chronic, destructive periodontal disease", and (2) a 100% occurrence of destructive periodontitis after the age of 40 years. Findings from other epidemiologic studies from the same period verified a high prevalence of destructive periodontal disease in the adult population in general, and a clear increase in disease prevalence with age. In the 1960s, Scherp (1964) reviewed the available literature on the epidemiology of periodontal disease and concluded that (1) periodontal disease appears to be a major, global public health problem affecting the majority of the adult population after the age of 35–40 years, (2) the disease starts as gingivitis in youth, which, if left untreated, leads to progressive destructive periodontitis, and (3) more than 90% of the variance of the periodontal disease severity in the population can be explained by age and oral hygiene. These notions, based on established concepts on the pathogenesis of periodontal disease of that time, dominated the periodontal literature until the late 1970s.
Studies performed during the 1980s provided a more thorough description of the site-specific features of periodontal disease and the high variation in periodontal conditions between and within different populations. Contrary to what was customary until then, the prevalence issue was no longer addressed through a mere assignment of individuals to a "periodontitis-affected" or a "disease-free" group, based on presence or absence of attachment or alveolar bone loss. Instead, studies began to unravel details concerning the _extent_ to which the dentition was affected by destructive disease (i.e. the percentage of tooth sites involved), and the _severity_ of the defects (expressed through the magnitude of the tissue support lost due to the disease). The traditional description of pocket depth and attachment loss scores through _subject mean values_ was soon complemented by _frequency distributions_ , revealing percentages of tooth sites exhibiting probing depth or attachment level of varying severity. Such an additional analysis appeared necessary after it became clear that mean values offer a crude description of periodontal conditions and fail to reflect the variability in the severity of periodontal disease within and between individuals. In an article presenting different methods of evaluating periodontal disease data in epidemiological research, Okamoto _et al_. (1988) proposed the use of _percentile plots_ in the graphic illustration of attachment loss data. As exemplified by Fig. 7-1, such plots make it possible to illustrate simultaneously both the proportion of subjects exhibiting attachment loss of different levels and the severity of the loss within the subjects. Similar plots may be produced for other parameters, such as gingivitis, probing depths and gingival recession, and may provide a comprehensive description of both the prevalence and the severity of periodontal disease in a given sample.
Pioneering research by a Danish research group made significant contributions to our current understanding of epidemiologic issues in periodontal research. Baelum _et al_. (1986) described cross-sectional findings on dental plaque, calculus, gingivitis, loss of attachment, periodontal pockets, and tooth loss in a sample of adult Tanzanians aged 30–69 years. Despite the fact that the subjects examined exhibited large amounts of plaque and calculus, pockets deeper than 3 mm and attachment loss of >6 mm occurred at less than 10% of the tooth surfaces. Edentulousness was virtually non-existent, and a very small percentage of subjects had experienced major tooth loss. Of particular interest was the analysis of the distribution of sites within subjects (Fig. 7-2). This analysis revealed that 75% of the tooth sites with attachment loss of ≥7 mm were found in 31% of the subjects, indicating that a subfraction of the sample was responsible for the major part of the observed periodontal breakdown. In other words, advanced periodontal disease was not evenly distributed in the population and not readily correlated to supragingival plaque levels; instead, the majority of the subjects examined exhibited negligible periodontal problems while a limited group was affected by advanced disease.
**Fig. 7-1** Attachment loss in a group of Japanese subjects 50–59 years of age. The mean value of attachment level and the standard deviation are shown in the top of the figure. The x-axis represents the subject percentile and the y-axis represents the percentage of sites in the subjects showing attachment loss of 3, 4, 5, 6, 7, and >7 mm (represented by 8). Subjects with no or only minor signs of attachment loss are reported to the left and subjects with increasing amounts of periodontal destruction are reported to the right of the graph. For example, the median subject (50th percentile), exhibited 5 mm attachment loss at 2%, 4 mm loss at 8%, and 3 mm attachment loss at 25% of its sites. From Okamoto _et al_. (1988), reproduced with permission.
In a study of similar design performed in Kenya, the same investigators analyzed data from 1131 subjects aged 15–65 years and confirmed their earlier observations (Baelum _et al_. 1988a). Poor oral hygiene in the sample was reflected by high plaque, calculus, and gingivitis scores. However, pockets ≥4 mm deep were found in less than 20% of the surfaces and the proportion of sites per individual with deep pockets and advanced loss of attachment revealed a pronounced skewed distribution. The authors suggested that "destructive periodontal disease should not be perceived as an inevitable consequence of gingivitis which ultimately leads to considerable tooth loss" and called for a more specific characterization of the features of periodontal breakdown in those individuals who seem particularly susceptible.
**Fig. 7-2** Cumulative distribution of individuals aged ≥50 years according to the cumulated proportion of surfaces with loss of attachment (L.A.) ≥7 mm. All individuals are arranged according to increasing number of surfaces with L.A. ≥7 mm present in each individual. Thus, individuals with few such surfaces are represented by the dots in the left side of the diagram and those with many such surfaces by dots in the right side. It is seen that 31% (100%–69%) of the individuals account for 75% (100%–25%) of the total number of surfaces with L.A. ≥7 mm present (shaded area). From Baelum _et al_. (1986), reproduced with permission.
At approximately the same time, Löe _et al_. (1986) published their landmark paper that showed that the _progression_ of untreated periodontitis also shared similar features. In a population never exposed to any preventive or therapeutic intervention related to oral diseases in Sri Lanka, an original cohort of 480 male tea-plantation laborers, aged 14–31 years, was initially recruited in 1970, and underwent subsequent follow-up examinations. A total of 161 of subjects were re-examined at the final examination in 1985, essentially generating data on the natural history of periodontal disease between the age of 14 and 46 years. Despite poor plaque control and virtually ubiquitous gingival inflammation in the entire sample, three distinct patterns of progression of periodontitis were observed over the follow-up period, based on interproximal longitudinal attachment loss and tooth mortality rates: one group, comprising approximately 8% of the total, with rapid progression of periodontal disease (RP); another group (approximately 11%) who exhibited no progression (NP) of periodontal disease beyond gingivitis; and a third group between the two extremes (approximately 81%) with moderate progression (MP). The mean loss of attachment in the RP group was 9 mm and 13 mm, at the age of 35 and 45 years, respectively, as opposed to 1 mm and 1.5 mm in the NP group, and 4 mm and 7 mm in the MP group. As a result, the annual rate of longitudinal attachment loss in the RP group varied between 0.1 and 1.0 mm, in the MP group between 0.05 and 0.5 mm, and in the NP group between 0.05 and 0.09 mm. Thus, what this study clearly demonstrated is the huge variability in progression of periodontitis in a seemingly homogeneous population, and suggested that variables other than age, plaque, and gingival inflammatory status are important determinants of periodontal deterioration over time.
Several epidemiological studies have been published in the last two decades, verifying the above principals. In these studies, periodontal disease has been assessed by means of clinical examination of the periodontal tissues (Brown _et al_. 1989, 1990; McFall _et al_. 1989; Stuck _et al_. 1989; Beck _et al_. 1990; Horning _et al_. 1990; Hunt _et al_. 1990; Matthesen _et al_. 1990; Gilbert & Heft 1992; Löe _et al_. 1992; Bagramian _et al_. 1993; Douglass _et al_. 1993; Kiyak _et al_. 1993; Locker & Leake 1993; Slade _et al_. 1993; Weyant _et al_. 1993; Querna _et al_. 1994; Söder _et al_. 1994; Anagnou Vareltzides _et al_. 1996; Oliver _et al_. 1998; Albandar _et al_. 1999; Albandar & Kingman 1999; Schürch & Lang 2004; Susin _et al_. 2004a; Krustrup & Erik Petersen 2006; Thomson _et al_. 2006); radiographic assessments of alveolar bone loss (Papapanou _et al_. 1988; Jenkins & Kinane 1989; Wouters _et al_. 1989; Salonen _et al_. 1991; Diamanti-Kipioti _et al_. 1995); or a combination of clinical and radiographic means (Hugoson _et al_. 1998a, 1992, 2005; Papapanou _et al_. 1990).
Table 7-1 summarizes the design and main findings from a number of cross-sectional studies in adults from geographically divergent areas that involve samples of a relatively large size. Most of the studies focus on assessments of prevalence of "advanced periodontitis", the definition of which is, however, far from identical among the studies, rendering comparisons difficult. Nevertheless, it appears that severe forms of periodontitis affect a minority of the subjects in the industrialized countries, at proportions usually not exceeding 10–15% of the population. The percentage of such subjects increases considerably with age and appears to reach its peak at the age of 50–60 years. The increased tooth loss occurring after this age appears to account for the subsequent decline in prevalence. It is worth pointing out that, among the studies reviewed in Table 7-1, the study employing probing assessments at six sites per tooth around all teeth (Susin _et al_. 2004a) reported the highest prevalence of advanced disease, suggesting that the impact of the methodology used may have been decisive. The interesting issue of disparities in the severity of periodontitis was brought up by Baelum _et al_. (1996). The authors recalculated their own data from a Kenyan (Baelum _et al_. 1988a) and a Chinese (Baelum _et al_. 1988b) adult population to conform with the methods of examination and data presentation utilized in each of six other surveys (from Japan (Yoneyama _et al_. 1988); Norway (Löe _et al_. 1978); New Mexico (Ismail _et al_. 1987); Sri Lanka (Löe _et al_. 1978); and two South Pacific islands (Cutress _et al_. 1982) ). Among the samples included in this analysis, only the Sri Lankan and the South Pacific subjects appeared to suffer a severe periodontal tissue breakdown, while the distribution of advanced disease was strikingly similar in six out of the eight samples, despite marked differences in oral hygiene conditions. Hence, the data failed to corroborate the traditional generalization that the prevalence and severity of periodontitis is markedly increased in African and Asian populations. On the other hand, data from the Third National Health and Nutrition Study (NHANES III; Albandar _et al_. 1999) which examined a large nationally representative, stratified, multistage probability sample in the USA clearly showed that the prevalence of deep pockets and advanced attachment loss was more pronounced in non-Hispanic black people and Hispanics than in non-Hispanic white subjects. This observation was consistent even when several alternative thresholds defining advanced disease were employed. Thus, current evidence suggests that the prevalence of severe periodontitis is not uniformly distributed among various races, ethnicities, or socioeconomic groups (Hobdell 2001).
Table 7-2 summarizes a number of prevalence studies of periodontal disease in elderly subjects. In five studies (Beck _et al_. 1990; Hunt _et al_. 1990; Gilbert & Heft 1992; Locker & Leake 1993; Weyant _et al_. 1993) data on attachment loss have been used to calculate extent and severity index scores (ESI) which appear to be relatively consistent between the surveys. It is evident that attachment loss of moderate magnitude was frequent and widespread in these subject samples; however, severe disease was again found to affect relatively limited proportions of the samples and generally only a limited proportion of teeth per subject. Similar findings were reported in more recent studies carried out in Iowa, USA (Levy _et al_. 2003), Pomerania, Germany (Mack _et al_. 2004), Japan (Hirotomi _et al_. 2002), and Sweden (Holm-Pedersen _et al_. 2006). Interestingly, a significant relationship was reported between advanced periodontitis and other co-morbidities in both institutionalized (Maupome _et al_. 2003) and home-dwelling elderly individuals (Ajwani _et al_. 2003).
The limitations of the findings from studies using the CPITN system were discussed above. However, a substantial part of the available information from the developing countries has been collected by the use of this index. An article providing a summary of almost 100 CPITN surveys from more than 50 countries performed over the period 1981–89 for the age group of 35–44 years was published by Miyazaki _et al_. (1991b). These studies indicate a huge variation in the percentage of subjects with one or several deep (≥6 mm) pockets both between and within different geographic areas. Hence, the percentage of subjects with such pockets ranged between 1 and 74% in Africa (data from 17 surveys), 8 and 22% in North and South America (4 surveys), 2 and 36% in the eastern Mediterranean (6 surveys), 2 and 40% in Europe (38 surveys), 2 and 64% in South-East Asia, and between 1 and 22% in the western Pacific area (17 surveys). The average number of sextants per subject with ≥6 mm deep pockets varied also considerably and ranged between 0 and 2.1 in Africa, 0.1 and 0.4 in America, 0.1 and 0.6 in the eastern Mediterranean, 0.1 and 0.8 in Europe, 0.1 and 2.1 in South-East Asia and between 0 and 0.4 in the western Pacific area. However, it is difficult to assess the extent at which these values reflect true differences in the periodontal conditions given the methodological limitations of the CPITN system.
**Table 7-1** Selected prevalence studies of periodontitis in adults
**Authors/country**| **Sample/methodology**| **Findings**
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Löe _et al_. (1978) Norway/Sri Lanka| Two samples, one comprising 565 Norwegian students and academicians and the other 480 Sri Lankan tea laborers, of ages 16–30+ yrs; assessments of plaque, gingivitis, calculus, PD and AL at the mesial and facial aspects of all teeth| Norwegian group: excellent oral hygiene, negligible amounts of plaque and gingivitis, virtually no deep pockets and minimal attachment loss; mean AL at the age of 30 < 1 mm. Sri Lankan group: poor oral hygiene, abundant plaque and calculus, attachment loss present at the age of 16, increasing with age; mean AL at the age of 30 ≈ 3 mm, a substantial number of teeth with AL of > 10 mm
Baelum _et al_. (1988a) Kenya| A stratified random sample of 1131 subjects, 15–65 yrs; full-mouth assessments of tooth mobility, plaque, calculus, bleeding on probing (BoP), PD and AL| Plaque in 75–95% and calculus in 10–85% of all surfaces; PD ≥ 4 mm in < 20% of the sites; AL of ≥ 1 mm in 10–85% of the sites; the percentage of sites/subject with PD or AL of ≥ 4 mm or ≥ 7 mm conspicuously skewed
Yoneyama _et al_. (1988) Japan| A random sample of 319 subjects, 20–79 years old; full-mouth probing assessments of PD, AL, and gingival recession| 0.2% of the sites in subjects 30–39 years and 1.2% of the sites in subjects 70–79 years had a PD of > 6 mm; AL > 5 mm affected 1% of the sites in the youngest group and 12.4% of the sites in the oldest group; skewed distribution of advanced AL; advanced disease more prevalent and widespread in older ages
Brown _et al_. (1990) USA| A sample of 15 132 subjects, stratified by geographic region, representing 100 million employed adults aged 18–64 years; probing assessments at mesial and buccal sites in one upper and one lower quadrant; mesial assessments performed from the buccal aspect of the teeth; assessments of gingivitis, PD, AL, and gingival recession| 44% of all subjects had gingivitis at an average of 2.7 sites/subject and at < 6% of all sites assessed; pockets 4–6 mm were observed in 13.4% of the subjects at an average of 0.6 sites/person and at 1.3% of all sites assessed; corresponding figures for pockets ≥ 7 mm were 0.6%, 0.01 and 0.03%; AL ≥ 3 mm was prevalent in 44% of the subjects (increasing with age from 16% to 80%) affecting an average of 3.4 sites/subject; corresponding figures for AL ≥ 5 mm were 13% (2–35%) and 0.7 sites/subject
Salonen _et al_. (1991) Sweden| A random sample of 732 subjects, 20–80+ yrs, representing 0.8% of the population a southern geographic region; full-mouth radiographic examination; alveolar bone level expressed as a percentage of the root length (B/R ratio); B/R of ≥ 80% represents intact periodontal bone support| Age group of 20–29 yrs: 38% of the subjects had no sites with B/R < 80% and 8% of the subjects had five or more sites below this threshold; corresponding figures for the age group 50–59 years were 5% and 75%; after the age of 40, women displayed more favorable B/R ratios than men
Hugoson _et al_. (1998a) Sweden| Three random samples of 600, 597, and 584 subjects aged 20–70 years, examined in 1973, 1983, and 1993, respectively; full-mouth clinical and radiographic examination; based on clinical and radiographic findings, the subjects were classified according to severity of periodontal disease in five groups, where group 1 included subjects with close to faultless periodontal tissues and group 5 subjects with severe disease| Edentulism decreased over the 20-year period from 11% to 8% to 5%; percentage distribution of the subjects in the five groups in 1973, 1983, and 1993 respectively, was as follows: G1: 8%/23%/22%, G2: 41%/22%/38%, G3: 47%/41%/27%, G4: 2%/11%/10%, G5: 1%/2%/3%; the increase in the prevalence of subjects with severe disease was apparently due to increase of dentate subjects in older ages
Albandar _et al_. (1999) USA| A nationally representative, multi-stage probability sample comprising 9689 subjects, 30–90 years old (NHANES III study); probing assessments at mesial and buccal sites in one upper and one lower quadrant; mesial assessments performed from the buccal aspect of the teeth; assessments of gingivitis, PD, and location of the gingival margin in relation to the CEJ| Pockets ≥ 5 mm were found in 8.9% of all subjects (7.6% in non-Hispanic white subjects, 18.4% in non-Hispanic black subjects, and 14.4% in Mexican Americans); AL ≥ 5 mm occurred in 19.9% of all subjects (19.9% in non-Hispanic white subjects, 27.9% in non-Hispanic black subjects, and 28.34% in Mexican Americans)
Schürch & Lang (2004) Switzerland| A total of 1318 subjects, randomly selected based on community rosters in seven regions, aged 20–89 years; probing assessments of PD and AL at all present teeth; assessments of plaque and gingivitis at index teeth| 7.1% of the subjects were edentulous; the mean number of present teeth in dentate subjects was 21.6; mean values of probing depth reached a plateau of 3 mm in the age of 49 years; however, but attachment levels increased dramatically after the age of 50 years and paralleled a marked loss of teeth
Susin _et al_. (2004a) Brazil| A sample of 853 dentate individuals, selected by multi-stage probability sampling, aged 30–103 years; full-mouth examination of AL at six sites per tooth| Moderate AL (≥ 5 mm) and advanced AL (≥ 7 mm) occurred in 70% and 52% of the subjects, affecting an average of 36% and 16% of their teeth, respectively; in comparison to 30–39-year-olds, 40–49-year-olds had three-fold increased risk for moderate and 7.4-fold increased risk for advanced AL; corresponding figures for ≥ 50 year olds were 5.9-fold and 25.4-fold, respectively
PD = probing depth; AL = attachment level; CEJ = cemento-enamel junction.
**Table 7-2** Selected prevalence studies of periodontitis in elderly subjects
**Authors/country**| **Sample/methodology**| **Findings**
---|---|---
Baelum _et al_. (1988b) China| 544 persons, aged 60+, from two urban and one rural area of Beijing area; assessments of plaque, calculus, gingivitis, loss of attachment, pocket depth, and tooth mobility| 0–29% edentulous; mean number of teeth 6.9–23.9, depending on age and sex; ≈ 50% of all surfaces with plaque and calculus; 50% of all sites with AL of ≥ 4 mm, < 15% with PD ≥ 4 mm; conspicuously skewed percentage of sites/person with AL of ≥ 7 mm and PD ≥ 4 mm
Locker & Leake (1993) Canada| 907 subjects, aged 50–75+ years, living independently in four communities; probing assessments at mesio-buccal and mid-buccal aspects of all teeth; mid-palatal and mesio-palatal probing assessments in upper molars; 23% of the subjects edentulous; calculation of extent and severity index (ESI) with AL threshold set at ≥ 2 mm; "severe disease": more than four sites with AL ≥ 5 mm and PD ≥ 4 mm at one or more of those sites| 59% of the subjects with PD of ≥ 4 mm, 16% with ≥ 6 mm and 3% with ≥ 8 mm; 86% of the subjects with AL of ≥ 4 mm, 42% with ≥ 6 mm and 16% with ≥ 8 mm; 20% of the subjects with a mean AL of ≥ 4 mm; severe disease at 22% of the subjects; mean ESI: 77, 2.44
Beck _et al_. (1990) USA| 690 community-dwelling adults, age 65+; probing assessments at mesio- and mid-buccal surfaces, all teeth; "advanced disease": four or more sites with AL of ≥ 5 mm and one or more of these sites with PD of ≥ 4 mm| Mean ESI in black people: 78, 4; in white people: 65, 3.1; advanced disease in 46% of the black people and 16% of the white people
Gilbert & Heft (1992) USA| 671 dentate subjects, 65–97 years old, attending senior activity centers; probing assessments at mesial and buccal surfaces of one upper and one lower quadrant; questionnaire data; calculation of ESI| An average of 17.0 teeth/subject; 50.7% of the subjects with most severe mesial pocket of 4–6 mm and 3.4% with pockets ≥ 7 mm; 61.6% with most severe AL of 4.6 mm and 24.2% with AL of ≥ 7 mm; ESI increased with age: 84.8, 3.6 (65–69 years); 88.7, 3.8 (75–79 years); 91.2, 3.9 (85+ years)
Douglass _et al_. (1993) USA| 1151 community-dwelling elders, age 70+ yrs; probing assessments at three or more sites/tooth, all teeth; 57% of the sample female, predominantly white (95%) ; 37.6% edentulous; mean no. of teeth present between 21.5 and 17.9, depending on age| 85% of the subjects with BOP; 66% with 4–6 mm deep pockets affecting an average of 5.3 teeth/subject; 21% with pockets of > 6 mm affecting an average of 2.2 teeth; 39% with AL of 4–6 mm at 6.7 sites/subject and 56% AL of > 6 mm at 2.7 teeth/subject
Kiyak _et al_. (1993) USA| 1063 residents in 31 nursing homes, 72–98 years old; visual inspection of the oral cavity; periodontal status assessed indirectly through registration of intraoral swelling or suppuration, sore or bleeding gums, increased tooth mobility, and poor oral hygiene| 42% of the subjects with remaining natural teeth; 43% of those with sore or bleeding gums, 18% with significant tooth mobility, 6% with intraoral swelling or suppuration and 72% with poor oral hygiene
Weyant _et al_. (1993) USA| 650 long-term residents of nursing home care units, mean age 72 years; probing assessments at mesial and buccal surfaces, all teeth; demographic, oral, and general health data recorded; sample predominantly male and white; calculation of ESI scores| 42% of the sample edentulous; 60% of the subjects with PD of mm at an average of 5.8 sites/person; 3.7% with PD of ≥ 6 mm at < 1 site/person; overall mean mesial ESI: 74, 2.91
Bourgeois _et al_. (1999) France| 603 non-institutionalized elderly, 65–74 years old; stratified sample with respect to gender, place of residence and socioeconomic group; periodontal conditions assessed by means of the CPITN| 16.3% of the sample edentulous; 31.5% of the subjects had pockets ≥ 4 mm; 2.3% had pockets ≥ 6 mm
Pajukoski _et al_. (1999) Finland| 181 hospitalized patients (mean age 81.9 yrs) and 254 home-living patients (mean age 76.9 yrs); periodontal conditions assessed by means of the CPITN| 66.3% of the hospitalized and 42.1% of the non-hospitalized subjects were edentulous; 26% of both the hospitalized and the non-hospitalized subjects had pockets ≥ 6 mm
Levy _et al_. (2003) USA| From a sample of 449 community-dwelling elders, mean age 85 years, 342 (76%) were dentate and 236 were examined with respect to PD and AL at four sites per tooth in all present teeth| 91% of the subjects had one or more site with ≥ 4 mm AL, 45% had one or more site with ≥ 6 mm AL, and 15% one or more site with ≥ 8 mm AL
Mack _et al_. (2004) Germany| 1446 randomly selected subjects aged 60–79 years; per tooth; plaque calculus and BoP were assessed at half-mouth examination of PD and AL at four sites index teeth| 16% of the 60–65 year olds and 30% of the 75–79 year olds were edentulous; among 70–79 year olds, the median BoP was 37.5% in men and 50% in women, the prevalence of PD ≥ 6 mm was 31.8% and 28.5%, and the prevalence of AL ≥ 5 mm 71.9% and 66.9%, respectively
PD = probing depth; AL = attachment level; BoP = bleeding on probing; CEJ = cemento-enamel junction; ESI = Extent and Severity Index; CPITN = Community Periodontal Index of Treatment Needs.
### Periodontal disease in children and adolescents
The form of periodontal disease that affects the _primary_ dentition, the condition formerly termed _prepubertal periodontitis_ , has been reported to appear in both a generalized and a localized form (Page _et al_. 1983). Information about this disease was mainly provided by clinical case reports and no data related to the prevalence and the distribution of the disease in the general population are available. However, a few studies involving samples of children have provided limited data on the frequency with which deciduous teeth may be affected by loss of periodontal tissue support. The criteria used in these studies are by no means uniform, hence the prevalence data vary significantly. In an early study, Jamison (1963) examined by the use of the Periodontal Disease Index the "prevalence of destructive periodontal disease" (indicated by PDI scores >3) in a sample of 159 children in Michigan, USA and reported figures of 27% for 5–7-year-old children, 25% for 8–10-year-olds and 21% for 11–14-year-olds. Shlossman _et al_. (1986) used an attachment level value of ≥2 mm as a cut-off point and reported a prevalence of 7.7% in 5–9-year-olds and 6.1% in 10–14-year-olds in a sample of Pima Indians. Sweeney _et al_. (1987) examined radiographs obtained from 2264 children, aged 5–11 years, who were referred to a University Clinic for routine dental treatment and reported that a distinct radiographic bone loss was evident at one or more primary molars in 19 children (0.8%), 16 of whom were black, 2 Caucasian and 1 Asian.
In contrast, relatively uniform criteria have been used in epidemiologic studies of _aggressive periodontitis_ in young subjects, the condition formerly termed _juvenile periodontitis_ (JP), and particularly the _localized_ form, formerly termed _localized juvenile periodontitis_ (LJP). Typically, a two-stage approach has been adopted in these studies: first, bite-wing radiographs are used to screen for bone lesions adjacent to molars and incisors and then a clinical examination is performed to verify the diagnosis. As illustrated by the data in Table 7-3, the prevalence of localized aggressive periodontitis (LAP) varies in geographically and/or racially different populations. In Caucasians, the disease appears to affect females more frequently than males and the prevalence is low (approximately 0.1%). In other races, and in particular in black subjects, the disease is more prevalent, probably at levels over 1%, and the sex ratio appears to be reversed, since males are affected more frequently than females. Smoking and low socioeconomic status have been confirmed to be associated with aggressive periodontitis in various populations (Lopez _et al_. 2001; Susin & Albandar 2005; Levin _et al_. 2006).
Epidemiological studies of periodontal conditions in adolescents have been also carried out by means of the CPITN system. Miyazaki _et al_. (1991a) presented an overview of 103 CPITN surveys of subjects aged 15–19 years from over 60 countries. The most frequent finding in these groups was the presence of calculus which was much more prevalent in subjects from non-industrialized than industrialized countries. Probing pocket depths of 4–5 mm were present in about two thirds of the populations examined. However, deep pockets (≥6 mm) were relatively infrequent: score 4 quadrants were reported to occur in only ten of the examined populations (in 4 out of 9 examined American samples, 1 out of 16 African, 1 out of 10 eastern Mediterranean, 2 out of 35 European, 2 out of 15 South-East Asian and in none out of 18 western Pacific samples).
The progression pattern of periodontitis in a sample of 167 adolescents in the UK was studied in a 5-year longitudinal study by Clerehugh _et al_. (1990). In this study, 3% of the initially 14-year-olds had loss of attachment of ≥1 mm affecting <1% of their sites. However, at age 19 years, 77% showed a similar level of attachment loss and 31% of their sites were affected. Presence of subgingival calculus at baseline was significantly linked to disease progression. In a study involving a larger sample size in the US, Brown _et al_. (1996) studied a nationally representative sample comprising 14 013 adolescents with respect to the pattern of progression of the disease entity formerly termed _early-onset periodontitis_ , i.e. the kind of periodontitis that occurs in individuals of a young age. Subjects were diagnosed at baseline as free from periodontitis, or suffering from localized aggressive periodontitis (LAP), generalized aggressive periodontitis (GAP), or incidental attachment loss (IAL). Of the individuals diagnosed with localized aggressive periodontitis at baseline, 62% continued to display localized periodontitis lesions 6 years later, but 35% developed a generalized disease pattern. Among the group initially diagnosed as suffering from IAL, 28% developed localized or generalized aggressive periodontitis, while 30% were reclassified in the no attachment loss group. Molars and incisors were the teeth most often affected in all three affected groups. Thus, the study indicated that these three forms of periodontitis may progress in a similar fashion, and that certain cases of localized, aggressive disease may develop into generalized aggressive periodontitis.
**Table 7-3** Selected prevalence studies of localized and generalized aggressive periodontitis (LAP and GAP) in adolescents and young adults
**Authors/country**| **Sample/methodology**| **Findings**
---|---|---
Saxén (1980) Finland| A random sample of 8096 16-year olds; radiographic and clinical criteria (bone loss adjacent to first molars without any obvious iatrogenic factors and presence of pathologic pockets)| Prevalence of LAP 0.1% (eight subjects, five of which were females)
Kronauer _et al_. (1986) Switzerland| A representative sample of 7604 16-year olds; two-step examination (radiographic detection of bone lesion on bite-wing radiographs, clinical verification of presence of pathological pockets)| Prevalence of LAP of 0.1%; 1 : 1 sex ratio
Saxby (1987) UK| A sample of 7266 schoolchildren; initial screening by probing assessments around incisors and first molars; LAP cases diagnosed definitively by full-mouth clinical and radiographic examination| Overall prevalence of LAP of 0.1%, 1 : 1 sex ratio; however, prevalence varied in different ethnic groups (0.02% in Caucasians, 0.2% in Asians and 0.8% in Afro-Caribbeans)
Neely (1992) USA| 1038 schoolchildren 10–12 years old, volunteers in a dentifrice trial; three-stage examination including radiographic and clinical assessments; bite-wing radiographs screened for possible cases; bone loss measurements of the CEJ–bone crest distance of ≥ 2 mm used to identify probable cases; LAP diagnosed clinically as PD of ≥ 3 mm at one or more first permanent molars in absence of local irritants| 117 possible and 103 probable cases identified in step 1 and 2, respectively; out of 99 probable cases contacted, 43 were examined clinically; two cases of LAP could be confirmed in stage 3, yielding a prevalence rate of 0.46%
Cogen _et al_. (1992) USA| 4757 children, age < 15 yrs, from the pool of a children's hospital; retrospective radiographic examination of two sets of bite-wings; LAP diagnosed in case of arc-shaped alveolar bone loss in molars and/or incisors| White people: LAP prevalence 0.3%, female:male ratio 4 : 1; black people: LAP prevalence 1.5%, female : male ratio ≈ 1 : 1; among black LAP cases with available radiographs from earlier examinations, 85.7% showed evidence of bone loss in the mixed dentition and 71.4% in the deciduous dentition
Löe & Brown (1991) USA| National Survey of US children, multi-stage probability sampling representing 45 million schoolchildren; 40 694 subjects, 14–17 years old examined; probing assessments at mesial and buccal sites, all teeth; LAP: ≥ 1 first molar and ≥ 1 incisor or second molar and ≤ 2 cuspids or premolars with ≥ 3 mm AL; GAP: if LAP criteria not met and four or more teeth (of which two or more were second molars, cuspids or premolars) with ≥ 3 mm attachment loss (AL); incidental loss of attachment (ILA) : if neither LAP nor GAP criteria met but one or more teeth with ≥ 3 mm AL; bivariate and multi-variate analysis| Population estimates: LAP 0.53%; GAP 0.13%; ILA 1.61%; altogether 2.27% representing almost 300 000 adolescents; black people at much higher risk for all forms of early-onset disease than whites; males more likely (4.3 : 1) to have GAP than females, after adjusting for other variables; black males 2.9 times as likely to have LAP than black females; white females more likely to have LAP than white males by the same odds
Bhat (1991) USA| A sample of 11 111 schoolchildren, 14–17 years old; probing assessments at mesial and buccal surfaces of all teeth; multi-stage cluster sampling stratified by age, sex, seven geographic regions, and rural or urban residence; not stratified by race or ethnicity| 22% of the children with one or more site with AL of ≥ 2 mm, 0.72% of ≥ 4 mm and 0.04% of ≥ 6 mm; supra- and subgingival calculus in 34% and 23% of the children, respectively
van der Velden _et al_. (1989) The Netherlands| 4565 subjects 14–17 years old examined; randomization among high school students; probing assessments at the mesio- and distofacial surfaces of first molars and incisors; one bacterial sample from the dorsum of the tongue and one subgingival plaque sample from the site with maximal attachment loss obtained from 103 out of the 230 subjects with AL and cultured for identification of _A. actinomycetemcomitans_| Overall, AL occurred in 5% of the sample and was more frequent in males; 16 subjects (0.3%) had one or more site with AL of 5–8 mm; female : male ratio in this group 1.3 : 1; _A. actinomycetemcomitans_ was identified in 17% of the sampled subjects with AL
Lopez _et al_. (1991) Chile| 2500 schoolchildren in Santiago (1318 male, 1182 female), 15–19 years of age; clinical and radiographic assessments; three stage screening: (1) clinical assessments of probing depth at incisors and molars, (2) children with two or more teeth with PD of ≥ 5.5 mm subjected to a limited radiographic examination, and (3) children with alveolar bone loss of ≥ 2 mm invited for a full-mouth clinical and radiographic examination| After screening, 27 subjects had a tentative diagnosis of LAP out of which eight were confirmed (seven female, one male); overall prevalence of LAP 0.32%, 95% confidence limits between 0.22% and 0.42%; LAP significantly more frequent in the low socioeconomic group
Ben Yehouda _et al_. (1991)
Israel| 1160 male Israeli army recruits, aged 18–19 years; panoramic radiography; juvenile periodontitis diagnosed on the basis of bone loss involving ≥ 30% of the root length adjacent to first molars or incisors| Ten recruits (0.86%, 95% CI 0.84–0.88%) had a bone loss pattern consistent with localized juvenile periodontitis
Melvin _et al_. (1991) USA| 5013 military recruits, 17–26 years old; panoramic radiography followed by full-mouth clinical examination; diagnosis of JP if bone loss and attachment loss was greater at first molars and/or incisors than at other teeth| Overall prevalence of JP 0.76%, female : male ratio 1.1 : 1; prevalence in black subjects 2.1%, female: male ratio 0.52 : 1; prevalence in white subjects 0.09%, female : male ratio 4.3 : 1
Tinoco _et al_. (1997) Brazil| 7843 schoolchildren, 12–19 years old; two-stage screening: (1) clinical assessment of PD at first molars, (2) children with one or more tooth with PF ≥ 5 mm examined further; LAP diagnosed if a person with no systemic disease presented with AL > 2 mm at one or more sites with radiographic evidence of bone loss and one or more infrabony defects at molars/incisors| 119 subjects identified at initial screening; 25 confirmed cases of LAP; overall prevalence 0.3%; ethnic origins and gender ratios not reported
Lopez _et al_. (2001) Chile| A random sample of 9162 high school students, 12–21 years old; probing assessments of AL at six sites per tooth at all incisors and molars| The prevalence of AL of ≥ 1 mm was 69.2%, of ≥ 2 mm was 16% and of ≥ 3 mm was 4.5%. Al was associated with higher age, female gender, poor oral hygiene, and lower socioeconomic status
Levin _et al_. (2006) Israel| 642 army recruits (87.5% men), 18–30 years old (mean 19.6); radiographic and clinical examination of first molars and incisors| AP prevalence was 5.9% (4.3% LAP, 1.6% GAP); current smoking and north African origin were significantly related to AP
Terms used in all but Levin **_et al_**. (2006) : "localized juvenile periodontitis" instead of "localized aggressive periodontitis" (LAP), and "generalized juvenile periodontitis" instead of "generalized aggressive periodontitis" (GAP).
PD = probing depth; AL = attachment level; CEJ = cemento-enamel junction; AP = aggressive periodontitis.
The possibility that _localized aggressive periodontitis_ and _prepubertal periodontitis_ are associated conditions, i.e. that the former is a development of the latter, has also attracted attention. In a pilot study, Sjödin _et al_. (1989) retrospectively examined radiographs of the primary dentition of 17 subjects with LAP and reported that 16 of the subjects showed a CEJ–bone crest distance of ≥3 mm in at least one tooth site of their deciduous dentition. The same research group (Sjödin & Matsson 1992) examined the CEJ–bone crest distance in radiographs from 128 periodontally healthy children aged 7–9 years, in order to define a threshold value that, if exceeded, would entail periodontal pathology around the deciduous teeth with high probability. Having set this threshold value to 2 mm, Sjödin _et al_. (1993) examined radiographs of the deciduous dentition retrospectively from 118 patients with aggressive periodontitis and 168 age-and gender-matched periodontally healthy controls. The patients were divided in two groups, one comprising subjects with only one affected site (45 subjects) and another (73 subjects) including subjects with 2–15 sites with bone loss in their permanent dentition. It was found that 52% of the subjects in the latter group, 20% of the subjects in the former group and only 5% of the controls exhibited at least one site with bone loss in their primary dentition. The authors concluded that, at least in some young subjects with aggressive periodontitis, the onset of the disease may be manifested in the primary dentition. Similar results were reported by Cogen _et al_. (1992), from a study in the US. Among systemically healthy young black people with aggressive periodontitis and available radiographs of the primary dentition, 71% showed alveolar bone loss adjacent to one or several primary teeth. Finally, an interesting recent radiographic study of the mixed dentition in Australian children aged 5–12 years was carried out by Darby _et al_. (2005). These authors investigated the prevalence of alveolar bone loss around first permanent molars, and first and second deciduous molars. Based on radiographs of 542 children, 13.0% were found to display definite bone loss, i.e. bone levels >3.0 mm from the CEJ. Half of all lesions with definite bone loss occurred at the second deciduous molars and, in the vast majority, at distal tooth surfaces. In other words, this study showed that the tooth surface of the deciduous dentition most frequently affected by bone loss was the one in close proximity with the most frequent localization of aggressive periodontitis in young age groups, i.e. the mesial surface of the first permanent molar.
### Periodontitis and tooth loss
Tooth loss may be the ultimate consequence of destructive periodontal disease. Teeth lost due to the sequels of the disease are obviously not amenable to registration in epidemiological surveys and may, hence, lead to an underestimation of the prevalence and the severity of the disease. The well established epidemiologic concept of _selection bias_ (also referred to as the _healthy survivor effect_ , indicating that the comparatively healthier subjects will present for an examination while the more severely affected may refuse participation or fail to present because of the morbidity itself) is in this context applicable on the individual tooth level, since the severely affected teeth may have already been extracted/lost. Aspects related to tooth loss on a population basis have been addressed in numerous publications. Important questions that were analyzed included: (1) the relative contribution of periodontitis as a reason underlying tooth extractions in subjects retaining a natural dentition (Cahen _et al_. 1985; Bailit _et al_. 1987; Brown _et al_. 1989; Corbet & Davies 1991; Heft & Gilbert 1991; Klock & Haugejorden 1991; MacDonald Jankowski 1991; Stephens _et al_. 1991; Reich & Hiller 1993; McCaul _et al_. 2001); (2) its role in cases of full-mouth extractions, the so-called _total tooth clearance_ (Eklund & Burt 1994; Takala _et al_. 1994), and (3) risk factors for tooth loss (Burt _et al_. 1990; Phipps _et al_. 1991; Krall _et al_. 1994; Drake _et al_. 1995; Hunt _et al_. 1995; Warren _et al_. 2002; Copeland _et al_. 2004; Neely _et al_. 2005; Susin _et al_. 2005b).
Typically, surveys addressing the first topic have utilized questionnaire data obtained from general practitioners instructed to document the reasons for which teeth were extracted over a certain time period. The results indicate that the reason underlying the vast majority of extractions in ages up to 40–45 years is dental caries. However, in older age cohorts, periodontal disease becomes about equally responsible for tooth loss. Overall, periodontitis is thought to account for 30–35% of all tooth extractions while caries and its sequelae for up to 50%. In addition, caries appears to be the principal reason for extractions in cases of total tooth clearance. Finally, identified risk factors for tooth loss include smoking, perceived poor dental health, sociobehavioral traits, and poor periodontal status.
Obviously, it is not feasible to "translate" tooth loss data into prevalence figures of periodontal disease. An evaluation, however, of the periodontal status on a population level, and in particular in older age cohorts, must weigh in information provided by tooth loss data, otherwise underestimation of the occurrence and the sequels of the disease is inevitable (Gilbert _et al_. 2005).
# Risk factors for periodontitis
### Introduction – definitions
There is an abundance of both empirical evidence and substantial theoretical justification for accepting the widespread belief that many diseases have more than one cause, i.e. that they are of _multi-factorial etiology_ (Kleinbaum _et al_. 1982). Consequently, in any particular instance when a _causal relationship_ is investigated, the specificity of the relation between exposure to an etiologic agent and effect, i.e. the _necessity_ or the _sufficiency_ of the condition, may be challenged. In the case of most infectious diseases for example, it is known that the presence of the microbial agent (which we define as the necessary condition) is not always accompanied by signs or symptoms characteristic of that disorder. Thus, the agent itself is not sufficient to cause any pathologic occurrence; rather, the disease development may be dependent on multiple, diverse additional factors, including specific host responses, toxic exposures, nutritional deficiencies, emotional stress, and the complex impact of social influences. In non-infectious diseases (except for genetic abnormalities), there is usually no factor known to be present in every single case of the disease. For example, smoking is not necessary for the development of lung cancer, and no degree of coronary atherosclerosis is a necessary condition for myocardial infarction.
The _causal inference_ , i.e. the procedure of drawing conclusions related to the cause(s) of a disease, is a particularly complex issue in epidemiological research. In the 1970s, Hill (1971) formalized the criteria that have to be fulfilled in order to accept a causal relation. These included:
1. _Strength of the association_. The stronger the association is between the potential ( _putative_ ) risk factor and disease presence, the more likely it is that the anticipated causal relation is valid.
2. _Dose–response effect_. An observation that the frequency of the disease increases with the dose or level of exposure to a certain factor supports a causal interpretation.
3. _Temporal consistency_. It is important to establish that the exposure to the anticipated causative factor occurred prior to the onset of the disease. This may be difficult in case of diseases with long latent periods or factors that change over time.
4. _Consistency of the findings_. If several studies investigating a given relationship generate similar results, the causal interpretation is strengthened.
5. _Biological plausibility_. It is advantageous if the anticipated relationship makes sense in the context of current biological knowledge. However, it must be realized that the less that is known about the etiology of a given disease, the more difficult it becomes to satisfy this particular criterion.
6. _Specificity of the association_. If the factor under investigation is found to be associated with only one disease, or if the disease is found to be associated with only one factor among a multitude of factors tested, the causal relation is strengthened. However, this criterion can by no means be used to reject a causal relation, since many factors have multiple effects and most diseases have multiple causes.
It is important to realize that the criteria described above are meant as guidelines when a causal inference is established. None of them, however, is either necessary or sufficient for a causal interpretation. Strict adherence to any of them without concomitant consideration of the other may result in incorrect conclusions.
A distinction has to be drawn between a _causal_ factor, assessed as above, and a _risk_ factor. In a broad sense, the term risk factor may indicate an aspect of personal behavior or life-style, an environmental exposure, or an inborn or inherited characteristic which, on the basis of epidemiologic evidence, is known to be associated with disease-related conditions. Such an attribute or exposure may be associated with an increased probability of occurrence of a particular disease without necessarily being a causal factor. A risk factor may be modified by intervention, thereby reducing the likelihood that the particular disease will occur.
The principles of the _risk assessment process_ were discussed by Beck (1994) and should consist of the following four steps:
1. The _identification_ of one or several individual factors that appear to be associated with the disease.
2. In case of multiple factors, a _multi-variate risk assessment model_ must be developed that discloses which combination of factors does most effectively discriminate between health and disease.
3. The _assessment_ step, in which new populations are screened for this particular combination of factors, with a subsequent comparison of the level of the disease assessed with the one predicted by the model.
4. The _targeting_ step, in which exposure to the identified factors is modified by prevention or intervention and the effectiveness of the approach in suppressing the _incidence_ of the disease is evaluated.
Thus, according to this process, _potential_ or _putative risk factors_ (often also referred to as _risk indicators_ ) are first identified and thereafter tested until their significance as _true risk factors_ is proven.
Finally, distinction must be made between _prognostic_ factors (or _disease predictors_ ), i.e. characteristics related to the progression of _pre-existing_ disease and _true risk factors_ , i.e. exposures related to the _onset_ of the disease. For example, it is established in longitudinal studies of periodontal disease (Papapanou _et al_. 1989), that the amount of alveolar bone loss or the number of teeth present at baseline may be used to predict further progression of the disease. These variables are, in fact, alternative measures of the disease itself and express the level of susceptibility of a given subject to periodontal disease. Although they may be excellent predictors for further disease progression, they clearly cannot be considered as risk factors.
There are several ways to study the relation between exposure to a certain factor and the occurrence of a particular disease, as required under point 1. One of these is described in Fig. 7-3 which illustrates a hypothetical situation where exposure to the potential risk factor Z is studied in a cross-sectional study including a sample of 1000 subjects, 180 of whom are found to suffer from the disease D ("diseased") while 820 are disease-free ("healthy"). In this particular setting, it was observed that 155 out of the 180 diseased subjects had been exposed to factor Z but this was also the case for 340 non-diseased subjects. The association between exposure and disease may, in this example, be expressed by the _odds ratio_ (OR), which is the ratio of exposure among the diseased and the healthy. For the data in Fig. 7-3, the odds ratio is calculated as (155/25) over (340/480) = (155×480) / (340×25) = 8.75. This indicates that the diseased were 8.75 times more likely to have been exposed to factor Z than the healthy. Note that the OR is frequently misinterpreted to describe the risk of an exposed subject to develop disease, something that is correctly assessed in a prospective cohort rather than a cross-sectional study and is described by the _relative risk_. In the example of Fig. 7-3, if a sample of 495 subjects exposed to factor Z and 505 subjects not exposed to factor Z are prospectively followed over a given time period, and 155 among the exposed and 25 among the non-exposed develop disease D over this period, then the relative risk is calculated as (155/495) over (25/505) = 6.4. In other words, an individual exposed to factor Z is 6.4 times more likely to develop disease D than a non-exposed subject.
**Fig. 7-3** Contingency table describing the distribution of a group of 1000 subjects according to exposure to a particular factor and disease status.
In a study of the association between exposure to a risk factor and the occurrence of disease, _confounding_ can occur when an additional factor associated with the disease is unevenly distributed among the groups under investigation. For instance, in a study between radon exposure and a form of cancer, smoking may act as a confounder, if the smoking habits of the subjects exposed to radon are different from those of the subjects not exposed.
There are various ways to assess simultaneously the effect of several putative risk factors identified in step 1 and generate the multi-variate model required for step 2. For example, the association between exposure and disease may, for reasons of simplicity, have the form of the following linear equation:
where y represents occurrence or severity of the disease, a is the intercept (a constant value), x1, x2,... xn describe the different exposures (putative risk factors), and b1, b2,... bn are _estimates_ defining the relative importance of each individual exposure as determinant of disease, after taking all other factors into account. Such an approach may identify factors with statistically and biologically significant effect and may eliminate the effect of confounders.
In the third step (assessment step), a new population sample that it is independent of the one used in the construction of the multi-variate model is screened for occurrence of disease and presence of the relevant factors included in the multi-variate model of step 2. Alternatively, in the case of a prospective cohort study, exposure to the relevant factors is assessed among the subjects of the new sample, and disease incidence, i.e. the number of new cases of disease, is determined over a time period after a longitudinal follow-up of the subjects. Subsequently, disease predicted by means of the model is compared to the actually observed disease, and the _external validity_ of the model (i.e., the "behavior" or "fitness" of the model in the new population) is evaluated.
Lastly, during the targeting step, aspects of causality or risk are verified if disease occurrence is suppressed when exposure is impeded. Ideally, such studies should be designed as randomized clinical trials, in which treatment is randomly assigned in one of two groups and the effectiveness of the intervention is assessed in direct comparison to outcomes in an untreated, control group. Additionally, an evaluation of the particular preventive/therapeutic strategy from a "cost–benefit" point of view is also facilitated in such studies.
In the context of periodontitis, it should be realized that few of the putative risk factors for disease development have been subjected to the scrutiny of all four steps. In fact, risk assessment studies in dental research in general have been frequently confined to the first two steps. Numerous cross-sectional studies identifying potential factors are available, but a relatively limited number of longitudinal studies has involved a multi-variate approach in the identification of exposures of interest while simultaneously controlling for the effect of possible confounders. Intervention studies in the form of randomized clinical trials are sparse. In the following text, the issue of risk factors is addressed according to the principles described above. Results from cross-sectional studies are considered to provide evidence for putative risk factors that may be further enhanced if corroborated by longitudinal studies involving multi-variate techniques, or prospective intervention studies. As reviewed by Borrell and Papapanou (2005), distinction is also made between putative factors that are not amenable to intervention (non-modifiable background factors) and modifiable factors (environmental, acquired, and behavioral).
## Non-modifiable background factors
### Age
The relationship between age and periodontitis is complex. Early evidence demonstrates that both the prevalence and severity of periodontitis increase with older age, suggesting that age may be a marker for periodontal tissue support loss (van der Velden 1984, 1991; Johnson 1989; Johnson _et al_. 1989; Burt 1994). However, the concept of periodontitis as an inevitable consequence of ageing has been challenged over the years and the alleged 'age effect' likely represents the cumulative effect of prolonged exposure to true risk factors (Papapanou _et al_. 1991). Notably, the association between age and periodontitis appears to be different for pocket depth and clinical attachment loss. While there is a pronounced effect of increasing attachment loss with age, the effect on pocket depth appears to be minimal (Albandar 2002a,b). Interestingly, the effect of age on attachment loss is reduced after adjustment for covariates, such as oral hygiene levels or access to dental care services (Albandar 2002a). However, studies have often failed to adjust for important covariates such as presence of systemic diseases, consumption of multiple medications, and co-morbidities related to nutritional disturbances in the older population. It is therefore difficult to rule out the possibility of an age-related, as opposed to an age-dependent, increased susceptibility to periodontitis in older people.
### Gender
There is no established, inherent difference between men and women in their susceptibility to periodontitis, although men have been shown to exhibit worse periodontal health than women in multiple studies from different populations (Okamoto _et al_. 1988; Brown _et al_. 1989; Hugoson _et al_. 1992; Albandar 2002a; Susin _et al_. 2004a). This difference has been traditionally considered to be a reflection of better oral hygiene practices (Hugoson _et al_. 1998b; Christensen _et al_. 2003) and/or increased utilization of oral health care services among women (Yu _et al_. 2001; Dunlop _et al_. 2002; Roberts-Thomson & Stewart 2003). On the other hand, periodontitis is a bacterial infection determined to a large extent by the host immunoinflammatory response to the bacterial challenge. Although gender-specific differences in these responses have not been unequivocally demonstrated, it is biologically plausible that such differences may in fact exist.
### Race/ethnicity
Differences in the prevalence of periodontitis between countries and across continents have been demonstrated (Baelum _et al_. 1996; Albandar 2002a), but no consistent patterns across racial/ethnic groups have been documented when covariates such as age and oral hygiene are accounted for (Burt & Eklund 1999). National surveys in the USA consistently show a racial/ethnic differential pattern in the prevalence of periodontitis, with African Americans exhibiting the highest prevalence of periodontitis followed by Mexican Americans and non-Hispanic white people, and these findings are fairly consistent regardless of the case-definition used (Albandar _et al_. 1999; Arbes _et al_. 2001; Borrell _et al_. 2002; Hyman & Reid 2003). However, race/ethnicity is usually a social construct that determines an array of opportunities related to access, status and resources (Williams 1997, 1999). As a result, race/ethnicity and socioeconomic status (SES) are strongly intertwined, suggesting that the observed racial/ethnic effect may be partially attributed to confounding by SES due to the unequal meaning of SES indicators across racial/ethnic groups (Williams 1996; Kaufman _et al_. 1997; Krieger _et al_. 1997; Lynch & Kaplan 2000). Corroborating this point, a recent study found that African Americans demonstrated a lower benefit from education and income on periodontal health status than their Mexican American and white peers (Borrell _et al_. 2004). Such findings confirm that socioeconomic indicators across racial/ethnic groups are not commensurable but, probably, reflect the broad implications of historic unequal opportunities among certain racial groups.
### Gene polymorphisms
Evidence from classical twin studies (Michalowicz _et al_. 1991) suggests that genetic determinants are significant modifiers of the periodontitis phenotype (Michalowicz 1994; Hart & Kornman 1997; Schenkein 2002) but the role of single nucleotide polymorphisms remains unclear. After the seminal work by Kornman _et al_. (1997) reporting an association of a composite genotype based on specific polymorphisms in the interleukin-1 gene cluster with severe periodontitis in non-smokers, there has been an exponential increase in publications that examined a plethora of gene polymorphisms as severity markers of periodontitis. These include additional investigations of the particular IL-1 gene polymorphism in cross-sectional and case–control settings (Gore _et al_. 1998; Diehl _et al_. 1999; Armitage _et al_. 2000; Mark _et al_. 2000; McDevitt _et al_. 2000; Parkhill _et al_. 2000; Socransky _et al_. 2000; Walker _et al_. 2000; Hodge _et al_. 2001; Laine _et al_. 2001; Papapanou _et al_. 2001; Caffesse _et al_. 2002; Meisel _et al_. 2002, 2003, 2004; Anusaksathien _et al_. 2003; Gonzales _et al_. 2003; Guzman _et al_. 2003; Sakellari _et al_. 2003; Li _et al_. 2004; Quappe _et al_. 2004; Scapoli _et al_. 2005), as well as longitudinal studies (Ehmke _et al_. 1999; De Sanctis & Zucchelli 2000; Lang _et al_. 2000; Cullinan _et al_. 2001; Christgau _et al_. 2003; Jepsen _et al_. 2003). Similar work was quickly expanded to include the study of other gene polymorphisms such as the interleukin-1 receptor antagonist (Tai _et al_. 2002); interleukin-6 (Anusaksathien _et al_. 2003; Trevilatto _et al_. 2003); interleukin-10 (Kinane _et al_. 1999; Yamazaki _et al_. 2001; Gonzales _et al_. 2002; Berglundh _et al_. 2003; Scarel-Caminaga _et al_. 2004); interleukin-4 (Michel _et al_. 2001; Scarel-Caminaga _et al_. 2003; Gonzales _et al_. 2004; Pontes _et al_. 2004); interleukin-2 (Scarel-Caminaga _et al_. 2002); tumor necrosis factor (Galbraith _et al_. 1998; Endo _et al_. 2001; Shapira _et al_. 2001; Craandijk _et al_. 2002; Fassmann _et al_. 2003; Soga _et al_. 2003; Perez _et al_. 2004; Shimada _et al_. 2004); transforming growth factor-beta 1 (TGF-beta 1) (Holla _et al_. 2002b); Fc receptor of immunoglobulin G (Kobayashi _et al_. 1997, 2000a,b, 2001; Sugita _et al_. 1999, 2001; Meisel _et al_. 2001; Chung _et al_. 2003; Loos _et al_. 2003; Yasuda _et al_. 2003; Yamamoto _et al_. 2004; Wolf _et al_. 2006); CD14 receptor (Holla _et al_. 2002a); vitamin D receptor (Hennig _et a_ l. 1999; Tachi _et al_. 2003; de Brito Junior _et al_. 2004; Park _et al_. 2006); N-acetyltransferase 2 (Meisel _et al_. 2000; Kocher _et al_. 2002); and matrix metalloproteinase 1 and 3 (Holla _et al_. 2004; Itagaki _et al_. 2004).
Typically, the majority of the cross-sectional studies above report positive associations between the investigated polymorphisms and the extent or the severity of periodontitis. The results, however, are not unequivocal, as the strength of the reported associations is not uniformly consistent across populations, the frequency of occurrence of these polymorphisms appears to vary extensively between ethnic groups, the subject samples involved are generally of limited size, the definitions of the outcome variable (periodontitis) vary considerably, and adequate adjustments for other important covariates and risk factors have frequently not been carried out. Importantly, there appear to be differences in the impact of these polymorphisms on early-onset versus adult forms of periodontitis. For example, in the case of IL-1 polymorphisms, while it is the rare allele (allele 2) that has been linked with severe disease in adults, it is allele 1 that has been found to be more prevalent in subjects with early-onset periodontitis (Diehl _et al_. 1999; Parkhill _et al_. 2000).
The relatively few longitudinal studies that have studied specific gene polymorphisms as exposures are similarly conflicting. Ehmke _et al_. (1999) reported no bearing of the IL-1 gene polymorphism on the prognosis of periodontal disease progression following non-surgical periodontal therapy. Jepsen _et al_. (2003) failed to provide evidence that the IL-1 risk genotype was associated with higher gingival crevicular fluid (GCF) volume and percentage bleeding on probing (BoP) during the development of experimental gingivitis. In contrast, Lang _et al_. (2000) concluded that IL-1 genotype-positive subjects have a genetically determined hyper-inflammatory response that is expressed clinically in the periodontal tissues as increased prevalence and incidence of bleeding on probing during maintenance. Three treatment studies examined the impact of this particular polymorphism in regenerative therapy: De Sanctis and Zucchelli (2000) reported that the IL-1 positive genotype was associated with inferior long-term outcome of regenerative therapy of intrabony defects. In contrast, Christgau _et al_. (2003) and Weiss _et al_. (2004) failed to document such an association in similar studies of the regenerative potential of such defects. Finally, in a 5-year prospective study of 295 subjects, Cullinan _et al_. (2001) reported an interaction between the positive genotype, age, smoking and colonization by _Porphyromonas gingivalis_ and concluded that the positive genotype is a contributory but non-essential factor for the progression of periodontal disease.
In conclusion, there is insufficient epidemiologic evidence that convincingly establishes any of the above polymorphisms as true risk factors for periodontitis.
## Environmental, acquired, and behavioral factors
### Specific microbiota
The microbial etiology of gingivitis (Löe _et al_. 1965; Theilade _et al_. 1966) and periodontitis (Lindhe _et al_. 1973) has been established for several decades. Yet, epidemiologic studies that systematically investigated the role of specific microbiota as risk factors for periodontitis were undertaken fairly recently. In a classic paper, Haffajee and Socransky (1994) adapted Koch's postulates to be used in the identification of periodontal pathogens and proposed the following criteria: (1) association, i.e. elevated odds ratios in disease; (2) elimination, i.e. conversion of disease to health when bacteria are suppressed; (3) development of a host response; (4) presence of virulence factors; (5) evidence from animal studies corroborating the observations in humans; and (6) support from risk assessment studies. Based on the above criteria, the consensus report of the 1996 World Workshop in Periodontics identified three species, _Actinobacillus actinomycetemcomitans_ , _Porphyromonas gingivalis_ , and _Bacteroides forsythus_ , as causative factors for periodontitis (since then, two of the three causative species have been renamed: _A. actinomytemcomitans_ to _Aggregatibacter actinomycetemcomitans_ (Norskov-Lauritsen & Kilian 2006) and _B. forsythus_ to _Tanerella forsythia_ (Sakamoto _et al_. 2002; Maiden _et al_. 2003) ). However, given that only approximately 50% of the bacteria of the oral cavity are currently recognized (Paster _et al_. 2001), it is clear that these three species cannot be considered to be the only causative pathogens, but are rather the ones for which sufficient data have accumulated.
Over the last decade, interesting data have emerged on the prevalence of these causative bacteria in different populations, in states of both periodontal health and disease. Studies performed in children (Tanner _et al_. 2002; Yang _et al_. 2002) that analyzed plaque from the gingival crevice, tooth surface and the dorsum of the tongue revealed that sizeable proportions of subjects harbored _P. gingiva-lis_ , _T. forsythia_ , and _A. actinomycetemcomitans_ despite absence of overt gingival inflammation. A comparably high carrier state was documented in studies that sampled infants, children, adolescents and adults with good clinical periodontal status (McClellan _et al_. 1996; Könönen 1993; Kamma _et al_. 2000; Lamell _et al_. 2000). Thus, contrary to the conclusions of earlier, culture-based studies that these bacteria occur infrequently in periodontally healthy oral cavities and behave as exogenous pathogens, the above studies that have employed molecular techniques for bacterial identification demonstrate the contrary. However, both the prevalence of and the level of colonization by these pathogens have been shown to vary significantly between populations of different racial or geographic origin (Sanz _et al_. 2000; Ali _et al_. 1994; Haffajee _et al_. 2004; Lopez _et al_. 2004).
Several epidemiologic studies have examined the prevalence of the established periodontal pathogens and its relation to clinical periodontal status in population samples from both developed and developing countries. Griffen _et al_. (1998) examined a convenience sample recruited from a university clinic, and reported that 79% of the diseased and 25% of the healthy subjects were positive for _P. gingivalis_. Interestingly, the prevalence of _P. gingivalis_ in the periodontally healthy group varied substantially with race/ethnicity, as it occurred in 22% of white people, 53% of African Americans, and 60% of Asian Americans. In a case–control study of periodontitis patients and age- and gender-matched controls with no or only minimal attachment loss in Sweden, Papapanou _et al_. (2000) reported a high prevalence of _P. gingivalis_ , _A. actinomycetemcomitans_ , _T. forsythia_ , and _Treponema denticola_ in periodontitis patients (95%, 83%, 97%, and 93%, respectively), but also similarly high prevalence rates among control subjects (82%, 90%, 82%, and 94%). However, in a quantitative analysis of bacterial load, substantial differences in colonization at high levels (i.e. at an average count ≥105 bacterial cells/plaque sample) were observed between patients and controls for three of the four bacteria: 19% versus 3% for _P. gingivalis_ , 54% vs. 12% for _T. forsythia_ , and 46% vs. 19% for _Tr. denticola_. In contrast, corresponding percentages were similar for _A. actinomycetemcomitans_ (1% in both cases and controls). Substantially different prevalence data were reported in a study of blue- and white-collar University employees in Australia (Hamlet _et al_. 2001). These authors detected _A. actinomycetemcomitans_ in 23% and _P. gingivalis_ in 15% of the subjects.
A number of studies investigated the epidemiology of periodontal pathogens in Asian populations. Timmerman _et al_. (1998) examined a sample of adolescents in rural Indonesia, and detected _P. gingivalis_ in 87% and _A. actinomycetemcomitans_ in 57% of the subjects. Mombelli _et al_. (1998) examined young factory workers in China and detected _A. actinomycetemcomitans_ in 62% and _P. gingivalis_ in 55% of the subjects. In contrast, an almost ubiquitous presence of _P. gingivalis_ and _T. forsythia_ was reported in rural subject samples in China (Papapanou _et al_. 1997) and Thailand (Papapanou _et al_. 2002), while _A. actinomycetemcomitans_ was detected in 83% and 93% of the subjects in the Chinese and Thai samples, respectively. Despite this high prevalence, a quantitative analysis of bacterial load correlated well with periodontal status in both studies. For example, a discriminant analysis performed on the data from the Thai study (Papapanou _et al_. 2002) identified threshold levels of average bacterial load which, when exceeded, conferred increased odds for presence of three or more sites with pocket depth ≥5 mm. For three species ( _P. gingivalis_ , _T. forsythia_ , and _Tr. denticola_ ), colonization above these calculated thresholds resulted in statistically significant, elevated odds for periodontitis. In addition, an analysis of the association between colonization at high levels by the "red complex" bacteria (Socransky _et al_. 1998) and specific periodontal conditions, defined in this particular study by the presence of three or more sites with pocket depth ≥5 mm and by two different levels of extent of periodontal tissue loss (≥10 and ≥30 sites with ≥5 mm attachment loss, respectively), revealed statistically significant odds ratios ranging between 3.7 and 4.3 for the "red complex" bacteria and all three disease definitions. Similar cross-sectional associations of statistically significant odd ratios for severe periodontitis conferred by specific bacteria have been also observed in several other studies involving subject samples from the western world (Grossi _et al_. 1994, 1995; Alpagot _et al_. 1996, Craig _et al_. 2001).
Importantly, the association between high levels of colonization by specific periodontal pathogens and the progression of periodontal disease has been corroborated by longitudinal data in untreated populations. For example, in the study by Papapanou _et al_. (1997), a discriminant analysis based on quantitative assessments of subgingival bacterial load classified correctly the substantial majority of the subjects with progression of periodontitis over a preceding 10-year period. Indeed, bacterial profiles classified correctly 75% of the subjects with ten or more sites with longitudinal attachment loss of ≥3 mm, and 85% of those that remained stable over the observation period. In a 7-year follow-up study of Indonesian adolescents (Timmerman _et al_. 2000, 2001), and in a subsequent 15-year follow-up of the same cohort (Van der Velden _et al_. 2006), it was shown that subgingival presence of _A. actinomycetemcomitans_ was associated with disease progression, defined as presence of longitudinal attachment loss of ≥2 mm. In a follow-up of 2–5 years' duration, Machtei _et al_. (1999) reported that subjects colonized by _T. forsythia_ at baseline exhibited greater alveolar bone loss, a larger proportion of "loser" sites, and twice as high longitudinal tooth loss than non-colonized subjects. In a 3-year study, Hamlet _et al_. (2004) reported odds ratios of 8.2 for attachment loss in adolescents with persistent colonization with _T. forsythensis_.
Collectively, data generated in the past 15 years have enhanced our knowledge on the role of specific periodontal bacteria as risk factors for periodontitis (Table 7-4), but have also clarified the significance of bacterial load rather than that of mere positive colonization in conferring risk for disease progression. Obviously, the "targeting" criterion of the risk assessment process has been abundantly fulfilled in the case of microbial risk factors. Indeed, a wide body of literature data, recently compiled in systematic reviews, has demonstrated that an antimicrobial approach, including removal of subgingival plaque with or without adjunctive antiseptics or antibiotics followed by adequate maintenance care, is the single most successful and consistent strategy in the treatment of periodontitis (Heitz-Mayfield _et al_. 2002, Herrera _et al_. 2002; Hallmon & Rees 2003).
**Table 7-4** Selected studies using bacteria as exposures of significance for periodontitis. **(L)** indicates a longitudinal study
**Authors/country**| **Sample/methodology**| **Findings**
---|---|---
Beck _et al_. (1990)
USA| 690 community-dwelling adults, age 65+; probing assessments at mesio- and mid-buccal surfaces, all teeth; logistic regression for advanced AL and deep pocketing; "advanced disease": four or more sites with AL of ≥ 5 mm and one or more of these sites with PD of ≥ 4 mm| Black people: 78% of their sites with attachment loss, mean AL on these sites 4 mm; white people: 65%, 3.1 mm; Odds ratios in black people: tobacco use 2.9; _Porphyromonas gingivalis_ > 2% 2.4; _Pr. intermedia_ > 2% 1.9; last dental visit > 3 years 2.3; bleeding gums 3.9; in white people: tobacco use 6.2; presence of _P. gingivalis_ (+) 2.4; no dental visits for > 3 years plus BANA (+) 16.8
Haffajee _et al_. (1991b)
USA| 38 subjects, 14–71 years old, with prior evidence of attachment loss; 2-month follow-up; probing assessments at six sites/tooth, all teeth; 28 subgingival samples per subject at baseline, DNA-probe analysis with respect to 14 bacterial species; progression threshold: ≥ 3 mm of LAL; the mean percentage of the total cultivable microbiota was averaged across active and inactive sites; odds ratios computed at different thresholds for each species| Significant odds ratios for new disease: _P. gingivalis_ 5.6, _Campylobacter rectus_ 3.8, _Veillonella parvula_ 0.16, and _Capnocytophaga ochracea_ 0.08; discriminant analysis using the significantly related species was useful in predicting subjects at risk for new attachment loss
Grossi _et al_. (1994)
USA| Random sample of 1426 subjects, aged 25–74 years, in a metropolitan community; full-mouth probing assessments; multi-variate analysis of risk indicators for attachment loss. Exposures: (1) clinical: supragingival plaque, gingival bleeding, subgingival calculus, PD, CAL; (2) microbial: _Aggregatibacter actinomycetemcomitans_ , _Tanerella forsythia, C. rectus, Eubacterium saburreum, Fusobacterium nucleatum, P. gingivalis, Capnocytophaga spp_ and _Pr. intermedia_ ; (3) co-variates: age, gender, race, education, income, smoking and numbers of packs/year, exposure to occupational hazards, systemic diseases| In a multivariable logistic regression model, _P. gingivalis_ (OR 1.59, 95% CI 1.11–2.25) and _T. forsythia_ (OR 2.45, 95% CI 1.87–3.24) were positively associated with severity of AL, while _Capnocytophaga_ spp. (OR 0.60, 95% CI 0.43–0.84) were protective against AL
Grossi _et al_. (1995)
USA| Same sample as in Grossi _et al_. (1994); 1361 subjects, aged 25–74 years; assessments of interproximal bone loss from full-mouth radiographs; the degree of association between bone loss and explanatory variables was analyzed by stepwise logistic regression| In a multivariable logistic regression model, _P. gingivalis_ (OR 1.73, 95% CI 1.27–2.37) and _T. forsythia_ (OR 2.52, 95% CI 1.98–3.17), were significantly associated with increasing severity of BL
Beck _et al_. (1997)
USA
**(L)**| 540 dentate adults, aged 65+ years, examined at baseline, 18, 36, and 60 months; incidence of AL was defined as additional AL ≥ 3 mm; microbial variables included presence of _A. actinomycetemcomitans, Pr. intermedia_ , and _P. gingivalis_ and the BANA test; covariates included age, gender, missing teeth, education, smoking, dental visit| BANA (+), and presence of _P. gingivalis_ were significantly associated with incident disease
Papapanou _et al_. (1997)
China
**(L)**| 148 subjects, 30–39 and 50–59 years old in a rural area examined 10 years apart; full-mouth assessments of PD and AL at six sites per tooth; 14 subgingival plaque samples were obtained from each subject at the follow-up examination (1864 in total) and analyzed with respect to 18 bacterial species| Ubiquitous prevalence for the majority of the investigated species on the subject level. Bacterial colonization at high levels by _P. gingivalis, Prevotella intermedia, Pr. nigrescens, T. forsythia, F. nucleatum, Tr. denticola, Micromonas micros_ , and _C. rectus_ conferred statistically significant odds ratios for being classified as "downhill" (ten or more sites with longitudinal AL loss of ≥ 3 mm)
Machtei _et al_. (1999)
USA
**(L)**| A sample of 415 subjects, aged 25–75 years, followed for a period of 2–4 years; full-mouth examination at six sites per tooth at all teeth present; full-mouth intraoral radiographs; bacterial samples obtained from 12 index teeth analyzed with respect to: _A. actinomycetemcomitans, T. forsythia, C. rectus, P. intermedia, Capnocytophaga_ species, _P. gingivalis, E. saburreum, F. nucleatum;_ covariates included age, gender, smoking (current smokers 15.4%), education, income| Subjects harboring _T. forsythia_ at baseline showed significantly higher longitudinal bone loss, greater proportion of "loser" sites (sites with additional AL of ≥ 2 mm) and twice as high tooth mortality
Timmerman _et al_. (2000)
Indonesia
**(L)**| A sample 255 subjects, 15–25 year old, in a rural area, examined 7 years apart; assessments of PD and AL at vestibular surfaces of all teeth; bacterial samples harvested from a variety of intraoral sites and analyzed with respect to _A. actinomycetemcomitans, P. gingivalis, P. intermedia_ , spirochetes, and motile microorganisms| Progressive disease (PDS) was defined as one or more site with longitudinal AL ≥ 2 mm; subgingival presence of _A. actinomycetemcomitans_ (OR 4.2, 95% CI 1.4–12.7), _P. gingivalis_ (OR 2.3, 95% CI 1.0–5.2) and motile microorganisms (OR 2.2, 95% CI 1.0–5.0) were associated with PDS; in a multivariable logistic model, including age and subgingival calculus, subgingival presence of _A. actinomycetemcomitans_ (OR 4.61, p = 0.01) was associated with PDS
Papapanou _et al_. (2002)
Thailand| Random sample of 356 subjects 30–39 and 50–59 years old, in a rural area; PD and CAL were assessed at six sites/tooth, at all teeth apart from third molars; subjects were grouped according to different levels of pocketing/attachment loss: subjects with three or more sites with PD ≥ 5 mm (59%, G1); ≥ 10 sites with CAL ≥ 5 mm (50%, G2); and ≥ 30 sites with CAL ≥ 5 mm (24%, G3). Subgingival plaque samples were obtained at maximally 14 sites/subject; checkerboard hybridizations were used to analyze a total of 4343 samples with respect to 27 bacterial species| Odds ratios for heavy colonization by "red complex" species ( _P. gingivalis, T. forsythia, Tr. denticola_ ) were 3.7 (95% CI 2.3–5.9) for G1; 4.0 (95% CI 2.5–6.6) for G2; and 4.3 (95% CI 2.6–7.1) for G3. Odds ratios for heavy colonization by selected "orange complex" species ( _F. nucleatum, Pr. intermedia, Pr. nigrescens, Pe. micros, E. nodatum, Campylobacter rectus, and C. showae_ ) were 1.5 (95% CI 0.8–2.9) for G1; 1.5 (95% CI 0.8–2.9) for G2; and 1.5 (95% CI 0.8–3.1) for G3
Van der Velden _et al_. (2006)
**(L)**| 15-year follow-up of 128 subjects from the above cohort (Timmerman _et al_. 2000)| In a multi-variable logistic model, subgingival presence of _A. actinomycetemcomitans_ (OR 4.3, 95% CI 1.2–15.7) was confirmed as a risk factor for the onset of the disease, i.e. longitudinal AL during the first 7-year period, but not for progression of disease during the subsequent 8-year period
PD = probing depth; AL= attachment level; CEJ = cemento-enamel junction; CPITN = Community Periodontal Index of Treatment Needs; BANA = N-benzoyl-DL-arginine-2-naphthylamide; a substrate hydrolyzed in the presence of _Treponema denticola, Porphyromonas gingivalis_ , and _Tannerella forsythia_.
### Cigarette smoking
The biological plausibility of an association between tobacco smoking and periodontitis was founded on the broad effects of multiple tobacco-related substances on cellular structure and function. Smoking has been shown to affect the vasculature, the humoral and cellular immune responses, cell signaling processes, and tissue homeostasis (for recent reviews see Kinane & Chestnutt 2000; Palmer _et al_. 2005). A substantial number of studies, a selection of which is summarized in Table 7-5, established the association of smoking to poor periodontal status (Axelsson _et al_. 1998; Bergström 1989; Goultschin _et al_. 1990; Haber & Kent 1992; Locker 1992; Ragnarsson _et al_. 1992; Haber _et al_. 1993; Jette _et al_. 1993; Stoltenberg _et al_. 1993b; Wouters _et al_. 1993; Martinez Canut _et al_. 1995; Albandar _et al_. 2000; Bergström _et al_. 2000b; Tomar & Asma 2000; Paulander _et al_. 2004b; Susin _et al_. 2004b; Kocher _et al_. 2005). Importantly, the inferior periodontal status of smokers cannot be attributed to poorer plaque control or more severe gingivitis (Bergström 1989). While earlier reports suggested a rather similar composition of the subgingival microflora in smokers and non-smokers (Stoltenberg _et al_. 1993b), recent studies demonstrated that shallow sites in smokers are colonized at higher levels by periodontal pathogens, such as _T. forsythia_ , _Treponema denticola_ , and _P. gingivalis_ , and that these differences are obscured in deep, diseased pockets. In an attempt to quantitate the effects of smoking on the periodontal conditions, Haber _et al_. (1993) suggested that the excess prevalence of periodontal disease in the population attributed solely to smoking is much greater than the that owed to other systemic predispositions, such as diabetes mellitus. Data derived from the NHANES III study (Tomar & Asma 2000) suggested that as many as 42% of periodontitis cases in the US can be attributed to current smoking, and another 11% to former smoking. Similarly, in a study from Brazil, Susin _et al_. (2004b) reported that the attributable fraction of clinical attachment loss due to cigarette smoking was 37.7% and 15.6% among heavy and moderate smokers, respectively. In longitudinal studies, smoking has been found to confer a statistically significant increased risk for periodontitis progression after adjustment for other covariates (Beck _et al_. 1995, 1997; Machtei _et al_. 1999; Norderyd _et al_. 1999; Chen _et al_. 2001; Ogawa _et al_. 2002; Paulander _et al_. 2004b).
Fig. 7-4 describes a _meta-analysis_ of data from studies studying the association between smoking and periodontal conditions. In essence, meta-analysis is a statistical method which combines results from different studies of similar design, in order to gain an overall increased _power_ , i.e. an enhanced potential to reveal biological associations which may exist but are difficult to detect (Chalmers 1993; Oakes 1993; Proskin & Volpe 1994). This analysis, initially published as part of the 1996 World Workshop in Periodontics (Papapanou 1996), incorporated data from six studies, including a total of 2361 subjects, with known smoking habits and periodontal status (Bergström & Eliasson 1989; Haber & Kent 1992; Locker 1992; Haber _et al_. 1993; Stoltenberg _et al_. 1993b; Grossi _et al_. 1994). It can be observed that smoking entailed an overall increased, statistically and clinically significant risk for severe disease (estimated overall odds ratio of 2.82; 95% confidence limits 2.36–3.39).
**Table 7-5** Selected studies using smoking as exposure of significance for periodontitis. **(L)** indicates a longitudinal study
**Authors/country**| **Sample/methodology**| **Findings**
---|---|---
Bergström (1989)
Sweden| Patients referred for periodontal therapy (155 subjects, 30, 40 and 50 years old); a random sample of the Stockholm population served as controls; full-mouth probing assessments; sites with PD ≥ 4 mm considered diseased; recording of plaque and gingivitis scores| 56% of the patients and 34% of the controls were smokers (odds ratio 2.5); significantly higher frequency of periodontally involved teeth in smokers; no notable difference between smokers and non- smokers with respect to plaque and gingivitis
Haber & Kent (1992)
USA| 196 patients with PD in a periodontal practice and 209 patients from five general practices; probing assessments at six sites/tooth and full-mouth radiographs; questionnaire on smoking habits; patients with negative history of periodontal therapy from the general practices included as controls; comparison of (1) the prevalence of smoking among the two patient groups, and (2) PD disease severity among current and never smokers| Overall smoking history in the periodontal practice 75%; in the general practice 54%; summary odds ratio for positive smoking history in perio versus general practice patients was 2.6; in the perio group, frequency of current smoking increased with increasing severity of PD
Locker (1992)
Canada| 907 adults, ≥ 50 years old, living independently in four Ontario communities; partial, probing assessments; half of the participants reported a positive history of smoking and 20% were current smokers| Current smokers had fewer teeth, were more likely to have lost all their natural teeth and had higher extent and severity of PD than those who had never smoked
Haber _et al._ (1993)
USA| 132 diabetics and 95 non-diabetics, 19–40 years old; probing assessments at six sites/tooth, all teeth; questionnaire on smoking habits; calculation of the population attributable risk percent (PAR%), as an estimate of the excess prevalence of periodontitis in the study population that is associated with smoking| The prevalence of periodontitis was markedly higher among smokers than non smokers within both the diabetic and non-diabetic groups; PAR% among non diabetics was 51% in ages 19–30 years and 32% in ages 31–40 years
Stoltenberg _et al._ (1993b)
USA| Out of 615 medically healthy adults, 28–73 years old, attending a health maintenance organization, selection of 63 smokers and 126 non-smokers of similar age, sex, plaque, and calculus scores; probing assessments at the proximal surfaces of premolars and molars in a randomly selected posterior sextant; detection of _P. gingivalis, Pr. intermedia, A. actinomycetemcomitans, Eikenella corrodens_ , and _F. nucleatum_ by a semi-quantitative fluorescence immunoassay, in one buccal and one lingual sample per tooth examined; logistic regression to determine if any of the bacteria or smoking were indicators of mean posterior probing depth of ≥ 3.5 mm| Odds ratio for a smoker having a mean PD of ≥ 3.5 mm was 5.3 (95% CI 2.0–13.8); no statistically significant difference between smokers and non-smokers with respect to prevalence of the bacteria examined; the logistic model revealed that a mean PD of ≥ 3.5 mm was significantly associated with the presence of _A. actinomycetemcomitans, Pr. intermedia, E. corrodens_ and smoking; smoking was a stronger indicator than any of the bacteria examined
Jette _et al._ (1993)
USA| 1156 community dwellers, age 70+ years; probing assessments at four sites/tooth, all teeth; evaluation if lifelong tobacco use is a modifiable risk factor for poor dental health; multiple regression analysis| 18.1% of men and 7.9% of women were tobacco users (overall 12.3%; including 1% smokeless tobacco users); years of exposure to tobacco products was a statistically significant factor for tooth loss, coronal root caries, and periodontal disease, regardless of other social and behavioral factors; periodontal disease (no. of affected teeth) was predicted by longer duration of tobacco use, male sex, and more infrequent practice of oral hygiene
Martinez Canut _et al._ (1995)
Spain| 889 periodontitis patients, aged 21–76 years; probing assessments at six sites/tooth, all teeth; analysis of variance to examine the role of smoking on the severity of periodontitis| Smoking was statistically related to increased severity of periodontitis in multi-variate analysis; a dose–response effect was demonstrated, with subjects smoking > 20 cigarettes/day showing significantly higher attachment loss
Kaldahl _et al._ (1996)
USA
**(L)**| 74 patients with moderate to advanced periodontitis including 31 heavy smokers (≥ 20 cigarettes/day); the effects of cigarette consumption and smoking history on the response to active periodontal treatment and to up to 7 years of supportive periodontal treatment was evaluated. Full-mouth examinations performed at baseline, 4 weeks after mechanical plaque control, 10 weeks following periodontal surgery, and yearly during 7 years of supportive periodontal treatment| Past and never smokers consistently exhibited a significantly greater reduction in PD and greater gains in AL than heavy and light smokers; all groups experienced a similar decrease in the prevalence of BoP following active therapy
Grossi _et al._ (1997b)
USA
**(L)**| 143 subjects aged 35–65 years with established periodontitis, including 60 current, 55 former, and 28 non-smokers, examined at baseline and 3 months after non-surgical periodontal therapy| Current smokers showed less reduction in PD and less AL gain than former- and non smokers; fewer smokers harbored no _P. gingivalis_ or _T. forsythia_ after treatment, compared to former and non-smokers
Axelsson _et al._ (1998)
Sweden| A random sample of 1093 subjects, aged 35, 50, 65, and 75 years; prevalence of smoking in the four age groups was 35%, 35%, 24%, and 12%, respectively; recordings included AL, CPITN scores, DMF surfaces, plaque, and stimulated salivary secretion rate (SSSR)| In the oldest age group, 41% of the smokers and 35% of the non-smokers were edentulous; in every age group, mean attachment loss was statistically significantly increased in smokers by 0.37, 0.88, 0.85, and 1.33 mm, respectively; smokers had higher CPITN and DMF scores, increased SSSR, but similar plaque levels
Tomar & Asma (2000)
USA| 12 329 subjects, aged ≥ 18 years, participants in the NHANES III study; probing assessments at mesial and buccal sites in one upper and one lower quadrant; mesial assessments performed from the buccal aspect of the teeth; assessments of gingivitis, PD, and location of the gingival margin in relation to the CEJ; "periodontitis" was defined as one or more site with AL ≥ 4 mm and PD ≥ 4 mm| 27.9% of the participants were current smokers and 9.2% met the definition for periodontitis; current smokers were four times as likely to suffer from periodontitis than never smokers, after adjustments for age, gender, race/ethnicity, education, and income: poverty ratio; among current smokers, there was a dose–response relationship between cigarettes/day and periodontitis; 41.9% of periodontitis cases were attributable to current smoking and 10.9% to former smoking
Bergström _et al._ (2000b)
Sweden| 257 subjects, aged 20–69 years, including 50 current smokers, 61 former smokers, and 133 non-smokers; full mouth clinical and radiographic assessments of the periodontal tissues; smoking exposure defined in terms of consumption (number of cig/day), duration (number of years of smoking) and life-time exposure (product of daily consumption and years of duration-cig/years); threshold levels used: heavy versus light consumption: ≥ 10 cigarettes/day versus < 10 cigarettes/day; duration: ≥ 15 years versus < 15 years; life-time exposure: ≥ 200 cig/years versus < 200 cig/years| Compared to former and non-smokers, current smokers had the highest prevalence of diseased sites (AL ≥ 4 mm); 40–69-year-old current smokers showed a significantly higher prevalence than 20–39-year-old current smokers (27% vs. 4%) ; the same pattern emerged when comparing heavy versus light smokers according to consumption, duration and life-time exposure; in multiple regression, life-time exposure was highly associated with the frequency of diseased sites and periodontal bone height after adjusting for age, gingival bleeding and plaque index
Albandar _et al._ (2000)
USA| 705 subjects, aged 21–92 years, 52% males and 87% white; full-mouth examination of PD and AL at six sites; periodontitis was classified as advanced, or mild; cigar, pipe, and cigarette smoking were classified as current, former and never| In multiple linear regression, current and former smoking, regardless of type, was associated with increased percentage of subjects with moderate/advanced periodontitis after adjusting for age, gender, race and numbers of years of being smoking cigarette, cigar and pipe; current smoking was also associated with higher number of missing teeth
Bergström _et al._ (2000a)
Sweden
**(L)**| 10-year follow-up of a sample of 84 dentally aware musicians, including 16 current, 28 former, and 40 non-smokers; full-mouth clinical and radiographic assessments of periodontal status| The prevalence of PD ≥ 4 mm (diseased sites) was 18.7% for current, 11.1% for former, and 8.7% for non-smokers at baseline. At 10 years, these figures were 41.6%, 7.8% and 6.6%; a similar pattern was observed for alveolar bone levels; after adjusting for age, gingival bleeding, plaque index, and frequency of diseased sites at baseline, current smoking was a significant predictor of the increase in diseased sites at 10 years
Susin _et al._ (2004b)
Brazil| 974 subjects, aged 30–103 years; full mouth examination of PD and AL; severe attachment loss was defined as AL ≥ 5 mm in ≥ 30% of the teeth; exposure to smoking classified as current/former, heavy/moderate/light/none, and quantified as lifetime consumption| Heavy and moderate smokers had significantly higher prevalence of AL ≥ 5 mm than non-smokers; in multivariate analysis heavy (OR 3.6, 95% CI 2.2–6.0) and moderate smoking (OR 2.0, 95% CI 1.4–2.9) conferred higher odds for AL; the attributable fraction of AL due to smoking was 37.7% and 15.6% among heavy and moderate smokers, respectively
PD = probing depth; AL = attachment level; BoP = bleeding on probing; CEJ = cemento-enamel junction; CPITN = Community Periodontal Index of Treatment Needs; DMF = decayed, missing, filled.
Studies examining the effects of smoking on the outcome of periodontal treatment have demonstrated that treatment responses are modified by cigarette consumption, with current smokers exhibiting poorer responses than former or never smokers (Ah _et al_. 1994; Kaldahl _et al_. 1996; Renvert _et al_. 1996; Grossi _et al_. 1997b; Kinane & Radvar 1997; Boström _et al_. 1998; Machtei _et al_. 1998; Tonetti _et al_. 1998; Scabbia _et al_. 2001; Trombelli _et al_. 2003; Van der Velden _et al_. 2003; Papantonopoulos 2004; Paulander _et al_. 2004a; Rieder _et al_. 2004; Stavropoulos _et al_. 2004; Sculean _et al_. 2005). Notably, these studies have confirmed the negative effect of smoking on the outcome of several periodontal treatment modalities including nonsurgical, surgical, and regenerative periodontal therapy. Two recent meta-analyses of the effects of smoking on the outcome of periodontal therapy (Garcia 2005; Labriola _et al_. 2005) support the above conclusions.
In contrast, smoking cessation was shown to be beneficial to the periodontal tissues. In a longitudinal study (Bolin _et al_. 1993), 349 subjects with ≥20 remaining teeth were examined on two occasions 10 years apart (1970 and 1980). Progression of periodontal disease was assessed on radiographs at all approximal tooth surfaces and was shown to be almost twice as rapid in smokers than in non-smokers. It was also observed that subjects who quit smoking at some time point within the observation period had a significantly retarded progression of bone loss than the one occurring in smokers. Similar observations were made by Krall _et al_. (1997) who reported that, over a mean follow-up period of 6 years, subjects who continued to smoke had a 2.4–3.5-fold risk of tooth loss when compared to non-smokers. Finally, in a 10-year follow-up study, Bergström _et al_. (2000a) observed an increase of periodontally diseased sites concomitant with loss of periodontal bone height in current smokers, as compared to non-smokers whose periodontal health condition remained unaltered throughout the period of investigation. The periodontal health condition in former smokers was similarly stable to that of non-smokers, underscoring the beneficial effects of smoking cessation.
In conclusion, cigarette smoking appears to fulfill the majority of the required steps of the risk assessment process stipulated by Beck (1994) and is considered one of the major risk factors for periodontitis.
### Diabetes mellitus
Diabetes as a risk factor for periodontitis has been debated for decades (Genco & Löe 1993), but several biologically plausible mechanisms by which the disease may contribute to impaired periodontal conditions have been identified over the past decade (for reviews see Lalla _et al_. 2000; Mealey & Oates 2006). Table 7-6 summarizes epidemiological evidence based on a number of case–control and prospective cohort studies that examine the periodontal status of patients with diabetes (Hugoson _et al_. 1989; Shlossman _et al_. 1990; Emrich _et al_. 1991; de Pommereau _et al_. 1992; Oliver & Tervonen 1993; Thorstensson & Hugoson 1993; Pinson _et al_. 1995). This association is especially pronounced in subjects with poor metabolic control and a long duration of the disease (Taylor _et al_. 1996; Grossi & Genco 1998; Taylor _et al_. 1998a; Lalla _et al_. 2004). The age of onset of diabetes-related manifestations in the periodontal tissues has also been addressed in studies examining children and adolescents with type 1 diabetes (de Pommereau _et al_. 1992; Pinson _et al_. 1995) and both type 1 and type 2 diabetes (Lalla _et al_. 2006). All three studies documented more pronounced gingival inflammation in subjects with diabetes in ages between 6 and 18 years. The case–control study by Lalla _et al_. (2006) further reported that attachment loss was more pronounced in young patients with diabetes after adjustment for age, gender, ethnicity, gingival bleeding, and frequency of dental visits. In a subsequent publication, Lalla _et al._ (2007b) reported data on 350 children with either type 1 or type 2 diabetes and found a strong positive association between mean HbA1c levels over the 2 years preceding the dental examination and periodontitis. Finally, in a report including a total of 700 children, 350 with diabetes and 350 nondiabetic controls, Lalla _et al._ (2007a) documented a statistically increased periodontal destruction in children with diabetes across all disease definitions tested and in both age subgroups of 6–11 and 12–18 years.
**Table 7-6** Selected studies using diabetes mellitus as exposure of significance for periodontitis. **(L)** indicates a longitudinal study
**Authors/country**| **Sample/methodology**| **Findings**
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Hugoson _et al._ (1989)
Sweden| 82 subjects with long- and 72 with short-duration IDDM; 77 non-diabetics (age 20–70 years); full-mouth, probing assessments at four sites/tooth; radiographs of lower molar–premolar regions; subjects assigned into five groups according to increasing severity of periodontal disease; no multi-variate analysis| No notable difference in plaque, calculus, and no. of teeth between diabetics and non-diabetics; long- duration diabetics were more frequently classified in groups 4 and 5 and had significantly more tooth surfaces with PD of ≥ 6 mm than non-diabetics; significantly more extensive ABL in long-duration diabetics 40–49 years old
Shlossman _et al._ (1990)
Arizona, USA| 3219 Pima Indians, ≥ 5 years; prevalence of NIDDM 23% (20% in men, 25% in women); probing assessments at six sites/tooth, at six index teeth; alveolar bone loss from panoramic radiographs; 2878 subjects with available radiographic data, probing assessments or both; comparison between diabetics and non-diabetics with respect to AL and ABL| Median attachment loss and alveolar bone loss higher in diabetics for all age groups and in both sexes
Emrich _et al._ (1991)
USA| Sample and methodology same as above (Shlossman _et al._ 1990); 1342 Pima Indians, 15 years and older, with natural teeth; 19% (254) with diabetes and 12% (158) with impaired glucose tolerance; linear logistic models to predict prevalence and severity of periodontal disease; prevalence: one or more sites with AL of ≥ 5 mm or ABL ≥ 25% of the root length; severity: square root of average AL or ABL| Diabetes, age, and calculus were significant risk markers for periodontitis; odds ratios for a diabetic to have PD was 2.8 (clinically assessed) and 3.4 (radiographically)
de Pommereau _et al._ (1992)
France| 85 adolescents with IDDM aged 12–18 years and 38 healthy age-matched controls; probing assessments at six sites/tooth, all teeth; bite-wing radiographs at molars and sites with AL > 2 mm; patients divided according to disease duration (more or less than 6 years); sexual maturation according to Tanner's classification; metabolic control expressed through glycosylated hemoglobin (HbA1c); non-parametric pair-wise analysis| None of the subjects had sites with AL ≥ 3 mm or radiographic signs of periodontitis; despite similar plaque scores, diabetic children had significantly more gingival inflammation; no significant relation between gingival condition and age, Tanner's index, HbA1c level or disease duration
Oliver & Tervonen (1993)
USA| 114 diabetic patients, 20–64 years old (60% with IDDM and 40% with NIDDM); half-mouth, probing assessments at four sites/tooth; data from the 1985–86 National Survey served as controls| Tooth loss was similar among diabetics and US employed adults; 60% of the diabetics and 16% of the controls had one or more site with PD ≥ 4 mm; attachment level data were comparable in both groups
Thorstensson & Hugoson (1993)
Sweden| 83 IDDM patients and 99 age- and sex-matched non-diabetics (age 40–70 years); full-mouth, probing assessments at four sites/tooth; radiographs of lower molar-premolar regions; subjects assigned into five groups according to increasing severity of periodontal disease; uni-variate analysis| Diabetics 40–49 years old (mean disease duration 25.6 years) had more periodontal pockets ≥ 6 mm and more extensive alveolar bone loss than non-diabetics, but this was not the case for subjects aged 50–59 or 60–69 years (mean disease duration 20.5 and 18.6 years, respectively). Disease duration appeared to be a significant determinant of periodontitis development
Pinson _et al._ (1995)
USA| 26 IDDM children, 7–18 years old and 24 controls, 20 of whom were siblings of the diabetic patients; full- mouth, probing assessments at six sites/tooth; metabolic control assessed through glycosylated hemoglobin (GHb); analysis of covariance| Overall, no statistically significant differences between cases and controls; no association between GHb and clinical variables; after correcting for plaque, diabetics showed more severe gingival inflammation in specific tooth regions
Bridges _et al._ (1996)
USA| A sample of 233 men, aged 24–78 years, including 118 diabetic (46 type 1 and 72 type 2) and 115 non- diabetic subjects, matched for age and BMI| Plaque and gingivitis, bleeding scores, PD, AL, and missing teeth were significantly higher in diabetic than non-diabetic men
Tervonen & Karjalainen (1997)
Finland
**(L)**| 36 patients with type 1 diabetes and 10 controls, aged 24–36 years, received non-surgical periodontal therapy and were followed at 4 weeks, 6 and 12 months; patient with diabetes were further grouped according to diabetic status as: D1 (n = 13) with no diabetic complications and good long-term metabolic control; D2 (n = 15) moderate metabolic control with/without retinopathy; D3 (n = 8) severe diabetes with poor metabolic control and/or multiple complications; periodontal status was monitored radiographically| The periodontal status of the diabetic patients with good control and no complications (D1) and those with moderate control (D2) was similar to non- diabetic controls. Diabetic subjects with poor metabolic control and/or multiple complications (D3) exhibited higher extent of AL ≥ 2 mm at baseline and higher recurrence of PD ≥ 4 mm during follow-up
Taylor _et al._ (1998a)
USA
**(L)**| 2-year study of 21 patients with type 2 diabetes, including 14 with poor and 7 with better metabolic control, and 338 controls, aged 15–57 years, Native Americans; progression of bone loss was assessed on radiographs; covariates included age, calculus, gingival and plaque indices, time to follow up, alcohol consumption, smoking, obesity (BMI > 27), coronary heart disease, and gender| In multiple logistic regression, poorly controlled diabetic subjects were 11 times more likely (95% CI 2.5–53.3) to have more pronounced bone loss progression than non-diabetic subjects; no such differences were found between better controlled and non-diabetic controls; age, time to follow-up, pronounced bone loss at baseline and calculus index were significant predictors of bone loss progression
Taylor _et al._ (1998b)
USA
**(L)**| 2-year study of 24 subjects with NIDDM and 362 subjects without diabetes, aged 15–57 years; degree of bone loss on panoramic radiographs was assessed in a scale of 0–4| A regression model having progression of bone loss as the dependent variable revealed a cumulative odds ratio for NIDDM of 4.23 (95% CI 1.8–9.9); the association was modified by age, with younger adults exhibiting higher risk for alveolar bone loss progression
Lalla _et al._ (2006)
USA| Case–control study of 182 children and adolescents (6–18 years of age) with diabetes (predominantly type 1) and 160 non-diabetic control subjects; half-mouth examination at four sites/tooth in all fully erupted teeth with respect to PD and AL| Children with diabetes had significantly more plaque and gingival inflammation than controls and higher number of teeth with AL; when controlling for age, gender, ethnicity, gingival bleeding, and frequency of dental visits, diabetes remained significantly correlated with attachment loss; body mass index was significantly correlated with AL in children with diabetes
PD = probing depth; AL = attachment level; CEJ = cemento-enamel junction.
IDDM and NIDDM = insulin-dependent and non-insulin-dependent diabetes mellitus, respectively; both terms have been abolished and replaced by type 1 and type 2 diabetes.
Several studies suggest a two-way relationship between diabetes and periodontitis, with more severe periodontal tissue destruction in people with diabetes but also a poorer metabolic control of diabetes in subjects with periodontitis (Lalla _et al_. 2000; Soskolne & Klinger 2001; Taylor 2001). Irrespective of the variability in the case definition employed in these studies, subjects with diabetes have higher prevalence, extent, and severity of periodontal disease (Grossi _et al_. 1994; Bridges _et al_. 1996; Firatli 1997; Tervonen & Karjalainen 1997; Taylor _et al_. 1998a,b; Lalla _et al_. 2004). These observations are consistent for both type 1 and type 2 diabetes. In addition, these studies provide evidence of a dose–response relationship between poor metabolic control and the severity as well as the progression of periodontitis (Seppälä _et al_. 1993; Tervonen & Oliver 1993; Tervonen & Karjalainen 1997; Taylor _et al_. 1998a; Guzman _et al_. 2003). Further expanding this observed dose–response relationship into the pre-diabetic state, a recent study also indicated that the level of glucose intolerance in non-diabetic individuals also correlated with the severity of periodontal disease (Saito _et al_. 2004). In line with the above observations, the outcome of periodontal treatment in well controlled diabetic patients is similar to that of non-diabetic subjects, while poorly controlled diabetics display an inferior outcome (Tervonen & Karjalainen 1997).
Collectively, the above data strongly indicate that diabetes mellitus is a major risk factor for periodontitis.
### Obesity
The biologic plausibility of a potential link between obesity and periodontitis has been suggested to involve a hyper-inflammatory state and an aberrant lipid metabolism prevalent in obesity, as well as the pathway of insulin resistance (Saito _et al_. 1998; Nishimura & Murayama 2001) all of which may collectively result in an enhanced breakdown of the periodontal tissue support. Indeed, a number of recent studies point to a positive association between obesity, defined as body mass index (BMI) ≥30, and periodontitis (Anon 2000; Saito _et al_. 2001; Al-Zahrani _et al_. 2003; Wood _et al_. 2003).
Three separate publications have documented such an association in the NHANES III database. In the first publication Al-Zahrani _et al_. (2003) reported a significant association between both BMI and waistto- hip ratio and periodontitis in younger adults, but no association in middle-aged or older adults (Table 7-1). Wood _et al_. (2003), using a subset of the NHANES III sample including Caucasian subjects aged 18 years and above, reported that BMI, waist-to-hip ratio, visceral fat, and fat-free mass were associated with periodontitis after adjusting for age, gender, history of diabetes, current smoking, and socioeconomic status. Finally, Genco _et al_. (2005), reported that overweight subjects in the upper quartile of insulin resistance index were 1.5 times more likely to have periodontitis compared to their counterparts with high BMI but low insulin resistance index.
In an independent subject sample including 643 apparently healthy Japanese adults, Saito _et al_. (2001) reported that waist-to-hip ratio, BMI, and body fat were significant risk indicators for periodontitis after adjustments for known risk factors. In addition, in a separate analysis of the subsample of subjects with high waist-to-hip ratio, higher BMI and increased body fat significantly increased the adjusted risk of periodontitis, when compared to subjects with low waist-to-hip ratios, BMI or body fat.
Given that the above publications are based on only two population samples, and that inferences on temporality or mechanisms are not possible based on cross-sectional studies, additional research on the role of obesity in periodontitis is warranted.
### Osteopenia/osteoporosis
Several cross-sectional studies, of limited sample size and largely confined to postmenopausal women, have suggested that women with low bone mineral density are more likely to have CAL, gingival recession and/or pronounced gingival inflammation (von Wowern _et al_. 1994; Mohammad _et al_. 1996, 1997; Tezal _et al_. 2000). In a radiographic study of 1084 subjects aged 60–75 years, Persson _et al_. (2002) reported a positive association between osteoporosis and periodontitis with an odds ratio of 1.8 (95% CI 1.2–2.5) However, studies that failed to report such an association have been published as well (Weyant _et al_. 1999; Lundström _et al_. 2001).
Based on these studies it has been hypothesized that the systemic loss of bone density in osteoporosis may, in combination with hormone action, heredity, and other host factors, provide a host system that is increasingly susceptible to the infectious destruction of periodontal tissue (Wactawski-Wende 2001). However, the data from longitudinal studies are similarly conflicting. Contrary to Payne _et al_. (1999, 2000) who reported an enhanced longitudinal alveolar bone loss in osteoporotic women versus women with normal mineral bone density, Reinhardt and colleagues (1999) reported no significant impact of serum estradiol levels on longitudinal attachment loss over a 2-year period. In contrast, Yoshihara _et al_. (2004) found, after adjustments, a significant association between bone mineral density and 3-year longitudinal attachment loss in Japanese subjects ≥70 years old. It appears therefore that additional research is needed to unequivocally establish or refute the role of osteoporosis as a risk factor for periodontitis.
### Human immunodeficiency (HIV) infection
After the early studies published in the late 1980s which seemed to indicate that both the prevalence and the severity of periodontitis were exceptionally high in patients with acquired immunodeficiency syndrome (AIDS) (Winkler & Murray 1987), a more tempered picture emerged in subsequent publications. While it cannot be ruled out that the initial reports actually included biased samples, it is also possible that the successful control of immunosuppression in HIV-positive subjects by means of high activity anti-retroviral therapy (HAART) and other continuously evolving drugs has influenced the incidence of periodontal disease progression in HIVseropositive subjects and has resulted in less severe periodontal manifestations of HIV infection (Chapple & Hamburger 2000). For example, a cross-sectional study of 326 HIV-infected adults (McKaig _et al_. 1998) revealed that, after adjustments for CD4 counts, persons taking HIV-antiretroviral medication were five times less likely to suffer from periodontitis than those not taking such medication, underscoring the importance of the host's immunologic competency in this context.
Nevertheless, publications of the last decade continue to generate conflicting results. Thus, although studies (Smith _et al_. 1995a; Robinson _et al_. 1996; Ndiaye _et al_. 1997; McKaig _et al_. 1998) indicated higher prevalence and severity of periodontitis in HIV-positive subjects when compared to controls, other studies are either not supportive of this notion or indicate that the differences in periodontal status between HIV-seropositive and -seronegative subjects are limited (Cross & Smith 1995; Lamster _et al_. 1997; Scheutz _et al_. 1997; Lamster _et al_. 1998; Vastardis _et al_. 2003). Studies investigating the pathobiology of periodontitis in HIV infected subjects suggested that specific IgG subclass responses to periodontopathic bacteria were similar in HIV-positive and HIV-negative subjects (Yeung _et al_. 2002), while CD4 count levels were not found to correlate with the severity of periodontitis (Martinez Canut _et al_. 1996; Vastardis _et al_. 2003).
The few available longitudinal studies are equally conflicting. Two companion publications reporting from a short-term follow-up study (Cross & Smith 1995; Smith _et al_. 1995b) involved a group of 29 HIV-seropositive subjects who were examined at baseline and 3 months and reported a low prevalence and incidence of attachment loss. The subgingival microbial profiles of the seropositive subjects resembled those obtained from non-systemically affected subjects, and were not correlated to their CD4 and CD8 lymphocyte counts. Similarly, in a small followup study of 12 months duration, Robinson _et al_. (2000) found no difference in the progression of periodontitis between HIV-positive and HIV-negative subjects. Hofer _et al_. (2002) demonstrated that compliant HIV-positive subjects can be successfully maintained in a manner similar to non-infected controls. However, a 20-month follow-up study of 114 homosexual or bisexual men by Barr _et al_. (1992) revealed a clear relationship between incidence of attachment loss and immunosupression, expressed through CD4 cell counts. The authors suggested that seropositivity in combination with older age confers an increased risk for attachment loss. Similar observations were reported by Lamster _et al_. (1997) who concluded that periodontitis in the presence of HIV infection is dependent upon the immunologic competency of the host as well as the local inflammatory response to both typical and atypical subgingival microbiota.
It appears therefore that there is no consensus in the literature on the association of HIV/AIDS and periodontitis. Variance due to ongoing advancements in therapy will likely further contribute to the diversity of the findings.
### Psychosocial factors
The mechanisms by which psychosocial stress may affect the periodontal status are complex. It has been suggested that one of the plausible pathways may involve behavioral changes leading to smoking and poor oral hygiene that, in turn, may affect periodontal health (Genco _et al_. 1998). In the absence of a biological measure of stress, a limited number of studies have used proxy measures of stress to study its association with periodontitis. In a study of 1426 subjects in Erie County, NY, USA, Genco _et al_. (1999) reported that adult subjects who were under financial strain and exhibited poor coping behaviors were at increased risk of severe periodontitis when compared with subjects who demonstrated good coping behavior patterns under similar financial strain, or with controls under no financial strain. In a limited size study that included 23 employed adults, Linden _et al_. (1996) evaluated the association between occupational stress and the progression of periodontitis and reported that longitudinal attachment loss was significantly predicted by increasing age, lower socioeconomic status, lower job satisfaction, and type A personality, characterized by aggressive, impatient, and irritable behavior. In contrast, a study of 681 subjects carried out in Lithuania (Aleksejuniene _et al_. 2002) could not document an association between psychosocial stress and periodontitis, although they reported that the disease did correlate with lifestyle factors.
Clearly, the study of the role of stress in periodontitis is in its infancy and multiple gaps in our knowledge knowledge exist. Nevertheless, given the established role of the sympathetic, parasympathetic, and the peptidergic/sensory nervous systems, as well as that of the hypothalamic–pituitary–adrenal axis on brain-toimmune regulatory pathways, such a role is clearly biologically plausible. Recent experimental animal studies have begun to shed light on basic mechanisms that may explain the link between psychosocial factors and periodontitis. For example, a recent study by Breivik _et al_. (2006) demonstrated that experimentally induced depression in rats accelerated tissue breakdown in a ligature periodontitis model and that pharmacologic treatment of depression attenuated this breakdown. Additional basic and epidemiologic research is needed to fully elucidate this relationship.
### Remarks
The analytical epidemiologic studies described above are obviously diverse with respect to important elements of design and methodology, such as definitions of disease, sample size, use of full-mouth or partial-mouth recording protocols, length of followup in longitudinal studies, comprehensive or not adjustment for potential confounders, etc. Nevertheless, despite these apparent shortcomings, a number of conclusions can be made with reasonable certainty:
1. Specific bacteria, cigarette smoking, and diabetes mellitus are the major established risk factors for periodontitis. A number of biologically plausible, potentially important additional factors are in need of further investigation in future studies.
2. There is a need to introduce a uniform definition of periodontitis to be used in analytical epidemiologic studies, to facilitate valid comparisons and establish whether seemingly conflicting data reflect true biological variation or are exclusively owed to methodological inconsistencies. To address this point, the Consensus Report of 5th European Workshop in Periodontology (Tonetti & Claffey 2005) suggested a two-level definition of periodontitis as follows: (i) presence of proximal attachment loss of ≥3 mm in two or more nonadjacent teeth, and (ii) presence of proximal attachment loss of ≥5 mm in ≥30% of teeth present. Likewise, the following case definition for the progression of periodontitis was proposed: presence of two or more teeth demonstrating a longitudinal loss of proximal attachment of ≥3 mm, or in cases where attachment level measurements are not available, longitudinal radiographic bone loss of ≥2 mm at two or more teeth may be used as a substitute. Obviously, no definition is devoid of shortcomings and the above proposals are no exception. Nevertheless, a consistent "common denominator" definition across studies will greatly facilitate valid comparisons.
3. Studies need to distinguish clearly between risk factors and disease predictors. Although the use of the latter as explanatory variables in multivariate models may increase the coefficient of determination (i.e. the proportion of the variance explained by means of the models), it may obscure the significance of true etiologic factors. For example, as shown by Ismail _et al_. (1990), factors with biologically plausible etiologic potential (such as dental plaque) may not retain their significance in multi-variate models that include alternative expressions of disease such as tooth mobility. It has been demonstrated that baseline levels of disease and morphologic features such as angular bony defects are powerful predictors of future disease progression (Papapanou _et al_. 1989; Papapanou & Wennström 1991). Haffajee _et al_. (1991a) showed that age, plaque, and bleeding on probing are related to both baseline disease levels as well as to incident disease. In the search of true exposures of significance for disease onset or progression, inclusion of a factor in a model may thus erroneously discredit a co-varying, biologically significant other factor.
4. The progression pattern of periodontitis over time appears to follow a skewed distribution similar to the skewed distribution of the prevalence of severe periodontitis in the population. In other words, although a majority of subjects may harbor sites which progress over time, it is a small subfraction of subjects that suffer substantial longitudinal attachment loss or bone loss at multiple sites.
Finally, an interesting observation was brought up in a report by Beck _et al_. (1995). In a longitudinal study, the authors compared characteristics of patients experiencing attachment loss at previously non-diseased sites with those of patients suffering progression of already established disease. While low income and medication with drugs associated with soft tissue reactions were features in common for both groups of patients, new lesions were more frequent in patients who used smokeless tobacco and had a history of oral pain. Risk for progression of established disease was higher in cigarette smokers, subjects with high levels of subgingival _P. gingivalis_ , and individuals with worsening financial problems. These data suggest that periodontitis may be like other diseases for which the factors associated with the initiation of the disease may be different from the ones involved in its progression. If this observation is verified in other studies, such a distinction may have implications for future assessment strategies and may improve the accuracy of the risk/prediction models.
# Periodontal infections and risk for systemic disease
During the past decade and a half, an entirely new area of periodontal research has emerged, commonly referred to as "periodontal medicine". Following some initial reports suggesting a link between periodontal infections and a number of systemic conditions, researchers are increasingly dwelling into the exploration of additional epidemiological and experimental evidence as well as possible underlying pathogenic mechanisms. The biological plausibility of the proposed associations between periodontitis and atherosclerosis, cardiovascular and cerebrovascular disease, pregnancy complications, and diabetes mellitus, and the relevant epidemiological evidence available today are summarized in the following text.
### Atherosclerosis – cardiovascular/cerebrovascular disease
A wealth of data originating from diverse areas of investigation have implicated chronic, low-level inflammation as an important factor in atherosclerotic cardiovascular disease (CVD) (Ross 1999). Supporting studies stemming from a variety of disciplines, such as cell biology, epidemiology, clinical trials, and experimental animal research, have consistently revealed that atherosclerotic lesions involve an inflammatory component. The cellular interactions in atherogenesis are fundamentally similar to those in chronic inflammatory–fibroproliferative diseases, and atherosclerotic lesions represent a series of highly specific cellular and molecular responses that can best be described, in aggregate, as an inflammatory disease (Ross 1993, 1999).
It is well established that the periodontal diseases represent mixed infections of the periodontal tissues caused by primarily anaerobic, Gram-negative bacteria (Haffajee & Socransky 1994). As discussed above, the prevalence of these infections, especially of mild or moderate severity, may be substantial in certain populations. The deepening of the periodontal sulcus which occurs during the course of these infections is concurrent with a marked bacterial proliferation, resulting in bacterial cell levels reaching 109 or 1010 bacteria within a single pathological periodontal pocket. The ulcerated epithelial lining of the periodontal pocket may constitute a substantial surface area in cases of generalized periodontitis (Hujoel _et al_. 2001) and provides a gate through which lipopolysaccharide (LPS) and other antigenic structures of bacterial origin challenge the immune system and elicit a local and systemic host response (Ebersole & Taubman 1994). Importantly, a number of pathogenic species involved in the periodontal infections display tissue invasion properties (Meyer _et al_. 1991; Sandros _et al_. 1994; Lamont _et al_. 1995). Frequent transient bacteremias occurring as a result of daily activities such as tooth brushing or chewing (Silver _et al_. 1977; Kinane _et al_. 2005; Forner _et al_. 2006) may confer a significant systemic bacterial challenge to the host. Circulating levels of several cytokines (IL-1 beta, IL-2, IL-6, and IL-8) induced during the course of several infections (Endo _et al_. 1992; Humar _et al_. 1999; Otto _et al_. 1999), but also locally in the periodontal tissues in conjunction with periodontitis (Salvi _et al_. 1998), have been identified as biomarkers of cardiovascular disease (Hackam & Anand 2003; Hansson 2005). Interestingly, these proinflammatory cytokines have also been detected within atheromatous lesions (Barath _et al_. 1990a,b; Galea _et al_. 1996). In line with the observation that chronic infection may contribute to a procoagulant state, elevated von Willebrand factor antigen, a measure of endothelial cell damage, has been demonstrated in individuals with multiple dental infections (Mattila _et al_. 1989; Torgano _et al_. 1999).
A number of studies have examined the presence of oral bacteria in atheromatic plaque lesions. Chiu (1999) investigated the relationship between the presence of multiple infectious agents in human carotid endarterectomy specimens and pathoanatomic features of the corresponding carotid plaques, and reported positive immunostainings for _P. gingivalis_ and _Streptococcus sanguis_ in several carotid plaque specimens. The bacteria were immunolocalized in plaque shoulders and within a lymphohistiocytic infiltrate, associated with ulcer and thrombus formation, and adjacent to areas of strong labeling for apoptotic bodies. A similar study using the polymerase chain reaction (Haraszthy _et al_. 2000) reported that 30% of the carotid endarderectomy specimens examined were positive for _T. forsythia_ , 26% for _P. gingivalis_ , 18% for _A. actinomycetemcomitans_ , and 14% positive for _Pr. intermedia_. The validity of these data has been recently confirmed in similar studies (Stelzel _et al_. 2002; Fiehn _et al_. 2005). Corroborating the above observations, in an experimental animal study, oral infection of with _P. gingivalis_ promoted atherogenesis and _P. gingivalis_ DNA was localized within the aortic tissue of infected mice (Lalla _et al_. 2003).
Emerging evidence from epidemiologic studies indicates that periodontal infections have an impact on a host of peripheral blood markers that have been linked to CVD. For example, periodontitis patients have been shown to display higher white blood cell counts (Kweider _et al_. 1993; Loos _et al_. 2000) and C-reactive protein (CRP) levels (Ebersole _et al_. 1997; Loos _et al_. 2000; Slade _et al_. 2000) than periodontally healthy controls. Wu _et al_. (2000) examined the relation between periodontal health status and serum total and high-density lipoprotein cholesterol, CRP, and plasma fibrinogen. Based on an analysis of a total of 10 146 subjects from NHANES III with available cholesterol and CRP and 4461 subjects with available fibrinogen, poor periodontal status was significantly associated with increased CRP and fibrinogen levels. Slade _et al_. (2000) explored the same database and reported that (1) people with extensive periodontal disease had an increase of approximately one third in mean CRP and a doubling in prevalence of elevated CRP compared with periodontally healthy people, and (2) similarly raised CRP levels in edentulous subjects. Based on data of 2973 participants ≥40 years old from the second phase of NHANES III, Dye _et al_. (2005) showed that high serum IgG antibody level to _P. gingivalis_ was significantly related to elevated serum CRP. In a sample comprising 5552 subjects aged 52–75 years from the Atherosclerosis Risk in Communities study (ARIC) (Slade _et al_. 2003), participants with extensive periodontal disease (≥30% of sites with pocket depth ≥4 mm) had 30% higher CRP levels than participants with extent of periodontal disease between 0 and 30%. In a multi-variate analysis stratified for BMI, extensive periodontal pocketing remained associated with CRP levels when adjusted for age, sex, diabetes mellitus, cigarette use, and use of non-steroidal anti-inflammatory medications. Finally, Schwahn _et al_. (2004) reported on associations between periodontitis, edentulism, and high plasma fibrinogen levels (>3.25 g/l), in 2738 persons aged 20–59 years, participants in the Study of Health in Pomerania (SHIP). In a two-way interaction model adjusted for multiple co-variates (age, gender, BMI, education, alcohol, gastritis, bronchitis, diabetes, use of medications, use of aspirin, LDL, and smoking), presence of ≥15 pockets with probing depth ≥4 mm was significantly associated with high plasma fibrinogen levels with an OR of 1.9 (95% CI 1.2–2.8). Less extensive pocketing or edentulism were not associated with high plasma fibrinogen levels.
Several studies have investigated the association between periodontitis and subclinical atherosclerosis, commonly measured by means of carotid artery intima media thickness (IMT) assessments. Increased IMT has been documented to be directly associated with increased risk or myocardial infarction and stroke (O'Leary _et al_. 1999). Beck _et al_. (2001) provided the first evidence that periodontitis may be linked to subclinical atherosclerosis. These authors analyzed cross-sectional data on 6017 persons, participants in the ARIC study, and demonstrated that severe periodontitis conferred increased odds for higher carotid artery intima media wall thickness (OR 2.09, 95% CI 1.73–2.53 for IMT of ≥1 mm). A couple of years later, the Oral Infection and Vascular Disease Epidemiology Study (INVEST; a prospective population-based cohort study of randomly selected subjects in a triethnic population, comprising a total of 1056 subjects aged ≥55 years, with no baseline history of stroke, myocardial infarction, or chronic inflammatory conditions) investigated the relationship between carotid artery plaque and IMT with tooth loss and measures of periodontitis. In a first report based on data from 711 subjects (Desvarieux _et al_. 2003), tooth loss of 10–19 teeth was associated with increase in prevalence of atherosclerotic plaques in a model adjusted for age, sex, smoking, diabetes, systolic blood pressure, LDL, HDL, ethnicity, education, tooth brushing, social isolation, physical activity, and years of residence (OR 1.9, CI 1.2–3.0). Since in this cohort a higher number of lost teeth paralleled an increased severity of periodontal disease at the remaining teeth, it was assumed that tooth loss reflected, in part, current or cumulative periodontal disease. In a subsequent publication, Engebretson _et al_. (2005) reported on a sub-sample of 203 subjects from the INVEST cohort with available panoramic radiographs. In a logistic regression model, severe bone loss was defined as a whole mouth average bone loss of ≥50% of the root length and was associated with presence of carotid atherosclerotic plaque after adjustment for age, sex, hypertension, coronary artery disease, diabetes, smoking, HDL, and LDL. In addition, logtransformed mean carotid plaque thickness increased over tertiles of periodontal bone loss, suggesting a dose-dependent association. A third INVEST report (Desvarieux _et al_. 2005) included 657 patients with available dental and medical variables as described above, as well as data on the prevalence and level of ten bacterial species, assessed by checkerboard DNA–DNA hybridization (Socransky _et al_. 1994) in up to eight subgingival plaque samples per subject. In this study, "etiological bacterial burden" was defined as the aggregate colonization per subject by _A. actinomycetemcomitans_ , _P. gingivalis_ , _T. forsythia_ , and _Tr. denticola_. The data revealed that IMT and while blood cell counts increased significantly over tertiles of etiologic periodontal bacterial burden in a fully adjusted model including age, BMI, gender, race/ethnicity, smoking, systolic blood pressure, education, diabetes, HDL, and LDL as co-variates. Importantly, the association was exclusively observed for "etiologic bacteria", as increased colonization by putative pathogens of the "orange complex" or a number of health-associated bacteria was not associated with increased IMT.
In an ARIC-based study including a sample of 4585 participants (Beck _et al_. 2005b), serum IgG titers for periodontal pathogens were associated with carotid IMT of ≥1 mm. The strongest association emerged when the combined titer against _Campylobacter rectus_ and _Micromonas micros_ was used. Similarly, a research group from Finland reported on the association between serum titers to periodontal pathogens and IMT in a sub-sample of 1023 men aged 46–64 from the Kuopio Ischemic Heart Disease Risk Factor study (Pussinen _et al_. 2005). Incident IMT assessed 10 years post baseline in participants with no prior coronary heart disease increased significantly across tertiles of IgA titer levels to _A. actinomycetemcomitans_ and _P. gingivalis_.
Another group of epidemiologic studies has focused on the association of periodontal infections with clinical events, primarily coronary heart disease (CHD), myocardial infacrtion (MI) or stroke. An early study by DeStefano _et al_. (1993) used a prospective cohort of 9760 subjects and found a nearly two-fold higher risk of CHD for individuals with periodontal disease. Beck _et al_. (1996) used data from a cohort of 1147 subjects who were medically healthy at baseline, 207 of which developed CHD over an average follow-up of 18 years. Radiographic evidence of alveolar bone loss was used to stratify the subjects according to minimal and severe periodontitis. The results, presented as incidence odds ratios adjusted for age and race, showed a significant association between severe bone loss and total CHD, fatal CHD, and stroke.
Another ARIC-stemming report based on a sample of 5002 people (Beck _et al_. 2005a) reported no significant association between incipient or severe periodontitis defined by clinical measurements and CHD. However, in regression models adjusted for age, sex, race, diabetes, hypertension, waist-to-hip ratio, HDL and LDL cholesterol, and education, detectable antibody levels to specific periodontal pathogens were associated with prevalent CHD. When stratified for smoking, titers _to Tr. denticola_ , _Prevotella intermedia_ , _Capnocytophaga ochracea_ , and _Veillonella parvula_ conferred significant odds for CHD in ever smokers, while titers to _Prevotella nigrescens_ and _A_. _actinomycetemcomitans_ conferred significant odds for CHD in never smokers. In a retrospective follow-up study of a Finnish cohort of 63 men who were free of CHD at entry, but who developed fatal or non-fatal MI during a subsequent 10-year period, and of 63 age-matched controls, Pussinen _et al_. (2004) analyzed serum samples with respect to IgG and IgA antibodies to different strains of _A. actinomycetemcomitans_ and _P. gingivalis_. In logistic regression models adjusted for traditional CHD risk factors such as smoking, serum cholesterol, blood pressure, BMI, and diabetes, increasing serum IgA titers to _P. gingivalis_ resulted in significantly increasing odds for MI.
Among the group of studies focusing on the potential association of periodontitis and stroke, an early case–control study by Syrjanen _et al_. (1989) compared the level of dental disease in 40 patients who had suffered a cerebrovascular accident with 40 randomly selected community controls, matched for gender and age, and reported that severe chronic dental infection was associated with cerebral infarction in males under 50 years of age. In another case–control study (Grau _et al_. 1997), multiple logistic regression adjusted for age, social status, and a number of established vascular risk factors revealed that poor dental status was independently associated with cerebrovascular ischemia (OR 2.6, 95% CI 1.18–5.7).
Obviously, critical information on the role of periodontal infection as risk factor for atherosclerotic vascular disease and its sequels should be derived from intervention trials, ideally from randomized, placebo-controlled clinical trials. Unfortunately the design and conduct of such studies is particularly challenging, primarily due to the long time between exposure and manifestation of CVD, the relatively low incidence of CVD-related clinical events necessitating the inclusion of large subject samples, and ethical considerations related to the follow-up of untreated periodontal disease over prolonged time periods. Therefore, intervention trials conducted to date have been limited to the study of the effects of periodontal therapy on surrogate markers of risk for CVD or on pathways related to the pathobiology of the disease. For example, D'Aiuto _et al_. (2004) reported on 94 systemically healthy patients with generalized severe periodontitis who received non-surgical therapy and extractions. In logistic regression analysis, the reduction of CRP-levels 6 months after periodontal therapy was significantly associated with the number of extracted teeth (OR 1.4, CI 1.1–1.8) and a greater than the median probing depth reduction in pockets initially ≥5 mm (OR 4.7, CI 1.4–15.8). In subsequent publications (D'Aiuto _et al_. 2005; D'Aiuto & Tonetti 2005), non-surgical periodontal therapy with and without adjunctive local antibiotics, resulted in a reduction of median CRP-levels at 2 months, with a more pronounced effect in non-smokers than in smokers. Circulating IL-6 levels were significantly reduced only in the group that received adjunctive local antibiotics (intensive treatment), but no significant changes were observed in LDL and HDL cholesterol and triglyceride levels. The same group (D'Aiuto _et al_. 2006) recently reported 6-month data on the effect of standard vs. intensive therapy. In comparison to baseline levels, a significant reduction in white blood cell counts, CRP levels, IL-6 levels, total cholesterol, LDL, and systolic blood pressure was observed in the intensive treatment group, whereas an increase in HDL levels was observed in the standard treatment group. Similarly, Taylor _et al_. (2006) reported that patients undergoing full-mouth extractions who had at least 2 teeth with probing depths ≥6 mm, attachment loss and bleeding on probing showed a significant reduction in CRP levels from 2.5 mg/L to 1.8 mg/L, and this effect was more pronounced in non-smokers.
Finally, another set of studies has focused on the effects of periodontal therapy on endothelial dysfunction, a biomarker of vascular disease (Verma _et al_. 2003). Endothelial dysfunction is defined as the reduced vasodilator capability of peripheral blood vessels and is assessed by measuring the difference in the diameter of a peripheral artery prior to and after reactive hyperemia induced through occlusion of blood flow (Celermajer _et al_. 1992). Endothelial dysfunction was more pronounced in periodontitis subjects than periodontally healthy controls in two studies (Amar _et al_. 2003; Mercanoglu _et al_. 2004). Three intervention studies reporting positive effects of periodontal therapy on endothelial dysfunction are available so far: one using non-surgical periodontal therapy (Mercanoglu _et al_. 2004), one using adjunctive systemic antibiotics (Seinost _et al_. 2005), and a third using a comprehensive "full-mouth disinfection" protocol (Elter _et al_. 2006).
Taken together, the studies above strongly suggest a biologically plausible association between periodontal infections and the pathogenesis of atherosclerotic cardiovascular disease. Obviously studies that have failed to document such an association or that point to a possibility of a more complex, conditional relationship exist as well (Hujoel _et al_. 2000, 2002b; Mattila _et al_. 2000). In particular, it has been suggested that the positive associations in epidemiologic studies between periodontal infections and atherosclerotic cardiovascular disease may be attributed to residual confounding due to insufficient accounting for the effects of smoking (Hujoel _et al_. 2002a; Spiekerman _et al_. 2003) or may be entirely spurious (Hujoel _et al_. 2003, 2006). While such a possibility is hard to rule out, it appears unreasonable to dismiss as an artifact the entire body of supportive data stemming from diverse investigational approaches (epidemiological, experimental, mechanistic, and intervention studies).
### Pregnancy complications
Preterm infants are born prior to completion of 37 weeks of gestation. An estimated 11% (Goldenberg & Rouse 1998) of pregnancies end in preterm birth (PTB), and this rate appears to be on the rise in several developed countries, despite significant advances in obstetric medicine and improvements in prenatal care utilization. Of particular interest are the very preterm infants, born prior to 32 gestational weeks, the majority of which require neonatal intensive care due to their increased perinatal mortality, primarily due to impaired lung development and function. Still, the overall contribution of PTB to infant mortality and morbidity is substantial and includes a number of acute and chronic disorders including respiratory distress syndrome, cerebral palsy, pathologic heart conditions, epilepsy, blindness, and severe learning disabilities (McCormick 1985; Veen _et al_. 1991).
Preterm infants often weigh lower at birth (<2500 g), and low birth weight has been used as a surrogate for prematurity in cases where the exact gestational age at birth is difficult to assess. Birth weight is further classified as very low (<1500 g) or moderately low (between 1500 g and 2500 g). An additional term used is small for gestational age, defined as birth weight within the 10th percentile of normal weight at a particular gestational age. The condition may, thus, affect even full term infants due to intra-uterine growth retardation (Ashworth 1998).
A number of risk factors for preterm birth has been identified (Goldenberg _et al_. 2000). These include young maternal age (Wessel _et al_. 1996; Lao & Ho 1997; Scholl _et al_. 1988), multiple gestation (Lee _et al_. 2006), small weight gain during pregnancy (Honest _et al_. 2005), cervical incompetence (Althuisius & Dekker 2005), smoking, alcohol and drugs of abuse (Myles _et al_. 1998), black race (Kleinman & Kessel 1987; David & Collins 1997), and a number of maternal infections (uterine track infections, bacterial vaginosis, chorioamnionitis) (Romero _et al_. 2001). Obstetric history of PTB is a robust marker of future PTB (Mutale _et al_. 1991). Importantly, approximately 50% of the variance in the incidence of preterm birth remains unexplained (Holbrook _et al_. 1989).
Despite the established role of genito-urinary tract infections in the pathobiology of preterm birth, women with preterm labor do not invariably present with positive amniotic fluid cultures (Romero _et al_. 1988), leading to the hypothesis that PTB may be indirectly mediated through _distant_ infections resulting in translocation of bacteria, bacterial vesicles or LPS in the systemic circulation. The possibility that periodontal infections may constitute such maternal infections that adversely influence birth outcome was raised for the first time in the late 1980s (McGregor _et al_. 1988). Transient bacteremias occur commonly in subjects with inflamed gingiva (Ness & Perkins 1980; Kinane _et al_. 2005; Forner _et al_. 2006) and may conceivably reach the placental tissues, providing the inflammatory impetus for labor induction (Offenbacher _et al_. 1998). An interesting publication in this context by Hill (1998) reported that amniotic fluid cultures from women with vaginosis rarely contained bacteria common to the vaginal tract but frequently harbored fusobacteria of oral origin, i.e. common constituents of the periodontal microbiota. Thus, these authors proposed that oral bacteria may reach amniotic fluids and influence maternal fetal tissues via hematogenous spread, resulting in a chorioamniotic challenge. In line with these observations, experimental evidence on the role of oral infections on pregnancy outcomes was first provided is a series of pioneering studies by Collins _et al_. (1994a,b), who demonstrated that injection of _P. gingivalis_ in the pregnant hamster resulted in intrauterine growth retardation, smaller fetuses, and an increase in proinflammatory mediators such as IL-1beta and PGE2 in the amniotic fluid. Subsequent studies in pregnant mice (Lin _et al_. 2003a,b) and rabbits (Boggess _et al_. 2005) confirmed and expanded these observations to include experimental infections by _Campylobacter rectus_.
The accumulating body of evidence available from human studies investigating a potential link between oral infections and adverse pregnancy outcomes were recently reviewed (Bobetsis _et al_. 2006; Xiong _et al_. 2006). In an early case–control study, Offenbacher _et al_. (1996) examined 124 mothers, of whom 93 ("cases") gave birth to children with birth weight of less than 2500 g, prior to 37 weeks of gestation. "Controls" were 46 mothers who delivered at term infants of normal birth weight. Assessments included a broad range of known obstetric risk factors, such as tobacco use, drug use, alcohol consumption, level of prenatal care, parity, genitourinary infections, and nutrition. The data showed a small, albeit statistically significant difference, in attachment loss between cases and controls (3.1 vs 2.8 mm). Multivariate logistic regression models, controlling for other risk factors and covariates, demonstrated that periodontitis, defined as ≥60% of all sites with attachment loss of ≥3 mm, conferred adjusted ORs of 7.9 for preterm, low birthweight babies. Following this report, several additional case–control studies were published, most of which reported a positive association between periodontitis and adverse pregnancy outcomes (Offenbacher _et al_. 1996; Dasanayake _et al_. 2001; Canakci _et al_. 2004; Goepfert _et al_. 2004; Mokeem _et al_. 2004; Radnai _et al_. 2004), although a number of studies that failed to document an association were published as well (Davenport _et al_. 2002; Buduneli _et al_. 2005; Moore _et al_. 2005).
Non-uniform data were also generated by cohort studies, i.e. studies that evaluated the periodontal status of pregnant women prior to completion of the second trimester and compared prospectively the incidence of adverse pregnancy outcomes in women with and without periodontitis. In the first prospective cohort study reporting a positive relationship between periodontitis and prematurity, Jeffcoat _et al_. (2001) assessed the periodontal conditions of 1313 primarily African American pregnant women at 21– 24 weeks of gestation and reported that for women with generalized periodontitis, defined as ≥90% of all sites with attachment loss of 3 mm or more, adjusted odds ratios were 4.45 for delivery prior to 37 weeks' gestational age, 5.28 for delivery before 35 weeks' gestational age, and 7.07 for delivery before 32 weeks' gestational age. Corroborating positive data were reported by additional cohorts in the US (Offenbacher _et al_. 2001), Chile (Lopez _et al_. 2002a), and Switzerland (Dortbudak _et al_. 2005). Similar positive associations were reported for very preterm delivery (Offenbacher _et al_. 2006), small-for gestational-age infant (Boggess _et al_. 2006a), pre-eclampsia (Boggess _et al_. 2003), fetal exposure to oral pathogens, assessed by the presence of IgM antibodies in the fetal cord blood (Madianos _et al_. 2001), and with ante-partum vaginal bleeding and risk for premature delivery prior to 35 gestational weeks (Boggess _et al_. 2006b). In contrast, four cohort studies (Romero _et al_. 2002; Holbrook _et al_. 2004; Moore _et al_. 2004; Rajapakse _et al_. 2005) failed to document such an association. Of particular interest is the study by Moore _et al_. (2004) who reported data on 3738 women recruited on attending an ultrasound scan at approximately 12 weeks of pregnancy. Regression analysis indicated no significant relationships between the severity of periodontal disease and either preterm birth or low birth weight, although a positive correlation was reported between poorer periodontal health and late miscarriage.
Five intervention studies on the effects of periodontal treatment on pregnancy outcomes have been published to date. The first (Mitchell-Lewis _et al_. 2001) examined a cohort of 213 young, minority, pregnant, and post-partum women with respect to clinical periodontal status and analyzed the available birth outcome data for 164 women, 74 of whom received oral prophylaxis during pregnancy, and 90 who received no prenatal periodontal treatment. In this cohort with particularly high incidence of preterm low birth weight (PLMW of 16.5%), no differences in clinical periodontal status were observed between PLBW cases and women with normal birth outcomes. However, PLBW mothers harbored statistically significantly higher levels of _T. forsythia_ and _C. rectus_ , and consistently elevated counts for a number of species examined. Interestingly, PLBW occurred in 18.9% of the women who did not receive periodontal intervention, and in 13.5% (ten cases) of those who received such therapy, reflecting a substantial, although statistically non-significant, incidence reduction of approximately 30%. However, the small sample size in combination with the fact that the participants were not randomly assigned into the two treatment groups were important shortcomings of the study design.
In a pilot intervention study, Jeffcoat _et al_. (2003) recruited 366 women with periodontitis between 21 and 25 weeks' gestation and randomized them to one of three treatment groups with stratification on previous spontaneous preterm birth prior to 35 weeks, BMI <19.8, or bacterial vaginosis assessed by Gram stain of vaginal smear samples. The treatment arms included a group that received supragingival dental prophylaxis and a placebo capsule; a group that received scaling and root planing (SRP) plus a placebo capsule; and a group that received SRP and systemic metronidazole 250 mg t.i.d. for 1 week. An additional group of 723 pregnant women who enrolled in a prospective study served as an untreated reference group. The results revealed that the rate of PTB before 35 gestational weeks was 4.9% in the prophylaxis group, 3.3% in the SRP plus metronidazole group, and 0.8% in the SRP plus placebo group. The corresponding PTB rate in the reference group was 6.3%. Although the difference between the prophylaxis and the SRP plus placebo group approached, but did not reach, statistical significance, the study suggested that periodontal therapy has the potential to reduce PTB, but that adjunctive systemic metronidazole did not enhance the pregnancy outcome. The latter observation is in line with the findings of a multicenter trial that suggested that systemic metronidazole used in the treatment of asymptomatic bacterial vaginosis does not reduce the occurrence of preterm delivery (Carey _et al_. 2000).
In contrast, impressive positive findings were reported from two randomized clinical trials conducted in Chile (Lopez _et al_. 2002b, 2005). In the first trial (Lopez _et al_. 2002b), 400 pregnant women with periodontal disease were enrolled and randomly assigned to either a treatment group which received periodontal therapy before 28 weeks of gestation or to a control group which received treatment after delivery. The incidence of PLBW (i.e. gestational age at birth <37 weeks or birth weight <2500 g) among the 351 women who completed the trial was 1.8% in the treatment group and 10.1% in the control group, resulting in an OR of 5.5 (95% CI 1.6–18.2, p = 0.001). In a multi-variate logistic regression model accounting for previous PLBW, frequency of prenatal visits, and maternal low weight gain, periodontitis remained the strongest factor with OR of 4.7 (95% CI 1.3–17.1). Of note in this trial is the relatively high drop-out rate (12.2%), as well as the fact that approximately one fifth of the women in the treatment group received adjunctive systemic antibiotics (amoxicillin and metronidazole) for the control of aggressive periodontitis. The second trial from the same group (Lopez _et al_. 2005) examined the effect of treatment of gingivitis on adverse pregnancy outcomes. Out of 870 pregnant women with gingivitis enrolled, two thirds received plaque control, scaling, and daily rinsing with 0.12% clorhexidine prior to 28 weeks of gestation, followed by maintenance every 2–3 weeks until delivery (treatment group) while a control group received therapy after delivery. With 834 women completing the trial, the incidence of PTLBW was 2.1% in the treatment group and 6.7% in the control group (OR 3.3, 95% CI 1.6–6.8; p =0.0009).
Finally, a multicentre randomized, blinded, controlled trial examined the effect of non-surgical periodontal treatment on preterm birth (Michalowicz _et al_. 2006). After screening a total of 3504 women for a minimum extent and severity of periodontitis to satisfy the study's enrollment criteria, 823 women were randomly assigned to either receive scaling and root planing before 21 weeks (413 women) or after delivery (410 women). Participants in the treatment group underwent additional recall visits. The findings (Fig. 7-5) showed that preterm birth before 37 gestational weeks occurred in 49 of 407 women (12.0%) in the treatment group and in 52 of 405 women (12.8%) in the control group (hazard ratio for treatment group vs. control group, 0.93; p = 0.70; 95% CI 0.63–1.37). There were no significant differences between the treatment and control groups in birth weight or in the rate of delivery of infants that were small for gestational age. However, almost three times as many spontaneous abortions or stillbirths occurred in the control group than in the treatment group (14 vs 5, p = 0.04). Thus, this study failed to document a positive effect of periodontal treatment on rates of preterm birth, low birth weight, or fetal growth restriction, although it demonstrated that periodontal treatment of pregnant women is safe.
**Fig. 7-5** Kaplan–Meier curve for the cumulative incidence of pregnancies ending before 37 weeks in the Obstetrics and Periodontal Therapy study. Adapted from Michalowicz _et al_. 2006, reproduced with permission. Copyright © 2006 Massachusetts Medical Society.
The observed discrepancy in spontaneous abortions and stillbirths between the two groups observed in the above study is clearly intriguing. An effect of periodontal treatment on early adverse outcomes is plausible in light of observational studies that suggest that periodontitis is more strongly associated with late miscarriage (Moore _et al_. 2004), stillbirth, and early spontaneous preterm birth rather than with preterm birth in general. It was suggested therefore (Goldenberg & Culhane 2006) that future studies may preferentially focus on late miscarriage, early stillbirth, and preterm birth prior to 32 weeks, rather than on all preterm births prior to 37 weeks. Additional issues to be addressed in future studies relate to the timing and the intensity of the periodontal intervention, as well as the possibility that such effects may vary with race/ethnicity. Currently, there are at least three randomized controlled trials underway, all of which involve larger subject samples that the study by Michalowicz _et al_. (2006), that will contribute with more definitive answers on whether periodontal treatment has a role in reducing the rate of adverse pregnancy outcomes.
### Diabetes mellitus
The role of diabetes as a risk factor for periodontitis has been discussed above; however, limited data seem to suggest that an inverse relationship may also be present. In line with the concept that infections may contribute to impaired metabolic control of diabetes (Rayfield _et al_. 1982; Lang 1992; Ling _et al_. 1994), studies of both type 1 (Thorstensson _et al_. 1996) and type 2 (Taylor _et al_. 1996) diabetic subjects have indicated that periodontal infections may also be detrimental in this context. The former study involved 39 diabetic subjects with severe periodontitis and an equal number of diabetic subjects with gingivitis or mild periodontitis. Both groups had a median duration of diabetes of 25 years. Over a median follow-up period of 6 years, significantly higher prevalence of proteinuria and cardiovascular complications was observed in the severe periodontitis group. A 2-year follow-up study of 90 subjects with type 2 diabetes with good to moderate metabolic control revealed that severe periodontitis at baseline was associated with increased risk for poor glycemic control.
A limited number of studies has examined the effect of treatment of periodontitis on diabetic metabolic control, as reflected by levels of glycated hemoglobin A1c (HbA1c) or plasma glucose. Interestingly, all studies that solely included mechanical periodontal therapy (Seppälä _et al_. 1993; Aldridge _et al_. 1995; Smith _et al_. 1996; Grossi _et al_. 1997a; Christgau _et al_. 1998) but one (Stewart _et al_. 2001) reveal no effect on diabetes metabolic control, regardless of periodontal disease severity, baseline level of metabolic control, type and duration of diabetes. Interestingly, Stewart _et al_. (2001) followed 72 patients with type 2 diabetes for 18 months, half of whom received mechanical periodontal therapy, but reported that both the periodontally treated and the untreated group showed statistically significant decreases in HbA1c levels (17.1% vs. 6.7%, respectively). In contrast, studies including antibiotics as an adjunct to mechanical therapy (Williams & Mahan 1960; Grossi _et al_. 1997a; Miller _et al_. 1992) reported a limited, short-term improvement in metabolic control. For example, Grossi _et al_. (1997a) reported a 10% improvement in glycated hemoglobin (HbA1c) at 3 months after the completion of non-surgical periodontal therapy combined with adjunctive systemic doxycycline, although this effect was not sustainable at later time points. Interestingly, no such effect on HbA1c was observed in subjects that did not receive adjunctive antibiotic therapy. Rodrigues _et al_. (2003) randomly assigned 30 type 2 patients to two treatment groups, one group receiving non-surgical periodontal therapy with amoxicillin/clavulanic acid and the other receiving only mechanical therapy. At 3 months, HbA1c levels were reduced in both groups, but the reduction was statistically significant only in the group that received scaling and root planing alone. Nevertheless, a recent meta-analysis of ten intervention studies aiming at the quantification of the effects of periodontal treatment on HbA1c level among diabetic patients, including a total of 456 patients, revealed a non-statistically significant decrease in actual HbA1c levels (Janket _et al_. 2005). Indeed, the weighted average decrease in actual HbA1c level was found to be 0.38% for all studies, 0.66% when restricted to type 2 diabetic patients, and 0.71% if adjunctive antibiotics were administered. Clearly, further studies are needed to clarify the conditions under which periodontal treatment can contribute to improved metabolic control, especially in type 1 diabetes.
### Concluding remarks
One of the issues related to the descriptive epidemiology of periodontal infections that is still under debate is whether their worldwide prevalence has been decreasing over the last decades. Unfortunately, the data do not allow a clear answer for a number of reasons. First, no universal conclusion is possible, since the prevalence of periodontal disease appears to vary with race and geographic region. Second, the quality of the data available from the developing and the developed countries is clearly not comparable. While some well conducted epidemiologic surveys that provide detailed information have been carried out in a number of countries, the majority of the studies in the developing world have used the CPITN system, which produced data of inadequate detail. Moreover, studies using the exact same methodology to evaluate random samples drawn from the same population over time are sparse. Among the few exceptions is a series of studies from Sweden (Hugoson _et al_. 1998b, 1992, 2005) that documented, by clinical and radiographic means, the frequency distribution of various levels of severity of periodontitis in four cross-sectional studies over a 30-year period (in 1973, 1983, 1993, and 2003). In these studies, subjects were grouped according to the severity of their periodontal conditions in five groups: groups 1 and 2 included subjects who were periodontally healthy or only had gingivitis, group 3 included subjects with moderate periodontitis, i.e. whose loss of periodontal tissues support did not extend beyond one third of the root length, while groups 4 and 5 included subjects with more severe destructive disease. As shown in Fig. 7-6, a clear increase in the frequency of subjects in groups 1 and 2 was noted over the 30-year period, from 49% in 1973 to 60% in 1993 to almost 62% in 2003. This increase occurred primarily at the expense of group 3 which declined from 38% in 1973 to 27% in 1993 and apparently reached a plateau at 28% in 2003. Nevertheless, the frequency of subjects in groups 4 and 5 was virtually stable over the 30-year period: 13% in 1973, 13% in 1993 and 10.5% in 2003. Based on these data derived from a population with arguably the best access to and utilization of oral health care in the world, we may conclude that the fraction of the population which is apparently most susceptible to severe periodontitis is apparently not declining in frequency. Instead, the main beneficiaries of the improved oral health awareness, access to care and increased utilization of therapeutic resources that occurred over the last decades appear to be the individuals with moderate levels of periodontitis whose prevalence is clearly lower.
**Fig. 7-6** Frequency distribution of subjects with healthy periodontal conditions or gingivitis (groups 1 + 2), moderate periodontitis (group 3), and advanced and severe periodontal disease (groups 4 + 5), in a Swedish cohort in 1973, 1993, and 2003. For definitions see text. Adapted after personal communication with Dr. Anders Hugoson, based on data by Hugoson _et al_. (1992, 1998, 2006).
What was also well documented in these and other studies is that the rate of edentulism has decreased substantially over the past 30 years, with elderly groups retaining their natural dentition and higher mean numbers of teeth than their counterparts a generation ago. As a consequence, this fact _per se_ should contribute to an increased prevalence of periodontal disease in older age cohorts, since retained teeth in the elderly are more likely to experience substantial cumulative attachment loss which forms the basis of the assessment of prevalence (Douglass & Fox 1993). It has been argued, however, that such a potential increase, may not necessarily result in increased need for periodontal therapy (Oliver _et al_. 1989). Additional research is clearly required to further elucidate these issues, and an adequate and consistent epidemiological methodology is essential for generating valid comparative data. On the other hand, the need for description of prevalence and incidence of periodontal diseases in every conceivable population has been questioned (Baelum & Papapanou 1996), although such information may be of value for local oral health planners. Instead, the principle task of future epidemiological research is arguably the identification of risk factors for disease development, laying the ground for an enhanced understanding of the pathobiology of periodontitis. Although several risk factors have already been established and a wide array of disease markers has been recognized, the impact of the intervention with such factors on the state of periodontal health on a population level has yet to be documented. To assess the magnitude of the clinical benefit achieved by such modulation, prospective, long-term epidemiological surveys have to be conducted.
Somewhat provocatively, it has been stated that modern science has a tendency to re-discover issues brought up a long time back and (then) rejected. One cannot help bringing the "focal infection" theory in mind, when encountering the emerging plethora of publications dealing with the role of periodontal infections as risk factors for systemic disease. Although the proposed associations appear to be biologically plausible, at this stage, we cannot draw any definitive conclusions on whether these associations are in fact causal, and if so, on the magnitude of their biological effects. Nevertheless, these studies underscore that the oral cavity is an integral part of the human body, and that systemic health must encompass oral, and periodontal, health as well. Last but certainly not least, these studies have provided a unique opportunity for us oral health researchers to expand our investigative sphere, interact fruitfully with our colleagues in medicine, and acquire more knowledge. Irrespective of the definitive conclusions of these research efforts, its by-products may prove to be just as important as the elucidation of the research task _per se_.
### Acknowledgments
Some of the tables included in this chapter are partly based on the publication of Papapanou (1986), by permission of the American Academy of Periodontology. Parts of the text on "Risk factors for periodontitis" have been adapted from the review by Borrell and Papapanou (2005).
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# Part 3: Microbiology
8 Oral Biofilms and Calculus
_Niklaus P. Lang, Andrea Mombelli, and Rolf Attström_
9 Periodontal Infections
_Sigmund S. Socransky and Anne D. Haffajee_
10 Peri-implant Infections
_Ricardo P. Teles, Anne D. Haffajee, and Sigmund S. Socransky_
# Chapter 8
# Oral Biofilms and Calculus
Niklaus P. Lang, Andrea Mombelli, and Rolf Attström
* * *
Microbial considerations
General introduction to plaque formation
Dental plaque as a biofilm
Structure of dental plaque
Supragingival plaque
Subgingival plaque
Peri-implant plaque
Dental calculus
Clinical appearance, distribution, and clinical diagnosis
Attachment to tooth surfaces and implants
Mineralization, composition, and structure
Clinical implications
* * *
# Microbial considerations
Throughout life, all the interface surfaces of the body are exposed to colonization by a wide range of microorganisms. In general, the establishing microbiota live in harmony with the host. Constant renewal of the surfaces by shedding prevents the accumulation of large masses of microorganisms. In the mouth, however, teeth provide hard, non-shedding surfaces for the development of extensive bacterial deposits. The accumulation and metabolism of bacteria on hard oral surfaces is considered the primary cause of dental caries, gingivitis, periodontitis, peri-implant infections, and stomatitis. Massive deposits are regularly associated with localized disease of the subjacent hard or soft tissues. In 1 mm3 of dental plaque weighing approximately 1 mg, more than 108 bacteria are present. Although over 300 species have been isolated and characterized in these deposits, it is still not possible to identify all the species present. In the context of the oral cavity, the bacterial deposits have been termed _dental plaque_ or _bacterial plaque_. Classical experiments have demonstrated that accumulation of bacteria on teeth reproducibly induces an inflammatory response in associated gingival tissues (Fig. 8-1a,b). Removal of plaque leads to the disappearance of the clinical signs of this inflammation (Löe _et al_. 1965; Theilade _et al_. 1966). Similar cause and effect relationships have been demonstrated for plaque and peri-implant mucositis (Pontoriero _et al_. 1994).
Germ-free animals provide an experimental model which has demonstrated that the absence of bacteria is associated with optimal dental and gingival health. Clinical studies have convincingly demonstrated that regular daily removal of dental plaque in most patients prevents further dental disease. Dental professionals and patients, therefore, consider regular mechanical removal of all bacterial deposits from non-shedding oral surfaces the primary prerequisite to prevent disease.
**Fig. 8-1** Experimental gingivitis model (Löe _et al_. 1965). (a) Human volunteer with clean teeth and clinically healthy gingival tissues at the start of the period of experimental plaque accumulation. (b) Same human volunteer after 21 days of abolished oral hygiene practices leading to plaque deposits covering almost all tooth surfaces and consequently developing a generalized marginal gingival inflammation.
At first, a direct relationship was often assumed to exist between the total number of accumulated bacteria and the amplitude of the pathogenic effect; biologically relevant differences in the composition of plaque were not usually considered. This bacterial mass, termed _plaque_ , was shown to produce a variety of irritants, such as acids, endotoxins, and antigens, which, over time, invariably dissolved teeth and destroyed the supporting tissues. Consequently, the need to discriminate among bacterial deposits from different patients or at healthy or diseased sites was not yet recognized in detail. Individuals with extensive periodontal disease were either suspected of having a weak resistance to bacterial plaque as a whole or were blamed for inadequate home care. Such a view of dental plaque as a biomass is referred to as the _non-specific plaque hypothesis_ (Theilade 1986).
The propensity of inflamed sites to undergo permanent tissue destruction was recognized later to be more specific in nature, because not all gingivitis lesions seemed invariably to progress to periodontitis. Most periodontal sites in most subjects do not always show clinical signs of active tissue destruction with loss of connective tissue fiber attachment to the root surface, even though they may constantly be colonized by varying numbers and species of bacteria. Possible pathogens have been suggested among the organisms regularly found at elevated levels in periodontal lesions in relation to those observed under clinically healthy conditions. Longitudinal studies have indicated an increased risk for periodontal breakdown in sites colonized by some potentially pathogenic organisms. Treatment outcomes were better if these organisms could no longer be detected at follow-up examinations (see Chapter 9). If periodontal disease is indeed due to a limited number of bacterial species, the continuous and maximal suppression of plaque as a whole may not be the only possibility to prevent or treat periodontitis. Hence, specific elimination or reduction of presumptive pathogenic bacteria from plaque may become a valid alternative. Treatment may only be necessary in those patients diagnosed as having the specific infection and may be terminated once the pathogenic agents are eliminated. Such a view of periodontitis being caused by specific pathogens is referred to as the _specific plaque hypothesis_ (Loesche 1979).
The term _infection_ refers to the presence and multiplication of a microorganism in body tissues. The uniqueness of bacterial plaque-associated dental diseases as infections relates to the lack of massive bacterial invasion of tissues. Infections caused by the normal microbiota are sometimes called endogenous infections. Endogenous infections result when indigenous microbes move from their normal habitats into unusual anatomic regions. _Staphylococcus epidermidis_ , for instance, is a non-pathogenic, commensal saprophyte on the skin. If this organism reaches the surface of a vascular prosthesis or an orthopedic implant, a serious infection may emerge. Infections caused by endogenous microbes are called _opportunistic infections_ if they occur at the usual habitat of the microorganisms. Such infections may be the result of changing ecologic conditions or may be due to a decrease of host resistance. In the prevention of opportunistic infections due to overgrowth of indigenous organisms, continuous control of ecologic conditions regulating bacterial growth has high priority. The majority of microorganisms in periodontitis plaque can also be found occasionally in low proportions in health. These organisms may, therefore, be viewed as putative opportunistic pathogens. A small number of suspected pathogens, e.g. the Gram-negative anaerobe _Porphyromonas gingivalis_ , are rare organisms in the mouth of healthy individuals. Some researchers have suggested that such bacteria may be considered exogenous pathogens. If some periodontal microorganisms were indeed exogenous pathogens, avoidance of exposure would become an important goal of prevention, and therapy should be aimed at the elimination of the microorganisms. Their mere presence would be an indication for intervention.
Dental plaque may accumulate supragingivally, i.e. on the clinical crown of the tooth, but also below the gingival margin, i.e. in the subgingival area of the sulcus or pocket. Differences in the composition of the subgingival microbiota have been attributed in part to the local availability of blood products, pocket depth, redox potential, and pO2. Therefore, the question of whether the presence of specific microorganisms in patients or distinct sites may be the cause or the consequence of disease continues to be a matter of dispute (Socransky _et al_. 1987). Many microorganisms considered to be periodontopathogens are fastidious, strict anaerobes and, as such, may contribute little to the initiation of disease in shallow gingival pockets. If their preferred habitat were the deep periodontal pocket, they would be linked to the progression in sites with pre-existing disease, rather than to the initiation of disease in shallow sites. These microbiologic aspects are to be put in perspective with the host response. Further discussions are presented in Chapter 9.
# General introduction to plaque formation
Growth and maturation patterns of bacterial plaque have been studied on natural hard oral surfaces, such as enamel and dentin, or artificial surfaces, such as metal or acrylic, using light and electron microscopy and bacterial culture (Theilade & Theilade 1985). Despite differences in surface roughness, free energy, and charge, the most important features of initial plaque development are similar on all these materials (Siegrist _et al_. 1991).
The ability to adhere to surfaces is a general property of almost all bacteria. It depends on an intricate, sometimes exquisitely specific, series of interactions between the surface to be colonized, the microbe, and an ambient fluid milieu (Mergenhagen & Rosan 1985).
**Fig. 8-2** Stages in the formation of a biofilm on a clean, hard and non-shedding surface following immersion into a fluid environment. Phase 1: Molecular adsorption to condition the biofilm formation. Phase 2: Bacterial adhesion by single organisms. Phase 3: Growth of extracellular matrix production and multiplication of the adhering bacteria. Phase 4: Sequential adsorption of further bacteria to form a more complex and mature biofilm. Adapted from Marshall (1992).
Immediately upon immersion of a solid substratum into the fluid media of the oral cavity, or upon cleaning of a solid surface in the mouth, hydrophobic and macromolecules begin to adsorb to the surface to form a conditioning film (Fig. 8-2, Phase 1), termed the acquired pellicle. This film is composed of a variety of salivary glycoproteins (mucins) and antibodies. The conditioning film alters the charge and free energy of the surface, which in turn increases the efficiency of bacterial adhesion. Bacteria adhere variably to these coated surfaces. Some possess specific attachment structures such as extracellular polymeric substances and fimbriae, which enable them to attach rapidly upon contact (Fig. 8-2, Phase 2). Other bacteria require prolonged exposure to bind firmly. Behaviors of bacteria change once they become attached to surfaces. This includes active cellular growth of previously starving bacteria and synthesis of new outer membrane components. The bacterial mass increases due to continued growth of the adhering organisms, adhesion of new bacteria (Fig. 8-2, Phase 4), and synthesis of extracellular polymers. With increasing thickness, diffusion into and out of the biofilm becomes more and more difficult. An oxygen gradient develops as a result of rapid utilization by the superficial bacterial layers and poor diffusion of oxygen through the biofilm matrix. Completely anaerobic conditions eventually emerge in the deeper layers of the deposits. Oxygen is an important ecologic determinant because bacteria vary in their ability to grow and multiply at different levels of oxygen. Diminishing gradients of nutrients supplied by the aqueous phase, i.e. the saliva, are also created. Reverse gradients of fermentation products develop as a result of bacterial metabolism.
Dietary products dissolved in saliva are an important source of nutrients for bacteria in the supragingival plaque. Once a deepened periodontal pocket is formed, however, the nutritional conditions for bacteria change because the penetration of substances dissolved in saliva into the pocket is very limited. Within the deepened pocket, the major nutritional source for bacterial metabolism comes from the periodontal tissues and blood. Many bacteria found in periodontal pockets produce hydrolytic enzymes with which they can break down complex macromolecules from the host into simple peptides and amino acids. These enzymes may be a major factor in destructive processes of periodontal tissues.
Primary colonization is dominated by facultatively anaerobic Gram-positive cocci. They adsorb onto the pellicle-coated surfaces within a short time after mechanical cleaning. Plaque collected after 24 hours consists mainly of streptococci; _S. sanguis_ is the most prominent of these organisms. In the next phase, Gram-positive rods, which are present in very low numbers initially, gradually increase and eventually outnumber the streptococci (Fig. 8-3). Gram-positive filaments, particularly _Actinomyces_ spp., are the predominating species in this stage of plaque development (Fig. 8-4). Surface receptors on the deposited Gram-positive cocci and rods allow subsequent adherence of Gram-negative organisms with poor ability to attach directly to pellicle. _Veillonella_ , fusobacteria, and other anaerobic Gram-negative bacteria can attach in this way (Fig. 8-5). The heterogeneity of plaque thus gradually increases and, with time, includes large numbers of Gram-negative organisms. A complex array of interrelated bacterial species is the result of this development. Exchange of nutrients between different species, but also negative interactions, e.g. the production of bacteriocins, play a role in the establishment of a stable bacterial community (Fig. 8-6). Due to the influences of local environmental factors, structurally different types of plaque evolve at different locations. Protection of the growing plaque from shear forces and local availability of certain nutrients are most important. A distinct composition of mature bacterial deposits can eventually be recognized at specific sites and under specific clinical conditions. Examples are the plaque on a smooth enamel surface versus fissure plaque, or the plaque in shallow and less shallow gingival crevices.
**Fig. 8-3** Primary colonization by predominantly Gram-positive facultative bacteria. Ss: _Streptococcus sanguis_ is most dominant. Av: _Actinomyces_ spp. are also found in 24-hour plaque.
**Fig. 8-4** Gram-positive facultative cocci and rods coaggregate and multiply.
**Fig. 8-5** Surface receptors on the Grampositive facultative cocci and rods allow the subsequent adherence of Gram-negative organisms, which have a poor ability to adhere directly to the pellicle. Fn: _Fusobacterium nucleatum_ ; BI: _Prevotella intermedia_.
**Fig. 8-6** The heterogeneity increases as plaque ages and matures. As a result of ecologic changes, more Gram-negative strictly anaerobic bacteria colonize secondarily and contribute to an increased pathogenicity of the biofilm. Bg: _Porphyromonas gingivalis_ ; Cg: _Capnocytophaga_ sp.
Accumulation of plaque along the gingival margin leads to an inflammatory reaction of the soft tissues. The presence of this inflammation has a profound influence on the local ecology. The availability of blood and gingival fluid components promotes growth of Gram-negative bacterial species with an increased periodontopathic potential. Bacterial samples from established gingivitis lesions have increased numbers of these bacteria. Because of the capability enzymatically to digest proteins, many of these organisms do not depend upon a direct availability of dietary carbohydrates. Such bacteria do not produce extracellular polymers and develop only loosely adherent plaque in the developing periodontal pocket. Cultivation of samples from advanced periodontal lesions reveals a predominance of Gram-negative anaerobic rods. Under the microscope, particularly high numbers of anaerobic uncultivable spirochetes can be demonstrated. Further details on the microbial ecology of subgingival plaque are discussed in Chapter 9.
In summary, immediately following immersion of hard, non-shedding surfaces into the fluid environment of the oral cavity, adsorption of macromolecules will lead to the formation of a _biofilm_. Bacterial adhesion to this glycoprotein layer will first involve primary plaque formers, such as Gram-positive facultative cocci and rods. Subsequent colonization on to receptors of these organisms will involve Gram-negative, strictly anaerobic bacteria, while the primary plaque formers also multiply to form colonies. The heterogeneity of the complex biofilm increases with time, as the ecologic conditions gradually change.
# Dental plaque as a biofilm
The term _biofilm_ describes the relatively undefinable microbial community associated with a tooth surface or any other hard, non-shedding material (Wilderer & Charaklis 1989). In the lower levels of most biofilms a dense layer of microbes is bound together in a polysaccharide matrix with other organic and inorganic materials. On top of this layer is a looser layer, which is often highly irregular in appearance and may extend into the surrounding medium. The fluid layer bordering the biofilm may have a rather "stationary" sublayer and a fluid layer in motion. Nutrient components may penetrate this fluid medium by molecular diffusion. Steep diffusion gradients, especially for oxygen, exist in the more compact lower regions of biofilms. The ubiquity with which anaerobic species are detected from these areas of biofilms provides evidence for these gradients (Ritz 1969).
Accumulation of bacteria on solid surfaces is not an exclusive dental phenomenon. Biofilms are ubiquitous; they form on virtually all surfaces immersed in natural aqueous environments. Biofilms form particularly fast in flow systems where a regular nutrient supply is provided to the bacteria. Rapid formation of visible layers of microorganisms due to extensive bacterial growth accompanied by excretion of copious amounts of extracellular polymers is typical for biofilms. Biofilms effectively protect bacteria from antimicrobial agents. Treatment with antimicrobial substances is often unsuccessful unless the deposits are mechanically removed. Adhesion-mediated infections that develop on permanently or temporarily implanted materials, such as intravascular catheters, vascular prostheses or heart valves, are notoriously resistant to antibiotics and tend to persist until the device is removed. Similar problems are encountered in water conduits, wherein potentially pathogenic bacteria may be protected from chlorination, or on ship hulls, where biofilms increase frictional resistance and turbulence (Gristina 1987; Marshall 1992).
In summary, _dental plaque_ as a naturally occurring microbial deposit _represents a true biofilm_ which consists of bacteria in a matrix composed mainly of extracellular bacterial polymers and salivary and/or gingival exudate products.
# Structure of dental plaque
## Supragingival plaque
Supragingival plaque has been examined in a number of studies by light and electron microscopy to gain information on its internal structure (Mühlemann & Schneider 1959; Turesky _et al_. 1961; Theilade 1964; Frank & Brendel 1966; Leach & Saxton 1966; Frank & Houver 1970; Schroeder & De Boever 1970; Theilade & Theilade 1970; Eastcott & Stallard 1973; Saxton 1973; Rönström _et al_. 1975; Tinanoff & Gross 1976; Lie 1978). The introduction of the electron microscope in dental research was a significant development for studies of dental plaque, both because the size of many bacteria approaches the ultimate resolving power of the light microscope, and because the resins used for embedding allowed for sections thinner than the smallest bacterial dimension. The substructure of plaque could therefore be identified.
In studies of the internal details of plaque, samples are required in which the deposits are kept in their original relation to the surface on which they have formed. This may be accomplished by removing the deposits with the tooth. If plaque of known age is the object of study, the tooth surfaces are cleaned at a predetermined time before removal (McDougall 1963; Frank & Houver 1970; Schroeder & De Boever 1970). Pieces of natural teeth or artificial surfaces may also be attached to solid structures in the mouth and removed after a given interval. This method of plaque collection was already used at the beginning of the last century by Black (1911). The systematic use of artificial surfaces for collection of plaque was reintroduced during the 1950s. Thin plastic foils of Mylar® were attached to mandibular incisor teeth for known periods, after which they were removed for histologic, histochemical, and electron microscopic examination of the deposited material (Mandel _et al_. 1957; Mühlemann & Schneider 1959; Zander _et al_. 1960; Schroeder 1963; Theilade 1964). Other types of plastic materials such as Westopal®, Epon®, Araldite®, and _spray plast_ have since been employed for this purpose (Berthold _et al_. 1971; Kandarkar 1973; Lie 1975; Listgarten _et al_. 1975; Rönström _et al_. 1975). Results from several such studies indicate that plaque formed on natural or artificial surfaces does not differ significantly in structure or microbiology (Hazen 1960; Berthold _et al_. 1971; Nyvad _et al_. 1982; Theilade _et al_. 1982a,b), indicating that at least some of the principal mechanisms involved in plaque formation are unrelated to the nature of the solid surface colonized. However, there are small, but important, differences in the chemical composition of the first layer of organic material formed on these artificial surfaces compared with that formed on natural tooth surfaces (Sönju & Rölla 1973; Sönju & Glantz 1975; Öste _et al_. 1981). Tooth surfaces, enamel as well as exposed cementum, are normally covered by a thin acquired pellicle of glycoproteins (Fig. 8-7). If removed, e.g. by mechanical instrumentation, it reforms within minutes. The pellicle is believed to play an active part in the selective adherence of bacteria to the tooth surface (Fig. 8-8). For details of the proposed mechanisms, see Chapter 9.
**Fig. 8-7** Electron micrographic illustration of a 4-hour dental pellicle. The pellicle has formed on an artificial surface of plastic, which was painted on to the surface of the tooth. The plastic surface was exposed to the environment for a 4-hour period. A thin condensed layer of organic material is covering the film. The material has a relatively homogeneous appearance but varies in thickness over the surface. From Brecx _et al_. (1981).
The first cellular material adhering to the pellicle on the tooth surface or other solid surfaces consists of coccoid bacteria with numbers of epithelial cells and polymorphonuclear leukocytes (Fig. 8-9). The bacteria are encountered either on (Fig. 8-10) or within the pellicle as single organisms (Fig. 8-11) or as aggregates of microorganisms (Fig. 8-12). Larger numbers of microorganisms may be carried to the tooth surface by epithelial cells.
**Fig. 8-8** Electron micrographic illustration of a 4-hour dental pellicle with a single bacterium included in the film. The microbe appears attached to the surface. The dental pellicle varies in thickness but has a homogeneous morphology. From Brecx _et al._ (1981).
**Fig. 8-9** Electron micrographic illustration of a 4-hour dental pellicle, formed on a plastic surface attached to the buccal surface of a tooth. A condensed layer of organic material is observed on the surface and cell remnants are embedded in the film. From Brecx _et al._ (1981).
**Fig. 8-10** High power electron micrographic illustration of a 4-hour pellicle with bacteria residing in the pellicle at a distance of around one micron from the condensed organic material. The pellicle is rather even in composition and, at the oral side, an irregular condensed organic material is seen close to the bacteria. From Brecx _et al._ (1981).
**Fig. 8-11** High power electron micrographic illustration of a 4-hour pellicle with an embedded bacterium. The bacterium is deposited on the film surface together with the dental pellicle. Around the bacterium empty spaces are observed representing the radius of extrusions of filaments radiating from the microorganisms. From Brecx _et al._ (1981).
The number of bacteria found on the surface a few hours after cleaning depends on the procedures applied to the sample before examination, the reason being that adherence to the solid surface is initially very weak. If no special precautions are taken during the preparatory processing, the early deposits are easily lost (Brecx _et al_. 1980). Apparently the adherence of microorganisms to solid surfaces takes place in two steps: (1) a reversible state in which the bacteria adhere loosely, and later (2) an irreversible state, during which their adherence becomes consolidated (Gibbons & van Houte 1980).
Another factor which may modify the number of bacteria in early plaque deposits is the presence of gingivitis, which increases the plaque formation rate so that the more complex bacterial composition is attained earlier (Saxton 1973; Hillam & Hull 1977; Brecx _et al_. 1980). Plaque growth may also be initiated by microorganisms harbored in minute irregularities in which they are protected from the natural cleaning of the tooth surface.
**Fig. 8-12** Electron micrographic illustration of a 4-hour dental pellicle with bacteria attached to a plastic surface, which had been adhering to a buccal tooth surface and was exposed to the oral environment. A single row of bacteria attached to the surface is seen to the left. On top of the bacteria, a layer of condensed organic material representing the oral lateral portion of the dental pellicle is noted. From Brecx _et al_. (1981).
During the first few hours, bacteria that resist detachment from the pellicle may start to proliferate and form small colonies of morphologically similar organisms (Fig. 8-13). However, since other types of organisms may also proliferate in an adjacent region, the pellicle becomes easily populated by a mixture of different microorganisms (Fig. 8-14). In addition, some organisms seem able to grow between already established colonies (Fig. 8-15). Finally, it is likely that clumps of organisms of different species will become attached to the tooth surface or to the already attached microorganism, contributing to the complexity of the plaque composition after a few days. At this time, different types of organisms may benefit from each other. One example is the corncob configurations resulting from the growth of cocci on the surface of a filamentous microorganism (Listgarten _et al_. 1973). Another feature of older plaque is the presence of dead and lysed bacteria which may provide additional nutrients to the still viable bacteria in the neighborhood (Theilade & Theilade 1970).
The material present between the bacteria in dental plaque is called the intermicrobial matrix and accounts for approximately 25% of the plaque volume. Three sources may contribute to the intermicrobial matrix: the plaque microorganisms, the saliva, and the gingival exudate.
The bacteria may release various metabolic products. Some bacteria may produce various extracellular carbohydrate polymers, serving as energy storage or as anchoring material to secure their retention in plaque (Fig. 8-16). Degenerating or dead bacteria may also contribute to the intermicrobial matrix. Different bacterial species often have distinctly different metabolic pathways and capacity to synthesize extracellular material. The intermicrobial matrix in plaque, therefore, varies considerably from region to region.
A fibrillar component is often seen in the matrix between Gram-positive cocci (Fig. 8-17) and is in accordance with the fact that several oral streptococci synthesize levans and glucans from dietary sucrose. In other regions, the matrix appears granular or homogeneous (Fig. 8-18). In parts of the plaque with the presence of Gram-negative organisms, the intermicrobial matrix is regularly characterized by the presence of small vesicles surrounded by a trilaminar membrane, which is similar in structure to that of the outer envelope of the cell wall of the Gram-negative microorganisms (Fig. 8-19). Such vesicles probably contain endotoxins and proteolytic enzymes, and may also be involved in adherence between bacteria (Hofstad _et al_. 1972; Grenier & Mayrand 1987).
**Fig. 8-13** Thin section of plaque colony consisting of morphologically similar bacteria deposited on plastic film (F) applied to the buccal surface of a premolar during an 8-hour period. Magnification ×35 000. Bar: 0.2 μm. From Brecx _et al._ (1980).
**Fig. 8-14** Electron micrographic illustration of early plaque formation. The film surface on which the pellicle and bacteria adhere is located to the left. Bacteria of varying morphology are attached to the film. They are surrounded by organic pellicle material. An epithelial cell remnant is seen in close vicinity to the microbes. From Brecx _et al._ (1981).
**Fig. 8-15** Electron micrographic illustration of 24-hour dental plaque formed on a plastic film surface attached to the buccal surface of the tooth. A multilayer bacterial plaque is noted. A remnant of an epithelial cell has been trapped in the microbial mass. From Brecx _et al._ (1981).
**Fig. 8-16** Thin section of old plaque stained for the demonstration of polysaccharides by reacting them with electron-dense material appearing dark in the illustration. Many bacteria contain large amounts of intracellular polysaccharide, and the intermicrobial matrix contains extracellular polysaccharides. Magnification ×7000. Bar: 1 μm. From Theilade & Theilade (1970).
It must be remembered, however, that the transmission electron microscope does not reveal all organic components of the intermicrobial matrix. The more soluble constituents may be lost during the procedures required prior to sectioning and examination of the plaque sample. Biochemical techniques may be used to identify such compounds (Silverman & Klein-berg 1967; Krebel _et al_. 1969; Kleinberg 1970; Hotz _et al_. 1972; Rölla _et al_. 1975; Bowen 1976). Such studies indicate that proteins and carbohydrates constitute the bulk of the organic material while lipids appear in much lower amounts.
**Fig. 8-17** High power electron micrographic illustration of a single bacterium attached to the pellicle by filaments which extend from the bacterial surface to the tooth surface. The surface had been exposed to the oral environment for an 8-hour period. From Brecx _et al._ (1981).
**Fig. 8-18** Thin section of plaque with granular or homogeneous intermicrobial matrix. Magnification ×20 000. Bar: 0.1 μm. From Theilade & Theilade (1970).
**Fig. 8-19** Thin section of plaque with a region predominated by Gram-negative bacteria. Between them, vesicles are surrounded by a trilaminar membrane (two thin electrondense layers with an electron-lucent layer in between). This substructure is also seen in the outermost endotoxin containing cell wall layer of the adjacent Gram-negative bacteria. Magnification ×110 000. Bar: 0.1 μm. From Theilade & Theilade (1970).
The carbohydrates of the matrix have received a great deal of attention, and at least some of the polysaccharides in the plaque matrix are well characterized: fructans (levans) and glucans. Fructans are synthesized in plaque from dietary sucrose and provide a storage of energy which may be utilized by microorganisms in times of low sugar supply. The glucans are also synthesized from sucrose. One type of glucan is dextran, which may also serve as energy storage. Another glucan is mutan, which is not readily degraded, but acts primarily as a skeleton in the matrix in much the same way as collagen stabilizes the intercellular substance of connective tissue. It has been suggested that such carbohydrate polymers may be responsible for the change from a reversible to an irreversible adherence of plaque bacteria.
The small amount of lipids in the plaque matrix are as yet largely uncharacterized. Part of the lipid content is found in the small extracellular vesicles, which may contain lipopolysaccharide endotoxins of Gram-negative bacteria.
## Subgingival plaque
Owing to the difficulty of obtaining samples with subgingival plaque preserved in its original position between the soft tissues of the gingiva and the hard tissues of the tooth, there is only a limited number of studies on the detailed internal structure of human subgingival plaque (Schroeder 1970; Listgarten _et al_. 1975; Listgarten 1976; Westergaard _et al_. 1978). From these it is evident that in many respects subgingival plaque resembles the supragingival variety, although the predominant types of microorganisms found vary considerably from those residing coronal to the gingival margin.
Between subgingival plaque and the tooth an electron-dense organic material is interposed, termed a _cuticle_ (Fig. 8-20). This cuticle probably contains the remains of the epithelial attachment lamina originally connecting the junctional epithelium to the tooth, with the addition of material deposited from the gingival exudate (Frank & Cimasoni 1970; Lie & Selvig 1975; Eide _et al_. 1983). It has also been suggested that the cuticle represents a secretory product of the adjacent epithelial cells (Schroeder & Listgarten 1977). Information is lacking concerning its chemical composition, but its location in the subgingival area makes it unlikely that salivary constituents contribute to its formation.
**Fig. 8-20** Semithin section of subgingival plaque. An electron-dense cuticle bordering the enamel space is visible to the left. Filamentous bacteria are less than in supragingival plaque. The surface toward the gingival tissue contains many spirochetes (between arrows). Various host tissue cells can be seen on the right side. Magnification ×775. Bar: 10 μm. From Listgarten (1976).
The subgingival plaque structurally resembles supragingival plaque, particularly with respect to plaque associated with gingivitis without the formation of deep pockets (Fig. 8-21). A densely packed accumulation of microorganisms is seen adjacent to the cuticular material covering the tooth surface (Fig. 8-22). The bacteria comprise Gram-positive and Gram-negative cocci, rods, and filamentous organisms. Spirochetes and various flagellated bacteria may also be encountered, especially at the apical extension of the plaque. The surface layer is often less densely packed and leukocytes are regularly interposed between the plaque and the epithelial lining of the gingival sulcus (Fig. 8-23).
When a periodontal pocket has formed, the appearance of the subgingival bacterial deposit becomes much more complex. In this case the tooth surface may either represent enamel or cementum from which the periodontal fibers are detached. Plaque accumulation on the portion of the tooth previously covered by periodontal tissues does not differ markedly from that observed in gingivitis (Fig. 8-24). In this layer, filamentous microorganisms dominate (Figs. 8-25, 8-26, 8-27), but cocci and rods also occur.
**Fig. 8-21** (a) Light microscopic image of the dento-gingival region of a dog with experimental gingivitis. A thin layer of dento-gingival plaque can be seen, extending from the supragingival region approximately 0.5 mm into the gingival sulcus. (b) Higher magnification of a region of the plaque shown in (a). The subgingival plaque has a varying thickness and the epithelial cells are separated from the surface by a layer of leukocytes. There are also numerous leukocytes in the superficial portion of the sulcus epithelium. The apical termination of the plaque is bordered by leukocytes separating the epithelium from direct contact with the plaque bacteria.
**Fig. 8-22** Semithin section of supragingival plaque with layer of predominantly filamentous bacteria adhering to the enamel (to the left). Lighter staining indicates calcification of part of the plaque close to the tooth. Magnification ×750. Bar: 10 μm. From Listgarten (1976).
**Fig. 8-23** Light microscopic image of a smear sample taken from the dento-gingival region in a subject who had abstained from mechanical oral hygiene during 3 weeks. Numerous leukocytes can be observed embedded in a dense accumulation of bacteria.
**Fig. 8-24** Semithin section of supragingival plaque on enamel (E), which has been dissolved prior to sectioning. Magnification ×750. Bar: 10 μm. From Listgarten (1976).
**Fig. 8-25** See Fig. 8.24. Filamentous organisms predominate. At the surface some of these organisms are surrounded by cocci. This configuration resembles a corncob. Magnification ×1400. Bar: 1 μm. From Listgarten (1976).
**Fig. 8-26** The corncob formations seen at the plaque surface in Fig. 8-24 and 8-25. Magnification ×1300. Bar: 1 μm. From Listgarten (1976).
However, in the deeper parts of the periodontal pocket, the filamentous organisms become fewer in number, and in the apical portion they seem to be virtually absent. Instead, the dense, tooth-facing part of the bacterial deposit is dominated by smaller organisms without particular orientation (Listgarten 1976) (Fig. 8-28).
The surface layers of microorganisms in the periodontal pocket facing the soft tissue are distinctly different from the adherent layer along the tooth surface, and no definite intermicrobial matrix is apparent (Figs. 8-28, 8-29). The microorganisms comprise a larger number of spirochetes and flagellated bacteria. Gram-negative cocci and rods are also present. The multitude of spirochetes and flagellated organisms are motile bacteria and there is no intermicrobial matrix between them. This outer part of the microbial accumulation in the periodontal pocket adheres loosely to the soft-tissue pocket wall (Listgarten 1976).
In cases of juvenile periodontitis (Listgarten 1976; Westergaard _et al_. 1978) the bacterial deposits in deep pockets are much thinner than those found in adult forms of periodontal disease. Areas of the tooth surface in the periodontal pocket may sometimes even be devoid of adherent microbial deposits. The cuticular material has an uneven thickness (Figs. 8-30, 8-31). The adherent layer of microorganisms varies considerably in thickness and shows considerable variation in arrangement. It may exhibit a palisaded organization of the bacteria (Fig. 8-32). The microorganisms in this layer are mainly cocci, rods or filamentous bacteria, primarily of the Gram-negative type (Fig. 8-33). A surface layer with some Gram-positive cocci, frequently associated with filamentous organisms in the typical corncob configuration, may also be found.
Subgingivally located bacteria appear to have the capacity to invade dentinal tubules, the openings of which have become exposed as a consequence of inflammatory driven resorptions of the cementum (Adriaens _et al_. 1988). Such a habitat might serve as the source for bacterial recolonization of the subgingival space following treatment of periodontal disease. The mechanisms involved in such reversed invasion of the subgingival space are unknown.
**Fig. 8-27** Thin section of supragingival plaque on a root surface (to the left). The Gram-positive bacteria are oriented in a palisading arrangement. Magnification ×6400. Bar: 1 μm. From Listgarten (1976).
The sequential events taking place during the development of subgingival plaque have not been studied in man. However, in dogs, subgingival plaque may develop in the gingival sulcus within a few days, if oral hygiene is discontinued (Matsson & Attström 1979; Ten Napel _et al_. 1983). From these studies it has been established that early dental plaque in the dog has many structural similarities with that occurring in man. This applies to the supragingival plaque (Fig. 8-21a) as well as to the subgingival accumulation (Fig. 8-21b). The deposits may either appear as an apical continuation of the supragingival plaque, or as discrete aggregates at some distance from the supragingival deposit. Old established subgingival plaque shows considerable variation in bacterial composition between dogs: in some, a subgingival microbiota dominated by spirochetes is seen; in others, colonies of Gram-negative cocci and rods are found in the gingival crevice, whereas spirochetes are virtually absent (Soames & Davies 1975; Theilade & Attström 1985). A characteristic feature of subgingival plaque is the presence of leukocytes interposed between the surfaces of the bacterial deposit and the gingival sulcular epithelium (Fig. 8-34). Some bacteria may be found between the epithelial cells. Evidence of phagocytosis (by polymorphonuclear leukocytes) is frequently encountered (Fig. 8-35).
Although subgingival plaque formation in the dog may not develop identically to that in man, the dog may still serve as a convenient model for investigating the basic phenomena governing the formation of subgingival plaque (Schroeder & Attström 1979).
In summary, there are four distinct subgingival ecologic niches which are probably different in their composition:
**Fig. 8-28** Thin section of subgingival plaque from a deep periodontal pocket. Small microorganisms predominate, many of which are spirochetes. Magnification ×13 000. Bar: 1 μm. From Listgarten (1976).
**Fig. 8-29** Thin section of subgingival plaque from a deep periodontal pocket with many spirochetes (S), which are recognized by their axial filaments. In the lower part of the figure is a curved organism with flagella at its concave surface. Magnification ×25 000. Bar: 0.5 μm. From Listgarten (1976).
**Fig. 8-30** Thin section of deposit in deep pocket of patient with juvenile periodontitis. The cementum (C) is covered with cuticular material and cellular remnants. Magnification ×5500. Bar: 1 μm. From Westergaard _et al._ (1978).
**Fig. 8-31** Thin section of deposit in deep pocket of patient with juvenile periodontitis. A cuticle of uneven thickness is seen to the right on the cementum. A small colony of degenerating bacteria adheres to the cuticle in the upper part of the illustration, and below a single rod-shaped microorganism is partly embedded in the cuticle. Magnification ×5500. Bar: 1 μm. From Westergaard _et al._ (1978).
**Fig. 8-32** Thin section of plaque in deep pocket of patient with juvenile periodontitis. Densely packed Gram-positive rods grow perpendicular to the cementum to the right in the illustration. Magnification ×23 000. Bar: 0.5 μm. From Westergaard _et al._ (1978).
1. The tooth (or implant) surface
2. The gingival exudate fluid medium
3. The surface of epithelial cells
4. The superficial portion of the pocket epithelium.
The composition of the bacteria in these niches has still not been completely investigated. The influence of the different bacterial compartments on the pathogenesis of the disease process is generally unknown.
## **Peri-implant plaque**
Biofilms form not only on natural teeth, but also on artificial surfaces exposed to the oral environment. As a consequence, the formation of bacterial plaque on oral implants deserves some attention. Although a number of studies have characterized the plaque deposits of the human peri-implant sulcus or pocket using either dark field microscopy (Mombelli _et al_. 1988; Quirynen & Listgarten 1990) or microbiologic culturing techniques (Rams _et al_. 1984; Mombelli _et al_. 1987, 1988; Apse _et al_. 1989; Leonhardt _et al_. 1992), no studies have attempted to document the structure of the supramucosal or the peri-implant (submucosal) microbiota. However, the similarities between periimplant and subgingival microbial deposits have clearly been demonstrated in cross-sectional (Mombelli _et al_. 1987, 1995) and longitudinal studies (Mombelli _et al_. 1988; Pontoriero _et al_. 1994), and it may be anticipated that the structure of peri-implant plaque deposits may resemble that encountered in the subgingival environment. Micrographs from an implant retrieved because of a peri-implant infection may provide some evidence for the similarity between the structural image of the submucosal peri-implant microbiota (Fig. 8-36).
**Fig. 8-33** Thin section of plaque in deep pocket of patient with juvenile periodontitis. The bacterial fl ora is characterized by cocci, rods or fi lamentous organisms, primarily of the Gram-negative type. Magnification ×9200. Bar: 1 μm. From Westergaard _et al_. (1978).
# Dental calculus
Although calculus formation has been reported to occur in germ-free animals as a result of calcification of salivary proteins, dental calculus or tartar usually represents mineralized bacterial plaque.
## Clinical appearance, distribution, and clinical diagnosis
Supragingivally, calculus can be recognized as a creamy-whitish to dark yellow or even brownish mass of moderate hardness (Fig. 8-37). The degree of calculus formation is not only dependent on the amount of bacterial plaque present but also on the secretion of the salivary glands. Hence, supragingival calculus is predominantly found adjacent to the excretion ducts of the major salivary glands, such as the lingual aspect of the mandibular anterior teeth and the buccal aspect of the maxillary first molars, where the parotid gland ducts open into the oral vestibule. The duct openings of the submandibular glands are located in the former region. It should be noted that calculus continually harbors a viable bacterial plaque (Zander _et al_. 1960; Theilade 1964; Schroeder 1969).
Subgingivally, calculus may be found by tactile exploration only, since its formation occurs apical to the gingival margin and, hence, is usually not visible to the naked eye. Occasionally, subgingival calculus may be visible in dental radiographs provided that the deposits present an adequate mass (Fig. 8-38). Small deposits or residual deposits following root instrumentation may barely be visualized radiographically. If the gingival margin is pushed open by a blast of air or retracted by a dental instrument, a brownish to black calcified hard mass with a rough surface may become visible (Fig. 8-39). Again, this mineralized mass reflects predominantly bacterial accumulations mixed with products from gingival crevicular fluid and blood. Consequently, subgingival calculus is found in most periodontal pockets, usually extending from the cemento-enamel junction and reaching close to the bottom of the pocket. However, a band of approximately 0.5 mm is usually found coronal to the apical extension of the periodontal pocket (Fig. 8-40). This zone appears to be free of mineralized deposits owing to the fact that gingival crevicular fluid is exuding from the periodontal soft tissues and acting as a gradient against the microbial accumulation. Like supragingival calculus, subgingival calculus also provides an ideal environment for bacterial adhesion (Zander _et al._ 1960; Schroeder 1969).
**Fig. 8-34** Thin section of old subgingival plaque in a dog with long-standing gingivitis. The most apical colony consists primarily of spirochetes attached to a dense cuticle and surrounded by migrated leukocytes. Single microorganisms are seen between them (arrows). Magnification ×2800. Bar: 1 μm. From Theilade & Attström (1985).
**Fig. 8-35** Thin section of part of a leukocyte situated between subgingival plaque and the junctional epithelium of the dog. The large membrane-bound compartment of the leukocyte cytoplasm contains a phagocytized Gram-negative microorganism. Another bacterium is in close apposition to the cytoplasmic membrane of the leukocyte. Magnification ×21 500. Bar: 0.5 µm. From Theilade & Attström (1985).
**Fig. 8-36** Peri-implant infection. (a) Human explant of an ITI® dentalimplant affected by a peri-implantitis with an infrabony lesion. Adhering plaque closely resembles the structure of subgingival microbiota encountered in advanced periodontitis. (b) Higher magnification of plaque adhering to the implant surface.
**Fig. 8-37** Abundance of supragingival calculus deposits. (a) Gross deposits as a result of long-term neglect of oral hygiene. Two mandibular incisors have been exfoliated. (b) Supragingival plaque usually covering the lingual aspect of mandibular incisors. Note the intense infl ammatory reaction adjacent to the deposits. (c) Same patient and region as in Fig. 8-37b following removal of the calculus. The gingival tissues demonstrate healing.
Plaque mineralization varies greatly between and within individuals and, as indicated above, also within the different regions of the oral cavity.
Not only the formation rate for bacterial plaque (amount of bacterial plaque per time and tooth surface), but also the formation rate for dental calculus (time period during which newly deposited supragingival plaque with an ash weight of 5–10% becomes calcified and yields an ash weight of approximately 80%) is subject to great variability. In some subjects, the time required for the formation of supra gingival calculus is 2 weeks, at which time the deposit may already contain approximately 80% of the inorganic material found in mature calculus (Fig. 8-41) (Mühlemann & Schneider 1959; Mandel 1963; Mühlemann & Schroeder 1964). In fact, evidence of mineralization may already be present after a few days (Theilade 1964). Nevertheless, the formation of dental calculus with the mature crystalline composition of old calculus may require months to years (Schroeder & Baumbauer 1966). Supragingival plaque becomes mineralized saliva and subgingival plaque in the presence of the inflammatory exudate in the pocket. It is, therefore, evident that subgingival calculus represents a secondary product of infection and not a primary cause of periodontitis.
**Fig. 8-38** Subgingival calculus may be visible (arrows) on radiographs if abundant deposits are present.
**Fig. 8-39** (a) Subgingival calculus presents as a black-brownish hard mass if the gingival margin is retracted or reflected during a surgical procedure. (b) Healing of the site following removal of all hard deposits.
**Fig. 8-40** Plaque- and calculus-free zone coronal to the epithelial attachment. SP: subgingival plaque bacteria; PFZ: plaque-free zone; EA: remnants of junctional epithelium.
**Fig. 8-41** Seven-day-old calcified plaque. Observe the isolated calcification centers indicated by the black areas (van Kossa stain).
## Attachment to tooth surfaces and implants
Dental calculus generally adheres tenaciously to tooth surfaces. Hence, the removal of subgingival calculus may be expected to be rather difficult. The reason for this firm attachment to the tooth surface is the fact that the pellicle beneath the bacterial plaque also calcifies. This, in turn, results in an intimate contact with enamel (Fig. 8-42), cementum (Fig. 8-43) or dentin crystals (Fig. 8-44) (Kopczyk & Conroy 1968; Selvig 1970). In addition, the surface irregularities are also penetrated by calculus crystals and, hence, calculus is virtually locked to the tooth. This is particularly the case on exposed root cementum, where small pits and irregularities occur at the sites of the previous insertion of Sharpey's fibers (Bercy & Frank 1980). Uneven root surfaces may be the result of carious lesions and small areas of cementum may have been lost due to resorption, when the periodontal ligament was still invested into the root surface (Moskow 1969). Under such conditions it may become extremely difficult to remove all calculus deposits without sacrificing some hard tissues of the root.
**Fig. 8-42** Thin section of enamel surface (E) with overlying calculus. The enamel and calculus crystals are in intimate contact, and the latter extends into the minute irregularities of the enamel. Magnification ×37 500. Bar: 0.1 μm. From Selvig (1970).
**Fig. 8-43** Thin section of cementum surface (C) with overlying calculus. The calculus is closely adapted to the irregular cementum and is more electron-dense and therefore harder than the adjacent cementum. To the right in the illustration, part of an uncalcified microorganism. Magnification ×32 000. Bar: 0.1 μm. From Selvig (1970).
**Fig. 8-44** Thin section of dentin (D) surface with overlying calculus. The interface between the calculus and dentin cannot be precisely determined because the calculus crystals fill the irregularities of the dentin surface, which is devoid of cementum as a result of a previous scaling of the root surface. The circular profiles in the calculus completely surround calcified bacteria. Magnification ×19 000. Bar: 1 μm. From Selvig (1970).
Although some irregularities may also be encountered on oral implant surfaces, the attachment to commercially pure titanium generally is less intimate than to root surface structures. This in turn, would mean that calculus may be chipped off from oral implants (Fig. 8-45) without detriment to the implant surface (Matarasso _et al_. 1996).
## **Mineralization, composition, and structure**
The mineralization starts in centers which arise intracellularly in bacterial colonies (Fig. 8-46) or extracellularly from matrix with crystallization nuclei (Fig. 8-47). Recent and old calculus consists of four different crystals of calcium phosphate (for review see Schroeder 1969) :
1. CaH (PO4) × 2H2O = brushite ( **B** )
2. Ca4H (PO4) 3 × 2H2O = octa calcium phosphate ( **OCP** )
3. Ca5(PO4) 3 × OH = hydroxyapatite ( **HA** )
4. β-Ca3 (PO4) 2 = whitlockite ( **W** ).
**Fig. 8-45** Calculus deposit on an oral implant in a patient without regular maintenance care.
**Fig. 8-46** Thin section of old plaque. A degenerating organism is surrounded by intermicrobial matrix in which initial mineralization has started by the deposition of small needle-shaped electron-dense apatite crystals. Magnification ×26 500. Bar: 0.5 μm. From Zander _et al._ (1960).
Supragingival calculus is clearly built up in layers and yields a great heterogeneity from one layer to another with regard to mineral content. On average, the mineral content is 37%, but ranges from 16% to 51%, with some layers yielding a maximal density of minerals of up to 80% exceptionally (Kani _et al_. 1983; Friskopp & Isacsson 1984). The predominant mineral in exterior layers is **OCP** , while **HA** is dominant in inner layers of old calculus. **W** is only found in small proportions (Sundberg & Friskopp 1985). **B** is identified in recent calculus, not older than 2 weeks, and appears to form the basis for supragingival calculus formation. The appearance of the crystals is characteristic for **OCP** as forming platelet-like crystals, for **HA** as forming sandgrain or rod-like crystals, while **W** presents with hexagonal (cuboidal, rhomboidal) crystals (Kodaka _et al_. 1988).
Subgingival calculus appears somewhat more homogeneous since it is built up in layers with an equally high density of minerals. On average the density is 58% and ranges from 32% to 78%. Maximal values of 60–80% have been found (Kani _et al_. 1983; Friskopp & Isacsson 1984). The predominant mineral is always **W** , although **HA** has been found (Sundberg & Friskopp 1985). **W** contains small proportions (3%) of magnesia (McDougall 1985).
****Fig. 8-47**** Thin section of old mineralizing plaque. The intermicrobial matrix is totally calcifi ed, and many microorganisms show intracellular crystal deposition. Magnification ×9500. Bar: 1 µm. From Theilade (1964).
In the presence of a relatively low plaque pH and a concomitant high Ca/P ratio in saliva, **B** is formed which may later on develop into **HA** and **W**. When supragingival plaque mineralizes, **OCP** forms and is gradually changed into **HA**. In the presence of alkaline and anaerobic conditions and concomitant presence of magnesia (or Zn and CO3), large amounts of **W** are formed, which are a stable form of mineralization.
## Clinical implications
Although strong associations between calculus deposits and periodontitis have been demonstrated in experimental (Wærhaug 1952, 1955) and epidemiologic studies (Lövdal _et al_. 1958), it has to be realized that calculus is always covered by an unmineralized layer of viable bacterial plaque. It has been debated whether or not calculus may exert a detrimental effect on the soft tissues owing to its rough surface. However, it has clearly been established that surface roughness alone does not initiate gingivitis (Wærhaug 1956). On the contrary, in monkeys a normal epithelial attachment with the junctional epithelial cells forming hemidesmosomes and a basement membrane on calculus could be established (Listgarten & Ellegaard 1973) if the calculus surface had been disinfected using chlorhexidine (Fig. 8-48). Furthermore, it has been demonstrated that autoclaved calculus may be encapsulated in connective tissue without inducing marked inflammation or abscess formation (Allen & Kerr 1965).
**Fig. 8-48** Hemidesmosomal attachment of junctional epithelium on dental calculus in the absence of bacteria following application of chlorhexidine. CA: calculus; HD: hemidesmosomes; BL: basement lamina; DC: dental cuticle. ×32 000. Data from Listgarten & Ellegaard (1973).
These studies clearly exclude the possibility of dental calculus being a primary cause of periodontal diseases. The effect of calculus seems to be secondary by providing an ideal surface configuration conducive to further plaque accumulation and subsequent mineralization.
Nevertheless, calculus deposits may have developed in areas with difficult access for oral hygiene or may – by the size of the deposits – jeopardize proper oral hygiene practices. Calculus may also amplify the effects of bacterial plaque by keeping the bacterial deposits in close contact with the tissue surface, thereby influencing both bacterial ecology and tissue response (Friskopp & Hammarström 1980).
Well controlled animal (Nyman _et al_. 1986) and clinical (Nyman _et al_. 1988; Mombelli _et al_. 1995) studies have shown that the removal of subgingival plaque on top of subgingival calculus will result in healing of periodontal lesions and the maintenance of healthy gingival and periodontal tissues, provided that the supragingival deposits are meticulously removed on a regular basis. One of these studies (Mombelli _et al_. 1995) clearly demonstrated that the diligent and complete removal of subgingival plaque on top of mineralized deposits after chipping off gross amounts of calculus showed almost identical results in the composition of the microbiota and the clinical parameters to those obtained with routine removal of subgingival calculus by root surface instrumentation. Again, it has to be realized that meticulous supragingival plaque control guarantees the depletion of the supragingival bacterial reservoir for subgingival recolonization. These studies have clearly elucidated the role of subgingival calculus as a plaque-retaining factor.
In summary, dental calculus represents mineralized bacterial plaque. It is always covered by unmineralized viable bacterial plaque, and hence, does not directly come into contact with the gingival tissues. Calculus, therefore, is a secondary etiologic factor for periodontitis. Its presence, however, makes adequate plaque removal impossible and prevents patients from performing proper plaque control. It is the most prominent plaque-retentive factor which has to be removed as a basis for adequate periodontal therapy and prophylactic activities.
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# Chapter 9
# Periodontal Infections
Sigmund S. Socransky and Anne D. Haffajee
* * *
Introduction
Similarities of periodontal diseases to other infectious diseases
Unique features of periodontal infections
Historical perspective
The early search
The decline of interest in microorganisms
Non-specific plaque hypothesis
Mixed anaerobic infections
Return to specificity in microbial etiology of periodontal diseases
Changing concepts of the microbial etiology of periodontal diseases
Current suspected pathogens of destructive periodontal diseases
Criteria for defining periodontal pathogens
Periodontal pathogens
Mixed infections
The nature of dental plaque – the biofilm way of life
The nature of biofilms
Properties of biofilms
Techniques for the detection and enumeration of bacteria in oral biofilm samples
The oral biofilms that lead to periodontal diseases
Microbial complexes
Factors that affect the composition of subgingival biofilms
Microbial composition of supra- and subgingival biofilms
Development of supra- and subgingival biofilms
Prerequisites for periodontal disease initiation and progression
The virulent periodontal pathogen
The local environment
Host susceptibility
Mechanisms of pathogenicity
Essential factors for colonization of a subgingival species
Effect of therapy on subgingival biofilms
* * *
# **Introduction**
Periodontal diseases are infections that are caused by microorganisms that colonize the tooth surface at or below the gingival margin. It is estimated that about 700 different species are capable of colonizing the mouth and any individual may typically harbor 150 or more different species. Counts in subgingival sites range from about 103 in healthy, shallow sulci to >108 in deep periodontal pockets. Numbers in supragingival plaque can exceed 109 on a single tooth surface. Thus, while hundreds of millions or even billions of bacteria continually colonize the tooth at or below the gingival margin throughout life, most periodontal sites in most individuals do not exhibit new loss of the supporting structures of the teeth at any given time. This recognition is critical. The ecologic relationships between the periodontal microbiota and its host are, by and large, benign, in that damage to the supporting structures of the tooth is infrequent. Occasionally, a subset of bacterial species either is introduced, overgrows or exhibits new properties that lead to the destruction of the periodontium. The resulting stressed equilibrium is usually spontaneously corrected, or corrected by therapy. In either instance, microbial species continue to colonize above and below the gingival margin; hopefully, in a new and "peaceful" equilibrium.
## **Similarities of periodontal diseases to other infectious diseases**
Our concepts of infectious diseases often appear to be influenced by our experiences with acute infections, particularly upper respiratory infections. In acute infections, an agent is acquired by exposure to an individual harboring that agent or from the environment. The agent establishes within tissues or on mucous membranes or skin. Within a short period of time, signs or symptoms of a disease appear at the site of introduction or elsewhere in the individual. A "battle" occurs between the parasite and the host resulting in increasingly obvious clinical signs and symptoms. This host–pathogen interaction often is resolved within a short period of time, usually, but not always, in favor of the host. Thus, daily experience suggests that colonization by a pathogen is rapidly followed by expression of disease. While certain infections follow this pattern, more commonly, colonization by a pathogenic species does not lead to overt disease, at least immediately. For example, 15% of the American population is colonized by _Neisseria meningitidis_ (Caugant _et al_. 1988), but only 0.5–1.1 cases of meningitis occur per 100 000 of the population (Summary of Notifiable Diseases – United States 2004, 2006). _Mycobacterium tuberculosis_ colonizes about 5% of Americans (Sudre _et al_. 1992), but only 2.6 new cases of tuberculosis per 100 000 of US-born individuals are reported each year (Summary of notifiable diseases – United States 2004, 2006). Finally, about one third of the adult population is colonized by _Haemophilus influenzae_ (Kilian & Frederiksen 1981) but only a tiny fraction exhibit disease. Even the highly virulent HIV virus may be detected in individuals for years prior to the development of clinical symptoms.
In a similar fashion, individuals may be colonized continuously by periodontal pathogens at or below the gingival margin and yet not show evidence of ongoing or previous periodontal destruction. Many of the organisms that colonize such sites are members of species thought to be periodontal pathogens. In spite of their presence, periodontal tissue damage does not take place. This is not an anomaly. This phenomenon is consistent with other infectious diseases in which it may be observed that a pathogen is necessary but not sufficient for a disease to occur.
Infectious diseases in a given organ system are caused by one or more of a relatively finite set of pathogens. Further, different species have different tissue specificities and cause diseases in different sites in the body. Lung infections may be caused by a wide range of species that includes _Streptococcus pneumoniae_ , _M. tuberculosis_ , _Klebsiella pneumoniae_ , _Legionella pneumophilia_ , and others. Infections of the intestine are caused by _Salmonella typhi_ , _Shigella dysenteriae_ , _Vibrio cholerae_ , _Escherichia coli_ , and _Campylobacter_ species. In a similar fashion periodontal diseases appear to be caused by a relatively finite group of periodontal pathogens acting alone or in combination. Such species include _Aggregatibacter_ (formerly _Actinobacillus_ ) _actinomycetemcomitans_ , _Tannerella forsythia_ , _Campylobacter rectus_ , _Eubacterium nodatum_ , _Fusobacterium nucleatum_ , _Peptostreptococcus micros_ , _Porphyromonas gingivalis_ , _Prevotella intermedia_ , _Prevotella nigrescens_ , _Streptococcus intermedius_ , and _Treponema_ sp. (Haffajee & Socransky 1994).
There is a number of other common themes observed in different infectious diseases, particularly those that affect mucous membranes, such as the need to attach to one or more surfaces, the need to "sense" the environment and turn on or off various virulence factors, and the need to overcome or evade host defense mechanisms. Infectious agents have evolved a set of common strategies to perform these tasks and the host has developed a series of responses to combat these infections. Thus, periodontal diseases are infectious diseases that have many properties that are similar to bacterial infections in other parts of the body and to a large extent can be combatted in similar fashions.
## **Unique features of periodontal infections**
Although periodontal diseases have certain features in common with other infectious diseases, there are several features of these diseases that are quite different. In certain ways, periodontal diseases may be among the most unusual infections of the human. The major reason for this uniqueness is _the unusual anatomic feature that a mineralized structure, the tooth, passes through the integument, so that part of it is exposed to the external environment while part is within the connective tissues_. The tooth provides a surface for the colonization of a diverse array of bacterial species. Bacteria may attach to the tooth itself, to the epithelial surfaces of the gingiva or periodontal pocket, to underlying connective tissues, if exposed, and to other bacteria which are attached to these surfaces. In contrast to the outer surface of most parts of the body, the outer layers of the tooth do not "shed" and thus microbial colonization (accumulation) is facilitated. Thus, a situation is set up in which microorganisms colonize a relatively stable surface, the tooth, and are continually held in immediate proximity to the soft tissues of the periodontium. This poses a potential threat to those tissues and indeed to the host itself.
The organisms that cause periodontal diseases reside in biofilms that exist on tooth or epithelial surfaces. The biofilm provides a protective environment for the colonizing organisms and fosters metabolic properties that would not be possible if the species existed in a free-living (planktonic) state. Periodontal infections and another biofilm-induced disease, dental caries, are arguably the most common infectious diseases affecting the human. The onset of these diseases is usually delayed for prolonged periods of time after initial colonization by the pathogen(s). The course of these diseases typically runs for years. The etiologic agents in most instances appear to be members of the indigenous microbiota and, thus, the infections might be thought of as endogenous. The source of the infecting agents for any given individual is usually unknown, although transfer from parents or significant others is thought to play a primary role (Petit _et al_. 1993a,b; Saarela _et al_. 1993; van Steenbergen _et al_. 1993; Preus _et al_. 1994). The major characteristics of these diseases are that they are caused by organisms that reside in biofilms outside the body. Their treatment is complex in that physical, antimicrobial, and ecologic approaches are required.
The presence of a tooth increases the complexity of the host–parasite relationship in a number of ways. The bacteria colonizing the tooth are, by and large, outside the body where they are less able to be controlled by the potent mechanisms which operate within the tissues. The environment within plaque may be conducive for microbial survival, but it is unlikely to be a particularly effective environment for the host to seek out and destroy microorganisms. Factors, such as _hydrogen ion concentration_ (pH), _oxidation reduction potential_ (Eh), and _proteolytic enzymes_ , can affect the performance of host defense mechanisms. In addition, the tooth provides "sanctuaries" in which microorganisms can hide, persist at low levels during treatment and then re-emerge to cause further problems. Bacteria in dentinal tubules, flaws in the tooth, or areas that were demineralized by bacteria are not easily approached by the much larger host cells. In a similar fashion, non-cellular host factors must face diffusion barriers, lytic enzymes, and absorption by the mineral structure of the tooth. Mechanical debridement other than vigorous removal of tooth material cannot reach organisms within the tooth. Chemotherapeutic agents will also have difficulty in reaching the organisms.
Taken together, the infections that affect the tooth and its supporting structures present a formidable problem for both the host and the therapist. The unique anatomic features of this "organ system" must be borne in mind as we attempt to unravel the etiology and pathogenesis of periodontal diseases and plan treatment or prevention strategies for their control.
# **Historical perspective**
The search for the etiologic agents of periodontal diseases has been in progress for over a century. The search started in the "golden age of microbiology" (approx. 1880–1920), when the etiologic agents of many medically important infections were determined. It is not surprising that parallel investigations of the etiology of periodontal diseases were initiated in this era. However, these investigations were not as successful as some of the investigations of extraoral infectious diseases. It seems worthwhile to review briefly the findings of the early era and to understand the effect that the inconclusive nature of many of the studies had on the concepts of etiology and treatment of disease. The references for this section may be found in Socransky and Haffajee (1994).
## The early search
Investigators in the period from 1880–1930 suggested four distinct groups of microorganisms as possible etiologic agents; amoeba, spirochetes, fusiforms, and streptococci. The basis of this determination was primarily the seeming association of these organisms with periodontal lesions. The identification of a suspected pathogen was heavily influenced by the nature of the techniques available. The major techniques at that time were wet mount or stained smear microscopy and limited cultural techniques. The different techniques suggested different etiologic agents. A situation not unlike that found today. While a greater variety of improved techniques is available, different techniques can and do emphasize the importance of different organisms.
### Amoeba
Certain groups of investigators used stained smears to seek amoeba in bacterial plaque. They found higher proportions of amoeba in lesions of destructive periodontal diseases than in samples taken from sites in healthy mouths or mouths with gingivitis. Local therapies for this organism included the use of dyes or other antiseptic agents to decrease the numbers of amoebae in the oral cavity. Other approaches employed agents such as the emitic, emitin, administered systemically or locally. The role of amoeba in periodontal disease was questioned by some authors because amoeba were found in sites with minimal or no disease and could not be detected in many sites with destructive disease and because of the failure of emitin to ameliorate the symptoms of the disease.
### Spirochetes
Other investigators used wet mount preparations or specific stains for spirochetes when they examined dental plaque. They reported higher proportions of spirochetes and other motile forms in lesions of destructive disease when compared with control sites in the same or other individuals. This finding led to the suggestion that spirochetes may be etiologic agents of destructive periodontal disease. Therapies were proposed that sought to control disease by the elimination or suppression of these microorganisms including the systemic administration of Neosalvarsan (compound 606), the anti-spirochetal agent used to treat syphilis, coupled with the use of subgingival scaling to control destructive periodontal disease. Other investigators employed bismuth compounds to treat oral spirochetal infections. Many investigators claimed success in controlling advanced destructive periodontal disease by combining local and systemic therapy. Others questioned the relationship of spirochetes to periodontal diseases.
### Fusiforms
The third group of organisms that were frequently suggested to be etiologic agents of destructive periodontal diseases, including Vincent's infection, were the spindle-shaped fusiforms. These organisms were originally recognized on the basis of their frequent appearance in microscopic examination of subgingival plaque samples. The organisms were first related to periodontal disease by Plaut (1894). Vincent (1899) distinguished certain pseudomembranous lesions of the oral cavity and throat from diphtheria and recognized the important role of fusiforms and spirochetes in this disease. In honor of this investigator the infection became known as Vincent's infection. The important role of spirochetes and fusiforms in Vincent's infection was widely recognized in the succeeding 2 decades.
As a footnote to this section, it is worth noting that acute necrotizing ulcerative gingivitis (ANUG) appears to have been declining in many "first world countries" for many decades. Many older practitioners can remember periods when they would see several cases of ANUG a month or even a week. Detection of this disease is much less common today. In reviewing the earlier literature, we were struck with how common the disease appeared to be from about 1915–1930. Most of us are aware of the devastation this disease caused in the combat troops of World War I, when the disease was commonly called trench mouth (due to its frequent occurrence in troops stationed in the trenches of the battlegrounds). What we are less aware of is how common the disease became in countries out of the war zone (e.g. the US) after World War I. For example, Daley (1927a,b) examined over 1000 patients who came to Tufts Dental College in Boston for operative dentistry (not periodontal problems). He found Vincent's infection in one of three people using clinical criteria and stained smears seeking the presence of fusiforms and spirochetes. Daley carefully described the lesions in terms acceptable today; i.e. as ulcerated lesions that bled easily on probing and had a distinctive fetid odor. He further pointed out that the disease was rare in Boston prior to 1917; at which time the troops began to return home. He described an outbreak stemming from a local barracks which led to 75 cases being treated at Tufts within 48 hours. Daley and others in the era felt that the severe outbreak after the war was due to the transmission of more virulent bacteria among an unprotected (not immune) population. Assuming that the disease described in this era was ANUG, it is interesting to note that there was a virtual epidemic. This is particularly intriguing in that it supports the notion that periodontal pathogens can be readily transmitted from one person to another as modern molecular techniques are documenting today.
### **Streptococci**
The fourth group of microorganisms that were proposed as etiologic agents of periodontal diseases in this era were the streptococci. These microorganisms were proposed on the basis of cultural examination of samples of plaque from subgingival sites of periodontal disease. The selection of the streptococci may have been predicated upon the fact these were the only species that could be consistently isolated from periodontitis lesions using the cultural techniques of that era. Since there were no methods available at that time for the specific control of streptococci, workers turned to non-specific agents such as the intramuscular injection of mercury or to the use of vaccines for the control of periodontal diseases.
### **Vaccines**
For the first 3 decades of the twentieth century, vaccines were commonly employed by physicians and dentists in attempts to control bacterial infections. Three types of vaccines were employed for the control of periodontal diseases. These included vaccines prepared from pure cultures of streptococci, and other oral organisms, autogenous vaccines, and stock vaccines such as Van Cott's vaccine, Goldenberg's vaccine or Inava Endocorps vaccine. These vaccines were administered systemically or locally in the periodontal tissues.
Autogenous vaccines were prepared from the dental plaque of patients with destructive periodontal diseases. Plaque samples were removed from the diseased site, "sterilized" by heat, and/or by immersion in iodine or formalin solutions, then re-injected into the same patient, either in the local periodontal lesion or systemically. Proponents of all three techniques claimed great efficacy for the vaccination methods employed, while others using the same techniques were more skeptical.
### Other forms of therapy directed against oral microorganisms
The difficulty in controlling microorganisms in the absence of specific antimicrobial agents gave rise to a series of rather remarkable treatment procedures. For example, ultraviolet light was widely used to attempt to control the oral microbiota and to improve the well-being of the local tissue (for review see Rasmussen 1929). Other measures were somewhat more dramatic and in some instances rather frightening. Dental practitioners used electrochemical techniques, caustic agents such as phenol, sulfuric, trichloracetic or chromic acids, nascent copper, castor oil soap (sodium ricolineate), and even radium was used to combat root canal infections. In the last instance radium at levels of up to 0.135 millicuries was placed in canals to "sterilize" them. As might be expected, the reports were glowing. The recent interest in controlling the epithelium in order to maximize reattachment had antecedents in this era. One technique which appears to have been commonly employed was the use of sodium sulfide to "dissolve" the epithelial lining of the pocket and permit reattachment.
### Invasion – the early years
One of the more interesting phenomena of research is the fact that research workers keep rediscovering the same phenomena in a cyclical fashion. Invasion of the periodontal tissues by bacteria was thought to be important in the pathogenesis of periodontal diseases in the early 1900s, forgotten and then rediscovered.
Beckwith _et al_. (1925) used stains specific for bacteria to study biopsy specimens from prisoners at San Quentin who had periodontitis. They regularly observed bacteria both within the epithelium and in the underlying tissues. Bacteria in the epithelium were usually streptococci or "diphtheroids". Gram-negative rods were observed in the connective tissue. They noted the rare occurrence of spiral forms in the tissues, although they were routinely detected in the plaque overlying the tissues. Other investigators also showed invasion into periodontal tissues. Invasion of spirochetes deep into the lesions of Vincent's infection was clearly documented. It was thought that the spirochetes moved into the connective tissues first and were followed by fusiform-shaped species.
### Comment
In this early period, literally hundreds of papers were published which suggested certain specific etiologic agents of periodontal diseases or advocated specific therapies directed at microbial control. In spite of this enthusiasm, the concept of the infectious nature of periodontal diseases and the recognition that treatment should be directed at the causative agents, disappeared. Reasons for the demise of this promising area of research could have included the possibility of incorrect etiologic agents, inadequate therapies and multiplicity of diseases. A more likely scenario was the failure of early researchers (and this is still true today) to recognize that periodontal diseases represent an array of infections, each requiring different specific therapies. Indeed, a similar situation exists today where a given adjunctive antibiotic therapy is effective in some individuals and not others. Finally, competing theories explaining the etiology of periodontal diseases in this era appeared to, temporarily at least, gain popularity, due primarily to their nebulous and untestable nature. Such hypotheses as "diffuse alveolar atrophy", "continuing eruption", "lack of function", and "constitutional defects" became acceptable alternatives (to some) to the recognition of the infectious nature of periodontal diseases.
## The decline of interest in microorganisms
The initial enthusiasm for the hunt for the etiologic agents of destructive periodontal diseases slowly subsided and by the mid 1930s there were virtually no workers involved in this quest. This state was eloquently described by Belding and Belding (1936) in the aptly titled "Bacteria – Dental Orphans". During the period from the mid 1920s to the early 1960s, the attitude toward the etiology of periodontal diseases changed. In the first 2 decades of this period it was thought that periodontal disease was due to some constitutional defect on the part of the patient, to trauma from occlusion, to disuse atrophy or to some combination of these factors. Bacteria were thought to be merely secondary invaders in this process or, at most, contributors to the inflammation observed in periodontal destruction.
## Non-specific plaque hypothesis
Treatment of patients based on the notion of constitutional defects or trauma from occlusion was not effective in controlling periodontal diseases. Clinicians recognized that plaque control was essential in the satisfactory treatment of periodontal patients. During the late 1950s, a group of clinicians, sometimes referred to as "plaque evangelists", heavily emphasized the need for plaque control in the prevention and treatment of periodontal diseases. Thus, once again bacteria were thought to play a role in the etiology of destructive periodontal disease, but as non-specific causative agents. According to this "nonspecific plaque" hypothesis, any accumulations of microorganisms at or below the gingival margin would produce irritants leading to inflammation. The inflammation in turn was responsible for the periodontal tissue destruction. The specific species of microorganisms that accumulated on the teeth was not considered to be particularly significant, providing that their numbers were sufficiently large to trigger a destructive process.
## Mixed anaerobic infections
Beginning in the late 1920s, a series of oral and medical microbiologists believed that periodontal disease was the result of "mixed infections". This hypothesis had been considered since the late 1800s when microscopic observations by Vincent in France suggested that certain forms of periodontal disease, particularly ANUG, were due to a combination of microorganisms dominated by fusiforms and spirochetes. These infections were known as fusospirochetal infections. In the early 1930s, investigators found that mixtures of microorganisms isolated from lung infections or subgingival plaque would induce lesions when injected subcutaneously into various experimental animals. A combination of a fusiform, a spirochete, an anaerobic vibrio and an alpha hemolytic streptococcus could cause transmissible infections in the guinea pig. Later investigators failed to reproduce their results either with the above combination of microorganisms or with many other combinations they tested. They did demonstrate, however, that mixed infections were due to bacteria (rather than a virus).
Macdonald and co-workers (1956) were later able to produce transmissible mixed infections in the guinea pig groin using combinations of pure cultures. The critical mixture of four organisms included a _Bacteroides melaninogenicus_ strain, a Gram-positive anaerobic rod and two other Gram-negative anaerobic rods. This combination of organisms was completely different from those used by earlier investigators to cause transmissible infections. These results led to the concept that mixed infections might be "bacteriologically non-specific but biochemically specific". In other words, any combination of microorganisms capable of producing an array of destructive metabolites could lead to transmissible infections in animals and, by extension, to destructive periodontal infections in humans. Later experiments suggested that members of the _B. melaninogenicus_ group were the key species in these infections.
## Return to specificity in microbial etiology of periodontal diseases
In the 1960s, interest in the specific microbial etiology of periodontal disease was rekindled by two groups of experiments. The first demonstrated that periodontal disease could be transmitted in the hamster from animals with periodontal disease to animals without periodontal disease by caging them together. Swabs of plaque or feces from diseased animals were effective in transmitting the disease to animals free of disease. It was demonstrated that a pure culture of a Gram-positive pleomorphic rod that later became known as _Actinomyces viscosus_ was capable of causing destructive periodontal disease in animals free of disease. Other species isolated from the plaque of hamsters with periodontal disease did not have this capability.
At about the same time, it was demonstrated that spirochetes with a unique ultrastructural morphology could be detected in practically pure culture in the connective tissue underlying lesions of ANUG and within the adjacent epithelium. Control tissue taken from healthy individuals and individuals with other forms of disease did not exhibit a similar tissue invasion. To date, the spirochete associated with ANUG has not been cultivated.
Such findings suggested that there might be more specificity to the microbial etiology of periodontal disease than had been accepted for the previous 4 decades. However, the emphasis of clinicians in the 1960s was on the mechanical control of plaque accumulation. This approach was consistent with the prevailing concept that periodontal disease was due to a non-specific accumulation of bacteria on tooth surfaces. This concept is very much in evidence today and still serves as the basis of preventive techniques in most dental practices. It is also clear that non-specific plaque control is not able to effectively prevent all forms of periodontal disease.
The transmissibility studies stimulated a new concept of periodontal diseases. The organisms which were responsible for the periodontal destruction observed in the hamster clearly differed from other organisms by their ability to form large amounts of bacterial plaque both in the hamster and in _in vitro_ test systems. A concept emerged that microorganisms that were capable of forming large amounts of plaque _in vivo_ and _in vitro_ should be considered as prime suspects in the etiology of periodontal diseases. Human isolates of _Actinomyces_ species were shown to have this ability _in vitro_ and led to plaque formation and periodontal destruction in animal model systems. These findings reinforced the notion that organisms that formed abundant plaque were responsible for destructive periodontal disease. Unfortunately, later research findings revealed major discrepancies in this hypothesis.
## Changing concepts of the microbial etiology of periodontal diseases
By the end of the 1960s it was generally accepted that dental plaque was in some way associated with human periodontal disease. It was believed that the presence of bacterial plaque initiated a series of as yet undefined events that led to the destruction of the periodontium. The composition of plaque was thought to be relatively similar from patient to patient and from site to site within patients. Variability was recognized, but the true extent of differences in bacterial composition was not appreciated. It was thought that the major event triggering destructive periodontal disease was an increase in mass of bacterial plaque, possibly accompanied by a diminution of host resistance. Indeed, in the mid 1960s the classic studies of Loe _et al_. (1965, 1967) and Theilade _et al_. (1966) convincingly demonstrated that plaque accumulation directly preceded and initiated gingivitis. Many investigators believed that gingivitis was harmful, and led to the eventual destruction of the periodontal tissues, probably by host-mediated events.
Yet, certain discrepancies continued to baffle clinicians and research workers alike. If all plaques were more or less alike and induced a particular tissue response in the host, why was periodontal destruction localized, taking place adjacent to one tooth but not another? If plaque mass was a prime trigger for periodontal destruction, why did certain subjects accumulate much plaque, frequently accompanied by gingivitis, but fail, even after many years to develop destruction of the supporting structures? On the other hand, why did some individuals with little detectable plaque or clinical inflammation develop rapid periodontal destruction? If inflammation was the main mediator of tissue destruction, why were so many teeth retained in the presence of continual gingivitis? One explanation may have been that there were inconsistencies in the host response, or disease required the superimposition of local factors such as trauma from occlusion, overhanging fillings etc. Other explanations can be derived from extensive studies of the microbiota adjacent to periodontal tissues.
The recognition of differences in the composition of bacterial plaque from subject to subject and site to site within subjects led to a series of investigations. Some studies attempted to determine whether specific microorganisms were found in lesion sites as compared to healthy sites. Others studies sought differences in the microorganisms in subgingival plaque samples taken from subjects with clinically different forms of periodontal disease or periodontal health. Newman _et al_. (1976, 1977) and Slots (1976) demonstrated that the microbial composition of subgingival plaque taken from diseased sites differed substantially from the samples taken from healthy sites in subjects with localized aggressive periodontitis (LAP). Tanner _et al_. (1979) and Slots (1977) demonstrated that the microbiota recovered from lesion sites from subjects with chronic periodontitis differed from the microbiota from healthy sites in the same subjects and also from lesion sites in LAP subjects. These studies, along with the demonstration that subjects with LAP could be treated successfully with local debridement and systemic antibiotics, provided the initial impetus to perform larger-scale studies attempting to relate specific microorganisms to the etiology of different periodontal diseases.
# **Current suspected pathogens of destructive periodontal diseases**
## Criteria for defining periodontal pathogens
For more than a century, the classical "Koch's postulates" have been used to define a causal relationship between an infectious agent and a disease. These postulates were: (1) the agent must be isolated from every case of the disease, (2) it must not be recovered from cases of other forms of disease or non-pathogenically, and (3) after isolation and repeated growth in pure culture, the pathogen must induce disease in experimental animals (Carter 1987). The criteria for defining pathogens of destructive periodontal diseases initially were based on Koch's postulates but have been amended and extended in recent years. These criteria include association, elimination, host response, virulence factors, animal studies, and risk assessment. The discrimination of a pathogen from a non-pathogenic species is not based on a single criterion but rather on a "weight of evidence" evaluation.
The criterion of association is really the same as Koch's first two postulates; i.e. the species should be found more frequently and in higher numbers in cases of the infection than in individuals without overt disease or with different forms of disease. However, periodontal microbiologists do not expect to find the pathogen in "all cases of the disease" because they currently cannot distinguish "all cases of a given disease". The criterion of elimination is based on the concept that elimination of a species should be accompanied by a parallel remission of disease. If a species is eliminated by treatment and the disease progresses, or if the level of a species remains high or increases in a site and the disease stops, doubt would be cast on that species' role in pathogenesis. This criterion (like all of the others) has certain problems in that therapy rarely (if ever) eliminates or suppresses only one species at a time. The criterion of host response, particularly the immunological response, appears to be of value in defining periodontal pathogens. If a species (or its antigens) gains access to underlying periodontal tissues and causes damage, it seems likely that the host will produce antibodies or a cellular immune response that is directed specifically to that species. Thus, the host response could act as a pointer to the pathogen(s). Biochemical determinants (virulence factors) may also provide valuable clues to pathogenicity. Potentially damaging metabolites produced, or properties possessed, by certain species may be suggestive that those species could play a role in the disease process.
Animal model systems provide suggestive evidence that a microbial species may play a role in human disease. Particularly noteworthy are studies of experimentally induced disease in dogs or monkeys, which can be manipulated to favor selection of single or subsets of species that may or may not induce pathology. These models usually suggest a possible etiologic role of a species indigenous to the test animal that may have analogues in the human subgingival microbiota. Finally, technological developments, such as checkerboard DNA–DNA hybridization (Fig. 9-1) and polymerase chain reaction (PCR), now permit assessment of specific microorganisms in large numbers of subgingival plaque samples. This allows prospective studies to be performed in which the risk of periodontal disease progression conferred by the presence of an organism at given levels may be assessed.
## Periodontal pathogens
The World Workshop in Periodontology (Consensus Report, 1996) designated _A. actinomycetemcomitans_ , _P. gingivalis_ , and _T. forsythia_ as periodontal pathogens. Tables 9-1, 9-2, and 9-3 summarize some of the data that indicate an etiologic role of these species in periodontal diseases, categorized according to the criteria defined above. The summary is by no means exhaustive but does indicate that a growing literature suggests some reasonable candidates as etiologic agents of destructive periodontal diseases.
#### _**_Aggregatibacter_**_ **(formerly** _**_Actinobacillus_**_ **)** _**_actinomycetemcomitans_**_
One of the clearest associations between a suspected pathogen and destructive periodontal disease is provided by _A. actinomycetemcomitans_. This species has recently been renamed _Aggregatibacter actinomycetemcomitans_ from its former name of _Actinobacillus actinomycetemcomitans_ (Norskov-Lauritsen & Kilian 2006). _A. actinomycetemcomitans_ is a small, non-motile, Gram-negative, saccharolytic, capnophilic, round-ended rod that forms small, convex colonies with a "star-shaped" center when grown on blood agar plates (Fig. 9-2). This species was first recognized as a possible periodontal pathogen by its increased frequency of detection and higher numbers in lesions of localized aggressive periodontitis (Newman _et al_. 1976; Slots 1976; Newman & Socransky 1977; Slots _et al_. 1980; Mandell & Socransky 1981; Zambon _et al_. 1983a; Chung _et al_. 1989) when compared with numbers in plaque samples from other clinical conditions including periodontitis, gingivitis, and health. Soon thereafter, it was demonstrated that the majority of subjects with localized aggressive periodontitis (LAP) had an enormously elevated serum antibody response to this species (Genco _et al_. 1980; Listgarten _et al_. 1981; Tsai _et al_. 1981; Altman _et al_. 1982; Ebersole _et al_. 1982, 1987) and that there was local synthesis of antibody to this species (Schonfeld & Kagan 1982; Ebersole _et al_. 1985; Smith _et al_. 1985; Tew _et al_. 1985a). When subjects with this form of disease were treated successfully, the species was eliminated or lowered in level; treatment failures were associated with failure to lower the numbers of the species in treated sites (Slots & Rosling 1983; Haffajee _et al_. 1984; Christersson _et al_. 1985; Kornman & Robertson 1985; Mandell _et al_. 1986; Preus 1988; Shiloah _et al_. 1998; Tinoco _et al_. 1998). The species produced a number of potentially damaging metabolites, including a leukotoxin (Baehni _et al_. 1979) and a cytolethal distending toxin (Saiki _et al_. 2001; Shenker _et al_. 2001), and induced disease in experimental animals (Irving _et al_. 1978). _A. actinomycetemcomitans_ has been shown, _in vitro_ , to have the ability to invade cultured human gingival epithelial cells (Blix _et al_. 1992; Sreenivasan _et al_. 1993), human vascular endothelial cells (Schenkein _et al_. 2000) and buccal epithelial cells _in vivo_ (Rudney _et al_. 2001). Further, studies have shown that _A. actinomycetemcomitans_ induced apoptotic cell death (Arakawa _et al_. 2000; Kato _et al_. 2000).
**Fig. 9-1** Example of checkerboard DNA–DNA hybridization being used to detect 40 bacterial species in 28 subgingival plaque samples from a single patient. The vertical lanes are the plaque samples numbered from 11 (upper right central incisor) to 47 (lower right second molar). In this subject, teeth 16, 17, 21, and 37 were missing. The two vertical lanes on the right are standards containing either 105 or 106 cells of each test species. The horizontal lanes contained the indicated DNA probes in hybridization buffer. A signal at the intersection of the vertical and horizontal lanes indicates the presence of a species. The intensity of the signal is related to the number of organisms of that species in the sample. In brief, samples of plaque were placed into individual Eppendorf tubes and the DNA released from the microorganisms by boiling in NaOH. After neutralization, the released DNA was transferred to the surface of a nylon membrane using the 30 channels of a Minislot device (Immunetics, Cambridge, MA). The DNA was fixed to the membrane by UV light and baking and placed in a Miniblotter 45 (Immunetics) with the lanes of DNA at right angles to the 45 channels of the Miniblotter device. Whole genomic DNA probes labelled with digoxigenin were placed in hybridization buffer into 40 of the lanes and hybridized overnight. After stringency washing, the signals were detected using phosphatase-conjugated antibody to digoxigenin and chemifluorescence substrates. Signals were compared to the standards using a Storm Fluorimager and converted to counts.
**Table 9-1** Summary of some of the types of data that suggest that _Aggregatibacter actinomycetemcomitans_ may be an etiologic agent of destructive periodontal diseases (for literature citations see text and Haffajee & Socransky 1994)
**Factor**| **Data**
---|---
Association | Elevated in lesions of localized juvenile periodontitis (LJP), prepubertal or adolescent periodontal disease
| Lower in health, gingivitis and edentulous subjects or sites
| Elevated in some adult periodontitis lesions
| Elevated in active lesions of juvenile periodontitis
| Detected in prospective studies
| Detected in apical ares of pocket or in tissues from LJP lesions
Elimination | Elimination or suppression resulted in successful therapy
| Recurrent lesions harbored the species
Host response | Elevated antibody in serum or saliva of LJP patients
| Elevated antibody in serum or saliva of chronic periodontitis patients
| Elevated local antibody in LJP sites
Virulence factors | Leukotoxin; collagenase; endotoxin; epitheliotoxin; fibroblast inhibitory factor; bone resorption inducing factor; induction of cytokine production from macrophages; modification of neutrophil function; degradation of immunoglobulins; cytolethal distending toxin (Cdt); induces apoptotic cell death
| Invades epithelial and vascular endothelial cells _in_ _vitro_ and buccal epithelial cells _i_ n _viv_ o
Animal studies | Induced disease in gnotobiotic rats
| Subcutaneous abscesses in mice
**Table 9-2** Summary of some of the types of data that suggest that _Porphyromonas gingivalis_ may be an etiologic agent of destructive periodontal diseases (for literature citations see text and Haffajee & Socransky 1994)
**Factor**| **Data**
---|---
Association | Elevated in lesions of periodontitis
| Lower in sites of health, gingivitis and edentulous subjects
| Elevated in actively progressing lesions
| Elevated in subjects exhibiting periodontal disease progression
| Detected in cells or tissues of periodontal lesions
| Presence indicates increased risk for alveolar bone loss and attachment level loss
Elimination | Elimination resulted in successful therapy
| Recurrent lesions harbored the species
| Successful treatment lowered level and/or avidity of antibody
Host response | Elevated antibody in serum or saliva in subjects with various forms of periodontitis
| Altered local antibody in periodontitis
Virulence factors | Collagenase; endotoxin; proteolytic trypsin-like activity; fibrinolysin; hemolysin; other proteases including gingipain; phospholipase A; degrades immunoglobulin; fibroblast inhibitory factor; H2S; NH3; fatty acids; factors that adversely affect PMNs; capsular polysaccharide; bone resorption inducing factor; induction of cytokine production from various host cells; generates chemotactic activities; inhibits migration of PMNs across epithelial barriers;
| Invades epithelial cells _in_ _vitr_ o
Animal studies | Important in experimental pure or mixed subcutaneous infections
| Induced disease in gnotobiotic rats
| Studies in sheep, monkeys and dogs
| Immunization diminished disease in experimental animals
**Table 9-3** Summary of some of the types of data that suggest that _Tannerella forsythia_ may be an etiologic agent of destructive periodontal diseases (for literature citations see text and Haffajee & Socransky 1994)
**Factor**| **Data**
---|---
Association | Elevated in lesions of periodontitis
| Lower in sites of health or gingivitis
| Elevated in actively progressing lesions
| Elevated in periodontal abscesses
| Increased in subjects with refractory periodontitis
| Detected in epithelial cells of periodontal pockets
| Presence indicates increased risk for alveolar bone loss, tooth and attachment level loss
Elimination | Elimination resulted in successful therapy
| Recurrent lesions harbored the species
| Reduced in successfully treated peri-implantitis
Host response | Elevated antibody in serum of periodontitis subjects and very high in a subset of subjects with refractory periodontitis
Virulence factors | Endotoxin; fatty acid and methylglyoxal production; induces apoptotic cell death; cytokine production from various host cells; invades epithelial cells _in_ _vitro_ and _in_ _viv_ o
Animal studies | Increased levels in ligature-induced periodontitis and peri-implantitis in dogs
| Induced disease in gnotobiotic rats
**Fig. 9-2** Photograph of a primary isolation plate of a subgingival plaque sample from a diseased site in a subject with LAP. A dilution of the plaque sample was grown for 7 days at 35˚C on an enriched blood agar plate in an atmosphere of 80% N2, 10% H2, and 10% CO2. The majority of the small, round, convex colonies on this plate were isolates of _Aggregatibacter actinomycetemcomitans_.
Perhaps the strongest association data came from studies of "active lesions" in which the species was elevated in actively progressing periodontal lesions when compared with non-progressing sites (Haffajee _et al_. 1984; Mandell 1984; Mandell _et al_. 1987; Haubek _et al_. 2004) and in prospective studies of as yet undiseased siblings of LAP subjects (DiRienzo _et al_. 1994). _A. actinomycetemcomitans_ was also elevated in studies of disease progression in young Indonesian subjects (Timmerman _et al_. 2001). Collectively, the data suggest that _A. actinomycetemcomitans_ is a probable pathogen of LAP. However, this should not be interpreted as meaning that it is the sole cause of this clinical condition, since a subset of subjects with LAP did not exhibit this species in samples of their subgingival plaque and had no elevated antibody response to the species (Loesche _et al_. 1985; Moore 1987).
The possibility that a subset of _A. actinomycetemcomitans_ clonal types was primarily responsible for LAP was raised in studies at the University of Pennsylvania. Strains of _A. actinomycetemcomitans_ were isolated from members of 18 families with at least one member with active LAP as well as from from 32 control subjects. Restriction fragment length polymorphisms (RFLP) indicated 13 distinct RFLP groups of _A. actinomycetemcomitans_ (DiRienzo & McKay 1994). Isolates from LAP subjects fell into predominantly RFLP pattern II, while RFLP patterns XIII and XIV were seen exclusively in isolates from periodontally healthy subjects. Further, disease progression was related strongly to the presence of RFLP group II (DiRienzo _et al_. 1994).
Haubek _et al_. (1996) demonstrated that strains of _A. actinomycetemcomitans_ isolated from families, initially of African origin living in geographically different areas, were characterized by a 530 base pair deletion in the leukotoxin gene operon leading to a significantly increased production of leukotoxin. They speculated that this virulent clonal type may account for an increased prevalence of LAP in African Americans and other individuals of African descent. A key isolate of this clonal type, strain JP2, was first isolated from an 8-year-old African American child with prepubertal periodontitis (Tsai _et al_. 1979; Kilian _et al_. 2006). There was a strong association between the presence of the JP2 clonal type of _A. actinomycetemcomitans_ and early onset periodontitis in Moroccan school children, but no association between the presence of _A. actinomycetemcomitans_ without the 530 bp deletion and early onset periodontitis (Haubek _et al_. 2001). Further, the odds ratio for disease progression in a subject in this population infected with the JP2 clone was 14.5 (Haubek _et al_. 2004). These observations were corroborated in a Brazilian population, where highly leukotoxic strains of _A. actinomycetemcomitans_ were more prevalent in aggressive periodontitis than in chronic periodontitis (Cortelli _et al_. 2005). This deletion in the leukotoxin operon was not detected in any strains of _A. actinomycetemcomitans_ isolated from adult Chinese subjects (Mombelli _et al_. 1999; Tan _et al_. 2001) or Asian subjects in the United States (Contreras _et al_. 2000). Subjects harboring _A. actinomycetemcomitans_ with the 530 bp deletion were 22.5 times more likely to convert to LAP than subjects who had _A. actinomycetemcomitans_ variants containing the full-length leukotoxin promoter region (Bueno _et al_. 1998). Interestingly, strains of _A. actinomycetemcomitans_ with the RFLP type II pattern described by DiRienzo & McKay (1994) that were found frequently in LAP subjects included strains of the JP2 clonal type (Kilian _et al_. 2006). The above data suggest that _A. actinomycetemcomitans_ is a major pathogen of LAP and that the JP2 clonal type is a key pathogen in certain human populations.
_A. actinomycetemcomitans_ has also been implicated in adult forms of destructive periodontal disease, but its role is less clear. The species has been isolated from chronic periodontitis lesions, but less frequently and in lower numbers than from lesions in LAP subjects (Rodenburg _et al_. 1990; Slots _et al_. 1990a). In addition, its numbers in plaque samples from lesions in adults were often not as high as those observed for other suspected pathogens in the same plaque samples. There appear to be at least six serotypes of _A. actinomycetemcomitans_ (a, b, c, d, e, and f) and these serotypes appear to be clonal in nature (Kilian _et al_. 2006). The most frequently isolated serotype of _A. actinomycetemcomitans_ from lesions of LAP in American subjects was serotype b (Zambon _et al_. 1983b), whereas serotype a was more commonly detected in samples from chronic periodontitis subjects (Zambon _et al_. 1983a). This finding was corroborated indirectly by examination of serum antibody levels to the two serotypes. Most elevated responses to _A. actinomycetemcomitans_ in LAP subjects were to serotype b while elevated responses to serotype a were more common in adult subjects with chronic periodontitis (Listgarten _et al_. 1981). Some subjects in each group exhibited elevated serum antibody responses to both serotypes. In Finnish subjects, serotypes a and b were more frequently isolated from subjects with periodontal disease and serotype c from periodontally healthy subjects (Asikainen _et al_. 1991). However, this pattern of serotype distribution was not observed in Korea (Chung _et al_. 1989) or Japan (Saito _et al_. 1993; Yoshida _et al_. 2003), where _A. actinomycetemcomitans_ serotype c was frequently observed in plaque samples from sites of periodontal pathology. Serotypes d, e, and f, have been recognized more recently (Dogan _et al_. 1999; Mombelli _et al_. 1999) and are found less frequently than serotypes a, b and c. For example, serotypes d, e or f were not detected in a Brazilian population (Teixeira _et al_. 2006) and serotypes d or e were not found in Taiwanese subjects <35 years of age with different forms of periodontitis (Yang _et al_. 2004a).
Antibody data and data from the treatment of _A. actinomycetemcomitans_ infected patients with adult or refractory periodontitis provide the most convincing evidence of a possible etiologic role of _A. actinomycetemcomitans_ in adult forms of periodontal disease. Thirty-six of 56 adults with destructive periodontal disease examined at multiple time periods at the Forsyth Institute exhibited an elevated serum antibody response to _A. actinomycetemcomitans_ serotypes a and/or b. Elevated responses to other suspected periodontal pathogens were far less common. Van Winkelhoff _et al_. (1992) treated 50 adult subjects with "severe generalized periodontitis" and 40 subjects with refractory periodontitis who were culture positive for _A. actinomycetemcomitans_ using mechanical debridement and systemically administered amoxicillin and metronidazole. Only one of 90 subjects was culture positive for _A. actinomycetemcomitans_ 3–9 months post-therapy (van Winkelhoff _et al_. 1992) and one of 48 subjects was culture positive 2 years post-therapy (Pavicic _et al_. 1994). There was a significant gain in attachment level and decrease in probing pocket depth in virtually all patients after therapy.
It is suspected that _A. actinomycetemcomitans_ initially colonizes the oral cavity by attachment to the surfaces of the oral epithelium (Fine _et al_. 2006). There is a specific protein adhesin, Aae, that binds to a carbohydrate receptor on buccal epithelial cells of humans and Old World monkeys. It is thought that _A. actinomycetemcomitans_ moves from the buccal epithelial cells to the supragingival plaque, possibly binding to the tooth by fimbriae comprised of repeating subunits of a 6.5 kDa protein, Flp 1. The fimbiriae, along with an extracellular carbohydrate polymer, PGA, mediate attachment to hard surfaces (Fine _et al_. 2006). Alternatively, _A. actinomycetemcomitans_ may attach to other colonizing bacterial species by coaggregation (Kolenbrander 2000). At some point these organisms may move from the supragingival to the subgingival environment. From this vantage point, they may then attach to and invade the epithelial lining of the periodontal pocket and possibly penetrate the underlying connective tissues (Rudney _et al_. 2001). _A. actinomycetemcomitans_ has been shown to be present in the intima of vessel walls (Marques de Silva _et al_. 2005) and has been cultured from atheromatous plaques (Kozarov _et al_. 2005). Finally, _A. actinomycetemcomitans_ may leave the oral cavity and cause or contribute to endocarditis, since it has been frequently found in lesions of this condition (Paturel _et al_. 2004).
#### _Porphyromonas gingivalis_
_P. gingivalis_ is a second consensus periodontal pathogen that continues to be intensely investigated. Isolates of this species are Gram-negative, anaerobic, non-motile, asaccharolytic rods that usually exhibit coccal to short rod morphologies. _P. gingivalis_ is a member of the much investigated "black-pigmented _Bacteroides_ " group (Fig. 9-3). Organisms of this group form brown to black colonies (Oliver & Wherry 1921) on blood agar plates and were initially grouped into a single species, _B. melaninogenicus_ ( _Bacterium melaninogenicum_ ; Burdon 1928). The black-pigmented _Bacteroides_ have a long history of association with periodontal diseases since the early efforts of Burdon (1928) through the mixed infection studies of Macdonald _et al_. (1960) to the current intense interest. In the late 1970s, it was recognized that the black-pigmented _Bacteroides_ contained species that were asaccharolytic (eventually _P. gingivalis_ ), and either had an intermediate level of carbohydrate fermentation (which eventually led to a group of species including _Prevotella intermedia_ ) or were highly saccharolytic (leading to the group that includes _Prevotella melaninogenica_ ).
**Fig. 9-3** Photograph of part of a primary isolation plate of a subgingival plaque sample from a subject with chronic periodontitis. The medium and growth conditions were as described in Fig. 9-2. The black-pigmented colony was an isolate of _Porphyromonas gingivalis_.
Early interest in _Porphyromonas gingivalis_ and other black-pigmented _Bacteroides_ arose primarily because of their essential role in certain experimental mixed infections (Macdonald _et al_. 1956, 1963; Socransky & Gibbons 1965) and their production of an unusually large array of virulence factors (Table 9-2) (Haffajee & Socransky 1994; Deshpande & Khan 1999; Holt & Ebersole 2005). Members of these species produce collagenase, gingipain, an array of proteases (including those that destroy immunoglobulins), hemolysins, endotoxin, fatty acids, ammonia, hydrogen sulfide, indole etc. _P. gingivalis_ can inhibit migration of PMNs across an epithelial barrier (Madianos _et al_. 1997), has been shown to affect the production or degradation of cytokines by mammalian cells (Darveau _et al_. 1998; Fletcher _et al_. 1998; Sandros _et al_. 2000). and produces extracellular vesicles that contribute to the loss of membrane-bound CD14 receptors on human macrophage-like cells (Duncan _et al_. 2004).
Studies initiated in the late 1970s and extending to the present have strengthened the association of _P. gingivalis_ with disease and demonstrated that the species is uncommon and in low numbers in health or gingivitis but more frequently detected in destructive forms of disease (Table 9-2) (Haffajee & Socransky 1994; O'Brien-Simpson _et al_. 2000; Takeuchi _et al_. 2001; van Winkelhoff _et al_. 2002; Lau _et al_. 2004; Yang _et al_. 2004b). In diseased subjects, there was a strong positive relationship with pocket depth (Kawada _et al_. 2004; Socransky & Haffajee 2005). This species has also been shown to be increased in numbers and or frequency of detection in deteriorating periodontal sites (Dzink _et al_. 1988; Lopez 2000; Kamma _et al_. 2001) or in subjects exhibiting periodontal disease progression (Albandar _et al_. 1997). The species has been shown to be reduced in successfully treated sites but was commonly encountered in sites that exhibited recurrence of disease or persistence of deep periodontal pockets post-therapy (Bragd _et al_. 1987; Haffajee _et al_. 1988a; van Winkelhoff _et al_. 1988; Berglundh _et al_. 1998; Shiloah _et al_. 1998; Winkel _et al_. 1998; Takamatsu _et al_. 1999; Chaves _et al_. 2000; Mombelli _et al_. 2000; Fujise _et al_. 2002; Kawada _et al_. 2004). _P. gingivalis_ has been associated with an increased risk of periodontal disease severity and progression (Beck _et al_. 1990, 1992, 1997; Grossi _et al_. 1994, 1995).
_P. gingivalis_ has been shown to induce elevated systemic and local immune responses in subjects with various forms of periodontitis (Table 9-2) (Haffajee & Socransky 1994; Mahanonda _et al_. 1991; O'Brien-Simpson _et al_. 2000). Indeed, there has been an effort in many laboratories, not only to compare the level of antibody response in subjects with and without disease, but to examine relative avidities of antibody (Lopatin & Blackburn 1992; Whitney _et al_. 1992; Mooney _et al_. 1993), subclass of antibody (Lopatin & Blackburn 1992; Wilton _et al_. 1992), the effect of treatment (Chen _et al_. 1991; Johnson _et al_. 1993), and the nature of the antigens which elicit the elevated responses (Ogawa _et al_. 1989; Yoshimura _et al_. 1989; Curtis _et al_. 1991; Papaioannou _et al_. 1991; Duncan _et al_. 1992; Schifferle _et al_. 1993). Noteworthy in this regard were the observations of Ogawa _et al_. (1989), which indicated that an average of approximately 5% of plasma cells in lesions of advanced periodontitis formed antibody to the fimbriae of _P. gingivalis_. The consensus of the antibody studies is that many, but not all, subjects who had experienced periodontal attachment loss exhibited elevated levels of antibody to antigens of _P. gingivalis_ , suggesting that this species gained access to the underlying tissues and may have initiated or contributed to the observed pathology.
_P. gingivalis_ -like organisms were also strongly related to destructive periodontal disease in naturally occurring or ligature-induced disease in dogs, sheep or monkeys (Table 9-2). The species or closely related organisms were higher in number in lesion sites than in non-lesion sites in naturally occurring disease. When disease was induced by ligature in dogs or monkeys, the level of the species rose at the diseased sites concomitant with the detection of disease. Of great interest were the observations of Holt _et al_. (1988) who demonstrated that a microbiota suppressed by systemic administration of rifampin (and without detectable _P. gingivalis_ ) would not cause ligature-induced disease, but the re-introduction of _P. gingivalis_ to the microbiota resulted in initiation and progress of the lesions. Ligature-induced periodontitis and peri-implantitis in dogs was also accompanied by a significant increase in the detection of _P. gingivalis_ (Nociti _et al_. 2001). Like _A. actinomycetemcomitans_ , _P. gingivalis_ has been shown to be able to invade human gingival epithelial cells _in vitro_ (Lamont _et al_. 1992; Duncan _et al_. 1993; Sandros _et al_. 1993), buccal epithelial cells _in vivo_ (Rudney _et al_. 2001), endothelial cells (Takahashi _et al_. 2006) and has been found in higher numbers on or in epithelial cells recovered from the periodontal pocket than in associated plaque (Dzink _et al_. 1989) or healthy sites (Colombo _et al_. 2006). Attachment to and invasion of epithelial cells appears to be mediated by the _P. gingivalis_ fimbriae (Njoroge _et al_. 1997; Weinberg _et al_. 1997; Nakajawa _et al_. 2006).
There have been several studies that have attempted to immunize experimental animals against periodontal disease induced by _P. gingivalis_. Studies in monkeys and gnotobiotic rats have indicated that immunization with whole organisms or specific antigens affected the progress of the periodontal lesions. In most instances, periodontal breakdown was decreased (Evans _et al_. 1992; Persson _et al_. 1994a). However, in one study, the disease severity was increased after immunization (Ebersole _et al_. 1991). In the monkey model, the percentage of _P. gingivalis_ cells in subgingival plaque was inversely related to the serum antibody titer to this species (Persson _et al_. 1994b). Reductions in alveolar bone loss in the monkey model could also be achieved by immunization with the cysteine protease porphypain-2 from _P. gingivalis_ (Moritz _et al_. 1998; Page 2000). In more recent years, investigators have used a mouse "oral challenge" (by cells of _P. gingivalis_ ) model to study the effects of immunization by various fractions of _P. gingivalis_ on alveolar bone loss induced by this species. Immunization by hemagglutinin B (Katz _et al_. 1999), capsular polysaccharide (Gonzalez _et al_. 2003), heat shock protein (Lee _et al_. 2006), gingipain R (Gibson & Genco 2001), and the active sites of RgpA and Kgp proteinases (O'Brien-Simpson _et al_. 2005) protected against alveolar bone loss in the mouse model. Thus, altering the host– _P. gingivalis_ equilibrium by raising the level of specific antibodies to _P. gingivalis_ antigens markedly affected disease outcome. Such data reinforce the importance of this bacterial species in periodontal disease, at least in the animal model systems employed.
#### _**_Tannerella forsythia_**_
The third consensus periodontal pathogen, _T. forsythia_ , was first described in 1979 (Tanner _et al_. 1979) as a "fusiform" _Bacteroides_. This species was difficult to grow, often requiring 7–14 days for minute colonies to develop. The organism is a Gram-negative, anaerobic, spindle-shaped, highly pleomorphic rod. The growth of the organism was shown to be enhanced by co-cultivation with _F. nucleatum_ and indeed it commonly occurred with this species in subgingival sites (Socransky _et al_. 1988). The need for co-cultivation could be overcome by providing Nacetylmuramic acid in the medium (Wyss 1989). Inclusion of this factor markedly enhanced growth and the resulting cells were regularly shaped, short, Gram-negative rods rather than the pleomorphic cells observed in the absence of this factor (Tanner & Izard 2006). A feature that _T. forsythia_ cells shares with certain other Gram-negative species is the presence of a serrated S-layer that is easily visible by electron microscopy (Tanner _et al_. 1986) that may contribute to the pathogenicity of the species in periodontal diseases (Sabet _et al_. 2003). The S-layer has been isolated and shown to mediate hemagglutination, adhesion/invasion of epithelial cells, and murine subcutaneous abscess formation. The S-layer is composed of two glycoproteins of molecular mass 200 and 210 kDa (Lee _et al_. 2006). This species has been shown to produce trypsin-like proteolytic activity (BANA test positive) (Loesche _et al_. 1992) and methylglyoxal (Kashket _et al_. 2002), and induce apoptotic cell death (Arakawa _et al_. 2000). In addition, _T. forsythia_ in co-cultures of macrophage and epithelial cells leads to the expression of pro-inflammatory cytokines, chemokines, PGE2, and MMP9 (Bodet _et al_. 2006).
Initially, _T. forsythia_ was thought to be a relatively uncommon subgingival species. However, the studies of Gmur _et al_. (1989) using monoclonal antibodies to enumerate the species directly in plaque samples, suggested that the species was more common than previously found in cultural studies and its levels were strongly related to increasing pocket depth. Lai _et al_. (1987) reported similar findings using fluorescent-labeled polyclonal antisera and demonstrated that _T. forsythia_ was much higher in subgingival than supragingival plaque samples. Data of Tanner _et al_. (1998) suggested that _T. forsythia_ was a major species found at sites that converted from periodontal health to disease. There was a greater risk of periodontal attachment loss in adolescents who were colonized by _T. forsythia_ than adolescents in whom the species was not detected (Hamlet _et al_. 2004). _T. forsythia_ was in much higher counts, proportions, and prevalence in subjects with various forms of periodontitis than in periodontally healthy subjects (van Winkelhoff _et al_. 2002; Yang _et al_. 2004b; Haffajee _et al_. 2006a). _T. forsythia_ was found in higher numbers in sites of destructive periodontal disease or periodontal abscesses than in gingivitis or healthy sites (Lai _et al_. 1987; Herrera _et al_. 2000; Papapanou _et al_. 2000; Lau _et al_. 2004). In addition, _T. forsythia_ was detected more frequently and in higher numbers in actively progressing periodontal lesions than inactive lesions (Dzink _et al_. 1988) (Table 9-3). Further, subjects who harbored _T. forsythia_ were at greater risk for alveolar bone loss, attachment loss and tooth loss compared with subjects in whom this species was not detected (Machtei _et al_. 1999).
Since these early studies, a large number of additional studies have demonstrated the association of _T. forsythia_ with periodontal disease using techniques such as PCR and DNA hybridization (Tanner & Izard 2006). _T. forsythia_ has also been shown to be present in the oral cavities of monkeys, cats, and dogs, and species related to _T. forsythia_ have been found in insects such as termites (Tanner & Izard 2006). An as yet uncultivated clone similar to _T. forsythia_ has been found more frequently in subjects who were periodontally healthy than subjects with periodontitis (Leys _et al_. 2002).
_T. forsythia_ has been shown to be decreased in frequency of detection and counts after successful periodontal therapy, including scaling and root planing (SRP) (Haffajee _et al_. 1997; Takamatsu _et al_. 1999; Cugini _et al_. 2000; Darby _et al_. 2001, 2005; van der Velden _et al_. 2003; Teles _et al_. 2006), periodontal surgery (Levy _et al_. 2002), or systemically administered antibiotics (Feres _et al_. 2000; Winkel _et al_. 1998, 2001; Haffajee _et al_. 2006b; Teles _et al_. 2006). _T. forsythia_ was found at higher levels at sites which showed breakdown after periodontal therapy than sites which remained stable or gained attachment (Shiloah _et al_. 1998; Fujise _et al_. 2002). Ligature-induced periodontitis and peri-implantitis in dogs were accompanied by a significant increase in the frequency of detection of _T. forsythia_ (Nociti _et al_. 2001). Finally, subjects with a low severity of chronic periodontitis who exhibited a persistent presence of _T. forsythia_ at periodontal sites had a 5.3 times greater chance of having at least one site in their mouths losing attachment compared with subjects with occasional or no presence of this species (Tran _et al_. 2001).
Studies using checkerboard DNA–DNA hybridization techniques to examine subgingival plaque samples not only confirmed the high levels of _T. forsythia_ detected using fluorescent-labeled antisera but demonstrated that _T. forsythia_ was the most common species detected on or in epithelial cells recovered from periodontal pockets (Dibart _et al_. 1998). It was infrequently detected in epithelial cell samples from healthy subjects. Double-labeling experiments demonstrated that _T. forsythia_ was both on and in periodontal pocket epithelial cells and indicated the species' ability to invade. Listgarten _et al_. (1993) found that the species most frequently detected in "refractory" subjects was _T. forsythia_. Serum antibody to _T. forsythia_ has been found to be elevated in a number of periodontitis patients (Taubman _et al_. 1992) and was often extremely elevated in a subset of refractory periodontal disease subjects. The observation that _T. forsythia_ shares antigens with _P. gingivalis_ suggests that protective antibody formed to one species may provide protection against both species (Vasel _et al_. 1996).
The role of _T. forsythia_ in periodontal diseases has been clarified and strengthened by studies in numerous laboratories involving non-cultural methods of enumeration, such as DNA probes, PCR or immunologic methods. For example, Grossi _et al_. (1994, 1995) considered _T. forsythia_ to be the most significant microbial risk factor that distinguished subjects with periodontitis from those who were periodontally healthy.
### Spirochetes
Spirochetes are Gram-negative, anaerobic, helicalshaped, highly motile microorganisms that are common in many periodontal pockets (Fig. 9-4). The role of spirochetes in the pathogenesis of destructive periodontal diseases deserves extended comment. Clearly, a spirochete has been implicated as the likely etiologic agent of acute necrotizing ulcerative gingivitis by its presence in large numbers in tissue biopsy specimens from affected sites (Listgarten & Socransky 1964; Listgarten 1965). The role of spirochetes in other forms of periodontal disease is less clear. The organisms have been considered as possible periodontal pathogens since the late 1800s and in the 1980s enjoyed a resurgence of interest for use as possible diagnostic indicators of disease activity and/or therapeutic efficacy (Keyes & Rams 1983; Rams & Keyes 1983). The major reason for the interest in this group of organisms has been their increased numbers in sites with increased pocket depth. Healthy sites exhibit few, if any, spirochetes, sites of gingivitis but no attachment loss exhibit low to moderate levels, while many deep pockets harbor large numbers of these organisms. Further, spirochetes such as _Treponema denticola_ , have been shown to be at the forefront of periodontal lesions as demonstrated in sections of undisturbed subgingival plaque using immunohistochemical localization (Kigure _et al_. 1995; Noiri _et al_. 2001). The localization of spirochetes next to the epithelial lining of the periodontal pocket may facilitate both attachment of these species to epithelial cells and invasion into the adjacent tissues.
**Fig. 9-4** Photomicrograph of a sample of subgingival plaque from a subject with advanced chronic periodontitis viewed by darkfield microscopy. The sample was dominated by large spirochetes with the typical corkscrew appearance.
The major difficulty encountered in defining the role of spirochetes has been the difficulty in distinguishing individual species. This is due in large part to difficulty in cultivating spirochetes in general and, in particular, species of spirochetes that are currently uncultivable. There are currently 10 cultivable species of spirochetes (Ellen & Galimanas 2005). At least 50 taxa of subgingival spirochetes can be recognized using 16S rRNA analysis (Dewhirst _et al_. 2000). The cultivable spirochetes require very complex media for their cultivation. These contain infusions of animal organs, trypsin digests of casein, various fatty acids and accessory growth factors, and serum (Ellen & Galimanas 2005). Wyss _et al_. (1999) have developed more defined media for the cultivation of some of the species of oral spirochetes. In spite of the ability to cultivate certain species of oral spirochetes, it has been difficult to use these media to enumerate the spirochetes in subgingival plaque samples. Therefore, in many of the earlier studies of plaque samples, spirochetes were combined either in a single group or groups based on cell size; i.e. small, medium or large. Thus, while there may be pathogens among the spirochetes, their role may have been obscured by unintentionally pooling their numbers with non-pathogenic spirochetes. This would be similar to combining in a single count, organisms with coccal morphologies, such as _P. gingivalis_ , _Veillonella parvula_ , and _Streptococcus sanguinis_.
In spite of the limitations of combining spirochetes into a single morphogroup, spirochetes as a group or as individual species have been related to periodontal disease (Ellen & Galimanas 2005). Spirochetes have been associated with an increased risk at a site for the development of gingivitis (Riviere & DeRouen 1998) and periodontitis (Riviere _et al_. 1997). The need to evaluate the role of individual species of spirochetes in periodontal diseases is reinforced by studies of serum antibody responses to different species. When antibody responses to individual species were examined in subjects with chronic or aggressive periodontitis or a healthy periodontium, different responses were observed to different species. Certain spirochetal species elicited an elevated response in one or more of the groups with destructive periodontal disease (Mangan _et al_. 1982; Tew _et al_. 1985c; Lai _et al_. 1986), while others were related to depressed antibody responses in certain patient groups (Steinberg & Gershoff 1968; Tew _et al_. 1985c). Such data suggest that pooling spirochete species into a collective group may obscure meaningful host–parasite interactions.
More recently, specific species of spirochetes have been related to periodontal breakdown using antibody-based or molecular techniques. _Treponema denticola_ was found to be more common in periodontally diseased than healthy sites, more common in subgingival than supragingival plaque (Simonson _et al_. 1988; Riviere _et al_. 1992; Albandar _et al_. 1997; Haffajee _et al_. 1998; Yuan _et al_. 2001), and more common in healthy sites that progressed to gingivitis (Riviere & DeRouen 1998). _Tr. denticola_ was shown to decrease in successfully treated periodontal sites, but not change or increase in non-responding sites (Simonson _et al_. 1992). Cultural studies suggested that _Tr. denticola_ and a "large treponeme" were found more frequently in patients with severe periodontitis than in healthy or gingivitis sites (Moore _et al_. 1982).
Riviere _et al_. (1991,a,b,c, 1992) employed a monoclonal antibody directed against _Treponema pallidum,_ the etiologic agent of syphilis, to examine supra- and subgingival plaque samples and/or tissues from healthy, periodontitis and ANUG subjects. This antibody cross-reacted with antigens of uncultivated spirochetes in many of the plaque samples. These "pathogen-related oral spirochetes" (PROS) were the most frequently detected spirochetes in supra- and subgingival plaques of periodontitis patients and were the most numerous spirochetes in periodontitis lesion sites. Their presence in periodontally healthy sites was related to an increased risk of development of periodontitis (Riviere _et al_. 1997). The PROS were also detected in plaque samples from ANUG (Riviere _et al_. 1991c) and tissue biopsies from ANUG lesions using immunohistochemical techniques (Riviere _et al_. 1991a). PROS were also shown to have the ability to penetrate a tissue barrier in _in vitro_ systems (Riviere _et al_. 1991b). This property was shared with _Tr. pallidum_ but not with other cultivated species of oral spirochetes such as _Tr. denticola_ , _Tr. socranskii_ , _Tr. pectinovorum_ or _Tr. vincentii_. In later studies, the PROS were shown by molecular techniques to share 16S rRNA gene sequences with _Tr. vincentii_ and _Tr. medium_ (Choi _et al_. 1996; Riviere _et al_. 1999). These studies and others suggested that certain specific species of spirochetes were important in the pathogenesis of ANUG and certain forms of periodontitis. Precise evaluation of the role of individual spirochete species appears to be realistic based on their detection in plaque samples by immunologic, PCR or DNA probe techniques. Indeed, enumeration of even uncultivable spirochete taxa is possible using oligonucleotide probes (Tanner _et al_. 1994) or specific antibody as described above. Studies performed using such techniques permit better distinction of species of spirochetes and a clearer understanding of their possible role in disease.
The mechanisms of pathogenicity of the spirochetes have been under active investigation in recent years. Spirochetes demonstrate pathogenicity in animal abscess model systems (Kesavalu _et al_. 1999; Kimizuka _et al_. 2003), and produce a wide range of potential virulence factors (Ellen 2005). Among the virulence factors that may play a major role is a subtilisin family protease, dentilisin, that is encoded by the _prtP_ gene. This enzyme affects a wide range of protein substrates including fibronectin, laminin, and fibrinogen (Ishihara _et al_. 1996). It is thought that spirochetes may prolong tissue remodeling and wound healing following periodontal treatment; thus, the chronic periodontal lesion may represent an "ever-healing" wound that is sustained during chronic infection (Ellen & Galimanas, 2005).
Successful treatment of periodontal infections is accompanied by a decrease in the numbers and proportions of oral spirochetes as a group and individual species. Indeed, this reduction is so consistent that it has been used in some studies as a measure of compliance in determining whether subjects used the prescribed antibiotics (Loesche _et al_. 1993).
#### _**_Prevotella intermedia/Prevotella nigrescens_**_
At present the data for other species as etiologic agents of destructive periodontal diseases are more limited, but certain organisms appear to merit further investigation (Zambon 1996). _Pr. intermedia_ is the second black-pigmented _Bacteroides_ to receive considerable interest (Fig. 9-5). The levels of this Gram-negative, short, round-ended anaerobic rod have been shown to be particularly elevated in acute necrotizing ulcerative gingivitis (Loesche _et al_. 1982), certain forms of periodontitis (Tanner _et al_. 1979; Dzink _et al_. 1983; Moore _et al_. 1985; Maeda _et al_. 1998; Herrera _et al_. 2000; Papapanou _et al_. 2000; Lee _et al_. 2003; van Winkelhoff _et al_. 2002; Alves _et al_ 2006; Boutaga _et al_. 2006), and progressing sites in chronic periodontitis (Tanner _et al_. 1996; Lopez 2000), and it has been detected by immunohistological methods in the intercellular spaces of periodontal pocket biopsies from rapidly progressive periodontitis subjects (Hillmann _et al_. 1998). Isolates of this species can induce alveolar bone loss in rats (Yoshida-Minami _et al_. 1997). _Pr. intermedia_ was reduced more markedly in subgingival plaque samples from subjects who received adjunctive systemically administered amoxicillin plus metronidazole than subjects receiving a placebo (Rooney _et al_. 2002). Persistence of _Pr. intermedia/nigrescens_ after standard mechanical therapy has been shown to be associated with a large proportion of sites exhibiting bleeding on probing (Mombelli _et al_. 2000). Berglundh _et al_. (1998) demonstrated that improved clinical parameters after the use of mechanical therapy and systemically administered amoxicillin and metronidazole were associated with a decrease of periodontal pathogens including _Pr. intermedia_.
**Fig. 9-5** Photograph of part of a primary isolation plate of a subgingival plaque sample from a subject with chronic periodontitis. The medium and growth conditions were as described in Fig. 9-2. The dark-pigmented colonies were isolates of _Prevotella intermedia_.
This species appears to have a number of the virulence properties exhibited by _P. gingivalis_ and was shown to induce mixed infections on injection in laboratory animals (Hafstrom & Dahlen 1997). Like _P. gingivalis_ , _Pr. intermedia/nigrescens_ appears to induce an increased release of MMP-8 and MMP-9 in gingival pockets as well as MMP-9 in plasma (Soder _et al_. 2006). It has also been shown to invade oral epithelial cells _in vitro_ (Dorn _et al_. 1998) and induce expression of nitric oxide synthase in tissue culture cells (Kim _et al_. 2004). Elevated seroantibodies to this species have been observed in some but not all subjects with refractory periodontitis (Haffajee _et al_. 1988b). Elevated IgG antibody to _Pr. intermedia_ was associated with coronary heart disease (CHD) in past and current smokers, while elevated IgG antibody to _Pr. nigrescens_ was associated with CHD in never smokers (Beck _et al_. 2005). Strains of _Pr. intermedia_ that show identical phenotypic traits have been separated into two species, _Pr. intermedia_ and _Pr. nigrescens_ (Shah & Gharbia 1992). This distinction makes earlier studies of this "species" difficult to interpret since data from two different species may have been inadvertently pooled. However, new studies which discriminate the species in subgingival plaque samples might strengthen the relationship of one or both species to periodontal disease pathogenesis.
#### _**_Fusobacterium nucleatum_**_
_F. nucleatum_ is a Gram-negative, anaerobic, spindle-shaped rod that has been recognized as part of the subgingival microbiota for over 100 years (Plaut 1894; Vincent 1899). This species was the most common isolate found in cultural studies of subgingival plaque samples, comprising approximately 7–10% of total isolates from different clinical conditions (Dzink _et al_. 1985, 1988; Moore _et al_. 1985). _F. nucleatum_ was prevalent in subjects with periodontitis (Papapanou _et al_. 2000; Colombo _et al_. 2002; Socransky _et al_. 2002; Boutaga _et al_. 2006) and periodontal abscesses (Herrera _et al_. 2000) and was reduced after successful periodontal therapy (van der Velden _et al_. 2003; Haffajee _et al_. 2006b). Although there were differences detected in levels of this species between active and inactive periodontal lesions (Dzink _et al_. 1988), the differences may have been minimized by the inadvertent pooling of subspecies of _F. nucleatum_. Support for this contention may be derived from the antibody responses in subjects with different forms of periodontal disease to different homology groups of _F. nucleatum_ (Tew _et al_. 1985b). The role of _F. nucleatum_ in periodontal diseases is being clarified by examining the relationship of individual subspecies, such as _F. nucleatum_ ss _nucleatum_ , _F. nucleatum_ ss _polymorphum_ , _F. nucleatum_ ss _vincentii_ , and _F. periodonticum_ , to disease status and progression.
IgG and IgM titers in serum against the lipopolysaccharide (LPS) of _F. nucleatum_ were higher in subjects with periodontitis than in healthy individuals (Onoue _et al_. 2003). Invasion of this species into human gingival epithelial cells _in vitro_ was accompanied by an increased secretion of IL-8 from the epithelial cells (Han _et al_. 2000). The species can induce apoptotic cell death in mononuclear and polymorphonuclear cells (Jewett _et al_. 2001), induces epithelial cells to produce collagenase 3 (Uitto _et al_. 2005), and produces a 65 kDa serine protease (Bachrach _et al_. 2004). In addition, _F. nucleatum_ induces cytokine, elastase, and oxygen radical release from leukocytes (Sheikhi _et al_. 2000). Perhaps the most important role of _F. nucleatum_ in the subgingival ecosystem is its function as a "bridging" species, facilitating coaggregation among species as described below.
#### _**_Campylobacter rectus_**_
_C. rectus_ is a Gram-negative, anaerobic, short, motile vibrio. The organism is unusual in that it utilizes hydrogen or formate as its energy source. It was first described as a member of the "vibrio corroders", a group of short nondescript rods that formed small convex, "dry spreading" or "corroding" (pitting) colonies on blood agar plates. These organisms were eventually shown to include members of a new genus _Wolinella_ (most species have been redefined as _Campylobacter_ ), and _Eikenella corrodens. C. rectus_ has a 150-kDa protein on its cell surface that forms a paracrystalline lattice or S-layer that surrounds the bacterium (Wang _et al_. 1998, 2000). _C. rectus_ may help to initiate periodontitis by increasing the expression of proinflammatory cytokines and the S-layer may help to moderate this response facilitating the survival of the species at the site of infection. _C. rectus_ is widely distributed in subgingival sites, even in the primary, mixed and permanent dentitions of children (Umeda _et al_. 2004; Hayashi _et al_. 2006). _C. rectus_ has been shown to be present in higher numbers in samples from diseased sites as compared with healthy sites (Moore _et al_. 1983, 1985; Lippke _et al_. 1991; Lai _et al_. 1992; Papapanou _et al_. 1997; Macuch & Tanner 2000; Dogan _et al_. 2003; Ihara _et al_. 2003; Suda _et al_. 2004; Nonnenmacher _et al_. 2005) and it was found in higher numbers and more frequently at sites exhibiting active periodontal destruction (Dzink _et al_. 1985, 1988; Tanner & Bouldin 1989; Rams _et al_. 1993) or converting from periodontal health to disease (Tanner _et al_. 1998). In addition, _C. rectus_ was found less frequently and in lower numbers after successful periodontal therapy (Tanner _et al_. 1987; Haffajee _et al_. 1988a; Levy _et al_. 1999; Colombo _et al_. 2005). _C. rectus_ was also found in combination with other suspected pathogens in sites of subjects with refractory periodontal diseases (Haffajee _et al_. 1988b) and was in higher levels in subjects with aggressive periodontitis than in subjects with other forms of periodontitis (Gajardo _et al_. 2005). Like _A. actinomycetemcomitans_ , _C. rectus_ has been shown to produce a leukotoxin. These are the only two oral species known to possess this characteristic (Gillespie _et al_. 1992). The species is also capable of stimulating human gingival fibroblasts to produce IL-6 and IL-8 (Dongari-Bagtzoglou & Ebersole 1996). Higher serum antibody levels to _C. rectus_ GroEL was detected in patients with periodontitis when compared with control subjects (Fukui _et al_. 2006).
_C. rectus_ has been associated with a number of systemic conditions. Elevated IgM antibody to _C. rectus_ in fetal chord blood has been associated with an increased rate of prematurity (Madianos _et al_. 2001) and increased levels of _C. rectus_ along with _Peptostreptococcus micros_ in subgingival plaque samples of pregnant females was associated with an increased risk of pre-term low birth weight (Buduneli _et al_. 2005). IgG antibody to these same two species was also associated with increased carotid intima–medial thickness (Beck _et al_. 2005). Finally, _C. rectus_ , as well as other oral species, has been detected in atherosclerotic vessels (Fiehn _et al_. 2005) and in occluded arteries in patients with Buerger disease (Iwai _et al_. 2005).
#### _**_Eikenella corrodens_**_
_E. corrodens_ is a Gram-negative, capnophilic, asaccharolytic, regular, small rod with blunt ends. It has been recognized as a pathogen in other forms of disease, particularly osteomyelitis (Johnson & Pankey 1976), infections of the central nervous system (Emmerson & Mills 1978; Brill _et al_. 1982), and root canal infections (Goodman 1977). This species was found more frequently in sites of periodontal destruction as compared with healthy sites in some (Savitt & Socransky 1984; Muller _et al_. 1997; Yuan _et al_. 2001), but not all studies (Papapanou _et al_. 2000). In addition, _E. corrodens_ was found more frequently and in higher levels in actively breaking down periodontal sites (Dzink _et al_. 1985; Tanner _et al_. 1987) and in sites of subjects who responded poorly to periodontal therapy (Haffajee _et al_. 1988b). Successfully treated sites harbored lower proportions of this species (Tanner _et al_. 1987). _E. corrodens_ has been found to be elevated in lesions in LAP subjects (Suda _et al_. 2002) as well as in association with _A. actinomycetemcomitans_ in such lesions (Mandell 1984; Mandell _et al_. 1987). In tissue culture systems, _E. corrodens_ has been shown to stimulate the production of matrix metalloproteinases (Dahan _et al_. 2001) and IL-6 and IL-8 (Yumoto _et al_. 1999, 2001). While there is some association of this species with periodontal disease, to date it has not been particularly strong (Chen _et al_. 1989).
#### _**_Peptostreptococcus micros_**_
_Pe. micros_ is a Gram-positive, anaerobic, small, asaccharolytic coccus. It has long been associated with mixed anaerobic infections in the oral cavity and other parts of the body (Finegold 1977). Two genotypes can be distinguished, with the smooth genotype being more frequently associated with periodontitis lesions than the rough genotype (Kremer _et al_. 2000). _Pe. micros_ has been detected more frequently and in higher numbers at sites of periodontal destruction as compared with gingivitis or healthy sites (Moore _et al_. 1983, 1985; Herrera _et al_. 2000; Papapanou _et al_. 2000; Choi _et al_. 2000; Riggio _et al_. 2001; van Winkelhoff _et al_. 2002; Lee _et al_. 2003; Nonnenmacher _et al_. 2005; Boutaga _et al_. 2006; Gomes _et al_. 2006), was elevated in actively breaking down sites (Dzink _et al_. 1988), and at higher mean levels in current smokers compared with non-smokers (van Winkelhoff _et al_. 2001). The levels and frequency of detection of the species were decreased at successfully treated periodontal sites (Haffajee _et al_. 1988a). Studies of systemic antibody responses to suspected periodontal pathogens indicated that subjects with severe generalized periodontitis had elevated antibody levels to this species when compared with healthy subjects or subjects with LAP (Tew _et al_. 1985a). _Pe. micros_ produces proteases (Grenier & Bouclin 2006) and, in a mouse skin model system, it was shown that this species in combination with either _Pr. intermedia_ or _Pr. nigrescens_ could produce transmissible abscesses (van Dalen _et al_. 1998). In a study of chronic periodontitis subjects with and without acute myocardial infarction, it was found that _Pe. micros_ was much higher in the plaque samples of the subjects exhibiting myocardial infarction (Dogan _et al_. 2005).
#### _**_Selenomonas_**_ **species**
_Selenomonas_ species have been observed in plaque samples using light microscopy for many decades. The organisms may be recognized by their curved shape, tumbling motility, and, in good preparations, by the presence of a tuft of flagella inserted in the concave side. The _Selenomonas_ spp. are Gram-negative, curved, saccharolytic rods. The organisms have been somewhat difficult to grow and speciate. However, Moore _et al_. (1987) described six genetically and phenotypically distinct groups isolated from the human oral cavity. _Selenomonas noxia_ was found at a higher proportion of shallow sites (pocket depth (PD) <4 mm) in chronic periodontitis subjects compared with similar sites in periodontally healthy subjects (Haffajee _et al_. 1998). Further, _S. noxia_ was found to be associated with sites that converted from periodontal health to disease (Tanner _et al_. 1998).
#### _**_Eubacterium_**_ **species**
Certain _Eubacterium_ species have been suggested as possible periodontal pathogens due to their increased levels in diseased sites, particularly those of severe periodontitis (Uematsu & Hoshino 1992). _E. nodatum, Eubacterium brachy_ , and _Eubacterium timidum_ are Gram-positive strictly anaerobic, small somewhat pleomorphic rods. They are often difficult to cultivate, particularly on primary isolation, and appear to grow better in roll tubes than on blood agar plates. To date, there is greater evidence supporting a possible etiologic role in periodontitis for _E. nodatum_ than the other _Eubacterium_ species. Moore _et al_. (1982, 1985) used the roll tube cultural technique to examine the proportions of bacterial species in subgingival plaque samples from subjects with various forms of periodontitis, gingivitis, and health. They found that _E. nodatum_ was absent or in low proportions in periodontal health and various forms of gingivitis, but was present in higher proportions in moderate periodontitis (2%), generalized early onset periodontitis (8%), LAP (6%), early onset periodontitis (5%), and adult (chronic) periodontitis (2%). _E. nodatum_ was in the top 2–14 species enumerated in these different periodontal states. Uematsu and Hoshina (1992) found _Eubacterium_ species to be the predominant species in subgingival plaque samples from subjects with advanced periodontitis using cultural techniques. More recent studies have confirmed an association of _E. nodatum_ with periodontitis using molecular techniques. Using species-specific oligonucleotide probes, Booth _et al_. (2004) found that _E. nodatum_ was at significantly higher counts in patients than in matched control subjects. The species was also at higher levels in deep compared with shallow pockets. Papapanou _et al_. (2000) found higher counts of _E. nodatum_ in 131 periodontitis patients than in 74 periodontally intact controls using checkerboard DNA–DNA hybridization. Colombo _et al_. (2002) also used checkerboard DNA–DNA hybridization to evaluate the microbiota in 25 untreated Brazilian subjects with chronic periodontitis and found a significant positive correlation of _E. nodatum_ with mean pocket depth and attachment level. Samples of subgingival plaque were taken from 21 832 periodontal sites in 635 chronic periodontitis and 189 periodontally healthy subjects and examined by checkerboard DNA–DNA hybridization (Haffajee _et al_. 2006a). It was found that _E. nodatum_ was strongly associated with chronic periodontitis both in the presence of high levels of _P. gingivalis_ and _T. forsythia_ and in subjects where these species were in lower proportions. It has also been demonstrated that the percentage of sites colonized by _E. nodatum_ was significantly higher in current smokers than non-smokers (Haffajee & Socransky 2001). Some of the _Eubacterium_ species elicited elevated antibody responses in subjects with different forms of destructive periodontitis (Tew _et al_. 1985a,b; Vincent _et al_. 1986; Martin _et al_. 1988).
### **The "milleri" streptococci**
Streptococci were frequently implicated as possible etiologic agents of destructive periodontal diseases in the early part of the twentieth century. Cultural studies of the last 2 decades have also suggested the possibility that some of the streptococcal species were associated with, and may contribute to, disease progression. At this time, evidence suggests that the "milleri" streptococci, _Streptococcus anginosus_ , _Streptococcus constellatus_ , and _S. intermedius_ , might contribute to disease progression in subsets of periodontal patients. The species was found to be elevated at sites which demonstrated recent disease progression (Dzink _et al_. 1988). Walker _et al_. (1993) found _S. intermedius_ to be elevated in a subset of patients with refractory disease at periodontal sites which exhibited disease progression. Colombo _et al_ (1998a) found that subjects exhibiting a poor response to SRP and then to periodontal surgery with systemically administered tetracycline had higher levels and proportions of _S. constellatus_ , than subjects who responded well to periodontal therapy. Refractory subjects also exhibited elevated serum antibody to _S. constellatus_ when compared with successfully treated subjects (Colombo _et al_. 1998b). In a study of 161 subjects with acute coronary syndrome (ACS) and 161 control subjects, it was suggested that the oral bacterial load of species including _S. intermedius_ and _S. anginosus_ may be a risk factor for ACS (Renvert _et al_. 2006). The data on streptococci are somewhat limited, but a continued examination of their role in disease seems warranted.
### **Other species**
It has long been recognized that many taxa in subgingival plaque were not being cultivated based on microscopic observations that revealed cell morpho-types that were never recovered in culture. In addition, there were marked differences between total viable counts (representing cultivable species) and total microscopic counts representing all organisms (Socransky _et al_. 1963; Olsen & Socransky 1981; Moore & Moore 1994). Currently, the best model for exploring microbial diversity is based on isolating DNA from the target environment, amplifying the rDNA using consensus primers and PCR, cloning the amplicons into _Escherichia coli_ , and sequencing the cloned 16S rDNA inserts (Pace _et al_. 1986; Hugenholtz & Pace 1996). The resulting sequences are compared with those of known species and phylotypes in sequence databases, such as GenBank and the Ribosomal Database Project (Cole _et al_. 2005). These culture-independent molecular phylogenetic methods have been used to deduce the identity of novel phylotypes from periodontitis subjects (Choi _et al_. 1994; Spratt _et al_. 1999). To date, based on sequence analysis of 16S rRNA clonal libraries from specimens of the oral cavity, over 700 bacterial taxa have been detected, of which over half have not yet been cultivated _in vitro_ (Dewhirst _et al_. 2000; Paster _et al_. 2001, 2002; Becker _et al_. 2002; Kazor _et al_. 2003). "New" putative pathogens were tentatively identified in a study in which the presence of 39 bacterial species were determined that were implicated in health or disease based on 16S rRNA clonal analysis. Samples from 66 subjects with chronic periodontitis and 66 age-matched healthy controls were examined for the presence of target species. Associations and relative risks were determined for these species. Several novel taxa, in addition to the classical putative pathogens, were suggested as potential periodontal pathogens or health-related species (Kumar _et al_. 2003).
Interest has grown in groups of cultivable species not commonly found in the subgingival plaque as initiators or possibly contributors to the pathogenesis of periodontal disease, particularly in individuals who have responded poorly to periodontal therapy. Species not commonly thought to be present in subgingival plaque can be found in a proportion of such subjects or even in subjects who have not received periodontal treatment. Studies have examined enteric organisms and staphylococcal species as well as other unusual mouth inhabitants. Slots _et al_. (1990b) used cultural techniques to examine plaque samples from over 3000 chronic periodontitis patients and found that 14% of these patients harbored enteric rods and pseudomonads. _Enterobacter cloacae_ , _Klebsiella pneumoniae_ , _Pseudomonas aeruginosa_ , _Klebsiella oxytoca_ , and _Enterobacter agglomerans_ comprised more than 50% of the strains isolated. Systemically administered ciprofloxacin improved the treatment response of patients whose periodontal pockets were heavily infected with enteric rods (Slots _et al_. 1990a). This group of investigators also examined 24 subjects with periodontal disease in the Dominican Republic and found that the prevalence of enteric rods in these subjects was higher than levels found in subjects in the US (Slots _et al_. 1991). In the 16 of 24 subjects in whom this group of organisms was detected, they averaged 23% of the cultivable microbiota. Rams _et al_. (1990, 1992) also identified a number of species of staphylococci and enterococci in subjects with various forms of periodontal disease. The presence of unusual species in periodontal lesions suggests the possibility that they may play a role in the etiology of periodontal diseases. However, such roles must be evaluated in the same manner as the species discussed earlier in this section.
In addition to the cultivable and uncultivable bacterial species, a number of studies have suggested that specific viruses, including cytomegalovirus, the Epstein Barr virus, papillomavirus, and herpes simplex virus, may play a role in the etiology or progression of periodontal lesions, possibly by changing the host response to the local subgingival microbiota (for a comprehensive review, see Slots 2005). A suspected role of various viruses was based primarily on association of the viruses with lesion sites when compared with periodontally healthy sites and the effect of successful therapy on reducing the detection frequency of these viruses in treated sites (Klemenc _et al_. 2005; Slots 2005; Slots _et al_. 2006).
## Mixed infections
To this point, attention has been paid to the possible role of individual species as risk factors for destructive periodontal diseases. However, the complex mixture of species colonizing the subgingival area can provide a spectrum of relationships with the host, ranging from beneficial (the organisms prevent disease), to harmful (the organisms cause disease). At the pathogenic end of the spectrum, it is conceivable that different relationships exist between pathogens. The presence of two pathogens at a site could have no effect or could diminish the potential pathogenicity of one or the other of the species. Alternatively, pathogenicity could be enhanced either in an additive or synergistic fashion. It seems likely that mixed infections occur in subgingival sites since so many diverse species inhabit this habitat. Evidence to support this concept has been derived mainly from studies in animals in which it was shown that combinations of species were capable of inducing experimental abscesses, even though the components of the mixtures could not (Smith 1930; Proske & Sayers 1934; Cobe 1948; Rosebury _et al_. 1950; Macdonald _et al_. 1956; Socransky & Gibbons 1965). It is not clear whether the combinations suggested in the experimental abscess studies are pertinent to human periodontal diseases. Studies in humans suggest that combinations of _P. gingivalis_ and _T. forsythia_ may be significant in determining diseased sites and disease progression after treatment (Fujise _et al_. 2002). In addition, it has been observed that species such as _P. gingivalis_ , _T. forsythia_ , and _A. actinomycetemcomitans_ may be components of a polymicrobial intracellular microbiota within human buccal epithelial cells (Rudney _et al_. 2005). At the very least, some species may set the stage for specific pathogens by providing essential nutrients, sites of attachment (co-aggregation), or means to evade or subvert host defenses (e.g. by producing protective capsules or enzymes that destroy host antibody). The relationship of microbial "complexes" to periodontal diseases will be discussed further below.
# The nature of dental plaque – the biofilm way of life
Biofilms colonize a widely diverse set of moist surfaces, including the oral cavity, the bottom of boats and docks, the inside of pipes, as well as rocks in streams. Infectious disease investigators are interested in biofilms that colonize a wide array of artificial devices that have been implanted in the human, including catheters, hip and voice prostheses, and contact lenses. Biofilms consist of one or more communities of microorganisms, embedded in a glycocalyx, that are attached to a solid surface. The biofilm allows microorganisms to stick to and multiply on surfaces. Thus, attached bacteria (sessile) growing in a biofilm display a wide range of characteristics that provide a number of advantages over single cell (planktonic) bacteria. The interactions among bacterial species living in biofilms take place at several levels including physical contact, metabolic exchange, small signal molecule mediated communication, and exchange of genetic information (Kolenbrander _et al_. 2006). References to pertinent biofilm literature may be found in the following publications: Newman & Wilson (1999); Socransky & Haffajee (2001); Marsh (2005).
## The nature of biofilms
Biofilms are fascinating structures. They are the preferred method of growth for many, perhaps most species of bacteria. This method of growth provides a number of advantages to colonizing species. A major advantage is the protection that the biofilm provides to colonizing species from competing microorganisms, from environmental factors such as host defense mechanisms, and from potentially toxic substances in the environment, such as lethal chemicals or antibiotics. Biofilms also can facilitate processing and uptake of nutrients, cross-feeding (one species providing nutrients for another), removal of potentially harmful metabolic products (often by utilization by other bacteria), as well as the development of an appropriate physicochemical environment (e.g. a properly reduced oxidation reduction potential).
A crude analogy to the development of a biofilm might be the development of a city. Successful human colonization of new environments requires several important factors including a stable nutrient supply, an environment conducive to proliferation, and an environment with limited potential hazards. Cities (like biofilms) develop by an initial "attachment" of humans to a dwelling site followed by multiplication of the existing inhabitants and addition of new inhabitants. Cities and biofilms typically spread laterally and then in a vertical direction often forming columnar habitation sites. Cities and biofilms offer many benefits to their inhabitants. These include shared resources and inter-related activities. Inhabitants of cities or biofilms are capable of "metabolic processes" and synthetic capabilities that could not be performed by individuals in an unattached (planktonic) or nomadic state. An important benefit provided by a city or biofilm is protection both from other potential colonizers of the same species, from exogenous species, and from sudden harmful changes in the environment. Individuals in the "climax community" of a flourishing city/biofilm can facilitate joint activities and live in a far more stable environment than individuals who live in isolation. Cities, like biofilms, require a means to bring in nutrients and raw materials, and to remove waste products. In cities, these are usually roads, water or sewage pipes, in biofilms they may be water channels such as those described below. Cities have maximum practical sizes based on physical constraints and nutrient/waste limits; so do biofilms. Cities that are mildly perturbed, e.g. by a snow storm or a local fire, usually reform a climax community that is similar to that which was present in the first place; as do biofilms. However, major perturbations in the environment such as prolonged drought or a radioactive cloud can lay waste to a city. Major perturbations in the environment such as a toxic chemical can severely affect the composition or existence of a biofilm. Communication between individuals in a city is essential to allow inhabitants to interact optimally. This is usually performed by vocal, written or pictorial means. Communication between bacterial cells within a biofilm is also necessary for optimum community development and is performed by production of signaling molecules such as those found in "quorum sensing" or perhaps by the exchange of genetic information. The long-term survival of the human species as well as a species in a biofilm becomes more likely if that species (or the human) colonizes multiple sites. Thus, detachment of cells from biofilms and establishment in new sites is as important for survival of biofilm dwellers as the migration of individuals and establishment of new cities is for human beings. Thus, we may regard mixed species biofilms as primitive precursors to the more complex organizations observed for eukaryotic species.
## Properties of biofilms
### **Structure**
Biofilms are composed of microcolonies of bacterial cells (15–20% by volume) that are non-randomly distributed in a shaped matrix or glycocalyx (75–80% by volume). Earlier studies of thick biofilms (>5 mm) that develop in sewage treatment plants indicated the presence of voids or water channels between the microcolonies that were present in these biofilms. The water channels permit the passage of nutrients and other agents throughout the biofilm acting as a primitive "circulatory" system. Nutrients make contact with the sessile (attached) microcolonies by diffusion from the water channel to the microcolony rather than from the matrix. Microcolonies occur in different shapes in biofilms which are governed by shear forces due to the passage of fluid over the biofilm. At low shear force, the colonies are shaped liked towers or mushrooms, while at high shear force, the colonies are elongated and capable of rapid oscillation. Individual microcolonies can consist of a single species, but more frequently are composed of several different species.
### Exopolysaccharides – the backbone of the biofilm
The bulk of the biofilm consists of the matrix or glycocalyx and is composed predominantly of water and aqueous solutes. The "dry" material is a mixture of exopolysaccharides, proteins, salts, and cell material. Exopolysaccharides (EPS), which are produced by the bacteria in the biofilm, are the major components of the biofilm making up 50–95% of the dry weight. They play a major role in maintaining the integrity of the biofilm as well as preventing desiccation and attack by harmful agents. In addition, they may also bind essential nutrients such as cations to create a local nutritionally rich environment favoring specific microorganisms. The EPS matrix could also act as a buffer and assist in the retention of extracellular enzymes (and their substrates) enhancing substrate utilization by bacterial cells. The EPS can be degraded and utilized by bacteria within the biofilm. One distinguishing feature of oral biofilms is that many of the microorganisms can both synthesize and degrade the EPS.
### Physiological heterogeneity within biofilms
Cells of the same microbial species can exhibit extremely different physiologic states in a biofilm even though separated by as little as 10 μm. Typically, DNA indicating the presence of bacterial cells is detected throughout the biofilm, but protein synthesis, respiratory activity, and RNA are detected primarily in the outer layers.
The use of micro-electrodes has shown that pH can vary quite remarkably over short distances within a biofilm. Two-photon excitation microscopy of _in vitro_ plaque made up of ten intra-oral species showed that, after a sucrose challenge, microcolonies with a pH <3.0 could be detected adjacent to microcolonies with pH values >5.0. The number of metal ions can differ sufficiently in different regions of a biofilm so that difference in ion concentration can produce measurable potential differences. Bacterial cells within biofilms can produce enzymes such as betalactamase against antibiotics, catalases, and superoxide dismutases against oxidizing ions released by phagocytes. These enzymes are released into the matrix producing an almost impregnable line of defense. Bacterial cells in biofilms can also produce elastases and cellulases which become concentrated in the local matrix and produce tissue damage. Measurement of oxygen and other gases has demonstrated that certain microcolonies are completely anaerobic even though composed of a single species and grown in ambient air. Carbon dioxide and methane can reach very high concentrations in specific microcolonies in industrial biofilms. Thus, studies to date indicate that sessile cells growing in mixed biofilms can exist in an almost infinite range of chemical and physical microhabitats within microbial communities.
### Quorum sensing and exchange of genetic information
Some of the functions of biofilms are dependent on the ability of the bacteria and microcolonies within the biofilm to communicate with one another. Quorum sensing in bacteria "involves the regulation of expression of specific genes through the accumulation of signaling compounds that mediate intercellular communication" (Prosser 1999). Quorum sensing is dependent on cell density. With few cells, signaling compounds may be produced at low levels, however, auto-induction leads to increased concentration as cell density increases. Once the signaling compounds reach a threshold level (quorum cell density), gene expression is activated. Quorum sensing may give biofilms their distinct properties. For example, expression of genes for antibiotic resistance at high cell densities may provide protection. Quorum sensing also has the potential to influence community structure by encouraging the growth of beneficial species (to the biofilm) and discouraging the growth of competitors. It is also possible that physiological properties of bacteria in the community may be altered through quorum sensing. Quoring-sensing signaling molecules produced by putative periodontal pathogens such as _P. gingivalis_ , _Pr. intermedia_ , and _F. nucleatum_ have been detected (Frias _et al_. 2001). Of particular importance may be a recently discovered molecule, autoinducer-2, which is thought to be a universal signal mediating messages among the species in mixed species communities (Kolenbrander _et al_. 2006). This family of molecules has been detected in the cell-free culture supernatants of multiple oral bacterial species. Kolenbrander _et al_. (2006) indicated that commensal bacterial species such as _Streptococcus oralis_ and _Actinomyces naeslundii_ produce and respond to low levels of autoinducer-2, while pathogens, such as _F. nucleatum_ , _Pr. intermedia_ and _P. gingivalis_ , produce and respond to high levels of these substances. They hypothesized that when the pathogens become established in a mixed species community, their production of high levels of autoinducer-2 may foster the growth of the pathogenic community and minimize the growth of commensal species.
Signaling is not the only way of transferring information in biofilms. The high density of bacterial cells growing in biofilms facilitates exchange of genetic information between cells of the same species and across species or even genera. Conjugation, transformation, plasmid transfer, and transposon transfer have all been shown to occur in naturally occurring or _in vitro_ prepared mixed species biofilms (described in greater detail in a later section). Of particular interest, was the demonstration of transfer of a conjugative transposon conferring tetracycline resistance from cells of one genus, _Bacillus subtilis_ , to a _Streptococcus_ species present in dental plaque grown as a biofilm in a constant depth film fermenter.
### **Attachment of bacteria**
The key characteristic of a biofilm is that the microcolonies within the biofilm attach to a solid surface. Thus, adhesion to a surface is the essential first step in the development of a biofilm. In the mouth, there is a wide variety of surfaces to which bacteria can attach including the oral soft tissues, the pellicle-coated teeth, other bacteria, as well as prosthetic replacements such dentures and implants. Many bacterial species possess surface structures such as fimbriae and fibrils that aid in their attachment to different surfaces. Fimbriae have been detected on a number of oral species including _Actinomyces naeslundii_ , _P. gingivalis_ , _A. actinomycetemcomitans_ and some strains of streptococci such as _Streptococcus salivarius_ , _Streptococcus parasanguinis_ , and members of the _Streptococcus mitis_ group. Fibrils can be found on a number of oral bacterial species. They are morphologically different and shorter than fimbriae and may be densely or sparsely distributed on the cell surface. Oral species that possess fibrils include _S. salivarius_ , the _S. mitis_ group, _Pr. intermedia_ , _Pr. nigrescens_ , and _Streptococcus mutans_.
### Mechanisms of increased antibiotic resistance of organisms in biofilms
Antibiotics have been and continue to be used effectively in the treatment of periodontal infections. However, the indiscriminate use of antimicrobials and biocides has the potential of leading to the development of resistant bacteria. It has also been suggested that resistance from one type of antimicrobial, such as a biocide, can be transferred to a different type of antimicrobial, such as an antibiotic. Thus, it is important to understand the factors leading to antimicrobial resistance in biofilms such as dental plaque.
It has been recognized for considerable periods of time that organisms growing in biofilms are more resistant to antibiotics than the same species growing in a planktonic (unattached) state. While the mechanisms of resistance to antibiotics of organisms growing in biofilms are not entirely clear, certain general principles have been described. Almost without exception, organisms grown in biofilms are more resistant to antibiotics than the same cells grown in a planktonic state. Estimates of 1000–1500 times greater resistance for biofilm-grown cells than planktonic grown cells have been suggested, although these estimates have been considered to be too high by some investigators. The mechanisms of increased resistance in biofilms differ from species to species, from antibiotic to antibiotic, and for biofilms growing in different habitats. One important mechanism of resistance appears to be the slower rate of growth of bacterial species in biofilms which makes them less susceptible to many but not all antibiotics. It has been shown in many studies that the resistance of bacteria to antibiotics, biocides or preservatives is affected by their nutritional status, growth rate, temperature, pH, and prior exposure to sub-effective concentrations of antimicrobials. Variations in any of these parameters can lead to a varied response to antibiotics within a biofilm. The matrix performs a "homeostatic function", such that cells deep in the biofilm experience different conditions, such as hydrogen ion concentration or redox potentials, than cells at the periphery of the biofilm or cells growing planktonically. Growth rates of these deeper cells will be decreased allowing them to survive better than faster growing cells at the periphery when exposed to antimicrobial agents. In addition, the slower growing bacteria often over-express "non-specific defense mechanisms", including shock proteins and multi-drug efflux pumps, and demonstrate increased exopolymer synthesis.
The exopolymer matrix of a biofilm, although not a significant barrier in itself to the diffusion of antibiotics, does have certain properties that can retard diffusion. For example, strongly charged or chemically highly reactive agents can fail to reach the deeper zones of the biofilm because the biofilm acts as an ion-exchange resin, removing such molecules from solution. In addition, extracellular enzymes, such as beta-lactamases, formaldehyde lyase, and formaldehyde dehydrogenase, may become trapped and concentrated in the extracellular matrix, thus inactivating susceptible, typically positively charged, hydrophilic antibiotics. Some antibiotics such as the macrolides, which are positively charged but hydrophobic, are unaffected by this process. Thus, the ability of the matrix to act as a physical barrier is dependent on the type of antibiotic, the binding of the matrix to that agent, and the levels of the agent employed. Since reaction between the agent and the matrix will reduce the levels of the agent, a biofilm with greater bulk will deplete the agent more readily. Further, hydrodynamics and the turnover rate of the microcolonies will also impact on antibiotic effectiveness.
Alteration of genotype and/or phenotype of the cells growing within a biofilm matrix is receiving increased attention. Cells growing within a biofilm express genes that are not observed in the same cells grown in a planktonic state and they can retain this resistance for some time after being released from the biofilm. For example, it was demonstrated that cells of _Pseudomonas aeruginosa_ liberated from biofilms were considerably more resistant to tobramycin than planktonic cells, suggesting that the cells became intrinsically more resistant when growing in a biofilm and retained some of this resistance even outside the biofilm.
The presence of a glycocalyx, a slower growth rate, and development of a biofilm phenotype cannot provide a total explanation for the phenomenon of antibiotic resistance. These features probably delay elimination of the target bacteria, allowing other selection events to take place. Recently, the notion of a subpopulation of cells within a biofilm that are "super-resistant" was proposed. Such cells could explain the remarkably elevated levels of resistance to certain antibiotics that have been suggested in the literature.
## Techniques for the detection and enumeration of bacteria in oral biofilm samples
The enumeration of specific bacterial species in oral biofilm samples is a challenging task, in part, because of the large number of bacterial species present in such samples and, in part, because of the fastidious nature of many of the resident species. Ideal methods of enumeration should be able to quantify multiple species, be sensitive, specific, inexpensive, and high throughput. Quantification is essential because the differences in the microbiota between periodontal health and disease, and between pre- and post-periodontal therapy, are quantitative rather than presence or absence of one or more species. The early light microscopy techniques were not satisfactory because they could not distinguish bacterial species only morphotypes. Cultural techniques are specific in their ability to distinguish species, but are so expensive that the number of samples that can be examined is severely limited. Antibody-based techniques such as immunofluorescence and enzyme-linked immunosorbent assay (ELISA) are very specific and can provide quantitative data. However, antisera to only a limited range of species have been developed and these techniques are somewhat cumbersome, diminishing the number of species and samples that may be conveniently examined. Molecular techniques, including PCR and DNA hybridization, have the advantage of being specific and readily extensible to a wide range of bacterial taxa. PCR is convenient and able to detect low numbers of cells but suffers from the inability to provide quantitative data. Real-time PCR overcomes this limitation, but is expensive and time-consuming, precluding examination of large numbers of species and samples. DNA hybridization using formats such as that described in Fig. 9-1, are sensitive, specific, inexpensive, and high throughput, providing at the moment, perhaps the most useful technique for quantifying a wide range of species in large numbers of biofilm samples.
There has been considerable interest in enumerating the uncultivable or as yet to be cultivated taxa in addition to the cultivable taxa in subgingival biofilms. Recent studies have employed amplification of the 16S rRNA genes directly from plaque samples using PCR and consensus primers. The products were cloned into _Escherichia coli_ and the sequences of the inserts determined. These studies provided a remarkably different view of the composition of the subgingival microbiota compared with other techniques such as culture, immunofluorescence, ELISA, PCR, real-time PCR, and DNA hybridization. The results of the cloning–sequencing studies must at present be viewed with considerable caution because these methods failed to detect or detected infrequently known prominent taxa such as _P. gingivalis_ , _T. forsythia_ , and members of the genera _Fusobacterium_ and _Actinomyces_. For more detail on microbiological techniques used to examine biofilm samples see Socransky and Haffajee (2005).
## The oral biofilms that lead to periodontal diseases
The section on biofilm biology presented above provided a background to help understand the ecology of the incredibly complex communities of organisms that colonize the tooth surface and lead to periodontal diseases. Figure 9-6 presents a clinical photograph of a subject with less than optimal home care. Evident in this photograph is stain on the tooth surfaces that may have resulted from smoking, coffee or tea drinking. Of greater concern, is the occurrence of a thin film of bacterial plaque on many of the tooth surfaces along with the quite obvious plaque formation in regions such as the mesial buccal surfaces of the upper left and lower right canines. These biofilm (plaque) regions are highlighted in Fig. 9-7, which shows the same dentition after staining with a disclosing solution. The thin films such as those on the lower incisors might consist of biofilm communities that are 50–100 cells thick. Thicker plaques, such as those on the upper left and lower right canines, might consist of biofilms that are 300 or more cell layers in thickness. The number of organisms that reside on the mesial surface of the upper left or lower right canine probably exceeds 300 million. This number is remarkable in that it is similar to the entire human population of the United States. These microbial communities are very complex. Over 700 bacterial species have been detected in the human oral cavity, and over 400 of these can be found in the periodontal pocket (Paster _et al_. 2006). It is thought that about half of these species may be as yet uncultivated. In any given plaque sample, it is not uncommon to detect 30 or more bacterial species. Thus, the biofilms that colonize the tooth surface may be among the most complex biofilms that exist in nature. This complexity is due in large part to the non-shedding surface of the tooth which permits persistent colonization and the opportunity for very complex ecosystems to develop. In addition, the relatively high nutrient abundance as well as the remarkable ability of oral species to coaggregate with one another may facilitate this complexity.
**Fig. 9-6** Clinical photograph of a subject exhibiting tooth stain and supragingival dental plaque.
**Fig. 9-7** Clinical photograph of the subject in Fig. 9-6 after staining with disclosing solution.
**Fig. 9-8** Histological section of human supragingival plaque stained with toluidine blue–methylene blue. The supragingival plaque was allowed to develop for 3 days on an epon crown in a human volunteer. The crown surface is at the left and the saliva interface is towards the right. (Courtesy of Dr. Max Listgarten, University of Pennsylvania.)
Figure 9-8 is a section of human supragingival dental plaque grown on an epon crown in a human volunteer (Listgarten _et al_. 1975; Listgarten 1976, 1999). The section demonstrates many of the features of biofilms outlined earlier. Bacterial species adhered to the solid surface, multiplied, and, in this section, formed columnar microcolonies. The heterogeneity of colonizing species is evident even at a morphological level and would be emphasized if the cells within the section had been characterized by cultural or molecular techniques. The surface layers of the biofilm exhibit morphotypes that are not evident in deeper layers and emphasize the role that coaggregation plays in the development of biofilms. Not evident in this section are the water channels in biofilms described earlier. This might be due to preparation or fixation artifacts (Costerton _et al_. 1999) or it might be because the plaque is typical of a "dense" bacterial model. Water channels have been observed in plaque grown in the human oral cavity by confocal microscopy (Wood _et al_. 2000). This dental biofilm has all of the properties of biofilms in other habitats in nature. It has a solid substratum, in this case an epon crown but more typically a tooth, it has the mixed micro-colonies growing in a glycocalyx, and it has the bulk fluid interface provided by saliva.
**Fig. 9-9** Histological section of human subgingival dental plaque stained with toluidine blue–methylene blue. The tooth surface is to the left and the epithelial lining of the periodontal pocket is to the right. Bacterial plaque attached to the tooth surface is evident towards the upper left of the section, while a second zone of organisms can be observed lining the periodontal pocket wall. (Courtesy of Dr. Max Listgarten, University of Pennsylvania.)
A second biofilm ecosystem is shown in Fig. 9-9. This is a section of human subgingival plaque. The section is at lower magnification than Fig. 9-8 to permit visualization of regions within the biofilm. The plaque attached to the tooth surface is evident in the upper left portion of the section. This tooth-associated biofilm is an extension of the biofilm found above the gingival margin and may be quite similar in microbial composition. A second, possibly epithelial cell-associated biofilm, may be observed lining the epithelial surface of the pocket. This biofilm contains primarily spirochetes and Gram-negative bacterial species (Listgarten _et al_. 1975; Listgarten 1976, 1999). _P. gingivalis_ and _Tr. denticola_ have been detected in large numbers in the epithelial cell-associated biofilms within the periodontal pocket, by immunocytochemistry (Kigure _et al_. 1995). _T. forsythia_ might also be numerous in this zone, since high levels of this species have been detected, using DNA probes, in association with the epithelial cells lining the periodontal pocket (Dibart _et al_. 1998). Between the tooth-associated and epithelial cell-associated biofilms, a less dense zone of organisms may be observed. These organisms may be "loosely attached" or they might be in a planktonic state. The critical feature of Fig. 9-9 is that there appear to be tooth-associated and epithelial cell-associated regions in subgingival plaque as well as a possible third weakly attached or unattached zone of microorganisms. It is strongly suspected that these regions differ markedly in microbial composition, physiological state, and their response to different therapies.
## Microbial complexes
The association of bacteria within mixed biofilms is not random, rather there are specific associations among bacterial species. Socransky _et al_. (1998) examined over 13 000 subgingival plaque samples from 185 adult subjects and used cluster analysis and community ordination techniques to demonstrate the presence of specific microbial groups within dental plaque (Fig. 9-10). Six closely associated groups of bacterial species were recognized. These included specific species of _Actinomyces_ , a yellow complex consisting of members of the genus _Streptococcus_ , a green complex consisting of _Capnocytophaga_ species, _A. actinomycetemcomitans_ serotype a, _E. corrodens_ and _Campylobacter concisus_ , and a purple complex consisting of _V_. _parvula_ and _Actinomyces odontolyticus_. These groups of species are early colonizers of the tooth surface whose growth usually precedes the multiplication of the predominantly Gram-negative orange and red complexes (Fig. 9-10). The orange complex consists of _Campylobacter gracilis_ , _C. rectus_ , _C. showae, E. nodatum_ , _F. nucleatum_ subspecies, _F. periodonticum_ , _Pe. micros_ , _Pr. intermedia_ , _Pr. nigrescens_ , and _S. constellatus_ , while the red complex consists of _T. forsythia_ , _P. gingivalis_ , and _Tr. denticola_. The last two complexes are comprised of the species thought to be the major etiologic agents of periodontal diseases.
Similar relationships have been demonstrated in _in vitro_ studies examining interactions between different pairs of oral bacterial species (Kolenbrander _et al_. 2006). These studies of oral bacteria have indicated that cell-to-cell recognition is not random but that each strain has a defined set of partners (Fig. 9-11). Further, functionally similar adhesins found on bacteria of different genera may recognize the same receptors on other bacterial cells. Most human oral bacteria adhere to other oral bacteria. This cell-to-cell adherence is known as coaggregation. It is interesting that the relationships among species determined by pair-wise _in vitro_ coaggregation studies depicted in Fig. 9-11 are similar to the microbial complexes (Fig. 9-10) determined by examination of _in vivo_ samples suggesting that coaggregation may be a powerful ecological determinant of community development. Figure 9-11 also suggests some of the mechanisms that might control the observed microbial succession in plaque development that will be discussed below. For example, the ability of many streptococcal species, particularly _S. mitis_ and _S. oralis_ (Nyvad & Kilian 1987; Li _et al_. 2004), to attach to different receptors found in tooth pellicle as well as to each other may contribute to their critical role as early colonizers of the tooth surface. The streptococci provide receptors for a wide range of species, including other early colonizing species and bridging species, such as _F. nucleatum_ , that in turn may coaggregate with late colonizers including many periodontal pathogens.
**Fig. 9-10** Diagram of the association among subgingival species (adapted from Socransky _et al_. 1998). The data were derived from 13 261 subgingival plaque samples taken from the mesial aspect of each tooth in 185 adult subjects. Each sample was individually analyzed for the presence of 40 subgingival species using checkerboard DNA–DNA hybridization. Associations were sought among species using cluster analysis and community ordination techniques. The complexes to the left are comprised of species thought to colonize the tooth surface and proliferate at an early stage. The orange complex becomes numerically more dominant later and is thought to bridge the early colonizers and the red complex species which become numerically more dominant at late stages in plaque development.
## Factors that affect the composition of subgingival biofilms
Although this chapter emphasizes the effect that microorganisms have on their habitat, the periodontal tissues, it is important to understand that the habitat has a major effect on the composition, metabolic activities, and virulence properties of the colonizing microorganisms. The importance of this axiom, that the microorganisms affect the habitat and the habitat affects the microorganisms, has recently begun to be fully appreciated. Thus, modifications of the supra- and subgingival microbiota certainly affect the outcome, periodontal health or disease; but changes in the host or local habitat also affect the composition and activities of the microbiota. Understanding this relationship should help to lead us into better approaches to diagnosing the etiology and contributing factors of a patient's disease and to optimizing appropriate therapy. In this section, we will provide examples of some of the factors that are known to modify subgingival microbial composition.
### **Periodontal disease status**
Perhaps the most influential factor on the composition of the subgingival microbiota is the periodontal disease status of the host. Figure 9-12 presents the counts, proportions and percentage of sites colonized at >105 of 40 subgingival taxa in subjects with chronic periodontitis or periodontal health (Haffajee _et al_. 2006a). Clearly, the major difference between health and disease, _on average_ , was the increased counts, proportions, and prevalence of the red complex species, _T. forsythia_ , _P. gingivalis_ , and _Tr. denticola_ in subjects with periodontal disease. In addition, other putative periodontal pathogens of the orange complex were also more prevalent and in higher levels in periodontitis subjects. However, individuals with different forms of disease have different subgingival microbial profiles. Even subjects with the "same" periodontal disease in terms of both clinical appearance and severity can exhibit quite different subgingival microbiotas (Fig. 9-13).
**Fig. 9-11** Spatiotemporal model of oral bacterial colonization, showing recognition of salivary pellicle receptors by early colonizing bacteria and coaggregations between early colonizers, fusobacteria and late colonizers of the tooth surface (Kolenbrander _et al_. 2002). Each coaggregation depicted is known to occur in a pairwise test. Collectively, these interactions are proposed to represent development of dental plaque. Starting at the bottom, primary colonizers bind via adhesins (round-tipped black line symbols) to complementary salivary receptors (blue–green vertical round-topped columns) in the acquired pellicle coating the tooth surface. Secondary colonizers bind to previously bound bacteria. Sequential binding results in the appearance of nascent surfaces that bridge with the next coaggregating partner cell. Several kinds of coaggregations are shown as complementary sets of symbols of different shapes. One set is depicted in the box at the top. Proposed adhesins (symbols with a stem) represent cell surface components that are heat inactivated (cell suspension heated to 85˚C for 30 minutes) and protease sensitive; their complementary receptors (symbols without a stem) are unaffected by heat or protease. Identical symbols represent components that are functionally similar but may not be structurally identical. Rectangular symbols represent lactose-inhibitable coaggregations. Other symbols represent components that have no known inhibitor. The bacterial species shown are _Aggregatibacter actinomycetemcomitans_ , _Actinomyces israelii_ , _Actinomyces naeslundii_ , _Capnocytophaga gingivalis_ , _Capnocytophaga ochracea_ , _Capnocytophaga sputigena_ , _Eikenella corrodens_ , _Eubacterium_ spp __., _Fusobacterium nucleatum_ , _Haemophilus parainfluenzae_ , _Porphyromonas gingivalis_ , _Prevotella denticola_ , _Prevotella intermedia_ , _Prevotella loescheii_ , _Propionibacterium acnes_ , _Selenomonas flueggei_ , _Streptococcus gordonii_ , _Streptococcus mitis_ , _Streptococcus oralis_ , _Streptococcus sanguinis_ , _Treponema_ spp., and _Veillonella atypica_. (Published with permission of Paul Kolenbrander, Kolenbrander _et al_. 2006 and Blackwell Publishing.)
**Fig. 9-12** Plots of mean counts (left panel), percents of the total DNA probe count (middle panel) and percentage of sites colonized by 40 bacterial species at counts >105 (right panel) in subgingival plaque samples taken from 189 periodontally healthy and 635 chronic periodontitis subjects. The "bands" represent the mean values ± the 95% confidence intervals after adjusting for 40 comparisons. Mean values for each species were computed by averaging up to 28 samples in each subject, and then averaging across subjects in the two clinical groups. Significance of differences between groups was sought using the nonparametric Mann Whitney test; * p < 0.05, ** p < 0.01, *** p < 0.001 after adjusting for multiple comparisons (Socransky _et al_. 1991). The species were ordered and grouped according to the complexes described by Socransky _et al_. (1998). The yellow profile represents the mean data for the healthy subjects and the red profile represents the data for the periodontitis subjects. Reprinted with permission from Blackwell Publishing (Haffajee _et al_. 2006a, _Oral Microbiology and Immunology_ , **21** , 1–14).
### **The local environment**
One host factor that markedly influenced the subgingival environment was pocket depth. Figure 9-14 demonstrates that the mean counts of subgingival species differed at sites of different pocket depths. Red complex species, _T. forsythia_ , _P. gingivalis_ , as well as _Tr. denticola_ (data not shown), increased strikingly in numbers with increasing pocket depth. All orange complex species also demonstrated this relationship. _S. sanguinis_ and _A. naeslundii_ genospecies 2 were typical of the majority of species in the other four complexes that showed little relationship to pocket depth. Thus, red and orange complex species were not only related to periodontal disease status in a subject, but to disease status at the periodontal site. The species of the red and orange complexes were also elevated at sites exhibiting gingival inflammation, as measured by gingival redness, bleeding on probing, and suppuration (Fig. 9-15). Other species such as _A. naeslundii_ genospecies 2 and _S. sanguinis_ did not show this relationship.
One remarkable feature of the microbiota of "healthy sites" (defined as sites with pocket depth <4 mm) in subjects with periodontitis was that their microbiota differed markedly from that found in healthy sites in periodontally healthy subjects (Fig. 9-16). The data in Fig. 9-16 once again demonstrate the strong relationship of orange and red complex species with pocket depth in the subjects with periodontitis. However, the figure also demonstrates that subjects who were periodontally healthy had clearly lower levels of periodontal pathogens, such as _E. nodatum_ , _P. gingivalis_ , _T. forsythia_ , and _Tr. denticola_ , in their shallow sulci/pockets than were detected in the shallow pockets in periodontitis subjects. This suggests that the "healthy sites" in the subjects with periodontitis would be at more risk for destructive disease initiation and progression than similar sites in periodontally healthy individuals and may warrant therapy to lower the levels of colonizing pathogens.
**Fig. 9-13** Mean counts (× 105) of the 40 test species in samples from six chronic periodontitis subjects with similar clinical and demographic features. Mean values for each species were computed by averaging up to 28 samples in each subject. Each panel represents an individual subject and the mean clinical features of the subjects are presented below each panel. The species were ordered and grouped according to microbial complexes (Socransky _et al_. 1998).
### **Host factors**
In addition to the impact of local factors on the composition of subgingival biofilms, host level factors can also affect biofilm composition. Some of these factors include the genetic background of the subject, environmental factors such smoking and diet, systemic conditions such as diabetes and obesity, and even geographic location. For example, subjects who are positive for a specific genotype of the polymorphic IL-1 gene cluster have been found to have increased levels of periodontal disease (Kornman _et al_. 1997) and increased counts of species of the red and orange complexes at sites with pocket depth >6 mm (Socransky & Haffajee 2005). Another condition that has been associated with a heightened inflammatory response, obesity, was associated with increased counts of red complex species in subgingival plaque samples, in particular, increased counts of _T. forsythia_ in very obese subjects (Socransky & Haffajee 2005). There are numerous studies in the literature indicating that subjects who are current smokers have significantly more periodontal disease than past or never smokers and respond less well to mechanical periodontal therapies (Haffajee & Socransky 2000). In addition, it has been shown that current smokers have a larger proportion of their "healthy" sites (pocket depth <4 mm) colonized by red and orange complex species compared to similar sites in subjects who have never smoked (Socransky & Haffajee 2005). Individuals with Sjogren's syndrome, an autoimmune disease, that leads to a variety of host changes including a decrease in salivary flow rates, exhibit decreased levels of supra- and subgingival plaque, but increased proportions of _V. parvula_ and _N. mucosa_ in supra- and subgingival biofilms (Socransky & Haffajee 2005). Even the geographic location of a subject can influence the composition of subgingival biofilms (Fig. 9-17). Samples of subgingival plaque from the four deepest sites in each subject with chronic periodontitis from five different countries evaluated using checkerboard DNA–DNA hybridization, demonstrated that the proportions of species such as _P. gingivalis_ , _Tr. denticola_ , and _E. nodatum_ differed markedly among subjects. The differences may have been due to oral hygiene habits, diet, socioeconomic status, genetic background, or transmission among individuals in the community.
**Fig. 9-14** Bar charts of the mean counts (× 105, ± SEM) of six subgingival species at selected pocket depths in samples from 635 chronic periodontitis subjects. _T. forsythia and P. gingivalis_ are representative of the red complex, _F. nucleatum ss vincentii_ and _Pr. intermedia_ are representative of the orange complex species, and _S. sanguinis_ and _A. naeslundii_ genospecies 2 are typical of other cluster groups. The mean counts of each species at each pocket depth category were computed for each subject and then averaged across subjects. The numbers above the bars in the _S. sanguinis_ panel represent the number of sampled sites in each pocket depth category, while the numbers above the bars in the _A. naeslundii_ panel represent the number of subjects who provided data for each pocket depth category. Significance of differences among pocket depth categories was tested using the Kruskal-Wallis test and adjusted for 40 comparisons.
### **Transmission**
In planning control of periodontal pathogens, it is essential to clarify their source. If an individual were fortunate enough not to encounter virulent periodontal pathogens, he or she would exhibit minimal periodontal disease even if susceptible. However, most individuals have acquired strains of suspected periodontal pathogens at some time in their lives. For the most part, it appears that subgingival species found in humans are unique to that environment. The subgingival species of the human, by and large, are not commonly encountered in the environment (e.g. soil, air, water) or indeed in the subgingival microbiota of other animal species. Thus, survival of subgingival species in the human requires the transmission of periodontal pathogens from the oral cavity of one individual to the oral cavity of another. Two types of transmission are recognized; "vertical", that is transmission from parent to offspring, and "horizontal", i.e. passage of an organism between individuals outside the parent–offspring relationship.
Evidence for both forms of transmission has been provided using molecular epidemiology techniques. For many of these techniques, the investigator isolates DNA from strains of a given species recovered from different individuals. The DNA is cut with restriction endonucleases, run on agarose gel electrophoresis and the resulting fingerprint patterns compared, either directly, or with the help of various DNA probes. When these techniques were employed on isolates from subgingival plaque, it was demonstrated that _A. actinomycetemcomitans_ and _P. gingivalis_ strains isolated from parents and children within the same family exhibited identical restriction endonuclease patterns. Different patterns were found for strains isolated from different families (DiRienzo & Slots 1990; Alaluusua _et al_. 1993; Petit _et al_. 1993a,b). In other studies it was found that _A. actinomycetemcomitans_ and _P. gingivalis_ strains isolated from husband and wife had the same restriction endonuclease patterns or ribotypes indicating that these species could be transmitted within married couples (Saarela _et al_. 1993; van Steenbergen _et al_. 1993).
**Fig. 9-15** Bar charts of the mean proportions (± SEM) of seven subgingival species at sites positive or negative for gingival redness, BOP and suppuration. _T. forsythia_ , _P. gingivalis_ , and _T. denticola_ are representative of the red complex, _E. nodatum_ and _Pr. nigrescens_ are representative of the orange complex species, while _A. naeslundii_ genospecies 2 and _S. sanguinis_ represent other cluster groups. The mean proportions of each species at positive or negative sites for each parameter were computed for each subject and then averaged across subjects. The green bars represent the sites negative for the clinical parameters and the purple bars represent the positive sites. Significance of differences in proportions of species between positive and negative sites was determined using the Wilcoxon signed ranks test and adjusted for 40 comparisons.
The above data should not be surprising in view of the fact that periodontal pathogens have to come from somewhere, and the most likely source would appear to be a family member, whether spouse, sibling or parent. However, while intra-family transmission has been demonstrated, it appears likely that transmission of pathogens also occurs between unrelated individuals. Earlier, the transmission of ANUG was described both within troops in trenches in World War I and in communities outside the war zone after World War I. Another example of transmission between members of different families is provided by the detection of the JP2 clone of _A. actinomycetemcomitans_ in individuals of African descent who were located in Africa or had relocated to Europe or the Americas (Kilian _et al_. 2006). Such reports suggest that periodontal pathogens can be transmitted, on occasion, between unrelated individuals. Thus, while there has been an intuitive feeling that the oral microbiota is relatively stable within an individual, it seems likely that new species or different clonal types of the same species can be introduced into an individual at various stages of his or her life. If the newly acquired strain is more virulent than the pre-existing strain of that species, then a change in disease pattern could occur.
Transmission of bacteria is not restricted to passage of strains from one subject to another, but frequently occurs from one type of intraoral biofilm to another. For example, it is thought that a species such as _A. actinomycetemcomitans_ may colonize the buccal mucosa long before it can be found in supra- or subgingival biofilms (Fine _et al_. 2006). When a species moves from one oral surface to another, different modes of attachment are employed. For example, for _A. actinomycetemcomitans_ a protein adhesin, Aae, may mediate attachment to buccal epithelial cells, while fimbriae and a polysaccharide mediate attachment to tooth surfaces as discussed previously. In a similar fashion streptococcal species, such as _S. mitis_ , that are found in high proportions on soft tissue surfaces may be important in dental plaque development on the tooth surfaces from 0–6 hours as described Li _et al_. (2004) and from 1–2 days as described by Socransky and Haffajee (2005). In more mature plaques, these species become a small proportion of the microbiota (Socransky & Haffajee 2005).
There is one more level of intraoral transmission that should be considered and that is the horizontal transfer of genetic material from one bacterial species to another (Roberts & Mullany 2006). This particular mechanism is important not only in providing potential virulence traits to a pathogenic species, but also in providing information that codes for factors such as adhesins or mechanisms of antibiotic resistance. Mechanisms of horizontal gene transfer include plasmids, conjugative transposons, bacteriophage, and transformation (for review of horizontal gene transfer within the oral cavity see Roberts and Mullany, 2006).
**Fig. 9-16** Mean counts (× 105) of 40 species in subgingival plaque samples from periodontal pockets/sulci <4, 4–6 and >6 mm in 635 chronic peridontitis subjects and from periodontally healthy sites in 189 periodontally healthy subjects. Subgingival plaque samples were taken at baseline and analyzed for their content of 40 subgingival species using checkerboard DNA–DNA hybridization. Counts of each species were averaged in each subject for each pocket depth category and then averaged across subjects for each category separately. The species were ordered according to microbial complexes (Socransky _et al_. 1998). Significance of differences among pocket depth categories was sought using the Kruskal Wallis test; * p < 0.05, ** p < 0.01, *** p < 0.001 after adjusting for multiple comparisons (Socransky _et al_. 1991).
## Microbial composition of supra- and subgingival biofilms
The bacteria associated with periodontal diseases reside within biofilms both above and below the gingival margin. The supragingival biofilm is attached to the tooth surface and is predominated by _Actinomyces_ species in most plaque samples. Figure 9-18 provides the counts, proportions, and prevalence (percentage of sites colonized) of 40 taxa grouped according to microbial complexes (Socransky _et al_. 1998) in supragingival plaque samples from periodontally healthy and periodontitis subjects. The _Actinomyces_ predominate in both health and disease. Further, all taxa examined could be found (on average) in both health and disease, although counts, proportions, and prevalence (percentage of sites colonized) of periodontal pathogens were significantly higher in the periodontally diseased subjects.
As described above, the nature of subgingival biofilms was more complex with both a tooth-associated and tissue-associated biofilm separated by loosely bound or planktonic cells. Figure 9-12 presented the counts, proportions, and prevalence of 40 taxa in subgingival plaque samples from periodontally diseased and periodontally healthy individuals (Haffajee _et al_. 2006a). Similar to supragingival plaque, the dominant species subgingivally were the _Actinomyces_ , but significantly higher counts, proportions, and prevalence of red and orange complex species were found in the samples from the periodontitis subjects. In particular, there were significantly higher levels, proportions, and prevalence of _P. gingivalis_ , _T. forsythia_ , and _Tr. denticola_ in both supra- and subgingival plaque of periodontitis subjects when compared with similar samples from periodontally healthy individuals. Figure 9-19 summarizes the major differences in microbial complexes between supra- and subgingival plaque in health and periodontitis. As one moves from the supragingival to the subgingival environment and from health to disease, there is a significant decrease in the _Actinomyces_ species and an increase in the proportion of members of the red complex.
**Fig. 9-17** Bar charts of adjusted mean percents (± SEM) of the total DNA probe count of the red complex species, _T. forsythia_ , _P. gingivalis_ , and _Tr. denticola_ and the orange complex species, _E. nodatum_ , in baseline subgingival plaque samples taken from the four deepest, sampled periodontal pockets in 58 Brazilian, 26 Chilean, 92 Swedish, 114 American, and 20 Greek chronic periodontitis subjects. The bars represent the mean percents after adjusting for age, mean pocket depth, gender and smoking status. The whiskers indicate the standard error of the mean. Significance of differences among groups for each species was sought using ANCOVA adjusting for age, mean pocket depth, gender and smoking status. The p values were adjusted for 40 comparisons.
## Development of supra- and subgingival biofilms
Prior to the advent of molecular techniques, few studies had comprehensively examined the microbial shifts that occurred during supra- or subgingival plaque development. Ritz (1967) described the changes that occur in plaque that formed on the labial surfaces of the six upper and six lower anterior teeth from 1–9 days using selective media techniques. The data indicated that streptococci were predominant at 1 day, comprising an average of 46% of the colonies detected. _Neisseria_ and _Nocardia_ were also high in mean proportions at 1 day but decreased in counts and proportions over time. _Actinomyces_ were initially low in proportion (0.18%) but rose to 23% of the microbiota by 9 days. Ritz (1967) felt that there was microbial succession in plaque development with aerobic or facultative species reducing the environment for the subsequent growth of anaerobic species. In a study of five "rapid" and six "slow" plaque formers, a single plaque sample was taken from each subject at days 1, 3, 7, and 14 and evaluated using cultural techniques (Zee _et al_. 1996). Gram-positive bacteria were the predominant cultivable species in both clinical groups, but Gram-negative species increased in proportion more rapidly in the "rapid" plaque formers. At 14 days, the "rapid" plaque formers had a mean of 38% Gram-negative rods compared with 17% in the 14 day samples from the "slow" plaque formers. The majority of cultivable Gram-negative rods were in the genera _Fusobacterium_ and _Capnocytophaga_. Striking in their data was the decrease in proportion of Gram-positive cocci from 50–60% at day 1 to <15% at day 14. This decrease was accompanied by an increase in the proportion of _Actinomyces_ species and Gram-negative rods.
**Fig. 9-18** Plots of mean counts (left panel), percents of the total DNA probe count (middle panel) and percentage of sites colonized by 40 bacterial species at counts >105 (right panel) in supragingival plaque samples taken from 58 periodontally healthy and 136 chronic periodontitis subjects. The "bands" represent the mean values ± the 95% confidence intervals after adjusting for 40 comparisons. Mean values for each species were computed by averaging up to 28 samples in each subject, and then averaging across subjects in the two clinical groups. Significance of differences between groups was sought using the nonparametric Mann Whitney test; * p < 0.05, ** p < 0.01, *** p < 0.001 after adjusting for multiple comparisons. The species were ordered and grouped according to microbial complexes. The yellow profile represents the mean data for the healthy subjects and the red profile represents the data for the periodontitis subjects.
**Fig. 9-19** Pie charts of the mean percentage DNA probe count of microbial groups in supragingival plaque samples from 58 periodontally healthy and 136 periodontitis subjects and subgingival plaque samples from 189 periodontally healthy and 635 periodontitis subjects. The species were grouped into seven microbial groups based on the description of Socransky _et al_. (1998). The areas of the pies were adjusted to reflect the mean total DNA probe counts at each of the sample locations. The significance of differences in mean percentages of the supra- and subgingival complexes in health and disease was tested using the Kruskal Wallis test. All complexes differed significantly among groups at p < 0.001 after adjusting for seven comparisons. The "other" category represents probes to species that did fall into a complex as well as probes to new species whose relationships with other species has not yet been ascertained.
The introduction of molecular techniques provided a more comprehensive description of biofilm development. Li _et al_. (2004) used checkerboard DNA–DNA hybridization to examine the early development (0–6 hours) of supragingival biofilm on the buccal/labial surfaces of 20 restoration-free tooth surfaces in 15 subjects. Figure 9-20 presents the mean counts of the 40 test species at 0, 2, 4, and 6 hours. Certain species, such as _S. mitis_ and _S. oralis_ , appeared to be "pioneer" species in supragingival biofilm development since they were the predominant species at 4 and 6 hours. These findings are in accord with _in vivo_ cultural studies that demonstrated the early colonization of enamel and root surfaces using cultural techniques (Nyvad & Kilian 1987). The development of the biofilm in the Li _et al_. (2004) study did not appear to be due to simple adsorption of species from saliva, because the microbial profile of saliva samples from the same subjects differed markedly from the biofilm that developed on the teeth (Fig. 9-20).
The development of supragingival and subgingival biofilm, over a 7-day period, in periodontally healthy and diseased subjects has been described (Socransky & Haffajee 2005). Figure 9-21 presents the total DNA probe counts of supra- and subgingival biofilm samples from chronic periodontitis subjects taken pre and post tooth cleaning and at 1, 2, 4, and 7 days in the absence of home care procedures. There was a marked reduction in supra- and subgingival total counts after tooth cleaning, demonstrating that plaque levels could be significantly reduced even in individuals who performed "reasonable" home care procedures. The total numbers of organisms increased rapidly, in the absence of oral hygiene, in both the supra- and subgingival areas reaching pre-cleaning levels by 2 days subgingivally and by 4 days supragingivally. These findings were in accord with other studies that demonstrated the rapid return of tooth-associated biofilms after their removal (Sharawy _et al_. 1966; Furuichi _et al_. 1992; Ramberg _et al_. 2003). However, as indicated by the Li _et al_. (2004) study, not all species returned at the same rate.
**Fig. 9-20** Microbial profiles of the mean counts (× 105) of 40 taxa in plaque biofilm samples pooled from at least 20 buccal surfaces immediately post cleaning (0), 2, 4, and 6 hours in 15 subjects. Samples were analyzed for their content of 40 bacterial species using checkerboard DNA–DNA hybridization. Counts of individual species were computed in each subject and then averaged across subjects for each time point. The red dashed profile superimposed on the 6-hour biofilm profile represents the microbial profile of saliva samples from the same subjects taken at baseline. The species are ordered according to the complexes described by Socransky _et al_. (1998). The data were adapted from Li _et al_. (2004).
Figure 9-22 (left panel) presents the mean counts of 4 of 40 tested species in subgingival biofilm samples from chronic periodontitis subjects at the six time points described above. All of the species were reduced in counts after tooth cleaning, but _S. oralis_ increased rapidly, exceeding baseline (pre-cleaning) levels at 1–2 days. Levels of _F. nucleatum_ ss _nucleatum_ and _Pr. intermedia_ increased more slowly and exceeded baseline levels at between 2 and 4 and 4 and 7 days respectively. The periodontal pathogen, _P. gingivalis_ , had not reached baseline values by 7 days. The shifts in the proportions of the same species are presented in Fig. 9-22 (right panel). Proportions of _S. oralis_ increased rapidly by 2 days and then declined, while proportions of the two orange complex species, _F. nucleatum_ ss _nucleatum_ and _Pr. intermedia_ , declined initially and slowly increased over the 7-day period. Proportions of _P. gingivalis_ decreased over time and were at their lowest levels at 7 days. These findings are instructive in terms of the role that mechanical debridement plays in controlling periodontal infections. While the total number of bacteria returns rapidly after mechanical debridement, reductions in the proportions of certain species, such as _P. gingivalis_ and other members of the red and orange complexes, occur and can be maintained for prolonged periods of time. However, it is important to recognize that pathogenic species are not usually eliminated by this form of therapy and can return to pre-treatment levels in periods varying from weeks to years.
**Fig. 9-21** Mean total DNA probe counts (× 105, ± SEM) of supra and subgingival plaque samples taken prior to, immediately post-cleaning, and after 1, 2, 4, and 7 days of no oral hygiene in 16 subjects with chronic periodontitis. The dashed horizontal lines are provided to indicate the pre-cleaning levels.
# **Prerequisites for periodontal disease initiation and progression**
It is a common feature of many infectious diseases that a pathogenic species may colonize a host and yet the host may not manifest clinical features of that disease for periods of time varying from weeks to decades or ever. Thus, it appears that periodontal disease progression is dependent on the simultaneous occurrence of a number of factors (Socransky & Haffajee 1992, 1993). The host must be susceptible both systemically and locally. The local environment has to contain bacterial species which enhance the infection or at very least do not inhibit the pathogen's activity. The environment also must be conducive to the expression of virulence factors by the pathogen. This might take the form of affecting the regulation of virulence factor expression or stressing the organism so that it manifests properties which lead to tissue damage. The pathogen(s) must achieve sufficient numbers to initiate or cause progression of the infection in that particular individual in the given local environment. Fortunately, the simultaneous occurrence of all these factors does not happen frequently or periodontal disease would be more prevalent and severe in the population.
**Fig. 9-22** Change in mean counts (× 105) (left panel) and percentage of DNA probe count (right panel) of four species in subgingival plaque samples from pre cleaning to immediately post cleaning, and after 1, 2, 4, and 7 days of no oral hygiene in 16 subjects with chronic periodontitis.
## The virulent periodontal pathogen
Detection of suspected periodontal pathogens in plaque samples from periodontally healthy mouths (Dahlen _et al_. 1989; McNabb _et al_. 1992; Haffajee _et al_. 1998) or healthy sites in periodontally diseased mouths (Socransky _et al_. 1991) raises the question as to whether all strains of a pathogenic species are virulent. A major recognition of the last decade was that all clonal types of a pathogenic species are not equally virulent. For many medically important pathogenic species, a very small proportion of clonal types account for the majority of the disease that is observed (briefly reviewed in Socransky & Haffajee 1991, 1992). The clear association of the virulent JP2 clone of _A. actinomycetemcomitans_ in LAP was discusssed above and in greater detail in Fine _et al_. (2006) and Kilian _et al_. (2006). Studies of the pathogenic potential of different strains of _P. gingivalis_ in animal model systems support the notion of strain differences in virulence (Grenier & Mayrand 1987a; van Steenbergen _et al_. 1987; Marsh _et al_. 1989; Neiders _et al_. 1989; Sundqvist _et al_. 1991; Baker _et al_. 2000). Certain clonal types of _P. gingivalis_ were detected more frequently in samples from periodontitis subjects than control periodontally healthy subjects, suggesting an association of more virulent clonal types with disease (Griffen _et al_. 1999). These studies highlight the fact that there are major differences in virulence of different isolates of _P. gingivalis_ and suggest that in some instances when suspected pathogens are found in periodontally healthy sites, the strains may be avirulent. _P. gingivalis fim_ A gene encoding fimbrillin, a subunit of fimbriae, has been classified into six genotypes based on their nucleotide sequences. Amano _et al_. (2000) examined the _P. gingivalis fim_ A genotypes in dental plaque samples from 380 periodontally healthy adults and 139 periodontitis patients. Type I and type V genotypes were most common in _P. gingivalis_ -positive periodontally healthy adults, while type II and type IV were far more common in subjects with periodontitis. Such data suggest that _fim_ A genotype may be an important factor influencing the pathogenicity of _P. gingivalis_.
Another requirement for a pathogen to express virulence is that the organism possess all of the necessary genetic elements. Some of these elements might be missing in a strain inhabiting the gingival crevice area, but could be received from other strains of that species (or possibly other species) via phage, plasmids or transposons (Roberts & Mullany 2006). Thus, periodontally healthy sites might be colonized with periodontal pathogens without a full complement of genes needed to lead to tissue destruction.
Finally, the pathogen must be in the right location in a site (e.g. at the apical area of the pocket or adjacent to the epithelium) in sufficient numbers to initiate disease. There are probably minimum numbers of a pathogen needed to initiate disease.
## The local environment
If periodontal disease progression is a comparatively infrequent phenomenon, most of the resident species are likely to be host-compatible and in some instances may be actively beneficial to the host. Thus, microbial interactions play a role in the nature of species that colonize a site and ultimately on the outcome health or disease. Some interactions might be harmful, leading to mixed infections as discussed earlier. Others might be more beneficial to the host. Host-compatible species could colonize sites that otherwise would be colonized by pathogens. They might "dilute" the number of pathogens in a pocket, compete for or alter binding sites for pathogens, or destroy virulence factors produced by pathogens (Socransky & Haffajee 1991).
One carefully studied interbacterial antagonism has implications for our understanding of the ecology of destructive periodontal diseases. Hillman and coworkers (1982, 1985, 1987) became interested in the long-term stability of LAP lesions after treatment with surgery and systemic tetracycline. They surmised that a microbiota was established after treatment that was antagonistic to the return of the presumed pathogen _A. actinomycetemcomitans_. This proved to be the case. It was shown that certain species such as _S_. _sanguinis_ , _Streptococcus uberis_ and _A. naeslundii_ genospecies 2 produced factors that were inhibitory to the growth of _A. actinomycetemcomitans_ (Hillman _et al_. 1985). These species were absent or in low numbers in lesion sites of LAP prior to therapy but in elevated numbers after therapy. The mechanism of inhibition was shown to be hydrogen peroxide formation by the "beneficial" species, (Hillman & Socransky 1987) which either directly, or via a host peroxidase system (Tenovuo & Pruitt 1984), inhibited the pathogen. Stevens _et al_. (1987) and Hammond _et al_. (1987) demonstrated the reverse antagonism. _A. actinomycetemcomitans_ was shown to specifically inhibit the growth of _S. sanguinis_ , _S. uberis_ , and _A. naeslundii_ genospecies 2 (but not other species) by the production of a bacteriocin. This mutual antagonism is highly specific and its outcome may strongly influence whether a subject or a site will exhibit disease due to _A. actinomycetemcomitans_. Such interactions demonstrate the potent role resident microbial species play in permitting or preventing the establishment or spread of pathogenic species. The tremendous controlling pressure of the resident microbiota is reinforced by the difficulty encountered when an investigator attempts to implant a human oral isolate into the microbiota of a conventional animal or purposely attempts to implant strains isolated from one human into the subgingival plaque of another.
The local subgingival environment can affect disease pathogenesis in other ways. One of the more intriguing ways centers around the recognition that virulent strains of pathogenic species do not always express their virulence factors (Socransky & Haffajee 1991). Often, a global "regulon" simultaneously turns on or off the production of multiple virulence factors. The regulon is affected by specific factors in the local environment, such as temperature, osmotic pressure, or the concentration of iron, magnesium or calcium. The effect of environment on protein expression has been shown in subgingival species. For example, the level of iron in the environment will affect the expression of outer membrane proteins of _P. gingivalis_ and will also affect virulence of the strain in animal model systems (McKee _et al_. 1986, Barua _et al_. 1990, Bramanti & Holt 1990). Even the presence of specific other species might lead to expression of virulence genes by pathogenic species. For example, the production of a surface protein by _Streptococcus cristatus_ caused repression of the _P. gingivalis fim_ A gene, possibly influencing the development a pathogenic plaque (Xie _et al_. 2000). The effect of environment on virulence factor expression seems a fertile area for investigation. It may help to explain the long lag phase that occurs prior to disease initiation. Conceivably, a pathogen may reside quietly in an area for years as a compatible member of the microbiota. However, some stress generated by a change in the environment might influence that organism to express long-hidden, rather damaging factors.
## Host susceptibility
For a period of time considerably longer than the search for microbial etiologic agents of periodontal diseases, dental practitioners have hypothesized that differences in disease pattern or severity may be due to differences in host susceptibility (in earlier years termed resistance). In spite of these hypotheses, it is remarkable how few "host susceptibly factors" have been identified. With increased research in this area and better methods for comparing populations, a number of host or environmental factors have been suggested that may impact on the initiation and rate of progression of periodontal diseases. Such factors include defects in polymorphonuclear leukocyte levels or function, a poorly regulated immunological response, smoking, diet, and various systemic diseases (Genco _et al_. 1986; Bergstrom & Eliasson 1987; Greenspan _et al_. 1989; Williams _et al_. 1990; de Pommereau _et al_. 1992; Greenspan & Greenspan 1993; Seppala _et al_. 1993; Thorstensson & Hugoson 1993).
### HIV infection
Debilitating systemic illness can alter the host's ability to cope with infections and may exacerbate existing infections. In early studies, it appeared that periodontal diseases were more prevalent and severe in HIV-positive individuals than in patients who were not infected with HIV (Greenspan _et al_. 1989; Williams _et al_. 1990; Greenspan & Greenspan 1993). In some HIV-positive subjects, unusual necrotic, rapidly destructive periodontal lesions were observed. These observations led to speculation that either unusual pathogenic species were involved or that the modification of host resistance was so severe that it led to extreme tissue destruction. Examination of plaque samples taken from periodontitis sites in HIV-positive individuals indicated that the subgingival microbiota was very similar to that seen in non-HIVinfected periodontitis subjects, except that occasionally unusual organisms were encountered (Murray _et al_. 1989, 1991; Zambon _et al_. 1990; Rams _et al_. 1991; Moore _et al_. 1993). Further, suspected periodontal pathogens, including _P. gingivalis_ , _Pr. intermedia_ , _F. nucleatum_ , and _A. actinomycetemcomitans_ , were found more frequently in periodontitis sites in HIV-infected subjects than in either gingivitis or, in particular, healthy sites in these subjects (Murray _et al_. 1989). Rams _et al_. (1991) in a study of 14 HIV-infected individuals with periodontitis found that _A. actinomycetemcomitans_ , _C. rectus_ , _Pe. micros_ , and _Pr. intermedia_ each averaged 7–16% of the cultivable microbiota in patients positive for the species. In addition, levels of spirochetes were high, while levels of _Candida albicans_ and Gram-negative enteric rods were low. Thus, the microbiota of lesions in HIV-positive individuals was quite similar to that in HIV-negative subjects. However, not all HIV-positive subjects exhibit periodontal disease, and certainly not the extremely rapid form of disease. In addition, patients with the mild or rapid forms of disease are successfully treated using conventional periodontal therapies including local debridement, antiseptic mouthwashes, and local and/or systemically administered antimicrobial agents (Williams _et al_. 1990; Winkler & Robertson 1992; Greenspan & Greenspan 1993).
### Diabetes
Another systemic illness which has been associated with increased prevalence and incidence of periodontal disease is diabetes. Many studies (de Pommereau _et al_. 1992; Seppala _et al_. 1993; Thorstensson & Hugoson 1993), but not all (Barnett _et al_. 1984; Rylander _et al_. 1987), indicated that periodontitis is more severe in juvenile or adult diabetic subjects than non-diabetic controls. Microbiologic studies of diabetic subjects have indicated that similar periodontal pathogens were found in diseased sites of diabetic subjects as in non-diabetic periodontal patients. _A. actinomycetemcomitans_ , _Capnocytophaga_ sp., and "anaerobic vibrios" were found to be elevated in subgingival plaque samples from juvenile diabetic subjects (Mashimo _et al_. 1983), while Sastrowijoto _et al_. (1989) found that _A. actinomycetemcomitans_ , _P. gingivalis_ , and _Pr. intermedia_ were elevated in diseased sites of adult diabetic subjects. Mandell _et al_. (1992) found that a number of suspected periodontal pathogens were elevated at disease sites in poorly controlled insulin-dependent diabetics, including _Pr. intermedia_ , _Pr. melaninogenica_ , _C. gracilis_ , _E. corrodens_ , _F. nucleatum_ , and _C. rectus_ , when compared with healthy sites in the same subject. Similar species were found in adult periodontitis patients with non-insulin-dependent diabetes. _Pr. intermedia_ was the most frequently detected species, while _C. rectus_ and _P. gingivalis_ were also very common (Zambon _et al_. 1988).
The intriguing aspect of the studies of HIV-positive and diabetic subjects, is that periodontal lesions, for the most part, appeared to be related to already suspected periodontal pathogens and not to some novel species. Studies such as these suggest that altered host susceptibility may change the rate of disease progression in affected individuals, but by and large the periodontal pathogens are likely to be the same as those found in uncompromised subjects.
### Smoking
The deleterious effects of cigarette smoking on the periodontium have been reported in numerous studies (briefly reviewed in Haffajee & Socransky 2000). It has been shown that cigarette smokers have more bone loss, attachment loss, deeper periodontal pockets, and less gingival bleeding than non-smokers. As described in an earlier section, suspected or known periodontal pathogens were more prevalent; i.e. colonized a larger proportion of sites, in current smokers than in past or never smokers. On average, this increased extent of colonization was from 10– 25%; i.e. three to seven teeth (of 28) in each subject. The species that differed significantly between smokers and non-smokers were primarily species of the red and orange complexes. The increased extent of colonization appeared to occur primarily at shallow periodontal pockets (<4 mm) rather than deeper pockets. The difference in prevalence of these species helps to explain the greater extent of periodontal destruction in smokers than in non-smokers, since more sites are at risk (colonized by potential pathogens) in subjects who smoke. The reason for this difference in colonization pattern is not clear. Cigarette smoke could directly affect the pathogens or their local habitats. Tobacco usage also could affect the host's ability to control the infection by diminishing the local and systemic immune response. Whatever the reason, the widespread colonization of potential pathogens even at clinically healthy sites is likely to lead to future tissue damage at these sites. Further, the greater extent of colonization by periodontal pathogens could complicate periodontal therapy, since elimination or control of species would be more difficult.
# **Mechanisms of pathogenicity**
## Essential factors for colonization of a subgingival species
For a periodontal pathogen to cause disease, it is essential that the pathogen be able to (1) colonize the subgingival area and (2) produce factors that either directly damage the host tissue or lead to the host tissue damaging itself. To colonize subgingival sites, a species must be able to (1) attach to one or more of the available surfaces, (2) multiply, (3) compete successfully against other species desiring that habitat, and (4) defend itself from host defense mechanisms.
### Adhesins
To establish in a periodontal site, a species must be able to attach to one or more surfaces, including the tooth (or host-derived substances binding to the tooth), the sulcular or pocket epithelium, or other bacterial species attached to these surfaces. Studies of bacterial adhesion have demonstrated specificity in the involved mechanisms. At the simplest level there are one or more specific receptors on the host cell or other surfaces to which specific "adhesin" molecule(s) on the bacterial surface may attach. It has been demonstrated that there is a multiplicity of receptors on tooth surfaces, epithelial or other mammalian cells, and other bacteria. Some of the adhesins that have been identified on subgingival species include fimbriae (Cisar _et al_. 1984; Clark _et al_. 1986; Sandberg _et al_. 1986, 1988; Isogai _et al_. 1988) and cell-associated proteins (Murray _et al_. 1986, 1988; Mangan _et al_. 1989; Weinberg & Holt 1990). Receptors on tissue surfaces include galactosyl residues (Cisar _et al_. 1984; Murray _et al_. 1988; Sandberg _et al_. 1988; Mangan _et al_. 1989), sialic acid residues (Murray _et al_. 1986), proline-rich proteins or statherin (Clark _et al_. 1986), and type I or IV collagens (Naito & Gibbons 1988; Winkler _et al_. 1988).
### **Coaggregation**
While many species attach directly to host surfaces, other species attach to bacteria attached to such surfaces. This phenomenon is called coaggregation. It has been shown that there is specificity in the attachment of one species to another in _in vitro_ systems and _in vivo_ (Kaufman & DiRienzo 1989; Kolenbrander _et al_. 2006). In some instances, coaggregation between non-coaggregating species may be mediated by cellular constituents (e.g. vesicles) of a third species (Ellen & Grove 1989; Grenier & Mayrand 1987b). Further, the mechanism of attachment of cells of a given pair of species appears to be mediated by specific receptor–adhesin interactions. Many of these interactions are lectin-like in that they are based on the attachment of a specific protein on the surface of one species to a specific carbohydrate on the surface of the other (Kinder & Holt 1989; Kolenbrander & Andersen 1989; Kolenbrander _et al_. 1989; Abeygunawardana _et al_. 1990), but other mechanisms exist (Kolenbrander & Andersen 1990; Kolenbrander _et al_. 1989). For example, the _S. sanguinis–A. naeslundii_ genospecies 2 interaction was shown to be due to the attachment of a fimbrial-associated lectin on _A. naeslundii_ genospecies 2 to a polysaccharide with a repeating heptasaccharide on _S. sanguinis_ (Abeygunawardana _et al_. 1990). In certain instances more than one type of adhesin–receptor interaction has been detected between a species pair. It is of interest that the same galactose-binding adhesin of _F. nucleatum_ to _P. gingivalis_ and _A. actinomycetemcomitans_ also binds the cell to human epithelial cells and fibroblasts (Weiss _et al_. 2000).
The initial stages of plaque development involves the adhesion of organisms to the tooth surfaces or pellicle proteins on the tooth surfaces. The early colonizers are dominated by members of the genus _Streptococcus_ (Fig. 9-20), followed by the _Actinomyces_ , the two genera that commonly exhibit intra-generic coaggregation. This intra-generic coaggregation may help to explain the detection of the yellow complex, which is made up of _Streptococcus_ species, and the species forming the _Actinomyces_ cluster demonstrated in Fig. 9-10. In addition, there are also frequent coaggregations between species of these two genera. If the _Streptococcus–Actinomyces_ coaggregations were random, thousands of potential interactions could result. However, only six specific coaggregation groups of streptococci and six coaggregation groups of _Actinomyces_ have been detected (Kolenbrander _et al_. 2006). Sequential colonization of different species during plaque development may be mediated in part by coaggregation. This leads to the concept of bridging species; i.e. one or more species that coaggregate with early colonizers and are in turn attached to by late colonizing species. The colonization would be mediated by specific adhesin–receptor interactions between the early colonizers and the bridging species and a second set of receptor–adhesin interactions between the bridging species and late colonizers. Members of the genus _Fusobacterium_ appear to be the major bridging species in dental plaque due to their ability to adhere to a very wide range of dental plaque species.
### Multiplication
The gingival crevice and/or periodontal pocket might be considered a lush area for microbial growth, but it is in fact a rather stringent environment for a bacterial species to live in. The mean temperature of the area averages about 35˚C and ranges from 30–38˚C (Haffajee _et al_. 1992), eliminating whole classes of potential colonizing organisms such as thermophiles and psychrophiles. The pH of 7.0–8.5 is rather restricted (Forscher _et al_. 1954; Kleinberg & Hall 1969; Cimasoni 1983), and numerous microbial species find this range unacceptable. Oxidation reduction potential measurements vary from an Eh of about −300 to +310 mv at pH 7.0 (Onisi _et al_. 1960; Kenney & Ash 1969). The wide range of Eh provides suitable microenvironments for numerous bacterial species, although extremes of Eh in a local environment could be limiting to certain species.
The selective physical environment of the gingival crevice area is accompanied by limited nutritional availability. Three sources of nutrient are available to subgingival organisms (diet, host, and other subgingival species). Certain nutrients essential to some bacterial species must be formed by other species in that area. The vitamin K analogues required by certain _Porphyromonas_ and _Prevotella_ species (Gibbons & Macdonald 1960) and the hydrogen or formate required by _Campylobacter_ species are produced by other species colonizing the subgingival ecosystem. However, the precursors to such substances and certain specific growth factors such as hemin (Evans 1951; Gibbons & Macdonald 1960) must be derived from the host. Gingival crevice fluid (GCF) is not particularly rich in nutrients, creating a major competition for the small amounts available. However, inflammation and damage to the host tissues, as a consequence of the colonizing species, lead to an increase in GCF and breakdown products of tissue, fostering the growth of resident species. Finally, nutrients delivered in relative abundance to the outer layers of plaque may not reach deeper layers.
### **Interbacterial relationships**
Bacterial interactions play important roles in species survival. Some inter-species relationships are favorable, in that one species provides growth factors for, or facilitates attachment of, another. Other relationships are antagonistic due to competition for nutrients and binding sites or to the production of substances which limit or prevent growth of a second species.
A number of types of inter-species interactions have been described. The inter-species agglutinations described above are an important means of bacterial attachment for some species. Bacterial attachment may also be influenced by the production of extracellular enzymes by one set of organisms which uncover binding sites fostering the attachment of a second set of organisms. For example, _S. mitis_ and _S. sanguinis_ bind in comparable levels to intact epithelial cells, as do strains of _P. gingivalis_ and _Pr. intermedia_. However, if epithelial cells are exposed to bacterial neuraminidase the attachment of the streptococci is diminished, but attachment of the _P. gingivalis_ and _Pr. intermedia_ strains is enhanced (Gibbons 1989). It is suspected that removal of sialic acid reveals galactosyl residues that foster attachment of the suspected pathogens. This mechanism may account for the greater level of such species on cells from periodontal pockets than from healthy sulci (Dzink _et al_. 1989).
Other beneficial interactions are mediated by one species providing growth conditions favorable to another. Such conditions include altered physicochemical parameters such as _Eh_ (Socransky _et al_. 1964), _pH_ (Kleinberg & Hall 1969), or _temperature_ (Haffajee _et al_. 1992). One of the more important environmental parameters is the oxygen level. Subgingival species differ in their ability to grow in the presence or absence of oxygen. Obligate aerobes require oxygen for growth and cannot multiply in its absence. Obligately anaerobic species are killed by even low levels of oxygen, while facultative species can grow in either situation. Dental plaque provides a spectrum of environments with high levels of oxygen available on outer surfaces and adjacent to periodontal tissues, but low levels of oxygen and a low oxidation reduction potential within the plaque. The differences in microenvironments are due in part to location within the periodontal pocket and in part due to the intense reducing abilities of many subgingival species. The survival of some anaerobic species may be due to the presence of facultative or aerobic species that utilize oxygen and/or detoxify its potentially cell damaging activated radicals, such as the hydroxyl radicals. Subgingival species also provide specific growth factors utilized by other species, including branched chain fatty acids and polyamines (Socransky _et al_. 1964), analogues of vitamin K (Gibbons & Macdonald 1960), lactate (Rogosa 1964), formate or hydrogen (Tanner & Socransky 1984).
Colonization of a pathogenic species in the presence of a species that produces substances antagonistic to its survival presents a different challenge to a pathogen. Antagonistic substances vary from those that affect binding (e.g. the enzymes that favored _Pr. intermedia_ above probably adversely affected _S. mitis_ ) to those that kill the species. Factors that kill other species include bacteriocins (Rogers _et al_. 1979; Hammond _et al_. 1987; Stevens _et al_. 1987), hydrogen peroxide (Holmberg & Hallander 1973; Hillman _et al_. 1985), and organic acids (Mashimo _et al_. 1985). These factors may be considered as virulence factors since they suppress the growth of competing species or different clonal types of the same species (Hillman & Socransky 1989). Defense against such factors varies. The simplest way to avoid such factors is to find sites that are not colonized by antagonistic species. A second method is to produce factors that destroy the antagonistic species. For example, _S. sanguinis_ produces hydrogen peroxide which inhibits the growth of _A. actinomycetemcomitans_ (Hillman _et al_. 1985), while _A. actinomycetemcomitans_ produces a bacteriocin that inhibits _S. sanguinis_ (Hammond _et al_. 1987; Stevens _et al_. 1987). Thus, the bacteriocin that protects the suspected pathogen _A. actinomycetemcomitans_ from the deleterious effect of the more commonly detected _S. sanguinis_ must be considered to be a virulence factor.
### **Overcoming host defense mechanisms**
Subgingival plaque microorganisms appear to overgrow and lead to severe disease in immune-compromised hosts particularly those with neutrophil disorders (Genco _et al_. 1986; Shenker 1987; Winkler _et al_. 1989). Such findings suggest that host defense mechanisms are important in limiting the numbers of bacteria in subgingival plaque and preventing tissue damage.
A bacterial species has a number of host-derived obstacles to overcome when colonizing a subgingival site. These include the flow of saliva and gingival crevice fluid and mechanical displacement by chewing and speaking. Substances in saliva and gingival crevice fluid may aid in the prevention of colonization by blocking the binding of bacterial cells to mammalian surfaces. Such factors include specific antibodies, salivary glycoproteins, mucins, and proline-rich proteins which may act as non-specific blocking agents (Gibbons 1984).
Once a bacterial cell has successfully attached to a surface in the subgingival area, other host mechanisms come into play. Desquamation of epithelial cells presents a new cleansing mechanism, which is overcome by certain species by their ability to bind to underlying epithelial cells (Freter 1985). Other species are able to invade the epithelial cells (Finlay & Falkow 1989; Rudney _et al_. 2001, 2005) and may multiply intracellularly and spread to adjacent cells.
Specific antibody in the subgingival area could act by preventing bacterial attachment or, in some instances, by making the bacterial cell susceptible to various phagocytic or killing mechanisms. A number of subgingival species have evolved mechanisms for evading the effect of specific antibody. Species including _P. gingivalis_ , _Pr. intermedia_ , _Pr. melaninogenica_ , and _Capnocytophaga_ species possess IgG and IgA proteases that can destroy antibody (Kilian 1981; Saito _et al_. 1987; Grenier _et al_. 1989). Other species are capable of evading antibody by changing their surface antigens (Gibbons & Qureshi 1980) or possibly by mimicking the host's antigens (Ellen 1985).
Polymorphonuclear leukocytes affect subgingival species in at least two ways: by phagocytosing and ultimately killing bacterial cells or by releasing their lysosomal enzymes into the crevice or pocket. A number of bacterial mechanisms exist that might counteract these effects, including the production of leukotoxin by _A. actinomycetemcomitans_ (Baehni _et al_. 1979) and capsules by _P. gingivalis_ and other species that inhibit phagocytosis (Okuda & Takazoe 1988). In addition, a number of species have developed strategies to interfere with the killing mechanisms of the polymorphonuclear leukocytes (Boehringer _et al_. 1986; Seow _et al_. 1987, 1989; Sela _et al_. 1988; Yoneda _et al_. 1990).
If a species enters the underlying connective tissue, it has moved into the area where the host's defense mechanisms are the most formidable. Polymorphonuclear leukocytes and antibodies are joined by macrophages and various types of lymphocytes, completing an awesome array of antagonistic cells and their biologically active substances. To be successful in this area a species would have to have evolved sophisticated mechanisms to evade, hide from or destroy opposition. Some of the periodontal pathogens may have devised such mechanisms. For example, it has been shown that _A. actinomycetemcomitans_ leukotoxin affects not only polymorphonuclear leukocytes and monocytes (Baehni _et al_. 1979) but also kills mature T and B lymphocyte cell lines (Simpson _et al_. 1988) or facilitates a non-lethal suppression of immune cells (Rabie _et al_. 1988). Other species such as _Pr. intermedia_ , _Porphyromonas endodontalis_ , and _Tr. denticola_ have been shown to produce substances that suppress immune mechanisms (Shenker _et al_. 1984, Ochiai _et al_. 1989, Shenker & Slots 1989).
Finally, artificial agents, including antiseptics and antibiotics, have been developed that augment the host's natural defense mechanisms against bacterial pathogens. In turn the microorganisms have evolved mechanisms of resistance to these agents and added insult to injury by having the ability to pass these resistance factors to one another, even across species (Guiney & Bouic 1990).
### **Factors that result in tissue damage**
The set of properties that results in a species causing periodontal tissue loss in destructive periodontal diseases is poorly understood. Some or all tissue damage may result from an immunopathologic reaction triggered by a species which is sustained until the species is eliminated or suppressed. However, the fact that disease progression is rare, is associated with specific species, and that inflammation without attachment loss is common, suggest specificity in the properties of organisms that lead to tissue damage. Two general mechanisms of pathogenesis have been hypothesized. The first involves invasion by subgingival species. The second suggests a "long-range" attack where cells of the pathogenic species remain in the pocket but fragments of cells as well as other "virulence factors" enter the underlying periodontal tissues and either directly damage the tissues or cause "immune pathology" (Allenspach-Petrzilka & Guggenheim 1982; Fillery & Pekovic 1982; Gillette & Johnson 1982; Sanavi _et al_. 1985; Saglie _et al_. 1986, 1988; Christersson _et al_. 1987; Liakoni _et al_. 1987; Listgarten 1988). More details on the mechanisms of pathogenesis may be found in Chapter 11.
### **Invasion**
The possibility of invasion in periodontal infections gained credence with the unequivocal demonstration of invasion by a spirochete with an unique ultrastructural morphology during active episodes of acute necrotizing ulcerative gingivitis (Listgarten & Socransky 1964; Listgarten 1965). Other instances of invasion have been reported in tissues obtained from advanced periodontitis (Frank & Voegel 1978; Vitkov _et al_. 2005), LAP (Gillett & Johnson 1982; Christersson _et al_. 1987), and progressing periodontal lesions (Saglie _et al_. 1988).
As discussed earlier, strains of _A. actinomycetemcomitans_ and _P. gingivalis_ have been shown to be capable of invading epithelial cells derived from human periodontal pockets or gingival sulci. Other studies demonstrated that _T. forsythia_ was present in high numbers in preparations of human periodontal pocket epithelial cells and cells of this species could be detected within the epithelial cells. The property of invasion of epithelial cells is a common property of a wide range of mucosal pathogens including members of the genera _Salmonella_ , _Shigella_ , _Yersinia_ , _Escherichia_ , and _Listeria_. The mechanisms of attachment to and subsequent entry differ from species to species. It is thought that fimbriae-mediated adhesion may be a prerequisite for bacterial invasion in periodontitis (Vitkov _et al_. 2005). The ability to enter into and survive within human cells confers an advantage to potential pathogens in that they are protected from many of the host's defense mechanisms.
Adherence to underlying tissues, such as basement membrane and various types of collagen, has been demonstrated (Winkler _et al_. 1987, 1988; Naito & Gibbons 1988). Strains of _F. nucleatum_ and _P. gingivalis_ adhere well to preparations of basement membrane and type IV collagen. _P. gingivalis_ also adheres well to type I collagen, a property that may be useful in invasion of deeper tissues.
Deeper invasion may be important in progression of disease and could be facilitated by the property of motility. The flexible, sinuous spirochete has the physical tools to move through amorphous jelly-like intercellular matrix. If other virulence factors were present, it is likely that spirochetes and other motile forms such as _Selenomonas_ and _Campylobacter_ would have unique invasive capacities.
### **Factors that cause tissue damage**
The microbial substances that lead to damage of the periodontal tissues are poorly understood, in large part because so many potential "virulence factors" have been described for subgingival species and their roles inadequately evaluated. Virulence factors can be arbitrarily divided into three categories: substances that damage tissue cells (e.g. hydrogen sulphide), substances that cause cells to release biologically active substances (e.g. lipopolysaccharide), and substances that affect the intercellular matrix (e.g. collagenase). There is an unfortunate overlap in this categorization, since some substances elicit more than one response. Further, factors that affect the cells involved in host defense mechanisms may inhibit protective responses and/or lead to the production of substances that can directly damage the tissues.
Some of the suspected virulence factors produced by three periodontal pathogens are summarized in Tables 9-1 to 9-3. Enzymes produced by subgingival species appear to be able to degrade virtually all of the macromolecules found in periodontal tissues. The periodontal pathogen, _P. gingivalis_ , produces an unusually wide array of proteases, including those that degrade collagen (Gibbons & Macdonald 1961; Smalley _et al_. 1988; Winkler _et al_. 1988; Jin _et al_. 1989), immunoglobulins (Kilian 1981; Saito _et al_. 1987; Grenier _et al_. 1989), and fibronectin (Wikstrom & Linde 1986; Smalley _et al_. 1988; Lantz _et al_. 1990). Of particular interest are the cysteine proteinases commonly referred to ARG-gingipain and LYS-gingipain which are important to the organism in order to break down proteins to peptides and amino acids necessary for its growth (Abe _et al_. 1998; Genco _et al_. 1999; Kadowaki _et al_. 2000). These proteinases are also important in the processing/maturation of cell surface proteins of _P. gingivalis_ such as _fim_ A fimbrillin. Other species produce additional or other lytic enzymes. It might be argued that enzymes produced by bacterial species might not be necessary to the pathogenesis of periodontal diseases since similar enzymes can be derived from host tissue. However, if a specific lytic enzyme is essential to disease progression, current data suggest that some subgingival species would form it.
A wide variety of cell preparations or substances have been shown to adversely affect the growth and/ or metabolism of mammalian cells in tissue culture. Some of the substances are low molecular weight end-products of metabolism such as hydrogen sulphide, ammonia, fatty acids or indole (Socransky 1970; Singer & Buckner 1981; van Steenbergen _et al_. 1986). Other factors are less defined and are present in the extracellular milieu of bacterial cultures or extracts of the bacterial cells themselves. The importance of this group of inhibitory factors in the pathogenesis of disease is unclear. However, even minor inhibitions of cell metabolism might adversely affect structural integrity of the periodontal tissues.
It has been known for some time that certain bacterial products can induce organ cultures or tissue cells, including cells involved in host defense, to elaborate biologically active substances. One such factor derived from cultured white blood cells was initially described as osteoclast activating factor, since it accelerated bone resorption in tissue culture systems (Horton _et al_. 1972), but was later recognized as interleukin-1β (Dewhirst _et al_. 1985). Production of this factor was shown to be induced in a number of ways including stimulation by bacterial lipopolysaccharides or whole cells (Uchida _et al_. 2001). Numerous other biologically active mediators including prostaglandins, tumor necrosis factor, thymocyte activating factor, IL-8 (Uchida _et al_. 2001), and chemotactic factors have been shown to be formed in response to the addition of bacterial cells or their products to mammalian cells in tissue culture (Bomvan Noorloos _et al_. 1986; Millar _et al_. 1986; Garrison _et al_. 1988; Hanazawa _et al_. 1988; Lindemann 1988; Lindemann _et al_. 1988; Takada _et al_. 1988; Sismey-Durrant _et al_. 1989; Uitto _et al_. 1989). _P. gingivalis_ can perturb the cytokine network not only by stimulating the release of cytokines from host cells, but by removing them from its local environment (Fletcher _et al_. 1997).
### Virulence determinants in the genomics era
The study of mechanisms of virulence by oral subgingival species has been ongoing for many years and should exhibit a quantum leap due to the sequencing of the genomes of a number of subgingival species. To date, 308 bacterial genomes have been sequenced, 15 of these represent 13 distinct oral species (Duncan 2005; Kolenbrander _et al_. 2006). The knowledge of the sequences can lead to the development of microarrays to monitor gene expression by suspected periodontal pathogens while colonizing or invading oral tissues. Microarrays are already available for _P. gingivalis_ , _S. mutans_ , _A. actinomycetemcomitans_ , _Tr. denticola_ , and _F. nucleatum_. The search of the sequence genomes of periodontal species will undoubtedly reveal a large number of potential virulence factors. Unfortunately, it is an expensive and time-consuming process to evaluate whether the proposed factors actually play a role in human disease.
# **Effect of therapy on subgingival biofilms**
There is an axiom in ecology that perturbations of a complex ecosystem are generally followed by a return to an ecosystem of essentially the same composition. Thus, if a clinician alters a complex ecosystem, such as the subgingival biofilm, the expectation of an ecologist would be that, in general, the microbiota would return to a microbiota with a composition similar to that observed pre-therapy. Indeed as discussed earlier, within 4–7 days of biofilm removal by SRP the total numbers of microorganisms at a site had returned to pre-cleaning levels in the absence of home care procedures. Thus, key questions are whether the _composition_ of the subgingival biofilm in periodontitis subjects is altered by periodontal therapy to one that is more compatible with health, and if it is, whether the beneficial changes are maintained for prolonged periods of time. Figure 9-23 presents the mean changes in the percentage of sites with bleeding on probing, mean probing pocket depth, and mean clinical attachment level before therapy and at 3, 6, and 12 months post therapy in 493 chronic periodontitis subjects who received different forms of periodontal therapy. All had received SRP and instruction in proper home care and some had received, in addition, periodontal surgery and/ or systemically administered antibiotics. The major improvement in the clinical parameters occurred between baseline and 3 months post therapy with little change or modest improvement occurring from 3–12 months. Also depicted in this figure are the changes in mean total DNA probe counts at the same time points. The microbiological changes followed the same pattern as the clinical changes and were characterized by marked reductions in total bacterial counts between baseline and 3 months with minimal change thereafter.
**Fig. 9-23** Mean (± SEM) percentage of sites with bleeding on probing, mean pocket depth and attachment level and mean total DNA probe counts at baseline (pre-therapy), and at 3, 6, and 12 months post therapy in 493 chronic periodontitis subjects. The data for each clinical parameter were measured at up to 168 sites in each subject and averaged within a subject and then across subjects at each time point separately. For the microbiological data, mean values were computed by summing the DNA probe counts for each species in up to 28 subgingival plaque samples in each subject, and then averaging across subjects at the four time points separately. The significance of differences over time was determined using the Friedman test.
Figure 9-24 presents the change in microbial composition of the subgingival biofilm from baseline to 12 months in the subjects presented in Fig. 9-23. There was a major reduction in the counts, proportions, and percentage of sites colonized at levels >105 for many of the test species. In particular, species of the red and orange complexes, the species associated with the etiology and pathogenesis of periodontal diseases, were significantly reduced by the various forms of therapy and the reductions were still evident 12 months after therapy. Thus, an improvement in mean clinical parameters was accompanied by a mean reduction in total bacterial counts and specifically reductions in the levels of many periodontal pathogens. However, not all sites within a subject responded equally well to therapy. Figure 9-25 presents the change in the 40 test species from before therapy to 12 months post therapy at sites that showed improvement in attachment level of >2 mm, sites that showed loss of attachment >2 mm, and sites where the change in attachment level was between these two extremes. There were significant reductions from baseline to 12 months in the mean counts of many of the test species at sites that exhibited change in attachment level ≤2 mm or a "gain" of >2 mm. Not surprisingly the majority of these species were those of the red and orange complexes. In contrast, sites that showed loss of attachment at 12 months post therapy exhibited few changes in the counts of any of the test species, underscoring the association between clinical improvement and reductions in the levels of periodontal pathogens.
**Fig. 9-24** Plots of mean counts (left panel), percents of the total DNA probe count (middle panel) and percentage of sites colonized by 40 bacterial species at counts >105 (right panel) in subgingival plaque samples taken from the subjects in Fig. 9-23 at baseline and 12 months post therapy. The "bands" represent the mean values ± SEM. Mean values for each species were computed by averaging up to 28 samples in each subject, and then averaging across subjects at the two time points. Significance of differences between groups was sought using the non-parametric Wilcoxon signed ranks test; * p < 0.05, ** p < 0.01, *** p < 0.001 after adjusting for multiple comparisons (Socransky _et al_. 1991). The species were ordered and grouped according to the complexes described by Socransky _et al_. (1998). The red profiles represent baseline data and the yellow profiles represent data at 12 months. Reprinted with permission from Blackwell Publishing (Haffajee _et al_. 2006b, _Periodontology 2000_ **43** , 219–258).
As mentioned earlier, not all periodontal therapies work equally well in all subjects, a finding likely related to, among other factors, the nature of the subgingival microbiota prior to therapy. Two systematic reviews have suggested that adjunctive systemically administered antibiotics can provide better clinical outcomes when compared with scaling and root planing only (Herrera _et al_. 2002; Haffajee _et al_. 2003). Figure 9-26 presents the 12-month microbiological findings in subjects who received SRP only (left panel) and those who received different systemically administered antibiotics as adjuncts to SRP (right panel). While, overall, both therapeutic modalities provided clinical improvements and reductions in bacterial counts, subjects receiving the adjunctive antibiotics exhibited a better clinical response as well as more species, particularly those of the red and orange complexes, with significant reductions which were maintained to 12 months post therapy. The reader may wonder why antibiotics have an effect on the composition of the subgingival microbiota, when these species are living in a protected biofilm environment as described earlier in this chapter. Among the possible explanations would be the disruption of the subgingival biofilm by scaling and root planing during or before antibiotic administration, the location of the red and orange complex species adjacent to the epithelial lining of the periodontal pocket (the site of entry of antibiotics into the periodontal pocket), and the possibility that antibiotics may affect pathogens that are located within mammalian tissue cells. Whatever the reason, it is clear that adjunctive systemic antibiotics lowered the levels of periodontal pathogens and improved clinical parameters significantly more than scaling and root planing alone and may be useful in the treatment of some periodontal infections.
**Fig. 9-25** Plots of mean counts (× 105) of 40 taxa in subgingival plaque samples at baseline and 12 months at sites that exhibited attachment level "gain" >2 mm, (left panel), change ≤2 mm (middle panel) or loss >2 mm (right panel) from baseline to 12 months. Counts of each species at sites in each of the three attachment level change categories were determined, averaged within a subject, and then averaged across subjects in the three site categories at pre-therapy and 12 months post-therapy separately. Significance of differences between counts at baseline and 12 months was determined using the Wilcoxon signed ranks test and adjusted for multiple comparisons; * p < 0.05; ** p < 0.01; *** p < 0.001. Species were ordered according to microbial complexes. The red panels represent the pre-therapy values and the yellow panels represent the 12 months post-therapy values. Reprinted with permission from Blackwell Publishing (Haffajee et al. 2006b, _Periodontology_ 2000 43, 219–258).
### Final comment
Infections of any organ system are caused by a relatively finite set of pathogens sometimes working individually or, occasionally, in small mixtures. For example, lung infections may be caused by any of a variety of organisms, including _M. tuberculosis_ , _S. pneumoniae_ , and _K. pneumoniae_. No single therapy is effective against all lung infections. Each of these infections requires the use of a different chemotherapeutic agent and the selection of the agent is based on the findings of diagnostic tests. The analogy to periodontal infections is clear. There is no single cause of these infections, no one treatment can control all the infections, and the choice of treatment should be guided by the nature of the infecting microbiota. Obviously a great deal of additional research is needed to define precisely the contribution of each periodontal pathogen to periodontal disease progression, to devise tests for their presence and to determine the best therapy for each pathogen's suppression. However, when the most appropriate anti-infective therapy is applied to a given subject or site, disease progression should, at least, be stopped and the potential for long-term periodontal stability should be markedly enhanced.
**Fig. 9-26** Profiles of mean counts (× 105) of 40 taxa in subgingival plaque samples taken pre-therapy and 12 months post-therapy from subjects who did not (left panel) or did receive systemic antibiotics (right panel) as part of their periodontal therapy. Plaque samples were taken from the mesial aspect of each tooth and analyzed separately for their content of 40 species. Data for each species were averaged within in each subject and then across subjects in the two treatment groups for each time point separately. Significance of differences between pre-therapy and 12 months post-therapy was sought using the Wilcoxon test and adjusted for multiple comparisons; * p < 0.05; ** p < 0.01; *** p < 0.001. Species were ordered according to microbial complexes. The red panels represent the pre-therapy values and the yellow panels represent the 12 months post-therapy values. Reprinted with permission from Blackwell Publishing (Haffajee et al. 2006b, _Periodontology_ 2000 43, 219–258).
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# Chapter 10
# Peri-implant Infections
Ricardo P. Teles, Anne D. Haffajee, and Sigmund S. Socransky
* * *
Introduction
Early biofilm development on implant surfaces
Time of implant exposure and climax community complexity
The microbiota on implants in edentulous subjects
The microbiota on implants in partially edentulous subjects
The microbiota on implants in subjects with a history of periodontal disease
The microbiota of peri-implantitis sites
* * *
# Introduction
The introduction of dental implants as a procedure to replace natural teeth lost due to dental caries, trauma or periodontal diseases has been a major advance in the management of edentulous and partially edentulous individuals. The insertion of these "new surfaces" also presents a new opportunity for bacterial colonization. One might surmise that the presence of these implant surfaces with different physical properties from teeth might select for bacterial species that are unique to this habitat, leading to a microbiota that may be substantially different from that found on natural teeth. This chapter will examine the nature of the microbiota on implant surfaces in individuals who have clinically healthy implants in the edentulous or in the partially edentulous dentition. After examining the microbiota associated with healthy implants, the nature of the microbiota associated with peri-implantitis will be described.
# Early biofilm development on implant surfaces
When an implant is inserted into the oral cavity, it provides a new and physically different surface for the colonization of microorganisms that might already be resident in the oral cavity or enter the oral cavity during biofilm development. The scanning electron micrographs provided in Fig. 10-1 indicate that implant surfaces are readily colonized by a variety of different bacterial morphotypes. The colonization of osseointegrated implants was studied using an immunoblot technique for the detection of antigens to six different species: _Porphyromonas gingivalis_ , _Prevotella intermedia_ , _Actinomyces naeslundii_ genospecies 2 (formerly _Actinomyces viscosus)_ , _Fusobacterium nucleatum_ , _Treponema socranskii_ , and _Treponema denticola_ (Koka _et al_. 1993). Supra- and subgingival plaque samples were collected from teeth close to the implants before implant exposure and at 14 and 28 days after exposure. Samples were taken from the implants 14 and 28 days after the second-stage surgery. The six test species were present in supragingival biofilm samples from the teeth at baseline, but _F. nucleatum_ and _Tr. denticola_ were not found in subgingival samples at this time point. The frequency of detection on teeth of most of the test species remained constant during the 28 days of observation. _Tr. denticola_ was not detected at any time point in subgingival plaque samples from both teeth and implants. All six species were recovered from supragingival plaque samples from implant fixtures after 14 days of exposure, while only _A. naeslundii_ genospecies 2 could be detected in the subgingival samples of implants at this time point. After 28 days of implant exposure, all but one species ( _Tr. denticola_ ) could be recovered from subgingival plaque samples of implants. The data suggested that implants in partially edentulous subjects were colonized by periodontal pathogens as early as 14 days after exposure to the oral environment and that establishment of a complex subgingival microbiota occurred as early as 28 days after exposure.
**Fig. 10-1** Scanning electron micrographs of the subgingival microbiota on a titanium smooth collar of a hydroxyapatite plasma spray-coated dental implant (a) and on the smooth collar of a titanium dental implant (b). Courtesy of Dr. Charles Cobb.
Biofilm development on teeth and implants was also compared during a 3-week study of experimental gingivitis and experimental peri-implant mucositis using phase contrast microscopy (Pontoriero _et al_. 1994). Biofilm samples revealed similar proportions of coccoid cells, motile rods, and spirochetes on both teeth and implants at baseline and after 3 weeks of plaque accumulation. The results were similar to those reported by Löe _et al_. (1965) and Theilade _et al_. (1966) of experimental gingivitis in dentate subjects, in which higher proportions of motile rods and spirochetes and lower proportions of coccoid cells were detected after 3 weeks of plaque accumulation. The authors suggested that plaque accumulated at similar rates on both teeth and implant surfaces.
The development of biofilms on the surface of implants was examined in partially edentulous subjects who required implants (Quirynen _et al_. 2006). Samples were taken from implant and teeth sites using paper points at 2, 4, 12, and 26 weeks after implant exposure and evaluated for their content of 40 bacterial species using checkerboard DNA–DNA hybridization. The mean counts (× 105) of the 40 test species evaluated in the samples from the teeth and implant surfaces at the different time points are presented in Fig. 10-2. Higher counts of red and orange complex species (for a description of the microbial complexes, see Chapter 9) were detected on the tooth surfaces at all time points, particularly at 2 weeks. At later time points the differences between the different sampled sites were less marked, although red and some orange complex species were still at higher levels in the samples from the teeth. Figure 10-3 presents the mean counts of the 40 test bacteria at tooth (left panel) and implant sites (right panel) at 2, 4, and 26 weeks after implant exposure. There was little change in the mean microbial profiles at the tooth sites over time. However, at the implant sites, there was an increase in counts of certain species including _F. nucleatum_ ss _vincentii_ , _Peptostreptococcus micros_ , _Prevotella nigrescens_ , and _P. gingivalis_. Figures 10-2 and 10-3 are interesting because they suggest that species thought to be "early colonizers" on teeth, dentures, and soft tissues (Socransky & Haffajee 2005; Kolenbrander _et al_. 2006), such as _Streptococcus mitis_ and _Streptococcus oralis_ , appear on implants by 2 weeks and are maintained at their initial levels for periods of 2 to 26 weeks. Other species, such as members of the genus _Fusobacterium_ , _Pe. micros_ , and _P. gingivalis_ , may be detected at early time intervals, but their levels increase more slowly over time. Some species thought to be periodontal pathogens, such as _Eubacterium nodatum_ and _Tr. denticola_ (Haffajee _et al_. 2006), were initially present in low numbers on implants with little evidence of an increase by 6 months at these clinically healthy implant sites.
**Fig. 10-2** Mean counts (×105) of 40 species in samples from 48 implants and 48 teeth in 12 subjects at 2, 4, 13, and 26 weeks after implant exposure. Mean counts of each species were computed by averaging the data for each site category separately in each subject, and then averaging across subjects at each time point separately. Significance of differences between site categories was sought using the Mann Whitney test. No significant differences were found after adjusting for multiple comparisons (Socransky _et al_. 1991). The species were ordered and grouped according to the complexes described by Socransky _et al_. (1998).
**Fig. 10-3** Mean counts (×105) of 40 species at 2, 4, and 26 weeks after implant exposure in samples from 48 teeth (left panel) and 48 implants (right panel) from 12 subjects. Mean counts of each species were computed by averaging the data for each site category separately in each subject, and then averaging across subjects at each time point separately. Significance of differences over time was sought using the Friedman test. No significant differences were detected after adjusting for multiple comparisons (Socransky _et al_. 1991). The species were ordered and grouped according to the complexes described by Socransky _et al_. (1998).
The above studies indicated that the early development of biofilms on implant surfaces was similar to that observed on natural teeth and other restorative materials that were placed in the oral cavity. It is likely that in the first step, proteins of saliva may form a pellicle on the surface of the implant providing receptors for the adhesins that occur on oral bacterial species. In this regard, Edgerton _et al_. (1996) examined _in vitro_ , experimental salivary pellicles formed on titanium surfaces. Several salivary components previously described in enamel pellicles were also found on titanium, including high-molecular weight mucins, α-amylase, secretory IgA, and proline-rich proteins. However, cystatins and low-molecular weight mucins, commonly found on enamel, were not detected on titanium surfaces. These differences in pellicle composition could result in qualitative differences in early biofilm formation on implants compared to teeth. Data comparing the initial bacterial colonization on titanium, hydroxyapatite, and amalgam surfaces suggested that this may not be the case (Leonhardt _et al_. 1995). Biofilm accumulation was examined at 10 minutes and 1, 3, 6, 24, and 72 hours in healthy volunteers who wore intraoral removable splints containing small sections of the three different materials. No significant differences were found in the species colonizing the three surfaces at any time point. It was concluded that although the salivary pellicle that formed on titanium surfaces might differ from that on enamel surfaces, these differences did not seem to influence the bacterial composition of the early biofilms formed on these surfaces.
It has been shown in studies of biofilm development on natural teeth that attachment of bacteria occurred within minutes (Socransky _et al_. 1977) and that increases in specific species could be detected in time periods as short as 2–6 hours (Li _et al_. 2004). It is likely that biofilm development on the implant follows a similar course and that "maturation" is well under way by 2 weeks. Data supporting this conjecture were provided by Quirynen _et al_. (2005b) who examined biofilm development on implant surfaces 1 week after their insertion and showed that there were quite marked differences in the microbiotas on the implants with either shallow or deep pockets compared with the microbiota found in shallow and deep pockets adjacent to the natural teeth. The differences had decreased by 2 weeks and were markedly reduced by 6 months, as shown in Figs. 10-2 and 10-3. It must be pointed out that colonization of a pristine implant surface may be different from that of a previously cleaned tooth. The pristine surfaces of the implant are devoid of an indigenous microbiota and may require initial colonization by early colonizers to set the stage for the subsequent complex community (Kolenbrander _et al_. 2006). The cleaned tooth is likely to have remnants of an attached microbiota (Li _et al_. 2004; Socransky & Haffajee 2005) that can immediately multiply and provide surfaces for attachment of later colonizing species. This may also account for the longer time period required for the biofilm developing on implant surfaces to reach a more complex climax community.
# Time of implant exposure and climax community complexity
Studies on early plaque development clearly demonstrated development of multi-species supra- and subgingival biofilms on implant fixtures within weeks of their exposure to the oral cavity (Fig. 10-1). However, microbiological data from fully and partially edentulous subjects suggested that the complete maturation of the implant biofilm might take months, if not years to occur. The microbial changes that took place over time on 68 implants inserted in 22 subjects with a history of advanced aggressive periodontitis were examined by De Boever and De Boever (2006). Microbial samples were collected at various time points after installation of transmucosal implants and processed using DNA probes. The frequency of detection of _P. gingivalis_ and _Tannerella forsythia_ at levels >105 increased from 0% of implants at 1 month after insertion to 10% and 4% respectively at the end of the 6-month follow-up (Fig. 10-4).
**Fig. 10-4** Stacked bar charts of the frequency of detection of _P. gingivalis_ (left panel) and _T. forsythia_ (right panel) at different levels on 68 implants inserted in 22 advanced aggressive periodontitis subjects at different time points. The bar colors indicate the different levels of detection of _P. gingivalis_ and _T. forsythia_ using DNA probes. Data adapted from De Boever & De Boever (2006).
The levels of subgingival species over time on implants inserted in subjects with a history of periodontitis were examined using cultural techniques (Leonhardt _et al_. 1993). The mean percentage of total viable counts increased between 2 and 36 months for periodontal pathogens including _P. gingivalis_ (0.3% to 1.8%), _Pr. intermedia_ (1.1% to 1.9%), and _Aggregatibacter actinomycetemcomitans_ (formerly known as _Actinobacillus actinomycetemcomitans_ ) (0.1% to 1.0%). In a second study, the colonization of implant fixtures over a period of 12 months was examined (van Winkelhoff _et al_. 2000). The percentage of subjects positive for the orange complex species _Pr. intermedia_ (60%), _Pe. micros_ (90%), and _F. nucleatum_ (85%) were already high 1 month after implant exposure, while the red complex species, _T. forsythia_ , was detected in 55% of subjects at 6 months.
Microbial colonization on implants that had been in place for up to 5 years was examined using dark-field microscopy in subjects treated for generalized aggressive periodontitis and up to 3 years in subjects treated for chronic periodontitis (Mengel _et al_. 2001; Mengel & Flores-de-Jacoby 2005). A clear increase in the complexity of the subgingival peri-implant microbiota over time was observed, with an increase in the proportions of motile rods, fusiforms, spirochetes, and filaments and a decrease in the proportion of coccoid cells. Interestingly, in the aggressive periodontitis group, there was a marked increase in the proportions of spirochetes, fusiforms, and motile rods between the 4- and 5-year time-points (Fig. 10-5) which was preceded by an increase in mean Gingival Index scores, mean pocket depth, and mean attachment level (Fig. 10-6). This change in the local habitat, in terms of increased inflammation and deeper pockets, may have been responsible for the observed shifts in the peri-implant microbiota.
**Fig. 10-5** Stacked bar chart of the distribution of bacterial morphotypes on ten implants from five aggressive periodontitis subjects at different time points. The bar colors indicate the percentage of the microbiota comprised by the different morphotypes identified using darkfield microscopy. Data adapted from Mengel et al. (2001).
**Fig. 10-6** Mean attachment level (AL), pocket depth (PD), and gingival index (GI) values around ten implants from five aggressive periodontitis subjects at different time points. The left Y-axis represents the scale for AL and PD in mm, while the right Y-axis presents the scale for the GI. Data adapted from Mengel et al. (2001).
**Fig. 10-7** Simplified diagrammatic representation of the microbial succession that may take place subgingivally on a 'pristine' implant surface exposed to the oral environment. Microbial species are colored according to the microbial complexes described by Socransky et al. (1998).
Indirect evidence of an increase in biofilm complexity over time has been provided by studies comparing the microbiota on implants exposed to the oral environment for different lengths of time. Implants present in the oral cavity for 3–4 years were significantly more frequently colonized by _A. actinomycetemcomitans_ and/or _P. gingivalis_ / _Pr. intermedia_ (44.4% of sites), compared to implants present for only 1–2 years (2.6%) (George _et al_. 1994). The implant microbiota in partially edentulous subjects harbored increased proportions of spirochetes and motile rods at implant sites with longer intraoral exposure times (Papaioannou _et al_. 1995). A statistically significant increase in the proportion of motile rods around implants from 1 year (2.7%) to 2 years (5%) after implant loading has also been reported (Sbordone _et al_. 1999). The sequence of colonization of microbial complexes at implants with different loading times, determined using checkerboard DNA–DNA hybridization, was found to be similar to that described on tooth surfaces (Lee _et al_. 1999a). Levels of yellow and green complex species (early colonizers) were relatively stable at all loading times examined. Orange complex species were detected at lower levels than the streptococci, and their levels appeared to peak 12–24 months after loading. Red complex species were either absent or detected at low levels on implants exposed for only 3 months and only increased at later times. _P. gingivalis_ and _T. forsythia_ were detected at their highest levels between 7 to 12 months after loading.
Studies on early colonization of "pristine" implant surfaces and on the impact of length of time of implant presence on the composition of the microbiota suggest a pattern and sequence of microbial succession on these surfaces quite similar to the one described for tooth surfaces (Socransky & Haffajee 2005; Kolenbrander _et al_. 2006). A salivary acquired pellicle forms on implant surfaces, providing the binding sites for adhesins on the surface of early colonizers such as members of the yellow complex (streptococci species) and _Actinomyces_ spp. Multiplication and coaggregation of these early colonizers will result in a dense accumulation of bacteria attached to the implant surface and/or to each other. A second wave of early colonizers will adhere to the coaggregates attached to the implant surface. These include members of the green and purple complexes, which will, in turn, form their own coaggregates. Members of the orange complex will form a more "loosely attached" mass of microorganisms interspersed between the implant-associated biofilm and the epithelial-associated biofilm, composed in large part by red complex species. Species that participate in multiple coaggregates, such as the fusobacteria, will act as coaggregation bridges between early and late colonizers (Fig. 10-7).
# The microbiota on implants in edentulous subjects
Early reports characterizing the microbiota on successful implants in fully edentulous subjects using darkfield microscopy described coccoid bacteria as the main morphotype, with a low proportion of spirochetes, fusiforms, and motile and curved rods. Results obtained using cultural techniques confirmed these findings and described high levels of Gram-positive facultative cocci, high levels of _Actinomyces_ and _Veillonella_ spp., low total anaerobic counts, low levels of Gram-negative anaerobic rods, low frequency of _Fusobacterium_ spp. and "blackpigmented _Bacteroides_ ", and no detection of _P. gingivalis_ (Mombelli _et al_. 1987, 1988; Mombelli & Mericske-Stern 1990). The levels of _A. actinomycetemcomitans_ , _P. gingivalis_ , and _Pr. intermedia_ were measured on successful implants exposed to the oral environment for 3–38 months (Ong _et al_. 1992). _P. gingivalis_ was not cultured from any sample, while _A. actinomycetemcomitans_ was present in only one sample and _Pr. intermedia_ was detected in 7/37 sampled sites. These data suggested that the microbiota colonizing clinically healthy implant fixtures in fully edentulous subjects was very similar to the microbiota associated with healthy periodontal sites in periodontally healthy subjects (Socransky & Haffajee 2005).
It was suggested that extraction of all of the teeth resulted in elimination of _P. gingivalis_ and _A. actinomycetemcomitans_ from the oral microbiota (Danser _et al_. 1994, 1995, 1997). _A. actinomycetemcomitans_ and _P. gingivalis_ could not be detected in samples from the oral mucosa and saliva 1–3 months after full-mouth extraction, even in subjects where these microorganisms were detected prior to tooth extraction (Danser _et al_. 1994). The prevalence of these pathogens in denture-wearing subjects with a history of periodontitis and an average of 9.3 years of edentulism was also investigated. _A. actinomycetemcomitans_ was not detected and _P. gingivalis_ was found in only 2/26 subjects in samples obtained from saliva, the oral mucous membranes, and biofilm accumulating on the dentures (Danser _et al_. 1995). These observations implied that the subgingival environment was the primary habitat of these periodontal pathogens and that the intraoral surfaces of edentulous subjects did not constitute a reservoir for these species. Indeed, the same group of investigators did not detect these periodontal pathogens in samples from the oral mucosa or from the peri-implant pockets in edentulous subjects with a past history of periodontitis who had received implants as part of the reconstruction of their dentition (Danser _et al_. 1997). The data suggested that even after the reestablishment of a "subgingival" environment by implant insertion, there was no intraoral reservoir of the two test species to re-colonize the peri-implant sulcus. Other investigators also reported a paucity of periodontal pathogens such as _P. gingivalis_ and spirochetes around healthy implants inserted in fully edentulous subjects, even after 5 years in function (Mombelli & Mericske-Stern 1990). However, both _P. gingivalis_ and _A. actinomycetemcomitans_ were detected in peri-implantitis cases occurring 5 years or more after loading in edentulous subjects (Leonhardt _et al_. 1999).
Later publications using molecular techniques to identify periodontal pathogens in the peri-implant microbiota have indicated a higher prevalence of pathogens around implants in fully edentulous subjects than initially described (Lee _et al_. 1999b; Hultin _et al_. 2002; Quirynen _et al_. 2005a; Devides & Franco 2006). The implant microbiota in fully and partially edentulous subjects was examined using checkerboard DNA–DNA hybridization (Lee _et al_. 1999b). Periodontal pathogens including _P. gingivalis_ , _T. forsythia_ , and _A. actinomycetemcomitans_ could be detected in samples from implants in the edentulous subjects, although less frequently than in samples from implants in partially dentate subjects. In addition, _P. gingivalis_ , _Pr. intermedia_ , _Pr. nigrescens_ , _T. forsythia_ , _A. actinomycetemcomitans_ , _F. nucleatum_ , _Tr. denticola_ , _Pe. micros_ , and _Streptococcus intermedius_ were detected by checkerboard DNA–DNA hybridization in subgingival samples obtained from stable implants in edentulous subjects, although at levels below 106 cells (Hultin _et al_. 2002). The microbiota of 37 fully edentulous subjects restored with overdentures or fixed full prostheses for at least 10 years was also examined using checkerboard DNA–DNA hybridization. Pooled subgingival plaque samples were collected from the overdenture subjects and two implants in the canine area in the fixed denture group (Quirynen _et al_. 2005a). The detection frequencies of several periodontal pathogens were higher than previously reported: _A. actinomycetemcomitans_ (35/37), _P. gingivalis_ (33/37), and _T. forsythia_ (10/37). The counts of most species were <105 cells. However, some subjects showed levels of key pathogens above 105 cells: _A. actinomycetemcomitans_ (8/37), _P. gingivalis_ (29/37), and _T. forsythia_ (3/37). Other pathogens such as _Tr. denticola_ and _Tr. socranskii_ were rarely detected.
The prevalence of _A. actinomycetemcomitans_ , _P. gingivalis_ , and _Pr. intermedia_ at implant sites in the mandible of fully edentulous subjects was also investigated using polymerase chain reaction (PCR) to detect the species (Devides & Franco 2006). The presence of these pathogens was evaluated before implant insertion, and at 4 and 6 months after restoration of the implants with immediately loaded fixed prostheses. Prior to implant placement, _A. actinomycetemcomitans_ and _Pr. intermedia_ were detected in 13.3% and 46.7% of subjects respectively, while _P. gingivalis_ was not detected. The values for these species at 4 and 6 months after prosthesis insertion were: 60.0% and 73.3%; 46.7% and 53.3%; 46.7% and 53.3%, for _A. actinomycetemcomitans_ , _P. gingivalis_ , and _Pr. intermedia_ , respectively. The data indicated a higher frequency of detection of periodontal pathogens around implants in fully edentulous subjects than had been described based on cultural techniques and latex agglutination assays, and also suggested an increased colonization of the fixtures over time. These data were in accord with a study that compared checkerboard DNA–DNA hybridization and culture methods for the detection of 18 subgingival species in samples from teeth and implants from the same subjects (Leonhardt _et al_. 2003). The frequency of detection of all test species in implant samples was lower when culture rather than checkerboard DNA–DNA hybridization was employed. Molecular techniques have also been shown to be more sensitive than culture for the detection of periodontal pathogens in periodontally healthy subjects (Borrell & Papapanou 2005). The use of molecular techniques has demonstrated a greater prevalence of periodontal pathogens at implant sites in fully edentulous subjects than was previously recognized.
The pre- and post-implantation microbiota on implants and the dorsum of the tongue were examined in fully edentulous subjects using checkerboard DNA–DNA hybridization (Lee _et al_. 1999b). The results demonstrated that species such as _Streptococcus sanguinis_ , _A. naeslundii_ , _Capnocytophaga ochracea_ , and _Campylobacter rectus_ were infrequently found in peri-implant samples when not present on the dorsum of the tongue. The authors concluded that the tongue may be the source of bacteria initially colonizing implant fixtures and suggested that other soft tissue surfaces might also be reservoirs. The microbiota in the oral cavity of edentulous subjects without implants has been examined using checkerboard DNA–DNA hybridization (Socransky & Haffajee 2005). Periodontal pathogens were detected in samples of saliva and in samples from different intraoral surfaces, such as: dorsum, lateral and ventral surfaces of the tongue; floor of the mouth; hard palate; attached gingiva; buccal mucosa; vestibule and the surface of the dentures. These data suggested that the soft tissues of edentulous subjects harbor periodontal pathogens and are the likely source for colonization of implants after insertion in fully edentulous subjects.
# The microbiota on implants in partially edentulous subjects
The literature comparing the microbiota around implants in edentulous subjects with the microbiota in partially edentulous subjects seemed to reinforce the role of the remaining dentition as a major source for colonization of implants by periodontal pathogens. Reported microbiological differences between samples from implants in partially and fully edentulous subjects included a higher percentage and frequency of detection of "black-pigmented _Bacteroides_ " (Nakou _et al_. 1987; Apse _et al_. 1989; Hultin _et al_. 1998), fewer coccoid cells and significantly more motile rods and spirochetes (Quirynen & Listgarten 1990; Papaioannou _et al_. 1995), and a higher frequency of detection of _P. gingivalis_ and _Pr. intermedia_ on implant surfaces in partially edentulous subjects (George _et al_. 1994; Kalykakis _et al_. 1998).
Investigations comparing the peri-implant microbiota with the microbiota of neighboring teeth described several similarities in the composition of the two. For instance, counts of different morphotypes did not differ significantly between subgingival samples from implants and natural teeth in partially edentulous subjects (Quirynen & Listgarten 1990). Similarities in the subgingival microbiota of implants and natural teeth were also found using darkfield microscopy and the benzoyl-DL-argininenaphthylamide (BANA) test, which detected the presence of trypsin-like enzymes produced primarily by the red complex species (Palmisano _et al_. 1991). The intraoral transmission of bacteria from teeth to implants was investigated in partially edentulous subjects using phase contrast microscopy (Quirynen _et al_. 1996). The results suggested that implants harbored more spirochetes and motile rods when teeth were present in the same jaw and when the pockets around teeth presented a pathogenic microbiota. The microbiota of implants that had been in function for 10 years in partially edentulous subjects was examined using DNA probes (Hultin _et al_. 2000). It was found that there were no significant differences between the microbiota around the natural teeth and fixtures and that the most common species isolated from both surfaces were _Tr. denticola_ , _S. intermedius_ , and _Pe. micros._ The microbiota of successfully osseointegrated implants in partially edentulous subjects was investigated using checkerboard DNA–DNA hybri dization (Lee _et al_. 1999a). _S. intermedius_ , _S. oralis_ , _S. sanguinis_ , _Streptococcus gordonii_ , _Veillonella parvula_ , _F. nucleatum_ , and _Capnocytophaga gingivalis_ were the dominant species in biofilms that formed on the fixtures. It was also demonstrated that the microbiota of healthy implants and clinically comparable crowned teeth present in the same subject were quite similar, suggesting that the major influence on the peri-implant microbiota was the microbiota on the remaining teeth.
The studies reporting similarities in the composition of the microbiota on teeth and implants were suggested but did not prove that teeth were the primary source of colonizing microorganisms for implant fixtures. Using pulsed field gel electrophoresis (PFGE), chromosomal DNA segmentation patterns of isolates of _P. gingivalis_ and _Pr. intermedia_ obtained from implants and natural teeth in the same subjects were compared (Sumida _et al_. 2002). The PFGE patterns of _P. gingivalis_ strains isolated from the implant and tooth samples from the same subject were identical, while PFGE patterns differed among samples from different subjects. Similarly, the PFGE patterns of _Pr. intermedia_ strains from teeth and implants were identical in two of three subjects examined. In another study using the same methodology, it was found that 75% of the _P gingivalis_ isolates in samples from teeth and implants were the same in a subject, while 100% of the _Pr. intermedia_ strains within a subject were a perfect match, clearly demonstrating transmission from the natural teeth to the implant fixtures (Takanashi _et al_. 2004). Unfortunately, PFGE patterns were not examined for the same test species isolated from soft tissues. Although the remaining dentition seems to be the primary source of bacteria for the colonization of implant surfaces in partially edentulous subjects, the potential role of soft tissues surfaces and saliva as reservoirs for implant infection cannot be discarded.
# **The microbiota on implants in subjects with a history of periodontal disease**
Since the remaining dentition has been implicated as a source of microorganisms that colonize implants, it might be surmised that higher levels of periodontal pathogens would colonize implants in subjects with a history of periodontal infection. The early colonization of dental implants in subjects who had been treated for aggressive periodontitis was examined in 22 subjects who were on a maintenance program for periods ranging from 12–240 months (De Boever & De Boever 2006). 68 non-submerged implants were microbiologically sampled at 10 days and 1, 3, and 6 months after implant installation. DNA probes were used to determine the levels of subgingival species such as _A. actinomycetemcomitans_ , _P. gingivalis_ , _Pr. intermedia_ , _T. forsythia_ , and _Tr. denticola_. The implants were colonized by all five periodontal pathogens as early as 10 days after implant insertion and an increase in the frequency of detection of most pathogens was observed over time. The number of implants with at least one periodontal pathogen increased from 36 to 66 implants after 6 months in the oral environment. However, some subjects presented with only low levels (103–104 cells) of these pathogens.
Other studies found that the composition of the microbiota on the implant fixtures in partially edentulous subjects was similar to the subgingival microbiota of the residual teeth, although lower levels of most species were detected on the implants. For example, subgingival plaque samples from teeth and implant fixtures in partially edentulous subjects previously treated for periodontal disease were evaluated for the presence of _A. actinomycetemcomitans_ , _P. gingivalis_ , and _Pr. intermedia_ using cultural techniques, (Leonhardt _et al_. 1993). The prevalence of subjects positive for the test bacterial species at both teeth and fixtures was similar after 6 months of implant exposure. The composition of the subgingival microbiota around implants and teeth 1 and 2 years after implant loading was examined in 25 subjects who had previously been treated for moderate to severe chronic periodontitis (Sbordone _et al_. 1999). There was an increase in the percentage of motile rods on implants over time and also an increase in the frequency of detection of _A. actinomycetemcomitans_ and _P. gingivalis_. Although periodontal pathogens were present at low levels on both teeth and implants (<1% of the total cultivable microbiota), _P. gingivalis_ and _Capnocytophaga_ spp. were the most frequent isolates around implants at both 1 and 2 years after loading.
Mombelli _et al_. (1995) also examined the colonization of implants placed in partially edentulous subjects previously treated for periodontal disease. Subgingival plaque samples were collected from the deepest residual periodontal pocket of each quadrant in 20 subjects prior to installation of single-stage implants or prior to exposure of two-stage implants in the oral cavity. After 3 and 6 months of exposure of the implant fixtures to the oral environment, the implants and the residual deepest pocket in each quadrant were also sampled. Darkfield microscopy demonstrated that, after 3 months, samples from implants presented a distribution of morphotypes similar to samples from the residual deepest pockets. Further, the composition of the implant microbiota did not change between 3 and 6 months. The frequency of detection of subgingival species identified by cultural methods on implants was similar to the frequency of detection in the deepest residual pocket samples. When _P. gingivalis_ , _Pr. intermedia_ , and _Fusobacterium_ spp. were found in high proportions in baseline samples from the residual deep pockets, they were also found in elevated proportions in the 3-month implant samples. The findings supported the notion that the residual pockets acted as reservoirs for colonization of the implant surfaces. They also suggested that compared with implants in fully edentulous and periodontally healthy subjects, the prevalence of periodontal pathogens on implants was higher in partially dentate periodontitis subjects.
A prospective study was designed to follow the clinical and microbiological outcomes at implants placed in subjects with a history of generalized aggressive and chronic periodontitis (Mengel _et al_. 1996, 2001; Mengel & Flores-de-Jacoby 2005). Fifteen generalized aggressive periodontitis (GAP), 12 generalized chronic periodontitis, and 12 periodontally healthy subjects were monitored for 3 years. Microbiological samples were collected yearly from both implants and teeth and examined using darkfield microscopy and DNA probe analysis for the detection of _A. actinomycetemcomitans_ , _P. gingivalis_ , and _Pr. intermedia_. The subjects with disease were extensively treated over a period for several years. This reduced the numbers and complexity of the colonizing microbiota on the natural dentition. Thus, after implant placement the microbiota colonizing the implants in samples from the two disease categories and periodontal health were similar in composition and dominated by coccoid cells over a period of 3 years. The clinical results indicated a continuous loss of attachment at both teeth and implants in GAP subjects. These subjects also exhibited the greatest amount of bone loss at teeth and implants. A small subset of five subjects with GAP was followed for up to 5 years. In these subjects, the microbiota around implants demonstrated a sharp increase in spirochetes, motile rods, filaments, and fusiforms from year 4 to year 5 (Fig. 10-5). Further, the levels of _P. gingivalis_ and _Pr. intermedia_ increased during the last 3 years of observation. These microbiological changes were preceded by a clear deterioration in the implant clinical parameters between years 3 and 4 (Fig. 10-6). The implant success rate for this subgroup was only 88.8%, compared to a 3-year success rate of 97.9% for the entire sample of 15 subjects.
The microbiota on implants and teeth from subjects with a previous history of periodontitis enrolled in a supportive maintenance program was also examined (Agerbaek _et al_. 2006). A total of 128 peri-implant samples and 1060 subgingival tooth samples were processed using checkerboard DNA–DNA hybridization. Overall, the proportions of the majority of the 40 test subgingival species were similar in implant and tooth samples; only the proportions of the _Actinomyces_ spp. and the purple complex species ( _V. parvula_ and _Actinomyces odontolyticus_ ) were higher at tooth sites. Taken together, the data indicated that the microbiota colonizing implants in subjects with periodontitis was similar to that observed in the samples from periodontal pockets in the same individuals and harbored more pathogenic species than observed in fully or partially edentulous subjects with minimal or no periodontal disease.
# **The microbiota of peri-implantitis sites**
Marked differences were found in the distribution of different morphotypes in the biofilms of successful implants (n = 10) in subjects with only healthy implants when compared with successful implants (control sites, n = 6) and peri-implantitis sites (test sites, n = 8) in subjects with peri-implantitis (Mombelli _et al_. 1987). Stable implants in healthy subjects were colonized primarily by coccoid cells, while fusiforms and motile rods were present at very low levels and spirochetes were absent. Spirochetes and fusiforms were detected in low proportions in samples from the healthy implants in peri-implantitis subjects. No significant differences could be found in the microbiotas of samples from healthy implants in subjects with or without peri-implantitis. The microbiota at peri-implantitis sites presented much higher levels of motile rods, spirochetes, and fusiforms, while coccoid cells accounted for only 50% of the microbiota (Fig. 10-8). Checkerboard DNA–DNA hybridization was employed to study the microbiota associated with peri-implantitis in 22 subjects with peri-implantitis sites, and eight control subjects with healthy implants (Salcetti _et al_. 1997). Forty subgingival taxa were examined and only four species were found to be positively associated with peri-implantitis versus healthy implants: _Pr. nigrescens_ , _Pe. micros_ , _F. nucleatum ss vincentii_ , and _F. nucleatum ss nucleatum_. Although not statistically significant, there was a trend for a higher prevalence of _P. gingivalis_ , _T. forsythia_ , and _Tr. denticola_ on implants present in subjects with failing implants compared to healthy implants from the control group. The healthy implants in the control subjects also displayed a tendency towards greater detection frequencies of streptococci, especially _S. gordonii_ and _S. mitis_ , as well as _Pr. intermedia_.
The presence of microorganisms in 18 samples of granulation tissue surgically removed from periimplant infrabony pockets (>5 mm) from edentulous subjects was examined using cultural techniques (Augthun & Conrads 1997). The species most frequently isolated were: " _Bacteroidaceae_ " (16/18), _A. actinomycetemcomitans_ (16/18 samples), _F. nucleatum_ (4/18), _Capnocytophaga spp_ (5/18), and _Eikenella corrodens_ (3/18). The microbiota associated with periimplantitis in 37 subjects with failing implants was compared with the microbiota in 51 subjects with healthy implants (Leonhardt _et al_. 2003). Microbiological samples were analyzed using cultural methods for the occurrence of _Pr. intermedia_ / _nigrescens_ , _A. actinomycetemcomitans_ , _P. gingivalis_ , enterics, yeast, and _Staphylococcus_ spp. There were four groups of subjects. None of the test species were detected in the healthy edentulous subjects. In the healthy dentate patient group _Pr. intermedia_ / _nigrescens_ was detected in 26% of subjects but _A. actinomycetemcomitans_ and _P. gingivalis_ were detected in only one subject each. The edentulous peri-implantitis group exhibited _P. gingivalis_ , _A. actinomycetemcomitans_ and _Pr. intermedia_ / _nigrescens_ in 25%, 13%, and 38% of subjects respectively, while 31%, 3%, and 66% of dentate periimplantitis subjects exhibited these species. _Staphylococcus epidermidis_ was found in 17% of the dentate peri-implantitis subjects, enterics were found in 30% of the peri-implantitis group, but in only 8% of the healthy group (p < 0.001). _Candida albicans_ was isolated in samples from 10% of the dentate peri-implantitis subjects.
**Fig. 10-8** Pie charts of the mean percentage of different morphotypes in the microbiota of samples from ten healthy implant sites in subjects with successful implants only, samples from six healthy implant sites and from eight peri-implantitis sites in subjects with peri-implantitis. The numbers correspond to the mean percentage of each morphotype within the microbiota. The areas of the pies have been adjusted to reflect mean total counts of each site category. Data adapted from Mombelli _et al_. (1987).
The distribution of periodontal pathogens recovered from peri-implantitis sites and teeth with chronic or recurrent periodontitis was examined using microbial samples sent to the Microbiological Testing Laboratory at University of Pennsylvania by different dental practitioners (Listgarten & Lai 1999). Forty-one consecutive samples from subjects with failing implants, chronic periodontitis or recurrent periodontitis were examined using darkfield microscopy and cultural methods for the detection of: _A. actinomycetemcomitans_ , _C. rectus_ , _Pr. intermedia/nigrescens_ , _E. corrodens_ , _P. micros_ , _Capnocytophaga_ , _Fusobacterium_ spp., _Staphylococcus aureus_ , _Staphylococcus_ spp., and yeast. _P. gingivalis_ and _T. forsythia_ were detected by indirect immunofluorescence. _T. forsythia_ was the most frequently detected species and was found in 83% of samples from chronic periodontitis, 85% of recurrent periodontitis samples, and 59% of samples of peri-implantitis sites, although at low levels (1–3% of the total cultivable microbiota). Most bacterial species had a higher frequency of detection and were present in higher levels in samples from teeth than in samples from implants. On the other hand, enteric rods were more prevalent (10% of subjects) and present in higher proportions on implants and in recurrent periodontitis compared with the chronic periodontitis. Yeasts were more prevalent in chronic periodontitis samples than on failing implants and _S. aureus_ and _Staphylococcus_ spp. were detected infrequently.
Checkerboard DNA–DNA hybridization was employed to examine the levels of 12 microorganisms in subgingival samples obtained from five different categories of sites: (1) peri-implantitis sites in partially edentulous subjects (n = 14); (2) healthy implant sites from the same subjects with periimplantitis (n = 17); (3) teeth from the same group with peri-implantitis (n = 17); (4) healthy implant sites from partially edentulous (n = 13) and fully edentulous subjects (n = 6) with only healthy implant sites; (5) teeth from subjects with healthy implant sites (n = 13) (Hultin _et al_. 2002). Periodontal pathogens, such as _P. gingivalis_ , _Pr. intermedia_ , _T. forsythia_ , _A. actinomycetemcomitans_ , and _Tr. denticola_ , were present in samples from all categories of sites, however, species were recovered at levels above 106 cells only around failing fixtures. When peri-implantitis sites and healthy sites from the same subjects were compared, peri-implantitis sites had higher levels of _A. actinomycetemcomitans_ , _F. nucleatum_ , and _Tr. denticola_ (Fig. 10-9). Further, _C. rectus_ and _S. noxia_ were only found around implants in subjects with peri-implantitis. Using cultural methods, Botero _et al_. (2005) compared the microbiota associated with 16 implants with peri-implantitis in 11 subjects with the microbiota on 15 healthy implants in 8 subjects. All subjects were partially edentulous and the microbiota associated with the remaining teeth in subjects with peri-implantitis was also examined. _P. gingivalis_ was detected only in peri-implantitis samples (43.7% of the samples), while peri-implant lesions harbored statistically significantly higher levels of enteric rods and _Pr. intermedia_ / _nigrescens_.
**Fig. 10-9** Bar chart of the mean frequency of detection of seven subgingival species in different implant site categories: implants affected by peri-implantitis, healthy implants in subjects with periimplantitis (PIS) and healthy implants in partially edentulous control subjects (CS). Data adapted from Hultin _et al_. (2002).
For the most part, the literature on the microbiota of failing implants describes the presence of elevated levels of species previously associated with periodontal infections. Other microorganisms, not commonly implicated as etiological agents of periodontal diseases, have also been recovered from peri-implant lesions, including staphylococci, enteric rods, and yeast, although a causal relationship between these microorganisms and peri-implant infections is premature.
### Summary
Although the microbiology of the dental implant in clinically healthy and diseased situations has been studied less intensively than the microbiology of the natural dentition, available data suggest the following:
1. The new "hard tissue" surface presented to the oral environment by the implant provides a surface for the attachment of salivary proteins, peptides, and other substances. These substances rapidly form a pellicle that is probably quite similar to the pellicle formed on natural teeth.
2. The pellicle provides receptors for the adhesins on specific species of oral bacteria that form the early colonizers of the implant. These species appear to be similar to those that colonize the teeth and include members of the genera _Streptococcus_ , _Actinomyces_ , and _Veillonella_.
3. The insertion of the implant appears to "set the clock back" for the development of the mature biofilm; i.e. for a number of years the microbial composition of biofilms on healthy implants may be similar to that observed on the surfaces of periodontally healthy teeth in the adolescent.
4. With time, varying from months to years, the implant microbiota becomes more complex. Pockets may develop around the implant, which harbor increased numbers and proportions of orange and red complex species in a fashion analogous to the increase in these species in deep periodontal pockets adjacent to natural teeth.
5. The development of peri-implantitis appears to be accompanied in large part by an increase in bacterial species that have been found to increase in periodontitis. These include periodontal pathogens, such as _P. gingivalis_ , _T. forsythia_ , and _A. actinomycetemcomitans_ , as well as additional taxa including staphylococci and enteric rods.
6. The microbiota of implants in partially edentulous subjects who have had periodontitis appears to harbor more periodontal pathogens than the microbiota at implants in partially edentulous subjects without periodontitis and implants in fully edentulous subjects. The presence of these species appears to increase the long-term risk for peri-implantitis in subjects with a history of periodontitis.
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# Part 4: Host–Parasite Interactions
11 Pathogenesis of Periodontitis
_Denis F. Kinane, Tord Berglundh, and Jan Lindhe_
12 Modifying Factors
_Richard Palmer and Mena Soory_
13 Susceptibility
_Bruno G. Loos, Ubele van der Velden, and Marja L. Laine_
# Chapter 11
# Pathogenesis of Periodontitis
Denis F. Kinane, Tord Berglundh, and Jan Lindhe
* * *
Introduction
Clinically healthy gingiva
Gingival inflammation
Histopathological features of gingivitis
Different lesions in gingivitis/periodontitis
The initial lesion
The early lesion
The established lesion
The advanced lesion
Host–parasite interactions
Microbial virulence factors
Host defense processes
Important aspects of host defense processes
The innate defense systems
The immune or adaptive defense system
* * *
# Introduction
Inflammatory and immune reactions to microbial plaque are the predominant features of gingivitis and periodontitis. The inflammatory reaction is visible both clinically and microscopically in the affected periodontium.
Inflammatory and immune processes operate in the gingival tissues to protect against local microbial attack and prevent microorganisms or their damaging products from spreading into or invading the tissues. These host defense reactions are, however, also considered potentially harmful to the host in that inflammation can damage surrounding cells and connective tissue structures. Furthermore, inflammatory and immune reactions that extend deep into the connective tissue beyond the cemento-enamel junction (CEJ) may include loss of connective tissue attachment to the tooth involved as well as loss of alveolar bone. These "defensive" processes could therefore paradoxically contribute to the tissue injury observed in gingivitis and periodontitis.
Whilst inflammatory and immune reactions within the periodontal tissues may appear similar to those seen elsewhere in the body, there are significant differences. To some extent this is a consequence of the anatomy of the periodontium, e.g. the permeable junctional epithelium that has remarkable cell and fluid dynamics, with its prime purpose to preserve epithelial continuity across the hard and soft tissue interface. Another important feature is that the "defensive processes" in the periodontal tissues occur in response to large numbers and varieties of microbes that reside on the tooth surface in a biofilm community, close to rather than within the gingiva.
Periodontal disease has sometimes been referred to as a "mixed bacterial infection" to denote that multiple microbial species contribute to the development of disease. Microbial species interact, and although some may not be overtly pathogenic they may still influence the disease process by aiding and assisting the pathogenic bacteria also contained within the microbial biofilm. Thus, purportedly 'commmensal' microbes may endorse the virulence potential of other microbes by providing specific growth conditions or defensive factors; this calls into question our definition of commensal and pathogen with respect to biofilm related diseases.
The microorganisms in the biofilm within periodontal pockets are in a continual state of flux; species, which are relevant at one stage of disease, may not be important at other disease phases. In other words, tissue destruction may result from combinations of bacterial factors, which vary over time. This contrasts with most other classical infectious diseases (e.g. tuberculosis, syphilis, gonorrhea) where the host contends with one organism and the diagnosis of the disease is indicated by the presence or absence of this particular pathogen.
The pathogenicity of microorganisms relates as much to the individual host's innate and/or inflammatory and/or immune capability, as to the virulence of the bacteria themselves. For example, periodontal tissue breakdown could result from microbial enzymes that directly digest the tissue but also, and more likely, from host responses to these enzymes. Furthermore, tissue destructive responses might result from the host's inflammatory or immune reaction to normal physiological components of the bacteria such as the lipopolysaccharides found in the outer membrane of Gram-negative bacteria.
Epidemiological studies have shown that even within the same individual, the severity of periodontal tissue injury often varies from tooth to tooth and from one tooth surface to another. Thus, whilst many teeth within an individual mouth may exhibit advanced loss of connective tissue attachment and alveolar bone, other teeth or tooth surfaces (sites) may be almost unaffected and surrounded by a normal periodontium. Hence, a patient who is susceptible to, and is exhibiting, periodontal disease is not afflicted with a "homogeneous" condition (see Chapter 18). Each affected site in his/her mouth represents an "individualized" or "specific" microenvironment. In some sites, the inflammatory lesion may be contained within the gingiva (gingivitis) for prolonged periods of time without any apparent progression of the disease into deeper tissues. In other sites, active periodontal tissue destruction (periodontitis) may occur and may be a consequence of a variety of host and parasite factors.
However, it is not presently understood why in some patients the inflammatory lesions remain confined to the marginal portion of the gingival tissues, whilst in other susceptible subjects they progress to involve more apical portions of the periodontium and cause loss of connective tissue attachment and alveolar bone. The same arguments are true for individual sites within a susceptible individual. Clearly some imbalance of the host–parasite relationship is occurring in the destructive lesions. This imbalance may be unique to that site and to gingivitis- and periodontitis-susceptible individuals generally.
# Clinically healthy gingiva
" _Clinically healthy gingiva_ " is a term used to describe the level of gingival health that may be attained by patients who clean their teeth in a meticulous manner. The oral surface of clinically healthy gingiva consists of keratinized oral epithelium that is continuous with the junctional epithelium (Fig. 11-1a) that is attached to the tooth surface by hemidesmosomes. Supporting the oral and junctional epithelia is a network of connective tissue that includes prominent collagen fibers, which maintain the shape of the gingival tissues and assist the relatively weak hemidesmosomal attachment of the junctional epithelium to the tooth. Immediately inside the junctional epithelium there is a dentogingival plexus, containing large numbers of venules, which supplies the epithelium with various nutrients as well as defense cells (leukocytes) (Fig. 11-1b,c).
The clinically healthy gingiva consistently features a small infiltrate of inflammatory cells that involves both the junctional epithelium and the subjacent connective tissue (Page & Schroeder 1976). This inflam-matory reaction occurs in response to the continuous presence of bacterial products in the crevice region (Fig. 11-2). The small inflammatory lesion also harbors lymphocytes and macrophages. Transudates and exudates of fluid that contains varying amounts of plasma proteins leave the vessels of the dentogingival plexus and arrive in the gingival crevice region as the gingival crevicular fluid (GCF) (Egelberg 1967; Cimasoni 1983). Among the leukocytes, neutrophils (polymor-phonuclear (PMN) cells) predominate in the crevice region (sulcus) and appear to migrate continuously through the junctional epithelium into the crevice (Figs. 11-3, 11-4). The recruitment of leukocytes from the gingival tissue to the crevice is due to the chemoattractant actions of products derived from the biofilm as well as from factors release by the host.
Sites with _clinically healthy gingiva_ appear to deal with continuous microbial challenges without progressing to clinical gingivitis (redness, swelling, bleeding on probing), probably because of several defensive factors that include:
* The intact barrier provided by the junctional epithelium
* The regular shedding of epithelial cells into the oral cavity
* The positive flow of fluid to the gingival crevice which may wash away unattached microorganisms and noxious products
* The presence in GCF of antibodies to microbial products
* The phagocytic function of neutrophils and macrophages
* The detrimental effect of complement on the microbiota.
The host–microbial interplay or balance, which constitutes the situation in clinically healthy gingiva, must clearly change if _gingivitis_ is to follow. Gingivitis will follow if there is sufficient plaque accumulation and retention such that microbial products evoke a more substantive inflammatory response. Lesions characteristic of gingivitis occupy a larger volume than those present in clinically healthy gingiva and are accompanied by more pronounced loss of collagen (Fig. 11-4). The inflammatory reaction will also initiate and perpetuate immune responses to the oral microorganisms. Gingival lesions may persist for many years without concomitant loss of periodontal attachment, destruction of periodontal ligament or evidence of bone loss. Clearly certain individuals (and sites), however, go on to develop periodontitis from gingivitis lesions. It is well known that individuals with obvious defects of the inflammatory system, e.g. neutrophil depletion or dysfunction, may rapidly develop advanced periodontitis. There is an accumulating body of evidence, which suggests that the host's immune response to periodontal pathogens may be quite different in subjects that become affected by advanced chronic periodontitis and those who will not progress beyond gingivitis.
# Gingival inflammation
The classical phases of "acute" and "chronic" inflammation are not easily applied in periodontal disease, probably because in clinically healthy gingiva a small lesion similar to an acute inflammatory reaction is already present. Subsequently developing chronic inflammatory changes become superimposed so that both acute and chronic elements co-exist in most gingival lesions.
**Fig. 11-1** (a) Buccal–lingual section of a normal beagle dog gingiva. The oral epithelium is continuous with a junctional epithelium, which is facing the enamel surface. (b) Micrograph of a buccal–lingual section of a normal (pristine) beagle dog gingiva illustrating the vasculature of the gingival unit. A thin vascular network is present beneath the junctional epithelium. (c) The thin vascular network (plexus) is shown in a mesial-distal section.
## Histopathological features of gingivitis
The clinical symptoms of inflammation may appear subtle in the early stages of gingivitis but the underlying histopathological changes, albeit present in a small compartment of the gingival tissues, are quite marked. Alterations in the vascular network occur with many capillary beds being opened up. Exudation of GCF and proteins from the dentogingival plexus will increase and this will make the tissue edematous and swollen. Inflammatory cells leave the vasculature and accumulate in the connective tissue lateral to the junctional epithelium. The connective tissue infiltrate is at first mainly comprised of macrophages and lymphocytes. As the cellular infiltrate becomes enlarged, plasma cells dominate the lesion and collagen depletion becomes quite substantial.
**Fig. 11-2** (a) Microphotograph of a buccal–lingual section of a normal beagle dog gingiva. A filter paper strip has been introduced between the junctional epithelium and the tooth. An increased permeability of the gingival vessels has occurred, identified by the presence of carbon particles, which were injected intravenously prior to biopsy. The carbon particles have become trapped in the open endothelial junctions, and so-called vascular labelling has occurred. (b) A mesio-distal section of the same gingival unit as in (a). (c) Higher magnification of (b) (from Egelberg 1967).
**Fig. 11-3** Leukocytes in the junctional epithelium. Observe that the volume of leukocytes decreases in an apical direction and approaches 0 in the most apical portion. Within the junctional epithelium, the mononuclear leukocytes are located in more basal layers, while the neutrophilic granulocytes are present primarily in the superficial portions of the junctional epithelium.
**Fig. 11-4** Immunostained section showing neutrophils in the junctional epithelium of healthy gingiva.
In this context it is important to emphasize that the lesion in the gingiva is closely related to the presence and extension of the biofilm on the associated tooth surface. Thus, findings from analyses of human autopsy material (Waerhaug 1952) indicated that the distance between plaque and calculus on the tooth surface and the inflammatory lesion in the gingiva never exceeded 1–2 mm.
# Different lesions in gingivitis/periodontitis
In 1976, Page and Schroeder divided the progressing lesion in the gingival/periodontal tissues into four phases: _initial, early, established_ , and _advanced_ stages or lesions. The descriptions of the initial and early lesion were intended to characterize the histopathology of clinically healthy gingiva and early stages of gingivitis, while the established lesion featured "chronic" gingivitis. The advanced lesion was considered to reflect the phase when gingivitis progressed to periodontitis and was a lesion that was consistently associated with attachment and bone loss. The evidence on which these descriptions were based was the prevailing information generated predominantly from animal biopsy material and some human adolescent samples.
Below we have used the terms initial, early, established, and advanced lesion to describe some features of the developing inflammatory process in the gingival and periodontal tissues. We have, however, not consistently adhered to the definitions and descriptions used in the original publication by Page and Schroeder.
## The initial lesion
Inflammation soon develops as plaque is allowed to form on the gingival third of the tooth surface. Within 24 hours marked changes are evident in the dentogingival plexus as more blood is brought to the area. Dilation of the arterioles, capillaries, and venules of the vascular network becomes a prominent feature (Fig. 11-2). Hydrostatic pressure within the microcirculation increases and intercellular gaps form between adjacent endothelial cells in the capillaries. Thus, an increase in the permeability of the microvascular bed results, so that proteins and, subsequently, fluids may exude into the tissues (Fig. 11-5).
The flow of GCF increases. Noxious substances released from the biofilm are diluted both inside the gingival tissue and in the crevice. Furthermore, bacteria and their products may be flushed away from the crevice region and end up in the saliva. Plasma proteins are part of GCF and include defensive proteins such as antibodies, complement and protease inhibitors, and other macromolecules with numerous functions. Already during this initial phase of the host response, PMN cell migration is facilitated by the presence of various adhesion molecules (intercellular adhesion molecule-1 (ICAM-1), endothelial leukocyte adhesion molecule-1 (ELAM-1) ), and other adhesions in the dentogingival vasculature. These molecules assist the binding of PMN cells to the venules and subsequently they help the cells to leave the blood vessel (Fig. 11-6). The PMNs migrate up a chemoattractant gradient to the crevice and are further assisted in their movement (1) by other adhesion molecules uniquely present on the junctional epithelial cells (Moughal _et al_. 1992) and (2) by the presence of microbial chemotactic factors. Lymphocytes are retained in the connective tissues on contact with antigens, cytokines or adhesion molecules and are therefore not so readily lost through the junctional epithelium and into the oral cavity, as are PMNs. Most lymphocytes have the ability to produce CD44 (CD, cluster determinant) receptors on their surfaces, which permit the binding of the cell to the connective tissue framework.
Within 2–4 days of plaque build-up the cellular response described above is probably well established and is maintained by chemotactic substances originating from the plaque microbiota as well as from host cells and secretions (Fig. 11-7).
## The early lesion
An ensuing and somewhat different gingival lesion will become present after several days of plaque accumulation (Fig. 11-8). The vessels in the dentogingival plexus remain dilated, but their numbers increase due to the opening up of previously inactive capillary beds. The increased size and enhanced numbers of vascular units are reflected in increased redness of the marginal gingiva that is a characteristic clinical symptom during this phase (Egelberg 1967; Lindhe & Rylander 1975).
Lymphocytes and PMNs are also the predominant leukocytes in the infiltrate at this stage of gingivitis and very few plasma cells are noted within the expanding lesion (Listgarten & Ellegaard 1973; Payne _et al_. 1975; Seymour _et al_. 1983; Brecx _et al_. 1987). Several fibroblasts within the lesion exhibit signs of degeneration. This probably occurs through apoptosis and serves to remove fibroblasts from the area, thus permitting more leukocyte infiltration (Page & Schroeder 1976; Takahashi _et al_. 1995). Similarly breakdown of collagen fibers occurs in the infiltrated area. This net loss of collagen fibers will provide space for the infiltrating cells.
The basal cells of the junctional and sulcular epithelium now proliferate. This represents an attempt by the body to enhance the "mechanical" barrier to plaque bacteria and their products. Epithelial rete pegs can be seen invading the coronal portion of the lesion in the connective tissue (Schroeder 1970; Schroeder _et al_. 1973). Tissue alterations during this phase also involve the loss of the coronal portion of the junctional epithelium. A niche forms between the epithelium and the enamel surface and a subgingival biofilm may now form.
**Fig. 11-5** Gingival alterations which occurred during a 28-day period of plaque accumulation and gingivitis development in beagles. (a) Normal gingiva. (b) Day 4. (c) Day 7. (d) Day 14. (e) Day 21. (f) Day 28 of undisturbed plaque accumulation. Note the gradually developing plaque on the tooth surfaces and the inflammatory changes in the gingiva. The vascular reaction is illustrated by a gradually increasing number of vessels in the gingival margin. (g) Gingival index (GI), plaque index (PLI) and gingival exudate alterations (exudate) that occurred during the experimental gingivitis period. (h) In gingival biopsy specimens obtained at various time intervals it can be seen that the inflammatory cell infiltrate (ICT) in the gingiva gradually increased in size.
This so-called early lesion may persist for long periods and the variability in time required to produce an established lesion may reflect variance in susceptibility between subjects.
## The established lesion
As the exposure of plaque continues there is a further enhancement of the inflammatory response of the gingival tissue. The flow of GCF is increased. The connective tissue as well as the junctional epithelium is transmigrated by an increased number of leukocytes.
The lesion, as defined by Page and Schroeder (1976), is dominated by plasma cells. This conclusion was based mainly on data from animal experiments. Results from examinations of human biopsies, however, revealed that in young individuals lymphocytes occupied a somewhat larger proportion of the infiltrate than plasma cells (Brecx _et al_. 1988; Fransson _et al_. 1996). On the other hand, in old subjects, plasma cells were the dominant cell type in established gingivitis lesions (Fransson _et al_. 1996).
Collagen loss continues as the inflammatory cell infiltrate expands, resulting in collagen-depleted spaces extending deeper into the tissues, which then become available for infiltration and accumulation of leukocytes (Figs. 11-9, 11-10). During this time the dentogingival epithelium continues to proliferate and the rete pegs extend deeper into the connective tissue in an attempt to maintain epithelial integrity and a barrier to microbial entry. The junctional epithelium is substituted by a pocket epithelium that is not attached to the tooth surface. This allows for a further apical migration of the biofilm. The pocket epithelium harbors large numbers of leukocytes, predominantly PMNs. In comparison to the original junctional epithelium, the pocket epithelium is more permeable to the passage of substances into and out of the underlying connective tissue. This pocket epithelium may be ulcerated in places. Figure 11-11 schematically illustrates the alterations which occur during the development of gingivitis and periodontitis.
**Fig. 11-6** (a) ICAM-1 immunohistochemical staining of a gingival biopsy sample during an experimental gingivitis study in humans after day 7. ICAM-1 positive blood vessels and junctional epithelium can be clearly seen. (b) Higher magnification of (a) showing the extensive junctional epithelium staining. (c) Higher magnification of (a) showing the ICAM-1 positive vessels within the connective tissue.
**Fig. 11-7** Schematic illustration of the process whereby neutrophils are attracted into the junctional epithelium and crevice region.
**Fig. 11-8** Buccal–lingual section of beagle dog gingiva with an early lesion. Note the epithelial rete pegs in the coronal portion of the lesion.
**Fig. 11-9** Buccal–lingual section of beagle dog gingiva exhibiting an established lesion. The junctional epithelium is replaced by a pocket epithelium and rete pegs extend deep into the infiltrated connective tissue.
**Fig. 11-10** Detail of Fig. 11-9. Note the large number of leukocytes in the inflammatory cell infiltrate and the pocket epithelium.
Two types of established lesion appear to exist: one remains stable and does not progress for months or years (Lindhe _et al_. 1975; Page _et al_. 1975), while the second becomes more active and converts more rapidly to a progressive and destructive advanced lesion.
## The advanced lesion
As the pocket deepens, the biofilm continues its apical downgrowth and flourishes in this anaerobic ecological niche. The gingival tissues offer reduced resistance to periodontal probing.
The inflammatory cell infiltrate extends further apically into the connective tissues. The advanced lesion has many of the characteristics of the established lesion but differs importantly in that loss of connective tissue attachment and alveolar bone occurs (Fig. 11-12). The damage to the collagen fibers is extensive. The pocket epithelium migrates apically from the cemento-enamel junction, and there are widespread manifestations of inflammation and immunopathological tissue damage. The lesion is no longer localized to the gingival tissues, but the inflammatory cell infiltrate extends laterally and apically into the connective tissue of the true attachment apparatus. It is generally accepted that plasma cells are the dominant cell type in the advanced lesion (Garant & Mulvihill 1972; Berglundh & Donati 2005).
In summary, in the progression from health to gingivitis and on to periodontitis there are many unknown factors related to timing. In addition, there is extensive subject and site variability in both exacerbating factors and innate susceptibility.
**Fig. 11-11** Schematic illustration of the changes in the gingival tissues during the development of gingivitis and periodontitis. The most significant differences are in the extent and composition of the inflammatory infiltrate and the epithelial proliferation in gingivitis, and the apical migration of epithelium and bone loss seen in periodontitis lesions. CEJ: cemento-enamel junction.
**Fig. 11-12** Buccal–lingual section of a periodontitis (advanced) lesion in a beagle dog. Note the apical extension of the inflammatory cell infiltrate and the loss of connective tissue attachment and supporting bone. CEJ: cemento-enamel junction.
# Host–parasite interactions
## Microbial virulence factors
Periodontal disease is initiated and sustained by factors (substances) produced by the subgingival microbiota (the biofilm). Some of these substances can directly injure host cells and tissues. Other microbial constituents may activate inflammatory or cellular and humoral immune systems that cause damage to the periodontal tissues. It is the latter pathway which accounts for most injury to the periodontal tissues.
### Microbial invasion
The invasion of the dentogingival epithelium by spirochetes was conclusively documented by Listgarten (1965) who studied the histopathology of lesions of necrotizing ulcerative gingivitis (ANUG). Although there have been numerous reports of microbial invasion in other forms of gingivitis and periodontitis, the significance of these observations is unclear. Even if bacteria can be found in the tissues, it is not known whether this represents true invasion (i.e. microbial colonization and proliferation within the tissues) or displacement or translocation of bacteria from the biofilm into the soft tissues. In conclusion, it is not known yet whether microbial invasion presents an important challenge to the host or represents an artifact.
### Enzymes
Microorganisms produce a variety of soluble enzymes that may digest extracellular host proteins and other molecules and thereby produce nutrients for bacterial growth. In addition to enzymes, bacteria also release numerous, harmful metabolic waste products, such as ammonia, indole, hydrogen sulfide, and butyric acid.
Amongst the enzymes released by bacteria in the biofilm, _proteases_ (proteinases) are capable of digesting collagen, elastin, fibronectin, fibrin, and various other components of the intercellular matrix of both epithelial and connective tissues. One protease that has attracted much attention is the Arg1-protease produced by _Porphyromonas gingivalis_ for which high potency is claimed. This protease, in addition, has the capability to induce a strong humoral immune response (Aduse-Opoku _et al_. 1995). Another protease, leukotoxin, was a focus of interest for many years, but as yet no _in vivo_ evidence exists for its claimed role in periodontal tissue destruction (Haubek _et al_. 1995). This leukotoxin has been studied in both America and Europe but it appears that the strains of _Aggregatibacter actinomycetemcomitans_ that produce the protease differed (Haubek _et al_. 1995). It seems that the more virulent form, which produces leukotoxin in excess and thus has great capacity to kill leukocytes, is common in strains from America but virtually absent in strains from Europe, despite identical disease prevalence.
### Endotoxin
_Lipopolysaccharide_ s (LPSs) of Gram-negative microorganisms are capable of invoking both the inflammatory and immune responses as they interact with host cells. Many of the functions attributed to LPS are associated with their ability to stimulate the production of cytokines. LPS also has profound effects on blood coagulation and on the complement system. The properties of LPS, as well as of _lipoteichoic acids_ (LTAs) of Gram-positive bacteria, are numerous and may be influenced by many other molecules that interact with these outer membrane structures. LPS and LTA are produced and released from microorganisms present in the subgingival biofilm and cause release of chemical mediators of inflammation to produce vascular permeability and encourage, through chemotactic actions, inflammatory cells to move into and accumulate in the gingival tissues. Furthermore, leukocytes are stimulated to release proinflammatory agents and cytokines.
_Summary_ : Microbes are capable of producing a variety of substances which either directly or indirectly harm the host. The main detrimental effect may be the host's own innate, inflammatory, and immune response to the foreign molecules and antigens of the microbe.
# Host defense processes
Host–parasite reactions can be divided into innate (non-specific) and adaptive (specific) responses. Innate reactions include the inflammatory response and do not involve immunological mechanisms. Adaptive reactions that include immunological responses tend to be very effective as the host response is specifically "tailored" to the offending pathogen (s).
## Important aspects of host defense processes
### Inflammatory processes
The host has an extensive repertoire of defensive responses to ward off invasion by pathogens. Such responses may either result in a rapid resolution of the lesion (e.g. a staphylococcal abscess which heals) or that no lesion at all develops in the affected tissue (e.g. smallpox infection in a successfully vaccinated host). An ineffective response may result in a chronic lesion that does not resolve (e.g. tuberculosis) or if excessively deployed, in a lesion in which the host responses contribute significantly to tissue destruction (e.g. rheumatoid arthritis or asthma).
In the classical description of inflammation, a tissue is presented that appears macroscopically red, swollen, hot, and painful, and with possible loss of function in specific sites. Redness and heat are due to vasodilatation and increased blood flow. Swelling is a result of increased vascular permeability and leakage of plasma proteins that create an osmotic potential that draws fluid into the inflamed tissues. Related to the vascular changes there is an accumulation of inflammatory cells infiltrating the lesion. Pain is rarely experienced in aggressive and chronic periodontal disease, but could theoretically occur due to stimulation of afferent nerves by chemical mediators of inflammation in necrotizing periodontal disease. Impairment of function is classically illustrated in arthritically swollen joints.
### Molecules, cells, and processes
#### _Proteinases (proteases)_
Periodontal disease results in tissue degradation, and thus proteases, derived both from the host and from bacteria, are central to the disease processes. Proteinases (collagenase, elastase-like and trypsin-like, as well as serine and cysteine proteinases) cleave proteins by hydrolyzing peptide bonds and may be classified into two major classes, _endopeptidases_ and _exopeptidases_ , depending on the location of activity of the enzyme on its substrate. Efforts have been made to assess endopeptidase activity in gingival tissues and in GCF. A reduction of protease levels following treatment was obtained in several studies.
#### _Proteinase inhibitors_
Release of proteinases in the gingiva and the crevicular area promotes inflammatory reactions and contributes to connective tissue damage via several pathways. In contrast, _proteinase inhibitors_ would dampen the inflammatory process. Among such inhibitors alpha-2 macroglobulin (A2-M) and alpha1 antitrypsin (A1-AT) must be recognized. In fact, gingival collagenase inhibition by A2-M has been demonstrated to occur in gingival tissues and polymorphonuclear leukocyte (PMN) collagenase is also inhibited by A1-AT.
Many host and microbial enzymes are likely to be present in the crevice at any one time. Realizing the potentially destructive features of such enzymes, consideration should be given to the source of these enzymes, their relative proportions and the inhibitory mechanisms available within the crevice. The main enzyme activity is host derived and specific and non-specific inhibitors are plentiful within the crevice and thus enzyme activity will be localized and short-lived.
### Matrix metalloproteinases
The periodontium is structurally comprised of fibrous elements, including collagen, elastin, and glycoproteins (laminin, fibronectin, proteoglycans), minerals, lipids, water, and tissue-bound growth factors. In addition there exists a large variety of extracellular matrix components, including tropocollagen, proteoglycans, and other proteins (elastin, osteocalcin, osteopontin, bone sialoprotein, osteonectin, and tenascin). All of these matrix components are constantly in a state of turnover and thus there is much matrix enzyme activity in health, disease, and tissue repair and remodeling (Kinane 2001). Matrix metalloproteinases (MMPs) are responsible for remodeling and degradation of the matrix components.
One of the MMPs that has received much attention is the _neutrophil (PMN) collagenase_ that is found in higher concentrations in inflamed gingival specimens than in clinically healthy gingiva. The increased presence of these MMP enzymes in diseased over healthy sites (Ohlsson _et al_. 1973), their increase during experimental gingivitis (Kowashi _et al_. 1979), and decrease after periodontal treatment (Haerian _et al_. 1995, 1996) suggest that MMPs from PMNs are involved in periodontal tissue breakdown.
The periodontal ligament is one of the most metabolically active tissues in the body, and collagen metabolism represents most of this activity. The biological reason for this activity probably relates to its ability to adapt to occlusal forces generated during function. An important feature of connective tissues in general and the periodontal ligament in particular, is the process of constant renewal of the extracellular matrix components involving MMP.
It is evident that the activity of MMPs and their inhibitors is associated with tissue turnover as well as with gingivitis, destructive periodontitis, and with the healing of the periodontal tissues following therapy.
### Cytokines
Cytokines are soluble proteins, secreted by cells involved in both the innate and adaptive host response, and act as messenger molecules that transmit signals to other cells. They have numerous actions that include initiation and maintenance of immune and inflammatory responses and regulation of growth and differentiation of cells. Cytokines are numerous, many have overlapping functions, and they are interlinked to form an active network which controls the host response. Control of cytokine release and action is complex and involves inhibitors and receptors. Many cytokines are capable of acting back on the cell that produced them so as to stimulate (or downgrade) their own production and the production of other cytokines.
_Interleukins_ are important members of the cytokine group and are primarily involved in communication between leukocytes and other cells, such as epithelial cells, endothelial cells, and fibroblasts engaged in the inflammatory process. In addition, _interleukin (IL)-1a_ , _IL-1b_ , and _tumor necrosis factor (TNF)-alpha_ stimulate bone resorption and inhibit bone formation.
A series of more than 20 molecules has been identified, that act to recruit defense cells (PMNs, macrophages, lymphocytes) to areas where they are required. These chemotactic cytokines play an important role in cell-mediated immune responses.
### Prostaglandins
Prostaglandins are derivatives of arachidonic acid and are important mediators of inflammation. Macrophages in particular, but also several other cells produce prostaglandins, particularly PGE2 which is a potent vasodilator and inducer of cytokine production by various cells. PGE2 acts on fibroblasts and osteoclasts to induce production of MMPs, which are of importance for tissue turnover and tissue destruction in gingivitis and periodontitis (see above).
### Polymorphonuclear leukocytes
The PMN is the predominant leukocyte within the gingival crevice/pocket in both health and disease. PMNs are attracted from the circulation to the affected area via chemotactic stimuli elicited from, for example, microorganisms in the biofilm, and hostderived chemokines. _Elastase_ , a serine protease, is contained in the primary granules of the PMN. Elastase may cause tissue breakdown and is present with increased activity at sites of gingival inflammation. _Lactoferrin_ is contained in the secondary granules of the PMN, and is released during PMN migration and is associated with PMN activation. Differences in the relative amounts of elastase and lactoferrin were found in periodontal sites with varying degrees of inflammation. A greater proportion of lactoferrin to elastase was found in advanced periodontitis lesions than in gingivitis sites. This variation in the release of primary and secondary granule enzymes by PMNs may indicate alterations in PMN function in different disease environments (Fig. 11-13).
### Bone destruction
Tissue destruction is one of the hallmarks of periodontitis and involves connective tissue structures and alveolar bone. Degradation of collagen and matrix components in the connective tissue is regulated by inflammatory processes in the periodontitis lesion and includes the production of various MMPs (see above).
Bone resorption is mediated by osteoclasts and takes place concomitant with the breakdown of the connective tissue attachment during disease progression. Thus, the mechanisms involved in bone resorption respond to signals from inflammatory cells in the lesion and initiate degradation of bone in order to maintain a "safety" distance to the periphery of the inflammatory cell infiltrate. Analyses of human autopsy material and biopsy specimens from animal experiments have demonstrated that the alveolar bone in periodontitis is separated from the inflammatory cell infiltrate by a 0.5–1 mm wide zone of a non-infiltrated connective tissue. This encapsulation of the lesion is an important feature of host defense mechanisms in periodontitis and bone resorption is thus required to re-establish dimensions of the connective tissue capsule following a phase of attachment loss during disease progression.
Osteoclasts are multinucleated cells that develop from osteoclast progenitor cells/macrophages and exhibit specific abilities to degrade organic and inorganic components of bone. As mentioned above, different mediators such as IL-1 beta, PGE2 and TNF-alpha but also IL-6, IL-11 and IL-17 may act as activators on osteoclasts. Another and more important system in osteoclast activation includes the receptor activator of nuclear factor-kappa beta (RANK), the RANK ligand (RANKL) and osteoprotegrin (OPG). RANK is a receptor expressed by osteoclast progenitor cells. RANKL and OPG are cytokines that belong to the TNF family and are produced by osteoblasts and bone marrow stromal cells. While RANKL promotes activation of osteoclasts, OPG has the opposite effect. Thus, the binding of RANKL to the RANK will result in the differentiation of osteoclast progenitor cells into active osteoclasts, while OPG that binds to RANKL will inhibit the differentiation process (for review see Lerner 2006). Analyses of human biopsy specimens revealed that levels of RANKL were higher and levels of OPG were lower in sites with periodontitis than in sites representing healthy gingiva (Crotti et al. 2003; Liu et al. 2003).
**Fig. 11-13** Major events in the encounter between PMNs and invading microorganisms. (a) Once PMNs emigrate from the microcirculation, they migrate toward bacteria under the influence of chemotactic factors. Upon contact PMNs adhere to the organisms (many types of bacteria must be opsonized to facilitate PMN adherence and phagocytosis). (b) Coincident with adhesion, PMNs begin to phagocytose these organisms. This is accomplished as the plasma membrane flows around and then invaginates to internalize attached organisms which are now contained within phagosomes. Several bacteria can be phagocytosed simultaneously by the PMN. (c) As these events occur PMNs demonstrate dramatic metabolic alterations including: an elevation in glycolysis; a marked rise in oxygen consumption; and increased glucose utilization by the hexose monophosphate shunt. Glycolytic metabolism of glucose provides the energy required by phagocytosis and also results in a drop in intracellular pH due to the formation of lactate. The oxidative burst is largely the result of NADPH oxidase activity (an enzyme associated with the cell membrane), which oxidizes NADPH to NADP and results in the reduction of oxygen to various free radicals. These oxidants are released into the phagosome to kill bacteria. The hexose monophosphate shunt provides for the regeneration of NADPH. At the same time, lysosomes are mobilized toward the developing phagosome and fuse with the phagosome membrane, giving rise to a phagolysosome. Lysosomal antimicrobial compounds (myeloperoxidase, lysozyme, lactoferrin, cationic proteins, etc.) are discharged into the vacuole. The combination of oxidative and non-oxidative (acid pH, lysosomal agents) pathways explains how PMNs kill ingested organisms. Lysozyme and neutral proteases (particularly elastase) derived from lysosomes digest and dispose of the dead organisms. Before invagination is completed, biologically active products can be released from the phagosome into the external environment. These agents play a role in extracellular killing of microorganisms but also may adversely affect surrounding host cells and tissue structures.
The RANK/RANKL/OPG system is also involved in bone degradation processes that are induced by proinflammatory cytokines such as PGE2, TNFalpha, IL-1 beta, IL-6, IL-11, and IL-17. In addition, the production of the RANKL is not confined to osteoblasts and bone marrow stromal cells. Thus, the contribution of RANKL by T cells and other cells in inflammation must be considered. The role of T cells, however, is unclear given that this cell not only produces RANKL but also inhibitors of RANKL, such as interferon (IFN)-gamma and IL-4 (Takayanagi 2005).
In summary, bone resorption is part of the encapsulation process of the inflammatory cell infiltrate in periodontitis. Osteoclasts develop from osteoclast progenitor cells or macrophages and are regulated by the RANK/RANKL/OPG system and/or proinflammatory cytokines.
## The innate defense systems
Innate immune mechanisms operate without any previous contact with the disease-causing microorganism. These mechanisms include the _barrier function_ of the oral epithelia and _vascular_ and _cellular_ aspects of the _inflammatory responses_.
The gingival crevice is the first region of the periodontium that comes into contact with microorganisms that attempt to attach and colonize the area. Several innate mechanisms serve to prevent such microbial colonization and include (1) the mechanical washing effect of the _saliva_ and _GCF_ , and (2) the detrimental effect on bacterial growth of _constituents_ of these fluids (e.g. antibodies and proteases, complement, salivary lactoferrin, and other proteins).
The oral mucosa itself is not simply a barrier but has a chemical composition that may be harmful to bacteria. Furthermore, the cells of the epithelium can respond to the bacteria by (1) producing antimicrobial peptides, including beta-defensin etc., that kill the microbes, (2) releasing other molecules, such as IL-1 beta, capable of inducing or enhancing the local inflammatory reaction, and (3) releasing IL-8, a chemokine which attracts host defense cells such as neutrophils and macrophages to reduce the microbial insult. The epithelium can also respond by increasing the expression of surface molecules such as cell adhesion molecules that, in turn, may interact with proinflammatory cytokines and chemokines to assist the recruitment of leukocytes to the crevice.
Molecules in saliva, such as _lactoferrin_ , may bind iron, change the local environment, and hence prevent microbial proliferation. In addition, lactoferrin is highly bactericidal. Molecules present in the GCF include _complement_ , which can kill bacteria directly or together with antibodies, and can bring PMNs to the region (via chemotaxis) and hereby initiate and facilitate the process of phagocytosis.
The concept that epithelial and endothelial cells and fibroblasts are structural cells not involved in specific immune or inflammatory reactions has been disproved. Toll-like receptors are structures evolved to detect bacterial challenge and are present on all human cells, including epithelial and endothelial cells, and may bind microbial cell molecules, such as lipopolysaccharides, microbial fimbriae, and lipoteichoic acid. This suggests that even innate responses of the host may be tailored to particular bacteria. The host and its pathogens have developed together over millions of years and have learned to recognize, mimic, and utilize each other's systems in highly sophisticated ways.
### Innate immune processes
The primary etiologic agent in the initiation of the gingivitis is the accumulation of the bacterial plaque biofilm in the gingival crevice. Irritation of the gingival tissues induces an "inflammatory response". The rapid inflammatory process that occurs in gingivitis is an early step in the initiation of the overall immune and inflammatory response, and is part of the _innate immune_ system; i.e. it is part of the inherent biologic responses that require no prior experience. Inflammation is an extremely well coordinated process that comprises increased vascular permeability, migration of PMN leukocytes, monocytes, and lymphocytes into the affected tissues, and activation of cells to secrete inflammatory mediators that guide an amplifying cascade of biochemical and cellular events. Although inflammation was once considered a nonspecific arm of the immune response, the inflammatory response is actually a relatively specific event, which is carefully orchestrated through a wideranging repertoire of receptors and corresponding ligands.
The specific nature of inflammation allows rapid identification and a better tailored response to infection. For example, bacterial lipopolysaccharide (LPS), a common antigen of Gram-negative bacteria, is specifically recognized by host receptors such as soluble LPS binding protein, membrane-associated CD14 and toll-like receptors (TLRs). The interactions between LPS and these host proteins activate an intracellular cascade of events which leads to secretion of specific inflammatory mediators and antimicrobial proteins. These specific interactions may explain why the inflammatory response to Gram-positive bacteria is less pronounced than the inflammatory response to Gram-negative bacteria during _in vitro_ and _in vivo_ inflammatory assays. In addition, the discovery that there is a group of TLRs that can recognize a wide but restricted set of pathogen-associated molecular structures may explain how different bacteria induce different responses. In fact, even LPS from different bacteria may activate different TLRs, and induce a different response. These interactions enable the host to sample and sort its current environmental condition, to discriminate between pathogenic bacterial challenges, and to mount a selective and appropriate response. Recent data indicate that TLRs may respond to bacterial and non-bacterial challenges, such as oxidized low-density lipoprotein cholesterol. Thus the host may respond through inflammation to a range of challenges, from bacteria to cholesterol. However, the nature of the response differs and its character depends on the microbial triggering of specific receptors, the signal transduction pathways, and the way cells and tissues respond to these signals in terms of cytokine and defensive protein production.
During experimental gingivitis studies, individual variations in the rate of development of gingival inflammation have been noted (see Chapter 17) and the difference in gingivitis susceptibility is not simply due to plaque differences. Trombelli _et al._ (2004) have also shown that while all individuals will develop some degree of inflammation, there are interindividual differences in response to dental plaque. These differences may be explained by genetics or environment. Using the "twin study approach", Michalowicz _et al_. (2000), could not demonstrate an association between gingival inflammation and genetics, perhaps due to the cross-sectional approach of the study. However, their data support the major role of genetics in the development of periodontitis, in which gingival inflammation is considered as a major part of the pathogenesis. In summary, all of the above studies are consistent with the hypothesis of genetically based host modulation of gingival inflammation.
### Variation in microbial modulation of innate responses
Innate immunity represents the inherited resistance to microbial infection, which is detected by patternrecognition receptors (PRRs). PRRs are strategically located at the interface between the mammalian host and the microbes, and have evolved to recognize conserved microbial motifs, known as microbeassociated molecular patterns (MAMPs). TLRs constitute an evolutionarily ancient PRR family, which plays a central role in the induction of innate immune and inflammatory responses. Not surprisingly, TLRs are expressed predominantly in cells which mediate first-line defense, such as neutrophils, monocytes/ macrophages, and dendritic cells, as well as epithelial cells. Distinct members of the TLR family respond to different types of MAMPs, endowing the innate response with a relative specificity. The discovery of TLRs and the identification of their ligand repertoire have prompted the "bar code" hypothesis of innate recognition of microbes. According to this concept, TLRs read a "bar code" on microbes which is then decoded intracellularly to tailor the appropriate type of innate response. For instance, simultaneous activation of TLR5 and TLR4 would be interpreted as infection with a flagellated Gram-negative bacterium, whereas activation of TLR2 together with TLR5 would likely indicate the presence of a flagellated Gram-positive bacterium. However, this "bar code" detection system would not readily distinguish between pathogens and commensals, since they both share similar invariant structures (e.g., LTA, LPS, or flagellae). The immune system, however, generally elicits a vigorous inflammatory response against pathogens aimed at eliminating them, whereas it normally tolerates commensals.
## The immune or adaptive defense system
In contrast to the innate host response, the adaptive response utilizes strategies of recognition, memory, and binding to support the effector systems in the elimination of challenging elements. Thus, the host response to factors released by microbial plaque in periodontal diseases involves a series of different effector mechanisms that are activated by the _innate_ immune response. The effector mechanisms in this first line of defense may be insufficient to eliminate a given pathogen. The _adaptive_ immune response, which is a second line of defense, is then activated. The adaptive response improves the host's ability to recognize the pathogen.
_Immune memory_ and _clonal expansion_ of immune cells are the hallmarks of adaptive immunity. Although the effector mechanisms activated by the adaptive system appear to be similar to those of the innate system, the antimicrobial activities in adaptive immunity are specialized functions regulated by lymphocytes. This means that the defense mechanisms in the gingiva are synchronized by the communication through signals (cytokines) between specific groups of cells.
**Fig. 11-14** Distribution of cell proportions in periodontitis lesions. Adapted from Berglundh & Donati (2005).
The cells involved in the adaptive response and which reside in the inflammatory lesion in sites with periodontitis have been described in several studies that included a histopathological analysis of the composition of the cell infiltrate. In a recent review on aspects of adaptive host response in periodontitis a meta-analysis was made with regard to the cell composition in periodontitis lesions (Berglundh & Donati 2005). Plasma cells represent about 50% of cells, while B cells comprise about 18%. The proportion of B cells is larger than that of all T cells. T helper cells occur in larger numbers than T cytotoxic cells. PMN cells and macrophages represent less than 5% of cells (Fig. 11-14). In the review it was further observed that lesions in aggressive and chronic forms of periodontitis exhibit similar features with respect to cellular composition. In both chronic and aggressive forms of periodontitis the proportions of plasma cells and B cells appear to be larger in lesions obtained from sites representing severe periodontitis than in lesions from areas with moderate or mild periodontitis.
The following outline provides an overview of T cell and B cell characteristics and immunoregulatory mechanisms of adaptive host response in periodontitis (Fig. 11-15).
### Antigen presentation
The biofilm is consistently challenging the host. The antigens produced include proteins from Gram-positive bacteria and LPSs (endotoxins) from Gram-negative microorganisms. Antigen-presenting cells (APCs) have a unique ability to internalize and process antigens. Langerhans cells, macrophages, and dendritic cells are professional APCs and contribute to antigen recognition and early response mechanisms in host defense. B cells are considered to be important APCs in periodontitis and use the capacity of their memory systems in antigen presentation within the adaptive host response. The processed antigen (e.g. a peptide) inside the APC binds to an important carrying molecule. This molecule, termed _class-II_ molecule of the major histocompatibility complex (MHC), transports the peptide to the cell surface. The peptide will thus, together with the MHC class-II molecule, become identifiable (i.e. presented) to T cells.
**Fig. 11-15** Immune regulation in periodontal disease.
### T cell receptors
The presentation of the processed antigen involves interactions with receptors on the T cells: T cell receptors (TCRs). It is in this context important to realize that the resulting immune response from this presentation varies with the build up of the TCR. The TCR is comprised of two glycoprotein chains, mainly alpha and beta (Fig. 11-15). The external portion of these alpha and beta chains contains a variable segment, which has many features in common with the antigen-binding site at immunoglobulins. This means that the composition of the variable segment in the alpha or the beta chain determines the type of immune reaction that will occur.
It is well known that the composition, or expression, of the variable chains of TCRs (TCR alpha/beta phenotype or genes) is of importance in several autoimmune diseases (Bröker _et al_. 1993) and also in periodontal disease (Nakajima _et al_. 1996; Yamazaki _et al_. 1997; Geatch _et al_. 1997; Berglundh _et al_. 1998). The results reported on TCRs in periodontitis have consistently revealed that the TCR repertoire of T cells in the local periodontitis lesions differs from that of T cells in peripheral blood. In other words, factors present at the local site, i.e. antigens released from microorganisms in the subgingival biofilm, may influence the expression of TCRs in the periodontitis lesion (Mathur _et al_. 1995). This fact also explains the differences observed in the distribution of TCRs in gingival tissues before and after periodontal therapy (Berglundh _et al_. 1999) as well as between adult subjects with advanced chronic periodontitis and children with aggressive periodontitis (Berglundh _et al_. 2001).
### T cell dependent (mediated) processes
Cytokines produced by T helper (Th) cells regulate most functions within the adaptive defense system in the periodontal tissues. Th cells occur as Th-1 and Th-2 cells. Both Th-1 and Th-2 cells express the CD4 marker but are distinguished from each other by their cytokine production (cytokine profiles) (Fig. 11-15). Th-1 cells produce _IL-2_ , _IFN-gamma_ , and _TNF-alpha._ These cytokines have several functions and may activate other T cells, including the so-called cytotoxic T cells (Tc).
Tc cells express the CD8 marker and serve as guards against microorganisms that are capable of invading host cells, i.e. viruses and invasive bacteria. In the infected host cells, the antigen (e.g. a peptide) produced by the intracellularly located pathogen binds to MHC class-I molecules, which carry the peptide to the surface of the infected host cell. The Tc cell has the ability to recognize this alteration in the MHC class-I molecules and exerts its host defense action by destroying the membrane of the infected cell and by activating its nucleases. This cell-mediated host response orchestrated by the Tc cell also includes activation of macrophages.
It is well established that CD8-positive cells are found in smaller numbers in gingivitis/periodontitis lesions than CD4-positive cells (Yamazaki _et al_. 1995; Berglundh _et al_. 2002a; Berglundh & Donati 2005). It may therefore be anticipated that viruses and other invasive microorganisms do not constitute a major part of the antigens in peridodontitis.
### B cell regulation processes
The large amounts of soluble and accessible antigens occurring in the periodontal environment require the involvement of host defense systems different from those involved in cell-mediated immunity. Specific antibodies (immunoglobulins), occurring in fluids such as plasma or GCF, have the ability to bind to antigens. This type of host defense is called _humoral immune response_. In the process through which the antigen becomes bound to the antibody, certain effector systems, e.g. _complement_ , are activated. The activation of the complement system, in turn, mediates PMN and macrophage migration to the site and phagocytosis is initiated. The process in which the antibody contributes to the elimination of antigens by enhancing phagocytosis is termed _opsonization._
Antibodies are produced by plasma cells that represent the final stage in B cell proliferation. The activation and differentiation of B cells require the presence of certain cytokines, IL-4, IL-5, and IL-6, that are mainly produced by Th-2 cells (Gemmell & Seymour 1998). Since plasma cells and B cells constitute a major part of the leukocytes in advanced periodontitis lesions, it is reasonable to assume that Th-2 functions may dominate over those dependent on Th-1. In early studies it was indeed suggested that the immunoregulatory mechanisms in the advanced periodontitis lesions involve Th-2 cells to a larger extent than Th-1 cells (Seymour _et al_. 1993, 1996). Several later studies have, however, failed to confirm this observation (Yamazaki _et al_. 1994, 1997; Fujihashi _et al_. 1996; Prabhu _et al_. 1996; Yamamoto _et al_. 1997). Berglundh _et al_. (2002a) reported that the connective tissue lesions in advanced periodontitis contained similar proportions of cells expressing cytokine profiles characteristic for Th-1 (IFN-gamma and IL-2) and Th-2 (IL-4 and IL-6) cells. Current data thus suggest that chronic periodontitis lesions are regulated by a combined Th-1 and Th-2 function.
The immunoglobulins produced by plasma cells in the gingival lesions are mainly directed towards antigens present in the subgingival biofilm. Data have been presented, however, which indicate that antibodies directed against host tissue components, i.e. _autoantibodies_ , may also occur in the gingival lesion (Hirsch _et al_. 1988, 1989; Jonsson _et al_. 1991). _Auto-reactive B cells_ , also referred to as _B-1 cells_ , are associated with the production of auto-antibodies. Large amounts of B-1 cells are present in the peripheral blood of patients with autoimmune disease, such as rheumatoid arthritis and Sjögren's syndrome (Youinou _et al_. 1988). The presence of circulating auto-reactive B cells in periodontitis patients has also been described. Thus, Afar _et al_. (1992) and Berglundh _et al_. (1998, 2002b) reported that B-1 cells occur in large numbers in the peripheral blood of patients with advanced chronic periodontitis. The gingival lesion in patients with such advanced periodontitis also contains a substantial number of B cells out of which about 30% exhibit auto-reactive characteristics (Sugawara _et al_. 1992; Berglundh _et al_. 2002b).
In this context it should be recognized that clinically successful, non-surgical periodontal therapy (i.e. resolution of gingivitis and reduction of sites with deep pockets) failed to alter the proportion of B-1 cells in peripheral blood (Berglundh _et al_. 1999). It was suggested that the elevated levels of B-1 cells in peripheral blood may not entirely reflect a response to microorganisms in the subgingival biofilm. Rather, it appears that the effector systems in the humoral immune response in periodontitis may also include production of antibodies directed to the periodontal tissues of the host.
In the humoral immune response the function, i.e. the avidity (binding strength to the antigen) of the antibody most also be considered. Thus, some but not all antibodies have a strong ability to opsonize bacteria and thereby prevent bacterial colonization. Account must also given to issues such as (1) whether antibody levels in the GCF or in serum or both are of importance for the protection of the host, (2) whether local levels of antibodies are merely a reflection of serum levels, or (3) whether significant antibody production by plasma cells present in the gingiva is taking place. In addition, there is evidence that the subclass of immunoglobulin produced has a bearing on aspects of its function such as complement fixation and opsonization. Thus, in aggressive periodontitis there seems to be a preponderance of IgG2 production over IgG1. This means that the functionally less effective IgG2 may play a role in rendering such patients more susceptible to periodontal tissue destruction (Wilson _et al_. 1995). Several studies suggest that assessments of the titer and avidity (the binding strength) of a patient's antibody to various microorganisms in the subgingival biofilm may be useful in the differential diagnosis and classification of periodontal diseases (Mooney _et al_. 1993).
IgG has four subclasses and IgA has two subclasses. Antibodies of different subclasses have different properties. Thus, IgG2 antibodies are effective against carbohydrate antigens (LPS) whereas the other subclasses are mainly directed against proteins. Kinane _et al_. (1997) studied the immunoglobulin subclasses (IgG1–4 and IgA1–2) produced by plasma cells in the gingival lesion of periodontitis patients (Fig. 11-16). The proportions of plasma cells producing IgG and IgA subclasses were similar to the proportions of these immunoglobulin subclasses in serum. IgG1-producing plasma cells were predominant (mean 63%) in the gingival lesions; 23% of all IgG-producing plasma cells produced IgG2 antibodies, while IgG3- and IgG4-producing cells were present in much smaller numbers (3% and 10% respectively).
**Fig. 11-16** Plasma cells within the periodontal gingiva. The mRNA for immunoglobulin production is noted in abundance within the plasma cell cytoplasms indicating that gingival plasma cells have the ability to produce antibodies locally (Kinane _et al_. 1997).
### The protective role of the immune responses
Recruitment of leukocytes into areas of injury or infection is essential for an effective host defense. The constant migration of T cells and other leukocytes to tissues throughout the body allows the immune system to protect the host from a variety of antigenic challenges.
Leukocyte migration into tissues is particularly prominent during inflammatory responses and results from the cytokine-induced expression of adhesion molecules on the surface of vascular endothelial cells (Kinane _et al_. 1991) (Fig. 11-7). Endothelial leukocyte adhesion molecule-1 (ELAM-1) and intercellular adhesion molecule-1 (ICAM-1) are crucial for cellular trafficking (Fig. 11-6). The changes in vascular adhesion molecule expression and numbers of infiltrating leukocytes during a 21-day experimental gingivitis episode were investigated by Moughal _et al_. (1992). ELAM-1 and ICAM-1 positive vessels as well as PMNs and T cells were identified within gingival biopsy specimens taken on days 0, 7, 14, and 21. Vascular endothelium expressed ELAM-1 and ICAM-1 both in clinically "healthy" tissue (day 0) and in experimentally inflamed tissue (days 7–21). Positive vessels were found mainly in the connective tissue subjacent to the junctional epithelium where the highest numbers of T cells and neutrophils were also seen. A gradient of ICAM-1 was found to exist in the junctional epithelium, with the strongest staining in the marginal (crevicular) portion. This observation, together with the vascular expression of ELAM-1 and ICAM-1 in both clinically "healthy" and inflamed tissue, suggests that the function of the adhesion molecules is crucial and that these molecules direct leu-kocyte migration towards the gingival crevice (Fig. 11-7). The importance of these mechanisms is highlighted by the rapid progress of periodontitis that is found in patients with insufficient levels of ELAM-1 and ICAM-1, i.e. subjects suffering from _leukocyte adhesion deficiency syndrome_ (LAD).
**Fig. 11-17** (a) Schematic illustration of the systemic humoral immune response to microbial antigens within the gingival crevice region. (b) Schematic illustration of the local cellular immune response within the gingival crevice region and how this is invoked by microbial antigens and the mechanism by which pertinent periodontal immune cells traffic to the periodontium.
### Specific antibody responses
_P. gingivalis_ and _A. actinomycetemcomitans_ are considered to be important pathogens in various forms of periodontal disease. Several studies have demonstrated that the antibody titers to these two organisms are increased in patients with periodontitis compared with subjects without disease (Kinane _et al_. 1993, 1999; Mooney & Kinane 1994).
Furthermore, Naito _et al_. (1987) and Aukhil _et al_. (1988) demonstrated that the serum titer to _P. gingivalis_ and _A. actinomycetemcomitans_ are con-Furthermore, Naito _et al_. (1987) and Aukhil sidered to be important pathogens in various forms _et al_. (1988) demonstrated that the serum titer to _P. gingivalis_ was _reduced_ in subjects with advanced periodontitis following successful treatment. In this regard a study by Mooney _et al_. (1995) must be recognized. They reported on specific antibody titer and avidity to _P. gingivalis_ and _A. actinomycetemcomitans_ in chronic periodontitis patients before and after periodontal therapy. The authors observed that _IgG avidities_ (the binding strength of the antibodies) to _P. gingivalis_ increased significantly and specific _IgA levels_ more than doubled as a result of treatment. Interestingly, only patients who had high levels of antibody before treatment showed a significant increase in antibody avidity. In addition, patients who originally had high levels of IgG and IgA to _P. gingivalis_ also had better treatment outcomes, in terms of a reduced number of deep pockets and sites which bled on probing, than patients with initially lower titers.
Antibody levels are probably dependent on a number of factors including previous exposure to the subgingival microbiota and the host's ability to respond to particular antigens. The effect of treatment on antibody level and avidity may be the result of an inoculation (transient bacteremia) effect that occurs during scaling and root planing. The reduction in the amount of bacteria, i.e. the antigen load, which occurs after subgingival scaling and root planing, may allow the activation of B cells (clones) that produce antibodies with high avidity.
The findings described above suggest that periodontal therapy affects the magnitude and quality of the humoral immune response to periodontal pathogens, that this effect is dependent on initial serostatus, and that, thus, initial serostatus may have a bearing on treatment outcome.
In conclusion, the humoral immune response, especially IgG and IgA, is considered to have a protective role in the pathogenesis of periodontal disease but the precise mechanisms are still unknown. Periodontal therapy may improve the magnitude and quality of the humoral immune response through a process of immunization.
### Homing – recruitment of cells to the periodontium
As explained previously, the recruitment of leukocytes into areas of injury or infection (homing) is essential for an effective host defense and the constant migration of leukocytes into the inflamed periodontal tissues results from the cytokineinduced expression of adhesion molecules on the surface of vascular endothelial cells. It has been suggested that antigen-presenting cells set up humoral immune response functions within peripheral lymph nodes (Fig. 11-17). Evidence exists, however, that homing of cells involved in both humoral and cellular immune responses is pronounced in diseased periodontal tissues. Recently Zitzmann _et al_. (2005a,b) reported on the specific "homing receptor" MadCAM-1 in periodontitis lesions. It is also possible that local proliferation of such leukocytes may occur in periodontitis. In an experimental gingivitis study in subjects who were treated for severe chronic periodontitis, Zitzmann _et al_. (2005b) reported that the presence of a residual inflammatory infiltrate influenced the reactions to _de novo_ plaque formation. Thus, the increase of (1) the size of the gingival lesion, (2) the proportions of T and B cells, and (3) the expression of vascular adhesion molecules (including MadCAM-1) that occurred during the 21-day plaque formation period was more pronounced in sites that contained residual inflammatory infiltrates than in sites with no or only small remaining lesions. In other words, the large number of T cells and B cells that occur in the periodontitis lesion may be attracted to the diseased site through selective homing which is enhanced by local T and B cell presence.
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# Chapter 12
# Modifying Factors
Richard Palmer and Mena Soory
* * *
Diabetes mellitus
Type 1 and type 2 diabetes mellitus
Clinical symptoms
Oral and periodontal effects
Association of periodontal infection and diabetic control
Modification of the host–bacteria relationship in diabetes
Periodontal treatment
Puberty, pregnancy, and the menopause
Puberty and menstruation
Pregnancy
Menopause and osteoporosis
Hormonal contraceptives
Tobacco smoking
Periodontal disease in smokers
Modification of the host–bacteria relationship in smoking
Smoking cessation
* * *
Diabetes, pregnancy, and tobacco smoking have profound and far-reaching effects on the host, including effects on the:
1. Physiological response
2. Vascular system
3. Inflammatory response
4. Immune system
5. Tissue repair.
They therefore have the potential to modify the:
1. Susceptibility to disease
2. Plaque microbiota
3. Clinical presentation of periodontal disease
4. Disease progression
5. Response to treatment.
Diabetes and smoking were cited as risk factors for periodontitis in Chapter 7 and the epidemiological evidence for their association with periodontitis was dealt with. Both factors are particularly important because they may affect the individual over a great many years, usually decades, and challenge the host to varying degrees. In contrast, pregnancy is of relatively short duration (although possibly with multiple episodes) but should be considered in relation to other hormonal changes which occur at puberty, menopause, and in women on hormonal contraceptives.
These three modifying factors are extremely important in many other disease processes, for example cardiovascular disease, which also affects people to varying degrees. Much of this variation in susceptibility is probably due to genetic interactions, and there is increasing evidence of important associations with many genetic polymorphisms. There will undoubtedly be emerging genetic evidence to link periodontal disease susceptibility to modifying factors considered in this chapter.
# Diabetes mellitus
Diabetes mellitus (DM) is a complex disease with varying degrees of systemic and oral complications, depending on the extent of metabolic control, presence of infection, and underlying demographic variables. This has led to conflicting results in epidemiologic studies, with regard to periodontal disease presentation in diabetic patients and their response to treatment. This section deals with diabetes and its implications on the host response to bacterial plaque, in the context of clinical and laboratory data pertaining to periodontal disease.
## Type 1 and type 2 diabetes mellitus
DM is categorized as type 1 and type 2 DM. Type 1 DM develops due to impaired production of insulin, while type 2 DM is caused by deficient utilization of insulin. Type 1 DM results from destruction of the insulin-producing β cells of the pancreas. This can occur when genetically predisposed individuals succumb to an inducing event such as a viral infection or other factors that trigger a destructive autoimmune response (Szopa _et al_. 1993). Approximately 10–20% of all diabetics are insulin-dependent or type Oral and periodontal effects 1. They usually have a rapid onset of symptoms associated with a deficiency or total lack of insulin and the condition may be difficult to control. Nearly 90% are diagnosed before the age of 21 years.
Type 2 DM results from insulin resistance, which also contributes to cardiovascular and other metabolic disturbances (Murphy & Nolan 2000). However, insulin production may decrease later in the disease process and require supplementation (Slavkin 1997), in addition to controlling diet or using oral hypoglycemic agents. The onset of symptoms in type 2 DM is more gradual and less severe, usually presenting after the age of 40 years.
## Clinical symptoms
The typical signs and symptoms of diabetes are polyuria, polydipsia, polyphagia, pruritus, weakness, and fatigue. These features are more pronounced in type 1 than in type 2 DM, and are a result of hyperglycemia. The complications of DM include retinopathy, nephropathy, neuropathy, macrovascular disease, and impaired wound healing (Lalla _et al_. 2000; Soory 2000a). The treatment of DM is aimed at reducing blood glucose levels to prevent such complications.
There is conclusive evidence of the importance of glycemic control in the prevention of diabetic complications. Patients regularly use blood glucose monitors to provide effective feedback for adjustment of insulin dosage to meet individual requirements (Mealey 1998). Recent studies have shown significant improvement in reducing complications associated with type 2 DM with controlled blood glucose levels (UKPDS 1998a,b). In these studies of over 5000 type 2 DM patients, the risk of retinopathy and nephropathy was reduced by 25% with effective glycemic control, using sulfonylureas, metformin or insulin. The risk of developing hypoglycemia needs to be monitored in these patients on intensive treatment regimes, particularly those on insulin.
## Oral and periodontal effects
Poorly controlled diabetic subjects may complain of diminished salivary flow and burning mouth or tongue. Diabetic subjects on oral hypoglycemic agents may suffer from xerostomia, which could predispose to opportunistic infections with _Candida albicans_. Candidiasis has been reported in patients with poorly controlled DM (Ueta _et al_. 1993), associated with suppressed oxygen free radical release by polymorphonuclear cells (PMNs) and reduced phagocytosis.
There is good evidence to support the concept that there is an association between poorly controlled diabetes mellitus and periodontitis (Fig. 12-1). Any differences in periodontal health between type 1 and type 2 DM patients may relate to differences in management of glycemic control, age, duration of disease, utilization of dental care, periodontal disease susceptibility, and habits such as smoking. Type 1 DM patients have an increased risk of developing periodontal disease with age, and with the severity and duration of their diabetes.
Periodontal attachment loss has been found to occur more frequently in moderate and poorly controlled diabetic patients, of both type 1 and type 2 DM, than in those under good control (Westfelt _et al_. 1996). In addition, diabetics with more advanced systemic complications present with a greater frequency and severity of periodontal disease (Karjalainen _et al_. 1994). Conversely, initial phase periodontal treatment comprising motivation and debridement of periodontal pockets in type 2 diabetic patients resulted in improved metabolic control of diabetes (Stewart _et al_. 2001). A recent study by Kiran _et al_. (2005) confirmed these findings. In a study population of patients with type 2 DM and glycosylated hemoglobin values of 6–8%, initial phase periodontal treatment resulted in a significant improvement in glycaemic control. Total cholesterol, triglyceride, and low density lipoprotein levels also decreased in the test group and increased in the control group. These findings demonstrate that the status of periodontal disease control can contribute to metabolic control of DM (Faria-Almeida _et al_. 2006). The release of cytokines such as tumor necrosis factor (TNF)-α have implications on glucose and lipid metabolism (Cutler & Iacopino 2005) relevant to DM (Iacopino 2001) and cardiovascular disease. There are similar potential interactions between other systemic conditions and oral diseases (Pihlstrom _et al_. 2005; Kinane _et al_. 2006; Meurman & Hamalainen 2006). Insulin resistance can develop in response to chronic bacterial infection seen in periodontal disease, resulting in worse metabolic control in diabetic patients (Grossi _et al_. 1996). There is evidence to support the hypothesis that adequate control of severe inflammatory periodontal disease could alleviate symptoms of co-existing systemic diseases in susceptible individuals. In a population of Pima Indians with type 2 DM and severe periodontal disease, the risk of cardiorenal mortality and diabetic nephropathy was three times greater than amongst those with mild or moderate disease (Saremi _et al_. 2005).
**Fig. 12-1** Poorly controlled type 1 diabetes mellitus in a young female aged 19 years. (a) Very inflamed and swollen gingival tissues. Early attachment loss was present. (b) The same patient after responding to a course of non-surgical periodontal treatment and improved oral hygiene.
**Fig. 12-2** A localized palatal periodontal abscess associated with a periodontal pocket in a 42-year-old poorly controlled diabetic patient.
**Fig. 12-3** Radiographs of a 50-year-old male who developed type 2 diabetes mellitus in the period between the two radiographs which were taken 3 years apart. There has been rapid bone loss and tooth loss associated with recurrent multiple periodontal abscesses.
Probably the most classic description of the un-diagnosed or poorly controlled diabetic is the patient presenting with multiple periodontal abscesses, leading to rapid destruction of periodontal support (Figs. 12-2, 12-3). Harrison _et al_. (1983) reported a case of deep neck infection of the submental, sublingual, and submandibular spaces, secondary to periodontal abscesses involving the mandibular incisors, in a poorly controlled diabetic patient. In a population study Ueta _et al_. (1993) demonstrated that DM was a predisposing factor for periodontal and periapical abscess formation due to suppression of neutrophil function. The effects on the host response, and in particular neutrophil function, may account for this finding.
## Association of periodontal infection and diabetic control
The presence of acute infection can predispose to insulin resistance (Atkinson & Maclaren 1990). This can occur independently of a diabetic state and persist for up to 3 weeks after resolution of the infection (Yki-Jarvinen _et al_. 1989). In a longitudinal study of subjects with type 2 DM, it was demonstrated that subjects with severe periodontal disease demonstrated significantly worse control of their diabetic condition than those with minimal periodontal involvement (Taylor _et al_. 1996) (Fig. 12-4). The incidence of proteinuria and cardiovascular complications, as a result of uncontrolled diabetes, was found to be significantly greater in diabetics with severe periodontal disease than those with gingivitis or early periodontal disease (Thorstensson _et al_. 1996). Some studies have shown that stabilization of the periodontal condition with mechanical therapy, in combination with systemic tetracycline, improves the diabetic condition in such patients (Grossi _et al_. 1997b). Reduced insulin dosage in type 1 diabetics following periodontal treatment has also been reported (Sastrowijoto _et al_. 1990). However, other studies have not shown improvement in diabetic control following non-surgical periodontal treatment (Aldridge _et al_. 1995). These effects of periodontal therapy may be more pronounced in poorly controlled diabetic patients with severe periodontal disease.
**Fig. 12-4** Diabetes control and periodontal disease progression.
Significant inflammatory lesions in severe periodontal disease could contribute to exacerbation of diabetes. Markers of inflammation common to diabetes and periodontal disease are an indication of disease control (Soory 2002, 2004).
## Modification of the host–bacteria relationship in diabetes
### Effects on microbiota
Hyperglycemia in uncontrolled diabetics has implications on the host response (Gugliucci 2000) and affects the regional microbiota. This can potentially influence the development of periodontal disease and caries in poorly controlled type 1 and type 2 DM patients. _Capnocytophaga_ species have been isolated as the predominant cultivable organisms from periodontal lesions in type 1 diabetics, averaging 24% of the cultivable flora (Mashimo _et al_. 1983). A similar distribution of the predominant putative pathogens, _Prevotella intermedia_ , _Campylobacter rectus_ , _Porphyromonas gingivalis_ , and _Aggregatibacter actinomycetemcomitans_ (formerly known as _Actinobacillus actinomycetemcomitans_ ), to those associated with chronic adult periodontal disease was detected in periodontal lesions of type 2 diabetics (Zambon _et al_. 1988), with potential for disease activity during poor metabolic control. In an insulin-dependent diabetic population with a large proportion of poorly controlled diabetics, Seppala and Ainamo (1996) showed significantly increased percentages of spirochetes and motile rods and decreased levels of cocci in periodontal lesions, compared with well controlled patients.
### Effects on the host response
Diabetes mellitus has far-reaching effects on the host response (Fig. 12-5).
#### _Polymorphonuclear leukocytes_
Reduced PMN function (Marhoffer _et al_. 1992) and defective chemotaxis in uncontrolled diabetics can contribute to impaired host defenses and progression of infection (Ueta _et al_. 1993). Crevicular fluid collagenase activity, originating from PMNs, was found to be increased in diabetic patients and this could be inhibited _in vitro_ by tetracycline through its enzyme inhibitory effects (Sorsa _et al_. 1992). The PMN enzymes beta-glucuronidase (Oliver _et al_. 1993) and elastase, in association with diabetic angiopathy (Piwowar _et al_. 2000), have been detected at significantly higher levels in poorly controlled diabetic patients.
#### _Cytokines, monocytes, and macrophages_
Diabetic patients with periodontitis have significantly higher levels of interleukin (IL)-1β and prostaglandin E2 (PGE2) in crevicular fluid compared to non-diabetic controls with a similar degree of periodontal disease (Salvi _et al_. 1997). In addition, the release of these cytokines (IL-1β, PGE2, TNF-α) by monocytes has been shown to be significantly greater in diabetics than in non-diabetic controls. Chronic hyperglycemia results in non-enzymatic glycosylation of numerous proteins, leading to the accumulation of advanced glycation end products (AGE), which play a central role in diabetic complications (Brownlee 1994). Increased binding of AGEs to macrophages and monocytes (Brownlee 1994) can result in a destructive cell phenotype with increased sensitivity to stimuli, resulting in excessive release of cytokines. Altered macrophage phenotype due to cell surface binding with AGE, prevents the development of macrophages associated with repair. This could contribute to delayed wound healing seen in diabetic patients (Iacopino 1995).
#### _Connective tissue_
A hyperglycemic environment, due to decreased production or utilization of insulin, can reduce growth, proliferation, and matrix synthesis by gingival and periodontal ligament fibroblasts and osteoblasts. The formation of AGE results in reactive oxygen species, which are damaging to cellular function in gingival tissues, due to oxidative stress (Schmidt _et al_. 1996). The accumulation of AGE in tissues alters the function of several intercellular matrix components, including vascular wall collagen, resulting in deleterious complications (Ulrich & Cerami 2001). This has adverse effects on cell–matrix interactions and vascular integrity, potentially affecting periodontal disease presentation and treatment responses in uncontrolled diabetics. Vascular changes, such as thickening of the capillary basement membrane in a hyperglycemic environment, can impair oxygen diffusion, metabolic waste elimination, PMN migration, and diffusion of antibodies. Binding of AGE to vascular endothelial cells can trigger responses that induce coagulation, leading to vasoconstriction and microthrombus formation (Esposito _et al_. 1992), resulting in impaired perfusion of tissues. Recent work using a cell culture model has demonstrated that glucose, AGE, and nicotine inhibit the synthesis of steroid markers of wound healing (Rahman & Soory 2006). This inhibition was overcome by the antioxidant glutathione and insulin-like growth factor (IGF), which also functions as an antioxidant. These findings can be extrapolated to the 'in vivo' situation, demonstrating the relevance of oxidative stress-induced mechanisms in periodontal disease and DM, with therapeutic implications of medications with antioxidant effects (Soory & Tilakaratne 2003). These findings may be extrapolated to healing responses in the uncontrolled diabetic smoker with periodontal disease (Graves _et al_. 2006).
**Fig. 12-5** Effects of diabetes mellitus on the host response.
### Effects on healing and treatment response
Wound healing is impaired due to the cumulative effects on cellular functions as described above. In summary, these factors include:
1. Decreased synthesis of collagen by fibroblasts
2. Increased degradation by collagenase
3. Glycosylation of existing collagen at wound margins
4. Defective remodeling and rapid degradation of newly synthesized, poorly cross-linked collagen.
## Periodontal treatment
The treatment of well controlled DM patients would be similar to that of non-diabetic patients for most routine dental procedures. The short-term non-surgical treatment response of stable diabetics has been found to be similar to that of non-diabetic con-trols, with similar trends in improved probing depths, attachment gain, and altered subgingival microbiota (Christgau _et al_. 1998). Well controlled diabetics with regular supportive therapy have been shown to maintain treatment results 5 years after a combination of non-surgical and surgical treatment (Westfelt _et al_. 1996). However, a less favorable treatment outcome may occur in long-term maintenance therapy of poorly controlled diabetics, who may succumb to more rapid recurrence of initially deep pockets (Tervonen & Karjalainen 1997).
# Puberty, pregnancy, and the menopause
The hormonal variations experienced by women during physiological and non-physiological conditions (such as hormone replacement therapy and use of hormonal contraceptives) result in significant changes in the periodontium, particularly in the presence of pre-existing, plaque-induced gingival inflammation. The implications of these changes on the tissues of the periodontium have been reviewed comprehensively (Mascarenhas _et al_. 2003; Guncu _et al_. 2005). Periods of hormonal flux are known to occur during puberty, menstruation, pregnancy, and the menopause. Changes in hormone levels occur when the anterior pituitary secretes follicle-stimulating hormone (FSH) and luteinizing hormone (LH), resulting in the maturation of the ovary and cyclical production of estrogen and progesterone.
The gingiva is a target tissue for the actions of steroid hormones. Clinical changes in the tissues of the periodontium have been identified during periods of hormonal fluctuation. The effects of estrogen and progesterone on the periodontium have received significant research attention. The main potential effects of these hormones on the periodontal tissues can be summarized as:
* Estrogen affects salivary peroxidases, which are active against a variety of microorganisms (Kimura _et al_. 1983), by changing the redox potential.
* Estrogen has stimulatory effects on the metabo-lism of collagen and angiogenesis (Sultan _et al_. 1986).
* Estrogen can trigger autocrine or paracrine polypeptide growth factor signaling pathways, whose effects may be partially mediated by the estrogen receptor itself (Chau _et al_. 1998).
* Estrogen and progesterone can modulate vascular responses and connective tissue turnover in the periodontium, associated with interaction with inflammatory mediators (Soory 2000b).
The interaction of estrogen and progesterone with inflammatory mediators may help to explain the increased levels of inflammation seen during periods of hormonal fluctuation. For example, when cultured human gingival fibroblasts were incubated with progesterone concentrations common in late pregnancy, there was a 50% reduction in the formation of the inflammatory mediator IL-6, compared with control values (Lapp _et al_. 1995). IL-6 induces the synthesis of tissue inhibitor of metalloproteinases (TIMP) in fibroblasts (Lotz & Guerne 1991), reduces the levels of TNF and enhances the formation of acute phase proteins (Le & Vilcek 1989). A progesterone-induced reduction in IL-6 levels could result in less TIMP, more proteolytic enzyme activity, and higher levels of TNF at the affected sites, due to less inhibition, resulting in inflammation and obvious clinical manifestations.
## Puberty and menstruation
During puberty, there are raised levels of testosterone in males and estradiol in females. Several studies have demonstrated an increase in gingival inflammation in children of circumpubertal age, with no change in plaque levels (Sutcliffe 1972). In a longitudinal study, Mombelli _et al_. (1989) reported that the mean papillary bleeding scores and percentage of interdental bleeding sites correlated with the development of secondary sexual characteristics at puberty, while other studies did not find a significant correlation between the onset of puberty and gingival changes in parapubescent women (Tiainen _et al_. 1992). These discrepancies may be attributed to factors such as the oral hygiene status of the population and study design.
The prevalence of certain periodontal pathogens reported during puberty may have a direct association with the hormones present and their utilization by selected pathogens. For example _Prevotella intermedia_ is able to substitute progesterone and estrogen for menadione (vitamin K) as an essential nutrient (Kornman & Loesche 1979). An association between pubertal gingivitis, _P. intermedia_ and serum levels of testosterone, estrogen, and progesterone has been reported in a longitudinal study (Nakagawa _et al_. 1994).
Pre-existing plaque-induced gingivitis may be an important factor in detecting hormone-induced changes during the menstrual cycle. Holm-Pedersen and Loe (1967) demonstrated that women with gingivitis experienced increased inflammation with an associated increase in crevicular fluid exudate during menstruation compared with healthy controls. Most female patients are not aware of any changes in their gingivae during the menstrual cycle (Amar & Chung 1994), while a few experience enlarged hemorrhagic gingivae in the days preceding menstrual flow. This has been associated with more gingivitis, increased crevicular fluid flow, and tooth mobility (Grant _et al_. 1988). Early studies demonstrated similar findings during the menstrual cycle in a population with preexisting gingivitis, in response to fluctuations in the levels of estrogen and progesterone (Lindhe & Attstrom 1967).
## Pregnancy
During pregnancy, the increased levels of sex steroid hormones are maintained from the luteal phase which results in implantation of the embryo, until parturition. Pregnant women, near or at term, produce large quantities of estradiol (20 mg/day), estriol (80 mg/day), and progesterone (300 mg/day). Gingival inflammation initiated by plaque, and exac-erbated by these hormonal changes in the second and third trimester of pregnancy, is referred to as pregnancy gingivitis. Parameters, such as gingival probing depths (Hugoson 1970; Miyazaki _et al_. 1991), bleeding on probing (Miyazaki _et al_. 1991), and crevicular fluid flow (Hugoson 1970), were found to be increased. These inflammatory features can be minimized by maintaining good plaque control.
According to early reports, the prevalence of pregnancy gingivitis ranges from 35% (Hasson 1966) to 100% (Lundgren _et al_. 1973). In a study of 130 pregnant women, Machuca _et al_. (1999) demonstrated gingivitis in 68% of the population, ranging from 46% in technical executives to 88% in manual workers. Cross-sectional studies examining pregnant and postpartum women have shown that pregnancy is associated with significantly more gingivitis than at postpartum, despite similar plaque scores (Silness & Loe 1963). Further observations were made by Hugoson (1970) in a longitudinal study of 26 women during and following pregnancy, which also demonstrated that the severity of gingival inflammation correlated with the gestational hormone levels during pregnancy (Fig. 12-6). A more recent study of a rural population of Sri Lankan women (Tilakaratne _et al_. 2000a) showed increased gingivitis of varying degrees of significance amongst all the pregnant women investigated, compared with matched non-pregnant controls. There was a progressive increase in inflammation with advancing pregnancy which was more significant in the second and third trimesters of pregnancy, despite the plaque levels remaining unchanged. At the third month after parturition, the level of gingival inflammation was similar to that observed in the first trimester of pregnancy. This suggests a direct correlation between gingivitis and sustained, raised levels of gestational hormones during pregnancy, with regression during the postpartum period. In investigations by Cohen _et al_. (1969) and Tilakaratne _et al_. (2000a), the values for loss of attachment remained unchanged during pregnancy and 3 months postpartum.
### Effects on the microbiota
There is an increase in the selective growth of periodontal pathogens such as _P. intermedia_ in subgingival plaque during the onset of pregnancy gingivitis at the third to fourth month of pregnancy. The gestational hormones act as growth factors, by satisfying the naphthoquinone requirement for bacteria (Di Placido _et al_. 1998). These findings were also confirmed by Muramatsu and Takaesu (1994) who showed that from the third to fifth month of pregnancy, the number of gingival sites which bled on probing corresponded with the percentage increase in _P. intermedia_. During pregnancy, progesterone is less actively catabolized to its inactive products, resulting in higher levels of the active hormone (Ojanotko-Harri _et al_. 1991). A 55-fold increase in the proportion of _P. intermedia_ has been demonstrated in pregnant women compared with non-pregnant controls (Jensen _et al_. 1981), implying a role for gestational hormones in causing a change in microbial ecology in the gingival pocket. Although an overall association has been demonstrated, a cause and effect relationship may be less clear.
### Effects on the tissues and host response
The increase in severity of gingivitis during pregnancy has been partly attributed to the increased circulatory levels of progesterone and its effects on the capillary vessels (Lundgren _et al_. 1973). Elevated progesterone levels in pregnancy enhance capillary permeability and dilatation, resulting in increased gingival exudate. The effects of progesterone in stimulating prostaglandin synthesis can account for some of the vascular changes (Miyagi _et al_. 1993).
The elevated levels of estrogen and progesterone in pregnancy affect the degree of keratinization of the gingival epithelium and alter the connective tissue ground substance. The decreased keratinization of the gingivae, together with an increase in epithelial glycogen, are thought to result in decreased effectiveness of the epithelial barrier in pregnant women (Abraham-Inpijn _et al_. 1996). Hormonal factors that affect the epithelium and increase vascular permea-bility can contribute to an exaggerated response to bacterial plaque during pregnancy. The influence of gestational hormones on the immune system can contribute further to the initiation and progression of pregnancy gingivitis. High levels of progesterone and estrogen associated with pregnancy (and the use of some oral contraceptives) have been shown to suppress the immune response to plaque (Sooriyamoorthy & Gower 1989). Neutrophil chemotaxis and phagocytosis, along with antibody and T cell responses, have been reported to be depressed in response to high levels of gestational hormones (Raber-Durlacher _et al_. 1993).
**Fig. 12-6** Gingivitis associated with pregnancy. (a) A patient in the last trimester of pregnancy with very inflamed edematous gingival tissue which tended to bleed with the slightest provocation. (b) The improvement in gingival health 6 months after birth of the baby and an intensive course of non-surgical periodontal treatment.
### Pregnancy granuloma or epulis
A pedunculated, fibrogranulomatous lesion can sometimes develop during pregnancy and is referred to as a pregnancy granuloma or epulis. A combination of the vascular response induced by progester-one and the matrix stimulatory effects of estradiol contributes to the development of pregnancy granulomas, usually at sites with pre-existing gingivitis (Fig. 12-7). The vascular effects result in a bright red, hyperemic, and edematous presentation. The lesions often occur in the anterior papillae of the maxillary teeth and usually do not exceed 2 cm in diameter. They can bleed when traumatized and their removal is best deferred until after parturition, when there is often considerable regression in their size (Wang _et al_. 1997). Surgical removal of the granuloma during pregnancy can result in recurrence due to a combination of poor plaque control and hormone-mediated growth of the lesion. Careful oral hygiene and debridement during pregnancy are important in preventing its occurrence (Wang _et al_. 1997).
### Periodontal treatment during pregnancy
Pregnant women need to be educated on the consequences of pregnancy on gingival tissues and thoroughly motivated in plaque control measures, with professional treatment as required. They are likely to be more comfortable to receive dental treatment during the second trimester than in the first or third trimester of pregnancy, although emergency treatment is permissible at any stage during pregnancy (Amar & Chung 1994). Since most medications cross the placental barrier and organogenesis occurs mainly in the first trimester, pregnant women are best treated in the second trimester, to avoid the occurrence of developmental defects. Any form of medication during pregnancy must only be used if the gravity of the condition being treated outweighs the consequences. Amongst the antibiotics, tetracycline, vancomycin, and streptomycin can contribute to staining of teeth and ototoxic and nephrotoxic effects during the fourth to ninth months of pregnancy; erythromycin, penicillins, and cephalosporins are relatively safer, but any medication must only be administered in consultation with the patient's obstetrician (Lynch _et al_. 1991).
## Menopause and osteoporosis
During menopause there is a decline in hormonal levels due to decreased ovarian function. This is characterized by tissue changes such as desquamation of gingival epithelium (Fig. 12-8) and osteoporosis (Fig. 12-9) which may be attributed to hormone deficiency. It has been demonstrated that women with early onset of menopause have a higher incidence of osteoporosis and significantly lower bone mineral density (Kritz-Silverstein & Barrett-Connor 1993).
A third of women over age 60 are affected by postmenopausal osteoporosis (Baxter 1987). The changes involved are a reduction in bone density, affecting its mass and strength without significantly affecting its chemical composition. An alteration in the calcium–phosphate equilibrium due to deficient absorption of dietary calcium and increased excretion due to diminished estrogen levels can account for some of the bone changes seen in postmenopausal women (Shapiro _et al_. 1985), usually involving the mandible more than the maxilla.
**Fig. 12-7** Multi-lobulated appearance of an early pregnancy epulis, demonstrating vascular elements and tissue oedema.
**Fig. 12-8** Clinical appearance of anterior maxillary gingiva with pronounced desquamation in a woman during menopause.
**Fig. 12-9** A DEXA scan used to measure mineral bone density in the hip. This technique is not routinely applied to the jaws.
Estrogen replacement therapy has been shown to prevent osteoporosis and maintain bone mineral content at several sites throughout the skeleton (Moore _et al_. 1990), with a 5% increase in bone mineral content in the region of the head compared to those taking placebo (Gotfredsen _et al_. 1986). The influence of estrogen on bone mineral density has been demonstrated in these studies, but a cause and effect relationship with periodontal disease is less clear.
A 2-year follow-up study of 42 171 postmenopausal women (Grodstein _et al_. 1996) showed that the risk of tooth loss was significantly lower amongst hormone users. These findings reinforce those of Paganini-Hill (1995), who showed a 36% decrease in tooth loss in estrogen users compared with nonusers. There is evidence to suggest that use of estrogen is necessary to protect against bone loss (Grady _et al_. 1992). Although osteoporosis in postmenopausal women may not be the cause of periodontal disease, it may affect the severity of pre-existing disease. The circulating levels of estrogen have been shown to have an influence on alveolar bone density in postmenopausal women (Payne _et al_. 1997).
### Effect of smoking on osteoporosis
A negative association between smoking and bone density has been demonstrated by Krall and Dawson-Hughes (1991). Smokers can differ from non-smokers in weight, caffeine intake, age at menopause, and alcohol consumption (Lindquist & Bengtsson 1979; Rigotti 1989); all these factors can potentially confound an association between smoking and bone density. A study on female twins by Hopper and Seeman (1994) showed that in the 20 pairs who varied most, by 20 or more pack years, the differences in bone density within pairs were 9.3% at the lumbar spine, 5.8% at the femoral neck, and 6.5% at the femoral shaft. This study also demonstrated increased serum levels of FSH and LH in smokers, implying reduced circulating levels of estrogen, leading to increased bone resorption. Other investigators have demonstrated the effects of smoking on the synthesis and degradation of estrogen (Jensen _et al_. 1985). The study by Jensen _et al_. (1985) investigated 136 postmenopausal women who were treated with three different doses of estrogen–progesterone or placebo. They showed reduced levels of estrogen in smokers (range of 1–30 cigarettes/day in the previous 6 months, mean 12.4), compared with non-smokers (not smoked in the previous 3 months). There was also a significant inverse correlation between the number of cigarettes smoked per day and the serum levels of estrogen, suggestive of increased hepatic metabolism of estrogen in postmenopausal smokers, resulting in lower serum levels of these hormones.
### Treatment of osteoporosis
In osteoporotic patients, the rate of bone loss during the early postmenopausal period increases to 3–4% per year. Estrogen replacement therapy, which slows bone turnover, results in increased bone density in the trabecular spaces during remodeling (Frost 1989). The increased skeletal bone mass which occurs in response to estrogen replacement therapy is apparent in the first 2 years of treatment and maintained with continuation of treatment (Kimmel _et al_. 1994). The effects of estrogen in regaining bone mass to premenopausal levels and in preventing/reversing postmenopausal osteoporotic changes in the long bones and spine have been demonstrated in several studies (Armamento-Villareal _et al_. 1992; Takahashi _et al_. 1994).
There is some controversy with regard to the benefits of hormone replacement due to the risk factors involved. Fractures due to osteoporosis and heart disease in postmenopausal women can be reduced by 50% with estrogen replacement therapy. However, hormone replacement with estrogen alone exposes such patients to the risk of endometrial cancer. Long-term hormone replacement therapy has been shown to correlate with an increased risk of breast cancer. Modern formulations utilize combined therapy with a suitable dose of progesterone in combination with estrogen in order to minimize some of these risk factors (Whitehead & Lobo 1988).
## Hormonal contraceptives
Contraceptives utilize synthetic gestational hormones (estrogen and progesterone), to reduce the likelihood of ovulation/implantation (Guyton 1987). Less dramatic but similar effects to pregnancy are sometimes observed in the gingivae of hormonal contraceptive users. The most common oral manifestation of elevated levels of ovarian hormones is an increase in gingival inflammation with an accompanying increase in gingival exudate (Mariotti 1994).
There are reported systemic risk factors associated with long-term use of hormonal contraceptives. The correlation between hormonal contraceptive use and significant cardiovascular disease associated with arterial and venous thromboembolic episodes has been reviewed by Westhoff (1996). Estrogen is responsible for both arterial and venous effects, while progesterone effects arterial changes. Women using oral contraceptives show elevated plasma levels of several clotting factors, related to the dose of estrogen. Raised levels of factors VIIc and XIIc are significant, since they increase the likelihood of coagulation and in men these factors have a strong positive correlation with ischemic heart disease. However, the relative risk is dependent on the contraceptive formulation used and there may not be a consistent biological plausibility to explain this association (Davis 2000).
There are several different formulations of hormonal contraceptives (Davis 2000) including:
1. Combined oral contraceptives containing artificial analogues of estrogen and progesterone
2. Progesterone-based mini-pill
3. Slow release progesterone implants placed subdermally that last up to 5 years (e.g. Norplant)
4. Depo Provera, a very effective progestin injection given by a doctor every 3 months.
Current combined oral contraceptives consist of low doses of estrogens (50 μg/day) and/or progestins (1.5 mg/day) (Mariotti 1994). The formulations used in the early periodontal studies contained higher concentrations of gestational hormones, e.g. 50 μg estrogen with 4 mg progestin (El-Ashiry _et al_. 1971), 100 μg estrogen with 5 mg progestin (Lindhe & Bjorn 1967). The results obtained in these studies would partly reflect the contraceptive preparation used. In one early study (Knight & Wade 1974) women who were on hormonal contraceptives for more than 1.5 years exhibited greater periodontal destruction compared to the control group of comparable age and oral hygiene. This could partly reflect higher dose of gestagens used in older contraceptive preparations. However, a recent study on a population of rural Sri Lankan women confirmed these findings (Tilakaratne _et al_. 2000b), showing significantly higher levels of gingivitis in contraceptive users (0.03 mg estradiol and 0.15 mg of a progestin), than non-users, despite similar plaque scores. There was also significant periodontal breakdown in those who used the progesterone injection (a depot preparation of 150 mg progesterone) 3-monthly for 2–4 years, compared with those who used it for less than 2 years. These findings may be attributed to the duration of use, and the effects of progesterone in promoting tissue catabolism, resulting in increased periodontal attachment loss. However, if low plaque levels are established and maintained for the duration of use, these effects could be minimized.
### Effect on tissue response
Both estrogen and progesterone are known to cause increased gingival exudate, associated with inflammatory edema (Lindhe & Bjorn 1967). A 53% increase in crevicular fluid volume has been demonstrated in hormonal contraceptive users compared with controls. El-Ashiry _et al_. (1971) observed that the most pronounced effects on the gingiva occurred in the first 3 months of contraceptive treatment, but the dose of gestational hormones was higher in the older formulations compared with those used currently (Davis 2000), accounting for a more florid response in the tissues.
It has been suggested that the interaction of estrogen with progesterone results in the mediation of the effects characteristic of progesterone. Human gingiva has receptors for progesterone and estrogen (Vittek _et al_. 1982; Staffolani _et al_. 1989), providing evidence that gingiva is a target tissue for both gestational hormones. In _in vitro_ studies of cultured gingival fibroblasts, estrogen enhanced the formation of anabolic androgen metabolites, while progesterone caused a diminished response. The combined effect of both gestational hormones on the yield of androgens was less pronounced than with estrogen alone, implying a more catabolic role for progesterone (Tila-karatne & Soory 1999).
Progesterone causes increased vascular permeability, resulting in the infiltration of polymorphonuclear leukocytes and raised levels of PGE2 in the sulcular fluid (Miyagi _et al_. 1993). Increased capillary permeability may be induced by estrogen by stimulating the release of mediators such as bradykinin, prostaglandins, and histamine. However, the main effects of estrogen are in controlling blood flow. Hence the combination of estrogen and progesterone in the contraceptive pill can contribute to vascular changes in the gingivae. The resultant gingivitis can be minimized by establishing low plaque levels at the beginning of oral contraceptive therapy (Zachariasen 1993).
# Tobacco smoking
Tobacco smoking is very common, with cigarettes being the main product smoked. In the European Union, an average of 29% of the adult population smoke, ranging from 17.5% in Sweden to 45% in Greece (<http://www.ash.org.uk>). The figure is higher for men (35%) than for women (24%). Most smokers start the habit as teenagers, with the highest prevalence in the 20–24-year-old age group. Socioeconomic differences also exist with higher smoking in the lower socioeconomic groups. These data are similar for the US population (Garfinkel 1997; <http://www.cdc.gov/tobacco/>) where an estimated 44.5 million adults smoke. Reported smoking rates for third world countries are even higher. Smoking is associated with a wide spectrum of disease including stroke, coronary artery disease, peripheral artery disease, gastric ulcer, and cancers of the mouth, larynx, esophagus, pancreas, bladder, and uterine cervix. It is also a major cause of chronic obstructive pulmonary disease and a risk factor for low birth weight babies. Approx-imately 50% of regular smokers are killed by their habit and smoking causes 30% of cancer deaths.
Cigarette smoke is a very complex mixture of substances with over 4000 known constituents. These include carbon monoxide, hydrogen cyanide, reactive oxidizing radicals, a high number of carcinogens, and the main psychoactive and addictive molecule – nicotine (Benowitz 1996). Many of these components could modify the host response in periodontitis. In most of the _in vitro_ studies considered in the latter parts of this chapter the experimenters utilized simple models with nicotine alone. Tobacco smoke has a gaseous phase and solid phase which contains tar droplets. The tar and nicotine yields of cigarettes have been reduced due to physical characteristics of the filters. However, there has been little change in the tar and nicotine content of the actual tobacco and the dose an individual receives is largely dependent upon the way in which they smoke (Benowitz 1989). Inter-subject smoking variation includes: frequency of inhalation; depth of inhalation; length of the cigarette stub left; presence or absence of a filter; and the brand of cigarette (Benowitz 1988).
The patient's exposure to tobacco smoke can be measured in a number of ways, including interviewing the subject using simple questions or more sophisticated questionnaires and biochemical analyses (Scott _et al_. 2001). The latter tests include exhaled carbon monoxide in the breath, which is commonly measured in smoking cessation clinics, and cotinine (a metabolite of nicotine) in saliva, plasma/serum or urine (Wall _et al_. 1988). Cotinine measurements are more reliable in determining a subject's exposure to tobacco smoke because the half-life is 14–20 hours compared with the shorter half-life of nicotine which is 2–3 hours (Jarvis _et al_. 1988). The mean plasma and salivary cotinine concentrations of regular smokers are approximately 300 ng/ml and urine concentrations are about 1500 ng/ml. Non-smokers typically have plasma/saliva concentrations under 2 ng/ml, but this may be raised slightly due to environmental exposure (passive smoking).
Inhalation of tobacco smoke allows very rapid absorption of nicotine into the blood and transport to the brain, which is faster than an intravenous infusion. Nicotine in tobacco smoke from most cigarettes is not well absorbed through the oral mucosa because the nicotine is in an ionized form as a result of the pH (5.5). In contrast cigar and pipe smoke is more alkaline (pH 8.5), which allows good absorption of un-ionized nicotine through the buccal mucosa (Benowitz 1988). Nicotine is absorbed rapidly in the lung where the smoke is well buffered. The administration of nicotine causes a rise in the blood pressure, an increase in heart rate, an increase in respiratory rate, and decreased skin temperature due to peripheral vasoconstriction. However, at other body sites, such as skeletal muscle, nicotine produces vasodilatation.
These differing actions of nicotine have led to some controversy over its action in the periodontal tissues. Clarke and co-workers (1981) showed that the infusion of nicotine resulted in a transient decrease in gingival blood flow in a rabbit model. However, Baab and Öberg (1987) using laser Doppler flowmetry to monitor relative gingival flow in 12 young smokers, observed an immediate but transient increase in relative gingival blood flow during smoking, compared to the presmoking or resting measurements. The authors hypothesized that the steep rise in heart rate and blood pressure due to smoking could lead to an increase in the gingival circulation during smoking. These results were confirmed by Meekin _et al_. (2000) who showed that subjects who smoked only very occasionally experienced an increase in blood flow to the head, whereas regular smokers showed no change in blood flow, demon-strating tolerance in the regular smoker. The increase in blood flow to the gingival and forehead skin following an episode of smoking in 13 casual consumers of tobacco was confirmed by Mavropoulos _et al_. (2003) and Morozumi _et al_. (2004) showed that the gingival blood flow significantly increased at 3 days following quitting, providing important information on the recovery of gingival tissue following quitting smoking.
## Periodontal disease in smokers
Pindborg (1947) was one of the first investigators to study the relationship between smoking and periodontal disease. He discovered a higher prevalence of acute necrotizing ulcerative gingivitis, a finding that was confirmed in many subsequent studies of this condition (Fig. 12-10) (Pindborg 1949; Kowolik & Nisbet 1983; Johnson & Engel 1986). Early studies showed that smokers had higher levels of periodontitis but they also had poorer levels of oral hygiene (Brandzaeg & Jamison 1984) and higher levels of calculus (Fig. 12-11) (Alexander 1970; Sheiham 1971). Later studies which took account of oral hygiene status and employed more sophisticated statistical analyses showed that smokers had more disease regardless of oral hygiene (Ismail _et al_. 1983; Bergstrom 1989; Bergstrom & Preber 1994).
**Fig. 12-10** The typical appearance of necrotizing ulcerative gingivitis in a heavy smoker with poor oral hygiene.
**Fig. 12-11** The lingual aspects of the lower incisors showing gross supragingival calculus formation and relatively little gingival inflammation in a female patient who has smoked 20 cigarettes per day for over 20 years.
**Fig. 12-12** A 30-year-old female smoker with advanced periodontitis. (a) The clinical appearance shows marginal gingiva with little signs of inflammation. Probing depths greater than 6 mm were present at most interproximal sites, but with little bleeding on probing. (b) Generalized advanced bone loss in this patient.
A large number of studies have established that in comparing smokers and non-smokers with periodontitis, smokers have:
1. Deeper probing depths and a larger number of deep pockets (Feldman _et al_. 1983; Bergstrom & Eliassson 1987a; Bergstrom _et al_. 2000a)
2. More attachment loss including more gingival recession (Grossi _et al_. 1994; Linden & Mullally 1994; Haffajee & Socransky 2001a)
3. More alveolar bone loss (Bergstrom & Floderus Myhred 1983; Bergstrom & Eliasson 1987b; Feldman _et al_. 1987; Bergstrom _et al_. 1991, 2000b; Grossi _et al_. 1995)
4. More tooth loss (Osterberg & Mellstrom 1986; Krall _et al_. 1997)
5. Less gingivitis and less bleeding on probing (Feldman _et al_. 1983; Preber & Bergstrom 1985; Bergstrom & Preber 1986; Haffajee & Socransky 2001a)
6. More teeth with furcation involvement (Mullally & Linden 1996).
The finding of less gingival bleeding on probing is associated with less inflamed marginal tissue and lower bleeding scores when probing the depth of the pockets. The typical clinical appearance of the smoker's gingival tissue is shown in Fig. 12-12, which demonstrates relatively low levels of marginal inflammation and a tendency to a more fibrotic appearance with little edema. Despite the clinical appearance of the gingival tissue, the patient has deep pockets, advanced attachment loss, and bone loss, as shown in Fig. 12-12b.
**Fig. 12-13** Effects of tobacco smoking on the host response.
## Modification of the host–bacteria relationship in smoking
There are several theories as to why smokers have more periodontal disease than non-smokers, involving both bacterial aspects and the host response (Barbour _et al_. 1997; Palmer _et al_. 2005). The potential interactions are illustrated in Fig. 12-13.
### Effects on plaque bacteria
Smokers may have higher levels of plaque than non-smokers, which may be accounted for by poorer levels of oral hygiene rather than higher rates of supragingival plaque growth (Bergstrom 1981; Bergstrom & Preber 1986). Several studies have shown that smokers harbor more microbial species which are associated with periodontitis than non-smokers, including _P. gingivalis_ , _A. actinomycetemcomitans_ , _Tanerella forsythia (Bacteroides forsythus)_ (Zambon _et al_. 1996), _P. intermedia_ , _Peptostreptococcus micros_ , _Fusobacterium nucleatum_ , _Campylobacter rectus_ (van Winkelhoff _et al_. 2001), _Staphylococcus aureus_ , _Eschericia coli_ , and _Candida albicans_ (Kamma _et al_. 1999). Smokers may have a higher proportion of sites harboring these putative periodontal pathogens, in particular the palatal aspects of the maxillary teeth and the upper and lower incisor regions (Haffajee & Socransky 2001a,b). In contrast several studies have failed to show differences in the bacterial species between smokers and non-smokers (Preber _et al_. 1992; Darby _et al_. 2000; Bostrom _et al_. 2001; van der Velden _et al_. 2003). Microbiological studies differ in their methodology, ability to identify and quantify putative pathogens, and the number of subjects included. Changes in the pocket environment secondary to the effect of smoking on the host tissues could result in a different microflora in smokers.
### Effects on the host response
The relationship between plaque accumulation and development of inflammation in smokers has been studied in classical experimental gingivitis studies (Bergstrom & Preber 1986). They demonstrated that there is no difference in plaque accumulation when comparing smokers and non-smokers. However, the development of inflammation was very much retarded in the smoking group with less sites exhibiting redness or bleeding on probing. They also showed lower amounts of gingival crevicular fluid (GCF) during the development of gingivitis. Smoking may result in lower resting GCF flow rate (Persson _et al_. 1999) and an episode of smoking may produce a transient increase in GCF flow rate (McLaughlin _et al_. 1993). The reduced bleeding has previously been proposed to be caused by nicotine-induced vasoconstriction, but as previously described in this chapter, more recent evidence has failed to show a reduction in blood flow to the gingiva following smoking a cigarette in regular smokers (Meekin _et al_. 2000). The reduced bleeding on the other hand is probably due to long-term effects on the inflammatory lesion. Histological comparisons of the lesions from smokers and non-smokers have shown fewer blood vessels in the inflammatory lesions of smokers (Rezavandi _et al_. 2001). It is pertinent to note that gingival bleeding on probing has been shown to increase within 4–6 weeks of quitting smoking (Nair _et al_. 2003), and this parallels reported recovery of reduced serum ICAM levels (Palmer _et al_. 2002).
Smoking has a profound effect on the immune and inflammatory system (reviewed by Barbour _et al_. 1997; Palmer _et al_. 2005). Smokers have an increased number of leukocytes in the systemic circulation (Sorenson _et al_. 2004), but fewer cells may migrate into the gingival crevice/pocket (Eichel & Shahrik 1969). Smoking is associated with chronic obstructive pulmonary disease (Barnes 2000) and many of the mechanisms indicated are paralleled in findings related to periodontal disease. It is thought that the main cell type responsible for destruction of lung parenchyma is the neutrophil, which is delayed in its transit through the pulmonary vasculature (McNee _et al_. 1989), where it is stimulated to release proteases including elastase, cathepsins, and matrix metalloproteases (Barnes 2000). These destructive molecules are balanced by inhibitors such as α-1-antitrypsin and tissue inhibitors of matrix metalloproteases.
Studies _in vitro_ have shown a direct inhibition of neutrophil and monocyte–macrophage defensive functions by high concentrations of nicotine that may be achieved in patients using smokeless tobacco (Pabst _et al_. 1995). MacFarlane and co-workers (1992) examined patients with refractory periodontitis and found a high proportion of smokers in this diagnostic group. These investigators demonstrated abnormal PMN phagocytosis associated with a high level of cigarette smoking.
The PMN is a fundamental defense cell in the periodontal tissue. There is a constant traffic of PMNs from the gingival vasculature through the connective tissue and junctional epithelium into the gingival sulcus/pocket. This is described in some detail in Chapter 11. The PMN is the first line of defense and is chemotactically attracted to bacterial challenge at the dentogingival junction. The PMN contains a powerful battery of enzymes including elastase and other collagenases that have been implicated in tissue destruction in periodontitis and pulmonary disease. Eichel and Shahrik (1969) suggested decreased PMN migration into the oral cavity of smokers. Subsequently, PMNs harvested from the gingival sulcus of smokers were shown to have reduced phagocytic capacity compared to PMNs from non-smokers (Kenney _et al_. 1977). Neutrophil defects have been associated with an increased susceptibility to periodontitis, including cyclic neutropenia where there is a reduction in the number of neutrophils, and conditions such as leukocyte adhesion deficiency (LAD 1 and LAD 2), which may be responsible for cases of generalized prepubertal periodontitis as described by Page _et al_. (1983). It is proposed that smoking causes alterations to PMN function which could be considered to be minor variations of these more profound defects.
The normal passage of the PMN from the microvasculature to the periodontal tissues involves a classic series of events including capture, rolling on the endothelium, firm adhesion to the endothelium, and transmigration through the vessel wall into the connective tissue (Ley 1996). This involves a complex interaction between receptors and ligands on the leu-kocyte surface and endothelium including selectins, ICAM-1 and LFA1 (CD18, CD11b) (Crawford & Watanabe 1994; Gemmel _et al_. 1994). Defects in the functional ligands for the selectins have been impli-cated in LAD 2 and mutations in the gene encoding CD18 resulting in absence of the β2 integrins with LAD 1. Subjects with LAD are susceptible to serious and life-threatening infections and have tremendous destruction of the periodontal tissues, often leading to total tooth loss in the deciduous dentition. These serious and rare conditions illustrate the overwhelming importance of the adhesion molecules and suggest that minor defects in them may also give rise to more subtle conditions that could lead to increased susceptibility to periodontal destruction. In this respect, it has been shown that smokers are affected by upregulation of molecules such as ICAM-1 on the endothelium and they have higher levels of circulating soluble ICAM-1 which could interfere with the normal recep-tor ligand binding and function of the leukocyte in the defense of the periodontal tissue (Koundouros _et al_. 1996; Palmer _et al_. 1999; Scott _et al_. 2000a). A poten-tial destructive mechanism is the release of elastase from neutrophils following binding of ICAM with CD18 (Mac 1 and LFA 1) (Barnett _et al_. 1996). Lower levels of elastase detected in the gingival fluid of smokers compared to non-smokers, may indicate more elastase release within the tissues (Alavi _et al_. 1995), and this is especially important considering the effects of smoking on protease inhibitors.
Tobacco smoking has a chronic effect on the elevated levels of soluble ICAM (sICAM) and there is evidence that the subject may return to more normal levels after quitting smoking (Scott _et al_. 2000b; Palmer _et al_. 2002). These molecules can be detected in the serum and in the GCF. It has also been shown that cotinine is present in the GCF in about the same concentration as it appears in serum, but the levels of sICAM are much lower in smokers despite very much higher serum levels than non-smokers (Fraser _et al_. 2001). Many other molecules have been studied in the GCF of smokers with many reporting reduced levels compared to non-smokers. Alavi _et al_. (1995) showed significantly lower concentrations of elastase and elastase complexed with α1-antitrypsin in smokers GCF. Although Bostrom _et al_. (1999) showed higher levels of TNF-α in GCF in smokers, they reported no differences in levels of IL-6 (Bostrom _et al_. 2000). Rawlinson _et al_. (2003) found levels of IL-1beta and IL-1ra to be significantly lower in GCF from diseased sites in smokers compared to non-smokers, and Petropoulos _et al_. (2004) showed that the concentration of IL-1alpha in GCF of smokers was approximately half that found in non-smokers.
PMN-related periodontal tissue destruction may also be related to suppression or exacerbation of the respiratory burst and generation of reactive oxygen species. For example Gustafsson _et al_. (2000) have shown that the priming capacity of TNF-α, measured as generation of oxygen radicals from stimulated neutrophils, is higher in neutrophils from smokers, compared to neutrophils from non-smokers. Thus, inappropriate activation of periodontal neutrophils is thought to contribute to the degradation of gingival tissues and the progression of inflammatory periodontal disease (Deas _et al_. 2003).
The effects of smoking on lymphocyte function and antibody production are very complex, with the various components having the potential to cause immunosuppression or stimulation. It is likely that the particulate phase of cigarette smoke confers immunosuppressive properties. Acute or chronic exposure to hydrocarbons may stimulate or inhibit the immune response, the net effect being dependent upon the dose and duration of the exposure to com-ponents of tobacco smoke. The leukocytosis observed in smokers results in increased numbers of circulating T and B lymphocytes (reviewed in Sopori & Kozak 1998). Studies that have examined T cell subsets report different findings of either reduced, increased or no change in the number of CD4 T cells (Loos _et al_. 2004). Smoking appears to affect both B and T cell function, inducing functional unresponsiveness in T cells.
It has been reported that serum IgG levels in smokers may be reduced (Quinn _et al_. 1998) with depression of IgG2, particularly in some racial groups (Quinn _et al_. 1996; Graswinkel _et al_. 2004). Reported levels of serum IgA and IgM classes are variable and IgE may be elevated (Burrows _et al_. 1981).
The clinical change in the tissues of smokers was described above. It is not surprising that histological evaluation of smokers' tissues has shown that there is a decrease in the vascularity of the tissues (Reza-vandi _et al_. 2001). This is a chronic effect due to smoking and may also be associated with alterations in the expression of adhesion molecules within the endothelium. The effect of tobacco smoking on the expression of adhesion molecules on leukocytes, within the inflammatory lesion, in the junctional epithelium and cells of the pocket epithelium could have important implications on the progession of periodontitis in smokers. The effect of smoking on macrovasular disease is well documented (Powell 1998) and its effects on microvascular disease could also be of importance in periodontal disease and in healing.
### Effects on healing and treatment response
The healing potential of tissues has important implications in any chronic inflammatory lesion and in repair following treatment. Smoking has been identi-fied as an important cause of impaired healing in orthopedic surgery, plastic surgery, dental implant surgery (Bain & Moy 1993), and in all aspects of periodontal treatment including non-surgical treatment, basic periodontal surgery, regenerative periodontal surgery, and mucogingival plastic periodontal surgery (Preber & Bergstrom 1986; Miller 1987; Tonetti _et al_. 1995; Grossi _et al_. 1996, 1997a; Kaldahl _et al_. 1996; Bostrom _et al_. 1998; Tonetti 1998; Kinane & Chestnutt 2000; Heasman _et al_. 2006).
In non-surgical treatment, smoking is associated with poorer reductions in probing depth and gains in clinical attachment. In most studies smokers have a lower level of bleeding at baseline, and following treatment bleeding scores are reduced in smokers in a similar manner to those in non-smokers. The poorer reductions in probing depths and gains in attachment level amount to a mean of approximately 0.5 mm. Much of this may be due to less recession of the marginal tissues in smokers as there is less edema and more fibrosis in the gingiva. The same may be true for the deeper tissues of the periodontium where there is less of an inflammatory infiltrate and vascularity at the depth of the pocket. These differences in the tissues between smokers and non-smokers in the untreated state may largely account for the differences in response to non-surgical treatment. It has been proposed that these differences may be manifest by differences in probe penetration in smokers and non-smokers, particularly in deep pockets (Biddle _et al_. 2001).
The poor response of smokers to non-surgical treatment may also apply to those treated with adjunctive antibiotics (Kinane & Radvar 1997; Palmer _et al_. 1999). Response to non-surgical treatment may be seen merely as resolution of inflammation and improvement of the epithelial attachment together with some formation of collagen. However, the response following periodontal surgery is more complex and involves an initial inflammatory reaction followed by organization of the clot, and formation of granulation tissue consisting of capillary buds and fibroblasts laying down collagen. The surgical flaps have to revascularize and the epithelial attachment has to reform on the surface. In regenerative surgery there also has to be formation of a connective tissue attachment and cementogenesis. Tobacco smoke and nicotine undoubtedly affect the microvasculature, the fibroblasts and connective tissue matrix, the bone and also the root surface itself. It has been shown in _in vitro_ studies that fibroblasts are affected by nicotine in that they demonstrate reduced proliferation, reduced migration and matrix production, and poor attachment to surfaces (Raulin _et al_. 1988; Tipton & Dabbous 1995; James _et al_. 1999; Tanur _et al_. 2000). The root surfaces in smokers are additionally contaminated by products of smoking such as nicotine, cotinine, acrolein, and acetaldehyde, and these molecules may affect the attachment of cells (Raulin _et al_. 1988; Cattaneo _et al_. 2000; Gamal & Bayomy 2002; Poggi _et al_. 2002). Smoking has a direct effect on bone and is an established risk factor in osteoporosis. It has also been proposed that it may have a direct affect on bone loss in periodontitis (Bergstrom _et al_. 1991) and it undoubtedly delays healing of bone in fracture wound repair. It is not surprising therefore that tobacco smoking has been implicated in poorer responses to periodontal surgical treatment.
## Smoking cessation
All patients should be assessed for smoking status and given advice to quit the habit. About 70% of people who smoke would like to quit and should be assisted. They should be referred to specialist cessation services if the treating practitioner does not feel confident in this area. They can be advised about nicotine replacement therapy. People's success with quitting is considerably improved using nicotine replacement therapy and drugs such as buproprion hydrochloride. Former smokers more closely resemble non-smokers in their periodontal health status and response to treatment, but the time required to revert to this status has not been defined. In one of the few papers that have attempted to combine a quit smoking and periodontal treatment interventional study, Preshaw _et al_. (2005) showed a more favorable periodontal treatment outcome in those subjects that managed to quit using well established quit smoking strategies including counseling, nicotine replacement therapy and bupropion. From the original group of 49 subjects there were only 11 continuous quitters at 12 months. It would be of great interest to determine what changes in periodontal status would have occurred with just the quit smoking intervention, and more randomized controlled clinical trials are required in this area.
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# Chapter 13
# Susceptibility
Bruno G. Loos, Ubele van der Velden, and Marja L. Laine
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Introduction
Evidence for the role of genetics in periodontitis
Heritability of aggressive periodontitis (early onset periodontitis)
Heritability of chronic periodontitis (adult periodontitis)
A gene mutation with major effect on human disease and its association with periodontitis
Disease-modifying genes in relation to periodontitis
IL-1 and TNF-α gene polymorphisms
FcγR gene polymorphisms
Gene polymorphisms in the innate immunity receptors
Vitamin D receptor gene polymorphisms
IL-10 gene polymorphisms
Miscellaneous gene polymorphisms
Disease-modifying genes in relation to implant failures and peri-implantitis
Early failures in implant dentistry
Late failures in implant dentistry
Conclusions and future developments
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# Introduction
Periodontitis is a chronic infectious disease of the supporting tissues of the teeth. Due to the bacterial infection, the periodontal tissues become inflamed and are slowly destroyed by the action of the inflammatory process. If left untreated, the teeth lose their ligamentous support to the alveolar bone, become mobile, and are eventually lost.
Periodontitis is considered to be a complex disease. Common features of complex human diseases (for example Alzheimer's disease, Crohn's disease, and cardiovascular diseases) are that these conditions present mostly with a relatively mild phenotype, and are slowly progressive and chronic in nature (Tabor _et al_. 2002). Furthermore, these types of disease are of relatively late onset (mostly adult onset) and relatively common. The pathophysiology of complex diseases is characterized by various biological pathways, leading to similar clinical phenomena. Importantly, complex diseases are associated with variations in multiple genes, each having a small overall contribution and relative risk for the disease process. Complex diseases are typically polygenic, i.e. multiple genes play each a limited role (low penetrance genes) ; the disease genes in complex diseases are therefore considered disease-modifying genes (Hart _et al_. 2000b). Analogous to other complex diseases, we estimate that for periodontitis, at least 10 and as many as 20 disease-modifying genes may be involved. However, it is important to realize that the number and type of disease-modifying genes for the same condition may not be equal for different forms of periodontitis and different ethnic populations; they are also influenced by environmental factors (gene–environment interactions).
Disease-modifying genes contrast to major disease genes. Aberrant allelic forms (see Box 13-1) of major genes are responsible for disease expression according to Mendel's laws (Hart _et al_. 2000b). For example, the fatal inherited disease cystic fibrosis is caused by a recessive mutation in the cystic fibrosis transmem-brane conductance regulator ( _CFTR_ ) gene (Brennan & Geddes 2002). This gene encodes for a protein that functions as a plasma membrane chloride channel in epithelial tissues, in particular in lung epithelium. If a person is homozygous for the _rare_ disease allele ( _R_ -allele), then he/she will develop cystic fibrosis. On the other hand, individuals will not develop the disease if they are homozygous for the _normal (N)_ allele (so called _wild type_ ) or when they are heterozygous, i.e. they have both the dominant _N_ -allele and the recessive _R_ -allele.
A genetic component in the etiology of periodontal disease was proposed as early as 1935 (reviewed in Loevy 1976). From the late 1990s a substantial increase in papers on putative genetic risk factors for susceptibility to and severity of periodontitis has appeared in the periodontal literature (Michalowicz _et al_. 1991; Hart 1994; Hart & Kornman 1997; Hart _et al_. 1997, 2000b; Page 1999; Page & Sturdivant 2002). The presence of genetic risk factors directly increases the probability of periodontal disease developing, and, if they are absent, this possibility is reduced. Genetic risk factors are part of the causal chain, or expose the host to the causal chain. Notably, it may be possible that an allele, which is originally defined as _R_ -allele, is associated with absence of disease; in such cases, the _R_ -allele could be considered protective.
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**Box 13-1** Human genes, polymorphisms and other definitions
Each normal human being has 23 pairs of chromosomes (the diploid human genome), 22 pairs of _autosomal_ chromosomes and 1 pair of sex chromosomes (XX for females and XY for males) (Fig. 13-1). From each pair, one chromosome is inherited from the father and one from the mother. Chromosomes show differences in size and have characteristic lateral series of bands (G-banding) ; therefore each chromosome can be identified by its characteristic size and banding pattern.
Each chromosome contains a long duplex of deoxyribonucleic acid (DNA). DNA consists of chemically linked sequences of nucleotides; these are the "building blocks" of the DNA and always contain a nitrogenous base. Four nitrogenous bases exist: adenine (A), guanine (G), cytosine (C), and thymine (T). The bases are linked to a sugar (2-deoxyribose), where a phosphate group is also added. The _haploid_ human genome (i.e. one copy of 22 autosomal chromosomes and one sex chromosome) consist of 3.3 ×109 nucleotides (also written as 3.3 ×109 base pairs (bp) ). In the chromosomes, DNA is arranged in a double helix model: two polynucleotide chains in the duplex are associated together by hydrogen bonding between the nitrogenous bases. These reactions are described as base pairing and they are complementary: G pairs only with C, and A pairs only with T. Therefore, if one chain of DNA is sequenced, the complementary chain of the duplex can be deduced.
DNA contains the genetic code and a given specific sequence of nucleotides encodes for the sequence of amino acids that constitutes the corresponding protein (Fig. 13-2). The genetic code is read in groups of three nucleotides; each trinucleotide sequence (triplet) is called a codon. Written in the conventional direction from left to right, the nucleotide sequence of the DNA strand, a gene can be deciphered. A gene consists of two parts (Fig. 13-2) : (1) a _coding region_ , i.e. a reading frame starting at nucleotide position +1, containing a multitude of triplets that codes for a sequence of amino acids to form a protein; and (2) a _promoter region_ , i.e. a sequence of nucleotides upstream (left) of the coding region starting with nucleotide position ‒1 read from right to left, that is not organized in a series of triplets but contains stretches of nucleotides that are essential for the regulation of the transcription of the coding region. Within the coding region intermittent areas of non-coding DNA exist; these regions are called introns. The true coding areas within the coding region are called exons (Fig. 13-2). From the recent results of the human genome project, it is estimated that about 25 000 human genes exist.
Variant forms (polymorphisms) of a gene that can occupy a specific chromosal site _(locus)_ are called _alleles._ Two or more alleles for a given locus may exist in nature throughout evolution, but may develop at any time. A _polymorphic_ locus is one whose alleles are such that the most common, _normal_ variant ( _N_ -allele) among them occurs with <99% frequency in the population. Thus, if a locus is for example _biallelic_ , the _rarer_ allele (designated _R_ -allele) must occur with a frequency >1% in the population. In this way, when different alleles of a given gene co-exist in the human population, we speak about _genetic polymorphisms_.
Polymorphisms arise as a result of gene mutations. All organisms undergo spontaneous mutations as a result of normal cellular function or random interactions with the environment. An alteration that changes only a single base pair is called a point mutation. Not all point mutations are repaired and can therefore be transmitted by inheritance through generations. The most common class of point mutations is the _transition_ , comprising the substitution of a G-C (guanine–cytosine) pair with an A-T (adenine–thymine) pair or vice versa. The variation at the site harboring such changes has recently been termed a "single nucleotide polymorphism" (SNP) (Schork _et al_. 2000).
The SNP may have no effects or may have some important biological effects. For example, if a transition has taken place within the coding region of a gene, it may result in an amino acid substitution and therefore an altered protein structure, which may then alter its function. Or, when such mutations have taken place in the promoter region of the gene, it may alter gene regulation, for example resulting in (completely) inhibited or reduced gene expression or, alternatively, result in over-expression of the gene, perhaps with biological consequences. SNPs occur more frequently than any other type of genetic polymorphism; the frequency of SNPs across the human genome is estimated at every 0.3–1 kilobases (Kb).
Other SNPs result from _insertions_ or _deletions_. The simple form of this polymorphism is where a single nucleotide pair may be deleted or may be inserted with the same potential effects as described above for the _transition_. Another common type of insertion/deletion polymorphism is the existence of variable numbers of repeated bases or nucleotide patterns in a genetic region. Repeated base patterns can consist of several hundreds of base pairs, known as "variable number of tandem repeats" (VNTRs or _minisatellites_ ). Also common are _microsatellites_ , which consist of two, three or four nucleotide repeats, on a variable number of occasions. Micro-satellites are also referred to as _simple tandem_ _repeats_ (STRs). Such repeats are considered highly polymorphic and often result in many alleles or gene variants due to the existence of many different repeat sizes within the population. The STRs may occur every 3–10 Kb genome wide.
Genetic polymorphisms are very useful in studies of population genetics. After genotyping individuals and assessing genotype frequencies among groups of interest, one can also calculate the frequency of the _N_ -allele and the _R_ -allele among the groups or populations under study. Frequencies of genotypes and alleles may differ between a diseased and a healthy group. Subsequently, when a given allele is identified to be associated with disease, functional studies can be started to investigate the possible role of that gene in the etiology and pathogenesis of the disease.
* * *
**Fig. 13-1** Schematic drawing of 23 pairs of chromosomes (the diploid human genome). Twenty-two pairs of autosomal chromosomes and one pair of sex chromosomes are present. In this case the genome of a male is shown (one X and one Y chromosome). In the case of a female, two X chromosomes would have been present. G-banding generates a characteristic lateral series of bands in each member of the chromosome set. Adapted from Hart _et al_. (2000a).
**Fig. 13-2** Schematic representation of a gene. The gene consists of a promoter and a coding region. Within the coding region, intermittent areas of non-coding DNA exist (intron). Exons contain triplets of nucleotides (codons) that code for a specific amino acid. The number and length of exons and introns within the coding region is variable per gene. Nucleotides are numbered throughout the whole coding region starting with number 1 for the first nucleotide. The nucleotides in the promoter region are also numbered, starting with –1.
# Evidence for the role of genetics in periodontitis
In the past it was thought that periodontitis would eventually develop in subjects with a longstanding history of poor oral hygiene and gingivitis. However, during the last decades the concept of high-risk groups was introduced. This concept arose on the basis of the results from epidemiologic studies as well as from longitudinal clinical studies and has been one of the factors that supported the development of the theory that periodontitis may have a genetic background.
A study from 1966 is one of the earliest studies from which it could be deduced that certain individuals are more at risk for periodontitis than others (Trott & Cross 1966). In this study the principal reasons for tooth extractions in over 1800 subjects were investigated. The figures showed that in each age category the percentage of teeth lost due to periodontal disease is always higher than the percentages of patients who lost teeth due to periodontal disease. This means that relatively many teeth are lost in relatively few patients. This phenomenon could be confirmed in a 28 year longitudinal study of an American population. It was found that in a group of subjects who had a full dentition at a mean age of 28 years, 28 years later 22% of the subjects were responsible for 77% of all teeth lost (Burt _et al_. 1990). The same phenomenon was found in two longitudinal studies evaluating the effect of periodontal therapy in periodontitis patients over more than 15 years (Hirschfeld & Wasserman 1978; McFall 1982). These studies showed that 20% of the patient populations accounted for about 75% of all lost teeth. The concept of high risk for the development of periodontitis was further confirmed in longitudinal studies investigating the natural history of periodontal disease. In a Sri Lankan population without dental care and absence of oral hygiene, investigators (Löe _et al_. 1986) were able to identify three subpopulations: a group with no progression (11%), a group with moderate progression (81%), and a group with rapid progression of periodontal breakdown (8%). In a recent study the initiation and progression of periodontal breakdown was studied in a population deprived from regular dental care in a remote village on Western Java (van der Velden _et al_. 2006). The authors found that 20% of the subjects developed severe breakdown whereas the remaining population developed minor to moderate breakdown.
The phenomenon that a relatively small proportion of the population is at risk for developing severe forms of periodontitis may suggest that not everybody is equally susceptible to periodontitis. The microbial causation of inflammatory periodontal diseases is well established (Löe _et al_. 1965; Socransky & Haffajee 1992). In addition the prevalence and proportions of periodontal pathogens are higher in periodontitis patients compared to healthy controls (Griffen _et al_. 1998; van Winkelhoff _et al_. 2002). However if periodontitis is simply and solely caused by one or more specific periodontal pathogens, the disease should develop in the majority of subjects infected by these organisms. In contrast, periodontal pathogens show a relatively high prevalence in subjects with gingivitis or minor periodontitis. For example, it was found in a large group of subjects with gingivitis or minor periodontitis (mean age 52 years) that there was a prevalence of 38% for _Aggregatibacter actinomycetemcomitans_ , 32% for _Porphyromonas gingivalis_ , and 42% for _Prevotella intermedia_ (Wolff _et al_. 1993). Therefore the existence of high-risk groups cannot be explained by the microbiology alone. There are, however, other factors that may play a major role in the development of periodontitis, i.e. the inflammatory and immune response both locally and systemically. These factors include systemic diseases, such as diabetes, and environmental factors, such as smoking and possible stress (Kinane _et al_. 2006). It is likely that the effectiveness of an individual's immune response influences the extent of periodontal destruction, which can be regarded as the susceptiblity of a subject to periodontitis.
## Heritability of aggressive periodontitis (early onset periodontitis)
Some time ago it was recognized that siblings of patients with juvenile periodontitis (JP) frequently also suffer from periodontitis. This was mainly based on case reports of one or a few families ascertained on the basis of one subject (the proband) with JP. In an American study on 77 siblings of 39 probands with localized (L) or generalized (G) JP, it was shown that almost 50% of the siblings also suffered from JP (Boughman _et al_. 1992). In 11 families a co-occurrence of LJP and GJP was present. As an epidemiological survey in the US showed that the prevalence of JP varies between 0.16 and 2.49% (Löe & Brown 1991), the high prevalence of JP in these families suggests a genetic background for the disease.
The largest JP family study included 227 probands with aggressive periodontitis (Marazita _et al_. 1994). There were 26 GJP individuals whose earlier records were consistent with LJP, i.e. demonstrating progression from the localized to a more generalized form. Furthermore, there were 16 families with co-occurrence of LJP and GJP, confirming the findings of Boughman _et al_. (1992). Out of the 227 probands, 104 had at least one first-degree relative clinically examined. Now it was possible to carry out a segregation analysis on 100 families (four families each had two probands). Segregation analysis is a formal method of studying families with a disease to assess the likelihood that the condition is inherited as a genetic trait. The family members included 527 subjects: 60 with LJP, 72 with GJP, 254 unaffected subjects, and 141 subjects with an unknown periodontal condition. The group of unaffected subjects included edentulous subjects, subjects with adult periodontitis, and periodontally healthy subjects. The majority of the families were of African American origin. The authors concluded that the most likely mode of inheritance was autosomal dominant in both African American and Caucasian kindred, with penetrance of 70% in African Americans and 73% in Caucasians.
## Heritability of chronic periodontitis (adult periodontitis)
Very few investigations exist with regard to family studies of probands with chronic (adult) periodontitis or younger subjects with minor periodontitis. In an early study of nuclear families, path models were used to investigate the relative influences of genetic and environmental factors in a large Hawaiian population in the age range of 14 to over 60 years (Chung _et al_. 1977). They concluded that the data failed to detect significant heritability, and common family environment proved to be a major determinant in the variation of periodontal health. In a periodontal study of families in the US published in 1993, 75 families consisting of 178 subjects largely <40 years of age were investigated (Beaty _et al_. 1993). To determine familiar aggregation, standard familial correlations were computed, i.e. father–mother, parent–offspring, sibling–sibling, etc. The results showed a statistically significant family effect for mean plaque index, but not for mean gingival index and mean attachment loss. Both the gingival index and attachment loss showed a stronger correlation between mothers and offspring compared to fathers and offspring. Yet another study analyzed the periodontal condition in an untreated population in Guatemala consisting of 109 siblings from 40 nuclear families with an age range of 35–60 years (Dowsett _et al_. 2002). They failed to show a familial clustering for periodontal disease.
The effect of sibling relationship on the periodontal condition was investigated in an epidemiologic study of a group of young Indonesians deprived of regular dental care (van der Velden _et al_. 1993). The study population included 23 family units consisting of three or more siblings. In all, 78 subjects aged 15–25 years were studied. The results of the analysis showed a significant sibling relationship effect for plaque, calculus, and loss of attachment but not for pocket depth. In order to study familial aspects of chronic (adult) periodontitis in a Dutch population, 24 families were selected at the Academic Center for Dentistry, Amsterdam (Petit _et al_. 1994), each consisting of a proband with chronic (adult) periodontitis, a spouse and one to three children. The mean age of the probands was 39 years, with a range from 30–50 years. In total 49 children were investigated with an age range of 3 months to 15 years. The results showed that none of the children under the age of 5 years was affected by periodontitis, whereas in the group of 5–15 years, 21% had at least 1 pocket ≥5 mm in conjunction with loss of attachment. In the group of 10–15 years this was 45%. This contrasts with the results of a cross-sectional epidemiological study carried out in the city of Amsterdam; it was shown that the prevalence of pockets ≥5 mm in conjunction with loss of attachment in 15-year-old adolescents is about 5% (van der Velden _et al_. 1989). Thus, and on the basis of the Petit _et al_. (1994) study, it can be suggested that chronic (adult) periodontitis may aggregate in families.
# A gene mutation with major effect on human disease and its association with periodontitis
This chapter focuses mainly on putative genetic risk factors that have been identified by the candidate gene approach, i.e. investigators have plausible arguments of a conceptual, biologic, and epidemiologic nature to investigate the association of the selected genetic polymorphism (s) with periodontitis. Nevertheless, by linkage analysis in specific families with several generations available and having among them one or more proband(s) with a strong disease phenotype, new disease genes may still be identified. Before the candidate genes and their respective genetic polymorphisms are explored in their association with periodontitis, we first discuss the discovery of a major disease gene associated with prepubertal periodontitis and Papillon-Lefèvre syndrome (PLS).
Periodontitis is recognized as a component of many single gene syndromes (Kinane & Hart 2003). Many of these disorders are characterized either by immune or structural deficiencies; of these syndromic disorders, PLS is relatively unique, in that periodontitis forms a significant component of the disease along with hyperkeratosis of the palms of the hands and soles of the feet.
The gene mutated in PLS was mapped to a specific band on the long arm of chromosome 11 (Fischer _et al_. 1997; Laass _et al_. 1997; Hart _et al_. 1998). Subsequently, this location was refined and a candidate gene within this region was identified that encoded for the lysosomal protease cathepsin C: the _CTSC_ gene (Toomes _et al_. 1999). Cathepsin C is a proteinase, which is found in neutrophils and lymphocytes as well as in epithelial cells. Toomes _et al_. (1999) elucidated its genomic organization, demonstrated mutations in the _CTSC_ gene in eight families, and showed that these mutations result in an almost complete loss of function of the enzyme. This was immediately confirmed (Hart _et al_. 1999) and Hart and co-workers demonstrated similar mutations in other families. To date more than 40 mutations have been reported in the _CTSC_ gene (Selvaraju _et al_. 2003; de Haar _et al_. 2004; Noack _et al_. 2004). Furthermore, interesting data from analyses in a single family with four different _CTSC_ mutations were reported (Hewitt _et al_. 2004) and the investigators proposed that minimal cathepsin C activity (∼13%) was necessary to prevent the clinical features of PLS. However, the exact mechanism by which an altered function of cathepsin C plays a role in the pathogenesis of the prepubertal form of periodontitis is unknown.
**Fig. 13-3** Through an internal marriage event in a family of Jordanian descent, Hart and co-workers have identified and localized a gene on chromosome 11 that is responsible for a severe form of prepubertal periodontitis (Hart _et al_. 2000a). Starting with four affected children from generation IV of two families, a disease causing _R_ -allele of the cathepsin C (CTS C) gene was discovered. Cathepsin C is a proteinase which is found in neutrophils and lymphocytes as well as epithelial cells. Affected children, but not their brothers and sisters, were homozygous for an A to G transition polymorphism at gene position +1040. This resulted in a substitution of the amino acid tyrosine by a cysteine. This polymorphism was shown to be functional as there was a decreased cathepsin C activity (Hart _et al_. 2000a). However, the mechanism by which an altered function of cathepsin C plays a role in the pathogenesis of the prepubertal form of periodontitis is unknown.
_CTSC_ mutations have also been identified in families with prepubertal periodontitis suggesting that this condition is allelic to PLS (Hart _et al_. 2000a) (Fig. 13-3). However, these mutations are not different to those observed in classical PLS and, notably, all cases of prepubertal periodontitis do not have mutations in _CTSC_. This suggests that prepubertal periodontitis is a genetically heterogeneous condition with some cases representing a variant of PLS (Hewitt _et al_. 2004). There has also been speculation that polymorphic functional variants of _CTSC_ may be involved in the more common type of aggressive periodontitis. However, given that carriers of a mutant copy of the gene are phenotypically unaffected and that very little cathepsin C activity appears to be necessary in order to prevent the disease, this seems an unlikely hypothesis. Indeed, evidence against this hypothesis was provided (Hewitt _et al_. 2004); it was shown that there was no difference in cathepsin C activity between 30 cases of aggressive periodontitis and controls.
# Disease-modifying genes in relation to periodontitis
Periodontitis develops in a limited subset of humans. About 10–15% of the population will develop severe forms of destructive periodontal disease. The disease is importantly influenced by the microorganisms in the subgingival biofilm, by acquired systemic diseases that reduce or hamper an "optimal" host response, and by environmental factors. Specific bacteria in the microbial biofilm and smoking are accepted as true rather than putative risk factors. On top of the above risk factors are disease-modifying genes, which contribute to susceptibility and severity of periodontitis. For these disease-modifying genes, Mendelian principles do not apply (Hart 1996; Hart _et al_. 2000b), because both heterozygous and homozygous subjects for a given disease-modifying gene may not necessarily develop the disease; other genetic risk factors (gene–gene interactions) and/or environmental risk factors (gene–environmental interactions) also need to be present simultaneously (definition of complex disease).
Currently, very little is known about which genes may be involved in periodontitis as disease-modifying genes. Table 13-1 summarizes the candidate gene polymorphisms investigated in relation to periodontitis. It is clear from this summary that, as the immune system plays a crucial role in the pathogenesis of periodontitis, researchers have concentrated on the identification of genetic polymorphisms in several aspects of host immunity.
Below we summarize the epidemiological findings in various studies of candidate genes as risk factors (Loos _et al_. 2005). We have grouped some candidate genes together and possible mechanisms of action are given in boxes, i.e. which arguments have been used and which hypotheses have been proposed to study the various modifying genes in relation to periodontitis.
**Table 13-1** Summary of candidate genes, and the corresponding encoded proteins, for which gene polymorphisms have been investigated as putative risk factors for periodontitis
**Gene** | **Coded protein**
---|---
_ACE_ | Angiotensin-converting enzyme
_CARD15 (NOD2)_ | Caspase recruitment domain-15
_CCR5_ | Chemokine receptor-5
_CD14_ | CD-14
_ER2_ | Estrogen receptor-2
_ET1_ | Endothelin-1
_FBR_ | Fibrinogen
_FcγRIIa_ | Fc γ receptor IIa
_FcγRIIb_ | Fc γ receptor IIb
_FcγRIIIa_ | Fc γ receptor IIIa
_FcγRIIIb_ | Fc γ receptor IIIb
_FPR1_ | _N-formylpeptide receptor-1_
_IFNGR1_ | Interferon γ receptor-1
_IL1A_ | Interleukin-1α
_IL1B_ | Interleukin-1β
_IL1RN_ | Interleukin-1 receptor antagonist
_IL2_ | Interleukin-2
_IL4_ | Interleukin-4
_IL6_ | Interleukin-6
_IL10_ | Interleukin-10
_LTA_ | Lymphotoxin-α
_MMP1_ | Matrix metalloproteinase-1
_MMP3_ | Matrix metalloproteinase-3
_MMP9_ | Matrix metalloproteinase-9
_MPO_ | Myeloperoxidase
_NAT2_ | _N-acetyltransferase-2_
_PAI1_ | Plasminogen-activator-inhibitor-1
_RAGE_ | Receptor for advanced glycation end products
_TGFB_ | Transforming growth factor-β
_TIMP2_ | Tissue inhibitor of matrix metalloproteinase
_TLR2_ | Toll-like receptor-2
_TLR4_ | Toll-like receptor-4
_TNFA_ | Tumor necrosis factor-α
_TNFR2_ | Tumor necrosis factor receptor-2
_VDR_ | Vitamin D receptor
## IL-1 and TNF-a gene polymorphisms
In Box 13-2, several arguments have been summarized to justify why the genes encoding for interleu-kin-1 (IL-1) and tumor necrosis factor-α (TNF-α) appear to be good candidates for genetic studies in relation to periodontitis.
### Epidemiological findings for gene polymorphisms in the _IL1_ gene cluster
The genes _IL1A_ , _IL1B_ , and _IL1RN_ encoding for the proteins IL-1α, IL-1β, and IL-RA respectively, are located in close proximity in the _IL1_ gene cluster on chromosome 2. Kornman _et al_. (1997) reported first on polymorphisms for the _IL1_ genes in relation to periodontitis. This study reports on an _IL1_ composite genotype (see below), however no data are presented for the carriage rates of the individual _IL1 R_ -alleles ( _IL1A_ , _IL1B_ , _IL1RN_ ). To date, the following _IL1_ genetic polymorphisms have been studied in relation to periodontitis: _IL1A_ ‒889 (in linkage with +4845), _IL1B_ ‒511 (in linkage with ‒31), _IL1B_ +3954 (also mentioned in the literature as +3953) and _IL1RN_ VNTR (in linkage with +2018).
It has become clear that among the different studies with exclusively Caucasian subjects, considerable variation is seen for the carriage rates of the _IL1 R-_ alleles. For example for the polymorphic _IL1A_ ‒889 (+4845), the carriage rate for the _R-_ allele varies from 34–64% for patients and 35–60% for controls. None of the studies involving Caucasians and non-Caucasians have found a significant association between periodontitis and/or disease severity and _IL1A_ ‒889 (+4845) as single risk factor, except when combined with other _IL1_ polymorphisms. The car-riage rate of the _IL1A_ ‒889 (+4845) _R-_ allele in Chil-eans was comparable to that reported by other reports (Quappe _et al_. 2004), while the carriage rate among Japanese people appears lower (Tai _et al_. 2002). The latter finding demonstrates an important issue, that is that carriage rate of genetic polymorphisms may vary among different ethnic populations. Therefore, possible positive associations between a genetic polymorphism and disease within one population may not necessarily be extrapolated to other populations.
Three studies have reported carriage rates for the _IL1B_ ‒511 (‒31) _R-_ allele, and to date this genetic poly-morphism has not been associated with periodonti-tis. The carriage of the _R-_ allele was higher among Japanese people (67–78%) than among Caucasians (59%) (Gore _et al_. 1998; Tai _et al_. 2002; Soga _et al_. 2003).
The SNP _IL1B_ +3954 (+3953) initially appeared promising as risk factor for periodontitis among Cau-casians. However there are conflicting results. Galbraith _et al_. (1998) found an association between the _R-_ allele and periodontitis and Gore _et al_. (1998) observed an association with the severity of periodontal destruction. Quappe _et al_. (2004) reported that the _N-_ allele might indeed be protective for periodontitis in Chileans. By contrast, Parkhill _et al_. (2000) observed an over-representation of the _N_ -allele among early onset periodontitis (EOP) patients, and they concluded that the _N-_ allele, and in particular in smokers, is associated with periodontitis, rather than the _R-_ allele. The latter observation was also shown in a family linkage analysis, which included both fami-lies of African American and Caucasian heritage, therefore implying a role in the disease process for the _N_ -allele (Diehl _et al_. 1999). Among Japanese subjects, the carriage rate of the _IL1B_ +3954 (+3953) is importantly low (< 10%), and given this low carriage rate, no association with periodontitis can be expected. Clearly, large-scale studies in homogeneous populations are needed to further investigate the potential of the _IL1_ +3954 (+3953) genotypes as risk factors for periodontitis.
**Box 13-2** Why are genes encoding for IL-1 and TNF good candidates as modifying disease genes for periodontitis?
There is evidence to suggest that IL-1 and TNF-αplay important roles in the pathogenesis of periodontitis. IL-1α, IL-1β, and TNF-α are potent immu-nologic mediators with proinflammatory properties. Moreover, IL-1 and TNF-α have the capacity to stimulate bone resorption and they can regulate fibroblast cell proliferation, of both gingival and periodontal ligament origin. IL-1 and TNF-α levels are increased in the gingival crevicular fluid of periodontitis subjects and these cytokines are found in higher levels in inflamed periodontal tissues com-pared to healthy tissues.
Various studies have suggested that polymor-phisms in the genes of the _IL1_ cluster and in the _TNFA_ gene, could predispose subjects to elevated IL-1 (decreased IL-1 receptor antagonist (RA) ) and TNF-α protein levels. The majority of these cited studies suggest that the _R_ -allele of a given polymor-phism in the promoter region results in an upregu-lation of protein production. These studies have often been performed with isolated cells of healthy individuals or with cultured cell lines or cell con-structs (transfected cells).
Inherent (most likely genetically determined) interindividual differences have also been observed for IL-1 and TNF-α production by peripheral blood mononuclear cells or oral leukocytes, isolated from individuals with and without periodontitis. It is conceivable that these differences in IL-1 and TNF-α production and secretion play a role as risk factors, however insufficient evidence currently exists to conclude that this is a key phenomenon occurring in the pathophysiology of periodontitis. Neverthe-less, the concept is attractive and may explain some of the epidemiologic findings of genetic polymor-phisms associated with the susceptibility to and severity of periodontitis.
Some _IL1_ and _TNFA R_ -alleles have been sug-gested as potential genetic markers for other complex diseases. For example, _IL1_ and _TNFA_ gene polymorphisms have been associated with several inflammatory and infectious disease processes, including inflammatory bowel disease, Sjögren syndrome, rheumatoid arthritis, meningo-coccal disease, systemic lupus erythematosus, and psoriasis.
Few studies have investigated polymorphisms in the _IL1RN_ gene and again conflicting results are reported. In Caucasians the _R-_ allele was not associ-ated as single risk factor with periodontitis, however in combination with other _IL1_ SNPs it was reported to have a possible relationship with periodontitis prevalence and severity (Laine _et al_. 2001; Meisel _et al_. 2002). In Japanese subjects the _IL1RN R_ -allele was significantly associated with periodontitis (Tai _et al_. 2002). In contrast, Parkhill _et al_. (2000) observed the _IL1RN N_ -allele in combination with the _IL1B_ +3954 _N_ -allele and smoking to be associated with early onset periodontitis (EOP).
Kornman _et al_. (1997) reported that the combined presence of the _R-_ allele of the _IL1A_ gene at nucleotide position ‒889 and the _R-_ allele of the _IL1B_ gene at nucleotide position +3954 (+3953) was associated with severity of periodontitis in non-smoking Cauca-sian patients. This combined carriage rate of the _R-_ alleles was designated the _IL1_ composite genotype (Kornman _et al_. 1997). Since that time a considerable number of studies investigating the _IL1_ composite genotype in Caucasians and non-Caucasians has been published. An association between the _IL1_ com-posite genotype and the severity of periodontal destruction has also been reported by two other cross-sectional studies (McDevitt _et al_. 2000; Papapanou _et al_. 2001). However, other studies have failed to corroborate that _IL1_ composite genotype alone may behave as a risk factor for periodontitis severity (Gore _et al_. 1998; Ehmke _et al_. 1999; Catta-briga _et al_. 2001; Laine _et al_. 2001; Meisel _et al_. 2002, 2003, 2004). In contrast to the results of Kornman _et al_. (1997), Meisel _et al_. (2002, 2003, 2004) observed the _IL1_ composite genotype to be associated with periodontitis in smokers. These conflicting results cast doubt on the utility of the _IL1_ composite genotype as a putative risk factor for severity of periodontitis in Caucasians. Nevertheless, it has also been reported that patients with the _IL1_ composite genotype more often harbored putative periodontal pathogens and have increased counts of these pathogens (Socransky _et al_. 2000). Interestingly, Laine _et al_. (2001) reported increased frequency of the _R_ -alleles of the _IL1A_ , _IL1B_ , and _IL1RN_ genes in non-smoking patients in whom
_P. gingivalis_ and _A. actinomycetemcomitans_ could not be detected. These latter results suggest that _IL1_ gene polymorphisms may play a role in the absence of other (putative) risk factors (Meisel _et al_. 2002, 2003, 2004).
Studies among Chinese Americans and African Americans have not resulted in interpretable findings, because the _IL1_ composite genotype was hardly present in these ethnic populations (Armitage _et al_.
2000; Walker _et al_. 2000). In South American subjects the carriage rate of the _IL1_ composite genotype (up to 25%) was somewhat lower than that reported for Europeans and North American study subjects (up to 48%) and no associations with periodontitis have been found.
Several longitudinal studies on _IL1_ polymorphisms have been performed. From these studies it may be possible to assess whether a given genotype can be considered a true risk factor. For example, it was reported among periodontitis patients in mainten-ance over 5–14 years, that the _IL1_ composite geno-type increased the risk of tooth loss by 2.7-fold (McGuire & Nunn 1999). The _IL1_ composite genotype in combination with heavy smoking increased the risk of tooth loss by 7.7-fold (McGuire & Nunn 1999). In an Australian study 295 gingivitis and moderate periodontitis subjects were followed for 5 years and the _IL1_ composite genotype was determined (Cul-linan _et al_. 2001) ; the investigators reported that among non-smoking subjects >50 years, those that were _IL1_ composite genotype positive, had deeper probing depths than _IL1_ composite genotype nega-tive subjects. Furthermore, a significant interaction was found between carriage of the _IL1_ composite genotype and age, smoking, and the presence of
_P. gingivalis_ , which suggests that the _IL1_ composite genotype is a contributory but non-essential risk factor (Cullinan _et al_. 2001).
In summary, for the global population, polymor-phisms in the _IL1_ gene cluster cannot be regarded as (putative) risk factors for periodontitis or severity of periodontal destruction. For Caucasian patients with chronic periodontitis the role of the _IL1_ composite genotype seems to hold some promise, however to date no clear evidence has emerged and there are currently too many conflicting and negative results. Large cohort studies of homogeneous composition should be initiated, in which all of the currently accepted non-genetic (putative) risk factors are included. Multi-variate analyses should be employed to estimate relative contributions of all factors.
### Epidemiological findings for _TNFA_ gene polymorphisms
The _TNFA_ gene is located on chromosome 6 within the major histocompatibility complex (MHC) gene cluster. Several case–control studies in both Cauca-sians and non-Caucasians have investigated genetic polymorphisms in the _TNFA_ gene as putative risk factors for periodontitis. SNPs in the gene encoding TNF-α are mainly studied in the promoter region at positions ‒1031, ‒863, ‒367, ‒308, ‒238 but also in the coding region in the first intron at position +489.
Similar to findings for genes of the _IL1_ cluster, dif-ferences for the carriage rate of the _R-_ alleles between Caucasians and other ethnic populations were appar-ent; at position ‒308 the _R_ -allele carriage rate for Caucasians varied between 20% and 3%, while this was 2–3% for Japanese subjects. For the _TNFA_ ‒238 the frequencies of _R_ -alleles were comparable between both ethnic populations (<10%). The carriage rates of the _R_ -alleles at positions ‒367 and ‒238 were <10%, making them less likely to be associated with periodontitis; indeed no associations have been found with periodontitis for these SNPs (Galbraith _et al_. 1998; Craandijk _et al_. 2002; Soga _et al_. 2003).
Among Japanese subjects, associations with periodontitis have been observed for the SNPs _TNFA_ ‒1031 and ‒863 (Soga _et al_. 2003) ; these polymorphisms have not been tested in Caucasians. Among Cauca-sians, the only association of a _TNFA_ polymorphism was observed at position ‒308 by Galbraith _et al_. (1998) and this was not corroborated by other studies with Caucasians in the study population. Among families with a high prevalence of EOP, the _TNFA_ ‒308 gene polymorphisms have also been investi-gated, but were found not to be associated with EOP (Shapira _et al_. 2001). Another marker in the TNF-αgene was investigated in relation to susceptibility for aggressive periodontitis. This marker was based on a variable number of micro-satellite repeats, but was not found to be associated with generalized juvenile periodontitis (GJP) (Kinane _et al_. 1999).
Investigations into the severity of periodontitis in relation to any of the _TNFA R-_ alleles did not reveal a positive association. The carriage of the _R-_ allele at nucleotide positions ‒308 and ‒238 revealed no asso-ciation between the percentage of teeth with ≥50% bone loss (Craandijk _et al_. 2002). Moreover, the car-riage rates of the _R-_ alleles at nucleotide positions ‒376, ‒308, ‒238, and +489 were not different between patients with moderate or severe periodontitis. Others reported also a lack of association of _TNFA_ genetic polymorphisms with the severity of periodontitis (Kornman _et al_. 1997; Galbraith _et al_. 1998).
Based on the available literature to date, there is very limited data to support associations between any of the reported _TNFA_ gene variations and periodontitis. _TNFA_ ‒1031 and ‒863 may have promise, but they have only been tested in one study among Japanese subjects. More studies are needed to address _TNFA_ polymorphisms and these studies should also involve investigations into other genetic polymor-phisms in genes like _IL1_ , for possible gene–gene interactions that may play a role in the complex pathogenesis of periodontitis.
## FcγR gene polymorphisms
In Box 13-3, some background has been summarized to explain why the genes encoding for Fc gamma receptors (FcγR) seem good candidates for genetic studies in relation to periodontitis.
Several studies have investigated the _Fc_ γ _RIIa_ poly-morphisms in relation to periodontitis in several populations. In Caucasians and African Americans, the carriage rate of the _R-_ allele is relatively high: 63– 77% (Colombo _et al_. 1998; Meisel _et al_. 2001; Fu _et al_. 2002; Loos _et al_. 2003; Yamamoto _et al_. 2004). In Japa-nese people the carriage rate is lower: 39–50%. In Japanese people and African Americans, the _Fc_ γ _RIIa_ polymorphisms are not associated with periodontitis or with the severity of the disease. However, in Cau-casians some studies showed an association, with the _N_ -allele rather than the expected _R-_ allele (Loos _et al_. 2003; Yamamoto _et al_. 2004). A weak relationship with aggressive periodontitis was observed for the _Fc_ γ _RIIa N_ -allele (Loos _et al_. 2003). Moreover, periodontitis patients (aggressive and chronic periodon-titis) homozygous for the _N_ -allele (H/H131 genotype) have more periodontal bone loss than the other patients carrying one or two _R-_ alleles. Homozygosity for the _N_ -allele was significantly more prevalent in periodontitis (Yamamoto _et al_. 2004).
* * *
**Box 13-3** Why are genes encoding for FcγR good candidates as disease-modifying genes for periodontitis?
Leukocytes from both the myeloid and lymphoid lineages express receptors (FcγR) for the constant (Fc) region of immunoglobulin G molecules. Indeed, FcγR are found on a wide variety of immune cells in the periodontal tissues. FcγRs are likely to play a role in the pathogenesis of periodontitis, as a bridge between the cellular and humoral branches of the immune system. Microorganisms and bacterial antigens, opsonized with antibody, can be phago-cytosed via FcγR on neutrophils or internalized via FcγR by a variety of antigen-presenting cells (APCs), including monocytes, macrophages and B cells. T cells and natural killer (NK) cells may become acti-vated, when IgG-opsonized bacteria are bound to these cells via FcγR; a variety of cytokines and che-mokines may also be released. When one or several of the FcγR-mediated leukocyte functions are com-promised or exaggerated due to genetic polymor-phisms in the FcγR genes, it is conceivable that the susceptibility to and/or severity of periodontitis is affected. This concept was proposed more than a decade ago.
The leukocyte _Fc_ γ _R_ genes are found on chromo-some 1, and encode three main receptor classes: FcγRI (CD64), FcγRII (CD32), and FcγRIII (CD16). These classes are further subdivided into subclasses: FcγRIa and b, FcγRIIa, b, and c, and FcγRIIIa and b. FcγRIIa is found on all granulocytes, on APCs, platelets, endothelial cells, and a subset of T cells. FcγRIIIa is present on monocytes and macrophages, NK cells and a subset of T cells. The FcγRIIIb is the most abundantly expressed IgG receptor on neutrophils.
Structural and functional differences in FcγRIIa, IIIa and b have been described (Fig. 13-4). G to A transition polymorphisms in the FcγRIIa gene result in the substitution of histidine (H) for arginine (R) at amino acid position 131 of the receptor. FcγRIIa-H131 binds IgG2 immune complexes efficiently, whereas the FcγRIIa-R131 allotype cannot mediate this interaction. The G to T transition polymorphism in the FcγRIIIa gene, results in an amino acid 158-valine (V) substitution for 158-phenylalanine (F). The FcγRIIIa-V158 has a higher affinity for IgG1 and 3 than FcγRIIIa-F158. Moreover, FcγRIIIa-V158 can bind IgG4 while FcγRIIIa-F158 is unable to do so. A bi-allelic polymorphism in the FcγRIIIb gene under-lies the FcγRIIIb-neutrophil antigen (NA) 1 or NA2 allotype. This is caused by four amino acid substitutions in the Fc-binding region resulting in differ-ences in glycosylation. The NA2 type binds less efficiently human IgG1 and IgG3 immune com-plexes than FcγRIIIb-NA1.
* * *
**Fig. 13-4** Schematic drawing of three of the human Fc receptors for IgG. They have an extracellular part, a transmembrane region and a cytoplasmic tail (except FcγRIIIb, which is anchored in the outer leaflet of the cell membrane via a glycosyl-phosphatidyl-inositol (GPI) molecule). The extracellular part of leukocyte FcγR class II and III consists of two immunoglobulin-like domains. The + sign in the intracellular signaling motifs (cylinder) indicates the capacity of signaling to the cytoplasmic environment of the cell. The FcγRIIa-mediated effector functions can be established through the intracellular signaling motif (cylinder) within the cytoplasmic tail of the molecule. The FcγRIIIa is associated with a γ-chain homodimer, which serves as signaling subunit. The FcγRIIIb-mediated effector functions are transmitted through the GPI. The functional genetic polymorphisms are depicted as black dots (•) in the extracellular Ig-like domains. For the FcγRIIa at amino acid position 131, arginine (R) or histidine (H) is present. For the FcγRIIIa at amino acid position 158, valine (V) or phenylalanine (F) is present. The FcγRIIIb polymorphism is caused by four amino acid substitutions at positions 18, 47, 64, and 88 and results in glycosylation differences, affecting receptor affinity. The CD indication in parentheses indicates the numbering within the cluster of differentiation system of immunological markers (van der Pol & van de Winkel 1998).
For the _Fc_ γ _RIIIa_ gene again a lower _R-_ allele car-riage rate is seen in Japanese than in Caucasian and African American subjects. The _Fc_ γ _RIIIa N_ -allele (V158) seems as a putative risk factor for periodonti-tis (Meisel _et al_. 2001; Loos _et al_. 2003). However, in Japan, both the _Fc_ γ _RIIIa R-_ allele (F158), as well as the _Fc_ γ _RIIIa N_ -allele, were proposed as risk factors. It is apparent that there are conflicting results and com-parisons between the different studies are difficult as the prevalences of _Fc_ γ _R_ genotypes are different among subjects of different ethnic background.
In Japanese patients, the _Fc_ γ _RIIIb R_ -allele (NA2) was associated with generalized (G) -EOP (Kobayashi _et al_. 2000) and was found more often in adult patients with disease recurrence (Kobayashi _et al_. 1997). The carriage rate of the _Fc_ γ _RIIIb R_ -allele in Caucasians is relatively high (>75%) and to date no associations with periodontitis have been found.
The possibility that genes encoding for Fcγ recep-tors are associated with periodontitis in different ethnic groups seems promising. However, to date no clear and convincing data are present to definitively designate one or more of the _Fc_ γ _R_ gene polymor-phisms as true risk factors for periodontitis. Further research is needed in larger groups of subjects from different global populations to confirm the current observations. Furthermore, functional studies among subjects with different FcγR genotypes need to be undertaken to investigate the corresponding pheno-types and unravel the role of the Fcγ receptors in the pathogenesis of periodontitis.
## Gene polymorphisms in the innate immunity receptors
There are some good arguments why the genes encoding for proteins of the innate immune response are good candidate genes in relation to periodontitis (Box 13-4).
Two studies with Caucasian subjects investigated the _CD14_ ‒260 polymorphism in chronic periodonti-tis, but did not find associations (Holla _et al_. 2002; Folwaczny _et al_. 2004a). However after stratification of the cohort according to gender, it was found that the _CD14_ ‒260 _N_ -allele was more prevalent among females with periodontitis (67%) than among healthy control subjects (44%) (Folwaczny _et al_. 2004a). In a Japanese study, again no association was found between the _CD14_ ‒260 polymorphism and periodontitis (Yamazaki _et al_. 2003). Nevertheless, Holla _et al_. (2002) found among Caucasians a tendency for an increased frequency of the _CD14_ ‒260 _R/R_ geno-type in patients with severe disease (19.2%) com-pared with the patients with moderate disease (8.3%). The _CD14_ ‒260 _R/R_ genotype was also associated with severe periodontitis in Dutch Caucasians; even stronger association was found after adjusting for age, gender, smoking, and presence of _P. gingivalis_ and _A. actinomycetemcomitans_ (Laine _et al_. 2005). Results for another polymorphism in the _CD14_ gene have also been reported (Holla _et al_. 2002) ; a higher frequency of the _N_ -allele and the _N/N_ genotype of the _CD14_ ‒1359 polymorphism was found in patients with severe periodontal disease than in patients with moderate periodontitis.
Two studies have attempted to associate _TLR_ polymorphisms with periodontitis (Folwaczny _et al_. 2004b; Laine _et al_. 2005). However, despite the perceived importance of these functional _TLR_ poly-morphisms, no relation with periodontitis has been observed.
Although the polymorphisms of the _CARD15_ ( _NOD2_ ) gene are strongly associated with Crohn's disease (Hugot _et al_. 2001), to date they have not been associated with periodontitis (Folwaczny _et al_. 2004c; Laine _et al_. 2004).
## Vitamin D receptor gene polymorphisms
Several arguments have been put forward for the vitamin D receptor ( _VDR_ ) gene to be proposed as candidate gene in relation to periodontitis (see Box 13-5).
Several studies have identified a _VDR_ polymor-phisms in relation to periodontitis at positions _Taq-1_ , _Bsm-1_ , and _Fok-1_ (Hennig _et al_. 1999; Tachi _et al_. 2001, 2003; Yoshihara _et al_. 2001; Sun _et al_. 2002; Taguchi _et al_. 2003; de Brito Junior _et al_. 2004). The studies on the _Taq-1_ and _Bsm-1_ SNPs of the _VDR_ gene have found some associations with periodontitis, however not unconditionally. The carriage rate of the _R_ -allele ranges between 12 and 66% across different ethnic populations, among Brazilians it was in the higher range (45–66%) and in Japanese the lower rate (5– 12%). In the study by Hennig _et al_. (1999) the carriage rate of the _R_ -allele ranged between 32 and 37%. Nev-ertheless, in five case–control studies an association of the _R_ -allele with several forms of periodontitis have been observed (Hennig _et al_. 1999; Tachi _et al_. 2001; Yoshihara _et al_. 2001; Sun _et al_. 2002; de Brito Junior _et al_. 2004), while in one Japanese study an association with the _N_ -allele has been found (Tachi _et al_. 2003). The apparent discrepancy cannot be explained, however it may relate to different gene–environment interactions affecting different ethnic populations and/or it is related to differences in the type of periodontitis being investigated. More-over, we cannot exclude that there is a lack of con-sistency in "case definition" for each disease type between studies.
* * *
**Box 13-4** Why are genes encoding for receptors of the innate immune response good candidates as disease-modifying genes for periodontitis?
The innate immune response is the first line of defense in infectious diseases. Without having to wait until an antigen-specific immune response is in full action (3–5 days), the host is challenged to detect the pathogen and to mount a rapid, immedi-ate defensive response. The innate immune system recognizes pathogen-associated molecular patterns (PAMPs) that are expressed on microorganisms, but not on host cells. Extra- and intracellular recep-tors like CD14, CARD15, and toll-like receptors (TLRs) recognize PAMPs of Gram-positive and Gram-negative bacteria and mediate the production of cytokines necessary for further development of effective immune response (Fig. 13-5). Both TLR2 and TLR4 use CD14 as a co-receptor.
The _R_ -allele in the promoter region of _CD14_ at position ‒260 (‒159) enhances the transcriptional activity of the gene. Individuals homozygous for the _R-_ allele have increased serum levels of soluble (s) CD14 and an increased density of CD14 in monocytes. The _CD14_ ‒260 SNP has previously been associated of increased risk with myocardial infarction and Crohn's disease. Furthermore, increased serum levels of sCD14 have been associated with periodontitis.
Two common co-segregating missense polymor-phisms of _TLR4_ , Asp299Gly and Thr399Ile, affect the extracellular domain of the TLR4 protein, leading to an attenuated efficacy of signaling and a reduced capacity to elicit inflammation. The _TLR4_ Asp299Gly gene polymorphism has been correlated with hypo-responsiveness to inhaled LPS, sepsis, and infections caused by Gram-negative bacteria.
The 3020insC and 2104 C > T polymorphisms of the _CARD15 (NOD2)_ gene lead to impaired activation of nuclear factor-kappa B, resulting in altered transcription of proinflammatory cytokine genes and reduced expression of these cytokines. These polymorphisms are strongly associated with Crohn's disease.
* * *
The _VDR_ gene is an interesting candidate gene for its association with periodontitis, because it affects both bone metabolism and immune functions. Moreover some encouraging results have been found for different ethnic populations. Further studies should be engaged to confirm the current preliminary data.
**Fig. 13-5** Schematic drawing of a cell and the intracellular activation of the NF-kappa B pathway. The NF-kappa B pathway stimulates the nucleus to increase production of inflammatory mediators. Extra- and intracellular receptors, toll-like receptors 4 and 2 (TLR-4 and TLR-2), MBL, IL-1 receptor (IL-1R) and CARD15, recognize pathogen-associated molecular patterns (PAMPs) of Gram-positive and Gram-negative bacteria and mediate the production of cytokines necessary for further development of effective immune response. Both TLR-2 and TLR-4 use CD14 as a co-receptor. PAMPs are lipopolysaccharide (LPS), lipoteichoic acid (LTA), peptidoglygan (PGN), and polysaccharide (PS).
## IL-10 gene polymorphisms
There are some interesting arguments why the gene encoding for interleukin-10 (IL-10) is a candidate gene for periodontitis (Box 13-6).
* * *
**Box 13-5** Why is the gene encoding for vitamin D receptor a good candidate as a disease-modifying gene for periodontitis?
Alveolar bone destruction results from the periodontitis disease process. If left untreated, conse-quences of periodontitis are tooth mobility and eventually tooth exfoliation. Therefore, it is conceivable that mediators of bone metabolism play a role in the pathophysiology of periodontitis. With this is in mind investigators have identified genetic polymorphisms in genes coding for mediators in bone homeostasis, in particular the _VDR_ gene. Bone homeostasis mediators are linked to factors affecting bone mineral density and have been related to disorders of bone metabolism, such as osteoporosis and osteoarthritis. Interestingly, genetic polymorphisms in the _VDR_ gene have also been associated with infectious diseases, in particular tuberculosis. In addition to mediating bone homeostasis, vitamin D and its receptor play a role in phagocytosis by monocytes and affect monocyte differentiation.
* * *
_IL10_ gene microsatellite markers have been investigated in relation to aggressive periodontitis (Kinane _et al_. 1999). However, no significant differences in frequencies of various _IL10_ alleles between patients and periodontally healthy controls were observed. In Japanese patients either with G-EOP or with adult periodontitis (AP), as well as controls, three polymorphisms in the promoter region of the _IL10_ gene were analyzed (Yamazaki _et al_. 2001). No significant differences for the carriage rates of the polymorphism in the _IL10_ gene were seen between all patients and controls. Also no significant differences were observed for these latter haplotypes between AP and EOP.
The _IL10_ ‒1087 polymorphism may be an interesting polymorphism for future studies among Caucasians. It has been shown in one study that the _N_ -allele is more abundant in periodontitis in particular in non-smokers (Berglundh _et al_. 2003). These observations have led the authors to speculate that the _N_ -allele prevalence in periodontitis patients may result in higher levels of auto-antibodies, which may lead to increased periodontal destruction (Berglundh _et al_. 2003). These observations were not corroborated by a Brazilian study (Scarel-Caminaga _et al_. 2004) ; the latter study observed a trend for increased carriage of the _IL10_ ‒1087 _N_ -allele among controls.
In summary, a limited number of studies have investigated genetic variations at three positions in the _IL10_ promoter region, but to date _IL10_ is not a strong candidate gene due to the mixed results in the various studies in the literature.
**Box 13-6** Why is the gene encoding for IL-10 a good candidate as a disease-modifying gene for periodontitis?
The gene encoding IL-10 is located on chromosome 1, in a cluster with closely related interleu-kin genes, including _IL19_ , _IL20_ , and _IL24_. IL-10 is produced by monocytes/macrophages and T cells and plays a role in the regulation of proinflammatory cytokines such as IL-1 and TNF-α. In particular, IL-10 is considered an anti-inflammatory cytokine, down-regulating the proinflammatory immune response of the monocyte/macrophage and stimulating the production of protective anti-bodies. However, it has also been suggested that IL-10 can stimulate the generation of auto-anti-bodies. As a matter of fact, auto-antibodies may play a role in periodontitis. Functional disturbance in the _IL10_ gene due to genetic polymorphisms could be detrimental to host tissues and could be linked to periodontal disease susceptibility. The _IL10_ SNPs have been associated with altered IL-10 production. _IL10_ genetic polymorphisms have been associated with systemic lupus erythematosus and rheumatoid arthritis.
## Miscellaneous gene polymorphisms
Table 13-2 lists various other candidate gene poly-morphisms that have been studied in relation to periodontitis. These are not discussed as the other candidates above, since mainly negative results have been obtained and/or too few studies are published for a meaningful analysis. However, the table illustrates the variety of candidates and the difficulty in interpreting results; if some positive results are reported, these are often in subgroups or conditional. Clearly, further studies are needed employing larger patient numbers, which focus on candidate genes that have a proven role in the patho-physiology of periodontitis, where gene polymorphisms result in functional changes or are linked to other gene polymorphisms which in turn are strong markers of inflammatory and/or infectious diseases.
# Disease-modifying genes in relation to implant failures and peri-implantitis
The success of implant dentistry is often reported as survival rate (i.e. the implant is functional and present in the mouth after a given observation period). Several longitudinal studies have reported survival rates of around 90–95% over periods of 5–10 years (Esposito _et al_. 1998; Berglundh _et al_. 2002; Roos-Jansaker _et al_. 2006). However, complications do occur; in the latter studies early implant loss has been reported to occur in 1–7% of the implants and late implant loss with a follow-up of 5–14 years can occur in 2–13% of the implants.
**Table 13-2** Polymorphisms in miscellaneous genes studied in relation to periodontitis and reported association (adapted from Loos _et al_. 2005) investigated as markers for early or late implant failure and/
**Polymorphism in gene** | **Number of studies** | **Associated with periodontitis reported respectively**
---|---|---
_ACE_ | 1 | − (+ 1)
_CCR5_ | 1 | −
_ER2_ | 1 | −
_ET1_ | 1 | −
_FBR_ | 1 | \+ 2
_FcγRIIb_ | 1 | +
_FPR1_ | 1 | − (+ 3)
_IL2_ | 1 | − (+ 4)
_IL4_ | 4 and 1 | − and +
_IL6_ | 1 and 2 | \+ and − (+ 5, 6)
_INFGR1_ | 1 | − (+ 7)
_LTA_ | 1 and 1 | \+ and − (+ 8)
_MMP1_ | 2 and 1 | − and − (+ 9)
_MMP3_ | 1 | −
_MMP9_ | 1 | −
_MPO_ | 1 | − (+ 10)
_NAT2_ | 1 and 1 | − (+ 11) and + (+ 11)
_PAI1_ | 1 | +
_RAGE_ | 1 | +
_TGFB_ | 1 and 1 | − and − (+ 12)
_TIMP2_ | 1 | −
_TNFR2_ | 1 | +
Symbols: – = association not found; + = association found.
1 in combination with LTA.
2 _R_ -allele associated with higher serum fibrinogen.
3 associated with LJP in African-Americans.
4 _R_ -allele associated with severity.
5 _R_ -allele protective.
6 _R_ -allele associated with higher serum levels of IL-6.
7 _R_ -allele in combination with smoking.
8 _N_ -allele protective in combination with _TNFA_ -308.
9 _R_ -allele associated in non-smokers.
10 _R_ -allele protective for females.
11 NAT2 slow phenotype associated with severity.
12 _R_ -allele possibly small effect in relation to severity.
Previous studies have indicated that peri-implantitis and implant failures appear to cluster in subsets of individuals and that a patient who has lost one dental implant is at elevated risk of experiencing another implant loss (Weyant & Burt 1993; Hutton _et al_. 1995). These observations have led to the question of whether there is a common denominator for susceptibility to implant failures and/or complications. At this time, little is known about the genetic susceptibility and genetic polymorphisms involved in periimplant complications; however, several scientific papers have appeared in the literature investigating this aspect. Table 13-3 summarizes the candidate genes studied in association with early or late implant failures and/or bone loss occurring around dental implants.
**Table 13-3** Summary of candidate genes, and corresponding encoded proteins, for which gene polymorphisms have been investigated as markers for early or late implant failure and/or peri-implantitis
**Gene** | **Coded protein**
---|---
_CTR_ | Calcitonin receptor
_BMP4_ | Bone morphogenetic protein
_IL1A_ | Interleukin-1α
_IL1B_ | Interleukin-1β
_IL1RN_ | Interleukin-1 receptor antagonist
_IL2_ | Interleukin-2
_IL6_ | Interleukin-6
_MMP1_ | Matrix metalloproteinase-1
_MMP9_ | Matrix metalloproteinase-9
_TGFB1_ | Transforming growth factor-β
_TNFA_ | Tumor necrosis factor-α
## Early failures in implant dentistry
### The IL-1 gene cluster polymorphisms in association with early failures
To date four studies have reported on the _IL1A_ ‒889, _IL1B_ ‒511, _IL1B_ +3954, and _IL1RN_ VNTR polymorphisms in early implant failures, either separately or in a combination (composite genotype; carriers of the _R_ -allele in _IL1A_ ‒889 and _IL1B_ +3954). Homozygosity of the _IL1B_ ‒511 _R_ -allele has been reported to be associated with marginal bone loss around the dental implants in Japanese patients (Shimpuku _et al_. 2003). However, another study did not observed an association between the _IL1B_ ‒511 _R_ -allele homozygosity and early implant loss in white Brazilians (Campos _et al_. 2005). No other associations have been reported for _IL1_ gene cluster polymorphisms and early implant failures/complications.
### Miscellaneous gene polymorphisms in association with early failures
Polymorphisms in the _IL2_ , _IL6_ , _TNFA_ , _TGFB1_ , _MMP1_ , and _MMP9_ genes (Table 13-3) have been studied in white Brazilians, and _CTR_ and _BMP4_ gene polymorphisms in a Japanese population. One study reported that carriage of the _MMP1_ ‒1607 _R_ -allele is associated with early implant loss (Santos _et al_. 2004). All patients who lost at least one implant during the first year appeared to be carriers of the _R_ -allele of _MMP1_ , while 38% of those who did not lose implants were carriers of the _R_ -allele of _MMP1_.
Bone morphogenetic protein (BMP) plays an important role in bone remodeling, and the _R_ -allele of the _Alu_ I polymorphism of the _BMP4_ gene has been associated with marginal bone loss around implants in Japanese patients (Shimpuku _et al_. 2003).
## Late failures in implant dentistry
The follow-up period of late implant failures in the available studies varied from 1–15 years and only genetic variation in the genes of the _IL1_ cluster have been investigated. Two studies reported on the _IL1A_ ‒889, _IL1B_ ‒511, _IL1B_ +3954, and _IL1RN_ VNTR poly-morphisms separately in association with late implant failures (Rogers _et al_. 2002; Laine _et al_. 2006). One study found an association between the carriage of the _IL1RN_ VNTR _R_ -allele and late implant failure, but not for the other _IL1_ gene polymorphisms (Laine _et al_. 2006).
As has been studied in relation to periodontitis, the composite _IL1_ genotype (carriage of the _R_ -allele in _IL1A_ ‒889 and _IL1B_ +3954) has also been investigated in relation to late implant failures. Two out of five available studies found only a conditional association between the late implant failures and _IL1_ composite genotype; the other studies reported negative findings. In the first positive study, 90 Caucasian patients were investigated for periimplant bone loss at the time of re-examination (mean 5.6 years after prosthetic rehabilitation) (Feloutzis _et al_. 2003). Twenty-eight patients carrying the _IL1_ composite genotype were stratified into non-smokers, former smokers, and heavy smokers. Heavy smokers were found to have more total and annual bone loss, when compared with non-smokers or former smokers. The other study also reported that the _IL1_ composite gen-otype and smoking were significantly associated with peri-implant bone loss after 8 years in function (Gruica _et al_. 2004). However, the results from both studies need to be interpreted with care; the number of subjects in both studies after stratification for geno-type carriage and heavy smoking was so low that the power of the studies is severely compromised (see below).
In summary, there are several studies that have shown an association between early or late dental implant failures in relation to genetic polymorphisms. However most of them still need to be confirmed in another study cohort, consisting of larger numbers of study subjects. For Caucasians who smoke, the _IL-1_ composite genotype may be a possible marker for late implant failures; this was also a genetic marker possibly associated with periodontitis. It is important to emphasize that is difficult to compare and summarize the available literature due to the fact that there is diversity of definitions for the dental implant failure and peri-implant disease, as well as heterogeneity in study design and implant systems.
# Conclusions and future developments
An important problem related to research in the heredity of periodontitis is that, whatever the cause of the disease is, the symptoms are the same; specifically, deepening of the periodontal pocket, loss of attachment, and alveolar bone loss. It is likely that overlapping clinical phenotypes exist between different forms of periodontitis. It is important that globally accepted definitions of "cases" of chronic, and localized and generalized aggressive forms of periodontitis are used in future studies, to allow valid comparisons to be made between gene polymorphism data from different parts of the world. In the majority of cases, it is likely that the development of periodontitis in an individual depends on the collective presence of a number of environmental risk factors in conjunction with a number of genetic risk factors at a given time point during life. The more genetic risk factors an individual has inherited, the greater the genetic predisposition and the higher the chance of early development of periodontitis. Whenever an individual has inherited a major disease gene mutation, we would expect early development of periodontitis. However to date, major disease gene mutations have not been identified, which result in the periodontitis phenotype in otherwise systemically healthy individuals. Since the children of patients with chronic periodontitis show a relatively high prevalence of incipient periodontitis, it is likely that some forms of early periodontitis share a common pathogenic pathway with that of chronic periodontitis in adults.
A multitude of polymorphisms in genes, most of which code aspects of the host immune response, have been explored. There are indications that some polymorphisms in the _IL1_ gene cluster, the _Fc_ γ _R_ gene cluster and in the genes encoding the vitamin D receptor and IL-10, may be associated with periodontitis in certain ethnic groups. However, in general, even among studies with subjects of the same ethnic background, no consistent results have been obtained. Often, only by defining small subgroups of individuals or after stratification, researchers have found some significant associations, but the studies appear underpowered for proper interpretation. Moreover, carriage of specific combinations of alleles within a given locus (haplotype analysis) and among various genes (gene-gene interactions) have only been sparsely investigated. Therefore we conclude that until now no specific genetic risk factor for periodontitis has been identified.
In general, the genetic studies in relation to periodontitis are hampered by population heterogeneity and differences in patient selection and diagnostic criteria. At the same time, it is also possible that inconsistent results may reflect the underlying complexity and heterogeneity of genetic influence in periodontitis. The heterogeneity in periodontitis case definitions is still one of the major problems in the interpretation of the various studies available in the literature in relation to genetic risk factors for periodontitis.
Another problem encountered in the literature, is that many studies have investigated putative genetic risk factors without considering other, established risk factors for periodontitis as covariates. For example, most would agree that in periodontal research, age, gender, and smoking, should always be included in multivariate statistical analyses. Further, the vast majority of studies has not consid ered the infectious component (gene–environment interaction). We recommend strongly that, where possible, the bacterial microorganisms or appropriate surrogate measures of bacterial infection should be included as co-variates in the analyses.
Future studies applying the candidate gene approach could be guided by results from genomewide searches or by results from gene expression signatures (Papapanou _et al_. 2004) or family linkage analyses (Diehl _et al_. 1999; Li _et al_. 2004). Furthermore, these types of studies need to be large scale, in consortium-based approaches, because single studies are greatly underpowered. It is estimated that meaningful results for the candidate gene approach may only be obtained with thousands of patients, since most associations refer to small odds ratios (range 1.1–1.50) (Ioannidis _et al_. 2003). Useful reviews and recommendations have been published on the topic of the candidate gene approach for complex diseases (Clayton & McKeigue 2001; Tabor _et al_. 2002; Colhoun _et al_. 2003; Ioannidis 2003).
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# Part 5: Trauma from Occlusion
14 Trauma from Occlusion: Periodontal Tissues
_Jan Lindhe, Sture Nyman, and Ingvar Ericsson_
15 Trauma from Occlusion: Peri-implant Tissues
_Niklaus P. Lang and Tord Berglundh_
# Chapter 14
# Trauma from Occlusion: Periodontal Tissues
Jan Lindhe, Sture Nyman, and Ingvar Ericsson
* * *
Definition and terminology
Trauma from occlusion and plaque-associated periodontal disease
Analysis of human autopsy material
Clinical trials
Animal experiments
* * *
# Definition and terminology
_Trauma from occlusion_ is a term used to describe pathologic alterations or adaptive changes which develop in the periodontium as a result of undue force produced by the masticatory muscles. _Trauma from occlusion_ is only one of many terms that have been used to describe such alterations in the peri-odontium. Other terms often used are: _traumatizing occlusion_ , _occlusal trauma_ , _traumatogenic occlusion_ , _periodontal traumatism_ , _overload_ , etc. In addition to producing damage in the periodontal tissues, excessive occlusal force may also cause injury in, for example, the temporomandibular joint, the masticatory muscles, and the pulp tissue. This chapter deals exclusively with the effects of _trauma from occlusion_ on the periodontal tissues.
Trauma from occlusion was defined by Stillman (1917) as "a condition where injury results to the supporting structures of the teeth by the act of bringing the jaws into a closed position". The World Health Organization (WHO) in 1978 defined _trauma from occlusion_ as "damage in the periodontium caused by stress on the teeth produced directly or indirectly by teeth of the opposing jaw". In "Glossary of Periodontic Terms" (American Academy of Periodontology 1986), _occlusal trauma_ was defined as "an injury to the attachment apparatus as a result of excessive occlusal force".
Traumatizing forces may act on an individual tooth or on groups of teeth in premature contact relationship; they may occur in conjunction with para-functions such as clenching and bruxism, or in conjunction with loss or migration of premolar and molar teeth with an accompanying, gradually developing spread of the anterior teeth of the maxilla, etc.
In the literature, the tissue injury associated with trauma from occlusion is often divided into _primary_ and _secondary_. The _primary_ form includes a tissue reaction (damage), which is elicited around a tooth with normal height of the periodontium, while the _secondary_ form is related to situations in which occlusal forces cause injury in a periodontium of reduced height. The distinction between a _primary_ and a _secondary_ form of injury – _primary_ and _secondary occlusal trauma_ – serves no meaningful purpose, since the alterations which occur in the periodontium as a consequence of trauma from occlusion are similar and independent of the height of the target tissue, i.e. the periodontium. It is, however, important to understand that symptoms of trauma from occlusion may develop only in situations when the magnitude of the load elicited by occlusion is so high that the peri-odontium around the exposed tooth cannot properly withstand and distribute the resulting force with unaltered position and stability of the tooth involved. This means that in cases of severely reduced height of the periodontium even comparatively small forces may produce traumatic lesions or adaptive changes in the periodontium.
# Trauma from occlusion and plaque-associated periodontal disease
Ever since Karolyi (1901) postulated that an interaction may exist between " _trauma from occlusion_ " and " _alveolar pyrrohea_ ", different opinions have been presented in the literature regarding the validity of this claim. In the 1930s, Box (1935) and Stones (1938) reported experiments in sheep and monkeys, the result of which seemed to indicate that "trauma from occlusion is an etiologic factor in the production of that variety of periodontal disease in which there is vertical pocket formation associated with one or a varying number of teeth" (Stones 1938). The experiments by Box and Stones, however, have been criticized because they lacked proper controls and because the experimental design of the studies did not justify the conclusions drawn.
The interaction between trauma from occlusion and plaque-associated periodontal disease in humans was frequently discussed in the period 1955–1970 in connection with "report of a case", "in my opinion" statements, etc. Even if such anecdotal data may have some value in clinical dentistry, it is obvious that conclusions drawn from research findings are much more pertinent. The research-based conclusions are not always indisputable but they invite the reader to a critique which anecdotal data do not. In this chapter, therefore, the presentation will be limited to findings collected from research endeavors involving: (1) human autopsy material, (2) clinical trials, and (3) animal experiments.
# Analysis of human autopsy material
Results reported from carefully performed research efforts involving examinations of human autopsy material have been difficult to interpret. In the specimens examined (1) the histopathology of the lesions in the periodontium have been described, as well as (2) the presence and apical extension of microbial deposits at adjacent root surfaces, (3) the mobility of the teeth involved, and (4) "the occlusion" of the sites under scrutiny. It is obvious that assessments made in specimens from cadavers have a limited to questionable value when "cause–effect" relationships between occlusion, plaque, and periodontal lesions are to be described. It is not surprising, therefore, that _conclusions_ drawn from this type of research can be controversial. This can best be illustrated if "Glickman's concept" is compared with "Waerhaug's concept" of what autopsy studies have revealed regarding trauma from occlusion and periodontal disease.
### Glickman's concept
Glickman (1965, 1967) claimed that the pathway of the spread of a plaque-associated gingival lesion can be changed if forces of an abnormal magnitude are acting on teeth harboring subgingival plaque. This would imply that the character of the progressive tissue destruction of the periodontium at a "traumatized tooth" will be different from that characterizing a "non-traumatized" tooth. Instead of an even destruction of the periodontium and alveolar bone (suprabony pockets and horizontal bone loss), which, according to Glickman, occurs at sites with uncomplicated plaque-associated lesions, sites which are also exposed to abnormal occlusal force will develop angular bony defects and infrabony pockets.
**Fig. 14-1** Schematic drawing of the zone of irritation and the zone of co-destruction according to Glickman.
Since Glickman's concept regarding the effect of trauma from occlusion on the spread of the plaque-associated lesion is often cited, a more detailed presentation of his theory seems pertinent. The periodontal structures can be divided into two zones (Fig. 14-1):
1. The zone of irritation
2. The zone of co-destruction.
The _zone of irritation_ includes the marginal and interdental gingiva. The soft tissue of this zone is bordered by hard tissue (the tooth) only on one side and is not affected by forces of occlusion. This means that gingival inflammation cannot be induced by trauma from occlusion but is the result of irritation from microbial plaque. The plaque-associated lesion at a "non-traumatized" tooth propagates in the apical direction by first involving the alveolar bone and only later the periodontal ligament area. The progression of this lesion results in an even (horizontal) bone destruction.
The _zone of co-destruction_ includes the periodontal ligament, the root cementum, and the alveolar bone, and is coronally demarcated by the trans-septal (interdental) and the dento-alveolar collagen fiber bundles (Fig. 14-1). The tissue in this zone may become the seat of a lesion caused by trauma from occlusion.
The fiber bundles which separate the zone of co-destruction from the zone of irritation can be affected from two different directions:
1. From the inflammatory lesion maintained by plaque in the _zone of irritation_
2. From trauma-induced changes in the _zone of co-destruction_.
Through this exposure from two different directions the fiber bundles may become dissolved and/or orientated in a direction parallel to the root surface. The spread of an inflammatory lesion from the _zone of irritation_ directly down into the periodontal ligament (i.e. not via the interdental bone) may hereby be facilitated (Fig. 14-2). This alteration of the "normal" pathway of spread of the plaque-associated inflammatory lesion results in the development of angular bony defects. Glickman (1967) stated in a review paper that _trauma from occlusion_ is an etiologic factor (co-destructive factor) of importance in situations where angular bony defects combined with infrabony pockets are found at one or several teeth (Fig. 14-3).
**Fig. 14-2** The inflammatory lesion in the zone of irritation can, in teeth not subjected to trauma, propagate into the alveolar bone (open arrow), while in teeth also subjected to trauma from occlusion, the inflammatory infiltrate spreads directly into periodontal ligament (filled arrow).
### Waerhaug's concept
Waerhaug (1979) examined autopsy specimens (Fig. 14-4) similar to Glickman's, but in addition measured the distance between the subgingival plaque and (1) the periphery of the associated inflammatory cell infiltrate in the gingiva, and (2) the surface of the adjacent alveolar bone. He concluded from his analysis that angular bony defects and infrabony pockets occur equally often at periodontal sites of teeth which are not affected by trauma from occlusion as in traumatized teeth. In other words, he refuted the hypothesis that trauma from occlusion played a role in the spread of a gingival lesion into the "zone of co-destruction". The loss of connective attachment and the resorption of bone around teeth are, according to Waerhaug, exclusively the result of inflammatory lesions associated with subgingival plaque. Waerhaug concluded that angular bony defects and infrabony pockets occur when the subgingival plaque of one tooth has reached a more apical level than the microbiota on the neighboring tooth, and when the volume of the alveolar bone surrounding the roots is comparatively large. Waerhaug's observations support findings presented by Prichard (1965) and Manson (1976) which imply that the pattern of loss of supporting structures is the result of an interplay between the form and volume of the alveolar bone and the apical extension of the microbial plaque on the adjacent root surfaces.
It is obvious, as stated above, that examinations of autopsy material have a limited value when determining "cause–effect" relationships with respect to trauma and progressive periodontitis. As a consequence, the conclusions drawn from this field of research have not been generally accepted. A number of authors tend to accept Glickman's conclusions that trauma from occlusion is an aggravating factor in periodontal disease (e.g. Macapanpan & Weinmann 1954; Posselt & Emslie 1959; Glickman & Smulow 1962, 1965) while others accept Waerhaug's concept, i.e. that there is no relationship between occlusal trauma and the degree of periodontal tissue break-down (e.g. Lovdahl _et al_. 1959; Belting & Gupta 1961; Baer _et al_. 1963; Waerhaug 1979).
**Fig. 14-3** (a) A radiograph of a mandibular premolar–canine region. Note the angular bony defect at the distal aspect of the premolar. (b) Histologic mesiodistal section of the specimen illustrated in (a). Note the infrabony pocket at the distal aspect of the premolar. From Glickman & Smulow (1965).
**Fig. 14-4** Microphotographs illustrating two interproximal areas with angular bony defects. "‒" denotes a tooth not subjected and "+" denotes a tooth subjected to trauma from occlusion. In categories "‒" and "+" the distance between the apical cells of the junctional epithelium and the supporting alveolar bone is about 1–1.5 mm, and the distance between the apical extension of plaque and the apical cells of the junctional epithelium about 1 mm. Since the apical cells of the junctional epithelium and the subgingival plaque are located at different levels on the two adjacent teeth, the outline of the bone crest becomes oblique. A radiograph from such a site would disclose the presence of an angular bony defect at a non-traumatized ("‒") tooth.
# Clinical trials
In addition to the presence of angular bony defects and infrabony pockets, _increased tooth mobility_ is frequently listed as an important sign of occlusal trauma. For details regarding tooth mobility, see Chapter 51. Conflicting data have also been reported regarding the periodontal conditions of mobile teeth. In one clinical study by Rosling _et al_. (1976) patients with advanced periodontal disease associated with multiple angular bony defects and mobile teeth were exposed to antimicrobial therapy (i.e. subgingival scaling after flap elevation). Healing was evaluated by probing attachment level measurements and radiographic monitoring. The authors reported that "the infrabony pocket located at hypermobile teeth exhibited the same degree of healing as those adjacent to firm teeth". In another study, however, Fleszar _et al_. (1980) reported on the influence of tooth mobility on healing following periodontal therapy including both root debridement and occlusal adjustment. They concluded that "pockets of clinically mobile teeth do not respond as well to periodontal treatment as do those of firm teeth exhibiting the same disease severity".
A third study (Pihlstrom _et al_. 1986) studied the association between trauma from occlusion and peri-odontitis by assessing a series of clinical and radio-graphic features at maxillary first molars. Parameters included in this study were: probing depth, probing attachment level, tooth mobility, wear facets, plaque and calculus, bone height, widened periodontal space, etc. Pihlstrom and his associates concluded from their measurements and examinations that teeth with increased mobility and widened periodontal ligament space had, in fact, deeper pockets, more attachment loss, and less bone support than teeth without these symptoms.
Burgett _et al_. (1992) studied the effect of occlusal adjustment in the treatment of periodontitis. Fifty subjects with periodontitis were examined at base-line and subsequently treated for their periodontal condition with root debridement ± flap surgery. Twenty-two out of the 50 patients, in addition, received comprehensive occlusal therapy. Re-examinations performed 2 years later disclosed that probing attachment gain was on average about 0.5 mm larger in patients who received the combined treatment, i.e. scaling and occlusal adjustment, than in patients in whom the occlusal adjustment was not included.
Nunn and Harrel (2001) and Harrel and Nunn (2001) examined the relationship between occlusal discrepancies and periodontitis in two studies. Their sample included about 90 subjects that had been referred for treatment of periodontal disease and who had at least two (≥1 year apart) complete peri-odontal records, including occlusal analysis. The patients were examined with respect to probing pocket depth (PPD), tooth mobility, and furcation involvement (at multirooted teeth). In addition, some occlusal contact relationships were studied such as (1) discrepancies in centric relation and centric occlusion, (2) premature occlusal contacts in protrusive movements (lateral and frontal) of the mandible in working and non-working quadrants. A treatment plan, including both periodontal and occlusal measures, was subsequently designed for each patient. About one third of the subjects decided to abstain from treatment, about 20 subjects accepted only a non-surgical approach of therapy (SRP), while about 50% of the patients accepted and received comprehensive treatment that included surgical pocket elimination (surgery) as well as occlusal adjustment (if indicated). Some teeth in the SRP group received occlusal therapy while other teeth with occlusal discrepancies were left untreated. It was observed that teeth with occlusal discrepancies had significantly deeper PPD values and higher mobility scores than teeth without occlusal "trauma" and also that teeth exposed to occlusal adjustment responded better (reduction in PPD) to non-surgical periodontal therapy than teeth with remaining occlusal discrepancies.
The findings in some of the clinical studies referred to above lend some support to the concept that trauma from occlusion (and increased tooth mobility) may have a detrimental effect on the periodontium. Neiderud _et al_. (1992), however, in a beagle dog study demonstrated that tissue alterations which occur at mobile teeth with clinically healthy gingivae (and normal height of the tissue attachment) may reduce the resistance offered by the periodontal tissues to probing. In other words, if the probing depth at two otherwise similar teeth – one non-mobile and one hypermobile – is recorded, the tip of the probe will penetrate 0.5 mm deeper at the mobile than at the non-mobile tooth. This finding must be taken into consideration when the above clinical data are interpreted.
Since neither analysis of autopsy material nor data from clinical trials can be used to properly determine the role trauma from occlusion may play in peri-odontal pathology, it is necessary to describe the contributions made by means of animal research in this particular field. Results from such experiments, describing the reactions of the normal and subsequently the diseased periodontium to occlusal forces, are presented below.
# Animal experiments
### Orthodontic type trauma
The reaction of the periodontal tissues to traumatic forces initiated by occlusion has been studied principally in animal experiments. In early experiments the reaction of the normal periodontium was studied following the application of forces which were inflicted on teeth in one direction only. Biopsy specimens, including tooth and periodontium, were harvested after varying experimental time intervals and prepared for histologic examinations. Analysis of the tissue sections (Häupl & Psansky 1938; Reitan 1951; Mühlemann & Herzog 1961; Ewen & Stahl 1962; Waerhaug & Hansen 1966; Karring _et al_. 1982) revealed the following: when a tooth is exposed to unilateral forces of a magnitude, frequency or duration that its periodontal tissues are unable to with-stand and distribute while maintaining the stability of the tooth, certain well defined reactions develop in the periodontal ligament, eventually resulting in an adaptation of the periodontal structures to the altered functional demand. If the crown of a tooth is affected by such horizontally directed forces, the tooth tends to tilt (tip) in the direction of the force (Fig. 14-5). This tilting force results in the development of _pressure_ and _tension zones_ within the marginal and apical parts of the periodontium. The tissue reactions which develop in the _pressure zone_ are characterized by increased vascularization, increased vascular permeability, vascular thrombosis, and disorganization of cells and collagen fiber bundles. If the magnitude of forces is within certain limits, allowing the maintenance of the vitality of the periodontal ligament cells, bone-resorbing osteoclasts soon appear on the bone surface of the alveolus in the _pressure zone_. A process of bone resorption is initiated. This phenomenon is called " _direct bone resorption_ ".
**Fig. 14-5** (a) If the crown of a tooth is exposed to excessive, horizontally directed forces (arrow), pressure (P) and tension (T) zones will develop within the marginal and apical parts of the periodontium. The supra-alveolar connective tissue remains unaffected by force application. Within the pressure and tension zones tissue alterations take place which eventually allow the tooth to tilt in the direction of the force. (b) When the tooth is no longer subjected to the trauma, complete regeneration of the periodontal tissues takes place. There is no apical downgrowth of the dentogingival epithelium.
If the force applied is of higher magnitude, the result may be necrosis of the periodontal ligament tissue in the _pressure zone_ , i.e. decomposition of cells, vessels, matrix, and fibers ( _hyalinization_ ). "Direct bone resorption" therefore cannot occur. Instead, osteoclasts appear in marrow spaces within the adjacent bone tissue where the stress concentration is lower than in the periodontal ligament and a process of undermining or " _indirect bone resorption_ " is initiated. Through this reaction the surrounding bone is resorbed until there is a breakthrough to the hyalinized tissue within the _pressurezone_. This breakthrough results in a reduction of the stress in this area, and cells from the neighboring bone or adjacent areas of the periodontal ligament can proliferate into the _pressure zone_ and replace the previously hyalinized tissue, thereby re-establishing prerequisites for "direct bone resorption". Irrespective of whether the bone resorption is of a direct or an indirect nature the tooth moves (tilts) further in the direction of the force.
Concomitant with the tissue alterations in the _pressure zone_ , apposition of bone occurs in the _tension zone_ in order to maintain the normal width of the peri-odontal ligament in this area. Because of the tissue reactions in the _pressure_ and _tension_ zones the tooth becomes, temporarily, hypermobile. When the tooth has moved (tilted) to a position where the effect of the forces is nullified, healing of the periodontal tissues takes place in both the _pressure_ and the _tension zones_ and the tooth becomes stable in its new position. In orthodontic tilting (tipping) movements, neither gingival inflammation nor loss of connective tissue attachment will occur in a healthy periodontium and, as long as the tooth is not moved through the envelope of the alveolar process, there is no apical migration of the dentogingival epithelium. In other words, since the supra-alveolar connective tissue is only bordered by hard tissue (the tooth) on one side (in the direction of the force), this structure remains unaffected by this type of force.
These tissue reactions do not differ fundamentally from those which occur as a consequence of _bodily tooth movement_ in orthodontic therapy (Reitan 1951). The main difference is that the _pressure_ and _tension zones_ , depending on the direction of the force, are more extended in an apical–coronal direction along the root surface than in conjunction with tipping movement (Fig. 14-6). The supra-alveolar connective tissue is not affected by the force, either in conjunction with tipping or in conjunction with bodily movements of the tooth. Unilateral forces directed to the crown of teeth, therefore, will not induce inflammatory reactions in the gingiva or cause loss of connective tissue attachment.
Studies have demonstrated, however, that orthodontic forces producing bodily (or tipping) movement of teeth may result in gingival recession and loss of connective tissue attachment (Steiner _et al_. 1981; Wennström _et al_. 1987). This breakdown of the attachment apparatus occurred at sites with gingivitis when, in addition, the tooth was moved through the envelope of the alveolar process. At such sites bone dehiscence becomes established and, if the covering soft tissue is thin (in the direction of the movement of the tooth), recession (attachment loss) may occur.
**Fig. 14-6** When a tooth is exposed to forces which produce "bodily tooth movement", e.g. in orthodontic therapy, the pressure (P) and tension (T) zones, depending on the direction of the force, are extended over the entire tooth surface. The supra-alveolar connective tissue is not affected in conjunction either with tipping or with bodily movements of teeth. Forces of this kind, therefore, will not induce inflammatory reactions in the gingiva. No apical downgrowth of the dentogingival epithelium occurs.
Criticism has been directed, however, at experiments in which only unilateral trauma is exerted on teeth (Wentz _et al_. 1958). It has been suggested that in humans, unlike in the animal experiments described above, the occlusal forces act alternately in one and then in the opposite direction. Such forces have been termed _jiggling forces_.
### Jiggling-type trauma
#### _Healthy periodontium with normal height_
Experiments have been reported in which traumatic forces were exerted on the crowns of the teeth, alternately in buccal and lingual or mesial and distal directions, and in which the teeth were not allowed to move away from the force (e.g. Wentz _et al_. 1958; Glickman & Smulow 1968; Svanberg & Lindhe 1973; Meitner 1975; Ericsson & Lindhe 1982). In conjunction with " _jiggling-type trauma_ " no clearcut _pressure_ and _tension zones_ can be identified but rather there is a combination of pressure and tension on both sides of the jiggled tooth (Fig. 14-7).
The tissue reactions in the periodontal ligament provoked by the combined _pressure_ and _tension_ forces were found to be similar, however, to those reported for the pressure zone at orthodontically moved teeth, with the one difference that the periodontal ligament space at jiggling gradually increased in width on both sides of the tooth. During the phase when the periodontal space gradually increased in width, (1) inflammatory changes were present in the ligament tissue, (2) active bone resorption occurred, and (3) the tooth displayed signs of gradually increasing ( _progressive_ ) mobility. When the effect of the forces applied had been compensated for by the increased width of the periodontal ligament space, the ligament tissue showed no signs of increased vascularity or exudation. The tooth was hypermobile but the mobility was no longer _progressive_ in character. Distinction should thus be made between _progressive_ and _increased_ tooth mobility.
**Fig. 14-7** Two mandibular premolars with normal periodontal tissues (a) are exposed to jiggling forces (b) as illustrated by the two arrows. The combined tension and pressure zones (encircled areas) are characterized by signs of acute inflammation including collagen resorption, bone resorption, and cementum resorption. As a result of bone resorption the periodontal ligament space gradually increases in size on both sides of the teeth as well as in the periapical region. (c) When the effect of the force applied has been compensated for by the increased width of the periodontal ligament space, the ligament tissue shows no sign of inflammation. The supra-alveolar connective tissue is not affected by the jiggling forces and there is no apical downgrowth of the dentogingival epithelium. (d) After occlusal adjustment the width of the periodontal ligament becomes normalized and the teeth are stabilized.
In _jiggling-type trauma_ experiments, performed on animals with a normal periodontium, the supra-alveolar connective tissue was not influenced by the occlusal forces, the reason being that this tissue compartment is bordered by hard tissue on one side only. This means that a gingiva which was uninflamed at the start of the experiment remained uninflamed, but also that an overt inflammatory lesion residing in the supra-alveolar connective tissue was not aggravated by the jiggling forces.
#### _Healthy periodontium with reduced height_
Progressive periodontal disease is characterized by gingival inflammation and a gradually developing loss of connective tissue attachment and alveolar bone. Treatment of periodontal disease, i.e. removal of plaque and calculus and elimination of pathologically deepened pockets, will result in the re-establishment of a healthy periodontium but with reduced height. The question is whether a healthy periodontium with reduced height has a capacity similar to that of the normal periodontium to adapt to traumatizing occlusal forces (secondary occlusal trauma).
**Fig. 14-8** (a) Dogs were allowed to accumulate plaque and calculus in the mandibular premolar regions over a 210-day period. (b) When around 40–50% of the periodontal tissue support had been lost the animals were treated by scaling, root planing, and pocket elimination. During surgery, a notch was prepared in the root at the level of the bone crest. (c, d) The dogs were subsequently placed on a plaque-control program and 2 months later (day 270) all experimental teeth (the lower fourth premolars; 4P and P4) were surrounded by a healthy periodontium with reduced height. (e) The mandibular left fourth premolar (T) was exposed to jiggling forces. (f) As a consequence, a widened periodontal ligament and increased tooth mobility resulted. (g) This increase in tooth mobility and the development of widened periodontal ligament space did not, however, result in apical downgrowth of the dentogingival epithelium. Arrowheads indicate the apical extension of the junctional epithelium which coincides with the apical border of the notch (N), prepared in the root surface prior to jiggling. C = control tooth; T = test tooth.
This problem has also been examined in animal experiments (Ericsson & Lindhe 1977). Destructive periodontal disease was initiated in dogs by allowing the animals to accumulate plaque and calculus for a period of 6 months (Fig. 14-8). When around 50% of the periodontal tissue support had been lost (Fig. 14-8a,b), the progressive disease was subjected to treatment by scaling, root planing, and pocket elimination (Fig. 14-8c). During a subsequent 8-month period, the animals were enrolled in a careful plaque-control program. During this period certain premolars were exposed to traumatizing jiggling forces. The peri-odontal tissues in the combined _pressure_ and _tension zones_ reacted to the forces by vascular proliferation, exudation, and thrombosis, as well as by bone resorption. In radiographs, widened periodontal ligaments (Fig. 14-8d) could be found around the traumatized teeth, which displayed signs of _progressive_ tooth mobility at clinical examination. The gradual increase in the width of the periodontal ligament and the resulting progressive increase in tooth mobility took place during a period of several weeks but eventually terminated. The active bone resorption ceased and the markedly widened periodontal ligament tissue regained its normal composition; healing had occurred (Fig. 14-8e). The teeth were hypermobile but surrounded by periodontal structures which had adapted to the altered functional demands.
During the entire experimental period the supra-alveolar connective tissue remained unaffected by the jiggling forces. There was no further loss of connective tissue attachment and no further downgrowth of dentogingival epithelium (Fig. 14-8e). The results from this study clearly reveal that within certain limits a healthy periodontium with reduced height has a capacity similar to that of a periodontium with normal height to adapt to altered functional demands (Fig. 14-9).
**Fig. 14-9** (a) Two mandibular premolars are surrounded by a healthy periodontium with reduced height. (b) If such premolars are subjected to traumatizing forces of the jiggling type a series of alterations occurs in the periodontal ligament tissue. (c) These alterations result in a widened periodontal ligament space and in an increased tooth mobility but do not lead to further loss of connective tissue attachment. (d) After occlusal adjustment the width of the periodontal ligament is normalized and the teeth are stabilized.
### Plaque-associated periodontal disease
Experiments carried out on humans and animals have demonstrated that _trauma from occlusion_ cannot induce pathologic alterations in the supra-alveolar connective tissue, i.e. cannot produce inflammatory lesions in a normal gingiva or aggravate a gingival lesion associated with plaque and cannot induce loss of connective tissue attachment. The question remains if abnormal occlusal forces can influence the spread of the plaque-associated lesion and enhance the rate of tissue destruction in periodontal disease. This has been studied in animal experiments (Lindhe & Svanberg 1974; Meitner 1975; Nyman _et al_. 1978; Ericsson & Lindhe 1982; Polson & Zander 1983). In these experiments progressive and destructive periodontal disease was first initiated in dogs or monkeys by allowing the animals to accumulate plaque and calculus. Teeth thus involved in a progressive peri-odontal disease process were also subjected to trauma from occlusion.
"Traumatizing" jiggling forces (Lindhe & Svanberg 1974) were exerted on premolars and were found to induce certain tissue reactions in the combined _pressure_ / _tension zones_. Within a few days of the onset of the jiggling forces, the periodontal ligament tissue in these zones displayed signs of inflammation, had increased numbers of vessels, showed increased vascular permeability and exudation, thrombosis, as well as retention of neutrophils and macrophages. On the adjacent bone surfaces there were a large number of osteoclasts. Since the teeth could not orthodontically move away from the jiggling forces, the periodontal ligament of both sides of the tooth gradually increased in width, the teeth became hypermobile ( _progressive_ tooth mobility) and angular bony defects could be detected in the radiographs. The forces were eventually nullified by the increased width of the periodontal ligament.
If the forces applied were of a magnitude to which the periodontal structures could adapt, the _progressive_ increase of the tooth mobility terminated within a few weeks. The active bone resorption ceased but the angular bone destruction persisted as well as the increased tooth mobility. The periodontal ligament had an increased width but a normal tissue composition. Histologic examination of biopsy specimens revealed that this adaptation had occurred with no greater apical proliferation of the dentogingival epithelium than was caused by the plaque-associated lesion (Fig. 14-10) (Meitner 1975). This means that occlusal forces which allow adaptive alterations to develop in the _pressure/tension_ zones of the periodontal ligament will not aggravate a plaque-associated periodontal disease (Fig. 14-11).
**Fig. 14-10** (a) A composite photomicrograph illustrating the interdental space between two pairs of teeth. The teeth have been subjected to experimental, ligature-induced periodontitis and in (b) also to repetitive mechanical injury. In (b), there is considerable loss of alveolar bone and an angular widening of the periodontal ligament space (arrows). However, the apical downgrowth of the dentogingival epithelium in the two areas (a) and (b) is similar. E indicates the apical level of the dentogingival epithelium. Courtesy of Dr. S.W. Meitner.
**Fig. 14-11** (a) Two mandibular premolars with supra- and subgingival plaque, advanced bone loss and periodontal pockets of a suprabony character. Note the connective tissue infiltrate (shadowed areas) and the uninflamed connective tissue between the alveolar bone and the apical portion of the infiltrate. (b) If these teeth are subjected to traumatizing forces of the jiggling type, pathologic and adaptive alterations occur within the periodontal ligament space. (c) These tissue alterations, which include bone resorption, result in a widened periodontal ligament space and increased tooth mobility but no further loss of connective tissue attachment. (d) Occlusal adjustment results in a reduction of the width of the periodontal ligament and in less mobile teeth.
If, however, the magnitude and direction of the jiggling forces were such that, during the course of the study (6 months), the tissues in the pressure/ tension zones could not become adapted, the injury in the _zones of co-destruction_ had a more permanent character. For several months the periodontal ligament in the pressure/tension zones displayed signs of inflammation (vascular proliferation, exudation, thrombosis, retention of neutrophils and macro-phages, collagen destruction). Osteoclasts residing on the walls of the alveolus maintained the bone-resorptive process, which resulted in a gradual widening of the periodontal ligament in the pressure/tension zones (Fig. 14-12). As a consequence, the resulting angular bone destruction was continuous and the mobility of the teeth remained progressive. The plaque-associated lesion in the "zone of irritation" and the inflammatory lesion in the "zone of co-destruction" merged; the dentogingival epithelium proliferated in an apical direction and periodontal disease was aggravated (Figs. 14-13, 14-14) (Lindhe & Svanberg 1974).
Similar findings were reported from another experiment in the dog (Ericsson & Lindhe 1982) in which the effect was assessed of a _prolonged_ period of jiggling force application on the rate of progression of plaque-associated, marginal periodontitis. Thus, in dogs with continuing periodontal disease, certain teeth were exposed to jiggling forces during a period of 10 months. Control teeth were not jiggled. Figure 14–15a illustrates the marked periodontal tissue breakdown around a tooth which was exposed to plaque infection combined with jiggling trauma for several months and Fig. 14-15b illustrates a control tooth which was exposed to plaque infection only.
On the other hand, more short-term experiments in the monkey (Polson & Zander 1983), evaluating the effect of _trauma from occlusion_ on teeth involved in an ongoing process of periodontitis, failed to support the findings by Lindhe and Svanberg (1974) and Ericsson and Lindhe (1982). Polson and Zander (1983) observed that trauma superimposed on peri-odontal lesions associated with angular bony defects (1) caused increased loss of alveolar bone but (2) failed to produce additional loss of connective tissue attachment.
### Conclusions
Experiments carried out in humans as well as animals, have produced convincing evidence that neither uni-lateral forces nor jiggling forces, applied to teeth with a healthy periodontium, result in pocket formation or in loss of connective tissue attachment. _Trauma from occlusion cannot induce periodontal tissue break-down_. Trauma from occlusion does, however, result in resorption of alveolar bone leading to an increased tooth mobility which can be of a transient or permanent character. This bone resorption with resulting increased tooth mobility should be regarded as a physiologic adaptation of the periodontal ligament and surrounding alveolar bone to the traumatizing forces, i.e. to altered functional demands.
**Fig. 14-12** Radiographic appearance of one test tooth (T) and one control tooth (C) at the termination of an experiment in which periodontitis was induced by ligature placement and plaque accumulation and in which trauma of the jiggling type was induced. Note angular bone loss particularly around the mesial root of the mandibular premolar (T) and the absence of such a defect at the mandibular premolar (C). From Lindhe & Svanberg (1974).
In teeth with progressive, plaque-associated peri-odontal disease, trauma from occlusion may, under certain conditions, enhance the rate of progression of the disease, i.e. act as a co-factor in the destructive process. From a clinical point of view, this knowledge strengthens the demand for proper treatment of plaque associated with periodontal disease. This treatment will arrest the destruction of the periodontal tissues even if the occlusal trauma persists. Treatment directed towards the trauma alone, however, i.e. occlusal adjustment or splinting, may reduce the mobility of the traumatized teeth and result in some regrowth of bone, but it will not arrest the rate of further breakdown of the supporting apparatus caused by plaque. (For a detailed discussion of treatment of teeth exhibiting increased mobility, see Chapter 51.)
**Fig. 14-13** Microphotographs from one control (C) and one test (T) tooth after 240 days of experimental periodontal tissue breakdown and 180 days of trauma from occlusion of the jiggling type (T). The arrowheads denote the apical position of the dentogingival epithelium. The attachment loss is more pronounced in T than in C. From Lindhe & Svanberg (1974).
**Fig. 14-14** (a) Illustration of a tooth where subgingival plaque has mediated the development of an infiltrated soft tissue (shadowed area) and an infrabony pocket. (b) When trauma from occlusion of the jiggling type is inflicted (arrows) on the crown of this tooth, the associated pathologic alterations occur within a zone of the periodontium which is also occupied by the inflammatory cell infiltrate (shadowed area). In this situation the increasing tooth mobility may also be associated with an enhanced loss of connective tissue attachment and further downgrowth of dentogingival epithelium; compare arrows in (c) and (d). Occlusal adjustment will result in a narrowing of the periodontal ligament, less tooth mobility, but no improvement of the attachment level (d) (Lindhe & Ericsson 1982).
**Fig. 14-15** (a) Periodontal conditions around a tooth which has been exposed to trauma from occlusion (of the jiggling type) for 300 days in combination with plaque-associated experimental periodontitis. (b) Condition of a control tooth from the same dog in which experimental periodontitis but no jiggling trauma had been in operation. Note the difference between (a) and (b) regarding the degree of bone destruction and loss of connective tissue attachment. Note also in (a) the location of the subgingival plaque at the apex of the root. From Ericsson & Lindhe (1982).
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# Chapter 15
# Trauma from Occlusion: Peri-implant Tissues
Niklaus P. Lang and Tord Berglundh
* * *
Introduction
Orthodontic loading and alveolar bone
Bone reactions to functional loading
Excessive occlusal load on implants
Static and cyclic loads on implants
Load and loss of osseointegration
Masticatory occlusal forces on implants
Tooth–implant supported reconstructions
* * *
# Introduction
Enosseous osseointegrated oral implants have been suggested to serve as anchorage for orthodontic appliances where the existing dentition does not provide sufficient anchorage (see Chapter 58). Both clinical (Turley _et al_. 1988; Ödman _et al_. 1988, 1994; Haanaes _et al_. 1991) and experimental (Wehrbein & Diedrich 1993; Wehrbein _et al_. 1996) studies have demonstrated that osseointegrated implants were able to provide sufficient and stable anchorage for tooth movement during the period of orthodontic therapy, hereby eliminating the need of observing Newton's third law (1687) according to which an applied force can be divided into an _action_ component and an equal and opposite _reaction_ moment.
In long-term clinical studies of various two-stage submerged implant systems, however, implant loss has been attributed to _overloading or excessive loading_. In patients with edentulous (Adell _et al_. 1981; Lindquist _et al_. 1988) and partially edentulous jaws (Jemt _et al_. 1989; Quirynen _et al_. 1992) most of the losses of implants were considered to be the result of excessive occlusal loading. While it has been shown that early loading of oral implants may impede successful osseointegration (Sagara _et al_. 1993), the effect of excessive occlusal functional forces following successful osseointegration has not been documented so far. However, studies by Isidor (1996, 1997) have demonstrated that loading of implants through the creation of a massive supra-occlusion, leading to excessive, and most likely unphysiologic, laterally directed occlusal forces, established a high risk for the loss of osseointegration. Nevertheless, in one out of four experimental animals, even such excessive loading forces were unable to jeopardize the interfacial union of the alveolar bone with the implant surface.
The forces applied in the studies mentioned were characterized as being very high and of short duration. However, they could not be quantified. None of the experimental studies performed up to date allowed for the analysis of a direct relationship between changes in the stress and strain applied to oral implants which are encountered during functional loading and of the tissue reactions of the surrounding alveolar bone. Such information would appear to be of crucial importance for the evaluation of the etiology and pathogenesis of implant loss due to overload.
# Orthodontic loading and alveolar bone
In order to evaluate the tissue reactions adjacent to oral implants following loading with well defined forces and to relate the strain values applied on the trabecular surface of the alveolar bone, an animal study was performed using finite element analysis (FEA) to determine the cellular activity (Melsen & Lang 2001).
In six adult monkeys, the lower first and the second premolars as well as the second molars were removed. After 6 months, two specially designed screw implants were inserted in the region of the lower left second premolar and second molar. After further 3 months, a square rod with three notches at different levels was inserted and tightened to the top of the implants. The notches served as reference for the measurements of the implant displacement. A flat disk was placed between the implant and the rod. To this disk two extensions were welded buccally and lingually in a way that a coil spring could be placed as close as possible to the estimated level of the center of resistance (Fig. 15-1). Immediately before buccal and lingual springs were inserted, the extensions were placed on the occlusal surface of the implants. Impressions of each segment were taken.
**Fig. 15-1** Clinical picture demonstrating the Ni-Ti coil springs applied for a continuous loading through the centre of resistance. From Melsen & Lang (2001).
Subsequently, two measurements were performed with an electronic strain gauge-based measuring device. For anchorage of the device, a cast splint was fitted to the anterior segment of the dentition and each of the implant screws. One measurement was made between the notches close to the implant connection, and another between the notches close to the top of the square rod extensions. These were repeated after 11 weeks, i.e. at the termination of orthodontic loading period. The direction and magnitude of the displacement of the implant as a result of loading could thus be calculated in the sagittal plane.
Following the baseline recordings, springs extending from the anterior to the posterior implant were attached to the power arms buccally and lingually (Fig. 15-1). Forces applied to the implants varied from 100 cN to each implant to a total load of 300 cN per implant. One monkey served as control, i.e. the implants in this animal were not subjected to any loading.
At the end of the experiment, the monkeys were sacrificed. Subsequently, parallel horizontal tissue sections from the coronal to the apical end of the implants were cut and stained with fast green. A grid consisting of three concentric circular gridlines was projected on to the sections (Fig. 15-2). The circular grid lines were intersected by four equidistant radial lines starting at the center of the grid and coinciding with the central axis of the implants. The four radial lines divided the regions between the circles and into eight areas, two in the direction of the force (A: compression zone), two in the opposite direction (B: tension zone), and four lateral to the implants (C and D: shear zone) (Fig. 15-2).
At a magnification of ×60, the extent of resorption lacunae and the extent of osteoid covered surfaces as a fraction of the total surface of trabecular bone were assessed. Also, using morphometry, bone density was evaluated within each quadrant. Furthermore, to measure the amount of osseointegration, the proportion of direct bone-to-implant contact was calculated by projecting a grid consisting of 32 radial lines extending from the center of the implants on to the section to be analyzed (Fig. 15-3).
**Fig. 15-2** Horizontal section of the implant with the projected grid used for the histomorphometrical evaluation of different regions surrounding the implant. Region A is submitted to compression, region B to tension, and regions C and D to shearing forces. From Melsen & Lang (2001).
**Fig. 15-3** Horizontal section of the implant on to which a grid with 32 radial lines was projected. The evaluation of the osseointegration included the determination of the percentage of direct bone-to-implant contact (magnification ×160). From Melsen & Lang (2001).
None of the implants had lost osseointegration after 11 weeks of orthodontic loading, but loading significantly influenced the turnover of the alveolar bone in the vicinity of the implants. Bone apposition was most frequently found when the calculated strain varied between 3400 and 6600 microstrain. On the other hand, when the strain exceeded 6700 microstrain, the remodeling of the bone resulted in a net loss of bone.
Clearly, the study supported the theory that apposition of bone around an oral implant is the biological response to a mechanical stress below a certain threshold, whereas loss of marginal bone or complete loss of osseointegration may be the result of mechanical stress beyond this threshold. Hence, occlusal forces would have to exeed the physiologic range substantially before occlusal contacts could jeopardize the tissue integrity of an implant.
Several other studies where orthodontic forces have been applied confirmed the apposition or increase in bone density rather than loss of bone surrounding an oral implant (Roberts _et al_. 1984; Wehrbein & Diedrich 1993; Asikainen _et al_. 1997; Akin-Nergiz _et al_. 1998).
# Bone reactions to functional loading
A recent study addressed the reaction of peri-implant bone after longstanding functional loading compared to non-loaded controls (Berglundh _et al_. 2005).
After extractions of all mandibular premolars, four AstraTech® implants were placed in one side, and four Bråmark System® fixtures were installed in the contralateral side of the mandible. Three months after abutment connection, fixed dental prostheses (FDPs) were fabricated in gold and cemented on the maxillary canines and premolars (Fig. 15-4). FDPs were also installed on three of the four mandibular implants in both sides. The fourth implant remained unloaded and served as a control (Fig. 15-5).
Radiographs were obtained from each site following implant installation, abutment connection, and FDP placement. All radiographs were repeated after 10 months of functional loading. At this time biopsies were obtained and analyzed histologically.
The radiographic analysis revealed that the largest amount of bone loss occurred following implant installation and abutment connection. This bone loss was more pronounced at Brånemark® than at Astra Tech® implants. However, bone loss as a result of functional loading was small and did not differ from the unloaded control sites (Fig. 15-6).
**Fig. 15-4** Clinical documentation of the fixed dental prosthesis (FDP) supported by maxillary canines and premolars. In the mandible a FDP is installed on implants to provide masticatory function. The non-loaded control implant is mesial to the FDP (arrow). From Berglundh _et al._ (2005).
The histologic analysis showed that implants subjected to 10 months of functional loading had more direct bone-to-implant contact than their unloaded counterparts. This was observed for both implant systems (Fig. 15-7).
Based on radiographic and histologic results this study has demonstrated that _functional loading of implants may enhance osseointegration_ (direct bone-to-implant contact) rather than induce marginal bone loss and, hence, such bone loss should not be attributed to loading of implants.
Whenever marginal bone loss is observed around implants in function, the most likely etiologic factor is bacterial in nature (see Chapters 10 and 24).
# Excessive occlusal load on implants
The effect of _excessive occlusal load_ following placement of titanium implants in the presence of healthy peri-implant mucosal tissues was evaluated in an experimental dog study (Heitz-Mayfield _et al_. 2004). In six Labrador dogs, two TPS (titanium plasma sprayed) implants and two SLA (sandblasted, large grit, acid etched) implants were placed on each side of the mandible (Fig. 15-8a). A total of 45 implants were evaluated. Following 6 months of healing (Fig. 15-8b), gold crowns were placed on implants on the test side of the mandible. The crowns were in supra-occlusal contact with the opposing teeth in order to create excessive occlusal load (Fig. 15-8c). Implants on the control side were not loaded. Plaque control was performed throughout the experimental period. Clinical measurements and standardized radiographs (Fig. 15-8d) were obtained at baseline and 1, 3, and 8 months after loading. At 8 months, all implants were osseointegrated, the dogs were killed, and histologic analyses were performed.
The mean probing depth was 2.5 ± 0.3 and 2.6 ± 0.3 mm at unloaded and loaded implants, respectively. Radiographically, the mean distance from the implant shoulder to the marginal bone level was 3.6 ± 0.4 mm in the control group and 3.7 ± 0.2 mm in the test group. There were no statistically significant changes for any of the parameters from baseline to 8 months in the loaded and unloaded implants. Histologic evaluation (Fig. 15-9) showed a mean mineralized bone-to-implant contact of 73% in the control implants and 74% in the test implants, with no statistically significant difference between test and control implants.
**Fig. 15-5** FDPs fabricated of gold and installed on implants for functional loading. Unloaded implant as control (arrows). (a) Astra Tech® implants. (b) Brånemark System®. From Berglundh _et al._ (2005).
**Fig. 15-6** Radiographs obtained from Astra Tech® (left side) and Brånemark® (right side) implants immediately after implant installation (top row) and following 10 months of functional loading (bottom row). Unloaded control implants are indicated with arrows. From Berglundh _et al._ (2005).
**Fig. 15-7** (a) Non-loaded control. Astra Tech® implant after 10 months (white star) and functionally loaded Astra Tech® implant (red star) after 10 months. (b) Non-loaded control. Brånemark® implant after 10 months (white star) and functionally loaded Brånemark® implant (red star) after 10 months. From Berglundh _et al._ (2005).
Table 15-1 describes the level of osseointegration in relation to the total length of the implant after 8 months of excessive loading or non-loading. These values were generally slightly below those of the alveolar bone height (Table 15-2) for all sites and surfaces in both test and control implants. The differences varied between 1.1 and 3.7% and were not statistically significant. Likewise, there were no statistically significant differences between the excessively loaded and the unloaded implants in terms of peri-implant bone density either at the implant–bone interface or at a distance of 1 mm from the implant surface (Fig. 15-9) after 8 months.
Since none of the clinical, radiographic or histologic parameters yielded statistically significant differences between non-loaded and excessively loaded implants, the study clearly demonstrated that, in the presence of peri-implant mucosal health, a period of 8 months of _excessive occlusal load_ on titanium implants _did not result in loss of osseointegration or marginal bone loss_ when compared with non-loaded implants.
# Static and cyclic loads on implants
While the study by Berglundh and co-workers (2005) addressed the possible influence of functional loading on the marginal bone levels of implants applying a flat occlusal plane scheme and physiologic forces, many authors have studied the influence of loading forces exceeding physiologic functional conditions and impacting on the implants in a non-axial direction (Barbier & Schepers 1997; Gotfredsen _et al_. 2001a,b,c; Heitz-Mayfield _et al_. 2004).
**Fig. 15-8** (a) A clinical view of four ITI® implants at the time of placement in one side of the mandible. (b) A clinical view of the ITI® implants after 6 months of non-submerged healing. (c) A clinical view of the test side of the mandible in one dog. Note the four single gold crowns in supra-occlusal contact with the opposing teeth. (d) A standardized radiograph illustrating the level of the implant shoulder (arrows), and the first bone to implant contact visible in the radiograph (arrow head), at the mesial and distal surfaces of the implant. From Heitz-Mayfield _et al._ (2004).
**Fig. 15-9** A histologic and diagrammatic representation of the histomorphometric measurements: (1) Implant length = distance from the base of the implant to the implant shoulder. (2) The distance from the base of the implant to the most coronal point of bone-to-implant contact. (3) The distance from the base of the implant to the alveolar bone crest. (A) Percentage of mineralized bone density adjacent to the implant surface. (B) Percentage of mineralized bone density 1 mm distant from the implant surface. From Heitz-Mayfield _et al._ (2004).
**Table 15-1** Buccal and lingual percentages of the level of osseointegration (bone-to-implant contact) in relation to the total length of the implant for control and test implants with a TPS or SLA surface after 8 months
**Table 15-2** Buccal and lingual percentages of alveolar bone height in relation to the total length of the implant for control and test implants with a TPS or SLA surface after 8 months
The bone tissue reaction to axial versus non-axial load was evaluated using conventional three-unit FDPs in the mandible of beagle dogs for axial loading, while non-axial loading was provoked by installing a distal cantilever of two implants (Barbier & Scheppers 1977). Bone remodeling was modest at the implant sites supporting conventional FDPs, while the non-axial load induced by the cantilever FDP yielded a more pronounced bone response including a higher activity of osteoclasts in the peri-implant bone. However, bone levels were not affected. This was interpreted as an adaptive phenomenon within the peri-implant bone as a result of non-axial loading.
Bone reactions around osseointegrated implants to static load was addressed in three studies in dogs (Gotfredsen _et al_. 2001a,b,c). In the first study (Gotfredsen _et al_. 2001a), lateral static load was induced by an orthodontic expansion screw at eight ITI® TPS hollow-screw implants in each dog. After loading period of 24 weeks during which time the screws were activated every 4 weeks from 0.0, 0.2, 0.4, and 0.6 mm, histologic and histometric analysis revealed no marginal bone loss at loaded and unloaded implant sites. Peri-implant bone density and mineralized bone-to-implant contact was higher at the loaded than at unloaded implant sites. This, again, was interpreted that lateral static load resulted in an _adaptive remodeling of the peri-implant bone_.
In the second study (Gotfredsen _et al_. 2001b), two TPS and two turned ITI® hollow-screw implants were subjected to the 24-week loading period in each dog using orthodontic expansion screws. These were, again, activated with 0.6 mm every 4 weeks. The histologic and histometric analysis yielded higher marginal bone levels around TPS implants than around turned implants. Likewise, the peri-implant bone density and mineralized bone-to-implant contact was higher around the roughened TPS than the turned implants. Hence, it was concluded that surface roughness influences the bone reactions to the applied load. This, in turn would indicate that surface roughness may also be a determining factor in the remodeling process triggered by load at the bone-to-implant interface.
The third study (Gotfredsen _et al_. 2001c), addressed the dynamics of applying static load of various durations to ITI® implants in three beagle dogs. Maximal activation of static load was set at 24 weeks on to the implants of the right mandibular side resulting in a total period of load of 46 weeks at sacrifice. At 60 weeks maximal activation of static load was set onto the implants of the left mandibular side resulting in a total period of load of 10 weeks at sacrifice. Fluorochrome labeling was performed at weeks 62, 64, 66, and 68. The dogs were sacrificed at week 70. Similar distribution of bone markers, bone density, and bone-to-implant contact was observed at 10 and 46 weeks of static lateral loading. However, higher fluorochrome proportions were seen at 10 weeks compared to 46 weeks of lateral loading, suggesting higher adaptive activity at 10 weeks. Nevertheless, the structural adaptation appeared to be similar at the two observation periods.
In all three studies, larger bone-to-implant contact was identified at lateral static load application compared to non-loaded implants. Moreover, lateral static load failed to induce peri-implant bone loss or to enhance peri-implant bone loss. Hence, _lateral static load does not appear to be detrimental_ to implants exhibiting peri-implant mucositis or peri-implantitis (Gotfredsen _et al_. 2001a,b,c).
In contrast to the findings of the studies presented are the results from a study in dogs (Hoshaw _et al_. 1994). In that study excessive cyclic axial forces had been applied to implants placed in the tibiae of ten animals. Bone loss was observed to occur around the neck of the Brånemark implants after 1 year and exposed to high cyclic (500 cycles/day) axial tension (10–300 N) for 5 consecutive days (Hoshaw _et al_. 1994). Similar results were reported for a rabbit model (Duyck _et al_. 2001) in which dynamic load to implants resulted in the establishment of marginal crater-like defects, while no effects on osseointegration could be identified at other parts of the implants.
# Load and loss of osseointegration
It has been reported (Isidor 1996, 1997) that excessive occlusal load may, under certain circumstances, lead to loss of osseointegration along the entire length of the implant, hereby resulting in implant mobility. In this study, four monkeys received 18 self-tapping screw implants in the mandible after the first molars (n = 7), premolars (n = 8), and incisors (n = 3) had been extracted. Using an opposing maxillary splint in heavy supra-occlusal contacts, _excessive occlusal load_ , predominantely in non-axial (lateral) direction was applied to eight implants. Furthermore, cotton ligatures for increased plaque retention were placed around another ten implants resulting first in mucositis and later in peri-implantitis (Lindhe _et al_. 1992; Lang _et al_. 1993). After 18 months of excessive occlusal loading, two of the eight implants were lost. Two implants out of ten revealed partial loss of osseointegration as a result of plaque-induced peri-implantitis (Fig. 15-10a). As for the remaining six implants subjected to excessive load, two implants yielded complete loss of osseointegration with a connective tissue capsule formed around the entire outline of the implants (Fig. 15-10b). Radiographically, the two implants showing complete loss of osseointegration and clinical mobility yielded a peri-implant radiolucency after 18 months of excessive occlusal load. However, no loss of marginal bone height was evident. Also, another two excessively loaded implants (in one monkey) showed no loss of osseointegration whatsoever. Instead, an increase in bone density and the highest percentage of bone-to-implant contact area was seen at these implants in relation to the remaining implants. Neither did this monkey develop ligature induced peri-implantitis (at three implants). Two implants under excessive occlusal load revealed a reduced bone-to-implant contact.
**Fig. 15-10** (a) Osseointegrated implant with plaque accumulation. The marginal bone level is located apical to the margin of the implant. (b) Excessively loaded implant with complete loss of osseointegration. The marginal bone level is located near the margin of the implant. Narrow zone of fibrous tissue interposed between implant and bone. MI = margin of implant; white arrows = apical extent of epithelium; C = cotton ligature. (Courtesy of F. Isidor, Århus, Denmark, _Clinical Oral Implants Research_ 8, 1–9.)
Thus, the study has demonstrated that excessive occlusal load can, indeed, result in loss of osseointegration characterized by a fibrous connective tissue capsule around the implant as opposed to the marginal bone loss encountered at implants with ligature induced peri-implantitis. It has to be realized, however, that the bone trabecular structure around the implant losing osseointegration as a result of excessive occlusal load (Fig. 15-10b) was much less dense than that of, for example, the implants subjected to experimental peri-implantitis (Fig. 15-10a). In that sense, the described study does not support the concept that occlusal overload may lead to implant losses. Rather, the study supports the fact that marginal bone loss at implants is associated with peri-implant disease.
# Masticatory occlusal forces on implants
Closing and occlusal functional force distributions have been studied using one-dimensional (Lundgren _et al_. 1987, 1989; Falk _et al_. 1989, 1990) or three-dimensional piezo-electric force transducers (Meriscke-Stern _et al_. 1996, 2000; Meriscke-Stern 1997, 1998). Eight strain gauge transducers were mounted bilaterally in a maxillary complete denture to occlude with a mandibular implant-supported fixed cantilever prosthesis (Fig. 15-11a) (Lundgren _et al_. 1989).
The study demonstrated that closing and chewing forces _increased_ distally along the cantilever beams when occluding with complete dentures. Moreover, on both the preferred and non-preferred chewing sides, significantly larger closing and chewing forces were measured over the cantilever segments than over the implant-supported area (Fig. 15-11b). Also, the distally increasing force distribution pattern could be altered to a distally _decreasing_ force distribution pattern by infraoccluding the second cantilever unit by as little as 100 μm. Such slight reductions in posterior occlusal contacts on cantilevers may have to be considered whenever the opposing masticatory unit is a complete removable dental prosthesis. However, maximal biting and chewing forces _decreased_ distally along the cantilever beams when occluding with tooth-supported fixed dental prostheses (FDPs) (Fig. 15-12) (Lundgren _et al_. 1987).
**Fig. 15-11** (a) Eight strain gauge transducers placed into a maxillary complete removable prosthesis and occluding against an implant supported fixed mandibular dental prosthesis with cantilever beams of 16 mm. (b) Chewing forces amounting to a maximum biting force of 80 N on the preferred (right) chewing side and 64 N on the non-preferred (left chewing side). While masticating higher forces are applied to the cantilever beams than to the implant-supported part of the mandibular FDP. (Courtesy of D. Lundgren, Göteborg, Sweden, _International Journal of Oral and Maxillofacial Implants_ **4** , 277–283.)
From this series of experimental clinical studies it was concluded that forces directed to the implants _per se_ are difficult to evaluate using the transducer methodology. Nevertheless, maximal closing forces were always substantially greater than chewing forces. In addition, each subject in the studies referred to developed a preferred chewing side that was associated with higher chewing forces than the non-preferred chewing side (Lundgren _et al_. 1987, 1989; Falk _et al_. 1989, 1990).
More recently, occlusal force distribution patterns have been studied for mandibular overdentures using three-dimensional piezo-electric transducers that were mounted on to two mandibular implants in the canine region designed to support either a ball-joint-retained or a bar-retained mandibular complete removable prosthesis. Rigid bars provided the best distribution of forces in a vertical direction on to the two mandibular implants (Mericske-Stern _et al_. 1996; Mericske-Stern 1998). Moreover, short distal bar extensions did not negatively influence the force pattern (Mericske-Stern 1997). When ball-joint anchors were used to retain the mandibular overdenture, rather low forces were measured on the implants, particularly in a vertical direction (Mericske-Stern 1998). Vertical forces amounted to 60–140 N, while horizontal forces were much smaller (15–60 N).
**Fig. 15-12** Chewing force patterns in implant-supported fixed dental prosthesis with cantilever beams occluding against tooth-supported FDPs. (Courtesy of D. Lundgren, Göteborg, Sweden, _Journal of Prosthetic Dentistry_ **58** , 197–203.)
**Fig. 15-13** Reconstruction of a chewing side in the left mandible using a fixed dental prosthesis. (a) Prepared abutment tooth 33 after having established adequate abutment height by the installation of a cast post and core prior to seating a three-unit FDP. (b) Tooth–implant-supported three-unit FDP, 10 years after placement.
# Tooth–implant supported reconstructions
In reconstructing patients with inadequate masticatory function, oral implants are often used to increase the patient's chewing comfort (see Chapter 52) and provide additional chewing units in an edentulous posterior region. Occasionally, it may be contemplated to reconstruct a chewing side with a reconstruction supported by both a tooth and an implant (Fig. 15-13). In this way, problems of the location of the mental nerve in an area of a planned implant installation or lack of an adequate bone volume may be overcome.
Combined tooth–implant reconstructions have been associated with numerous clinical problems including root intrusion as a potential clinical hazard of non-rigid connection. Hence, it has been claimed that natural teeth should not be connected to implants beneath a fixed prosthesis. However, experimental studies have clearly established that no detrimental effects on the periodontium of abutment teeth could be demonstrated despite a different biomechanical condition mediated by a periodontal ligament as opposed to the ankylotic anchorage of an implant (Biancu _et al_. 1995).
**Fig. 15-14** Ten-year randomized controlled clinical trial of three-unit FDPs, either implant–implant (type I) or tooth–implant (type II) supported. No differences in the crestal bone levels after 1, 2, 5, and 10 years in function. (Courtesy of J. Gunne _et al_. _International Journal of Prosthodontics_ **12** , 216–221.)
_In vivo_ measurements of vertical forces and bending moments during biting and chewing were carried out on ten three-unit prostheses in the posterior mandibles of five patients. Each patient had two prostheses, one supported by two implants and the other supported by one implant and one tooth. The results demonstrated no major difference in functional load magnitudes related to the support type. Obviously, functional loads were shared between the teeth and the implants (Gunne _et al_. 1997; Rangert _et al_. 1991, 1995). Further studies using finite element analysis yielded no increased risk of stress concentrations at the implant's neck (Gross & Laufer 1997; Laufer & Gross 1998).
Clinical studies reporting life table statistics in combined implant and tooth restorations do not show adverse effects of splinting teeth to implants. No increased risk of tooth intrusion were reported if the implant was rigidly connected to the tooth (Fugazzotto _et al_. 1999; Lindh _et al_. 2001; Naert _et al_. 2001a,b). The results of 843 consecutive patients treated in a private practice (Fugazzotto _et al_. 1999) with 1206 natural tooth–implant supported prostheses utilizing 3096 screw-fixed attachments showed that only 9 intrusion problems were noted after 3–14 years in function. All problems were associated with fractured or lost screws.
Probably the most relevant clinical study was a 10-year randomized controlled prospective study on 23 patients with residual mandibular anterior teeth (Gunne _et al_. 1999). Each patient received two three-unit FDPs either supported by two implants or, on the contralateral side, by one implant and one tooth, thus permitting intraindividual comparison. The distribution of the two types of FDPs in each jaw was randomized. Implant success rates, marginal bone changes, and mechanical complications were studied. The tooth–implant connection did not demonstrate any negative influences on the overall success rates for the 10-year period when compared to the implant–implant supported FDPs (Fig. 15-14). Hence, it was suggested that a prosthetic construction supported by both a tooth and an implant may be recommended as a predictable and reliable treatment alternative in the posterior mandible (Gunne _et al_. 1999).
Based on the evidence available today it can be stated that a combination of implant and tooth support for FDPs is acceptable (Belser _et al_. 2000). While a recent systematic review (Lang _et al_. 2004) indicated that tooth–implant reconstructions reveal a 5-year survival rate of 94.1%, comparing very well with the 5-year survival rate of implant–implant reconstructions of 95.0% (Pjetursson _et al_. 2004), the 10-year survival of tooth–implant reconstructions (77.8%) appears to be significantly lower than the 10-year survival of implant–implant reconstructions (86.7%). However, owing to the fact that the former 10-year survival rate was based on only 60 (I-T) FDPs and the latter on only 219 (I–I) FDPs, the reliability of such 10-year survival has to be questioned.
The biomechanical aspects of implant–tooth-supported fixed dental prostheses have been presented (Lundgren & Laurell 1994). As the implant is rigidly fixed within the alveolus, and the tooth is surrounded by a periodontal ligament that allows minute movement, rigid FDP designs have been advocated. The movement of the natural tooth abutment was found to affect the load-bearing capacity of the FDP, whenever a long-span FDP was constructed (e.g. a beam length of 24 mm or two premolar or molar pontics). Before occlusal load is applied, the FDP acts as a cantilever construction. Upon loading, an angular deflection of implant–crown unit of approximately 50 μm are noted. Together with bending of the long-span beam an apical deflection of the tooth of approximately 50 μm is allowed, hereby leading to a bilateral (tooth and implant) support of the FDP. If the tooth and implant only support a short-span FDP (e.g. a beam length of 12 mm or one premolar pontic only), however, angular deflection of the implant–crown unit of approximately 50 μm and the bending of the short-span beam are insufficient to achieve a bilateral support of the bridge. The apical deflection of the tooth will not be reached and the implant will cope with the entire occlusal load applied to the FDP. As indicated above, there is no doubt that osseointegration will cope with such functional loads.
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# Part 6: Periodontal Pathology
16 Non-Plaque Induced Inflammatory Gingival Lesions
_Palle Holmstrup_
17 Plaque-Induced Gingival Diseases
_Angelo Mariotti_
18 Chronic Periodontitis
_Denis F. Kinane, Jan Lindhe, and Leonardo Trombelli_
19 Aggressive Periodontitis
_Maurizio S. Tonetti and Andrea Mombelli_
20 Necrotizing Periodontal Disease
_Palle Holmstrup and Jytte Westergaard_
21 Periodontal Disease as a Risk for Systemic Disease,
_Ray C. Williams and David W. Paquette_
22 The Periodontal Abscess
_Mariano Sanz, David Herrera, and Arie J. van Winkelhoff_
23 Lesions of Endodontic Origin
_Gunnar Bergenholtz and Domenico Ricucci_
# Chapter 16
# Non-Plaque Induced Inflammatory Gingival Lesions
Palle Holmstrup
* * *
Gingival diseases of specific bacterial origin
Gingival diseases of viral origin
Herpes virus infections
Gingival diseases of fungal origin
Candidosis
Linear gingival erythema
Histoplasmosis
Gingival lesions of genetic origin
Hereditary gingival fibromatosis
Gingival diseases of systemic origin
Mucocutaneous disorders
Allergic reactions
Other gingival manifestations of systemic conditions
Traumatic lesions
Chemical injury
Physical injury
Thermal injury
Foreign body reactions
* * *
Gingival inflammation, clinically presenting as gingivitis, is not always due to accumulation of plaque on the tooth surface, and non-plaque induced inflammatory gingival reactions often present characteristic clinical features (Holmstrup 1999). They may occur due to several causes, such as specific bacterial, viral or fungal infection without an associated plaque-related gingival inflammatory reaction. Gingival lesions of genetic origin are seen in hereditary gingival fibromatosis, and several mucocutaneous disorders manifest as gingival inflammation. Typical examples of such disorders are lichen planus, pemphigoid, pemphigus vulgaris, and erythema multiforme. Allergic and traumatic lesions are other examples of non-plaque induced gingival inflammation. Dentists, and especially specialists in periodontology, are the key persons in the diagnostic unraveling and treatment of patients affected by such lesions.
This chapter focuses on those non-plaque induced inflammatory gingival lesions of the gingival tissues which are most relevant, either because they are common or because they are important examples for the understanding of the variety of tissue reactions that take place in the periodontium. For further information the reader is referred to oral medicine textbooks. The modifying factors of plaque-related gingivitis such as smoking, sexual hormones, and metabolic anomalies (diabetes) are dealt with in Chapter 12.
# Gingival diseases of specific bacterial origin
Infective gingivitis and stomatitis may occur on rare occasions in both immunocompromised and non-immunocompromised individuals, when non-plaque-related pathogens overwhelm innate host resistance (Rivera-Hidalgo & Stanford 1999). The lesions may be due to bacteria and may not be accompanied by lesions elsewhere in the body. Typical examples of such lesions are due to infections with _Neisseria gonorrhoeae_ (Scully 1995; Siegel 1996), _Treponema pallidum (_ Scully 1995; Ramirez-Amador _et al_. 1996; Siegel 1996; Rivera-Hidalgo & Stanford 1999), streptococci, _Mycobacterium chelonae_ (Pedersen & Reibel 1989) or other organisms (Blake & Trott 1959; Littner _et al_. 1982). The gingival lesions manifest as fiery red edematous painful ulcerations, as asymptomatic chancres or mucous patches, or as atypical non-ulcerated, highly inflamed gingivitis. Biopsy supplemented by microbiologic examination reveals the background of the lesions.
# Gingival diseases of viral origin
## Herpes virus infections
Several viral infections are known to cause gingivitis (Scully _et al_. 1998b). The most important are the herpes viruses: herpes simplex viruses type 1 and 2 and varicella-zoster virus. These viruses usually enter the human body in childhood and may give rise to oral mucosal disease followed by periods of latency and sometimes reactivation. Herpes simplex virus type 1 (HSV-1) usually causes oral manifestations, whereas herpes simplex virus type 2 (HSV-2) is mainly involved in anogenital infections and only occasionally is involved in oral infection (Scully 1989).
### Primary herpetic gingivostomatitis
Herpes simplex infections are among the most common viral infections. Herpes simplex is a DNA virus with low infectiousness, which after entering the oral mucosal epithelium, penetrates a neural ending and, by retrograde transport through the smooth endoplasmatic reticulum (200–300 mm/day), travels to the trigeminal ganglion where it can remain latent for years. The virus has also been isolated in extraneural locations such as the gingiva (Amit _et al_. 1992). Sometimes herpes simplex viruses may also play a role in recurring erythema multiforme. It is presently unknown whether the virus plays a role in other oral diseases, but herpes simplex virus has been found in gingivitis (Ehrlich _et al_. 1983), acute necrotizing gingivitis (Contreras _et al_. 1997), and periodontitis (Parra & Slots 1996).
When a baby is infected, sometimes from the parent's recurrent herpes labialis, it is often wrongly diagnosed as "teething". With increased hygiene in the industrialized society, more and more primary infections occur at higher ages, i.e. during adolescence or even adulthood. It is estimated in the US that there are about half a million cases per year (Overall 1982). The primary herpetic infection may run an asymptomatic course in early childhood, but may also give rise to severe gingivostomatitis, which usually occurs before adolescence (Fig. 16-1). This manifestation includes painful severe gingivitis with redness, ulcerations with serofibrinous exudate and edema accompanied by stomatitis (Figs. 16-2 and 16-3). The incubation period is 1 week. A characteristic feature is the formation of vesicles, which rupture, coalesce, and leave fibrin-coated ulcers (Scully _et al_. 1991; Miller & Redding 1992). Fever and lymphadenopathy are other classic features. Healing occurs spontaneously without scarring in 10–14 days (Fig. 16-4). During this period pain can render eating difficult.
The virus remains latent in the ganglion cell, probably through integration of its DNA in that of the chromosomal DNA (Overall 1982). Reactivation of the virus resulting in recurrent infections occurs in 20–40% of individuals with the primary infection (Greenberg 1996) and usually presents in the form of herpes labialis, but recurrent intraoral herpes infections are also seen. Recurrent infections occur in general more than once per year, usually at the same location on the vermilion border and/or the skin adjacent to it, where neural endings are known to be clustering. A large variety of factors trigger reactivation of latent virus. These are trauma, ultraviolet light exposure, fever, menstruation and others (Scully _et al_. 1998b).
**Fig. 16-1** Herpetic gingivostomatitis in a 3-year-old child. Erythematous swelling of attached gingiva with serofibrinous exudate along the gingival margin.
**Fig. 16-2** Herpetic gingivostomatitis affecting palatal gingiva. Numerous vesicles and small ulcerations.
**Fig. 16-3** Herpetic gingivostomatitis in a 38-year-old woman. Widespread ulceration of lower lip mucosa and gingiva.
**Fig. 16-4** Same patient as shown in Fig. 16-3, 4 weeks later. Healing without loss of tissue or scar formation.
**Fig. 16-5** Recurrent intraoral herpes infection. Ruptured vesicles of right palatal gingiva and mucosa.
While recurrences at the vermilion border are well recognized, recurrent intraoral herpes lesions often remain undiagnosed because they are considered aphthous ulcerations (Lennette & Magoffin 1973; Sciubba 2003), irrespective of the fact that aphthous ulcers do not affect keratinized mucosa. Recurrent intraoral herpes typically presents a less dramatic course than does the primary infection. A characteristic manifestation is a cluster of small painful ulcers in the attached gingiva and hard palate (Yura _et al_. 1986) (Fig. 16-5). The diagnosis can be made on the basis of the patient history and clinical findings supported by isolation of HSV from lesions. A reliable isolation of virus is best obtained from intact vesicular lesions, for instance by aspiration of the vesicle fluid with a small syringe. Isolation and growth of herpes viruses are elaborate because of their fragility. The virus must be transferred to a special cell line in the laboratory within 24 hours, or stored at ‒70ºC. The herpes virus is detected within 5 days, and while a positive viral culture can be taken as evidence of viral infection, a negative result does not rule out such an infection. Laboratory diagnosis may also involve examination of a blood sample for increased antibody titer against herpes virus. However, this is most relevant in cases of primary infection, because the antibody titer remains elevated for the rest of the lifetime. The histopathologic features of cytologic smears from the gingival lesions are not specific, but the presence of giant cells and intranuclear inclusion bodies may indicate intracellular activity of virus (Burns 1980).
Immunodeficient patients, such as HIV-infected individuals, are at increased risk of acquiring the infection (Holmstrup & Westergaard 1998). In the immunocompromised patient the recurrence of herpes infection, either gingival or elsewhere, may be severe and even life-threatening.
The treatment of herpetic gingivostomatitis includes careful plaque removal to limit bacterial superinfection of the ulcerations, which delays their healing. In severe cases, including patients with immunodeficiency, the systemic use of antiviral drugs such as aciclovir, valaciclovir or famciclovir is recommended (O'Brien & Campoli-Richards 1989; Mindel 1991; Arduino & Porter 2006). Resistance to aciclovir, especially among immunodeficient patients on long-term therapy, is a growing concern (Westheim _et al_. 1987) and explains why other antiviral drugs may be relevant. Prophylactic antiviral treatment before dental treatment has been recommended for patients at risk of experiencing a recurrence as well as to minimize transmission of the disease (Miller _et al_. 2004).
### Herpes zoster
Varicella-zoster virus causes varicella (chicken pox) as the primary self-limiting infection. It occurs mainly in children and later reactivation of the virus in adults causes herpes zoster (shingles). Both manifestations can involve the gingiva (Straus _et al_. 1988; Scully 1995). Chicken pox is associated with fever, malaise, and a skin rash. The intraoral lesions are small ulcers usually on the tongue, palate, and gingiva (Miller 1996; Scully _et al_. 1998b). The virus remains latent in the dorsal root ganglion from where it can be reactivated years after the primary infection (Rentier _et al_. 1996). Later reactivation results in herpes zoster, with unilateral lesions following the infected nerve (Miller 1996). The reactivation normally affects the thoracic ganglia in elderly or immunocompromised patients. Reactivation of virus from the trigeminal ganglion occurs in 20% of reported cases (Hudson & Vickers 1971). If the second or third branch of the trigeminal nerve is involved, skin lesions may be associated with intraoral lesions, or intraoral lesions may occur alone (Eisenberg 1978), for instance affecting the palatal gingiva (Fig. 16-6). Initial symptoms are pain and paresthesia, which may be present before lesions occur (Greenberg 1996). The associated pain is usually severe. The lesions, which often involve the gingiva, initiate as vesicles. They soon rupture to leave fibrin-coated ulcers, which often coalesce to irregular forms (Millar & Traulis 1994) (Fig. 16-6). In immunocompromised patients, including HIV-infected individuals, the infection can result in severe tissue destruction with tooth exfoliation and necrosis of alveolar bone and high morbidity (Melbye _et al_. 1987; Schwartz _et al_. 1989). The diagnosis is usually obvious due to the unilateral occurrence of lesions associated with severe pain. Healing of the lesions usually takes place in 1–2 weeks.
**Fig. 16-6** Herpes zoster of left palatal gingiva and mucosa. Irregular fibrin coated ulcerations with severe pain.
Treatment consists of soft or liquid diet, rest, atraumatic removal of plaque, and diluted chlorhexidine rinses. This may be supplemented by antiviral drug therapy.
# Gingival diseases of fungal origin
Fungal infection of the oral mucosa includes a range of diseases such as aspergillosis, blastomycosis, candidosis, coccidioidomycosis, cryptococcosis, histoplasmosis, mucormycosis, and paracoccidioidomycosis infections (Scully _et al_. 1998b), but some of the infections are very uncommon and not all of them manifest as gingivitis. The present chapter focuses on candidosis and histoplasmosis, both of which may cause gingival infection.
## Candidosis
Various _Candida_ species are recovered from the mouth of humans including _C. albicans_ , _C. glabrata_ , _C._ _krusei_ , _C. tropicalis_ , _C. parapsilosis_ , and _C. guillermondii_ (Cannon _et al_. 1995). _C. albicans_ is by far the most common. It is a normal commensal of the oral cavity but also an opportunistic pathogen. The prevalence of oral carriage of _C. albicans_ in healthy adults ranges from 3–48% (Scully _et al_. 1995), the large variation being due to differences in examined populations and the procedures used. The proportion of _C. albicans_ in the total oral yeast population can reach about 50–80% (Wright _et al_. 1985), and by far the most common fungal infection of the oral mucosa is candidosis mainly caused by the organism _C. albicans_ (Scully _et al_. 1998b); the proteinase-positive strains of _C. albicans_ are associated with disease (Negi _et al_. 1984; Odds 1985) and invasion of keratinized epithelia such as that of the gingiva. Invasion and increased desquamation is due to the hyaluronidase production. Infection by _C. albicans_ usually occurs as a consequence of reduced host defense systems (Holmstrup & Johnson 1997), including immunodeficiency (Holmstrup & Samaranayake 1990) (Figs. 16-7 to 16-9), reduced saliva secretion, smoking, and treatment with corticosteroids, but may be due to a wide range of predisposing factors. The occurrence of oral candidosis may act as a predictor of immune and virologic failure in HIV-infected patients treated with antiviral drugs (Miziara & Weber 2006). Disturbances in the oral microbial flora, such as after therapy with broad-spectrum antibiotics, may also lead to oral candidosis. The predisposing factors are, however, often difficult to identify. Based on their site, infections may be defined as superficial or systemic. Candidal infection of the oral mucosa is usually a superficial infection, but systemic infections are not uncommon in debilitated patients.
**Fig. 16-7** Pseudomembranous candidosis of maxillary gingiva and mucosa in HIV-seropositive patient. The lesions can be scraped off, leaving a slightly bleeding surface.
**Fig. 16-8** Erythematous candidosis of attached mandibular gingiva of HIV-seropositive patient. The mucogingival junction is invisible.
**Fig. 16-9** Same patient as shown in Fig. 16-8 after topical antimycotic therapy. The mucogingival junction is visible.
**Fig. 16-10** Chronic erythematous candidosis of maxillary attached gingiva of the incisor region.
In otherwise healthy individuals, oral candidosis rarely manifests in the gingiva. This is surprising, considering the fact that _C. albicans_ is frequently isolated from the subgingival flora of patients with severe periodontitis (Slots _et al_. 1988). The most common clinical characteristic of gingival candidal infections is redness of the attached gingiva, often associated with a granular surface (Fig. 16-10).
Various types of oral mucosal manifestations are pseudomembranous candidosis (also known as thrush in neonates), erythematous candidosis, plaque-type candidosis, and nodular candidosis (Holmstrup & Axéll 1990). Pseudomembranous candidosis shows whitish patches (Fig. 16-7), which can be wiped off the mucosa with an instrument or gauze leaving a slightly bleeding surface. The pseudomembranous type usually has no major symptoms. Erythematous lesions can be found anywhere in the oral mucosa (Fig. 16-10). The intensely red lesions are usually associated with pain, which is sometimes severe. The plaque type of oral candidosis is a whitish plaque, which cannot be removed. There are usually no symptoms and the lesion is clinically indistinguishable from oral leukoplakia. Nodular candidal lesions are infrequent in the gingiva; they are characterized by slightly elevated nodules of white or reddish color (Holmstrup & Axéll 1990).
A diagnosis of candidal infection can be accomplished on the basis of culture, smear, and biopsy. A culture on Nickersons medium at room temperature is easily handled in the dental premises. Microscopic examination of smears from suspected lesions is another easy diagnostic procedure, either performed as direct examination by phase contrast microscopy or as light microscopic examination of periodic-acid-Schiff-stained or Gram-stained smears. Myceliumforming cells in the form of hyphae or pseudohyphae and blastospores are seen in great numbers among masses of desquamated cells. Since oral carriage of _C. albicans_ is common among healthy individuals, positive culture and smear does not necessarily imply candidal infection (Rindum _et al_. 1994). Quantitative assessment of the mycological findings and the presence of clinical changes compatible with the above types of lesions are necessary to obtain a reliable diagnosis, which can also be obtained on the basis of identification of hyphae or pseudohyphae in biopsy specimens from the lesions.
Topical treatment involves application of antifungals, such as nystatin, amphotericin B or miconazole. Nystatin may be used as an oral suspension. Since it is not absorbed it can be used in pregnant or lactating women. Miconazole exists as an oral gel. It should not be given during pregnancy and it can interact with anticoagulants and phenytoin. The treatment of the severe or generalized forms also involves systemic antifungals such as fluconazole.
## Linear gingival erythema
Linear gingival erythema (LGE) is regarded as a gingival manifestation of immunosuppression characterized by a distinct linear erythematous band limited to the free gingiva (Consensus Report 1999) (Fig. 16-11). It is characterized by a disproportion of inflammatory intensity for the amount of plaque present. There is no evidence of pocketing or attachment loss. A further characteristic of this type of lesion is that it does not respond well to improved oral hygiene or to scaling (EC Clearinghouse on Oral Problems 1993) and it is now a requirement for the diagnosis to be considered that the lesion persists after removal of plaque in the initial visit (Umadevi _et al_. 2006). The extent of gingival banding measured by number of affected sites has been shown to depend on tobacco usage (Swango _et al_. 1991). While 15% of affected sites were originally reported to bleed on probing and 11% exhibited spontaneous bleeding (Winkler _et al_. 1988), a key feature of LGE is now considered to be lack of bleeding on probing (Robinson _et al_. 1994).
**Fig. 16-11** Linear gingival erythema of maxillary gingiva. Red banding along the gingival margin, which does not respond to conventional therapy.
Some studies of various groups of HIV-infected patients have revealed prevalences of gingivitis with band-shaped patterns in 0.5–49% (Klein _et al_. 1991; Swango _et al_. 1991; Barr _et al_. 1992; Laskaris _et al_. 1992; Masouredis _et al_. 1992; Riley _et al_. 1992; Ceballos-Salobrena _et al_. 1996; Robinson _et al_. 1996). These prevalence values reflect some of the problems with non-standardized diagnosis and selection of study groups. A few studies of unbiased groups of patients have indicated that gingivitis with band-shaped or punctate marginal erythema may be relatively rare in HIV-infected patients, and probably a clinical finding which is no more frequent than in the general population (Drinkard _et al_. 1991; Friedman _et al_. 1991).
It is interesting to note that, whereas there was no HIV-related preponderance of red banding, diffuse and punctate erythema was significantly more prevalent in HIV-infected than in non-HIV-infected individuals in a British study (Robinson _et al_. 1996). Red gingival banding as a clinical feature alone was, therefore, not strongly associated with HIV infection.
There are indications that candidal infection is the background of some cases of gingival inflammation including LGE (Winkler _et al_. 1988; Robinson _et al_. 1994), but studies have revealed a microflora comprising both _C. albicans_ , and a number of periopathogenic bacteria consistent with those seen in conventional periodontitis, i.e. _Porphyromonas gingivalis_ , _Prevotella intermedia_ , _Actinobacillus actinomycetemcomitans_ , _Fusobacterium nucleatum_ , and _Campylobacter rectus_ (Murray _et al_. 1988, 1989, 1991). By DNA probe detection, the percentage of positive sites in HIV-associated gingivitis as compared with matched gingivitis sites of HIV-seronegative patients for _A. actinomycetemcomitans_ was 23% and 7% respectively, for _P. gingivalis_ 52% and 17%, _Pr. intermedia_ 63% and 29%, and for _C. rectus_ 50% and 14% (Murray _et al_. 1988, 1989, 1991). _C. albicans_ has been isolated by culture in about 50% of HIV-associated gingivitis sites, in 26% of unaffected sites of HIV-seropositive patients and in 3% of healthy sites of HIV-seronegative patients. The frequent isolation and the pathogenic role of _C. albicans_ may be related to the high levels of the yeasts in saliva and oral mucosa of HIV-infected patients (Tylenda _et al_. 1989).
An interesting histopathologic study of biopsy specimens from the banding zone has revealed no inflammatory infiltrate but an increased number of blood vessels, which explains the red color of the lesions (Glick _et al_. 1990). The incomplete inflammatory reaction of the host tissue may be the background of the lack of response to conventional treatment.
A number of diseases present clinical features resembling those of LGE and which do not resolve after improved oral hygiene and debridement. Examples are (1) oral lichen planus, which is frequently associated with an inflammatory red band of the attached gingiva (Holmstrup _et al_. 1990) and so is sometimes mucous membrane pemphigoid (Pindborg 1992), or (2) erythematous lesions associated with renal insufficiency because of the salivary ammonia production associated with the high levels of urea.
There is little information about treatment based on controlled studies of this type of condition. Conventional therapy plus rinsing with 0.12% chlorhexidine gluconate twice daily has shown significant improvement after 3 months (Grassi _et al_. 1989). It was mentioned above that some cases of LGE might be related to the presence of _Candida_ strains; clinical observations suggest that improvement is frequently dependent on successful eradication of intraoral _Candida_ strains (Winkler _et al_. 1988). Consequently, attempts to identify the presence of fungal infection either by culture or smear is recommended, followed by antimycotic therapy in _Candida-_ positive cases.
## Histoplasmosis
Histoplasmosis is a granulomatous disease caused by _Histoplasma capsulatum_ , a soil saprophyte found mainly in feces from birds and cats. The infection occurs in the north-eastern, south-eastern, mid Atlantic and central states of the US. It is also found in Central and South America, India, East Asia, and Australia. Histoplasmosis is the most frequent systemic mycosis in the US. It is mediated by airborne spores from the mycelial form of the organism (Rajah & Essa 1993). In the normal host, the course of the infection is subclinical (Anaissie _et al_. 1986). The clinical manifestations include acute and chronic pulmonary histoplasmosis and a disseminated form, mainly occurring in immunocompromised patients (Cobb _et al_. 1989). Oral lesions have been seen in 30% of patients with pulmonary histoplasmosis and in 66% of patients with the disseminated form (Weed & Parkhill 1948; Loh _et al_. 1989). The oral lesions may affect any area of the oral mucosa (Chinn _et al_. 1995), including the gingiva, which appears to be one of the most frequent sites affected (Hernandez _et al_. 2004). The lesions are initially nodular or papillary and later may become ulcerative, with loss of gingival tissue, and painful (Figs. 16-12 and 16-13). They are sometimes granulomatous and the clinical appearance may resemble a malignant tumor (Boutros _et al_. 1995). The diagnosis is based on clinical appearance and histopathology and/or culture, and the treatment consists of systemic antifungal therapy.
**Fig. 16-12** Gingival histoplasmosis with loss of periodontal tissue around second premolar.
**Fig. 16-13** Same patient as shown in Fig. 16-12. Lingual aspect with ulceration in the deeper part of crater-like lesion.
# Gingival lesions of genetic origin
## Hereditary gingival fibromatosis
Gingival hyperplasia (synonymous with gingival overgrowth, gingival fibromatosis) may occur as a side effect to systemic medications, including phenytoin, cyclosporine, and nifedipine (Coletta & Graner 2006). These lesions are to some extent plaque-dependent and they are reviewed in Chapter 17. Gingival hyperplasia may also be of genetic origin. Such lesions are known as hereditary gingival fibromatosis (HGF), which is an uncommon condition characterized by diffuse gingival enlargement, sometimes covering major parts of, or the total, tooth surfaces. The lesions develop irrespective of effective plaque removal.
HGF may be an isolated disease entity or part of a syndrome (Gorlin _et al_. 1990), associated with other clinical manifestations, such as hypertrichosis (Horning _et al_. 1985; Cuestas-Carneiro & Bornancini 1988), learning difficulties (Araiche & Brode 1959), epilepsy (Ramon _et al_. 1967), hearing loss (Hartsfield _et al_. 1985), growth retardation (Bhowmick _et al_. 2001), and abnormalities of extremities (Nevin _et al_. 1971; Skrinjaric & Basic 1989). Most cases are related to an autosomal dominant mode of inheritance, but cases have been described with an autosomal recessive background (Emerson 1965; Jorgensen & Cocker 1974; Singer _et al_. 1993). The most common syndrome of HGF includes hypertrichosis, epilepsy and learning difficulties; the two latter features, however, are not present in all cases (Gorlin _et al_. 1990).
**Fig. 16-14** Hereditary gingival fibromatosis. Facial aspect with partial coverage of teeth.
**Fig. 16-15** Same patient as shown in Fig. 16-14. The maxillary gingival fibromatosis is severe and has resulted in total disfiguration of the dental arch.
Typically, HGF presents as large masses of firm, dense, resilient, insensitive fibrous tissue that cover the alveolar ridges and extend over the teeth, resulting in extensive pseudopockets. The color may be normal or erythematous if inflamed (Figs. 16-14 and 16-15). Depending on extension of the gingival enlargement, patients complain of functional and esthetic problems. The enlargement may result in protrusion of the lips, and they may chew on a considerable hyperplasia of tissue covering the teeth. HGF is seldom present at birth but may be noted at an early age. If the enlargement is present before tooth eruption, the dense fibrous tissue may interfere with or prevent eruption (Shafer _et al_. 1983).
Studies have suggested that an important pathogenic mechanism may be enhanced production of transforming growth factor (TGF-beta 1) reducing the proteolytic activities of HGF fibroblasts, which again favor the accumulation of extracellular matrix (Coletta _et al_. 1999). A locus for autosomal dominant HGF has previously been mapped to a region on chromosome 2 (Hart _et al_. 1998; Xiao _et al_. 2000), although at least two genetically distinct loci seem to be responsible for this type of HGF (Hart _et al_. 2000); a novel locus for maternally inherited human gingival fibromatosis has recently been reported at human chromosome 11p15 (Zhu _et al_. 2006).
The histologic features of HGF include moderate hyperplasia of a slightly hyperkeratotic epithelium with extended rete pegs. The underlying stroma is almost entirely made up of dense collagen bundles with only a few fibroblasts. Local accumulation of inflammatory cells may be present (Shafer _et al_. 1983). Histologic examination may facilitate the differential diagnosis from other genetically determined gingival enlargements such as Fabry disease, which is characterized by telangiectasia.
Treatment of HGF is surgical removal, often in a series of gingivectomies, but relapses are not uncommon. If the volume of the overgrowth is extensive, a repositioned flap to avoid exposure of connective tissue by gingivectomy may better achieve elimination of pseudopockets.
# Gingival diseases of systemic origin
## Mucocutaneous disorders
Various mucocutaneous disorders present with gingival manifestations, sometimes in the form of desquamative lesions or ulceration of the gingiva. The most important of these diseases are lichen planus, pemphigoid, pemphigus vulgaris, erythema multiforme, and lupus erythematosus.
### Lichen planus
Lichen planus is the most common mucocutaneous disease manifesting on the gingiva. The disease may affect skin and oral as well as other mucous membranes in some patients while others may present with either skin or oral mucosal involvement alone. Oral involvement alone is common and concomitant skin lesions in patients with oral lesions have been found in 5–44% of cases (Andreasen 1968; Axéll & Rundquist 1987). The disease may be associated with severe discomfort; it has been shown to possess a premalignant potential, although this is still a controversial issue (Holmstrup 1992), so it is important to diagnose and treat cases and to have regular oral examinations as follow-up (Holmstrup _et al_. 1988; Mattson _et al_. 2002; Mignogna _et al_. 2006).
**Fig. 16-16** Skin lesions of lichen planus. Papules with delicate white striations.
The prevalence of oral lichen planus (OLP) in various populations has been found to be 0.1–4% (Scully _et al_. 1998a). The disease may afflict patients at any age although it is seldom observed in childhood (Scully _et al_. 1994). Skin lesions are characterized by papules with white striae (Wickham striae) (Fig. 16-16). Itching is a common symptom, and the most frequent locations are the flexor aspects of the arms, the thighs and the neck. In the vast majority of cases the skin lesions disappear spontaneously after a few months, which is in sharp contrast with the oral lesions, which usually remain for years (Thorn _et al_. 1988).
A variety of clinical appearances is characteristic of OLP. These include:
* Papular (Fig. 16-17)
* Reticular (Figs. 16-18 and 16-19)
* Plaque-like (Fig. 16-20)
* Atrophic (Figs. 16-21 to 16-25)
* Ulcerative (Figs 16-22 and 16-27)
* Bullous (Fig. 16-29).
Simultaneous presence of more than one type of lesion is common (Thorn _et al_. 1988). The most characteristic clinical manifestations of the disease and the basis of the clinical diagnosis are white papules (Fig. 16-17) and white striations (Figs 16-18, 16-19, 16-26 and 16-27), which often form reticular patterns (Thorn _et al_. 1988), usually of bilateral occurrence (Ingafou _et al_. 2006). Sometimes atrophic and ulcerative lesions are referred to as erosive (Rees 1989). Papular, reticular, and plaque-type lesions usually do not give rise to significant symptoms, whereas atrophic and ulcerative lesions are associated with moderate to severe pain, especially in relation to oral hygiene procedures and eating. OLP frequently persists for many years (Thorn _et al_. 1988). Any area of the oral mucosa may be affected by OLP, but the lesions often change in clinical type and extension over the years. Such changes may imply the development of plaque-type lesions, which are clinically indistinguishable from oral leukoplakia. This may give rise to a diagnostic problem if other lesions more characteristic of OLP have disappeared (Thorn _et al_. 1988).
**Fig. 16-17** Oral lichen planus. Papular lesion of right buccal mucosa.
**Fig. 16-18** Oral lichen planus. Reticular lesion of lower lip mucosa. The white striations are denoted Wickham striae.
**Fig. 16-19** Oral lichen planus. Reticular lesions of gingiva in lower left premolar and molar region.
**Fig. 16-20** Oral lichen planus. Plaque-type lesion of maxillary gingiva.
**Fig. 16-21** Oral lichen planus. Atrophic lesions of facial maxillary and mandibular gingiva. Such lesions were previously termed desquamative gingivitis.
**Fig. 16-22** Oral lichen planus. Atrophic and ulcerative lesion of maxillary gingiva. Note that the margin of the gingiva has a normal color in the upper incisor region, which distinguishes the lesions from plaque-induced gingivitis.
**Fig. 16-23** Oral lichen planus. Atrophic and reticular lesion of maxillary gingiva. Several types of lesions are often present simultaneously.
**Fig. 16-24** Oral lichen planus. Atrophic and reticular lesion of lower left canine region. Plaque accumulation results in exacerbation of oral lichen planus, and atrophic lesions compromise oral hygiene procedures. This may lead to a vicious circle that the dentist can help in breaking.
**Fig. 16-25** Oral lichen planus. Atrophic and reticular lesion of right maxillary gingiva in a patient using an electric toothbrush, which is traumatic to the marginal gingiva. The physical trauma results in exacerbation of the lesion with atrophic characteristics and pain.
**Fig. 16-26** Same patient as shown in Fig. 16-25 after modified toothbrushing procedure with no traumatic action on marginal gingiva.
**Fig. 16-27** Oral lichen planus. Atrophic and ulcerative/ reticular lesions of maxillary and mandibular incisor region. The patient, a 48-year-old woman, suffers from severe discomfort from food, beverages, and toothbrushing.
**Fig. 16-28** Same patient as shown in Fig. 16-27 after periodontal treatment and extraction of teeth with deep pockets. An individual oral hygiene program, which ensured gentle, meticulous plaque removal has been used by the patient for 3 months. The atrophic/ulcerative lesions are now healed and there are no more symptoms.
**Fig. 16-29** Oral lichen planus. Bullous/reticular lesion of left palatal mucosa.
A characteristic histopathologic feature in OLP is a subepithelial, band-like accumulation of lymphocytes and macrophages characteristic of a type IV hypersensitivity reaction (Eversole _et al_. 1994). The epithelium shows hyperortho- or hyperparakeratinization and basal cell disruption with transmigration of lymphocytes into the basal and parabasal cell layers (Eversole 1995). The infiltrating lymphocytes have been identified as CD4+ and CD8+ cells (Buchner 1984; Walsh _et al_. 1990; Eversole _et al_. 1994). Other characteristic features are Civatte bodies, which are dyskeratotic basal cells. Common immunohistochemical findings of OLP lesions are fibrin in the basement membrane zone, but deposits of IgM, C3, C4, and C5 may also be found. None of these findings are specific to OLP (Schiødt _et al_. 1981; Kilpi _et al_. 1988; Eversole _et al_. 1994).
The subepithelial inflammatory reaction in OLP lesions is presumably due to an as yet unidentified antigen in the junctional zone between epithelium and connective tissue or to components of basal epithelial cells (Holmstrup & Dabelsteen 1979; Walsh _et al_. 1990; Sugerman _et al_. 1994). A lichen planus specific antigen in the stratum spinosum of skin lesions has been described (Camisa _et al_. 1986), but this antigen does not appear to play a significant role in oral lesions since it is rarely identified there. It is still an open question whether OLP is a group of etiologically diverse diseases with common clinical and histopathologic features or a disease entity characterized by a type IV hypersensitivity reaction to an antigen in the basement membrane area. The clinical diagnosis is based on the presence of papular or reticular lesions. The diagnosis may be supported by histopathologic findings of hyperkeratosis, degenerative changes of basal cells, and subepithelial inflammation dominated by lymphocytes and macrophages (Holmstrup 1999).
The uncertain background of OLP results in several borderline cases of so-called oral lichenoid lesions (OLL) for which a final diagnosis is difficult to establish (Thornhill _et al_. 2006). The most common OLLs are probably lesions in contact with dental restorations (Holmstrup 1991) (see later in this chapter). Other types of OLL are associated with various types of medications including antimalarials, quinine, quinidine, non-steroidal anti-inflammatory drugs, thiazides, diuretics, gold salts, penicillamine, beta-blockers, and others (Scully _et al_. 1998a). Graft-versushost reactions are also characterized by a lichenoid appearance (Fujii _et al_. 1988) and a group of OLLs is associated with systemic diseases, including liver disease (Fortune & Buchanan 1993; Bagan _et al_. 1994; Carrozzo _et al_. 1996). This appears to be particularly evident in Southern Europe and Japan where hepatitis C has been found in 20–60% of OLL cases (Bagan _et al_. 1994; Gandolfo _et al_. 1994; Nagao _et al_. 1995).
Several follow-up studies have demonstrated that OLP is associated with increased development of oral cancer, the frequency of cancer development being in the range of 0.5–2% (Holmstrup _et al_. 1988; Mattson _et al_.2002; Mignogna _et al_. 2006; Ingafou _et al_. 2006).
The most important part of the therapeutic regimen is an atraumatic meticulous plaque control, which results in significant improvement in many patients (Holmstrup _et al_. 1990) (Figs. 16-25 to 16-28). Individual oral hygiene procedures with the purpose of effective plaque removal without traumatic influence on the gingival tissue should be established for all patients with symptoms. In cases of persistent pain, typically associated with atrophic and ulcerative affections, antifungal treatment may be necessary if the lesions contain yeast, which occurs in 37% of OLP cases (Krogh _et al_. 1987). In painful cases, which have not responded to the treatment above, topical corticosteroids, preferably in a paste or an ointment, should be used three times daily for a number of weeks. However, relapses in such cases are very common, and intermittent episodes of treatment may be needed over an extended period.
### Pemphigoid
Pemphigoid is a group of disorders in which autoantibodies towards components of the basement membrane result in detachment of the epithelium from the connective tissue. Bullous pemphigoid predominantly affects the skin, but oral mucosal involvement may occur (Brooke 1973; Hodge _et al_. 1981). If only mucous membranes are affected, the term benign mucous membrane pemphigoid (BMMP) is often used. The term cicatricial pemphigoid is also used to describe subepithelial bullous disease limited to the mouth or eyes and infrequently other mucosal areas. This term is problematic at least for the oral lesions, because usually oral lesions do not result in scarring, whereas this is a serious risk in ocular lesions (Scully _et al_. 1998b). It is now evident that BMMP comprises a group of disease entities characterized by an immune reaction involving autoantibodies directed against various basement membrane zone antigens (Scully & Laskaris 1998). These antigens have been identified as hemidesmosome or lamina lucida components (Leonard _et al_. 1982, 1984; Manton & Scully 1988; Domloge-Hultsch _et al_. 1992, 1994), and sera from patients with oral lesions have been shown to recognize the alpha6 integrin subunit (Rashid _et al_. 2006). In addition, complement-mediated cell destructive processes may be involved in the pathogenesis of the disease (Eversole 1994). The trigger mechanisms behind these reactions, however, have not yet been ascertained.
**Fig. 16-30** Benign mucous membrane pemphigoid affecting the attached gingiva of both jaws. The lesions are erythematous and resemble atrophic lichen planus lesions. They result in pain associated with oral procedures including eating and oral hygiene.
**Fig. 16-31** Benign mucous membrane pemphigoid with intact and ruptured gingival bulla.
**Fig. 16-32** Benign mucous membrane pemphigoid with hemorrhagic gingival bulla. The patient uses chlorhexidine for daily plaque reduction.
The majority of affected patients are females with a mean age at onset of 50 years or over (Shklar & McCarthy 1971). Oral involvement in BMMP is almost inevitable and usually the oral cavity is the first site of disease activity (Silverman _et al_. 1986; Gallagher & Shklar 1987). Any area of the oral mucosa may be involved in BMMP, but the main manifestation is desquamative lesions of the gingiva presenting intensely erythematous attached gingiva (Laskaris _et al_. 1982; Silverman _et al_. 1986; Gallagher & Shklar 1987) (Fig. 16-30). The inflammatory changes, as always when not caused by plaque, may extend over the entire gingival width and even over the mucogingival junction. Rubbing of the gingiva may precipitate bulla formation (Dahl & Cook 1979). This is denoted a positive Nicholsky sign and is caused by the destroyed adhesion of the epithelium to the connective tissue. The intact bullae are often clear to yellowish or they may be hemorrhagic (Figs. 16-31 and 16-32). This, again, is due to the separation of epithelium from connective tissue at the junction resulting in exposed vessels inside the bullae. Usually, the bullae rupture rapidly leaving fibrin-coated ulcers. Sometimes, tags of loose epithelium can be found due to rupture of bullae. Other mucosal surfaces may be involved in some patients. Ocular lesions are particularly important because scar formation can result in blindness (Williams _et al_. 1984) (Fig. 16-33).
The separation of epithelium from connective tissue at the basement membrane area is the main diagnostic feature of BMMP. A non-specific inflammatory reaction is a secondary histologic finding. In addition, immunohistochemical examination can help distinguish BMMP from other vesiculobullous diseases, in particular pemphigus, which is life threatening. Deposits of C3, IgG, and sometimes other immunoglobulins as well as fibrin are found at the basement membrane zone in the vast majority of cases (Laskaris & Nicolis 1980; Daniels & Quadra-White 1981; Manton & Scully 1988). It is important to involve peri-lesional tissue in the biopsy because the characteristic features may be lost within lesional tissue (Ullman 1988). Circulating immunoglobulins are found only occasionally in BMMP by indirect immunofluorescence (Laskaris & Angelopoulos 1981).
**Fig. 16-33** Benign mucous membrane pemphigoid. Eye lesion with scar formation due to coalescence of palpebral and conjunctival mucosa.
**Fig. 16-34** Pemphigus vulgaris. Initial lesion resembling recurrent aphthous stomatitis.
**Fig. 16-35** Pemphigus vulgaris. Erosions of soft palatal mucosa. The erosive lesions are due to loss of the superficial part of the epithelium, leaving the connective tissue covered only by the basal cell layers.
Therapy consists of professional atraumatic plaque removal and individual instruction in gentle but careful daily plaque control, eventually supplemented with daily use of chlorhexidine and/or topical corticosteroid application if necessary. As for all the chronic inflammatory oral mucosal diseases, oral hygiene procedures are very important and controlling the infection from plaque bacteria may result in considerable reduction of disease activity and symptoms. It is also important to prevent the development of attachment loss due to periodontitis in these patients with difficulties in maintaining oral hygiene (Tricamo _et al_. 2006). However, the disease is chronic in nature and formation of new bullae is inevitable in most patients. Topical corticosteroids, preferably applied as a paste at night, temper the inflammatory reaction.
### Pemphigus vulgaris
Pemphigus is a group of autoimmune diseases characterized by formation of intraepithelial bullae in skin and mucous membranes. The group comprises several variants, pemphigus vulgaris (PV) being the most common and most serious form (Barth & Venning 1987).
Individuals of Jewish or Mediterranean background are more often affected by PV than others. This is an indication of a strong genetic background of the disease (Pisanti _et al_. 1974). The disease may occur at any age, but is typically seen in the middle-aged or elderly. It presents with widespread bulla formation often including large areas of skin, and if left untreated the disease is life threatening. Intraoral onset of the disease with bulla formation is very common and lesions of the oral mucosa including the gingiva are frequently seen. Early lesions may resemble aphthous ulcers (Fig. 16-34), but widespread erosions are common at later stages (Fig. 16-35). Gingival involvement may present as painful desquamative lesions or as erosions or ulcerations, which are remains of ruptured bullae (Fig. 16-36). Such lesions may be indistinguishable from BMMP (Zegarelli & Zegarelli 1977; Sciubba 1996). Since the bulla formation is located in the spinous cell layer, the chance of seeing an intact bulla is even more reduced than in BMMP. Involvement of other mucous membranes is common (Laskaris _et al_. 1982). The ulcers heal slowly, usually without scar formation, and the disease runs a chronic course with recurring bulla formation (Zegarelli & Zegarelli 1977).
Diagnosis is based on the characteristic histological feature of PV that is intraepithelial bulla formation due to destruction of desmosomes resulting in acantholysis. The bullae contain non-adhering free epithelial cells, denoted Tzank cells, which have lost their intercellular bridges (Coscia-Porrazzi _et al_. 1985; Nishikawa _et al_. 1996). Mononuclear cells and neutrophils dominate the associated inflammatory reaction. Immunohistochemistry reveals pericellular epithelial deposits of IgG and C3. Circulating auto-antibodies against interepithelial adhesion molecules are detectable in serum samples of most patients, but at the initial stage of intraoral signs antiepithelial antibody may not be elevated (Melbye _et al_. 1987; Manton & Scully 1988; Lamey _et al_. 1992; Lever & Schaumburg-Lever 1997). The background of bulla formation in PV is damage to the intercellular adhesion caused by autoantibodies to cadherin-type epithelial cell adhesion molecules (desmoglein 1 and 3) (Nousari & Anhalt 1995; Nishikawa _et al_. 1996; Lanza _et al_. 2006). The mechanism by which these molecules trigger the formation of autoantibodies has not yet been established.
**Fig. 16-36** Pemphigus vulgaris. Intact and ruptured gingival bullae.
**Fig. 16-37** Erythema multiforme with crust formation of the vermilion border of the lower lip.
**Fig. 16-38** Erythema multiforme with ulceration covered by heavy fibrin exudate.
Immediate referral of patients with PV to a dermatologist or internal medicine specialist is important because when recognized late the disease can be fatal, although systemic corticosteroid therapy can presently solve most cases. Supplementary local treatment consists of gentle plaque control and professional cleaning as mentioned for the chronic inflammatory oral mucosal diseases above. Sometimes, additional topical corticosteroid application is needed to control the intraoral disease.
### Erythema multiforme
Erythema multiforme (EM) is a reactive acute, sometimes recurrent, vesiculobullous disease affecting mucous membranes and skin. A general malaise often precedes the lesions. The disease spectrum comprises a self-limiting, mild, exanthematic, cutaneous variant with minimal oral involvement to a progressive, fulminating, severe variant with extensive mucocutaneous epithelial necrosis. The latter form of the disease has been described as Stevens-Johnson syndrome, with widespread mucous membrane lesions, i.e. oral, ocular and genital, in addition to skin lesions (Lozada-Nur _et al_. 1989; Assier _et al_. 1995; Bystryn 1996; Ayangco & Rogers 2003). The multilocular entity has to be differentiated from other disorders such as Reiter and Behçet's syndromes, which also affect the eyes, the oral mucosa, and often the genitalia. The pathogenesis of EM remains unknown, but the disease appears to be a cytotoxic immune reaction towards keratinocytes (Ayangco & Rogers 2003) precipitated by a wide range of factors including herpes simplex virus (Lozada & Silverman 1978; Nesbit & Gobetti 1986; Ruokonen _et al_. 1988; Miura _et al_. 1992; Aurelian _et al_. 1998), _Mycoplasma pneumoniae_ (McKellar & Reade 1986; Stutman 1987), and various drugs (Bottiger _et al_. 1975; Gebel & Hornstein 1984; Kauppinen & Stubb 1984).
EM may occur at any age but most frequently affects young individuals. It may or may not involve the oral mucosa, but oral involvement occurs in as many as 25–60% of cases (Huff _et al_. 1983); sometimes it is the only involved site. The characteristic oral lesions comprise swollen lips often with extensive crust formation of the vermilion border (Fig. 16-37). The basic lesions, however, are bullae that rupture and leave extensive ulcers usually covered by heavy yellowish fibrinous exudates sometimes described as pseudomembranes (Figs. 16-38 and 16-39). Such lesions may also involve the buccal mucosa and gingiva (Huff _et al_. 1983; Lozada-Nur _et al_. 1989; Scully _et al_. 1991; Barrett _et al_. 1993). The skin lesions are characteristic due to the iris appearance with a central bulla formation surrounded by a blanched halo within an erythematous zone (Fig. 16-40). Similar intraoral lesions do occur but they are infrequent. The disease is usually self-limiting but recurrences are common. Healing of the lesions may take several weeks (Fabbri & Panconesi 1993).
**Fig. 16-39** Erythema multiforme. Fibrin-coated ulcerations of ventral surface of tongue and lower lip.
**Fig. 16-40** Erythema multiforme. Skin lesion with characteristic iris appearance. Central bulla formation surrounded by a blanched halo within an erythematous zone.
Histopathology of EM shows intra- or subepithelial separation of epithelium from connective tissue with non-specific inflammation (Reed 1985). Immunohistochemical findings are non-specific and in most instances the diagnosis relies on the clinical findings.
Although periodontal lesions are not the most frequent intraoral manifestation, they can sometimes pose a differential diagnostic problem. The typical crusty ulcerations of the vermilion border and the heavy fibrin exudates covering intraoral lesions are indicative of EM, sometimes therefore denoted erythema multiforme exudativum. The mucosal ulcerations may take weeks to heal and they are painful (Lozada-Nur _et al_. 1989).
As for any intraoral ulcerations, gentle plaque control and professional cleaning are mandatory. The treatment often involves systemic corticosteroids, but topical treatment may be sufficient in cases with minor lesions.
### Lupus erythematosus
Lupus erythematosus (LE) is a group of autoimmune connective tissue disorders in which autoantibodies form to various cellular constituents including nucleus, cytoplasmic membrane and others. All parts of the body may be affected, and the disease is much more prevalent among women than among men. The etiology of LE remains unknown, but deposits of antigen–antibody complexes appear to play a role in the tissue damage characteristic of the disease (Schrieber & Maini 1984). LE includes two major traditional forms: discoid LE (DLE) and systemic LE (SLE) which may involve a range of organ systems including kidney, heart, central nervous system, vascular system, and bone marrow. Recently two new forms, acute and subacute cutaneous LE, have been added to the classification, these forms representing different degrees of disease activity and increased risk of development of SLE (Wouters _et al_. 2004). The prevalence of LE has been estimated at 0.05% (Condemi 1987).
DLE is a mild chronic form, which affects skin and mucous membranes, sometimes involving the gingiva as well as other parts of the oral mucosa (Schiødt 1984a,b). The typical lesion presents a central atrophic area with small white dots surrounded by irradiating fine white striae with a periphery of telangiectasia (Fig. 16-41). The lesions can be ulcerated or clinically indistinguishable from leukoplakia or atrophic oral lichen planus (Fig. 16-42) (Schiødt 1984b). Sometimes patients present brownish gingival lesions, which is a side effect of antimalarial drugs prescribed to these patients as part of their treatment (Fig. 16-43). Eight percent of patients with DLE develop SLE, and ulcerations may be a sign of SLE; SLE demonstrates oral lesions in 25–40% of patients (Schiødt 1984a; Pisetsky 1986; Johnsson _et al_. 1988). The characteristic bordeaux-colored "butterfly" skin lesions are photosensitive, scaly, erythematous macules located on the bridge of the nose and the cheeks (Standefer & Mattox 1986). The systemic type, which can still be fatal because of nephrologic and hematologic complications, also has skin lesions on the face but they tend to spread over the entire body.
Diagnosis is based on clinical and histopathologic findings. The epithelial changes, characteristic of oral LE lesions, are hyperkeratosis, keratin plugging and variation in epithelial thickness, liquefaction degeneration of basal cells, and increased width of the basement membrane. The subepithelial connective tissue harbors inflammation, sometimes resembling OLP but often with a less distinct band-shaped pattern (Schiødt & Pindborg 1984). Immunohistochemical investigation reveals deposits of various immunoglobulins, C3, and fibrin along the basement membrane (Reibel & Schiødt 1986).
**Fig. 16-41** Gingival discoid lupus erythematosus lesion. A central erythematous area with small white dots is surrounded by delicate white striae.
**Fig. 16-42** Gingival plaque-type discoid lupus erythematosus lesion resembling frictional keratosis and leukoplakia.
**Fig. 16-43** Antimalarial drugs may result in brownish gingival discoloration. This is a patient with discoid lupus erythematosus receiving an antimalarial drug, chloroquine, as part of the treatment regimen.
Systemic corticosteroid and other anti-inflammatory treatment regimens are required for SLE. Additional topical treatment is sometimes needed for symptomatic intraoral lesions to resolve.
### Drug-induced mucocutaneous disorders
A number of drugs cause adverse effects in the oral mucosa. Best known in the periodontal field is gingival hyperplasia related to the intake of phenytoin, cyclosporine, and nifedipine. Because these lesions to some extent are plaque dependent, they are reviewed in Chapter 17. Other types of drugs may give rise to EM as mentioned above.
Several other drugs may be associated with adverse effects that include lesions of the oral mucosa. An example is azathioprine, which is an antimetabolite used for immunosuppression in the treatment of autoimmune and other diseases and to prevent rejection of transplants. Its mode of action is through inhibition of purine base synthesis, resulting in suppression of nucleic acid and protein synthesis, whereby the immune response is inhibited at various stages. Rapidly proliferating tissues such as the bone marrow, the hair follicles, and the gastrointestinal and the oral mucosa may show side effects, e.g. oral ulceration. These ulcerations may include the gingiva. Other examples of drugs frequently resulting in adverse effects in the form of stomatitis are antineoplastic drugs used in cancer chemotherapy. Methotrexate is a cytostatic drug sometimes used in the treatment of leukemia. Epithelial atrophy, superficial sloughing, intense erythema, and ulceration are characteristic findings in the oral mucosa of patients with adverse effects of the chemotherapeutic treatment (Fig. 16-44) (Pindborg 1992). The ulcerative lesions are frequent portals of entry for microorganisms from the mouth, and thereby often sources of serious systemic infection in patients with suppression of the bone marrow and reduced defense systems against infection. Professional plaque removal, mouth rinsing with 0.1% chlorhexidine, and a prophylactic antibiotic regimen are important in such patients (Sonis 1998; Holmstrup & Glick 2002).
## Allergic reactions
Allergic manifestations in the oral mucosa are uncommon. Several mechanisms may be involved in allergy, which is an exaggerated immune reaction. Oral mucosal reactions may be type I reactions (immediate type), which is mediated by IgE, or more often they are type IV reactions (delayed type), mediated by T cells. The rare intraoral occurrence may be due to the fact that much higher concentrations of allergen are required for an allergic reaction to occur in the oral mucosa than in skin and other surfaces (Amlot _et al_. 1985; Lüders 1987; Holmstrup 1999). This chapter includes allergies to dental restorative materials, toothpastes, mouthwashes, and food.
**Fig. 16-44** Drug-induced stomatitis sometimes involves the gingiva. This is a mucosal lesion due to azathioprine, which is an antimetabolite used for immunosuppression.
### Dental restorative materials
The clinical manifestation of type IV allergy (contact allergy) occurs after a period of 12–48 hours following contact with the allergen. The effects on oral mucosa have been denoted contact lesions and prior contact with the allergen resulting in sensitization is prerequisite for these reactions to occur (Holmstrup 1991). Oral mucosal reactions to restorative materials include reactions to mercury, nickel, gold, zinc, chromium, palladium, and acrylics (Ovrutsky & Ulyanow 1976; Zaun 1977; Bergman _et al_. 1980; Council on Dental Materials, Instruments and Equipment Workshop 1984; Fisher 1987). The lesions, which may sometimes affect the gingiva, have clinical similarities with oral lichen planus affections, which is why they are denoted OLL (see earlier in this chapter) or oral leukoplakia (Fig. 16-45). They are reddish or whitish, sometimes ulcerated lesions, but one of the crucial diagnostic observations is that the lesions resolve after removal of the offending material. Additional patch testing to identify the exact allergen gives supplementary information, but for dental amalgam it has been shown that there is no obvious correlation between the result of an epicutaneous patch test and the clinical result after removal of the fillings (Skoglund 1994). A clinical manifestation confined to the area of contact with the offending restorative material and the result after replacing this material indicates the diagnosis (Holmstrup 1999).
**Fig. 16-45** Lichenoid contact lesion of left buccal mucosa due to type IV hypersensitivity to mercury. The lesion is confined to the zone of contact with the amalgam fillings. These lesions usually recover after replacement of the mercury-containing fillings with composites or other materials devoid of allergy-provoking components.
**Fig. 16-46** Diffuse gingivitis and cheilitis due to contact allergy to flavor additive in dentifrice.
### Reactions to oral hygiene products, chewing gum, and food
#### _Toothpastes, mouthwashes and chewing gum_
Contact allergy rarely occurs after the use of toothpastes (Sainio & Kanerva 1995; Skaare _et al_. 1997) and mouthwashes (Sainio & Kanerva 1995). The constituents responsible for the allergic reactions may be flavor additives, for instance carvone and cinnamon (Drake & Maibach 1976) or preservatives (Duffin & Cowan 1985). The flavoring constituents may be used, also, in chewing gum and result in similar forms of gingivostomatitis (Kerr _et al_. 1971). The clinical manifestations of allergy include a diffuse fiery red edematous gingivitis sometimes with ulcerations or whitening (Fig. 16-46). Similar signs may involve the labial, buccal, and tongue mucosa and cheilitis may also be seen. The clinical manifestations, which are characteristic, form the basis of the diagnosis, which may be supported by resolution of the lesions after stopping use of the allergen-containing agent (Holmstrup 1999).
#### _Foods_
The gastrointestinal tract is the largest immunologic organ in the body. It is constantly bombarded by a myriad of dietary proteins. Despite the extent of protein exposure, very few patients contract food allergies due to development of oral tolerance to these antigens (Chehade & Mayer 2005). Allergic reactions attributable to food may manifest both as type I and type IV reactions. Type I reaction with severe swelling has been described after intake of food components such as peanuts and pumpkin seed. Birch pollen allergy is associated with some types of oral mucosa allergy, and more than 20% of patients with oral allergy may be hypersensitive to kiwi, peach, apple, chestnut, and salami (Yamamoto _et al_. 1995; Antico 1996; Asero _et al_. 1996; Liccardi _et al_. 1996; Rossi _et al_. 1996; Helbling 1997; Wutrich 1997). Another food allergen resulting in gingivitis or gingivostomatitis is red pepper (Serio _et al_. 1991; Hedin _et al_. 1994). Unless it has been demonstrated that the lesions resolve after removal of the allergen, the diagnosis is difficult to establish.
## Other gingival manifestations of systemic conditions
### Gastrointestinal diseases
#### _Crohn's disease_
Crohn's disease is characterized by chronic granulomatous infiltrates of the wall of the last ileal loops, but any part of the gastrointestinal tract can be affected. The oral cavity is part of the gastrointestinal tract. It is thus not surprising that Crohn's disease can occur from the rectum to the lips.
The number of reports of lesions involving the periodontium is limited (van Steenberghe _et al_. 1976), which is probably related to a tradition by many clinicians of using the term aphthous lesions for any ulcerative disease of the oral mucosa. The oral lesions have striking similarity with those of the intestinal tract as revealed by rectoscopy, i.e. irregular long ulcerations with elevated borders with a cobblestone appearance. Usually, the periodontal lesions appear after the diagnosis has been established on the basis of the intestinal signs, but sometimes the oral lesions are the first findings leading to diagnosis. Characteristic clinical findings are mucosal foldings of the buccal or labial sulcus (Fig. 16-47). Exacerbations of the oral lesions appear in parallel with those of the intestine. An increased risk of periodontal destruction has been reported associated with defective neutrophil function (Lamster _et al_. 1982).
The term orofacial granulomatosis has been used as a collective diagnosis of Crohn's disease, Melkersson-Rosenthal syndrome, and sarcoidosis, because these diseases show the same histopathologic features, i.e. non-caseating, epitheloid cell granulomas in the affected tissue. Rarely, all three diseases may present gingival lesions, characterized by swellings (Pindborg 1992; Mignogna _et al_. 2001); sarcoidosis sometimes causes fiery red granular gingival overgrowth (Fig. 16-48). Among 45 cases of oral sarcoidosis, 13% had gingival lesions (Blinder _et al_. 1997). A recent study of 35 patients with orofacial granulomatosis demonstrated ileal and colonic abnormalities in 54%, and granulomas were revealed in gut biopsies of 64% of the patients. Intestinal abnormality was significantly more likely if the age of onset was less than 30 years (Sanderson _et al_. 2005).
**Fig. 16-47** A frequent oral finding in patients with Crohn's disease is mucosal foldings, usually located in the buccal or labial sulcus. Such lesions may be the first clinical finding leading to the diagnosis of the disease. Histopathologic examination of biopsies from these foldings reveal epitheloid cell granulomas. The foldings are characteristic for the other types of orofacial granulomatosis as well.
**Fig. 16-48** Granulomatous gingival hyperplasia may be due to sarcoidosis, which is one of the orofacial granulomatoses; others are Crohn's disease and Melkersson-Rosenthal syndrome.
Local treatment consists of intralesional steroid injection (Mignogna _et al_. 2004; El-Hakim & Chauvin 2004) or paste application daily or twice daily during painful exacerbations and meticulous oral hygiene to reduce additional inflammation of the oral cavity. Treatment of any inflammatory condition in the affected oral region, including periodontitis, periapical inflammation, and even mucosal lesions due to hypersensitivity to restorative dental materials, is important for resolution in some cases (Guttman-Yassky _et al_. 2003).
### Hematologic disorders
#### _Leukemia_
Leukemia is a malignant hematologic disorder with abnormal proliferation and development of leukocytes and their precursors in blood and bone marrow. It can involve any of the subsets of leukocytes, polymorphonuclear leukocytes, lymphocytes or monocytes. Normal hematopoiesis is suppressed and, in most cases of leukemia, the white blood cells appear in the circulating blood in immature forms. The leukemic cell proliferation at the expense of normal hematopoietic cell lines causes bone marrow failure and depressed blood cell count. As a consequence of the inability to produce sufficient functional white blood cells and platelets, death may result from infection or bleeding associated with neutropenia and thrombocytopenia.
The classification of leukemia is based on its course, acute or chronic, and origin of cells involved. The basic forms are: acute lymphocytic leukemia (ALL), acute myelogenous leukemia (AML), chronic lymphocytic leukemia (CLL), and chronic myelogenous leukemia (CML). Acute leukemias have an aggressive course resulting in death within 6 months if untreated. They occur rather seldom and patients are usually either under 20 or over 60 years of age. Chronic leukemias, of which the lymphocytic form is the most common, have less pronounced bone marrow failure and a more indolent course usually lasting several years. They occur during adulthood and normally after the age of 40. Whereas the peripheral granulocyte count is markedly elevated in chronic leukemia, it may be elevated, decreased or normal in acute leukemia (McKenna 2000).
Gingival manifestations in leukemia, which include extensive swelling (Fig. 16-49), ulceration (Fig. 16-50), petechiae (Fig. 16-51), and erythema, are much more common in acute than in chronic forms. Sometimes the manifestations lead to the diagnosis of leukemia; 69% of patients with acute leukemia had oral signs of leukemia on examination and 33% of the patients had gingival swelling (Pindborg 1992). In another study gingival swelling was revealed in 21% of AML patients but in no patients with ALL (Meyer _et al_. 2000). In the latter group, on the other hand, 36% showed both gingival erythema and ulcers. In leukemic children, only 10–17% appear to have gingival swelling (Curtis 1971; Michaud _et al_. 1977). The pronounced gingival swelling seen in leukemic patients is mostly due to plaque-induced inflammation, since stringent plaque control appears to resolve the swelling (Barrett 1984); it may also be due to the presence of leukemic infiltrates, although this has been reported to be an uncommon feature of leukemic patients (Barrett 1984). Gingival bleeding, due to secondary thrombocytopenia, is a common sign in leukemic patients. It has been reported as the initial sign in 17.7% of patients with acute leukemias and in 4.4% of patients with chronic forms (Lynch & Ship 1967).
In general, the periodontal treatment of patients with leukemia is important; it aims at reducing plaque as a source of bacteremia and damage to the periodontal tissues both during disease and during periods of chemotherapy. In such periods, potentially pathogenic bacteria occur in plaque simultaneous with granulocytopenia in these patients (Peterson _et al_. 1990). The reduction of periodontal inflammation may also prevent episodes of gingival bleeding. As with many other patients, chemical plaque control in combination with mechanical debridement appears to be most effective and is the preferred method of periodontal therapy in leukemic patients (Holmstrup & Glick 2002). However, the increased tendency to bleeding in many of these patients may necessitate the use of alternative methods to toothbrushing. A study of professional plaque removal preceding mouthrinsing with 0.1% chlorhexidine in patients with AML showed that the additional initial removal of plaque and calculus was more effective in reducing gingival inflammation than mouthrinsing with chlorhexidine alone (Bergman _et al_. 1992). A 1-day antibiotic prophylaxis regimen with a combination of piperacillin and netilmicin was given prior to and after the mechanical debridement. Periodontal treatment always involves a close cooperation with the medical department or specialist responsible for coordination of the patient's treatment.
**Fig. 16-49** Acute myelogenous leukemia with extensive swelling of the gingiva.
**Fig. 16-50** Acute lymphocytic leukemia with gingival ulceration in a child.
**Fig. 16-51** Acute myelogenous leukemia with petechiae and swelling of the gingiva. This patient had several episodes of spontaneous bleeding from the gingiva, which prevented oral hygiene procedures from being undertaken.
# Traumatic lesions
The background of traumatic lesions of the oral tissues may be self-inflicted, iatrogenic or accidental. Chemical as well as physical and thermal injuries may affect the periodontium (Armitage 1999).
## Chemical injury
Surface etching by various chemical products with toxic properties may result in mucosal reactions including reactions of the gingiva. Chlorhexidine-induced mucosal desquamation (Fløtra _et al_. 1971; Almquist & Luthman 1988) (Fig. 16-52), acetylsalicylic acid burn (Najjar 1977), cocaine burn (Dello Russo & Temple 1982), and slough due to dentifrice detergents are examples of such reactions (Muhler 1970). These lesions are reversible and resolve after quitting the toxic influence. Chemical injury to the gingival tissue may be caused by incorrect use of caustics by the dentist. Paraformaldehyde used for pulp mummification may give rise to inflammation and necrosis of the gingival tissue if the cavity sealing is insufficient (Di Felice & Lombardi 1998). Usually, the diagnosis is obvious from the clinical findings and the patient history.
## Physical injury
Oral hygiene agents and inexpedient procedures can be injurious to the gingival tissues. If physical trauma is limited, the gingival response is hyperkeratosis, resulting in a white leukoplakia-like, frictional keratosis (Fig. 16-53). In case of more violent trauma the damage varies from superficial gingival laceration to major loss of tissue resulting in gingival recession (Axéll & Koch 1982; Smukler & Landsberg 1984). Abrasiveness of dentifrice, strong brushing force, and horizontal movement of the toothbrush contribute to the gingival injury even in young patients. Characteristic findings in these patients are extremely good oral hygiene, cervical tooth abrasion, and unaffected tops of the interdental papillae at the site of injury (Figs. 16-54 to 16-57). The condition has been termed traumatic ulcerative gingival lesion (Axéll & Koch 1982). Dental flossing may also cause gingival ulceration and inflammation primarily affecting the top of the interdental papillae (Fig. 16-58). The prevalence of such findings is unknown (Gillette & Van House 1980). Diagnosis of physical injuries is based on the clinical findings. An important differential diagnosis is necrotizing gingivitis (Blasberg _et al_. 1981), see Chapter 20. The latter normally reveals itself as a necrotic gingival margin and interdental papillae, while brushing trauma leads to ulcerations of a few millimeters of the gingival margin.
**Fig. 16-52** Chlorhexidine-induced mucosal desquamation. This is a reversible type of lesion, which is completely normalized after stopping chlorhexidine use.
**Fig. 16-53** Frictional keratosis due to violent toothbrushing. Note the cervical abrasion of adjacent teeth.
**Fig. 16-54** Gingival wounding due to improper toothbrushing. Note the characteristic horizontal extension of the lesion, affecting the most prominent part of the tooth arch.
**Fig. 16-55** Gingival wounding due to improper toothbrushing. Note the characteristic horizontal extension of the lesion and the uninflamed, unaffected interdental papillae.
**Fig. 16-56** Severe gingival recession and wounding due to improper toothbrushing. Note the unaffected interdental papillae.
**Fig. 16-57** Healing of lesion shown in Fig. 16-56. The damage to the periodontal tissues is severe, leaving extended gingival recession.
**Fig. 16-58** Lesions after dental flossing are common and sometimes result in permanent fissures of the gingival tissue.
**Fig. 16-59** Self-inflicted gingival recession with ulcerated margin due to a 7-year-old boy's scratching with fingernail.
Self-inflicted physical injury to the gingival tissues can occur; sometimes the lesions are termed gingivitis artefacta. The lesions often show ulceration of the gingival margin often associated with recession (Figs. 16-59 and 16-60). Such lesions are most common in children and young individuals and two thirds appear to involve female patients. The lesions, which may be hemorrhagic, are usually produced by picking at or scratching the gingiva with a finger or a fingernail; sometimes the lesions are made by instruments (Pattison 1983). The correct diagnosis is often difficult to establish based on clinical findings, and identification of the cause may be impossible.
## Thermal injury
Extensive thermal burns of the oral mucosa are very rare, but minor burns particularly from hot beverages are seen occasionally. Their predilection by site is the palatal and labial mucosa but any part of the oral mucosa can be involved including the gingiva (Colby _et al_. 1961). The area involved is painful and erythematous and may slough a coagulated surface. Vesicles may also occur (Laskaris 1994) and sometimes the lesions present as ulceration, petechia or erosion (Fig. 16-61). Obviously, the history is important for reaching the correct diagnosis. Common causes are hot coffee, pizza, and melted cheese, but dental treatments involving improper handling of hot hydrocolloid impression material, hot wax or cautery instruments are other causes (Colby _et al_. 1961).
**Fig. 16-60** Self-inflicted gingival ulceration of palatal gingiva of the upper right incisor region in the same boy as shown in Fig. 16-59. This lesion was also caused by fingernail scratching.
**Fig. 16-61** Thermal burn with slight erosion and petechiae of palatal gingiva due to hot coffee intake.
**Fig. 16-62** Amalgam tattoo of attached gingiva.
## Foreign body reactions
Another type of tissue reaction is established through epithelial ulceration that allows entry of foreign material into gingival connective tissue. This can happen via abrasion or cutting (Gordon & Daley 1997b), a route of tissue injury which is best exemplified by the amalgam tattoo (Buchner & Hansen 1980) (Fig. 16-62). Gingival inflammation associated with foreign bodies has been termed foreign body gingivitis. A clinical study of this condition has shown that it often presents as a red or combined red–white painful chronic lesion frequently misdiagnosed as lichen planus (Gordon & Daley 1997a). An X-ray microanalysis of foreign body gingivitis showed that most of the identified foreign bodies were of dental material origin, usually abrasives (Gordon & Daley 1997b). Another way of introducing foreign substances into the tissues is self-inflicted injury, for instance due to chewing on sticks or self-induced tattooing (Gazi 1986). It is uncertain whether the inflammatory reaction in such cases is due to a toxic or in some instances an allergic reaction.
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# Chapter 17
# Plaque-Induced Gingival Diseases
Angelo Mariotti
* * *
Classification criteria for gingival diseases
Plaque-induced gingivitis
Gingival diseases associated with endogenous hormones
Puberty-associated gingivitis
Menstrual cycle-associated gingivitis
Pregnancy-associated gingival diseases
Gingival diseases associated with medications
Drug-influenced gingival enlargement
Oral contraceptive-associated gingivitis
Gingival diseases associated with systemic diseases
Diabetes mellitus-associated gingivitis
Leukemia-associated gingivitis
Linear gingival erythema
Gingival diseases associated with malnutrition
Gingival diseases associated with heredity
Gingival diseases associated with ulcerative lesions
Treatment of plaque-induced gingival diseases
The significance of gingivitis
* * *
For almost four millennia the clinical manifestations of gingival diseases have been noted by mankind. Throughout the centuries the notion of cause, effect, and management of these diseases was largely dormant, resulting in a dubious realm of remedies that were dominated by superstition, frequently were subjective, often palliative, sometimes painful, and rarely successful. It was not until the last half of the twentieth century that our views about the nature of gingival diseases began to emerge, where pivotal human experiments showed the unmistakable role of dental biofilms in the initiation and progression of gingival inflammation (Löe _et al_. 1965). During the twenty-first century, we are living in a time of radical shifts of culture and science, one in which evidence-based dentistry increasingly plays a pervasive role in our knowledge regarding gingival diseases.
As more clinical evidence becomes available, the scope and nature of various forms of gingivitis become evident. More specifically, there has been growing acceptance that gingivitis does not represent a single disease but rather a spectrum of diseases that are the outcome of a variety of different processes. It is true that inflammation of the gingiva induced by bacteria is the most common form of gingivitis; however, this has created a bias toward naming all manifestations that affect the gingival tissues (e.g. atrophic, desquamative, neoplastic, etc.) as gingivitis. Although inflammation of the gingival tissues can be induced by a variety of methods (e.g. trauma, chemical agents, temperature extremes, ionizing radiation, viruses, fungi, immune defects, etc.), at this time gingival diseases are considered to be disease entities that are initiated by dental plaque and are restricted to gingival tissues. This chapter will focus on the commonly occurring and diverse family of complex and distinct pathological entities found within the gingiva that are initiated by dental plaque and that can be influenced by systemic conditions, endogenous hormones, genetic factors, drugs, and malnutrition.
# Classification criteria for gingival diseases
Categorization of diseases affecting the gingiva requires evaluation of patient signs and symptoms, medical and dental histories, a clinical examination that includes the extent, distribution, duration, and physical description of lesions affecting the gingiva, clinical or relative attachment levels, and radiographs. The universal features of gingival diseases include clinical signs of inflammation, signs and symptoms that are confined to the gingiva, reversibility of the diseases by removal of etiology(ies), the presence of bacteria-laden plaque to initiate and/or exacerbate the severity of the lesion, and a possible role as a precursor to attachment loss around teeth (Table 17-1).
Clinical signs of gingival inflammation involve enlarged gingival contours due to edema or fibrosis (Muhlemann & Son 1971; Polson & Goodson 1985), color transition to a red and/or bluish red hue (Muhlemann & Son 1971; Polson & Goodson 1985), elevated sulcular temperature (Haffajee _et al_. 1992; Wolff _et al_. 1997), bleeding upon probing (Löe _et al._ , 1965; Muhlemann & Son, 1971; Greenstein _et al_. 1981; Engelberger _et al_. 1983), and increased gingival exudates (Löe & Holm-Pedersen 1965; Engelberg 1966; Oliver _et al_. 1969; Rudin _et al_. 1970) (see Table 17-2 and Fig. 17-2). Clinical signs of gingival inflammation indicative of a gingival disease must be associated with stable (i.e. unchanging) attachment levels on a periodontium with no loss of attachment or alveolar bone or on a stable but reduced periodontium.
**Table 17-1** Universal features of gingival diseases (Mariotti 1999)
Signs and symptoms that are confined to the gingiva
---
The presence of dental plaque to initiate and/or exacerbate the severity of the lesion
Clinical signs of inflammation (enlarged gingival contours due to edema or fibrosis, color transition to a red and/or bluish red hue, elevated sulcular temperature, bleeding upon stimulation, increased gingival exudate)
Clinical signs and symptoms associated with stable attachment levels on a periodontium with no loss of attachment or on a stable but reduced periodontium (see Fig. 17-1)
Reversibility of the disease by removing the etiology(ies)
Possible role as a precursor to attachment loss around teeth
**Table 17-2** Common clinical changes from gingival health to gingivitis
**Parameter** | **Normal gingiva** | **Gingivitis**
---|---|---
Color | Coral pink (correlated to mucocutaneous pigmentation) | Red/bluish red hue
Contour | Scalloped outline that envelops teeth. Papillary gingiva fills interdental space while marginal gingival forms a knife-edged appearance with tooth surface | Edema blunts marginal tissues leading to loss of knife edge adaptation to tooth and produces bulbous papillary tissues resulting in minimization of tissue scalloping
Consistency | Firm and resilient | Tissue is soft and exhibits pitting edema
Bleeding on provocation | Negative | Positive
Gingival exudate | Minimal | Significantly increased
Sulcular temperature | ∼34ºC | Slight increase
**Fig. 17-1** A treated peridontitis case displaying gingival health on a reduced periodontium. If such a case developed inflammation and no further loss of attachment could be demonstrated, the diagnosis of plaque-induced gingivitis would be appropriate.
**Fig. 17-2** Changes in gingival color and contour associated with plaque-induced gingivitis.
The classification of gingival diseases relies on the presence of dental plaque and factors that modify the inflammatory status of the gingiva. The modification of plaque-induced gingivitis can occur by local or systemic factors. Local factors include tooth anatomic factors (Fig. 17.3), dental restorations (Fig. 17.4) and appliances (Fig. 17.5), root fractures (Fig. 17.6), and cervical root resorption (Fig. 17.7) (Blieden 1999), whereas, systemic factors involve the endocrine system, hematologic diseases, drugs, or malnutrition (Mariotti 1999). Table 17-3 presents a classification of plaque-induced gingival diseases (Mariotti 1999).
**Table 17-3** Plaque-induced gingival diseases (modified from Mariotti 1999)
Associated with bacterial plaque only | Associated with a periodontium that exhibits no attachment loss | Plaque-induced gingivitis
---|---|---
| Associated with a stable but reduced periodontium |
Associated with bacterial plaque and modified by systemic factors | Associated with endogenous sex steroid hormones | Puberty-associated gingivitis
Menstrual cycle-associated gingivitis
Pregnancy-associated gingivitis
Pregnancy-associated pyogenic granuloma
| Associated with medications | Drug-influenced gingival enlargements
Oral contraceptive-associated gingivitis
| Associated with systemic diseases | Diabetes mellitus-associated gingivitis
Leukemia-associated gingivitis
| Associated with malnutrition | Ascorbic acid deficiency gingivitis
**Fig. 17-3** Gingival inflammation as a result of tooth anatomic factors (malocclusion).
**Fig. 17-4** Gingival inflammation associated with violation of the biologic width and overhanging restorations retaining plaque.
**Fig. 17-5** The presence of appliances, such as braces, allows for the accumulation of plaque resulting in gingival inflammation.
**Fig. 17-6** Root fracture with associated periodontal destruction and gingival inflammation.
**Fig. 17-7** Early cervical resorption and associated inflammation.
# Plaque-induced gingivitis
Plaque-induced gingivitis is inflammation of the gingiva resulting from bacteria located at the gingival margin. The relationship of plaque to gingival inflammation has often been postulated as the cause for gingivitis, but it was not until the elegant experimental human gingivitis studies that a plaque bacterial etiology was confirmed (Löe _et al_. 1965). Epidemiological data have shown plaque-induced gingivitis to be prevalent at all ages of dentate populations (US Public Health Service 1965, 1972, 1987; Stamm 1986; Bhat 1991; Albandar 2002; Gjermo _et al_. 2002; Baelum & Schutz 2002; Sheiham & Netuveli 2002; Corbet _et al_. 2002) and this disease has been considered to be the most common form of periodontal disease (Page 1985). In children, the prevalence of plaque-induced gingivitis continues to increase until it reaches a zenith at puberty (Parfitt 1957; Hugoson _et al_. 1981; Stamm 1986). The initial changes from health to plaque-induced gingivitis may not be detectable clinically (Page & Schroeder 1976), but as plaque-induced gingivitis progresses to more advanced forms of this disease, clinical signs and symptoms become more obvious.
**Fig. 17-8** Typical generalized marginal and papillary gingivitis.
Plaque-induced gingivitis begins at the gingival margin and can spread throughout the remaining gingival unit. Clinical signs of gingival inflammation involving changes to gingival contour, color and consistency (Muhlemann & Son 1971; Polson & Goodson 1985), are associated with a stable periodontium which exhibits no loss of periodontal attachment or alveolar bone (Fig. 17-8). In children, gingivitis is not as intense as that found in young adults with similar amounts of dental plaque (Matsson 1978; Matsson & Goldberg 1985). This age-related difference in the development and severity of gingivitis may be associated with the quantity and/or quality of dental plaque, response of the immune system, and/or morphological differences in the periodontium between children and adults (Bimstein & Matsson 1999). More specifically, dental plaque of children usually contains lower concentrations of putative periodontal pathogens and the thicker junctional epithelium is coupled with increased vascularity in the gingival connective tissues and a developing immune system (Bimstein & Matsson 1999). In contrast to children and young adults, gingival inflammation in senior adult populations is more pronounced even when similar amounts of dental plaque are present (Fransson _et al_. 1996). The reason for the difference in senior adults may be the result of age-related differences in cellular inflammatory response to plaque (Fransson _et al_. 1996, 1999).
The intensity of the clinical signs and symptoms of gingivitis will vary between individuals (Tatakis & Trombelli 2004; Trombelli _et al_. 2004) as well as between sites within a dentition. The common clinical findings of plaque-induced gingivitis include erythema, edema, bleeding, sensitivity, tenderness, and enlargement (Löe _et al_. 1965; Suzuki 1988). Radiographic analysis and/or probing attachment levels of individuals with plaque-induced gingivitis will not indicate loss of supporting structures. Histopathologic changes include proliferation of basal junctional epithelium leading to apical and lateral cell migration, vasculitis of blood vessels adjacent to the junctional epithelium, progressive destruction of the collagen fiber network with changes in collagen types, cytopathologic alteration of resident fibroblasts, and a progressive inflammatory/immune cellular infiltrate (Page & Schroeder 1976). Although the composition of bacterial flora associated with plaque-induced gingivitis differs from the flora associated with gingival health, there are no specific bacterial flora that are pathognomonic for plaque-induced gingivitis (Ranney 1993).
# Gingival diseases associated with endogenous hormones
Since the nineteenth century, evidence has accumulated to support the concept that tissues of the periodontium are modulated by androgens, estrogens, and progestins. The majority of information concerning sex hormone-induced effects have been gender-specific observations in the gingiva. Much of the evidence that has been documented concerning the effects of sex steroid hormones on the periodontium has come from observing the changes in gingival tissues during distinct endocrinological events (e.g. menstrual cycle, pregnancy, etc.). Although a significant amount of data have shown the gingiva to be a target for sex steroid hormones, the etiology for the changes has not been thoroughly elucidated. The principal explanations for sex steroid hormone-induced changes in the gingiva have pointed to changes of microbiota in dental plaque, immune function, vascular properties, and cellular function in the gingiva (Mariotti 1994, 2005). The actions of sex steroid hormones in the periodontium are multifactorial (Mariotti 1994). Theoretically, sex steroid hormones will affect the host by influencing cellular (i.e. in the blood vessels, epithelium, and connective tissue) and immune function and, together with hormone-selected bacterial populations that occupy the gingival sulcus, induce specific changes in gingival tissues that become clinically observable (Mariotti 1994).
## Puberty-associated gingivitis
Puberty is not a single episode but a complex process of endocrinologic events that produce changes in the physical appearance and behavior of adolescents. The incidence and severity of gingivitis in adolescents are influenced by a variety of factors, including plaque levels, dental caries, mouth breathing, crowding of the teeth, and tooth eruption (Stamm 1986); however, the dramatic rise in steroid hormone levels during puberty in both sexes has a transient effect on the inflammatory status of the gingiva (Mariotti 1994). Several studies have demonstrated an increase in gingival inflammation in circumpubertal age individuals of both sexes without a concomitant increase in plaque levels (Parfitt 1957; Sutcliffe 1972; Hefti _et al_. 1981) (Fig. 17-9). Although puberty-associated gingivitis has many of the clinical features of plaque-induced gingivitis, this disease will develop frank signs of gingival inflammation in the presence of relatively small amounts of plaque during the circumpubertal period.
**Fig. 17-9** Gingival inflammation can result from an increased secretion of sex steroid hormones during puberty.
## Menstrual cycle-associated gingivitis
Following menarche, there is a periodicity of sex steroid hormone secretion over a 25- to 30-day period: the menstrual cycle. A clinical case report of significant and observable inflammatory changes in the gingiva during the menstrual cycle has been described (Muhlemann 1948); however, women rarely exhibit overt gingival changes that fluctuate in conjunction with the menstrual cycle (Mariotti 1994). The more common gingival inflammatory changes involve less dramatic signs of inflammation in the gingiva during ovulation (Machtei _et al_. 2004). More specifically, gingival exudate increased approximately 20% during ovulation in roughly three quarters of women tested (Hugoson 1971), while observable signs of gingival inflammation have been shown to be clinically insignificant (Machtei _et al_. 2004). Since these changes in crevicular fluid flow and gingival color are not readily observable, most young women with gingival inflammation induced by the menstrual cycle will present with a very mild form of the disease.
## Pregnancy-associated gingival diseases
Some of the most remarkable endocrine and oral alterations accompany pregnancy due to the prominent increase in plasma hormone levels over several months. During human gestation, pregnancy-associated gingivitis is characterized by an increase in the prevalence and severity of gingivitis during the second and third trimester of pregnancy (Löe & Silness 1963; Löe 1965; Hugoson 1971; Arafat 1974b) (Fig. 17-10). Both longitudinal and cross-sectional studies have found the prevalence and severity of gingival inflammation significantly higher in the pregnant versus the post-partum subject even though plaque scores remained the same between the two groups (Löe & Silness 1963; Hugoson 1971; Moss _et al_. 2005). In addition, gingival probing depths are deeper (Löe & Silness 1963; Hugoson 1971; Miyazaki _et al_. 1991), bleeding on probing or toothbrushing is increased (Arafat 1974b; Miyazaki _et al_. 1991), and gingival crevicular fluid flow is elevated (Hugoson 1971) in pregnant women. The features of pregnancy-associated gingivitis are similar to plaque-induced gingivitis, except for the propensity to develop frank signs of gingival inflammation in the presence of relatively little plaque during pregnancy.
**Fig. 17-10** A heightened gingival response to plaque during pregnancy results in pregnancy-associated gingivitis.
**Fig. 17-11** (a) Pyogenic granuloma of pregnancy. (b) Large pyogenic granuloma of pregnancy interfering with occlusal function.
Pregnancy-associated pyogenic granuloma or "pregnancy tumor" was described over a century ago (Coles 1874); this is not a tumor but an exaggerated inflammatory response during pregnancy to an irritation resulting in a solitary polyploid capillary hemangioma which can easily bleed upon mild provocation (Sills _et al_. 1996) (Fig 17-11). Pregnancy-associated pyogenic granuloma presents clinically as a painless protuberant, mushroom-like, exophytic mass that is attached by a sessile or pedunculated base and arises from the gingival margin or more commonly from an interproximal space (Sills _et al_. 1996). Pregnancy-associated pyogenic granuloma has been reported to occur in 0.5–5.0% of pregnant women (Ziskin & Nesse 1946; Maier & Orban 1949; Arafat 1974a; Kristen 1976). It is more common in the maxilla (Sills _et al_. 1996) and may develop as early as the first trimester (Sills _et al_. 1996), ultimately regressing or completely disappearing following parturition (Ziskin & Nesse 1946).
# Gingival diseases associated with medications
In the past century, an astonishing array of medications for the alleviation of human diseases has lead to the creation of new side effects in the oral cavity. Drugs that specifically affect the gingival tissues have principally caused an increase in either inflammation and/or size.
## Drug-influenced gingival enlargement
Esthetically disfiguring overgrowth of gingiva is a significant side effect which may be associated with (Hassell & Hefti 1991; Seymour _et al_. 1996; Seymour 2006):
* Anticonvulsant (e.g. phenytoin, sodium valproate, etc.)
* Immunosuppressant (e.g. cyclosporine A) (Fig. 17-12)
* Calcium channel blocking agents (e.g. nifedipine, verapamil, etc.).
The common clinical characteristics of drug-influenced gingival enlargements (Table 17-4) include patient variations in the pattern of enlargement (i.e. genetic predisposition) (Hassell & Hefti 1991; Seymour _et al_. 1996), a tendency to occur more often in anterior gingiva (Hassell & Hefti 1991; Seymour _et al_. 1996), a higher prevalence in younger age groups (Esterberg & White 1945; Rateitschak-Pluss _et al_. 1983; Hefti _et al_. 1994), onset within 3 months of use (Hassell 1981; Hassell & Hefti 1991; Seymour 1991; Seymour & Jacobs 1992) that is usually first observed in the papilla (Hassell & Hefti 1991); although it can be found in a periodontium with or without bone loss, it is not associated with attachment loss or tooth mortality (Hassell & Hefti 1991; Seymour _et al_. 1996). Furthermore, all of these drugs produce clinical lesions and histologic characteristics that are indistinguishable from one another (Hassell & Hefti 1991; Seymour _et al_. 1996).
**Fig. 17-12** Severe enlargement of the gingiva associated with cyclosporine medication in a kidney transplant patient.
The influence of plaque on the induction of gingival enlargements by drugs in humans has not been fully elucidated (Hassell & Hefti 1991); however, it does appear that the severity of the lesion is affected by the oral hygiene of the patient (Steinberg & Steinberg 1982; Addy _et al_. 1983; Hassell _et al_. 1984; Tyldesley & Rotter 1984; Daley _et al_. 1986; McGaw _et al_. 1987; Modeer & Dahllof 1987; Yahia _et al_. 1988; Barclay _et al_. 1992).
The first description of a drug causing an enlargement of the gingiva was reported in 1939 and was associated with the use of phenytoin (Kimball 1939). Phenytoin, which is used on a chronic regimen for the control of epileptic seizures, induces gingival enlargements in approximately 50% of patients using this agent (Angelopoulous & Goaz 1972). One prominent theory of the etiology of phenytoin-associated gingival enlargements suggests that the accumulation of genetically distinct populations of gingival fibroblasts results in the accumulation of connective tissues resulting from reduced catabolism of the collagen molecule (Hassell & Hefti 1991).
Calcium channel blockers have also been identified as agents that affect enlargement of the gingiva. Calcium channel blockers are a class of drugs that exert effects principally at voltage-gated Ca2+ channels located in the plasma membrane and are commonly prescribed as antihypertensive, anti-arrhythmic and anti-anginal agents. In 1984, calcium channel blockers were first linked to gingival enlargements (Ramon _et al_. 1984) and the prevalence of gingival lesions associated with these drugs has been estimated to be approximately 20% (Barclay _et al_. 1992), with nifedipine being the primarily calcium channel blocker associated with gingival enlargement (Ellis _et al_. 1999). Presently, the cause (s) of gingival enlargement by calcium channel blockers are still under investigation but these drugs may directly influence gingival connective tissues by stimulating an increase of gingival fibroblasts as well as an increase in the production of the connective tissue matrix (Fu _et al_. 1998).
**Table 17-4** Characteristics of drug-influenced gingival enlargement (Mariotti 1999)
Variation in interpatient and intrapatient pattern
---
Predilection for anterior gingiva
Higher prevalence in children
Onset within 3 months
Change in gingival contour leading to modification of gingival size
Enlargement first observed at the interdental papilla
Change in gingival color
Increased gingival exudate
Bleeding upon provocation
Found in gingiva with or without bone loss but is not associated
with attachment loss
Pronounced inflammatory response of gingiva in relation to the plaque present
Reductions in dental plaque can limit the severity of lesion
Must be using phenytoin, cyclosporine A or certain calcium channel blockers; the plasma concentrations to induce the lesion have not
been clearly defined in humans
The final drug class that has been associated with increases in gingival mass is cyclosporine A (CsA), which is a powerful immunoregulating drug used primarily in the prevention of organ transplant rejection (Seymour & Jacobs 1992). The clinical features of cyclosporine-influenced gingival enlargement were first described in 1983 (Rateitschak-Pluss _et al_. 1983) and cyclosporine appears to affect between 25 and 30% of the patients taking this medication (Hassell & Hefti 1991; Seymour _et al_. 1987). Hypotheses explaining why cyclosporine A affects the gingiva are diverse but a leading theory suggests that the principal metabolite of cyclosporine A, hydroxycyclosporine (M-17), in conjunction with the parent compound, stimulates fibroblast proliferation (Mariotti _et al_. 1998). This increase in cell number coupled with a reduction in the breakdown of gingival connective tissues (Hassell & Hefti 1991) has been speculated to be the cause of excessive extracellular matrix accumulation in cyclosporine A associated gingival enlargements.
## Oral contraceptive-associated gingivitis
Oral contraceptive agents are one of the most widely utilized classes of drugs in the world. Today, as a result of the early onset of menarche, changing social mores and increased emphasis on family planning, the use of oral contraceptives in adolescents and young adults has increased to reduce unwanted pregnancies. Clinical case reports have described gingival enlargement induced by oral contraceptives in otherwise healthy females with no history of gingival overgrowth (Lynn 1967; Kaufman 1969; Sperber 1969). In all cases, the increased gingival mass was reversed when oral contraceptive use was discontinued or the dosage reduced. Early clinical studies demonstrated that women using hormonal contraceptive drugs had a higher incidence of gingival inflammation in comparison to women who did not use these agents (Lindhe & Bjorn 1967; El-Ashiry _et al_. 1970; Pankhurst _et al_. 1981) and that long-term use of oral contraceptives may affect periodontal attachment levels (Knight & Wade 1974). All studies prior to the 1980s recording changes to gingival tissues by oral contraceptives were completed when contraceptive concentrations were at much higher levels than are currently available today. A recent clinical study evaluating the effects of low-dose oral contraceptives on gingival inflammation in young women found no effect of these hormonal agents on gingival tissues (Preshaw _et al_. 2001). Furthermore, cross-sectional data from NHANES III have failed to show a relationship between low-dose oral contraceptive use and increased levels of gingivitis (Taichman & Eklund 2005). From these data it appears that current low-dose compositions of oral contraceptives are probably not as harmful to the periodontium as the early formulations.
# Gingival diseases associated with systemic diseases
## Diabetes mellitus-associated gingivitis
Diabetes mellitus (DM) is a chronic systemic disease characterized by disorders in insulin production, metabolism of carbohydrate, fat, and protein, and the structure and function of blood vessels. DM most commonly appears as one of two recognized clinical entities: type 1 DM (insulin-dependent DM or juvenile onset) and type 2 DM (non-insulin-dependent DM or adult onset). DM-associated gingivitis is a consistent feature found in children with poorly controlled type 1 DM (Cianciola _et al_. 1982; Gusberti _et al_. 1983; Ervasti _et al_. 1985). The features of gingivitis associated with DM are similar to plaque-induced gingivitis, except that the level of diabetic control is more of an important aspect than plaque control in the severity of the gingival inflammation (Cianciola _et al_. 1982; Gusberti _et al_. 1983; Ervasti _et al_. 1985). In adults with DM, it is difficult to detect the effects of this endocrine disease on gingival diseases since most studies have evaluated gingival inflammation in association with attachment loss (AAP 1999); however, young adults with type I DM developed an earlier and more pronounced inflammatory response compared to non-diabetic controls in experimental gingivitis studies (Salvi _et al_. 2005). These data suggest that the gingival inflammatory response in adult diabetics is an overt response to the dental biofilm. In addition to the effects of DM on the gingiva, reports in the literature have suggested that reductions in gingival inflammation of diabetic patients will also reduce the amount of insulin needed to control blood glucose levels (Mealey & Oates 2006). This has been a controversial premise given the competing results of numerous studies; however, a meta-analysis of interventional studies suggest that control of gingival inflammation will not substantially affect glycemic control in diabetic patients (Janket _et al_. 2005).
## Leukemia-associated gingivitis
Leukemia is a progressive, malignant hematologic disorder characterized by an abnormal proliferation and development of leukocytes and precursors of leukocytes in the blood and bone marrow. Leukemia is classified on the duration (acute or chronic) and the type of cell involved (myeloid or lymphoid) and the number of cells in the blood (leukemic or aleukemic). There are noticeable correlations of leukemias with age. For example, acute lymphoblastic leukemia comprise 80% of all childhood leukemias while acute myelogenous leukemia usually affects adults. Oral manifestations have primarily been described in acute leukemias and consist of cervical adenopathy, petechiae, mucosal ulcers, as well as gingival inflammation and enlargement (Fig. 17-13) (Lynch & Ship 1967). Signs of inflammation in the gingiva include swollen, glazed, and spongy tissues which are red to deep purple in appearance (Dreizen _et al_. 1984). Gin-gival bleeding is a common sign in patients with leukemia and is the initial oral sign and/or symptom in 17.7% and 4.4% of patients with acute and chronic leukemias, respectively (Lynch & Ship 1967). Gingival enlargement has also been reported, initially beginning at the interdental papilla followed by marginal and attached gingiva (Dreizen _et al_. 1984). Although local irritants can predispose and exacerbate the gingival response in leukemia, they are not prerequisites for lesions to form in the oral cavity (Dreizen _et al_. 1984).
**Fig. 17-13** Gingival changes associated with acute monocytic leukemia. Note the acute candidosis superimposed upon the infiltrative gingival changes.
## Linear gingival erythema
Infection with the human immunodeficiency virus (HIV) produces an irreversible and progressive immunosuppression that renders a person susceptible to a variety of oral diseases. In humans, HIV depletes CD4+ lymphocytes (T helper cells) which leads to the development of a variety of fungal, viral, and bacterial oral infections (Connor & Ho 1992).
Oral manifestations of HIV infection have been used to stage HIV disease (Justice _et al_. 1989; Royce _et al_. 1991; Prevention CDC 1992), identify prophylactic treatment of other serious infections (Force USPHST 1993), and indicate disease prognosis (Dodd _et al_. 1991; Katz _et al_. 1992). In the gingiva, manifestations of HIV infection were formerly known as HIV-associated gingivitis but currently are designated as linear gingival erythema (LGE). LGE is distinguished by a 2–3 mm marginal band of intense erythema in the free gingiva (Winkler _et al_. 1988). This band of gingival erythema may extend into the attached gingiva as a focal or diffuse erythema and/or extend beyond the mucogingival line into the alveolar mucosa (Winkler _et al_. 1988). LGE may be localized to one or two teeth but it is more commonly a generalized gingival condition.
The etiology of this gingival lesion is not well understood; however, research has begun to investigate the relationship of periodontal pathogens and the local host response in regard to how HIV infection affects the gingiva. Although LGE does not respond to conventional scaling, root planing, and plaque control (Winkler & Murray 1987; Grassi _et al_. 1988; Winkler _et al_. 1988, 1989), the anaerobic micro-flora from subgingival sites of HIV-infected patients with gingivitis seems to be essentially the same as seen in non-infected patients (Moore _et al_. 1993). Despite the similarities in anaerobic microflora between infected and uninfected individuals, organisms not generally associated with gingivitis in HIV-negative patients, such as _Candida_ species, have been identified with LGE (Lamster _et al_. 1998). In addition, LGE lesions have been shown to have reduced proportions of T cells and macrophages and an increased number of IgG plasma cells and PMNs (Gomez _et al_. 1995). These host cell responses and unusual microbiota may be responsible for the refractory nature of this lesion to conventional periodontal treatment of gingivitis.
With the advent of antiretroviral therapy for HIV-positive patients, the prevalence of HIV-specific lesions has been dramatically reduced; even so, plaque accumulation with reduced CD4+ counts will still account for a pronounced gingival inflammatory response (Kroidl _et al_. 2005).
# Gingival diseases associated with malnutrition
Although some nutritional deficiencies can significantly exacerbate the response of the gingiva to plaque bacteria, the precise role of nutrition in the initiation or progression of periodontal diseases remains to be elucidated. The studies that have attempted to investigate the relationship of nutrition to periodontal disease have examined the periodontal status of individuals in developed and in developing countries and have failed to show a relationship between periodontal disease and nutrition (Russell 1962; Waerhaug 1967; Wertheimer _et al_. 1967). While there is a paucity of information available regarding the effects of a specific, single nutritional deficiency on human periodontal tissues, severe vitamin C deficiency or scurvy has been one of the earliest nutritional deficiencies to be examined in the oral cavity (Lind 1953). Even though scurvy is unusual in areas with an adequate food supply, certain populations on restricted diets (e.g. infants from low socioeconomic families) are at risk of developing this condition (Oeffinger 1993). The classic clinical signs of scurvy describe the gingiva as being bright red, swollen, ulcerated, and susceptible to hemorrhage (van Steenberghe 1997). Although there is no dispute about the necessity of dietary ascorbic acid for periodontal health, in the absence of frank scurvy the effect of declining ascorbic acid levels on the gingiva can be difficult to detect clinically (Woolfe _et al_. 1980) and when it is detected usually has characteristics that are similar to plaque-induced gingivitis (Fig. 17-14).
**Fig. 17-14** Gingival changes associated with vitamin C deficiency. Note the absence of dental plaque and the distances of the color changes from marginal gingiva.
# Gingival diseases associated with heredity
Benign, non-inflammatory fibrotic enlargement of the maxillary and/or mandibular gingiva associated with a familial aggregation has been designated by such terms as gingivomatosis elephantiasis, familial elephantiasis, juvenile hyaline fibromatosis, congenital familial fibromatosis, idiopathic fibromatosis, idiopathic gingival fibromatosis, hereditary gingival hyperplasia, and hereditary gingival fibromatosis. Although there have been over 100 reports of gingival enlargements associated with heredity in the literature over the past century, our knowledge concerning the natural history of this disease is extremely limited and the etiology of this rare condition has not been determined.
Hereditary gingival fibromatosis appears to be a slowly progressive gingival enlargement that develops upon eruption of the permanent dentition; however, gingival enlargement can also occur in the primary dentition (Emerson 1965; Jorgenson & Cocker 1974; Lai _et al_. 1995; Miyake _et al_. 1995). The disease can be localized or generalized and may ultimately cover the occlusal surfaces of teeth. The enlarged gingiva is non-hemorrhagic and firm but there can be an overlay of gingival inflammation which can augment the enlargement (Fig. 17-15). The histologic features of hereditary gingival fibromatosis include dense fibrotic connective tissue as well as epithelial hyperplasia with elongated and increased rete pegs (Johnson _et al_. 1986; Clark 1987).
**Fig. 17-15** Generalized, benign, non-inflammatory, fibrotic enlargement of gingival tissues.
Hereditary gingival fibromatosis can be inherited as a simple Mendelian trait in some chromosomal disorders, and as a malformation syndrome (Witkop 1971; Jones _et al_. 1977; Skrinjaric & Bacic 1989; Takagi _et al_. 1991; Goldblatt & Singer 1992; Hallet _et al_. 1995). Currently, a mutation in the _son of sevenless-1_ gene has been implicated as a genetic factor responsible for hereditary gingival fibromatosis (Hart _et al_. 2002). Recent research into the cellular responses of this disease suggest an accumulation of specific populations of gingival fibroblasts that result in an abnormal accumulation of connective tissues (Huang _et al_. 1997; Tipton _et al_. 1997; Lee _et al_. 2006).
# Gingival diseases associated with ulcerative lesions
Necrotizing ulcerative gingivitis (NUG) has been observed for centuries and has been recognized by numerous names including trench mouth and Vincent's infection. At this time, acute necrotizing ulcerative gingivitis is a term used to describe the clinical onset of the disease and should not be used as a diagnostic classification since some forms of NUG may be recurrent or possibly chronic.
NUG is most often distinguished by a sudden onset. The clinical signs of NUG include intense gingival pain that usually is responsible for the patient seeking professional care, papillary necrosis, that has been described as a "punched out" appearance of the gingival papilla, and gingival bleeding that requires little or no provocation (Fig. 17-16) (Grupe & Wilder 1956; Goldhaber & Giddon 1964; Johnson & Engel 1986). Although these three signs must be present to diagnosis NUG, other signs and symptoms may be present but do not necessarily occur in all individuals with this disease. These signs and symptoms include fever, malaise, lymphadenopathy, metallic taste, and malodor (Schluger 1943; Wilson 1952; Murayama _et al_. 1994). Systemic reactions of acute NUG are usually more severe in children. Significant destruction of the gingival connective tissue is possible with NUG but when attachment loss occurs this condition should be considered as a necrotizing ulcerative periodontitis (NUP).
**Fig. 17-16** Necrotizing ulcerative gingivitis. (a) Destruction of the interdental papilla, pseudomembrane and spontaneous bleeding. (b) Although usually confined to the papilla, occasionally the marginal tissues are involved.
The etiology of NUG has been associated with a bacterial infection. The four zones of the NUG gingival lesion include the bacterial zone (the superficial area that consists of various bacteria and some spirochetes), neutrophil-rich zone (follows the bacterial zone and contains leukocytes and bacteria including spirochetes), necrotic zone (consists of disintegrated cells and connective tissue elements with many large and intermediate spirochetes) and the spirochetal infiltration zone (the deepest zone that is infiltrated with no other bacteria but intermediate and large spirochetes) (Listgarten 1965). The cultivable flora of NUG that predominates includes _Provetella intermedia_ and _Fusobacterium_ species while microscopically _Treponema_ and _Selenomonas_ species are observed (Loesche _et al_. 1982; Rowland _et al_. 1993b). Additional factors such as smoking (AAP 1996), psychological stress (Moulton _et al_. 1952; Cohen-Cole _et al_. 1983), malnutrition (Grupe & Wilder 1956; Goldhaber & Giddon 1964; Johnson & Engel 1986), and immune suppression (Moulton _et al_. 1952; Rowland _et al_. 1993a) can predispose an individual to NUG.
NUG can affect any age group but is considered to be a disease of young adults in industrialized countries (Melnick _et al_. 1988). In developing countries, NUG is a disease found in children from families with a low socioeconomic status (Melnick _et al_. 1988). The onset of NUG in children is associated with inappropriate nutritional intake, especially low protein consumption (Sheiham 1966; Taiwo 1995). In addition, viral infections such as measles can induce NUG in malnourished children (Enwonwu 1972; Osuji 1990). Even though NUG has occurred in epidemic patterns, this disease is not considered communicable (Rosebury 1942).
# Treatment of plaque-induced gingival diseases
Personal and professional mechanical oral hygiene measures are critical aspects for the treatment of plaque-induced gingival diseases. Proper oral hygiene reduces the build-up of dental plaque on tooth surfaces and diminishes the incidence of various types of gingival diseases (Garmyn _et al_. 1998). For effective, self-care, mechanical plaque control, the appropriate use of manual (Jepsen 1998) or powered (van der Weijden _et al_. 1998) toothbrushes combined with interdental mechanical cleaning (Kinane 1998) is essential. Dentifrices also have important roles in the reduction of dental plaque. First of all, dentifrices can be used to help in the removal of dental plaque by enhancing the mechanical scrubing and cleaning power of the toothbrush (Mariotti & Burrell 2006). Secondly, since dentifrices are also drug-delivery systems; agents (e.g. tricolsan) present in a toothpaste will provide a pharmacologic advantage by reducing the bacteria found in dental biofilms and/or inflammation in gingival tissues (DeVizio & Davies 2004). Additionally, adjunctive, self-applied, locally delivered, pharmacologic agents (e.g. chlorhexidine) can also be an effective option for individuals with physical or medical limitations that constrain their ability to perform adequate home care.
Professional intervention is required as an adjunct to self-performed hygiene when plaque-retaining factors, such as dental calculus, defective restorations or anatomic factors, prevent an individual from effectively removing dental plaque. In instances where systemic factors modify the gingival response to dental biofilms, a combined treatment plan with the appropriate medical professional can be effective in addressing the root causes of the gingival inflammation.
# The significance of gingivitis
The presence of gingival inflammation was at one time considered a normal variant of health but in the mid-twentieth century that concept changed dramatically when it was hypothesized that sites with untreated gingivitis were destined to progress to destructive periodontal disease. Although this concept was supported by some clinical studies showing an association between gingivitis and bone loss (Marshall-Day _et al_. 1955), longitudinal studies examining the natural history of periodontal disease failed to show complete conversion of chronic gingivitis to periodontitis (Löe _et al_. 1986). Gingival inflammation is probably a necessary precursor for periodontitis (Löe & Morrison 1986; Page & Kornman 1997) but this does not mean that all sites which exhibit gingival inflammation progress to periodontitis (Schätzle, _et al_. 2003).
If the majority of the adult population exhibit some form of gingivitis how does one determine which inflamed sites within particular individuals are susceptible to conversion to destructive periodontal disease? There has been an awareness that differences in the inflammatory responsiveness to dental plaque cannot be fully accounted for by the quantity or quality of the plaque (Tatakis & Trombelli 2004). More specifically, there seems to be a differential gingival inflammatory response that is independent of the amount or rate of accumulation of dental plaque (Trombelli _et al_. 2004). Hence, the predilection of inflamed gingival sites to convert to destructive forms of periodontal disease may be dependent on the susceptibility and responsiveness of the individual to gingivitis (van der Velden _et al_. 1985a,b; Abbas _et al_. 1986; Winkel _et al_. 1987; Dietrich _et al_. 2006). In other words, these data suggest that specific types of inflammatory responses in the gingiva are necessary to initiate destruction of connective tissue attachment apical to the cementoenamel junction. As we learn more about different gingival inflammatory phenotypes our notions about the initiation of periodontal destruction continue to emerge.
### Acknowledgment
The author thanks Professor Noel Claffey for supplying some of the photographs in this chapter.
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# Chapter 18
# Chronic Periodontitis
Denis F. Kinane, Jan Lindhe, and Leonardo Trombelli
* * *
Clinical features of chronic periodontitis
Overall characteristics of chronic periodontitis
Gingivitis as a risk for chronic periodontitis
Susceptibility to chronic periodontitis
Prevalence of chronic periodontitis
Progression of chronic periodontitis
Risk factors for chronic periodontitis
Bacterial plaque
Age
Smoking
Systemic disease
Stress
Genetics
Scientific basis for treatment of chronic periodontitis
* * *
Chronic periodontitis is considered to start as _plaqueinduced gingivitis_ (see Chapter 17), a reversible condition that, left untreated, may develop into _chronic periodontitis_. Chronic periodontitis lesions include loss of attachment and bone and are regarded as irreversible. In this chapter, various aspects of chronic periodontitis will be described, including its links to plaque-induced gingivitis.
# Clinical features of chronic periodontitis
The clinical features of chronic periodontitis include symptoms such as (1) color, texture and volume alterations of the marginal gingiva, (2) bleeding on probing (BoP) from the gingival pocket area, (3) reduced resistance of the soft marginal tissues to probing (increased pocket depth or periodontal pocketing), (4) loss of probing attachment level, (5) recession of the gingival margin, (6) loss of alveolar bone (even or angular pattern), (7) root furcation exposure, (8) increased tooth mobility, (9) drifting and eventually exfoliation of teeth.
Figure 18-1 illustrates the clinical status of a 30-year-old male with severe chronic periodontitis. The clinical examination revealed that (1) most approximal and lingual/palatal sites exhibited BoP, (2) most teeth showed increased mobility, and (3) gingival recession had occurred at a large number of buccal and interproximal sites. Tooth 16 had erupted beyond the occlusal plane. Teeth 37 and 38 had tilted mesially. The altered position of the molars had evidently compromised the occlusion. Forces elicited during function may have caused the maxillary incisors to tilt in a buccal direction and multiple open spaces, diastemata, had developed in the front tooth segment of the maxilla.
Figure 18-2 presents the radiographic status of the same patient. In the radiographs it can be observed that a large number of teeth have lost substantial amounts of bone support. At teeth 17, 16, 27, 37, 36, and 47 the furcation areas have lost their periodontal tissue support and are open for "through and through" probing.
# Overall characteristics of chronic periodontitis
* Chronic periodontitis is prevalent in adults but may occur in children.
* The amount of destruction of the periodontal tissues seen in a given patient is commensurate with oral hygiene and plaque levels, local predisposing factors, smoking, stress, and systemic risk factors.
* The subgingival biofilm harbors a variety of bacterial species; the composition of the biofilm may vary between subjects and sites.
* Subgingival calculus is invariably present at diseased sites.
* Chronic periodontitis is classified as localized when <30% of sites are affected and generalized when this level is exceeded.
* Severity of chronic periodontitis at the site level may be classified based on the degree of probing attachment loss (PAL) as _mild_ (PAL = 1–2 mm), _moderate_ (PAL = 3–4 mm), and _severe_ (PAL ≥ 5 mm).
* Although chronic periodontitis is initiated and sustained by microbial plaque, host factors deter mine the pathogenesis and (rate of) progression of the disease.
* The rate of progression of chronic periodontitis is in most cases slow to moderate; periods of rapid tissue destruction may, however, occur.
* Additional periodontal tissue breakdown is likely to occur in diseased sites that are left untreated.
**Fig. 18-1** A 30-year-old male patient with chronic periodontitis, clinical status prior to treatment.
**Fig. 18-2** Same patient as in Fig. 18-1. Radiographs from the initial examination.
# Gingivitis as a risk for chronic periodontitis
Findings from epidemiologic studies (cross-sectional as well as longitudinal) indicate that gingival inflammation is invariably a component of chronic periodontitis and that gingivitis precedes the onset of periodontitis (see Chapter 11). The interpretation of data from early cross-sectional studies led to the belief that untreated gingivitis always progressed to chronic periodontitis. More recent studies have demonstrated, however, that this is not the case. Gingivitis lesions may remain stable for many years, and may never progress to become periodontitis lesions that include features such as attachment and bone loss. The two conditions have been considered, therefore, as separate disease entities with the explanation being that the bacterial plaque challenge will induce overt gingivitis but that the degree of response of the host (the susceptibility) will determine whether or not chronic periodontitis will develop. In a review paper, Kinane and Attström (2005) evaluated epidemiologic and experimental data on gingivitis and chronic periodontitis. The independence of these two conditions was called into question. It was proposed that gingivitis and periodontitis most likely represented different aspects of the same disease, namely chronic periodontitis.
Gingivitis becomes manifest after only days or weeks of plaque accumulation (Löe _et al_. 1965) while destructive chronic periodontitis is a condition that in the majority of cases requires far longer periods (years) of plaque and calculus exposure to develop (Lindhe _et al_. 1975; Löe _et al_. 1978). The proportion of untreated gingival lesions in a given subject or in a population that converts to destructive periodontitis lesions is at present unknown. Furthermore, the factors that cause the conversion are not well understood (Schätzle _et al_. 2003).
Findings from epidemiologic studies and prospective clinical trials have indicated that the presence of gingivitis may be regarded as a risk factor for chronic periodontitis. In a 2-year longitudinal study of 15–24-year-old Chinese adolescents from a rural district, it was observed that the percentage of sites that bled on probing at a baseline examination was related to overall attachment loss after 2 years of monitoring (Suda _et al_. 2000). This suggests that gingival inflammation was a risk indicator for additional attachment loss in this cohort. The role of gingivitis in the pathogenesis of chronic periodontitis was further elucidated by Schätzle _et al_. (2004) in longitudinal studies on the initiation and progression of periodontal disease in a Norwegian population. The results demonstrated that gingival sites, which during a 20-year interval never showed signs of inflammation, experienced modest loss of attachment (1.86 mm). For sites which presented with mild inflammation at each examination, the corresponding attachment loss was 2.25 mm, while at sites with severe gingival inflammation, the mean loss of attachment was 3.23 mm. Moreover, while teeth surrounded with healthy gingival tissues were maintained during the study period, teeth with gingivitis lesions were 46 times more likely to be lost.
The above data indicate that gingival inflammation may represent a relevant risk factor not only for destructive chronic periodontitis but also for tooth loss. This conclusion is in agreement with results documenting the absence of gingivitis as a good indicator for long-term maintenance of periodontal health in a subject (Joss _et al_. 1994) as well as at a site (Lang _et al_. 1990) level.
# Susceptibility to chronic periodontitis
As stated above plaque-induced gingivitis and chronic periodontitis represent different aspects of the same disease (Kinane & Attström 2005). An important question is whether both gingivitis and chronic periodontitis are affected by the same subject response (the host response) to plaque. If this is the case, the corollary is that susceptibility to gingivitis will reflect susceptibility to chronic periodontitis and may have prognostic utility.
Even in the very first reports from studies called "Experimental gingivitis in man" (Löe _et al_. 1965; Theilade _et al_. 1966) (see Chapters 11 and 17), evidence was presented that suggested that the onset and severity of the inflammatory response of the gingiva to plaque accumulation differed markedly among participants. The differences were, however, at that time attributed to differences in plaque accumulation rates (quantitative plaque differences) and/or differences in bacterial species present in plaque (qualitative plaque differences). More recent studies utilizing the "Experimental gingivitis" model have documented that significant differences in the inflammatory response occurred in different subjects although their plaque accumulation was quantitatively and/or qualitatively similar (Trombelli _et al_. 2004, 2005). It was suggested that the intensity of the inflammatory response to the plaque challenge may represent an individual trait (Tatakis & Trombelli 2004). Thus, an individual's susceptibility to gingivitis may be dependent on host-related factors, possibly of genetic origin (Shapira _et al_. 2005; Scapoli _et al_. 2005).
With the use of the "Experimental gingivitis" model it was also demonstrated that the susceptibility to gingivitis differed between two groups of patients consistent with different susceptibilities to periodontitis (Abbas _et al_. 1986; Winkel _et al_. 1987). Thus, the group with greater periodontitis susceptibility had also a greater susceptibility to gingivitis. Furthermore, in more recent studies it was documented that subjects with a history of aggressive periodontitis presented significantly more gingivitis in response to _de novo_ plaque accumulation when compared to periodontally healthy subjects matched for extent and rate of supragingival plaque accumulation (Trombelli _et al_. 2006).
# Prevalence of chronic periodontitis
From epidemiologic studies (see Chapter 7) it was concluded that chronic periodontitis is the most commonly occurring form of periodontal disease. While most subjects over 50 years of age have suffered moderate amounts of periodontal tissue destruction, advanced forms of chronic periodontitis are seen in only a small (<10%) subset of the population. Both age of onset of chronic periodontitis and subsequent rate of progression of the disease vary between individuals and are probably influenced by genetics (see Chapter 13) and environmental risk factors (see Chapters 7 and 12). Findings from examination of dizygotic and monozygotic twins (Michalowicz _et al_. 1991, 2000) indicated that (1) between 38% (regarding probing attachment loss) and 82% (regarding gingivitis) of the population variance could be attributed to genetic factors (Michalowicz _et al_. 1991), and (2) chronic periodontitis has about 50% heritability (Michalowicz _et al_. 2000).
On a population basis chronic periodontitis is often classified according to number (prevalence) of diseased sites (extent) and severity of tissue breakdown (probing attachment loss) at such sites. For the extent of chronic periodontitis, the low category would involve one to ten diseased (probing attachment loss) sites, the medium category would involve 11–20 sites, while the high category would involve more than 20 diseased sites. The amount of PAL at a given site may be used to describe the severity of chronic periodontitis. The severity may be considered as mild (PAL = 1–2 mm), moderate (PAL = 3–4 mm) or severe (PAL ≥ 5 mm). It has been documented that the extent and severity of chronic periodontitis are useful predictors of future disease progression.
Clinical (probing) attachment loss of 1–2 mm at one or several sites can be found in nearly all members of an adult population. The prevalence of subjects with one or more sites with PAL ≥ 3 mm increases with age. Furthermore the number of diseased sites in any one individual increases with age, as does the population prevalence (extent and severity) of chronic periodontitis with age.
# Progression of chronic periodontitis
Chronic periodontitis is generally a slowly progressing form of periodontal disease that at any stage may undergo exacerbation resulting in additional loss of attachment and bone.
Tissue destruction in chronic periodontitis does not affect all teeth evenly, but has site predilection. In other words, in the same dentition some teeth may be severely affected with periodontal tissue destruction while other teeth are almost free of signs of attachment and bone loss. Figure 18-3 illustrates the clinical condition of a subject with chronic periodontitis. Clinically (Fig. 18-3a) it can be observed that most teeth exhibit advanced recession of the soft tissue margin. In the corresponding radiographs (Fig. 18-3b) it is noted that the mesial surface of tooth 16 has a normal periodontal tissue support, while the neighboring tooth, i.e. the first premolar (tooth 14), has lost several millimeters of bone support on the distal aspect. The mesial surface of tooth 14, on the other hand, has a comparatively normal tissue support.
When considering changes in attachment level over time, it is also peculiar that only relatively few sites in a subject with chronic periodontitis undergo marked, additional tissue destruction during any given observation period. Based on data from a series of longitudinal studies, Socransky _et al_. (1984) proposed that chronic periodontitis progressed in episodes of exacerbation and remission. They termed this the "burst hypothesis" of disease progression. Findings from other similar studies, however, indicated that the progression of chronic periodontitis may be a continuous, slowly destructive process rather than exhibiting a "burst" pattern. The current consensus is that the progression of chronic periodontitis in most subjects and at most sites is a continuous process but that periods of exacerbation occasionally may occur. Clinically, the progressive nature of the disease can only be confirmed by repeated examinations over time but it is a safe assumption that untreated lesions of chronic periodontitis will progress and cause additional attachment and bone loss. Flemmig (1999) reported a mean additional PAL of ≥3 mm in up to 27% of subjects in untreated populations during a 1-year period. When progression was studied on a site basis, the overall annualized incidence ranged from 0.3–4.2% (Flemmig 1999). This indicates that the number of sites that actually exhibited progression within a given time varied considerably between subjects.
It is important to realize that factors associated with the initiation of chronic periodontitis may also influence disease progression. Furthermore, the extent and severity of disease within an individual, i.e. number of sites with attachment loss, bone loss, and/or deep pockets, are good predictors of future disease occurrence. In fact the best predictor of disease progression is previous disease experience.
# Risk factors for chronic periodontitis
The term "risk factor" means an aspect of lifestyle, an environmental exposure, or an inborn or inherited characteristic, which on the basis of epidemiologic evidence is known to be associated with a given disease. Risk factors may be part of the causal chain of a disease and/or may predispose the host to develop a disease. An individual presenting with one or more risk factors has an increased probability of contracting the disease or of the disease being made worse.
## Bacterial plaque
Bacterial aspects of periodontal disease are dealt with in Chapters 8 and 9. From the data presented it is obvious that a cumulative risk for a given microbiota can be estimated. It is not clear, however, if the specific microbiota is the principal disease-causing factor or whether it reflects the disease process. Specific microorganisms have been considered as potential periodontal pathogens but it is clear that, although pathogens are necessary, their mere presence may not be enough for the progressive disease to occur. Microbial plaque (biofilm) is a crucial factor in inflammation of the periodontal tissues, but the progression of gingivitis to periodontitis is largely governed by host-based risk factors (Michalowicz 1994; Shapira _et al_. 2005). Microbial biofilms of particular compositions will initiate chronic periodontitis (Marsh 2005) in certain individuals whose host response and cumulative risk factors predispose them to periodontal tissue destruction and attachment loss.
## Age
Although the prevalence of periodontal disease increases with age it is unlikely that becoming older in itself greatly increases susceptibility to periodontal disease. It is more likely that the cumulative effects of disease over a lifetime, i.e. deposits of plaque and calculus, and the increased number of sites capable of harboring such deposits, as well as attachment and bone loss experience, explain the increased prevalence of disease in older people.
## Smoking
The association between periodontal disease and smoking is dealt with in detail in Chapter 12. Only a brief discussion of smoking as a risk factor for chronic periodontitis is thus given here. The literature consistently indicates a positive association between smoking and chronic periodontitis across the many cross-sectional and longitudinal studies performed over the years (Kinane & Chestnutt 2000) and the risk attributable to tobacco for chronic periodontitis is between 2.5 and 7.0. It is not only the risk of developing the disease that is enhanced by smoking, but also the response to periodontal therapy is impaired in smokers. A further feature in smokers is that their signs and symptoms of both gingivitis and chronic periodontitis, mainly gingival redness and bleeding on probing (BOP), are masked by the dampening of inflammation seen for smokers as compared to non-smokers.
## Systemic disease
It is difficult to determine the precise role any systemic disease may play in the pathogenesis of chronic periodontitis. There are several reasons for this. Firstly, in epidemiologic studies attempting to evaluate the effect of systemic disease, control groups should be carefully matched in respect of age, sex, oral hygiene, and socioeconomic status. Many studies, particularly before the etiologic importance of dental plaque was recognized, failed to include such controls. Secondly, because of the chronic nature of periodontal disease, longitudinal studies spanning several years are preferable in individuals both with and without systemic disease. Unfortunately, most of the available data are derived from cross-sectional studies (Kinane 1999).
A reduction in number or function of polymorphonuclear leukocytes (PMNs) generally results in increased rate and severity of periodontal tissue destruction (Wilton _et al_. 1988). Many drugs, such as phenytoin, nifedipine, and cyclosporine, predispose to gingival overgrowth in response to plaque and thus may modify pre-existing chronic periodontitis (Ellis _et al_. 1999). Changes in circulating hormone levels may increase severity of plaque-induced gingival inflammation but typically do not result in any increased susceptibility to periodontitis. Hormonal changes following menopause have been associated with osteoporosis but studies are lacking to link this disease or an estrogen deficient state to a higher susceptibility to periodontal disease. Immunosuppressive drug therapy and any disease resulting in suppression of inflammatory and immune processes (such as HIV infection) may predispose the individual to exaggerated periodontal tissue destruction (Barr _et al_. 1992).
_Nutritional deficiencies_ in animals have been shown to affect the periodontal tissues. Epidemiologic data do not support the suggestion that such deficiencies play an important role in chronic periodontal disease although nutritional influences on inflammation are now accepted and are now actively being researched (Ritchie & Kinane 2005). Gingival bleeding is the most consistent oral feature of vitamin C deficiency or scurvy but there is also some evidence to suggest that avitaminosis-C may aggravate established chronic periodontitis.
The periodontal features of _histiocytosis X_ and other conditions in the rare histiocytoses disease group may present as necrotizing ulcerative periodontitis (Kinane 1999). Diabetes appears to be one of the most fascinating systemic diseases that interacts with periodontitis. On the one hand periodontitis severity and prevalence are increased in subjects with long-duration diabetes and more so in poorly controlled diabetics, than non-diabetics. On the other hand, periodontitis may also exacerbate diabetes as it may decrease glycemic control (Thorstenson 1995).
Despite the paucity of high quality data on individuals both with and without systemic disease the following general conclusions can be drawn (Kinane 1999):
**Fig. 18-3** (a) The clinical condition in quadrants 1 and 3 of a subject with chronic periodontitis. Most teeth in both quadrants exhibit advanced recession of the soft tissue margin. (b) Corresponding radiographs: the mesial surface of tooth 16 (arrow) has a normal periodontal tissue support, while the neighboring tooth, tooth 14, has lost several millimeters of bone support on the distal aspect (arrow). The mesial surface of tooth 14 has a comparatively normal tissue support (arrow).
* The _blood cells_ have a vital role in supplying oxygen, hemostasis and protection to the tissues of the periodontium. Systemic hematological disorders can thus have profound effects on the periodontium by denying any of these functions necessary for the integrity of the periodontium.
* The _polymorphonuclear leukocyte_ (PMN cell) is undoubtedly crucial to the defense of the periodontium. To exert this protective function several activities of PMNs must be integrated, namely chemotaxis, phagocytosis, and killing or neutralization of the ingested organism or substance. Individuals with either quantitative (neutropenia) or qualitative (chemotactic or phagocytic) PMN deficiencies, exhibit severe destruction of the periodontal tissues, which is strong evidence that PMNs are an important component of the host's protective response to the subgingival biofilm. Quantitative deficiencies are generally accompanied by destruction of the periodontium of all teeth, whereas qualitative defects are often associated with localized destruction affecting only the periodontium of certain teeth (i.e. chronic periodontitis may be modified).
* _Leukemias_ which give excessive numbers of leukocytes in the blood and tissues also cause a greatly depleted bone marrow function with concomitant anemia, thrombocytopenia, neutropenia, and reduced range of specific immune cells which give some characteristic periodontal features: anemic gingival pallor; gingival bleeding; gingival ulceration. Leukemic features are further complicated by the potential for the proliferating leukocytes to infiltrate the gingiva and result in gingival enlargement. In broad terms leukemias result in gingival pathologies, whereas periodontal bone loss is the consequence of neutrophil functional defects or deficient numbers and other severe functional defects such as deficiency of leukocyte adhesion receptors.
* _Diabetes mellitus:_ there are numerous confounding variables which must be considered in determining the true relationship between periodontitis and diabetes. The current consensus is that diabetics are at increased risk of periodontal disease, and whilst periodontitis can be successfully treated, both disease susceptibility and the outcome of therapy are influenced by poor metabolic control. Thus, it may be of benefit to the dentist to have knowledge of the control status of diabetes in an individual patient, as in the longer term metabolic control could indicate the probable outcome of periodontal therapy. In addition, it is now accepted that periodontal therapy can improve metabolic control in diabetics, meaning that the relationship is two-way and periodontal therapy is beneficial to the control of both diseases.
* _Medications_ such as phenytoin, cyclosporine, and nifedipine may predispose to gingival overgrowth in patients with gingivitis.
* _Genetic traits_ , which result in diseases that modify the periodontal structures or change the immune or inflammatory responses, can result in gross periodontal destruction in the affected individual; although the destruction seen may imitate periodontitis, this is not etiopathologically chronic periodontitis.
## Stress
Stressful life events and negative emotions have been shown to modulate several physiologic systems, including the endocrine and the immune system, leading to health changes (Kiecolt-Glaser _et al_. 2002; LeResche & Dworkin 2002). The association between stress and disease is particularly strong for infectious diseases, inflammatory conditions, and impaired wound healing (Kiecolt-Glaser _et al_. 2002; LeResche & Dworkin 2002; Broadbent _et al_. 2003). Specific periodontal conditions have been associated with psychosocial variables, including chronic periodontitis (Green _et al_. 1986; Linden _et al_. 1996; Genco _et al_. 1999; Wimmer _et al_. 2002; Pistorius _et al_. 2002), necrotizing ulcerative gingivitis (Shields 1977; Cohen-Cole _et al_. 1983; Horning & Cohen 1995), chronic and experimental gingivitis (Minneman _et al_. 1995; Deinzer _et al_. 1998; Waschul _et al_. 2003). In adults, the reported contribution of psychosocial factors to enhanced gingivitis expression (Deinzer _et al_. 1998) may relate to the stress-associated increase in plaque accumulation (Deinzer _et al_. 2001). However, the possible association of other psychosocial variables, such as personality traits and coping behavior, which are associated with either susceptibility or resistance to stress, with changes in the inflammatory response of the gingiva to _de novo_ plaque accumulation, remains uncertain (Trombelli _et al_. 2005).
Most of the literature on stress and periodontal conditions is quite old, and reports of acute necrotizing ulcerative gingivitis (or trench mouth) were made on stressed soldiers on the front line during World War I. It is understood that stress may be immunosuppressive and that acute necrotizing ulcerative gingivitis may occur in the immunosuppressed (also in HIV patients), but there is insufficient data as yet to substantiate the assumption that psychosocial factors are indeed of etiologic importance in chronic periodontitis.
## Genetics
There is convincing evidence from twin studies for a genetic predisposition to the periodontal diseases. The twin studies have indicated that risk of chronic periodontitis has a high inherited component. A great deal of research is underway attempting to identify the genes and polymorphisms associated with all forms of periodontitis. It is likely that chronic periodontitis involves many genes, the composition of which may vary across individuals and races. Much attention has focused on polymorphisms associated with the genes involved in cytokine production (Shapira _et al_. 2005). Such polymorphisms have been linked to an increased risk for chronic periodontitis but these findings have yet to be corroborated (Kinane & Hart 2003; Kinane _et al_. 2005).
# Scientific basis for treatment of chronic periodontitis
Chronic periodontitis is initiated and sustained by microorganisms living in biofilm communities which are present in supra- and subgingival plaque in the form of uncalcified and calcified biofilms. Prevention of initiation or primary prevention of periodontitis is clearly related to preventing formation and/or eradication of the microbial biofilm and it follows that prevention of gingivitis is a primary preventive measure for chronic periodontitis. Initial periodontal therapy or basic treatment of periodontitis involves the removal of both sub- and supragingival plaque. The clinical outcome is largely dependent on the skill of the operator in removing subgingival plaque and the skill and motivation of the patient in practicing adequate home care. A further variable is the innate susceptibility of the patient which is related to the way in which their innate, inflammatory, and immune systems operate in response to the microbial challenge. In addition, local and systemic risk factors can influence the quantity and quality of both the microbial challenge and the host response to these pathogens. The relative contribution of these risk factors has yet to be fully determined but their influence would be limited if the periodontium were kept free of microbial plaque. Thus, sub- and supragingival debridement and the quality of the patient's home care are of vital importance in preventing inflammation that manifests as both gingivitis and periodontitis.
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# Chapter 19
# Aggressive Periodontitis
Maurizio S. Tonetti and Andrea Mombelli
* * *
Classification and clinical syndromes
Epidemiology
Primary dentition
Permanent dentition
Screening
Etiology and pathogenesis
Bacterial etiology
Genetic aspects of host susceptibility
Environmental aspects of host susceptibility
Current concepts
Diagnosis
Clinical diagnosis
Microbiologic diagnosis
Evaluation of host defenses
Genetic diagnosis
Principles of therapeutic intervention
Elimination or suppression of the pathogenic flora
* * *
Periodontitis is an infection that can have many different clinical presentations. This has led to the recognition of different clinical syndromes. Until recently, the question of whether or not these dissimilar clinical presentations represented different forms of disease has been open to discussion. Today several lines of evidence support the existence of truly different forms of periodontitis. These include:
1. The growing clinical consensus of differential prognosis and need for specific treatment approaches for the various syndromes
2. Heterogeneity in etiology with possible therapeutic implications
3. Heterogeneity in genetic and environmental susceptibility.
At the 1999 international classification workshop, the different forms of periodontitis were reclassified into three major forms (chronic, aggressive, and necrotizing forms of periodontitis) and into periodontal manifestations of systemic diseases. This chapter deals with aggressive, type 1, periodontitis. Until recently, this group of diseases was defined primarily based on the age of onset/diagnosis and was thus named early onset periodontitis (EOP). Features of this form of disease, however, can present themselves at any age and this form of periodontitis is not necessarily confined to individuals under the arbitrarily chosen age of 35.
Aggressive periodontitis (AgP) comprises a group of rare, often severe, rapidly progressive forms of periodontitis often characterized by an early age of clinical manifestation and a distinctive tendency for cases to aggregate in families. At the above mentioned classification workshop, AgP was characterized by the following major common features (Lang _et al_. 1999):
* Non-contributory medical history
* Rapid attachment loss and bone destruction
* Familial aggregation of cases.
Frequently AgP presents early in the life of the individual; this implies that etiologic agents have been able to cause clinically detectable levels of disease over a relatively short time. This fact is central to the current understanding of these diseases, since it implies infection with a highly virulent microflora and/or a high level of subject susceptibility to periodontal disease. AgP, however, can occur at any age. Diagnosis of AgP requires exclusion of the presence of systemic diseases that may severely impair host defenses and lead to premature tooth loss (periodontal manifestations of systemic diseases).
The existence of specific forms of AgP has also been recognized based on specific clinical and laboratory features: localized aggressive periodontitis (LAP, formerly known as localized juvenile periodontitis or LJP) and generalized aggressive periodontitis (GAP, formerly termed generalized juvenile periodontitis (GJP) or generalized early onset periodontitis, G-EOP) (Tonetti & Mombelli 1999).
In spite of its rare occurrence AgP has been the focus of many investigations aimed at understanding its etiology and pathogenesis. Difficulties in gathering sufficiently large populations, however, have resulted in few clinical studies addressing both diagnostic and therapeutic procedures for these subjects. Utilization of both clinical and advanced diagnostic procedures as well as a variety of treatment approaches remains largely anecdotal and based on the specific experience of individual clinicians rather than on well documented scientific evidence.
# Classification and clinical syndromes
In the absence of an etiologic classification, aggressive forms of periodontal disease have been defined based on the following primary features (Lang _et al_. 1999):
* Non-contributory medical history
* Rapid attachment loss and bone destruction
* Familial aggregation of cases.
Secondary features that are considered to be generally but not universally present are:
* Amounts of microbial deposits inconsistent with the severity of periodontal tissue destruction
* Elevated proportions of _Actinobacillus actinomycetemcomitans_ (recently renamed _Aggregatibacter actinomycetemcomitans_ ) and, in some Far East populations, _Porphyromonas gingivalis_
* Phagocyte abnormalities
* Hyper-responsive macrophage phenotype, including elevated production of prostaglandin E2 (PGE2) and interleukin-1β (IL-1β) in response to bacterial endotoxins
* Progression of attachment loss and bone loss may be self-arresting.
The international classification workshop identified clinical and laboratory features deemed specific enough to allow subclassification of AgP into localized and generalized forms (Lang _et al_. 1999; Tonetti & Mombelli 1999). The following features were identified:
* _Localized aggressive periodontitis_ (LAP) (Fig. 19-1):
* Circumpubertal onset
* Localized first molar/incisor presentation with interproximal attachment loss on at least two permanent teeth, one of which is a first molar, and involving no more than two teeth other than first molars and incisors
* Robust serum antibody response to infecting agents
* _Generalized aggressive periodontitis_ (GAP) (Fig. 19-2):
* Usually affecting persons under 30 years of age, but patients may be older
* Generalized interproximal attachment loss affecting at least three permanent teeth other than first molars and incisors
* Pronounced episodic nature of the destruction of attachment and alveolar bone
* Poor serum antibody response to infecting agents.
Diagnosis of one of these AgP forms requires the absence of systemic diseases that may severely impair host defenses and lead to premature exfoliation of teeth. In such instances the appropriate clinical diagnosis will be periodontal manifestation of systemic disease.
GAP represents the most heterogeneous group and includes the most severe forms of periodontitis. They comprise forms originally described as generalized juvenile periodontitis (emphasis on a possible relationship with LAP), severe periodontitis (emphasis on the advanced destruction in comparison with patient age), or rapidly progressing periodontitis (emphasis on the fast rate of progression of lesions in these forms). Each of these GAP forms, however, remains highly heterogeneous in terms of clinical presentation and response to therapy. The European Workshop on Periodontology has therefore suggested that, while a better etiologic classification remains unavailable, these forms should be considered as a group to be further defined by the use of various clinical descriptors of the disease based on clinical, microbiologic, and immunologic parameters (Attström & Van der Velden 1993). Further rationale for an imprecise classification of these GAP forms comes from the fact that, given the severity of the disease and the heterogeneity of clinical presentation, each of these rare cases deserves individual consideration.
Subjects often present with attachment loss that does not fit the specific diagnostic criteria established for AgP or chronic periodontitis; this occurrence has been termed _incidental attachment loss_. It includes: recession associated with trauma or tooth position; attachment loss associated with impacted third molars; attachment loss associated with removal of impacted third molars, etc. It may include initial clinical presentations of periodontitis. Patients with this clinical diagnosis should be considered as a high-risk group for AgP or chronic periodontitis.
Besides clinical presentation, a variety of radiographic, microbiologic, and immunologic parameters are currently being used, along with the assessment of environmental exposures such as cigarette smoking, to further describe the AgP affecting the individual subject. These descriptors are important in treatment selection and to establish long-term prognosis. They will be further discussed in the section on diagnosis later in this chapter.
It is also important to underline that, in the present state of uncertainty regarding both the causative agents and the genetic and environmental susceptibility to AgP, it is possible that, in spite of the lines of evidence presented above, LAP and GAP may simply represent phenotypic variations of a single disease entity. Conversely, it is possible that different AgP forms may manifest themselves with a common clinical presentation. This aspect is of great diagnostic and therapeutic importance.
**Fig. 19-1** (a–c) Clinical appearance of the periodontal tissues of a 15-year-old girl suffering from localized aggressive periodontitis. Note the proper oral hygiene conditions and the scalloped outline of the gingival margin. In the lower anterior region, the interdental papilla between teeth 31 and 32 has been lost. (d) Intraoral radiographs show the presence of localized angular bony defects, associated with clinical attachment level loss, at the mesial aspect of tooth 46, 36 and at the distal aspect of tooth 31. No significant bone loss and/or attachment loss was detectable in other areas of the dentition. Diagnosis: localized aggressive periodontitis (LAP). (e–g) Clinical appearance of the 14-year-old sister of the proband depicted in (a–d). Note that in spite of the excellent oral hygiene status, bleeding on probing was provoked in the mesial of the molars, where deep pockets were present. (h) Angular bone loss is evident on the mesial of 16, 26 and 46.
Some case reports have indicated that some subjects may experience periodontitis affecting the primary dentition, followed by LAP and later by GAP (Shapira _et al._ 1994). One investigation indicated that the primary dentition of LAP patients presented bone loss at primary molars in 20–52% of cases, suggesting that at least some LAP cases may initially affect the primary dentition (Sjodin _et al._ 1989, 1993). Furthermore, in LAP subjects an association between the number of lesions and the age of the subject has been described, suggesting an age-dependent shift from localized to generalized forms of AgP (Hormand & Frandsen 1979; Burmeister _et al._ 1984).
# Epidemiology
Given the recent definition of AgP and the fact that it does not represent just a new term for the previously defined EOP, epidemiologic studies available relate primarily to EOP. Relatively few investigations employing different epidemiologic techniques have estimated the prevalence and the progression of EOP in the primary and permanent dentition (s) of children and young adults. All available investigations, however, indicate that early onset (aggressive) forms of periodontal diseases are detectable in all age and ethnic groups (Papapanou 1996). Wide variation in prevalence, however, has been reported, with some studies showing up to 51.5% affected individuals. These differences are probably due to differences in the employed epidemiologic methodologies and definition of EOP.
**Fig. 19-2** (a–c) Clinical presentation in 1990 of a 32-year-old female with generalized severe bone loss and clinical attachment loss, recession of the gingival margin and presence of deep periodontal pockets. Presence of local factors, and intense inflammation and edema of the gingival margin are evident. (d–f). Previous radiographic examinations were available from 1984 and 1987. Comparison of the radiographs obtained over the 6-year period from 1984 to 1990 indicates that most of the periodontal destruction occurred during the last 3 years. The patient had been smoking 20 cigarettes/day for more than 10 years. Diagnosis: generalized aggressive periodontitis (GAP) in a cigarette smoker.
## Primary dentition
Little evidence is available concerning the prevalence of AgP affecting the primary dentition. In the few studies from industrialized countries, marginal alveolar bone loss has been found to affect the primary dentition of 5–11-year-olds with frequencies ranging from 0.9–4.5% of subjects (Sweeney _et al_. 1987; Bimstein _et al_. 1994; Sjodin & Mattson 1994). In this respect, it should be emphasized that periodontitis affecting the primary dentition does not necessarily mean presence of an aggressive form of periodontitis, but may indicate a chronic form of disease with relative abundance of local factors (plaque and calculus). A clinical case of localized periodontitis affecting the primary dentition is illustrated in Fig. 19-3. More severe cases affecting the primary dentition and leading to tooth exfoliation early in life are usually interpreted as periodontal manifestations of systemic (hematologic) diseases, such as leukocyte adhesion deficiency (see Chapter 7 and Fig. 19-4).
## Permanent dentition
In the permanent dentition of 13–20-year-old individuals, the majority of studies have reported a prevalence of periodontitis of less than 1% (usually 0.1–0.2% in Caucasian populations). The risk of developing periodontitis at such an early age, however, does not seem to be shared equally in the population: among US schoolchildren 5–17 years of age, the prevalence of periodontitis has been estimated to range from about 0.2% for white subjects to about 2.6% for black subjects (Löe & Brown 1991). Furthermore, in these young age groups higher prevalence of periodontitis has been reported in studies from some developing countries (see Chapter 7).
Longitudinal studies of disease progression in adolescents indicate that subjects with signs of destructive periodontitis at a young age are prone to further deterioration. Such deterioration appears to be more pronounced at initially affected sites, and in patients diagnosed with LAP and from low socioeconomic groups. Deterioration of the periodontal status involves both an increase in extent (number of lesions within the dentition) and in severity of lesions (further alveolar bone loss at initially diseased sites) (Fig. 19-5) (Clerehugh _et al_. 1990; Lissau _et al_. 1990; Albandar _et al_. 1991a,b; Albandar 1993; Aass _et al_. 1994).
Some epidemiologic investigations have reported high prevalence of attachment loss in adolescents and young adults that did not fit the characteristics of recognized periodontitis clinical syndromes. Such occurrences have been termed _incidental attachment loss_ , and have been reported in 1.6–26% of the subjects. This group is thought to comprise both initial forms of periodontitis (including AgP) and a variety of defects, such as recession due to traumatic tooth-brushing, attachment loss associated with removal of impacted third molars, etc.
### Conclusion
A small but significant proportion of children and young adults is affected by some form of periodontitis. A substantial proportion of these subjects is thought to be affected by AgP. Given the severity of these forms of periodontal disease and their tendency to progress, early detection of periodontitis, and AgP in particular, should be a primary concern of both practitioners and public health officers. The whole population, including children and young adults, should receive a periodontal screening as part of their routine dental examination.
## Screening
Given the low prevalence of AgP patients within the population, cost-effective detection of cases requires utilization of a sensitive screening approach, i.e. the application of a diagnostic approach able to correctly identify most of the cases with disease. The objective of screening is the detection in a population of possibly diseased subjects that would require a more comprehensive examination. In periodontology, the most sensitive diagnostic test for the detection of periodontitis is the measurement of attachment loss by probing. Application of this diagnostic procedure in the mixed dentition and in teeth that are not fully erupted, however, may be difficult.
**Fig. 19-3** Seven-year-old African American female presenting with radiographic alveolar bone loss and probing attachment loss at the primary molars and permanent first molars and incisors. (a–c) Clinical photographs, buccal view. (d–e) Bite-wing radiographs. Clinical presentation shows moderate plaque accumulation, localized gingival inflammation, with ulceration of the gingival margin and loss of the interdental papilla mesial of #65. In the primary molar regions there were 4–6 mm pockets with bleeding on probing. Bone loss and attachment loss were limited to the molar region. The mesial aspects of the first permanent molars are also initially involved. Radiographic subgingival calculus is evident. Note that the upper left posterior sextant seems to be more severely affected than the other posterior segments. Diagnosis: localized aggressive (type 1) periodontitis.
In younger subjects, therefore, a currently utilized screening approach is the measurement of the distance between the alveolar crest and the cementoenamel junction on bite-wing radiographs. An advantage of this approach relates to the fact that in most industrialized countries bite-wing radiographs of children and young adolescents in mixed dentition are routinely taken for caries prevention programs; these radiographs should therefore be screened not only for carious lesions but also for the presence of marginal alveolar bone loss.
Recent investigations have attempted to determine the "normal" distance between the cemento-enamel junction and the alveolar crest of primary and permanent molars in 7–9-year-old children (Sjodin & Mattson 1992; Needleman _et al_. 1997). Median distances at primary molars were 0.8–1.4 mm. These values were in agreement with those previously reported for primary molars of 3–11-year-old children (Bimstein & Soskolne 1988). The cemento enamel junction of permanent molars was 0–0.5 mm apical to the alveolar crest in 7–9-year-olds. These values were age-dependent, and related to the state of eruption of the tooth. In general, however, it should be noted that the majority of children present with distances significantly smaller than the 2–3 mm considered normal for the completely erupted dentitions of adults. In children, significantly greater distances have been detected at sites with caries, fillings or open contacts, indicating that these factors may contribute to bone loss in similar ways to those in adult patients. Furthermore, presence of one of these local factors may suggest a local cause of bone loss, other than periodontitis. A distance of 2 mm between the cemento-enamel junction and the alveolar crest, in the absence of the above-mentioned local factors, argues therefore for a suspected diagnosis of periodontitis (Figs. 19-6 and 19-7) (Sjodin & Mattson 1992). This tentative diagnosis will have to be confirmed by a complete periodontal examination. In utilizing bite-wing radiographs for the screening of patients, clinicians should be aware that radiographic marginal bone loss (in the presence of probing attachment loss) is a highly specific diagnostic sign of periodontitis. Its sensitivity, however, is lower than that of periodontal probing because initial intrabony lesions may not appear on radiographs as a result of the masking effects of intact cortical plates (Suomi _et al_. 1968; Lang & Hill 1977). Some initial cases of periodontitis may therefore remain undetected.
**Fig. 19-4** Radiographs obtained from a Caucasian female with generalized prepubertal periodontitis. Radiographic situation in (A) April 1978 when she was 4–5 years old, (B) December 1978, and (C) August 1979. The radiographs illustrate the extent of alveolar bone loss that occurred over the 15-month period. Note the widespread bone loss. During infancy, this patient had severe, recurrent skin and ear infections sustained by _Staphylococcus aureus_ and _Pseudomonas aeruginosa_ , respectively. Delayed healing was also observed following minor injuries. White cell counts revealed a persistent leukocytosis, with absolute neutrophil counts always above 8000/mm3. Gingival biopsy indicated that the inflammatory infiltrate consisted almost completely of plasma cells and lymphocytes. No neutrophils were present, in spite of the abundance of these cells in the circulation. This history and clinical manifestation appears to be consistent with the diagnosis of periodontal manifestations of systemic disease in a subject with leukocyte adhesion deficiency (LAD). From Page _et al_. (1983b) with permission from the American Academy of Periodontology.
**Fig. 19-5** Radiographs illustrating bone loss at the distal aspect of the mandibular first molar in a 15-year-old girl (a) and progression of disease 1 year later (b).
**Fig. 19-6** Diagrammatic representation of the use of bite-wing radiographs to screen for prepubertal periodontitis in mixed dentition. The distance from the cemento-enamel junction (CEJ) and the alveolar bone crest (ABC) is measured from a line connecting the CEJ of the two adjacent teeth. Measurements are taken for each mesial and distal surface. Normal CEJ-ABC distances for 7–9 year olds are less than 2.0 mm. If the measurement exceeds this value, prepubertal periodontitis should be suspected, and a comprehensive periodontal examination should be performed.
**Fig. 19-7** Bite-wing radiographs illustrating advanced bone loss at primary molars, and initial involvement of the mesial aspect of the first molar in a child with early onset periodontitis. Note the marginal pattern of bone loss, which is significantly different from the pattern expected in association with the normal exfoliation of deciduous teeth. Subgingival calculus can also be observed.
In older adolescents and adults, periodontal probing is a more appropriate screening examination than the use of radiographs. It is important to differentiate between clinical use of periodontal probing to perform a complete periodontal examination, and its use as a screening tool. Using probing to detect attachment loss during a screening examination requires circumferential probing to evaluate all sites around the tooth. In a screening examination, however, attachment loss values for all sites are usually not recorded. Furthermore, the screening examination can be stopped once evidence of attachment loss has been detected, and therefore the need for a comprehensive examination has been established. The American Academy of Periodontology has recently endorsed a simplified screening examination for this purpose. This examination is based on a modification of the Community Periodontal Index of Treatment Needs (CPITN) (Ainamo _et al_. 1982; American Academy of Periodontology & American Dental Association 1992).
Once a case has been detected by a screening examination, a comprehensive periodontal examination will be necessary to establish a proper diagnosis. At this stage, once a case of periodontitis has been confirmed, a differential diagnosis between aggressive (type 1) periodontitis and chronic (type 2) periodontitis needs to be made in accordance with the criteria mentioned above and keeping in mind that cases which do not fit the AgP criteria should be diagnosed as chronic periodontitis.
### Conclusion
Screening periodontal examinations should be performed as part of every dental visit. Marginal bone loss assessed on bite-wing radiographs, though less sensitive than periodontal probing, may be used as a screening tool in subjects with primary and mixed dentitions. Attachment loss evaluated by periodontal probing is the most sensitive screening approach currently available; it should be used in older adolescents and adults. Differential diagnosis between AgP and chronic periodontitis is made based on exclusion of AgP.
# Etiology and pathogenesis
As a group, aggressive forms of periodontitis are characterized by severe destruction of the periodontal attachment apparatus at an early age. This early manifestation of clinically detectable lesions is generally interpreted as being the expression of highly virulent causative agents or high levels of susceptibility of the individual patient, or a combination of the two.
## Bacterial etiology
The evidence implicating bacteria in the etiology of periodontitis has been described in Chapter 9. The most abundant evidence regarding a bacterial etiology of AgP comes from studies of LAP. Evidence relating to other forms of AgP (GAP) will be discussed only when specifically different from LAP.
Acceptance of bacterial etiology of aggressive forms of periodontitis has been particularly difficult since clinical presentation of cases frequently shows little visible plaque accumulation, and proximal caries, another dental disease of bacterial origin affecting younger individuals, seems much less prevalent in LAP patients than in age-, gender-, and racematched controls (Fine _et al_. 1984; Sioson _et al_. 2000). Of great importance, in this respect, were microscopic studies demonstrating the presence of a layer of bacterial deposits on the root surface of advanced AgP lesions (Listgarten 1976; Westergaard _et al_. 1978). Early studies attempting the identification of the involved bacteria using culture techniques were performed by Newman _et al_. and by Slots (Newman _et al_. 1976; Slots 1976; Newman & Socransky 1977). In these studies, Gramnegative organisms comprised approximately two thirds of the isolates from deep periodontal pockets. In contrast, these organisms averaged only about one third of the isolates in control sites with normal gingiva. A substantial part of the isolates was not identifiable at that time due to methodological limitations and ambiguous classification schemes. Dominant microorganisms in LAP included _Actinobacillus actinomycetemcomitans_ ( _A.a._ , now termed _Aggregatibacter actinomycetemcomitans)_ , _Capnocytophaga_ sp., _Eikenella corrodens_ , saccharolytic Bacteroides-like organisms now classified as _Prevotella_ sp., and motile anaerobic rods today labeled _Campylobacter rectus_. Gram-positive isolates were mostly streptococci, actinomycetes, and peptostreptococci. _A.a._ , _Capnocytophaga_ sp., and _Prevotella_ sp. were also shown to be the most prominent members of the subgingival microbiota of periodontitis lesions in the primary dentition. The microbial patterns observed in periodontal lesions of the primary dentition seemed, however, to be more complex than the ones found in LAP patients.
One of these organisms, _A. actinomycetemcomitans_ , a short, facultatively anaerobic, non-motile, Gram-negative rod, received particular attention and was increasingly viewed as a key microorganism in LAP. This view was principally based on four lines of evidence (Socransky & Haffajee 1992):
1. Association studies, linking the organism to the disease: _A.a._ was isolated in periodontal lesions from more than 90% of LAP patients and was much less frequent in periodontally healthy individuals (Table 19-1) (for more recent investigations, see also Ashley _et al_. 1988; Van der Velden _et al_. 1989; Albandar _et al_. 1990; Gunsolley _et al_. 1990; Slots _et al_. 1990; Asikainen _et al_. 1991; Aass _et al_. 1992; Ebersole _et al_. 1994; Listgarten _et al_. 1995). In some studies it was possible to demonstrate elevated levels of _A.a._ in sites showing evidence of recent or ongoing periodontal tissue destruction (Haffajee _et al_. 1984; Mandell 1984; Mandell _et al_. 1987).
2. Demonstration of virulence factors: _A.a._ was shown to produce several potentially pathogenic substances, including a leukotoxin, was capable of translocating across epithelial membranes, and could induce disease in experimental animals and non-oral sites (for review see Zambon _et al_. 1988; Slots & Schonfeld 1991).
3. Findings of immune responses towards this bacterium: investigators repeatedly reported significantly elevated levels of serum antibodies to _A.a._ in LAP patients (Listgarten _et al_. 1981; Tsai _et al_. 1981; Altman _et al_. 1982; Ebersole _et al_. 1982, 1983; Genco _et al_. 1985; Vincent _et al_. 1985; Mandell _et al_. 1987; Sandholm _et al_. 1987). Such patients were furthermore shown to produce antibodies locally against this organism at diseased sites (Schonfeld & Kagan 1982; Ebersole _et al_. 1985b; Tew _et al_. 1985).
4. Clinical studies showing a correlation between treatment outcomes and levels of _A.a._ after therapy: unsuccessful treatment outcomes were linked to a failure in reducing the subgingival load of _A.a._ (Slots & Rosling 1983; Haffajee _et al_. 1984; Christersson _et al_. 1985; Kornman & Robertson 1985; Mandell _et al_. 1986, 1987; Preus 1988).
**Table 19-1** Classical studies on the distribution of _A.a._ in LAP, gingivitis, adult periodontitis, and in normal non-diseased subjects
In consideration of these findings, _A.a._ was one of the few oral microorganisms recognized by many to be a true infectious agent, and LAP as an infection essentially caused by _A.a._ Accepting such a concept has far-reaching consequences with regards to strategies for prevention and therapy. For example, if _A.a._ is a real exogenous pathogen for LAP, or AgP in general, avoidance of exposure to the organism becomes a relevant issue in prevention (the mere presence of _A.a._ would be an indication for intervention), and the elimination of _A.a._ may be a valid treatment goal. Consequently, highly sensitive tests to detect the bacterium would be useful diagnostic tools. Several studies have, in fact, provided evidence for transmission of _A.a._ between humans, e.g. from parent to child or between spouses (DiRienzo _et al_. 1990, 1994b; Preus _et al_. 1992; Petit _et al_. 1993a,b; Poulsen _et al_. 1994; Von Troil-Lindén _et al_. 1995). Other studies have indicated that _A.a._ can be eliminated with appropriate mechanical treatment and adjunctive antibiotic therapy (Rams _et al_. 1992; Pavicic _et al_. 1994).
However, the view of LAP as an _A.a._ infection did not remain undisputed. It was contested by citing cross-sectional studies showing a high general _A.a._ prevalence in certain populations, particularly from developing countries (Eisenmann _et al_. 1983; Dahlén _et al_. 1989; McNabb _et al_. 1992; Al-Yahfoufi _et al_. 1994; Gmür & Guggenheim 1994). It was also argued that _A.a._ could be detected in subgingival plaque samples from sites with and without disease, and that there were patients with LAP who apparently neither showed presence of _A.a._ in the oral flora nor had elevated antibody titers to the organism (Loesche _et al_. 1985; Moore 1987). A systematic review with the purpose of determining to what extent adjunctive microbiological testing could distinguish between chronic and aggressive periodontitis concluded that the presence or absence of _A.a._ (as well as of four other suspected periodontal pathogens) could not discriminate between subjects with aggressive periodontitis from those with chronic periodontitis (Mombelli _et al_. 2002). Although a diagnosis of AgP was more likely in a subject positive for _A.a._ than in an individual negative for this organism, any _A.a._ -positive individual with periodontitis was three times more likely to be suffering from chronic than from aggressive periodontitis.
If a putative pathogen can be detected frequently in subjects without a given clinical diagnosis, this suggests that not all humans are equally susceptible and/or that there is variation in virulence and pathogenic potential. Strong evidence has been produced in recent years demonstrating that the virulence of _A.a._ is in fact variable, and proving the existence of at least one particularly virulent subpopulation of _A.a._
Using monoclonal antibody technology, five serotypes (a, b, c, d, e) of _A.a._ can be distinguished. Each of these serotypes represents a separate evolutionary lineage. A serotype-dependent pattern of association with LAP was found in the United States, where serotype b strains were more often isolated from patients with localized juvenile periodontitis than from other subjects (Zambon _et al_. 1983b, 1996). A higher frequency of serotype b strains was also reported from Finnish subjects with periodontitis (Asikainen _et al_. 1991, 1995). Differing results were, however, reported from other parts of the world, suggesting that there may be specific distribution patterns in ethnically distinct populations (Chung _et al_. 1989; Gmür & Baehni 1997; Hölttä _et al_. 1994). Using restriction fragment length polymorphism (RFLP) analysis, DiRienzo _et al_. (1994a,b) could discriminate twelve genotypes of _A.a._ One of them (RFLP type II) was uniquely associated with periodontal disease. Others, however, were linked to healthy periodontal conditions.
Several properties of _A.a._ are regarded as important determinants of virulence and pathogenic potential (Table 19-2). All Gram-negative bacteria are enveloped by two membranes, of which the outer is rich in endotoxin. This identifying feature of Gram-negative bacteria consists of a lipid and a polysaccharide part and is therefore frequently termed lipopolysaccharide (LPS). LPS is set free when bacterial cells die or multiply. _A.a._ can also secrete membrane vesicles that can serve as transport vehicles to spread endotoxin as well as other pathogenic substances produced by the bacterium. The LPS of _A.a._ can activate host cells, and macrophages in particular, to secrete inflammatory mediators such as prostaglandins, interleukin-1β and tumor necrosis factor-α. It is also highly immunogenic, since high titers of antibodies against its antigenic determinant are frequently detected in infected individuals. Additional virulence factors interfering with fibroblast proliferation have been identified for certain strains of _A.a._ Immunosuppressive properties of _A.a._ , as well as collagenolytic activity and inhibition of neutrophil chemotaxis, have been demonstrated (for review see Fives-Taylor _et al_. 1996). The key element of virulence and pathogenicity of _A.a._ , however, is considered to be the production of a leukotoxin, playing an important role in the evasion of local host defenses. The leukotoxin produced by _A.a._ exhibits cytotoxic specificity and destroys human polymorphonuclear leukocytes and macrophages, but neither epithelial and endothelial cells nor fibroblasts. It belongs to the family of the RTX (Repeats in ToXin) toxins, which are poreforming lytic toxins (for details see Lally _et al_. 1996).
**Table 19-2** Determinants of virulence and pathogenic potential of _A. actinomycetemcomitans_
**Factor** | **Significance**
---|---
Leukotoxin | Destroys human polymorphonuclear leukocytes and macrophages
Endotoxin | Activates host cells to secrete inflammatory mediators (prostaglandins, interleukin-1β, tumor necrosis factor-α)
Bacteriocin | May inhibit growth of beneficial species
Immunosuppressive factors | May inhibit IgG and IgM production
Collagenases | Cause degradation of collagen
Chemotactic inhibition factors | May inhibit neutrophil chemotaxis
Leukotoxin production varies significantly among strains of _A.a._ (Brogan _et al_. 1994; Kolodrubetz _et al_. 1989; Spitznagel _et al_. 1991; Zambon _et al_. 1983a). The strainspecific difference in leukotoxin production seems to be regulated at the level of transcription (Spitznagel _et al_. 1991). Brogan _et al_. (1994) detected a 530 bp deletion in the promoter region of the leukotoxin operon and found that strains with this feature produced 10–20 times more leukotoxin. Subsequent analysis showed that the occurrence of such highly toxigenic strains coincided with the high frequency of serotype b in patients with localized juvenile periodontitis, and that these strains actually constituted a specific clone of serotype b, now referred to as the JP2 clone (the initial isolate of this clone is strain JP2, from an African American child with prepubertal periodontitis) (Tsai _et al_. 1984). Extensive further research (Poulsen _et al_. 1994; Haubek _et al_. 1995, 1996, 1997, 2001; Tinoco _et al_. 1997; Bueno _et al_. 1998; He _et al_. 1999; Macheleidt _et al_. 1999; Mombelli _et al_. 1999; Contreras _et al_. 2000; Haraszthy _et al_. 2000; Tan _et al_. 2001; Cortelli _et al_. 2005) has clearly identified the JP2 clone as a common isolate in patients of North and West African descent suffering from aggressive periodontitis, even if they lived in another geographical region (e.g. North and South America or Europe). The disease association of RFLP type II reflects the fact that the JP2 clone represents a subpopulation of strains showing the RFLP type II pattern.
Our current knowledge with regards to the genetic and phenotypic diversity of _A.a._ , and its distribution in various populations and cohorts, with or without a clinical diagnosis of LAP, suggests that _A.a._ may be considered an opportunistic pathogen, or even a commensal bacterial species as a whole. However, at least one distinct subpopulation, the JP2 clone, displays the properties of a true pathogen in at least one group of humans of North and West African descent (Kilian _et al_. 2006). Prevention of vertical transmission of such virulent clones may a be feasible measure to prevent AgP (Van Winkelhoff & Boutaga 2005).
Generalized aggressive periodontitis (GAP), formerly named generalized early onset periodontitis (G-EOP) and rapidly progressive periodontitis (RPP), has been frequently associated with the detection of _Porphyromonas gingivalis_ , _Bacteroides forsythus_ and _A.a._ In contrast to _A.a._ , which is facultatively anaerobic, _P. gingivalis_ and _B. forsythus_ are fastidious strict anaerobes. _P. gingivalis_ produces several potent enzymes, in particular collagenases and proteases, endotoxin, fatty acids, and other possibly toxic agents (Shah 1993). A relationship between the clinical outcome of therapy and bacterial counts has also been documented for _P. gingivalis_ , and non-responding lesions often contain this organism in elevated proportions. High local and systemic immune responses against this bacterium have been demonstrated in patients with GAP (Tolo & Schenck 1985; Vincent _et al_. 1985; Ebersole _et al_. 1986; Murray _et al_. 1989).
### Bacterial damage to the periodontium
Disease-associated bacteria are thought to cause destruction of the marginal periodontium via two related mechanisms: (1) the direct action of the micro-organisms or their products on the host tissues, and/or (2) as a result of their eliciting tissue-damaging inflammatory responses (see Chapter 11) (Tonetti 1993). The relative importance of these two mechanisms in AgP remains speculative. Human investigations have indicated that _Aggregatibacter actinomycetemcomitans_ is able to translocate across the junctional epithelium and invade the underlying connective tissue (Saglie _et al_. 1988). These data support the hypothesis that direct bacterial invasion may be responsible for some of the observed tissue breakdown. Data from chronic periodontitis, however, seem to indicate that two thirds of attachment loss and alveolar bone resorption is preventable through the action of non-steroidal anti-inflammatory drugs, and therefore tissue destruction seems to be driven by the inflammatory process (Williams _et al_. 1985, 1989). Apical spread of bacteria loosely adhering to the hard, non-shedding surface of the tooth is thought to be controlled through a first line of defense consisting of mechanisms such as the high turnover of junctional epithelium keratinocytes, the outward flow of crevicular fluid, and the directed migration of polymorphonuclear leukocytes through the junctional epithelium; the efficiency of these innate immune mechanisms is highly enhanced by the presence of specific antibodies and complement fragments in the gingival crevicular fluid (Page 1990) (Table 19-3) (see Chapter 11).
### Host response to bacterial pathogens
Both local and systemic host responses to AgPassociated microflora have been described. Local inflammatory responses have been characterized by an intense recruitment of polymorphonuclear leukocytes (PMNs) both within the tissues and into the periodontal pocket. Such a preponderance of PMNs underlines the importance of these cells in the local defense against bacterial aggression and their potential role in host-mediated tissue destruction. B cells and antibody-producing plasma cells represent a significant component of the mononuclear cell-dominated connective tissue lesion (Liljenberg & Lindhe 1980). Plasma cells have been shown to be predominantly IgG-producing cells, with a lower proportion of IgA-producing cells (Mackler _et al_. 1977, 1978; Waldrop _et al_. 1981; Ogawa _et al_. 1989). Local IgG4-producing cells, in particular, seem to be elevated. Another important component of the local inflammatory infiltrate are T cells. Subset analysis of local T cells has indicated a depressed T-helper to T-suppressor ratio as compared to both healthy gingiva and peripheral blood. These findings have been interpreted to suggest the possibility of altered local immune regulation (Taubman _et al_. 1988, 1991). Peripheral blood mononuclear cells from AgP patients have been reported to exhibit a reduced autologous mixed lymphocyte reaction, as well as a higher than normal response to B cell mitogens (for review see Engel 1996). Local inflammatory responses are characterized by high levels of PGE2, IL-1α and IL-1β in both crevicular fluid and tissue (Masada _et al_. 1990; Offenbacher _et al_. 1993). PGE2 production, in particular, has been shown to be highly elevated in AgP subjects when compared to periodontally healthy individuals and chronic periodontitis patients.
**Table 19-3** Host defense mechanisms in the gingival sulcus (modified from Page 1990)
Intact epithelial barrier and epithelial attachment
---
Salivary flushing action, agglutinins, antibodies
Sulcular fluid flushing action, opsonins, antibodies, complement and other plasma components
Local antibody production
High levels of tissue turnover
Presence of normal flora or beneficial species
Emigrating PMNs and other leukocytes
Specific antibodies against AgP-associated micro-organisms (Lally _et al_. 1980; Steubing _et al_. 1982; Ebersole _et al_. 1984, 1985a,b) and cleaved complement fragments (Schenkein & Genco 1977; Patters _et al_. 1989) have also been detected in crevicular fluid from AgP lesions. Of interest is the evidence indicating that crevicular fluid titers of antibodies against AgP-associated microorganisms are frequently higher than in the serum of the same patient (Ebersole _et al_. 1984, 1985a,b). This observation, together with substantial _in vitro_ and _ex vivo_ data, strongly suggests that substantial fractions of these antibodies are locally produced in the inflammatory infiltrate (Steubing _et al_. 1982; Hall _et al_. 1990, 1991, 1994). Substantial titers of antibodies against _A.a._ and _P. gingivalis_ have also been detected in the serum of AgP patients. Furthermore, in some patients, titers of antibodies reactive with _A.a._ have been shown to be as high as the ones against _Treponema pallidum_ present in tertiary syphilis (0.1–1 g/ml) ; this clearly indicates the extent of host response that can be mounted against these periodontal pathogens (for a review see Ebersole 1990, 1996).
Recent investigations have identified the immunodominant _A. actinomycetemcomitans_ antigen to be the serotype-specific carbohydrate; furthermore, it has been shown that the vast majority of antibodies reactive with this carbohydrate in AgP patients consist of IgG2 (Califano _et al_. 1992). High titers and high avidity of _A.a.-_ specific IgG2 have been demonstrated in LAP patients, where high antibody titers are thought to be associated with the host's ability to localize attachment loss to few teeth; conversely, GAP patients are frequently seronegative for _A.a._ or display low titers and avidity. Anti- _A.a._ serotype polysaccharide IgG2, therefore, are considered to be protective against widespread AgP (Tew _et al_. 1996).
Of importance are findings reporting antibody response to _P. gingivalis_ in GAP forms. Patients suffering from these forms of disease frequently show both low levels of serum antibodies against _P. gingivalis_ and low levels of antibody avidity, indicating a specific inability of some GAP patients to cope effectively with these bacteria. Importantly, however, both titers and avidity of antibodies reacting with _P. gingivalis_ can be improved as a result of therapy.
Another important aspect of host response towards AgP microorganisms has been the recognition that PMNs of some LAP and GAP patients present decreased migration and antibacterial functions (Genco _et al_. 1980, 1986; Van Dyke _et al_. 1982, 1986, 1988). These abnormalities are frequently minor in the sense that they are usually not associated with infections other than periodontitis. A key report has indicated that PMN abnormalities in LAP patients seem to cluster in families much in the same way as AgP does (Fig. 19-8) (Van Dyke _et al_. 1985). This evidence has been interpreted as a suggestion that the LAP-associated PMN defect may be inherited. Other recent reports have indicated that PMN abnormalities in LAP patients may be, at least in part, the result of a hyper-inflammatory state resulting in the presence of proinflammatory cytokines in the serum of some AgP patients (Shapira _et al_. 1994; Agarwal _et al_. 1996).
## Genetic aspects of host susceptibility
Several family studies have indicated that the prevalence of AgP is disproportionately high among certain families, where the percentage of affected siblings may reach 40–50% (Saxen & Nevanlinna 1984; Beaty _et al_. 1987; Long _et al_. 1987; Boughman _et al_. 1992; Marazita _et al_. 1994; Llorente & Griffiths 2006). Such a dramatic familial aggregation of cases indicates that genetic factors may be important in susceptibility to AgP. Genetic studies in these families suggest that the pattern of disease transmission is consistent with mendelian inheritance of a gene of major effect (Saxen & Nevanlinna 1984; Beaty _et al_. 1987; Boughman _et al_. 1992; Hart _et al_. 1992; Marazita _et al_. 1994). This means that the observed familial pattern can be partly accounted for by one or more genes that could predispose individuals to develop AgP.
**Fig. 19-8** (a) Patients suffering from LAP in 22 families are represented by solid black figures. In each family the proband is on the left. (b) Diagrammatic representation of sibships involved in study group. Numbers are the same as in (a). Solid black figures represent patients exhibiting depressed neutrophil chemotaxis. In this group, after correcting for sampling bias, 40% of subjects present with abnormal chemotaxis. Subjects in sibship 8 are identical twins. From Van Dyke et al. (1985).
Segregation analyses have indicated that the likely mode of inheritance is autosomal dominant (Fig. 19-9a) (Saxen & Nevanlinna 1984; Beaty _et al_. 1987; Hart _et al_. 1992; Marazita _et al_. 1994). Most of these investigations, however, were carried out in African-American populations; it is therefore possible that other modes of inheritance may exist in different populations. Segregation analysis can provide information about the mode of inheritance of a genetictrait but does not provide information about the specific gene (s) involved. The chromosomal location of a gene of major effect for a trait such as AgP susceptibility can be determined by linkage analysis. An investigation utilizing this methodology reported linkage of LAP to the vitamin D binding locus on region q of chromosome 4 in a large family of the Brandywine population (Boughman _et al_. 1986). These results, however, were not confirmed in a sub-sequent study utilizing a different population (Hart _et al_. 1993). A recent study has linked localized AgP with the q25 region of chromosome 1 in an area close to the cyclo-oxygenase 2 (COX-2) gene (Li _et al_. 2004). Another has established evidence of linkage with the q13–14 region of chromosome 2 that contains the IL-1 gene complex (Scapoli _et al_. 2005). Such data are currently considered to support the existence of genetic heterogeneity in LAP forms, and of distinct forms of AgP. Therefore, it is currently maintained that although formal genetic studies of AgP support the existence of a gene of major effect, it is unlikely that all forms of AgP are due to the same genetic variant (Hart 1996; Loos _et al_. 2005). This notion is consistent with the fact that numerous diseases and syndromes with similar clinical appearance are known to result from different genetic polymorphisms.
**Fig. 19-9** (a) Genetic predisposition to AgP is determined by a single gene of major effect, inherited as an autosomal dominant trait. (b) Modifying genes may control immune responses that determine the clinical extent and severity of periodontal destruction in AgP. Here an allele controlling IgG2 levels is inherited as a codominant trait. (c) Independent inheritance of major locus and modifying locus illustrating how LAP and GAP may segregate within the same family. The propensity to develop AgP is dependent upon inheritance of a major susceptibility gene. The clinical phenotype is dependent upon host ability to produce IgG2 in response to periodontopathic bacteria. High IgG2 titers limit disease extension. Intermediate and low IgG2 titers are less effective in limiting intermediate disease progression. From Schenkein (1994), as modified by Hart (1996), with permission from the American Academy of Periodontology.
A recent study providing an additional line of evidence for a genetic component to aggressive periodontitis has shown that quantitative measures of periodontal parameters show substantial levels of hereditability in AgP patients (Diehl _et al_ ,. 2005).
Based on current knowledge that AgP subjects present high prevalence of PMN function defects, that they have been shown to produce high levels of inflammatory mediators in response to LPS stimulation, and of the relevance of connective tissue homeostasis in periodontitis, several loci have been proposed as genes conferring increased susceptibility to AgP. Hart (1996) compiled a list of candidate genes (Table 19-4) associated with increased susceptibility to AgP.
**Table 19-4** Genes known to affect human PMN function or host response to LPS load and/or thought to be among the candidate genes of major effect in EOP susceptibility
A series of studies has been performed to assess whether or not specific polymorphisms in these candidate genes were associated with AgP (for a recent review see Shapira _et al_. 2005 and Loos _et al_. 2005). Significant associations have been observed for genes encoding for proteins that are associated with neutrophil function (Fu _et al._ 2002; Loos _et al._ 2003; Kaneko _et al._ 2004; Jordan _et al._ 2005; Nibali _et al._ 2006; de Souza & Colombo 2006), with inflammation and with the host ability to effectively deal with exposure to bacterial components such as endotoxin (Suzuki _et al._ 2004; Scapoli _et al._ 2005; Brett _et al._ 2005; Noack _et al._ 2006), and with connective tissue homeostasis (Suzuki _et al._ 2004; Park _et al._ 2006; Soedarsono _et al._ 2006). It should be emphasized, however, that the validity of the conclusions of the majority of these studies suffers from small sample sizes, study of a single or few specific polymorphisms in the gene, as well as failure to account for ethnic variations and correction for environmental factors (e.g. cigarette smoking) (Tonetti & Claffey 2005). These three factors may be responsible for false-positive associations and bigger studies need to be performed to establish consistent associations.
Besides genes of major effect that may determine susceptibility to AgP, other genes may act as modifying genes and influence clinical expression of the disease. In this respect, particular interest has been focused on the impact of genetic control on antibody responses against specific AgP-associated bacteria and against _A.a._ in particular. These studies have indicated that the ability to mount high titers of specific antibodies is race-dependent and probably protective (Gunsolley _et al_. 1987, 1988). This has been shown to be under genetic control as a co-dominant trait, independent of the risk for AgP. In individuals susceptible to AgP, therefore, the ability to mount high titers of antibodies (IgG2 in particular) may be protective and prevent extension of disease to a generalized form (Schenkein 1994; Diehl _et al._ 2003) (Fig. 19-9b,c). Allelic variations in the Fc receptor for IgG2 immunoglobulins have also been suggested to play a role in suboptimal handling of _A.a_. infections. PMN expressing the R131 allotype of FcγRIIa (i.e. an Fc receptor containing an arginine instead of a histidine at amino acid 131) show decreased phagocytosis of _A.a_. (Wilson & Kalmar 1996).
## Environmental aspects of host susceptibility
Recent evidence has indicated that, besides genetic influences, environmental factors may affect the clinical expression of AgP. In a large study, cigarette smoking was shown to be a risk factor for patients with generalized forms of AgP (Schenkein _et al_. 1995). Smokers with GAP had more affected teeth and greater mean levels of attachment loss than patients with GAP who did not smoke (Table 19-5). Environmental exposure to cigarette smoking, therefore, seems to add significant risk of more severe and prevalent disease to this group of already highly susceptible subjects. The mechanism (s) for this observation are not completely understood, but findings from the same group indicate that IgG2 serum levels as well as antibody levels against _A.a._ are significantly depressed in subjects with GAP who smoke. Since these antibodies are considered to represent a protective response against _A.a._ , it is possible that depression of IgG2 in smokers may be associated with the observed increase in disease extent and severity in these subjects.
**Table 19-5** Effect of smoking on extent and severity of GAP
**Smoking status** | **Mean percentage of sites with PAL ≥5 mm*** | **Mean PAL (mm)***
---|---|---
Smokers | 49.0 ± 3.9 | 2.78 ± 0.2
Non-smokers | 36.8 ± 3.8 | 2.14 ± 0.2
* Values adjusted for age and mean plaque index, subject as unit of analysis. Smokers showed significantly greater extent and severity of periodontal disease than non-smokers after correcting for age and oral hygiene level.
Modified from Schenkein _et al_. (1995).
## Current concepts
Aggressive forms of periodontitis are currently considered to be multifactorial diseases developing as a result of complex interactions between specific host genes and the environment. Inheritance of AgP susceptibility is probably insufficient for the development of disease: environmental exposure to potential pathogens endowed with specific virulence factors is also a necessary step. Host inability to effectively deal with the bacterial aggression and to avoid inflammatory tissue damage results in the initiation of the disease process. Interactions between the disease process and environmental (e.g. cigarette smoking) and genetically controlled (e.g. IgG2 response to _A.a._ ) modifying factors are thought to contribute to determining the specific clinical manifestation of disease (Figs. 19–9a-c and 19-10).
# Diagnosis
## Clinical diagnosis
Clinical diagnosis is based on information derived from a specific medical and dental history and from the clinical examination of the periodontium. Limitations that will be discussed in this section, however, frequently require supplementation of clinical and anamnestic parameters with other, more advanced aids to properly diagnose, plan treatment for and monitor these diseases. The purpose of clinical diagnosis is the identification of patients suffering from AgP and of factors that have an impact on how the case should be treated and monitored.
In the diagnosis of AgP the initial question that the clinician should ask is:
* Is there periodontitis?
This may sound like a trivial question, but in fact many cases of AgP are currently not identified because of a failure to detect signs of periodontitis. Conversely, some clinicians attribute to periodontitis pathological changes associated with other unrelated and sometimes self-limiting processes. Correctly answering this question requires systematic collection of clinical information regarding the following items:
**Fig. 19-10** Diagrammatic representation of the current understanding of the ecogenetic interactions leading to development of LAP and GAP in African-American populations. (See text for explanation.)
* Is there loss of periodontal support (loss of clinical attachment and marginal resorption of alveolar bone) ?
* Is the loss of attachment accompanied by pocket formation or mostly the result of recession?
* Is there a plausible cause for attachment loss other than periodontitis?
* Is there another process imitating periodontal disease by pseudopocket formation?
From a clinical standpoint, it is important to realize that clinically detectable loss of attachment may occur as a result of pathological events other than periodontitis. Examples are traumatic injuries, removal or presence of impacted teeth (Kugelberg 1992), tooth position, orthodontic tooth movement, advanced decay, subgingival margins of restorations, etc. This means that the clinician must recognize different causes for attachment loss and must rule out other causes of attachment loss by a combination of careful clinical examination and assessment of the dental history. Orthodontic considerations are necessary to evaluate attachment loss without pocket formation (recession). In such instances the appropriate clinical diagnosis may be _incidental attachment loss_.
After establishing the presence of periodontitis, the clinician should determine which clinical diagnosis best describes the disease in the individual patient: chronic, aggressive or necrotizing periodontitis. Since the current classification is based on the combination of clinical presentation, rate of disease progression, and pattern of familial aggregation of cases in the absence of a systemic cause for the clinical observations, the next questions should address these parameters:
* Does the patient have a systemic condition that would in itself explain the presence of periodontitis?
As indicated, the diagnosis of chronic, aggressive or necrotizing periodontitis implies presence of periodontal destruction in the absence of systemic diseases that may severely impair host defense. A well constructed and well taken medical history is fundamental for identifying the presence of systemic involvements accompanied with periodontitis (see Chapter 7). Careful questioning regarding recurrent infections, their familiarity, presence of severe diseases or their symptoms and signs should be part of the evaluation of all periodontal patients. Consultation with the attending physician and evaluation of laboratory parameters are frequently necessary. Understanding of the medical condition that may be associated with periodontitis is fundamental. Some conditions are relatively frequent disorders such as poorly controlled diabetes mellitus; others are rare inherited disorders such as the palmo-plantar keratosis (Papillon-Lefèvre and Heim-Munk syndromes) or hypophosphatasia. Some are inborn defects such as the leukocyte adhesion deficiencies (LAD) ; others are acquired following exposure to pharmacological agents such as drug-induced granulocytopenia. Positive confirmed history of a significant systemic condition results in the diagnosis of _periodontal manifestation of systemic disease_.
In such instances, the periodontitis is likely to represent an oral manifestation of the systemic disease. Examples of significant conditions are AIDS, leukemia, neutropenia, diabetes or rare genetic diseases such as histiocytosis X, Papillon-Lefèvre syndrome or Chediak-Steinbrinck-Higashi syndrome (see Chapter 11 and Fig. 19-4).
In the absence of significant systemic components, the next questions relate to the exclusion of the rare but clearly identified necrotizing/ulcerative forms. The question will then be:
* Does the patient have signs or symptoms of necrotizing periodontitis?
If the answer to both of the previous questions is negative, differential diagnosis between chronic or aggressive periodontitis will be required. In this respect it is important to observe that chronic periodontitis has been defined as the common form of periodontitis whose diagnosis is done by excluding the presence of aggressive periodontitis (Armitage 1999). Diagnosis of AgP is made by verification of the satisfaction by the individual cases of the primary and secondary features described in the international classification workshop (see discussion above).
In this respect it must be recognized that the features include both clinical and laboratory aspects. In the diagnosis of a case, clinical and history parameters are initially utilized to suspect the presence of AgP, while laboratory tests are frequently utilized to confirm the diagnosis. In this respect, it is important to realize that periodontal diagnosis based only on periodontal probing and dental radiography does not classify causes; rather, it describes destruction patterns.
A tentative clinical diagnosis of AgP is made based on the following criteria:
* Absence of significant systemic conditions
* Rapid attachment loss and bone destruction
* Familial aggregation of cases
* Lack of consistency between clinically visible bacterial deposits and severity of periodontal breakdown.
A rapid rate of destruction of the periodontium is a major criterion for the diagnosis of AgP. It is aimed at identifying subjects characterized by high virulence of the microflora and/or high levels of susceptibility. Although correct application of this criterion requires availability of clinical or radiographic data from more than one time point, presence of severe destruction in relation to the age of the subject is frequently considered to be sufficient information to infer rapid progression.
Establishing the presence of familial aggregation of cases is based on a combination of history and clinical examination of family members of the affected individual. At this stage there is inadequate evidence to establish the best approach to obtain a significant estimation of familial aggregation. A recent study, in particular, questioned the reliability of family history as a way to establish familial aggregation (Llorente & Griffiths 2006).
It is maintained that in the majority of AgP cases the amount of periodontal destruction seems to be higher than that expected from the mere accumulation of local factors. This observation, however, may not be true for all cases. In general, a discrepancy between local factors and the amount of periodontal tissue breakdown is considered to be an indication for either infection with particularly virulent micro-organisms, or presence of a highly susceptible host. This information may be consequential in determining surgical goals of therapy, the impact of antibiotics, and the possible impact of sub-optimal hygiene as a risk factor for disease recurrence.
The international classification workshop consensus indicated that not all listed primary and secondary features need to be present in order to assign an AgP diagnosis and that the diagnosis may be based on clinical, radiographic, and historical data alone. It also indicated that laboratory testing, although helpful, might not be essential in making an AgP diagnosis.
Once an AgP diagnosis has been made based on the criteria above, differential diagnosis between LAP and GAP needs to be made. In this respect specific clinical features have been suggested. A diagnosis of LAP is made based on evidence of circumpubertal onset and localized first molar/incisor presentation with interproximal attachment loss on at least two permanent teeth, one of which is a first molar, and involving no more than two teeth other than first molars and incisors. A diagnosis of GAP takes into account the fact that this form of disease usually affects persons under 30 years of age (but patients may be older) and that it presents with generalized interproximal attachment loss affecting at least three permanent teeth other than first molars and incisors. Furthermore this pathology is characterized by a pronounced episodic nature of the destruction of attachment and alveolar bone. The differential diagnosis may benefit from additional laboratory investigations of the individual host response to the infecting organisms.
In order to properly describe the specific AgP case, modifying factors should also be explored by addressing the question of the presence of modifying or contributory factors such as smoking or drug abuse. Such additional information is relevant since these factors may explain a specific presentation of disease in terms of its extent and severity. Furthermore, these factors, unlike genetic factors, are amenable to modification through appropriate intervention. Therapy should therefore include an approach aimed at controling the impact of these factors.
Even though differential diagnosis between AgP and chronic periodontitis and differentiation between LAP and GAP is mostly based on history and clinical presentation, it must be emphasized that clinical parameters alone cannot further discriminate between forms of disease with similar clinical appearance. Inferences regarding a specific etiology are speculative under such circumstances and require further laboratory testing for confirmation.
In the previous classification system, age at onset or age at diagnosis was considered helpful to further characterize specific clinical syndromes. LAP, in particular, is thought to occur in adolescents, 13–14 years old to 25 years, while GAP is generally found in adolescents or young adults of less than 30–35 years. It should be realized, however, that (1) some cases may present initial LAP at an earlier age, (2) LAP may start before puberty and affect the primary dentition, (3) patterns of periodontal destruction compatible with LAP may be initially detected at an age older than 25, and (4) there may be a tendency toward spreading from a localized to a generalized pattern of AgP in older subjects of these groups.
Another difficulty is related to the fact that periodontal destruction is often diagnosed when the attachment loss is already fairly advanced. In general, distinct alterations in the morphology of the periodontium and substantial tissue damage are necessary for establishing a clear diagnosis. Milder or initial stages of disease or sites at risk for future periodontal breakdown cannot be detected based on clinical parameters. This makes it difficult to intercept and treat initial forms of AgP. Furthermore, such difficulty makes it extremely important to examine the other members of the family of the proband as well: siblings may present with clinically undetectable disease in spite of the presence of the putative pathogens. A common strategy employed to overcome the insufficient ability of clinical parameters to detect early disease is to closely monitor high-risk patients such as the siblings of the probands. It is in this respect important to underline that "incidental attachment loss" may, in some cases, represent an initial manifestation of AgP. In such a case an isolated periodontal lesion characterized by attachment loss with pocketing may represent the only clinically evident AgP lesion. Such subjects should, therefore, be considered at high risk for the development of AgP and require close monitoring and possibly further microbiologic diagnosis.
## Microbiologic diagnosis
The presence of specific microorganisms is considered as one of the secondary features of AgP. A systematic review has, however, clearly indicated that the presence or absence of suspected periodontal pathogens such as _A.a._ on the species level cannot fully discriminate subjects with AgP from subjects with chronic periodontitis. Although it is more than ten times more likely that _A.a._ -negative patients suffer from chronic than from aggressive periodontitis, any _A.a._ -positive individual with periodontitis is three times more likely to be suffering from chronic than from aggressive periodontitis (Mombelli _et al_. 2002). The noted limitations in discriminating power to distinguish AgP from ChP should not be interpreted to mean that a test aiming at the detection of target microorganisms is completely useless in any clinical situation. Treatment studies suggest that _A.a._ is particularly difficult to suppress with conventional mechanical therapy (Mombelli _et al_. 1994a, 2000), longitudinal and retrospective studies have indicated an increased risk for periodontal breakdown in positive sites (Fine 1984; Slots _et al_. 1986; Bragd _et al_. 1987; Slots & Listgarten 1988; Rams _et al_. 1996), and results of treatment seemed to be better if _A.a._ could not be detected any more at follow up (Bragd _et al_. 1987; Carlos _et al_. 1988; Haffajee _et al_. 1991; Grossi _et al_. 1994; Haffajee & Socransky 1994). Therefore, even if microbiologic testing alone cannot distinguish between chronic and aggressive periodontitis, access to microbiologic data may improve the outcome of periodontal therapy. This should be taken into account particularly with regards to the highly leukotoxic variant of _A.a._ , which shows a stronger association with AgP than _A.a._ as a whole. In discussing the diagnostic potential of a test, one should also consider that the main difference between clinical groups may not be the prevalence but rather the amount of putative pathogens found in positive samples (Gunsolley _et al_. 1990).
Microbiologic data may be useful to establish a differential diagnosis in patients clinically diagnosed with AgP. Knowledge of whether a clinical condition is associated with _A.a._ , and/or with other periodontal pathogens, such as _P. gingivalis_ , has an impact on the need to supplement conventional therapy with antibiotics and on the choice of the antimicrobial drug (see Chapter 42). Microbiologic information can be useful at different stages of the treatment plan, i.e. as a part of the initial diagnosis, at re-evaluation or during the recall phase. The need for microbiologic information before therapy depends on the general strategy for treatment. Many clinicians prefer to remove bacterial deposits mechanically in a first treatment phase without the adjunctive use of systemic antibiotics. As microbiologic findings have no influence on the way this initial treatment is performed, microbiologic testing may be postponed until the first phase is completed. One should keep in mind, however, that the reduction in bacterial load might increase the possibility of false-negative results when an insensitive microbiologic test is used. If the specific clinical diagnosis is LAP, then the clinician can assume even without a microbiologic test that the treatment should be directed towards a maximal suppression of _A.a._ This is due to the fact that the great majority of LAP patients are infected with this organism. This is different for all other forms of AgP, where such a close association of one microbial species with the disease cannot be assumed, and therefore microbial testing should be performed.
Since _A.a._ and _P. gingivalis_ can be transmitted from periodontal patients to family members, microbial testing of spouses, children or siblings of AgP patients may be indicated to intercept early disease in susceptible individuals.
## Evaluation of host defenses
Several forms of AgP have been associated with impairment of host defenses. Classic studies have indicated that in some populations both LAP and GAP forms are associated with high incidence of phagocyte functional disturbances, such as depressed neutrophil chemotaxis and other phagocyte anti-bacterial dysfunctions. In many of these patients, AgP was the only infection that was associated with the reduced phagocyte function (s) ; this observation is important in two respects. First, AgP-associated phagocyte defects are frequently insignificant in terms of increasing susceptibility to infections other than periodontitis. Furthermore, it is likely that such "mild" leukocyte defects may go unnoticed until laboratory testing is performed in conjunction with periodontal diagnosis. Reports of such phagocyte defects relate mostly to AgP subjects from African American groups; systematic evaluations of PMN and monocyte functions associated with clinical diagnosis of AgP in European Caucasians failed to confirm a high prevalence of abnormalities (Kinane _et al_. 1989a,b). Testing for these host defense parameters, therefore, may be more restricted to specific populations. Another important aspect is that, so far, no specific study has attempted to associate treatment response or incidence of recurrent disease with the presence of the above-mentioned abnormalities.
More recent investigations have indicated that specific patterns of host response to bacterial pathogens are associated with different forms of AgP; this early evidence may be extremely helpful for the development of clinically useful tests to estimate the risk of developing AgP. In this respect two findings deserve to be mentioned:
1. AgP patients present significantly higher levels of crevicular fluid PGE2 than chronic periodontitis patients or healthy subjects. This finding may indicate that monocytes from these patients respond to bacterial and inflammatory stimuli with very high levels of local release of inflammatory mediators. These may induce an exuberant inflammatory reaction associated with high levels of activation of tissue-degrading matrix-metalloproteinases.
2. GAP patients have a decreased ability to mount high titers of specific IgG2 antibodies to _A.a._ These subjects exhibit a tendency towards progressive periodontal destruction leading to tooth loss over a relatively short period of time. LAP patients, on the other hand, seem to have better prognosis and do not express this trait. Since there are indications that at least some LAP cases may progress into generalized forms, early detection of patients infected with _A.a._ but producing low levels of specific antibodies may allow early identification of a high-risk group for development of GAP. Serum antibody titers (IgG2 in particular) and/or avidity to _A.a._ may be particularly useful in the differential diagnosis of GAP and LAP syndromes and in the early detection of the LAP cases with high risk for progression into the more widespread forms of disease.
## Genetic diagnosis
Given the disproportionately high incidence of AgP in the families of affected individuals, evaluation of siblings of the proband and other family members is a requirement. Clinical determination of different disease forms in the family should be followed by construction of a pedigree of the AgP trait. Such diagnosis may bring considerable information regarding the level of risk eventually shared within the family. Furthermore, it helps to establish the need for monitoring clinically unaffected individuals.
All the evidence gathered during the diagnostic process should contribute to the definition of a specific diagnosis. An example of such diagnosis is illustrated in Fig. 19-11: LAP in a 22-year-old systemically healthy African American female patient, associated with _A.a._ infection without detectable levels of _P. gingivalis_ , inconsistency between local factors and amount of clinically detectable breakdown, absence of demonstrable leukocyte defects, no known contributory factors, and no siblings displaying clinically detectable periodontitis.
# Principles of therapeutic intervention
Treatment of AgP should only be initiated after completion of a careful diagnosis by a specifically trained periodontist. The severity of some of the AgP forms suggests that specialists, possibly working in association with highly specialized centers, could best perform both diagnosis and treatment of these rare forms of periodontitis. The roles of the general practitioner, the pedodontist or the orthodontist, however, are fundamental in the detection of possible cases to be referred for further evaluation and therapy.
Successful treatment of AgP is considered to be dependent on early diagnosis, directing therapy towards elimination or suppression of the infecting microorganisms and providing an environment conducive to long-term maintenance. The differential element of treatment of AgP, however, relates to specific efforts to affect the composition and not only the quantity of the subgingival microbiota.
## Elimination or suppression of the pathogenic flora
_A.a._ elimination has been associated with successful therapy; conversely, recurrent lesions have been shown to still harbor this organism. Several investigators have reported that scaling and root planing of juvenile periodontitis lesions could not predictably suppress _A.a._ below detection levels (Slots & Rosling 1983; Christersson _et al_. 1985; Kornman & Robertson 1985). Soft tissue curettage and access flap therapy also had limited success in eliminating _A.a_. (Christersson _et al_. 1985).
_A.a._ is also difficult to eliminate by conventional mechanical therapy in adult periodontitis patients, and it is therefore not surprising to observe the presence of this microorganism in the subgingival microflora of many non-responding periodontitis patients (Bragd _et al_. 1985; van Winkelhoff _et al_. 1989; Renvert _et al_. 1990a,b; Rodenburg _et al_. 1990; Mombelli _et al_. 1994a). Similar, but less systematic observations have also been reported for the ability to suppress the microflora associated with some GAP forms, where high subgingival loads of _P. gingivalis_ , _B. forsythus_ , _A.a._ , and other highly virulent bacteria are frequently detected.
**Fig. 19-11** (a,b) Clinical and radiographic presentation of a 22-year-old African-American female. Clinical attachment loss and alveolar bone loss are localized on the mesial aspect of the first molars, where deep, vertical defects are apparent. (c–e) Detailed views of the defect on the mesial aspect of 26. No other tooth appears to be affected. Microbiology (DNA probe analysis of _A. actinomycetemcomitans_ , _P. gingivalis_ and _P. intermedia_ ) confirmed the presence of high levels (>104 bacteria/sample) of _A. actinomycetemcomitans_ in all four deep lesions. _Pr. intermedia_ was also detectable in three of four sites, while _P. gingivalis_ was undetectable. The patient did not display abnormal leukocyte functions; furthermore, she had a non-contributory medical history, and did not smoke. She had a younger brother (15 years old) and an older sister (27 years old) ; on clinical examination, the periodontium of both of them appeared to be within normal limits. The following diagnosis was made: "LAP in a 22-year-old systemically healthy African-American female; associated with _A. actinomycetemcomitans_ infection without clinically detectable levels of _P. gingivalis_ ; absence of demonstrable leukocyte defects; no known contributory factors; no cigarette smoking; no siblings displaying clinically detectable AgP".
Use of antibiotics has been suggested as a rational complement to mechanical debridement in these cases. Regimens, including the adjunctive administration of tetracyclines or metronidazole, have been tested for the treatment of LAP and other forms of AgP (see Chapter 42).
The choice of antibiotic can either be empiric (based on published information on the efficacy of the regimen in similar populations) or guided by information about the nature of the involved pathogenic microorganism (s) and/or their antibiotic susceptibility profile. Both approaches have been suggested but currently there is no direct evidence that microbiologic diagnosis and targeted selection of the antibiotic regimen provides an additional benefit compared to empiric use.
With regards to empiric use, effectiveness is based on outcomes of a series of trials that have specifically assessed the clinical outcomes following administration of a specific antibiotic regimen or placebo in combination with mechanical instrumentation of the root surface and oral hygiene instructions. The approach is supported by a meta-analysis (Haffajee _et al._ 2003) indicating significantly greater clinical improvements following systemic antibiotic administration upon completion of subgingival instrumentation. Metronidazole in combination with amoxicillin may suppress _A.a._ more effectively than single antibiotic regimes and has thus become increasingly popular. Substantial evidence indicates that subgingival _A.a._ can be eliminated or suppressed for a prolonged period by mechanical debridement supplemented with systemic metronidazole plus amoxicillin.
Systemic antibiotics should only be administered as an adjunct to mechanical debridement because in undisturbed subgingival plaque the target organisms are effectively protected from the antibiotic agent due to the biofilm effect (see Chapter 42).
Antibiotics have been used in essentially two ways for the treatment of AgP: (1) in combination with intensive instrumentation over a short period of time after achievement of adequate plaque control in a pretreatment motivation period; or (2) as a staged approach after completion of the initial therapy.
A recent randomized controlled clinical trial (Guerrero _et al._ 2005) has provided evidence of a significant benefit arising from a treatment approach consisting of: (1) achievement of adequate supragingival plaque control (less than 25% of tooth sites with detectable plaque) ; (2) subgingival instrumentation with a combination of hand and mechanical instruments delivered intensively over a 2-day period; (3) an adjunctive systemic antibiotic regimen consisting of metronidazole (500 mg, tid for 7 days) combined with amoxicillin (500 mg, tid for 7 days). The results of the placebo arm showed highly significant improvements in clinical parameters including reductions of probing depth and improvement of clinical attachment levels throughout the dentition. The adjunctive antibiotic provided additional benefits in the deeper pockets in terms of all parameters.
As part of the second option, treatment is started with an initial phase of mechanical therapy, including systematic scaling and planing of all accessible root surfaces and the introduction of meticulous oral hygiene. After a period of 4–6 weeks, the case is re-assessed clinically. Based on persistence of periodontal lesions, a second phase of therapy is planned. Decisions are made as to how to gain access to deep lesions with appropriate surgical procedures and concerning the administration of antimicrobial agents. Microbial samples from the deepest pocket in each quadrant may provide additional information about the presence and relative importance of putative pathogens. Systemic antimicrobial therapy with the appropriate agent is usually initiated immediately upon completion of the surgical interventions or immediatedly after another round of mechanical instrumentation to ensure that subgingival plaque deposits have been reduced as much as possible and to disrupt the subgingival biofilm.
Microbiologic testing, if performed, may be repeated at 1–3 months after completion of therapy to verify the elimination or marked suppression of the putative pathogen(s). After resolution of the periodontal infection, the patient should be placed on an individually tailored maintenance care program, including continuous evaluation of the occurrence and of the risk of disease progression. Optimal plaque the host immune response, and re-assessment of the control by the patient is of paramount importance for local and systemic modifying factors. Further therapy a favorable clinical and microbiologic response to should be targeted against putative periodontal therapy. Recurrence of disease is an indication for a pathogens and should take into account the systemic repetition of microbiologic tests, for re-evaluation of immune responses of the subject.
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# Chapter 20
# Necrotizing Periodontal Disease
Palle Holmstrup and Jytte Westergaard
* * *
Nomenclature
Prevalence
Clinical characteristics
Development of lesions
Interproximal craters
Sequestrum formation
Involvement of alveolar mucosa
Swelling of lymph nodes
Fever and malaise
Oral hygiene
Acute and recurrent/chronic forms of necrotizing gingivitis and periodontitis
Diagnosis
Differential diagnosis
Histopathology
Microbiology
Microorganisms isolated from necrotizing lesions
Pathogenic potential of microorganisms
Host response and predisposing factors
Systemic diseases
Poor oral hygiene, pre-existing gingivitis, and history of previous NPD
Psychologic stress and inadequate sleep
Smoking and alcohol use
Caucasian background
Young age
Treatment
Acute phase treatment
Maintenance phase treatment
* * *
# Nomenclature
Necrotizing gingivitis (NG), necrotizing periodontitis (NP), and necrotizing stomatitis (NS) are the most severe inflammatory periodontal disorders caused by plaque bacteria. The necrotizing diseases usually run an acute course and therefore the term acute is often included in the diagnoses. They are rapidly destructive and debilitating, and they appear to represent various stages of the same disease process (Horning & Cohen 1995). A distinction between NG and NP has not always been made in the literature, but parallel to the use of the term gingivitis, NG should be limited to lesions only involving gingival tissue with no loss of periodontal attachment (Riley _et al_. 1992). Most often, however, the disease results in loss of attachment (MacCarthy & Claffey 1991), and a more correct term in cases with loss of attachment is NP, provided the lesions are confined to the periodontal tissues including gingiva, peri-odontal ligament, and alveolar bone. Further progression to include tissue beyond the mucogingival junction is characteristic of necrotizing stomatitis and distinguishes this disease from NP (Williams _et al_. 1990).
The necrotizing periodontal diseases have had several names, including ulceromembranous gingivitis, acute necrotizing ulcerative gingivitis (ANUG), Vincent's gingivitis or Vincent's gingivostomatitis, necrotizing gingivostomatitis, and trench mouth (Pickard 1973; Johnson & Engel 1986; Horning & Cohen 1995). Vincent first described the mixed fuso-spirochetal microbiota of the so-called "Vincent's angina", characterized by necrotic areas in the tonsils (Vincent 1898). A similar mixed microbiota has been isolated from NG lesions, but Vincent's angina and NG usually occur independently of each other, and should be regarded as separate disease entities.
NS has features in common with the far more serious _cancrum oris_ , also denoted noma. This is a destructive and necrotizing, frequently fatal, stomatitis in which the same mixed fusospirochetal flora dominates. It occurs almost exclusively in certain developing countries, mostly in children suffering from systemic diseases including malnutrition (Enwonwu 1972, 1985). It has been suggested that cancrum oris always develops from pre-existing NG (Emslie 1963) but this connection has not been confirmed (Pindborg _et al_. 1966, 1967; Sheiham 1966).
In the literature, a distinction between NG, NP, and NS is seldom made. However, the reader should be aware of this uncertainty and the consequences of the lack of distinction between the three diagnoses in reports. The uncertainty is reflected in the present chapter by the use of the term necrotizing periodontal disease (NPD) as a common denominator for necrotizing gingivitis, necrotizing periodontitis, and necrotizing stomatitis.
# Prevalence
During World War II, up to 14% of Danish military personnel encountered NPD (Pindborg 1951a). Large numbers of civilians also suffered from the disease (King 1943; Stammers 1944). After World War II, the prevalence of NPD declined substantially and it is now rare in industrialized countries. It occurs particularly among young adults. In the 1960s NPD was found in 2.5% of 326 US students during their first college year, but over the next year more students became affected, with a total of 6.7% demonstrating the disease during their first two college years (Giddon _et al_. 1964). Among 9203 students in Chile, 6.7% showed at least one necrotic ulcerated lesion on the papillae (Lopez _et al_. 2002), and the presence of necrotizing lesions was associated with the occurrence of clinical attachment loss (Lopez & Bælum 2004). Other studies in industrialized countries have reported prevalence of 0.5% or less (Barnes _et al_. 1973; Horning _et al_. 1990). In Scandinavia, the disease is now very rare among otherwise healthy individuals, with a prevalence of 0.001% among young Danish military trainees (personal communication, F. Prætorius). NPD can be observed in all age groups but there are geographic differences in the age distribution.
The disease seems to occur slightly more often among HIV-infected individuals. Studies among groups of HIV-infected individuals have revealed prevalences of NPD between 0% and 27.7% (Reichart _et al_. 2003; Holmstrup & Westergaard 1994). However, most studies have included cohorts of individuals connected with hospitals or dental clinics. Studies conducted outside these environments have shown relatively low prevalence figures. NP was found in 1% of 200 HIV-seropositive individuals in Washington, DC (Riley _et al_. 1992), and the prevalence may not, in fact, differ so much from that of the general population (Drinkard _et al_. 1991; Friedman _et al_. 1991; Barr _et al_. 1992); this is particularly true after introduction of antiretroviral therapy (Tappuni & Flemming 2001).
In developing countries, the prevalence of NPD is higher than in the industrialized countries, and the disease frequently occurs in children. This is practically never seen in western countries. In Nigerian villages, between 1.7% and 26.9% of 2–6-year-old children were found with NPD (Sheiham 1966). In India, 54–68% of NPD cases occurred in children below 10 years of age (Migliani & Sharma 1965; Pindborg _et al_. 1966).
# Clinical characteristics
## Development of lesions
NG is an inflammatory destructive gingival condition, characterized by ulcerated and necrotic papillae and gingival margins resulting in a characteristic punched-out appearance. The ulcers are covered by a yellowish white or grayish slough, which has been termed "pseudomembrane". However, the sloughed material has no coherence, and bears little resemblance to a membrane. It consists primarily of fibrin and necrotic tissue with leukocytes, erythrocytes, and masses of bacteria. Consequently, the term is misleading and should not be used. Removal of the sloughed material results in bleeding and ulcerated underlying tissue becomes exposed.
The necrotizing lesions develop rapidly and are painful, but in the initial stages, when the necrotic areas are relatively few and small, pain is usually moderate. Severe pain is often the chief reason for patients to seek treatment. Bleeding is readily provoked. This is due to the acute inflammation and necrosis with exposure of the underlying connective tissue. Bleeding may start spontaneously as well as in response to even gentle touch. In early phases of the disease lesions are typically confined to the top of a few interdental papillae (Fig. 20-1). The first lesions are often seen interproximally in the mandibular anterior region, but they may occur in any interproximal space. In regions where lesions first appear, there are usually also signs of pre-existing chronic gingivitis, but the papillae are not always edematous at this stage and gingival stippling may be maintained. Usually, however, the papillae swell rapidly and develop a rounded contour; this is particularly evident in the facial aspect. The zone between the marginal necrosis and the relatively unaffected gingiva usually exhibits a well demarcated narrow erythematous zone, sometimes referred to as the linear erythema. This is an expression of hyperemia due to dilation of the vessels in the gingival connective tissue in the periphery of the necrotic lesions (see Fig. 20-17a).
**Fig. 20-1** Necrotizing gingivitis with initial punched out defects at the top of the interdental papillae of the mandibular incisor region. Courtesy of Dr. Finn Prætorius.
A characteristic and pronounced _foetor ex ore_ is often associated with NPD, but can vary in intensity and in some cases is not very noticeable. Strong _foetor ex ore_ is not pathognomonic of NPD as it can also be found in other pathologic conditions of the oral cavity such as chronic destructive periodontal disease.
## Interproximal craters
The lesions are seldom associated with deep pocket formation, because extensive gingival necrosis often coincides with loss of crestal alveolar bone. The gingival necrosis develops rapidly and within a few days the involved papillae are often separated into one facial and one lingual portion with an interposed necrotic depression, a negative papilla, between them. The central necrosis produces considerable tissue destruction and a regular crater is formed. At this stage of the disease, the disease process usually involves the periodontal ligament and the alveolar bone, and loss of attachment is now established. The diagnosis of the disease process is consequently NP.
**Fig. 20-2** Necrotizing gingivitis progressing along the gingival margin of the right maxilla. The interproximal necrotizing processes have merged.
**Fig. 20-3** Necrotizing periodontitis with more advanced lesions of interdental papillae and gingival margin. Note the irregular morphology of the gingival margin as determined by the progressive loss of the interdental papillae.
Along with the papilla destruction, the necrosis usually extends laterally along the gingival margin at the oral and/or facial surfaces of the teeth. Necrotic areas originating from neighboring interproximal spaces frequently merge to form a continuous necrotic area (Figs. 20-2 and 20-3). Superficial necrotic lesions only rarely cover a substantial part of the attached gingiva, which becomes reduced in width as the result of disease progression. The palatal and lingual marginal gingiva is less frequently involved than the corresponding facial area. Frequently, gingiva of semi-impacted teeth and in the posterior maxillary region are affected (Figs. 20-4 and 20-5). Progression of the interproximal process often results in destruction of most interdental alveolar bone (Fig. 20-6). In more advanced cases, pain is often considerable and may be associated with a markedly increased salivary flow. As a result of pain it is often difficult for the patients to eat, and a reduced food intake may be critical to HIV-infected patients because they may already lose weight in association with their HIV infection.
**Fig. 20-4** Necrotizing gingivitis affecting gingiva of semiimpacted right mandibular third molar. Courtesy of Dr. Finn Prætorius.
**Fig. 20-5** Necrotizing periodontitis affecting right maxillary second molar periodontium. Note the extensive punched out lesion.
**Fig. 20-6** (a) Necrotizing periodontitis often results in major loss of interdental tissue including alveolar bone of the molar regions as demonstrated in the radiograph (b).
**Fig. 20-7** (a) Necrotizing periodontitis with sequestration of alveolar bone between left mandibular lateral incisor and canine. (b) The extension of the sequestrum as seen in the radiograph covers the interdental septum almost to the apices of the roots.
## Sequestrum formation
The disease progression may be rapid and result in necrosis of small or large parts of the alveolar bone. Such a development is particularly evident in severely immunocompromised patients including HIV-seropositive individuals. The necrotic bone, denoted a sequestrum, is initially irremovable but after some time becomes loosened, whereafter it may be removed with forceps. Analgesia may not be required. A sequestrum may not only involve interproximal bone but also include adjacent facial and oral cortical bone (Fig. 20-7).
## Involvement of alveolar mucosa
When the necrotic process progresses beyond the mucogingival junction, the condition is denoted NS (Figs. 20-8 and 20-9) (Williams _et al_. 1990). The severe tissue destruction characteristic of this disease is related to seriously compromised immune functions typically associated with HIV infection and malnutrition (Fig. 20-10). Importantly, it may be life-threatening. NS may result in extensive denudation of bone, resulting in major sequestration with the development of oro-antral fistula and osteitis (SanGiacomo _et al_. 1990; Felix _et al_. 1991).
**Fig. 20-8** (a) Necrotizing stomatitis affecting periodontium of left mandibular premolar region and adjacent alveolar mucosa. (b) After treatment and healing, no attached gingiva remains.
**Fig. 20-9** Necrotizing stomatitis of right maxilla with extensive necrotic ulcer of palatal mucosa.
## Swelling of lymph nodes
Swelling of the regional lymph nodes may occur in NPD but is particularly evident in advanced cases. Such symptoms are usually confined to the submandibular lymph nodes, but the cervical lymph nodes may also be involved. In children with NPD, swelling of lymph nodes and increased bleeding tendency are often the most pronounced clinical findings (Jiménez & Baer 1975).
## Fever and malaise
Fever and malaise is not a consistent characteristic of NPD. Some investigations indicate that elevated body temperature is not common in NG and that, when present, the elevation of body temperature is usually moderate (Grupe & Wilder 1956; Goldhaber & Giddon 1964; Shields 1977; Stevens _et al_. 1984). A small decrease in body temperature in NG has even been described. The disagreement on this point may, in fact, be due to misdiagnosis of primary herpetic gingivostomatitis as NG (see below).
## Oral hygiene
The oral hygiene in patients with NPD is usually poor. Moreover, brushing of teeth and contact with the acutely inflamed gingiva is painful. Therefore, large amounts of plaque on the teeth are common, especially along the gingival margin. A thin, whitish film sometimes covers parts of the attached gingiva (Fig. 20-11). This film is a characteristic finding in patients who have neither eaten nor performed oral hygiene for days. It is composed of desquamated epithelial cells and bacteria in a meshwork of salivary proteins. The film is easily removed.
In general, the clinical characteristics of NPD in HIV-seropositive patients do not essentially differ from those in HIV-seronegative patients. However, the lesions in HIV-seropositive patients may not be associated with large amounts of plaque and calculus. Thus, the disease activity in these patients sometimes shows limited correlation with etiologic factors as determined by the amount of bacterial plaque (Holmstrup & Westergaard 1994). Further, lesions of NPD in HIV-seropositive patients have sometimes been revealed in gingival tissue affected by Kaposi's sarcoma (Fig. 20-12).
## Acute and recurrent/chronic forms of necrotizing gingivitis and periodontitis
In most instances the course of the diseases is acute, characterized by the rapid destruction of the peri-odontal tissue. However, if inadequately treated or left untreated, the acute phase may gradually subside. The symptoms then become less unpleasant to the patient, but the destruction of the periodontal tissues continues, although at a slower rate, and the necrotic tissues do not heal completely. Such a condition has been termed chronic necrotizing gingivitis, or peri-odontitis in the case of attachment loss (Fig. 20-13).
**Fig. 20-10** (a) Necrotizing stomatitis affecting the mandible of an HIV-seropositive patient. (b) Two years after treatment the result of treatment is satisfactory, and there has been no recurrence.
**Fig. 20-11** A whitish film sometimes covers parts of the attached gingiva in patients with NPD as demonstrated in the maxillary gingiva. The film is composed of desquamated epithelial cells which have accumulated because the patient has not eaten or performed oral hygiene for days.
**Fig. 20-12** Necrotizing periodontitis affecting Kaposi's sarcoma of left maxillary central incisor gingiva in an HIV-infected patient. The sarcoma affected almost the entire maxillary gingiva after 9 months.
The necrotizing lesions persist as open craters, frequently with a content of subgingival calculus and bacterial plaque. Although the characteristic ulcerative, necrotic areas of the acute phase usually disappear, acute exacerbations with intervening periods of quiescence may also occur. In recurrent acute phases, subjective symptoms again become more prominent and necrotic ulcers reappear. Some authors prefer the term recurrent rather than chronic to describe this category of necrotizing disease (Johnson & Engel 1986). Plaque and necrotic debris are often less conspicuous in these phases than in the acute forms, because they are located in pre-existing interdental craters. Several adjoining interdental craters may fuse, resulting in total separation of facial and oral gingivae, which form two distinct flaps. Recurrent forms of NG and NP may produce considerable destruction of supporting tissues. The most pronounced tissue loss usually occurs in relation to the interproximal craters.
**Fig. 20-13** Chronic necrotizing periodontitis with edematous gingiva particularly of mandible. The slightly active necrotizing processes at the bottom of the negative papillae are not visible.
# Diagnosis
The diagnosis of NG, NP, and NS is based on clinical findings as described above. The patient has usually noticed pain and bleeding from the gingiva, particularly upon touch. The histopathology of the necrotizing diseases is not pathognomonic for NG, and biopsy is certainly not indicated in the heavily infected area.
## Differential diagnosis
NPD may be confused with other diseases of the oral mucosa. Primary herpetic gingivostomatitis (PHG) is not infrequently mistaken for NPD (Klotz 1973). The important differential diagnostic criteria for the two diseases are listed in Table 20-1. It should be noted that in the USA and in northern Europe, NPD occurs very rarely in children, whereas PHG is most commonly found in children. If the body temperature is markedly raised, to 38°C or more, PHG should be suspected. NG and NP has a marked predilection for the interdental papillae, while PHG shows no such limitation and may occur anywhere on the free or the attached gingiva, or in the alveolar mucosa (Fig. 20-14). In PHG erythema is of a more diffuse character and may cover the entire gingiva and parts of the alveolar mucosa. The vesicular lesions in PHG, which disrupt and produce small ulcers surrounded by diffuse erythema, occur both on the lips and tongue as well as on the buccal mucosa. PHG and NPD may occur simultaneously in the same patient, and in such cases there may be mucosal lesions outside the gingiva, and fever and general malaise tend to occur more frequently than with NPD alone.
**Table 20-1** Important characteristics for differential diagnosis between NPD and PHG
| **NPD** | **PHG**
---|---|---
Etiology | Bacteria | Herpes simplex virus
Age | 15–30 years | Frequently children
Site | Interdental papillae. Rarely outside the gingiva | Gingiva and the entire oral mucosa
Symptoms | Ulcerations and necrotic tissue and a yellowish white plaque | Multiple vesicles which disrupt, leaving small round fibrin-covered ulcerations
| _Foetor ex ore_ | _Foetor ex ore_
| Moderate fever may occur | Fever
Duration | 1–2 days if treated | 1–2 weeks
Contagious | – | +
Immunity | – | Partial
Healing | Destruction of periodontal tissue remains | No permanent destruction
Oral mucosal diseases that have been confused with NPD include desquamative gingivitis, benign mucous membrane pemphigoid, erythema multi-forme exudativum, streptococcal gingivitis, gonococcal gingivitis, and others. All of these are clinically quite distinct from NPD.
In some forms of leukemia, especially acute leukemia, necrotizing ulcers may occur in the oral mucosa and are not infrequently seen in association with the gingival margin, apparently as an exacerbation of an existing chronic inflammatory condition. The clinical appearance can resemble NPD lesions, and the symptoms they produce may be the ones that first make the patient seek professional consultation. In acute leukemia the gingiva often appears bluish red and edematous with varying degrees of ulceration and necrosis. Generally, the patient has more marked systemic symptoms than with ordinary NPD, but can feel relatively healthy for a while. The dentist should be aware of the possibility that leukemias present such oral manifestations, which require medical examination of the patient, whereas biopsy is usually not indicated.
**Fig. 20-14** Primary herpetic gingivostomatitis. Note that the ulcers affect the gingival margin but not primarily interdental papillae. A circular ulcer of the second premolar gingiva is highly suggestive of the diagnosis.
# Histopathology
Histopathologically, NG lesions are characterized by ulceration with necrosis of epithelium and superficial layers of the connective tissue and an acute, non-specific inflammatory reaction (Fig. 20-15). An important aspect is the role of the microorganisms in the lesions, because they have been demonstrated not only in the necrotic tissue components but also in vital epithelium and connective tissue.
Sometimes the histologic findings demonstrate the formation of regular layers with certain characteristics (Listgarten 1965) but there may be variations in regularity. The surface cover of yellowish white or grayish slough can be observed clinically; under the light microscope it appears to be a meshwork of fibrin with degenerated epithelial cells, leukocytes and erythrocytes, bacteria, and cellular debris. At the ultrastructural level, bacteria of varying sizes and forms including small, mediumsized, and large spirochetes have been revealed between the inflammatory cells, the majority of which are neutrophilic granulocytes. Moreover, in presumably vital parts of the surface epithelium, compact masses of spirochetes and short, fusiform rods have been found intercellularly.
**Fig. 20-15** Photomicrograph of gingival tissue affected by necrotizing gingivitis. (a) Upper right part of gingival biopsy shows gingival oral epithelium whereas upper left is ulcerated surface. Underneath the ulcer the connective tissue is heavily infiltrated by inflammatory cells.
(b) Higher magnifi cation of margin of ulcer shows necrotic tissue infi ltrated with neutrophils. Right border is covered by epithelium. Courtesy of Dr. Finn Prætorius.
The vital connective tissue in the bottom of the lesion is covered by necrotic tissue, characterized by disintegrated cells, many large and mediumsized spirochetes, and other bacteria which, judging from their size and shape, may be fusobacteria. In the superior part of the vital connective tissue, characterized by intact tissue components, the tissue is infiltrated by large and mediumsized spirochetes, but no other microorganisms have been seen. In the vital connective tissue the vessels are dilated. They also proliferate to form granulation tissue, and the tissue is heavily infiltrated by leukocytes. As always in acute processes the inflammatory infiltrate is dominated by neutrophils (Figs. 20-15b and 20-16). In the deeper tissue, the inflammatory process also comprises large numbers of monocytes and plasma cells (Listgarten 1965; Heylings 1967).
# Microbiology
## Microorganisms isolated from necrotizing lesions
Microbial samples from NPD lesions have demonstrated a constant and a variable part of the flora. The "constant flora" primarily contained _Treponema_ sp., _Selenomonas_ sp., _Fusobacterium_ sp., and _B. melaninogenicus_ ss _intermedius_ ( _Prevotella intermedia_ ), and the "variable flora" consisted of a heterogeneous array of bacterial types (Loesche _et al_. 1982). Although the characteristic bacterial flora of spirochetes and fusobacteria has been isolated in large numbers from the necrotic lesions in several studies, their presence is not evidence of a primary etiologic importance. Their presence could equally well result from secondary overgrowth. Moreover, the microorganisms associated with NG are also harbored by healthy mouths and mouths with gingivitis or periodontitis (Johnson & Engel 1986). An important role for _Treponema_ sp. and _B. intermedius_ ( _P. intermedia_ ) has been suggested by studies of antibodies in NPD patients to such bacteria, compared to levels in age- and sex-matched controls with healthy gingiva or simple gingivitis (Chung _et al_. 1983).
There is little available information about the microbiology of HIV-associated NPD. _Borrelia_ , Gram-positive cocci, β-hemolytic streptococci and _Candida albicans_ have been isolated from the lesions (Reichart & Schiødt 1989). It has also been proposed that human cytomegalovirus (HCMV) may play a role in the pathogenesis of NPD (Sabiston 1986). This virus has been found in the digestive tract of HIV-patients (Kanas _et al_. 1987; Langford _et al_. 1990), and a case of oral HCMV infection with similarities to necrotizing periodontitis has been reported (Dodd _et al_. 1993). An increased frequency of HCMV and other herpes viruses found in necrotizing lesions among Nigerian children supports a contributory role of the viruses (Contreras _et al_. 1997), although it remains to be demonstrated in future studies whether cytomegalovirus does play a causal role.
## Pathogenic potential of microorganisms
Our knowledge of the pathogenic mechanisms by which the bacterial flora produces the tissue changes characteristic of NPD is limited. One reason is that it has been difficult to establish an acceptable animal experimental model. However, several of the pathogenic mechanisms which have been associated with chronic gingivitis and periodontitis may also be of etiologic importance in the necrotizing forms of the diseases.
An important aspect in the pathogenesis of periodontitis is the capacity of the microorganisms to invade the host tissues. Among the bacteria isolated from necrotizing lesions, spirochetes and fusiform bacteria can, in fact, invade the epithelium (Heylings 1967). The spirochetes can also invade the vital connective tissue (Listgarten 1965). The pathogenic potential is further substantiated by the fact that both fusobacteria and spirochetes can liberate endotoxins (Mergenhagen _et al_. 1961; Kristoffersen & Hofstad 1970).
**Fig. 20-16** Electronmicrograph demonstrating phagocytosing neutrophil (N) close to the surface of a sequestrum (C), covered by numerous microorganisms including spirochetes (S) and rods (R). Bar = 1 μm.
A number of observations indicate that the effects of endotoxins are more prominent in NPD than in chronic gingivitis and periodontitis. The large masses of Gram-negative bacteria liberate endotoxins in close contact with connective tissue. Endotoxins may produce tissue destruction both by direct toxic effects and indirectly, by activating and modifying tissue responses of the host (Wilton & Lehner 1980). Through a direct toxic effect, endotoxins may lead to damage of cells and vessels. Necrosis is a prominent feature in the so-called "Shwartzman reaction", which is caused by endotoxins. Indirectly, endotoxins can contribute to tissue damage in several ways: they can function as antigens and elicit immune reactions; they can activate complement directly through the alternative pathway and thereby liberate chemotoxins; but they can also activate macrophages, B and T lymphocytes, and influence the host's immune reactions by interfering with cytokines produced by these cells. Studies have shown that endotoxins can stimulate catabolic processes with degradation of both connective tissue and bone induced by the released cytokines. The extent to which such reactions contribute to host defense or to tissue damage is not yet known.
An aspect which has been of major concern, especially in wartime, is the communicability of the disease. Several reports have considered this aspect but it has been concluded that the necrotizing diseases are not transmissible by ordinary means of contact (Johnson & Engel 1986). Attempts to transmit the disease from one animal to another, or to produce necrotic lesions in experimental animals, have failed to yield conclusive results (MacDonald _et al_. 1963). Several suspect microorganisms and several combinations of microorganisms can produce similar lesions in experimental animals. A combination of four different bacteria, none of them fusobacteria or spirochetes, has been found to possess such properties and there are indications that among the four bacterial species, _Bacteroides melaninogenicus_ was the true pathogen (MacDonald _et al_. 1956, 1963). _B. melaninogenicus_ may, under certain conditions, produce an enzyme which degrades native collagen (Gibbons & MacDonald 1961). It is still not clear, however, whether this microorganism is of particular importance in the pathogenesis of NPD. NG lesions have also been induced in dogs pretreated with steroids and inoculated with a fusiform–spirochete culture from dogs which had gingival lesions similar to the NG lesions seen in humans (Mikx & van Campen 1982). The lesions produced in experimental animals may not be identical to those which occur in humans. It is also important to note that even if necrotic lesions can be transmitted by transmission of infectious material or bacterial cultures, this does not necessarily mean that the disease is truly contagious.
It is obvious from the above observations and assumptions that a fundamental question remains to be answered, and at this point it may be stated that the necrotizing periodontal diseases belong to those diseases to which Pasteur referred when he said: "there are some bacteria that cause a disease, but there are some diseases that bring about a condition that is ideal for the growth of some bacteria" (Wilson 1952). If the microorganisms mentioned above play a role in the etiology of the disease, then, presumably, the disease is an opportunistic infection. Consequently, the pathogenic characteristics of the micro-organisms are normally overcome by the host defenses, and disease occurs when the host defenses are impaired. The isolated microorganisms do possess biologic activities which may contribute to the pathogenesis, but the exact role of the various microorganisms has not yet been clarified (Johnson & Engel 1986).
# Host response and predisposing factors
It is particularly evident for HIV-infected patients that the disease is associated with diminished host resistance; among other predisposing factors, the basic mechanism may include altered host immunity. Changes in leukocyte function and the immune system have been observed in some studies, although the biologic reason for, and significance of, these findings are unclear (Johnson & Engel 1986).
Significantly increased IgG and IgM antibody titers to intermediatesized spirochetes and higher IgG titers to _B. melaninogenicus_ ssp _intermedius_ have been found in NG patients as compared to age- and sex-matched healthy and gingivitis control groups (Chung _et al_. 1983). These results, however, are in disagreement with other data showing no differences in serum antibody levels to bacterial antigens (Wilton _et al_. 1971).
Total leukocyte counts have been found to be similar for patients and controls. NG patients, however, displayed marked depression in polymor-phonuclear leukocyte chemotaxis and phagocytosis as compared with control individuals. Reduced mitogen-induced proliferation of peripheral blood lymphocytes has also been found in NG patients. It was suggested that elevated blood steroids may account for the reduced chemotactic and phagocytic responses (Cogen _et al_. 1983).
For many years it has been known that a number of predisposing factors may interact with the host defense systems and render the patient susceptible to NPD. Usually, a single one of these factors is not sufficient to establish disease. The various factors, which have been focused upon, comprise systemic diseases, including HIV infection and malnutrition, poor oral hygiene, pre-existing gingivitis and history of previous NPD, psychologic stress and inadequate sleep, smoking and alcohol use, Caucasian background, and young age.
A recent analysis of suspected predisposing factors among American patients with NPD has shown that HIV seropositivity overwhelmed all other factors in importance when present (Horning & Cohen 1995). Among the HIV-seronegative patients the ranked importance of the predisposing factors was: history of previous NPD; poor oral hygiene; inadequate sleep; unusual psychologic stress; poor diet; recent illness; social or greater alcohol use; smoking; Caucasian background; and age under 21 years. The various predisposing factors mentioned below are obviously not equally important in industrialized and developing countries, but many of these factors are known to relate to impaired immunity.
## Systemic diseases
Systemic diseases which impair immunity predispose to NPD. This is why NPD occurs more frequently in HIV-infected individuals and in patients with other leukocyte diseases including leukemia (Melnick _et al_. 1988). Examples of other diseases pre-disposing to NPD are measles, chicken pox, tuberculosis, herpetic gingivostomatitis, and malaria, but malnutrition is also important. Whereas these examples of predisposing factors are rare in western patients, they are evident in developing countries, where they often predispose to NPD and noma in children (Emslie 1963; Pindborg _et al_. 1966, 1967; Sheiham 1966; Enwonwu 1972, 1985). It is important to note that NPD is sometimes an early signal of impending serious illness (Enwonwu 1972).
### HIV infection
In Africa, the general population shows a high HIV-seropositive prevalence rate, ranging up to 33% in some populations. In Europe, prevalence figures have been established for areas in the UK, where the prevalence figures were 0.1–0.2% (Nicoll _et al_. 2000). In South Africa NPD in otherwise systemically healthy individuals was correlated with HIV infection, with a predictive value of 69.6% (Shangase _et al_. 2004). In industrialized countries, a significant portion of patients with NPD are HIV-infected patients, and no characteristics have been revealed that distinguish NPD in HIV-seropositive from that in HIV-seronegative patients. A history of frequent relapses and poor response to traditional or drug therapy may be suggestive (Greenspan _et al_. 1986; Horning & Cohen 1995). Suspicion of HIV infection is also supported by the simultaneous presence of oral candidosis, "hairy leukoplakia", or Kaposi's tumor, but these lesions are far from always present in HIV-infected patients.
HIV infection attacks the T-helper cells of the body, causing a drastic change in the T-helper (CD4+) / T-suppressor (CD8+) ratio with severe impairment of the host's resistance to infection. Depleted peripheral T-helper lymphocyte counts correlate closely with the occurrence of NG as demonstrated in a study of 390 US HIV-seropositive soldiers (Thompson _et al_. 1992). Furthermore, a complete absence of T cells in gingival tissue of HIV-infected patients with peri-odontitis has been reported (Steidley _et al_. 1992). The lack of local immune effector and regulatory cells in HIV-seropositive patients could in fact explain the characteristic and rapidly progressive nature of peri-odontitis in these patients. Moreover, a protective effect has been encountered with antiviral treatment of the HIV infection against NPD (Tappuni & Fleming 2001) as well as against HIV-associated gingivitis and periodontitis (Masouredis _et al_. 1992). NP has been revealed as a marker for immune deterioration, with a 95% predictive value that CD4+ cell counts were below 200 cells/mm3, and, if untreated, a cumulative probability of death within 24 months (Glick _et al_. 1994). As a consequence of this finding, if possible all NPD patients should be recommended to have a test for HIV infection.
### Malnutrition
In developing countries malnutrition has often been mentioned as a predisposing factor to NPD (Enwonwu 1972; Osuji 1990). Malnutrition results in lowered resistance to infection and protein malnutrition has been emphasized as the most common public health problem affecting underprivileged Nigerian children who are most often affected by NPD (Enwonwu 1985, 1994). In response to periodontal pathogens, phagocytes elaborate destructive oxidants, proteinases, and other factors. Periodontal damage may occur as the result of the balance between these factors, the antioxidants and host-derived antiproteinases. Malnutrition is characterized by marked tissue depletion of the key antioxidant nutrients, and impaired acutephase protein response to infections. This is due to impairment in the production and cellular action of the cytokines. Other features of malnutrition include inverted helper/suppressor T lymphocyte ratio, histaminemia, hormonal imbalance with increased blood and saliva levels of free cortisol, and defective mucosal integrity. Malnutrition usually involves concomitant deficiencies of several essential macro- and micronutrients, and therefore has the potential to adversely influence the prognosis of periodontal infections (Enwonwu 1994).
## Poor oral hygiene, pre-existing gingivitis, and history of previous NPD
Many of the early studies of NPD showed that a low standard of oral hygiene contributed to the establishment of the disease (Johnson & Engel 1986). This has been supported by recent studies in the USA and Nigeria (Taiwo 1993; Horning & Cohen 1995). Consequently, NPD is usually established on the basis of preexisting chronic gingivitis (Pindborg 1951b). It should be emphasized, however, that plaque accumulation as seen in NPD patients may also be enhanced by the discomfort experienced with oral hygiene practices due to the disease. Based on questionnaires and personal interviews, 28% of NPD patients have been found with a history of previous painful gingival infection and 21% had gingival scars suggestive of previous NPD (Horning & Cohen 1995).
## Psychologic stress and inadequate sleep
Just as other ulcerative gastrointestinal conditions have been shown to have psychogenic origins, psychologic stress has often and for many years been mentioned as a predisposing factor (Johnson & Engel 1986). Epidemiologic investigations seem to indicate a more frequent occurrence of necrotizing diseases in periods when the individuals are exposed to psychologic stress (Pindborg 1951a,b; Giddon _et al_. 1963; Goldhaber & Giddon 1964). New recruits and deploying military personnel, college students during examination periods, patients with depression or other emotional disorders, and patients feeling inadequate at handling life situations are more susceptible to NPD (Pindborg 1951a,b; Moulton _et al_. 1952; Giddon _et al_. 1963; CohenCole _et al_. 1983). Urine levels of corticosteroids have been used as a physiologic measure of stress, and increased free cortisol levels have been encountered in the urine of NPD patients as compared with controls. The NPD patients showed significantly higher levels of trait anxiety, depression, and emotional disturbance than did control individuals (Cohen-Cole _et al_. 1983). The role of anxiety and psychologic stress in the pathogenesis of NG has been borne out by both psychiatric and biochemical investigations (Moulton _et al_. 1952; Shannon _et al_. 1969; Maupin & Bell 1975). There are several ways by which psychologic stress factors may interfere with host susceptibility. Host tissue resistance may be changed by mechanisms acting through the autonomic nervous system and endocrine glands resulting in elevation of corticosteroid and catechol-amine levels. This may reduce gingival microcirculation and salivary flow and enhance nutrition of _Prevotella intermedia_ , but also depress neutrophil and lymphocyte functions which facilitate bacterial invasion and damage (Johnson & Engel 1986; Horning & Cohen 1995).
Inadequate sleep, often as the result of lifestyle choices or job requirements, has been mentioned by many patients with NPD (Horning & Cohen 1995).
## Smoking and alcohol use
Smoking has been listed as a predisposing factor to NPD for many years and presumably predisposes to other types of periodontitis as well (The American Academy of Periodontology 1996). Two studies from the 1950s found that 98% of the patients were smokers (Pindborg 1951a; Goldhaber 1957). More recent data have confirmed this by finding only 6% non-smokers among NPD patients in contrast to 63% in a matched control group (Stevens _et al_. 1984). The amount smoked also appears important since 41% of subjects with NG smoked more than 20 cigarettes daily whereas only 5% of controls smoked that much (Goldhaber & Giddon 1964).
The relationship between tobacco usage and NPD appears to be complex. It has often been stated that smokers in general have poorer oral hygiene than non-smokers but studies have shown that there is little difference in the level of plaque accumulation in smokers versus non-smokers. Also, there have been no conclusive studies to show that smoking adversely affects periodontal tissues by altering the microbial composition of plaque (The American Academy of Periodontology 1996). Smoking could lead to increased disease activity by influencing host response and tissue reactions. As examples, smokers have depressed numbers of T-helper lymphocytes, and tobacco smoke can also impair chemotaxis and phagocytosis of oral and peripheral phagocytes (Eichel & Shahrik 1969; Kenney _et al_. 1977; Ginns _et al_. 1982; Costabel _et al_. 1986; Lannan _et al_. 1992; Selby _et al_. 1992). Nicotine-induced secretion of epi-nephrine resulting in gingival vasoconstriction has been proposed as one possible mechanism by which smoking may influence tissue susceptibility (Schwartz & Baumhammers 1972; Kardachi & Clarke 1974; Bergström & Preber 1986). The exact mechanism of tobacco smoking predisposing to NPD, however, remains to be determined.
Social or heavy drinking has been admitted by NPD patients and its role as a predisposing factor has been accounted for by its numerous physiologic effects which add to other factors as general sources of debilitation (Horning & Cohen 1995).
## Caucasian background
A number of American studies have demonstrated a 95% preponderance of Caucasian patients with NPD including a study in which the referring population was 41% African American (Barnes _et al_. 1973; Stevens _et al_. 1984; Horning & Cohen 1995), but a proportion of 49% of African Americans in another study casts doubt on race as a predisposing factor alone, and the mechanism for this factor is unknown.
## Young age
In industrialized countries, young adults appear to be the most predisposed to NPD. The disease can occur at any age, the reported mean age for NPD being between 22 and 24 years. This may reflect a number of factors such as military population age, wartime stress, and probably is related to the involvement of other factors such as smoking (Horning & Cohen 1995).
# Treatment
The treatment of the necrotizing periodontal diseases is divided into two phases: acute and maintenance phase treatment.
## Acute phase treatment
The aim of the acute phase treatment is to eliminate disease activity as manifest by ongoing tissue necrosis developing laterally and apically. A further aim is to avoid pain and general discomfort which may severely compromise food intake. Among patients suffering from systemic diseases resulting in loss of weight, further weight loss due to reduced food intake should be avoided by rapid therapeutic intervention.
At the first consultation scaling should be attempted, as thoroughly as the condition allows. Ultrasonic scaling may be preferable to the use of hand instruments. With minimal pressure against the soft tissues, ultrasonic cleaning may accomplish the removal of soft and mineralized deposits. The continuous water spray combined with adequate suction usually allows good visibility. How far it is possible to proceed with debridement at the first visit usually depends on the patient's tolerance of pain during instrumentation. Obviously toothbrushing in areas with open wounds does not promote wound healing. Therefore, patients should be instructed in substituting toothbrushing with chemical plaque control in such areas until healing is accomplished.
Hydrogen peroxide and other oxygen-releasing agents also have a long-standing tradition in the initial treatment of NPD. Hydrogen peroxide (3%) is still used for debridement in necrotic areas and as a mouth rinse (equal portions 3% H2O2 and warm water). It has been thought that the apparently favorable effects of hydrogen peroxide may be due to mechanical cleaning, and the influence on anaerobic bacterial flora of the liberated oxygen (Wennström & Lindhe 1979; MacPhee & Cowley 1981). Further adjunctive local oxygen therapy of NDP showed a more rapid clinical restitution with less periodontal destruction than in a group without oxygen therapy (Gaggl _et al_. 2006).
Twice daily rinsing with a 0.2% chlorhexidine solution is a very effective adjunct to reduce plaque formation, particularly when toothbrushing is not performed. It also assists self-performed oral hygiene during the first weeks of treatment. Its effect is discussed elsewhere in this book. For an optimal effect of this medicament, it should be used only in conjunction with and in addition to systematic scaling and root planing. The chlorhexidine solution does not penetrate subgingivally and the preparation is readily inactivated by exudates, necrotic tissues, and masses of bacteria (Gjermo 1974). The effectiveness of chlorhexidine mouth rinses is therefore dependent upon a simultaneous, thorough mechanical, debridement.
In some cases of NPD the patient's response to debridement is minimal or the general health is affected to such an extent that the supplementary use of systemic antibiotics or chemotherapeutics is indicated. This also applies to patients with malaise, fever, and lassitude. The choice of drug aims at a direct action on bacteria which are the cause of the inflammatory process in NPD. Supplementary treatment with metronidazole 250 mg three times daily has been found effective against spirochetes and appears to be the first choice in the treatment of NPD (Proctor & Baker 1971; Shinn 1976; Loesche _et al_. 1982). The adjunctive use of metronidazole in HIV-associated NPD is reported to be extremely effective in reducing acute pain and promoting rapid healing (Scully _et al_. 1991). Acute pain usually disappears after a few hours (Fig. 20-17).
Antibiotics such as penicillins and tetracyclines are also effective. Penicillin (1 million i.u. three times daily) should be used as an adjunct to scaling as for metronidazole until the ulcers are healed. Topical application of antibiotics is not indicated in the treatment of NPD, because intralesional bacteria are frequent, and topical application does not result in sufficient intralesional concentration of antibiotics.
It is important to emphasize that many HIV-seropositive patients with NPD at their initial visit are not aware of their serostatus. If HIV infection is a suspected predisposing factor, the patient can be referred to her or his physician for further examination. Some patients may prefer referral to a hospital department. Information on HIV-serostatus is frequently not available at initiation of therapy, but the lack of information has no serious implications for the choice of treatment or for the handling of the patient. As a consequence of a lack of information on HIV-serostatus of patients seeking dental treatment in general, all procedures in the dental office must always include precautions to protect against transmission of the virus to the dentist, to the dental auxiliaries, and to other patients.
If the dentist asks the patient about his or her possible chance of having contracted HIV infection this should be done with great care, because HIV infection has serious implications for the patient. Consequently, a successful outcome depends on a confidential relationship between patient and dentist. In the case of a new patient, such a relationship is first established after at least a couple of appointments in the clinic.
**Fig. 20-17** Necrotizing periodontitis with severe pain. The entire gingival margin is the seat of a necrotic ulcer. (a) Facial aspect. (b) Palatal aspect. (c,d) The patient was treated with scaling supplemented with metronidazole and the next day the patient was free of symptoms and the clinical features were significantly improved.
In HIV-infected patients antibiotic prophylaxis in relation to scaling does not usually appear to be necessary. Bacteria recovered from venipuncture 15 minutes after scaling were not detectable in samples obtained at 30 minutes (Lucartoto _et al_. 1992). Neither does removal of sequestra always appear to require antibiotic cover (Robinson 1991). HIV-infected patients are susceptible to candidal infections (Holmstrup & Samaranayake 1990) and if oral candidosis is present or occurs throughout the period of antibiotic treatment, treatment with appropriate antimycotic drugs such as miconazole may be necessary.
Patients with NPD should be seen almost daily as long as the acute symptoms persist. Appropriate treatment alleviates symptoms within a few days. Thereafter the patient should return in approximately 5 days. Systematic subgingival scaling should be continued with increasing intensity as the symptoms subside. Correction of restoration margins and polishing of restorations and root surfaces should be completed after healing of ulcers. When the ulcerated areas are healed, local treatment is supplemented with oral hygiene instruction and patient motivation. Instruction in gentle but effective toothbrushing and approximal cleaning is mandatory. In many cases the extensive tissue destruction results in residual soft tissue defects that are difficult for the patient to keep clean. Oral hygiene in these areas often requires the use of interproximal devices and soft, smaller brushes. Sometimes healing is delayed in HIV-infected patients and intensive professional control may be necessary for prolonged periods of time.
Patients with NPD are not always easily motivated to carry out a proper program of oral hygiene. They frequently have poor oral hygiene habits and possibly a negative attitude to dental treatment in general. As a result, some patients discontinue treatment as soon as pain and other acute symptoms are alleviated. Motivation and instruction should be planned to prevent this happening, and should be reinforced during later visits. Patients with severely impaired immune function, for instance due to HIV infection, may suffer from other infections or diseases during the period of treatment. This may complicate the treatment, because patients may be hospitalized.
## Maintenance phase treatment
When the acute phase treatment has been completed, necrosis and acute symptoms in NPD have disappeared. The formerly necrotic areas are healed and the gingival craters are reduced in size, although some defects usually persist. Bacterial plaque readily accumulates in such areas, and the craters, therefore, predispose to recurrence of NPD or to further destruction because of a persisting chronic inflammatory process, or both. These sites, therefore, may require surgical correction. Shallow craters can be removed by simple gingivectomy, while the elimination of deep defects may require flap surgery. Treatment of necrotizing gingivitis has not been completed until all gingival defects have been eliminated and optimal conditions for future plaque control have been established. If possible, elimination of predisposing factors is also very important to prevent recurrence. Due to delayed healing in HIV-infected patients, periodontal surgery is not recommended in these patients. Instead, intensive approximal cleaning is necessary to prevent recurrence of disease.
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# Chapter 21
# Periodontal Disease as a Risk for Systemic Disease
Ray C. Williams and David W. Paquette
Early twentieth century concepts
Periodontitis as a risk for cardiovascular disease
Biologic rationale
Periodontitis as a risk for adverse pregnancy outcomes
Association of periodontal disease and pre-eclampsia
Periodontitis as a risk for diabetic complications
Periodontitis as a risk for respiratory infections
Effects of treatment of periodontitis on systemic diseases
Throughout the history of mankind, there has been the belief that diseases which affect the mouth, such as periodontal disease, can have an effect on the rest of the body. Over the centuries, writings from the ancient Egyptians, Hebrews, Assyrians, Greeks, and Romans, to name a few, have all noted the importance of the mouth in overall health and wellbeing. Thus, one could say that the concept linking systemic disease and periodontitis can be traced back to the beginning of recorded history and medicine (O'Reilly & Claffey 2000).
This chapter examines the evidence which has emerged since the early 1990s implicating periodontal disease as a risk factor for several systemic conditions such as cardiovascular disease, adverse pregnancy outcomes, diabetes, and pulmonary disease. But first, it is helpful for the student of dentistry to understand the historical perspective under which this relationship emerged. The concept of "focal infection" which emerged around 1900 has resurfaced and has stimulated much new interest and research into the role of periodontitis as a risk for systemic disease.
# Early twentieth century concepts
At the beginning of the twentieth century, medicine and dentistry were searching for reasons to explain why people became afflicted with a wide range of systemic diseases. Medicine at that time had very little insight into what caused diseases such as arthritis, pneumonia, and pancreatitis. Through the writings and lectures of principally two individuals, Willoughby D. Miller, a microbiologist in Philadelphia, and William Hunter, a London physician, the concept that oral bacteria and infection were likely causes of most systemic illnesses suddenly became very popular (O'Reilly & Claffey 2000). For the next 40 years, physicians and dentists would embrace the idea that infections, especially those originating in the mouth, caused most human suffering and illness. This era, which came to be known as the "era of focal infection", can be attributed primarily to Willoughby D. Miller and William Hunter (O'Reilly & Claffey 2000).
Willoughby Miller was an instructor at the University of Pennsylvania School of Dental Medicine around the turn of the twentieth century. Miller had earlier trained in microbiology in Berlin in Robert Koch's institute. Koch was a pioneer in microbiology and the father of the modern "germ theory" of disease. While under the influence of Robert Koch, Miller too became intensely interested in the role of "germs" or bacteria in causing diseases. Miller returned to the US following his training, convinced that the bacteria residing in the mouth could cause or be attributed to most systemic diseases in patients. In a paper published in 1891, entitled "The human mouth as a focus of infection", Miller argued that the oral flora caused ostitis, osteomyelitis, septicemia, pyemia, disturbances of the alimentary tract, noma, dyptheria, tuberculosis, syphilis, and thrush (Miller 1891). Clearly from this one publication, one can appreciate just how extensively the mouth and oral infection were blamed for causing systemic disease (O'Reilly & Claffey 2000).
While attending one of Miller's lectures at the International Congress of Hygiene in London, William Hunter, a physician from the London Fever Hospital, noted that he and Miller were in strong agreement about the systemic impact of oral infections or oral sepsis. Shortly after, Hunter was invited to speak at the opening of the Strathcona Medical Building at McGill University in Montreal in 1910. In his address to the audience, he blamed poor dentistry and the resulting oral sepsis for causing most of mankind's systemic disease. Hunter remarked that the crowns, bridges and partial dentures he saw in his patients in London were built on teeth surrounded by a "mass of sepsis". Indeed, this oral sepsis could explain why most individuals developed chronic diseases (Hunter 1900; O'Reilly & Claffey 2000). It is likely that Hunter was referring to the untreated periodontal diseases, caries, and defective restorations he was noting in his adult patients at the London Fever Hospital. But whatever Hunter thought he observed in the mouths of his sick patients, his speech at McGill University and his subsequent publication on the role of sepsis and antisepsis in medicine (Hunter 1910) ushered in an era of belief that periodontitis, caries, and poor oral hygiene were the primary cause of systemic illness. The term "oral sepsis" used by Hunter was replaced with the term "focal infection" in 1911 (Billings 1912). Focal infection implied that there was a nidus of infection somewhere in the body, such as periodontitis, which could affect distant sites and organs via the bloodstream. Throughout the 1920s and 1930s, dentists and physicians believed that the bacteria on the teeth and the resultant infectious diseases, such as caries, gingivitis, and periodontitis, were a focus of infection that led to a wide variety of systemic problems. It became popular during this period to extract teeth as a means of ridding the body of oral bacteria and preventing and/or treating diseases affecting the joints, as well as diseases of the heart, liver, kidneys, and pancreas (Cecil & Angevine 1938; O'Reilly & Claffey 2000).
However, by 1940, medicine and dentistry were realizing that there was much more to explain a patient's general systemic condition than bacteria in the mouth. Dentists and physicians realized that (1) extracting a person's teeth did not necessarily make the person better or make their disease go away, (2) people with very healthy mouths and no obvious oral infection developed systemic disease, and (3) people who had no teeth and thus no apparent oral infection still developed systemic diseases (Galloway 1931; Cecil & Angevine 1938).
By 1950, it was apparent to medicine and dentistry that oral infections, such as dental caries, gingivitis, and periodontitis, could not explain why individuals developed a wide range of systemic diseases. By this time medicine was making strides in discovering the true etiologies of many diseases, and dentistry was making great strides in the prevention as well as the treatment of caries and periodontal disease. Thus, the era of focal infection as a primary cause of systemic diseases came to an end (O'Reilly & Claffey 2000).
Throughout the second half of the twentieth century, several researchers and clinicians continued to question whether oral infection (and inflammation) might in some way contribute to a person's overall health, but the reasons given were mostly speculative. Clinicians continued to propose that bacteria and bacterial products within the periodontal pocket, and which could enter the bloodstream from the mouth, could surely in some way be harmful to the body as a whole (Thoden van Velzen _et al_. 1984). However, it was not until the last decade of the twentieth century that dentistry and medicine again began to examine the relationship of periodontitis as a risk for systemic disease. The student of dentistry thus needs to appreciate the intense focus on oral infection as a "likely" cause of many systemic diseases from 1900–1950, then the era of retreat from the focal infection theories of disease causation from 1950 to around 1989, and now the new look at emerging science that suggests periodontitis as a possible risk factor for several systemic diseases, including cardiovascular disease, adverse pregnancy outcomes, diabetes mellitus, and bacterial pneumonia.
# Periodontitis as a risk for cardiovascular disease
In 1989 Kimmo Mattila and co-workers in Finland conducted a case–control study on patients who had experienced an acute myocardial infarction and compared these patients to control subjects selected from the community. A dental examination was performed on all of the subjects studied and a dental index computed. The dental index used by Mattila was the sum of scores from the number of carious lesions, missing teeth and periapical lesions, and probing depth measures to indicate periodontitis and the presence or absence of pericoronitis. Mattila and his group reported a highly significant association between poor dental health, as measured by the dental index, and acute myocardial infarction. The association was independent of other risk factors for heart attack such as age, total cholesterol, high density lipoprotein (HDL) triglycerides, C peptide, hypertension, diabetes, and smoking (Mattila _et al_. 1989).
Mattila's findings initiated a great deal of interest in the scientific community. Might it be possible that there was a significant association between periodontitis and cardiovascular disease? Physicians and dentists noted the following commonalities. Patients with periodontal disease share many of the same risk factors as patients with cardiovascular disease, including age, gender (predominantly male), lower socioeconomic status, stress, and smoking (Beck _et al_. 1998). Additionally, a large proportion of patients with periodontal disease also exhibit cardiovascular disease (Umino & Nagao 1993). These observations suggest that periodontal disease and atherosclerosis share similar or common etiologic pathways. Scannapieco and colleagues (2003a) conducted a systematic review of the evidence supporting or refuting any relationship. In response to the focused questions, "Does periodontal disease influence the initiation/progression of atherosclerosis and therefore cardiovascular disease, stroke and peripheral vascular disease?" the investigators identified 31 human studies. Table 21-1 lists selected influential studies identified in the review plus additional recent observational studies discussed below. Although the authors did not perform a meta-analysis due to differences in reported outcomes, the authors noted relative (not absolute) consistency and concluded, "Periodontal disease may be modestly associated with atherosclerosis, myocardial infarction and cardiovascular events." An accompanying consensus report approved by the American Academy of Periodontology recommends, "Patients and health care providers should be informed that periodontal intervention may prevent the onset or progression of atherosclerosis-induced diseases."
**Table 21-1** Summary of select case–control and cohort observational studies supporting an association between periodontal disease and cardiovascular disease
Since Scannapieco's review and consensus report, other meta-analyses on the cardiovascular–periodontal disease association have been conducted and published. Meurman and co-workers (2004) reported a 20% increase in the risk for cardiovascular disease among patients with periodontal disease (95% CI 1.08–1.32), and an even higher risk ratio for stroke varying from 2.85 (95% CI 1.78–4.56) to 1.74 (CI 1.08– 2.81). Similarly, Vettore and co-workers reported relative risk estimates of 1.19 (95% CI 1.08–1.32) and 1.15 (95% CI 1.06–1.25) respectively (Khader _et al_. 2004; Vettore 2004). These meta-analyses of the available observational human data suggest a modest but statistically significant increase in the risk for cardiovascular disease with periodontal disease.
Recent findings from several worldwide population studies also should be noted. These studies include the Atherosclerosis Risk in Communities Study (ARIC), the Health Professional Follow-up Study (HPFS), the Nurses Health Study (NHS), and the Oral Infections and Vascular Disease Epidemiology Study (INVEST) conducted in the United States. Other studies have involved populations from Sweden, Finland, and China.
Periodontal probing data were collected on 6017 persons, 52–75 years of age, participating in the ARIC study (Beck _et al_. 2001, 2005; Elter _et al_. 2004). The investigators assessed both the presence of clinical cardiovascular disease (MI or revascularization procedure) and subclinical atherosclerosis (carotid artery intima media wall thickness (IMT) using B-mode ultrasound) as dependent variables in the population. Individuals with both high attachment loss (≥10% of sites with attachment loss >3 mm) and high tooth loss exhibited elevated odds of prevalent cardiovascular disease as compared to individuals with low attachment loss and low tooth loss (OR = 1.5, 95% CI 1.1–2.0 and OR = 1.8, CI 1.4–2.4 respectively) (Elter _et al_. 2004). A second logistic regression analysis indicated a significant association between severe periodontitis and thickened carotid arteries after adjusting for covariates like age, gender, diabetes, lipids, hypertension, and smoking (Beck _et al_. 2001). Accordingly, the odds ratio for severe periodontitis (i.e. 30% or more of sites with ≥3 mm clinical attachment loss) and subclinical carotid atherosclerosis was 1.31 (95% CI 1.03–1.66). In a third report, these investigators quantified serum IgG antibody levels specific for 17 periodontal organisms using a whole bacterial checkerboard immunoblotting technique (Beck _et al_. 2005). Analyzing mean carotid IMT (≥1 mm) as the outcome and serum antibody levels specific as exposures for this same population, the investigators noted the presence of antibody to _Campylobacter rectus_ increased the risk for subclinical atherosclerosis two-fold (OR = 2.3, 95% CI 1.83–2.84). In particular, individuals with both high _C. rectus_ and _Peptostreptococcus micros_ antibody titers had almost twice the prevalence of carotid atherosclerosis as compared to those with only a high _C. rectus_ antibody (8.3% versus 16.3%). Stratification by smoking indicated that all microbial models significant for smokers were also significant for never smokers except for _Porphyromonas gingivalis_. Thus, clinical signs of periodontitis are associated with cardiovascular disease and subclinical atherosclerosis in the ARIC population, and exposures to specific periodontal pathogens significantly increase the risk for atherosclerosis in smoking and nonsmoking subjects.
Self-reported periodontal disease outcomes and incident cardiovascular disease were assessed in two extant databases, HPFS (n = 41 407 males followed for 12 years) and NHS (n = 58 974 females followed for 6 years) (Hung _et al_. 2004). After controlling for important cardiovascular risk factors, males with a low number of teeth (≤10 at baseline) had a significantly higher risk of cardiovascular disease (RR = 1.36; 95% CI 1.11–1.67) as compared to males with a higher number of teeth (25 or more). For females with the same reported extent of tooth loss, the relative risk for cardiovascular disease was 1.64 (95% CI 1.31–2.05) as compared to women with at least 25 teeth. The re lative risks for fatal cardiovascular disease events increased to 1.79 (95% CI 1.34–2.40) for males and 1.65 (95% CI 1.11–2.46) for females with tooth loss respectively. In a second report, the investigators evaluated the association between self-reported periodontal disease and serum elevations in cardiovascular disease biomarkers cross-sectionally in a subset of HPFS participants (n = 468 males) (Joshipura _et al_. 2004). Serum biomarkers included C-reactive protein (CRP), fibrinogen, factor VII, tissue plasminogen activator (t-PA), LDL cholesterol, von Willebrand factor, and soluble TNF receptors 1 and 2. In multivariate regression models controlling for age, cigarette smoking, alcohol intake, physical activity, and aspirin intake, self-reported periodontal disease was associated with significantly higher levels of CRP (30% higher among periodontal cases compared with non-cases), t-PA (11% higher), and LDL cholesterol (11% higher). These analyses reveal significant associations between self-reported number of teeth at baseline and risk of cardiovascular disease and between self-reported periodontal disease and serum biomarkers of endothelial dysfunction and dyslipidemia.
One population study called INVEST has been planned _a priori_ and conducted exclusively to evaluate the association between cardiovascular disease and periodontal outcomes in a cohort population. It was reported that for a group of 203 stroke-free subjects (ages 54–94) at baseline, mean carotid plaque thickness (measured with B-mode ultrasound) was significantly greater among dentate subjects with severe periodontal bone loss (≥50% measured radiographically) as compared to those with less bone loss (<50%) (Engebretson _et al_. 2005). These investigators noted a clear dose–response relationship when they graphed subject tertiles of periodontal bone loss versus carotid plaque thickness. The investigators next collected subgingival plaque from 1056 subjects and tested for the presence of 11 known periodontal bacteria using DNA techniques (Desvarieux _et al_. 2005). The investigators found that cumulative periodontal bacterial burden was significantly related to carotid IMT after adjusting for cardiovascular disease risk factors. Whereas mean IMT values were similar across burden tertiles for putative (orange complex) and health-associated bacteria, IMT values rose with each tertile of etiologic bacterial burden ( _Actinobacillus acinomycetemcomitans_ (recently renamed _Aggregatibacter acinomycetemcomitans_ ), _P. gingivalis, Treponema denticola_ and _Tannerella forsythia_ ). Similarly, white blood cell values (but not serum CRP) increased across these burden tertiles. These data from INVEST provide evidence of a direct relationship between periodontal microbiology and subclinical atherosclerosis independent of CRP.
Consistent associations between periodontal outcomes and atherosclerosis have been recently demonstrated among populations in Europe and Asia. For 131 adult Swedes, mean carotid IMT values were significantly higher in subjects with clinical and/or radiographic evidence of periodontal disease compared to periodontally healthy controls (Soder _et al_. 2005). Multiple logistic regression analysis identified periodontal disease as a principal independent predictor of carotid atherosclerosis with an odds ratio of 4.64 (95% CI 1.64–13.10). Pussinen _et al_. (2004) monitored antibody responses for _A. actinomycetemcomitans_ and _P. gingivalis_ among 6950 Finnish subjects for whom cardiovascular disease outcomes over 13 years were available (Mobile Clinic Health Survey). Compared with the subjects who were seronegative for these pathogens, seropositive subjects had an odds ratio of 2.6 (95% CI 1.0–7.0) for a secondary stroke. In a second report on 1023 males (Kuopio Ischemic Heart Disease Study), Pussinen and co-workers (2005) observed that cases with myocardial infarction or cardiovascular disease death were more often seropositive for _A. actinomycetemcomitans_ than those controls who remained healthy (15.5% versus 10.2%). In the highest tertile of _A. actinomycetemcomitans_ antibodies, the relative risk for MI or coronary heart disease death was 2.0 (95% CI 1.2–3.3) compared with the lowest tertile. For _P. gingivalis_ antibody responses, the relative risk was of 2.1 (95% CI 1.3–3.4). Abnet and co-workers (2005) recently published findings from a cohort study of 29 584 healthy, rural Chinese adults monitored for up to 15 years. Tooth loss was evaluated as an exposure outcome for periodontal disease, and mortality from heart disease or stroke were modeled as dependent variables. Individuals with greater than the age-specific median number of teeth lost exhibited a significantly increased risk of death from MI (RR = 1.28, 95% CI 1.17–1.40) and stroke (RR = 1.2, 95% CI 1.02–1.23). These elevated risks were present in male and females irrespective of smoking status. Collectively, these findings indicate consistent associations for periodontal disease and pathogenic exposures with cardiovascular disease for European and Asian populations.
## Biologic rationale
Many investigators have asked the question: what is the biologic rationale to explain how periodontitis may be related to cardiovascular disease? Scientists have noted that a patient who has, for example, 28 teeth with pocket depths of 6–7 mm and bone loss, has a large overall surface area of infection and inflammation (Waite & Bradley 1965). In patients with moderate periodontitis, the surface area could be the size of the palm of the hand or larger. In addition, the subgingival bacteria in periodontal pockets exists in a highly organized biofilm. Since periodontal infections result in low-grade bacteremias and endotoxemias in affected patients (Sconyers _et al_. 1973; Silver _et al_. 1980), systemic effects on vascular physiology via these exposures appear biologically plausible. Four specific pathways have been proposed to explain the plausibility of a link between cardiovascular disease and periodontitis (Fig. 21-1). These pathways (acting independently or collectively) include: (1) direct bacterial effects on platelets, (2) autoimmune responses, (3) invasion and/or uptake of bacteria in endothelial cells and macrophages, and (4) endocrine-like effects of proinflammatory mediators. In support of the first pathway, two oral bacteria, _P. gingivalis_ and _Streptococcus sanguis_ express virulence factors called "collagen-like platelet aggregation associated proteins" (PAAP) that induce platelet aggregation _in vitro_ and _in vivo_ (Hertzberg & Meyer 1996, 1998). Secondly, autoimmune mechanisms may play a role since antibodies that cross react with periodontal bacteria and human heat shock proteins have been identified (Hinode _et al_. 1998; Sims _et al_. 2002). Deshpande _et al_. (1998) have thirdly demonstrated that _P. gingivalis_ can invade aortic and heart endothelial cells via fimbriae. Several investigative groups have independently identified specific oral pathogens in atheromatous tissues (Chui 1999; Haraszthy _et al_. 2000). In addition, macrophages incubated _in vitro_ with _P. gingivalis_ and LDL uptake the bacteria intracellularly and transform into foam cells (Giacona _et al_. 2004). In the last potential pathway, systemic proinflammatory mediators are up-regulated for endocrine-like effects in vascular tissues, and studies consistently demonstrate elevations in CRP and fibrinogen among periodontally diseased subjects (Slade _et al_. 2000; Wu _et al_. 2000a,b).
Experiments with animal models demonstrate that specific infections with periodontal pathogens accelerate atherogenesis. For example, inbred heterozygous and homozygous apoE-deficient mice exhibit increased aortic atherosclerosis when challenged orally or intravenously with invasive strains of
_P. gingivalis_ (Li _et al_. 2002; Lalla _et al_. 2003; Chi _et al_. 2004; Gibson _et al_. 2004). While _P. gingivalis_ challenges increased aortic atherosclerosis in apoE-deficient mice in a hypercholesterolemic background only, normocholesterolemic pigs were recently shown to develop both coronary and aortic lesions with _P. gin-givalis_ challenges (Brodala _et al_. 2005). This finding suggests that _P. gingivalis_ bacteremia may exert an atherogenic stimulus independent of high cholesterol levels in pigs. It is worth noting that a wide range of _P. gingivalis_ doses was used in these animal studies. While the clinically relevant dose for human subjects is unknown at present, it probably varies greatly (Daly _et al_. 2001; Haynes & Stanford 2003; Ide _et al_. 2004). Importantly, _P. gingivalis_ challenges enhance atherosclerosis despite these different routes of administration and dosing regimens in both species. _P. gingivalis_ 16 ribosomal DNA was detected by polymerase chain reaction (PCR) in atheromas from some but not all of these mutant mice and the pigs. These experiments suggest that both the host response and the virulence of the specific _P. gingivalis_ strains appear to be important variables in these infection–atherogenesis models. Collectively, when one looks at the body of evidence gathered so far since 1989, there appears to be a compelling association between periodontitis and coronary heart disease.
**Fig. 21-1** Proposed model and mechanisms linking periodontal disease and cardiovascular disease.
# Periodontitis as a risk for adverse pregnancy outcomes
In 1996, following a landmark report by Offenbacher and colleagues (1996), there has been much interest and research into whether periodontitis may be a possible risk factor for adverse pregnancy outcomes. Adverse pregnancy outcomes that have been linked to periodontal disease include preterm birth, low birthweight, miscarriage or early pregnancy loss, and pre-eclampsia. Pre-eclampsia and preterm births are major causes of maternal and prenatal morbidity and mortality.
Preterm infants who are born with low birth-weights represent a major social and economic public health problem, even in industrialized nations. Although there has been an overall decline in infant mortality in the US over the past 40 years, preterm low birthweight remains a significant cause of perinatal mortality and morbidity. A 47% decrease in the infant mortality rate to a level of 13.1 per 1000 live births occurred between 1965 and 1980. But from 1980 to 2000, the percentage of low birthweight infants increased by 11.8% and that of very low birth-weight infants increased by 24.3% in the US; among survivors, low birthweight is a major contributor to long-term disability.
Preterm low birthweight deliveries represent approximately 10% of annual births in industrialized nations and account for two-thirds of overall infant mortality. Approximately one-third of these births are elective while two-thirds are spontaneous preterm births. About a half of the spontaneous preterm births are due to premature rupture of membranes and the other half are due to preterm labor. For the spontaneous preterm births, 10–15% occur before 32 weeks gestation, result in very low birthweight (<1500 g) and often cause long-term disability, such as chronic respiratory diseases and cerebral palsy (Offenbacher _et al_. 1996, 1998; Champagne _et al_. 2000; Scannapieco _et al_. 2003c; Xiong _et al_. 2006).
Among the known risk factors for preterm low birthweight deliveries are young maternal age (<18 years), drug, alcohol and tobacco use, maternal stress, genetic background, and genitourinary tract infections. Although 25–50% of preterm low birthweight deliveries occur without any known etiology, there is increasing evidence that infection may play a significant role in preterm delivery (Hill 1998; Goldenberg _et al_. 2000; Sobel 2000; Williams _et al_. 2000; Scannapieco _et al_. 2003c; Xiong _et al_. 2006).
One of the more important acute exposures that has been implicated in preterm birth is an acute maternal genitourinary tract infection at some point during the pregnancy. Bacterial vaginosis (BV) is a Gram-negative, predominantly anaerobic infection of the vagina, usually diagnosed from clinical signs and symptoms. It is associated with a decrease in the normal lactobacillus-dominated flora and an increase in anaerobes and facultative species including _Garde-nerella vaginalis_ , _Mobiluncus curtsii_ , _Prevotella bivia_ , and _Bacteroides ureolyticus._ Bacterial vaginosis is a relatively common condition that occurs in about 10% of all pregnancies. It may ascend from the vagina to the cervix and even result in inflammation of the maternal fetal membranes (chorioamnionitis). Extending beyond the membranes, the organisms may appear in the amniotic fluid compartment that is shared with the fetal lungs and/or involve placental tissues and result in exposure to the fetus via the bloodstream. Despite the observed epidemiologic linkage of bacterial vaginosis with preterm birth, the results from randomized clinical trials to determine the effects of treating bacterial vaginosis with systemic antibiotics on incident preterm birth are equivocal (Goldenberg _et al_. 2000). Still, there are compelling data linking maternal infection and the subsequent inflammation to preterm birth. It appears that inflammation of the uterus and membranes represents a common effector mechanism that results in preterm birth, and, thus, either clinical infection or sub clinical infection is a likely stimulus for increased inflammation.
In the early 1990s, it was hypothesized that oral infections, such as periodontitis, could represent a significant source of both infection and inflammation during pregnancy. It was noted that periodontal disease is a Gram-negative anaerobic infection with the potential to cause Gram-negative bacteremias in persons with periodontal disease. It was hypothesized that periodontal infections, which serve as reservoirs for Gram-negative anaerobic organisms, lipopolysaccharide (LPS, endotoxin), and inflammatory mediators including prostaglandin E2 (PGE2) and tumor necrosis factor-α (TNF-α), may be a potential threat to the fetal–placental unit (Fig. 21-2) (Collins _et al_. 1994a,b).
As a first step in testing this hypothesis, Greg Collins in Offenbacher's laboratory conducted a series of experiments in the pregnant hamster animal model. It had been noted earlier by Lanning _et al_. (1983) that pregnant hamsters challenged with _Escherichia coli_ LPS had malformation of fetuses, spontaneous abortions, and low fetal weight. The work by Lanning and co-workers clearly demonstrated that infections in pregnant animals could elicit many pregnancy complications including spontaneous abortion, preterm labor, low birthweight, fetal growth restriction, and skeletal abnormalities. It was not clear, however, if these findings from _E. coli_ would be similar if endotoxin from oral anaerobes was studied. First of all, LPS from Gram-negative enteric organisms differs in structure and biological activity from oral LPS. Thus, Collins needed to demonstrate that LPS from oral organisms had similar effects on fetal outcomes when administered to pregnant animals. Secondly, the oral cavity represents a distant site of infection. Although pneumonia has been a recognized example of a distant site of infection triggering maternal obstetric complications, it was important to demonstrate that distant, non-disseminating infections with oral pathogens could elicit pregnancy complications in animal models. Thirdly, oral infections are chronic in nature. Increased obstetric risk is generally associated with acute infections that occur during pregnancy. Thus, in concept, maternal adaptation to a chronic infectious challenge was assumed to afford protection to the fetus, even during acute flareups that may occur during pregnancy.
Fig. 21-2 Proposed model for relationship between periodontal disease and adverse pregnancy outcomes.
Collins' landmark hamster studies (Collins _et al_. 1994a,b) demonstrated that chronic exposure to oral pathogens like _P. gingivalis_ in a chamber model (Genco & Arko 1994) does not in fact afford protection, but actually enhances the fetal–placental toxicity of exposure during pregnancy. Thus during pregnancy the mother does not become "tolerant" of infectious challenge from oral organisms. Collins and Offenbacher also wanted to demonstrate that the low-grade infections with low numbers of oral pathogens were not of sufficient magnitude to induce maternal malaise or fever. They noted however a measurable local increase of PGE2 and TNF-α in chamber fluid with _P. gingivalis_ as well as a 15–18% decrease in fetal weight. Further, the magnitude of the PGE2 and TNF-α response was inversely related to the weight of the fetuses, mimicking the intra-amniotic changes seen in humans with preterm low birthweight. LPS dosing experiments demonstrated that higher levels of LPS could induce fever and weight loss in pregnant animals and resulted in more severe pregnancy outcomes including spontaneous abortions and malformations. These more noteworthy outcomes were not seen in the low-challenge oral infection models, but rather resulted in a consistent decrease in fetal weight. Previous sensitization or exposures to these pathogens prior to pregnancy enhanced the severity of the fetal growth restriction when a secondary exposure occurred during pregnancy.
Collins and colleagues (1994b) next studied infection and pregnancy in the hamster by experimentally inducing periodontal disease in the animal model. Four groups of animals were fed either control chow or plaque-promoting chow for an 8-week period to induce experimental periodontitis prior to mating.
Two additional groups of animals (i.e. one control chow and one plaque-promoting chow) received exogenous _P. gingivalis_ via oral gavage. Animals fed the plaque-promoting diet beginning 8 weeks prior to mating developed periodontitis. These animals also had litters with a mean fetal weight of 1.25 ± 0.07 g that was 81% of the weight of the control groups. Animals receiving both plaque-promoting diet and _P. gingivalis_ gavage also had significantly smaller fetuses. The mean fetal weight for this group was 1.20 ± 0.19 g which represented a significant 22.5% reduction in fetal weight compared to controls. Exogenous _P. gingivalis_ challenge by gastric gavage did not appear to promote either more severe periodontal disease or more severe fetal growth restriction. This experiment indicated that experimentally induced periodontitis in the hamster could also alter fetal weight in the hamster.
More recently this group has focused on a possible role for _Campylobacter rectus_ in contributing to adverse pregnancy outcomes (Madianos _et al_. 2001). In recent animal studies utilizing the BALB/C mouse model, Yeo _et al_. (2005) have reported that maternal _Campy-lobacter rectus_ infection mediates fetal growth restriction in pregnant mice. More recently, Bobetsis and colleagues (Offenbacher _et al_. 2005) found that maternal _C. rectus_ infection induced placental inflammation and decidual hyperplasia as well as a concomitant increase in fetal brain IFN-γ. Maternal infection with
_C. rectus_ increased mouse pup mortality and also affected the hippocampal region of the neonatal brain, suggesting that maternal infection with _C. rectus_ may also affect perinatal neurological growth and development (Offenbacher _et al_., 2005).
In what is now viewed as a landmark human study, Offenbacher and colleagues (1996) conducted a case–control study on 124 pregnant or postpartum women (Table 21-2). Preterm low birthweight cases were defined as a mother whose infant had a birth-weight of less than 2500 g and also had one or more of the following: gestational age <37 weeks, preterm labor or preterm premature rupture of membranes. Controls were all mothers whose infant had a normal birthweight. Assessments included a broad range of known obstetric risk factors such as tobacco usage, drug use, and alcohol consumption, level of prenatal care, parity, genitourinary tract infections, and weight gain during pregnancy. Each subject received a full-mouth periodontal examination to determine clinical attachment levels. Mothers of preterm low birth-weight (PLBW) cases and first birth PLBW cases had significantly more advanced periodontal disease as measured with attachment loss than the respective mothers of normal birthweight controls. Multi-variate logistic regression models, controlling for other known risk factors and co-variates, demonstrated that periodontitis was a statistically significant risk factor for preterm low birthweight, with adjusted odds ratios of 7.9 and 7.5 for all PLBW cases and primiparous PLBW cases respectively. This research was the first to demonstrate an association between periodontal infection and adverse pregnancy outcomes in humans (Offenbacher _et al_. 1996).
Table 21-2 Summary of case–control observational studies on periodontal disease and adverse pregnancy outcomes
Offenbacher and co-workers proceeded to conduct a prospective cohort study, entitled Oral Conditions and Pregnancy (OCAP), which was designed to determine whether maternal periodontal disease was predictive of preterm (<37 weeks) or very preterm (<32 weeks) birth. One thousand and twenty pregnant women were periodontally examined antepartum (<26 weeks gestation) and postpartum. Again, logistic regression models were developed using maternal exposure to either periodontal disease at enrollment or disease progression during pregnancy (clinical attachment loss ≥2 mm at one or more sites) as independent variables and adjusting for known risk factors (e.g. previous preterm delivery, race, smoking, social domain variables, and other infections). Overall, the incidence of preterm was 11.2% among periodontally healthy women, compared with 28.6% in women with moderate–severe periodontal disease (adjusted risk ratio or RR = 1.6, 95% CI 1.1–2.3). Antepartum moderate–severe periodontal disease was associated with an increased incidence of spontaneous preterm births (15.2% versus 24.9%, adjusted RR = 2.0, 95% CI 1.2–3.2). Similarly, the unadjusted rate of very preterm delivery was 6.4% among women with periodontal disease progression, significantly higher than the 1.8% rate among women without disease progression (adjusted RR = 2.4, 95% CI 1.1–5.2). This second study by the Offenbacher group implicated maternal periodontal disease exposure and progression as independent risk factors for PTB outcomes (Offenbacher _et al_. 2001, 2006; Lieff _et al_. 2004).
A subsequent analysis of OCAP data further indicates that maternal periodontal disease is associated with small-for-gestational-age births (Boggess _et al_. 2006). Defining "small-for-gestational-age" as birth-weight less than the tenth percentile for gestational age, Boggess _et al_. (2006) reported that its prevalence was significantly higher among women with moderate or severe periodontal disease, compared with those with health or mild disease (13.8% versus 3.2%). Indeed, mothers with moderate or advanced periodontal disease were 2.3 times (RR, 95% CI 1.1–4.7) more likely to have small-for-gestational-age infants as compared to mothers with periodontal health even after adjusting for age, smoking, drugs, marital/ insurance status, and pre-eclampsia (i.e. pregnancy-related hypertension with proteinuria or edema).
Jeffcoat and co-workers (2001a,b) also found a positive association between maternal periodontal disease and preterm birth in a comparable US cohort study involving 1313 pregnant subjects. Complete periodontal, medical, and behavioral assessments were made between 21 and 24 weeks gestation for each subject. Gestational ages of the infants were determined following delivery, and logistic regression modeling was performed to assess any relationship between periodontal disease and preterm birth while making adjustments for other known risk factors. Notably, subjects with severe or generalized periodontal disease had an adjusted OR of 4.45 (95% CI 2.16–9.18) for preterm delivery (<37 weeks) as compared with periodontally healthy subjects. The adjusted OR increased with advancing prematurity to 5.28 (95% CI 2.05–13.60) before 35 weeks gestational age and to 7.07 (95% CI 1.70–27.4) before 32 weeks gestational age. Hence, mothers with severe periodontal disease were four to seven times more likely to deliver a preterm infant relative to mothers with periodontal health.
Two other observational studies involving US populations report a consistent association for maternal periodontal disease and preterm low birthweight. One case–control study, involved 59 women with early spontaneous preterm births (<32 weeks of gestation), 36 women with early indicated preterm births (<32 weeks of gestation), and 44 controls with uncomplicated births at term (≥37 weeks) (Goepfert _et al_. 2004). Severe periodontal disease (clinical attachment loss ≥5 mm) was more common in the spontaneous preterm birth group (49%) as compared to the indicated preterm and term control groups (25% and 30% respectively). The odds for severe periodontal disease and spontaneous preterm birth were 3.4 (95% CI 1.5–7.7). For the second observational study involving 83 preterm cases (<37 weeks gestation) and 120 term delivery controls, preterm birth was associated with severe periodontitis, i.e. five or more sites with clinical attachment loss ≥3 mm, adjusted OR = 2.75, (95% CI 1.1–7.54) (Jarjoura _et al_. 2005).
This relationship has been explored in other cross-sectional and cohort populations around the globe (Tables 21-2 and 21-3). Bosnjak _et al_. (2006) reported an adjusted OR of 8.13 (95% CI 2.73–45.9) for maternal periodontal disease and preterm birth for a Croatian population (17 preterm cases and 64 controls). Similarly, a Finnish study (Oittinen _et al_. 2005) involving 130 consecutively enrolled pregnant mothers found that those with periodontal disease were 5.5 times (95% CI 1.4–21.2) more likely to have preterm deliveries or adverse pregnancy outcomes. Two case–control studies involving Hungarian subjects found positive associations between maternal early localized periodontitis (more than one site with probing depth ≥4 mm and bleeding on probing ≥50%) and preterm low birth weight (OR = 5.4, 95% CI 1.7– 17.3; OR = 3.32, 95% CI 1.64–6.69) (Radnai _et al_. 2004, 2006). Another observational study with 96 Spanish pregnant women found a higher severity of periodontal disease (percentage of sites with probing depths ≥4 mm) among those having low birthweight infants relative to those with normal weight infants (Moreu _et al_. 2005). Moliterno and co-workers (2005) measured periodontal disease and birth outcomes for 150 Brazilian mothers and reported a significant association between periodontitis and low birthweight with an OR of 3.48 (95% CI 1.17–10.36). Chilean mothers with periodontal disease appear to be 3.5 times (RR, 95% CI 1.5–7.9) more likely to have a preterm low birthweight infant versus mothers with periodontal health (Lopez _et al_. 2002a).
Table 21-3 Summary of cohort observational studies on periodontal disease and adverse pregnancy outcomes
A smaller number of observational studies involving populations in Europe and Asia have failed to detect any significant association between maternal periodontal disease and adverse pregnancy outcomes (Davenport _et al_. 2002; Holbrook _et al_. 2004; Buduneli _et al_. 2005; Moore _et al_. 2005; Rajapakse _et al_. 2005; Skuldbol _et al_. 2006; Meurman _et al_. 2006). One prospective study finding no association was conducted at Guy's and St. Thomas' Hospital Trust in London and involved a large cohort of 3738 pregnant subjects (Moore _et al_. 2004). Regression analysis indicated no significant relationships between the severity of periodontal disease (periodontal pocketing or clinical attachment loss) and either preterm birth or low birthweight. The investigators did note a correlation between poorer periodontal health and mothers who experienced a late miscarriage. A subsequent analysis on non-smokers within this same population confirmed no associations between poor periodontal health and either preterm birth or low birthweight (Farrell _et al_. 2006). Again, non-smoking mothers who experienced late miscarriages exhibited a higher mean probing depth as compared with the subjects with term births. This same group of investigators performed genetic testing (restriction fragment length polymerase techniques) on a sub-cohort of 48 preterm cases and 82 control subjects (Moore _et al_. 2004). There were no significant associations reported for the tested cytokine polymorphisms (interleukin1β+3953 and TNF-α-308 allelic variants), prematurity, and the severity of periodontal disease. In addition, the combination of genotype and periodontal disease did not increase the risk of preterm delivery in this subcohort. These studies reporting no association are a small proportion of the total available evidence collected to date and suggest that differences in the susceptibility to periodontal disease-associated prematurity may occur in certain global populations.
## Association of periodontal disease and preeclampsia
Pre-eclampsia is a common hypertensive disorder of pregnancy that independently contributes to maternal and infant morbidity and mortality. Accordingly, atherosclerotic-like changes in placental tissues involving oxidative and inflammatory events are thought to initiate the development of pre-eclampsia (Ramos _et al_. 1995). Boggess and co-workers (2003) hypothesized that maternal exposure to periodontal disease or infection may be associated with the development of pre-eclampsia. Using data collected as part of the OCAP study, the investigators conducted logistic regression analyses on outcomes collected from 763 women who were enrolled at less than 26 weeks gestation and who delivered live infants.
Pre-eclampsia (defined here as blood pressure >140/90 mmHg on two separate occasions, and ≥1+proteinuria on catheterized urine specimen) affected 5.1% of subjects. The adjusted OR for severe periodontal disease at delivery (≥15 sites with pocket depths ≥4 mm in depth) and pre-eclampsia was 2.4 (95% CI 1.1–5.3). For women exhibiting periodontal disease progression during pregnancy (four or more sites with increases in pocket depth ≥2 mm and resulting in pockets ≥4 mm in depth) the adjusted OR was 2.1 (95% CI 1.0–4.4). After adjusting for other risk factors, such as maternal age, race, smoking, gestational age at delivery, and insurance status, the results from this cohort study indicate that severe and progressive maternal periodontal disease during pregnancy is associated with an increased risk for pre-eclampsia.
This same hypothesis was tested in a case–control study conducted in Colombia and including 130 pre-eclamptic (blood pressure ≥149/90 mmHg and ≥2+ proteinuria) and 243 non-pre-eclamptic women recruited between 26 and 36 weeks of pregnancy (Contreras _et al_. 2006). In addition to sociodemographic data, obstetric risk factors, and clinical periodontal outcomes, Contreras and co-workers examined the maternal subgingival microbial flora with sampling and anaerobic culture techniques. Sixty-four percent of pre-eclamptic women had chronic periodontitis (pocket depth and clinical attachment loss ≥4 mm and bleeding on probing) (OR = 3.0, 95% CI 1.91–4.87) versus 37% of controls. Notably, a higher proportion of pre-eclamptic women were infected subgingivally with periodontal pathogens including _P. gingivalis_ (OR = 1.77, 95% CI 1.12– 2–8), _T. forsythia_ (OR = 1.8, 95% CI 1.06–3.00), and _Eikenella corrodens_ (OR = 1.8, 95% CI 1.14–2.84). This case–control report demonstrates a consistent relationship between exposure to periodontal disease or subgingival pathogens and pre-eclampsia in pregnant women.
Xiong and co-workers (2006) have recently reviewed all of the existing evidence to date that examines the influence of periodontitis on adverse pregnancy outcomes. Twenty-two studies (13 case–control and 9 cohort) focused on preterm low birth-weight, low birthweight, preterm birth, birthweight by gestational age, miscarriage or pregnancy loss, and pre-eclampsia. Fifteen studies suggested an association between periodontal disease and increased risk of adverse pregnancy outcome (odds ratio ranging from 1.10 to 20.0) while seven found no evidence of an association (odds ratio ranging from 0.78 to 2.54). This report concludes that more methodologically vigorous studies are needed and those studies are currently being conducted.
# Periodontitis as a risk for diabetic complications
Similar to cardiovascular disease, diabetes mellitus is a common, multifactorial disease process involving genetic, environmental, and behavioral risk factors. Affecting up to 5% of the general population and over 124 million persons worldwide (King _et al_. 1998), this chronic condition is marked by defects in glucose metabolism that produce hyperglycemia in patients. Diabetes mellitus is broadly classified under two major types (American Diabetes Association Expert Committee on the Diagnosis and Classification of Diabetes Mellitus 1997). In patients with type I diabetes, (formerly called insulin-dependent diabetes mellitus), the defect occurs at the level of the pancreatic beta cells that are destroyed. Consequently type 1 diabetics produce insufficient levels of the hormone insulin for homeostasis. In contrast, patients with type 2 diabetes (formerly called non-insulin-dependent diabetes mellitus), exhibit the defect at the level of the insulin molecule or receptor. Cells in type 2 diabetics cannot respond or are resistant to insulin stimulation.
Diabetes mellitus is usually diagnosed via laboratory fasting blood glucose levels that are greater than 7 mmol/L (126 mg/dL). Additionally, casual or non-fasting blood glucose values are elevated above 11.1 mmol/L (200 mg/dL). Thirdly, diabetic patients exhibit abnormal glucose tolerance tests (i.e. blood glucose levels greater than 8.3 mmol/L (150 mg/dL) at 2 hours following a 100 g glucose load). Elevated glycated hemoglobin levels (HbA1 and HbA1c) comprise a fourth laboratory parameter and one that provides a 30–90-day record of the patient's glycemic status. Classic signs and symptoms of diabetes include polyuria, polydipsia, polyphagia, pruritis, weakness, and fatigue. End-stage diabetes mellitus is characterized by problems with several organ systems including micro- and macrovascular disease (atherosclerosis), retinopathy, nephropathy, neuropathy, and periodontal disease.
Although environmental exposures, viral infection, autoimmunity, and insulin resistance are currently considered to play principal roles in the etiology of diabetes mellitus (Yoon 1990; Atkinson & Maclaren 1990), pathogenesis of the disease and end-organ damage relies heavily on the formation and accumulation of advanced glycation end-products (AGEs) (Brownlee 1994). Accordingly, the chronic hyperglycemia in diabetes results in the nonenzymatic and irreversible glycation of body proteins. These AGEs, in turn, bind to specific receptors for advanced glycation end-products (RAGEs) on monocytes, macrophages, and endothelial cells, and alter intracellular signaling (transduction) pathways (Esposito _et al_. 1992; Kirstein _et al_. 1992). With AGE– RAGE binding, monocytes and macrophages are stimulated to proliferate, up-regulate proinflammatory cytokines, and produce oxygen free radicals (Vlassara _et al_. 1988; Yan _et al_. 1994; Yui _et al_. 1994). While oxygen free radicals directly damage host tissues, proinflammatory cytokines like IL-1, IL-6 and TNF-α exacerbate this damage via a cascade of catabolic events and the recruitment of other immune cells (T and B lymphocytes). Patients with diabetes exhibit elevated levels of AGEs in tissues including those of the periodontium (Brownlee 1994; Schmidt _et al_. 1996). Diabetics also present with elevated serum and gingival crevicular fluid levels of proinflammatory cytokines (Nishimura _et al_. 1998; Salvi _et al_. 1998). Furthermore, monocytes isolated from diabetics and stimulated with LPS secrete higher concentrations of proinflammatory cytokines and prostaglandins (Salvi _et al_. 1998). Chronic hyperglycemia, the accumulation of AGEs and the hyper-inflammatory response may promote vascular injury and altered wound healing via increased collagen cross-linking and friability, thickening of basement membranes, and altered tissue turnover rates (Weringer & Arquilla 1981; Lien _et al_. 1984; Salmela _et al_. 1989; Cagliero _et al_. 1991). Lastly, diabetic patients exhibit impairments in neutrophil chemotaxis, adherence, and phagocytosis (Bagdade _et al_. 1978; Manouchehr-Pour _et al_. 1981; Kjersem _et al_. 1988), and thus are at high risk for infections like periodontitis.
Numerous epidemiologic surveys demonstrate an increased prevalence of periodontitis among patients with uncontrolled or poorly controlled diabetes mellitus. For example, Cianciola _et al_. (1982) reported that 13.6% and 39% of type 1 diabetics, 13–18 and 19–32 years of age respectively, had periodontal disease. In contrast, none of the non-diabetic sibling controls and 2.5% of the non-diabetic, unrelated controls exhibited clinical evidence of periodontitis. In a classic study, Thorstensson and Hugoson (1993) examined the severity of periodontitis in patients with diabetes mellitus and compared severity of periodontitis with the duration a patient had been diagnosed with diabetes. In looking at three age cohorts, 40–49 years, 50–59 years, and 60–69 years, the 40–49 years age group diabetics had more periodontal pockets ≥6 mm and more extensive alveolar bone loss than non-diabetics. In this same age group, there were also more subjects with severe periodontal disease experience among the diabetics than among the non-diabetics. In noting that the younger age diabetics had more periodontitis than the older age diabetics, these authors reported that early onset of diabetes is a much greater risk factor for periodontal bone loss than mere disease duration.
Safkan-Seppala and Ainamo (1992) conducted a cross-sectional study of 71 type 1 diabetics diagnosed with the condition for an average of 16.5 years. Diabetics identified with poor glycemic control demonstrated significantly more clinical attachment loss and radiographic alveolar bone resorption as compared to well controlled diabetics with the same level of plaque control. Two longitudinal cohort studies monitoring type 1 diabetics for 5 and 2 years respectively documented significantly more periodontitis progression among diabetics overall and among those whose diabetes was poorly controlled (Seppala _et al_. 1993; Firatli 1997).
Investigators from the State University of New York at Buffalo have published a number of papers documenting the periodontal status of Pima Indians, a population with a high prevalence of type 2 diabetes mellitus. Shlossman _et al_. (1990) first documented the periodontal status of 3219 subjects from this unique population. Diagnosing type 2 diabetes with glucose tolerance tests, the investigators found a higher prevalence of clinical and radiographic periodontitis for diabetics versus non-diabetics independent of age. This investigative group next focused on a cross-sectional analysis of 1342 dental subjects (Emrich _et al_. 1991). A logistic regression analysis indicated that type 2 diabetics were 2.8 times more likely to exhibit clinical attachment loss and 3.4 times more likely to exhibit radiographic alveolar bone loss indicative of periodontitis relative to non-diabetic controls. In a larger study of 2273 Pima subjects, 60% of type 2 diabetics were affected with periodontitis versus 36% of non-diabetic controls (Nelson _et al_. 1990). When a cohort of 701 subjects with little or no evidence of periodontitis at baseline were followed for approximately 3 years, diabetics were 2.6 times more likely to present with incident alveolar bone resorption as compared to non-diabetics. Taylor _et al_. (1998a,b) similarly reported higher odds ratios of 4.2 and 11.4 for the risk of progressive periodontitis among diabetic Pima Indians in general and poorly controlled diabetics (i.e. with glycated hemoglobin levels >9%) respectively.
The studies cited above review the evidence that diabetes is a modifier or risk factor for periodontitis. Of tremendous importance also are the data that have emerged indicating that the presence of periodontitis or periodontal inflammation can increase the risk for diabetic complications, principally poor glycemic control. Taylor _et al_. (1996) tested this hypothesis using longitudinal data on 88 Pima subjects. Severe periodontitis at baseline as defined clinically or radiographically was significantly associated with the risk of worsening glycemic control (glycated hemoglobin >9%) by six-fold over a 2-year period. Other significant co-variates in the regression modeling included subject age, smoking, and baseline severity and duration of type 2 diabetes. Collin and co-workers (1998) studied older adults in Finland and found that people with advanced periodontitis were more likely to have higher HbAlc levels than those who had no or moderate periodontitis at follow-up.
With the emerging evidence reviewed earlier in this chapter that periodontal disease is a significant risk factor for cardiovascular disease, Saremi _et al_. (2005) conducted a longitudinal trial to examine the effect of periodontal disease on overall mortality and cardiovascular disease-related mortality in 600 subjects with type 2 diabetes. In subjects with severe periodontitis, the death rate from ischemic heart disease was 2.3 times as high as the rate in subjects with no or mild periodontitis after accounting for other known risk factors. The death rate from diabetic nephropathy was 8.5 times higher in those with severe periodontitis. When deaths from renal and cardiac causes were analyzed together, the mortality rate from cardiorenal disease was 3.5 times higher in patients with severe periodontitis. These findings further suggest that periodontal disease is a risk for cardiovascular and renal mortality in people with diabetes (Janket _et al_. 2003; Scanniapieco _et al_. 2003a; Mealey & Rose 2005; Saremi _et al_. 2005; Mealey & Oates 2006).
# Periodontitis as a risk for respiratory infections
There is emerging evidence that in certain at risk populations, periodontitis and poor oral health may be associated with several respiratory conditions. Respiratory diseases contribute considerably to morbidity and mortality in human populations. Lower respiratory infections were ranked as the third most common cause of death worldwide in 1990, and chronic obstructive pulmonary disease (COPD) was ranked sixth (Scannapieco 1999; Scannapieco _et al_. 2003).
Bacterial pneumonia is either community-acquired or hospital-acquired (nosocomial). Community-acquired pneumonia is usually caused by bacteria that reside on the oropharyngeal mucosa, such as _Streptococcus pneumoniae_ and _Haemophilus influenzae_. Hospital-acquired pneumonia is often caused by bacteria within the hospital or health care environment, such as Gram-negative bacilli, _Pseudomonas aerugi-nosa_ , and _Staphylococcus aureus_ (Scannapieco 1999; Mealey & Klokkvold 2006). As many as 250 000 to 300 000 hospital-acquired respiratory infections occur in the US each year with an estimated mortality rate of about 30%. Pneumonia also contributes to a significant number of other deaths by acting as a complicating or secondary factor with other diseases or conditions.
COPD is another common severe respiratory disease characterized by chronic obstruction to airflow with excess production of sputum resulting from chronic bronchitis and/or emphysema. Chronic bronchitis is the result of irritation to the bronchial airway causing an expansion of the propagation of mucus-secreting cells within the airway epithelium. These cells secrete excessive tracheobronchial mucus sufficient to cause cough with expectoration for at least 3 months of the year over 2 consecutive years. Emphysema is the distention of the air spaces distal to the terminal bronchiole with destruction of the alveolar septa (Scannapieco 1999).
Beginning in 1992 with a report by Scannapieco's group at SUNY-Buffalo (Scannapieco _et al_. 1992), several investigators have hypothesized that oral and/or periodontal infection may increase the risk for bacterial pneumonia or COPD. It seems plausible from all the evidence reviewed in this chapter that the oral cavity may have a critical role in respiratory infections. For example, oral bacteria from the periodontal pocket can be aspirated into the lung to cause aspiration pneumonia. The teeth may also serve as a reservoir for respiratory pathogen colonization and subsequent nosocomial pneumonia. Typical respiratory pathogens have been shown to colonize the dental plaque of hospitalized intensive care and nursing home patients. Once established in the mouth, these pathogens may be aspirated into the lung to cause infection. Also, periodontal disease-associated enzymes in saliva may modify mucosal surfaces to promote adhesion and colonization by respiratory pathogens, which are then aspirated into the lungs. These same enzymes may also destroy salivary pellicles on pathogenic bacteria to hinder their clearance from the mucosal surface. Lastly, cytokines originating from periodontal tissues may alter respiratory epithelium to promote infection by respiratory pathogens (Scannapieco 1999).
Data from a longitudinal study of more than 1100 men revealed that alveolar bone loss was associated with the risk of COPD. Over a 25-year period, 23% of subjects were diagnosed with COPD. Subjects who had more severe bone loss at the baseline dental examination had a significantly increased risk of subsequently developing COPD compared with subjects with less bone loss (Hayes _et al_. 1998). Scannapieco and co-workers (1998) found that individuals with poor oral hygiene were at increased risk for chronic respiratory diseases such as bronchitis and emphysema. Scannapieco and Ho (2001) reported that patients with a history of COPD had significantly more periodontal attachment loss (1.48 ±1.35 mm) than subjects without COPD (1.17 ±1.09 mm). However, two recent systematic reviews of all of the current evidence indicate that at present there is not sufficient evidence to say that there is an association between periodontal disease and COPD (Scannapieco _et al_. 2003; Azarpazhooh & Leake 2006). There is emerging evidence for an association between hospital-acquired (nosocomial) bacterial pneumonia and periodontal disease. It is thought that potential respiratory pathogens, usually from the gastrointestinal tract, can colonize the oral cavity, where they are subsequently aspirated, leading to pneumonia (Mealey & Klokkevold 2006).
# Effects of treatment of periodontitis on systemic diseases
This chapter has examined the evidence, gathered by many investigators since the early 1990s, which suggests that periodontitis may be a risk for certain systemic conditions such as cardiovascular disease, adverse pregnancy outcomes, diabetes mellitus, and pulmonary disease. Collectively, the findings gathered from investigators world-wide are very compelling. It would certainly appear that periodontal disease is strongly associated with systemic conditions.
Students of dentistry will next ask, "If you treat periodontitis, do you prevent the onset or reduce the severity of these systemic complications?" It is clear that dentistry must now focus on intervention studies to determine whether treating periodontitis will have a beneficial effect on systemic diseases. This is not an easy task and some studies will take considerable time before we know the answer. However, there are initial data which examine intervention and the impact of periodontal treatment on several systemic conditions and the results are promising.
Regarding cardiovascular disease, evidence in human subjects demonstrating the beneficial effects of periodontal therapy on cardiovascular disease outcomes is limited and indirect at present. D'Aiuto and co-workers (2004) demonstrated that periodontitis patients treated with scaling and root planing exhibited significant serum reductions in the cardiovascular disease biomarker, CRP, and IL-6. In particular, patients who clinically responded to periodontal therapy in terms of pocket depth reductions were four times more likely to exhibit serum decreases in CRP relative to patients with a poor clinical periodontal response. Elter and colleagues (2006) also reported decreases in these serum biomarkers plus improved endothelial functions (i.e. flow-mediated dilation of the brachial artery) for 22 periodontitis patients treated with "complete mouth disinfection"
(i.e. scaling and root planing, periodontal flap surgery, and extraction of hopeless teeth within a 2-week interval). Similarly, Seinost and co-workers (2005) tested endothelial function in 30 patients with severe periodontitis versus 31 periodontally healthy control subjects. Prior to interventions, flow-mediated dilation was significantly lower in patients with periodontitis than in control subjects. Periodontitis patients with favorable clinical responses to nonsurgical periodontal therapy (i.e. scaling and root planing, topical and peroral antimicrobials plus mechanical retreatment) exhibited concomitant improvements in flow-mediated dilatation of the brachial artery and serum CRP concentrations. While the effects of periodontal therapy on cardiovascular disease events in patients have yet to be determined, the available pilot data suggest that periodontal therapies can improve surrogate cardiovascular disease outcomes like serum biomarkers and endothelial dysfunction.
In considering adverse pregnancy outcomes, four published intervention studies provide early evidence that preventive and treatment interventions aimed at reducing maternal periodontal infection and inflammation may reduce the likelihood of preterm low birthweight infants, while one study did not find an effect. Mitchell-Lewis and co-workers (2000) conducted a non-randomized pilot trial involving 164 US inner-city minority pregnant women. One group received full mouth debridement (scaling with hand and/or ultrasonic instruments) plus tooth polishing and oral hygiene instructions. The second group received no periodontal intervention. No differences in clinical periodontal status were observed between preterm low birthweight cases and women with normal birth outcomes, but preterm low birth-weight mothers had significantly higher levels of subgingival pathogens like _T. forsythia_ and _C. rectus._ Strikingly, while 18.9% of women receiving no periodontal intervention delivered preterm low birth-weight infants, only 13.5% of the treated women had preterm low birthweight infants.
A second pilot trial conducted in the US involved 366 women with periodontitis recruited between 21 and 25 weeks gestation (Jeffcoat _et al_. 2003). Subjects were stratified for risk factors (previous spontaneous PTB at <35 weeks, body mass index <19.8 or bacterial vaginosis as assessed by Gram stain) and randomized to one of three treatment groups as follows: (1) dental prophylaxis plus placebo capsule; (2) scaling and root planing plus placebo capsule; or (3) scaling and root planing plus metronidazole capsule (250 mg tid for 1 week). An additional group of 723 pregnant women meeting the same criteria for periodontitis but receiving no intervention served as the negative control. Women treated with scaling and root planing plus placebo capsules exhibited the lowest incidence rate for PTB <35 weeks (0.8%). Those treated with dental prophylaxis plus placebo capsules or scaling and root planing plus metronidazole capsules exhibited intermediate incidence rates for preterm deliveries (4.9% and 3.3% respectively). In contrast, the rate of PTB for the untreated reference group was 6.3%. This trial supported the hypothesis that mechanical periodontal therapy alone may reduce PTB in pregnant women with periodontitis.
Lopez and co-workers (2002a, 2005) have reported results from two intervention studies conducted in Chile demonstrating consistent, significant, and beneficial effects of mechanical periodontal therapy on preterm low birthweight outcomes. In the first trial, the investigators enrolled 351 pregnant women with clinical evidence of periodontitis (four or more teeth with one or more site exhibiting pocket depth ≥4 mm and clinical attachment loss ≥3 mm) and randomized them to immediate mechanical periodontal therapy (scaling and root planing) versus delayed (postpartum) treatment. The total incidence of PLBW in this cohort of periodontitis subjects was 6.26%. For women treated for periodontal disease, the incidence of PLBW was only 1.84%, while the incidence was 10.11% in untreated women. When a multivariate logistic regression analysis was performed controlling for other risk factors, delayed periodontal disease treatment was the strongest factor related to PLBW with an OR of 4.70 (95% CI 1.29–17.13). In the second trial, 870 pregnant women with gingivitis (≥25% of sites bleeding on probing but no clinical attachment loss ≥2 mm) were randomly assigned to immediate versus postpartum periodontal treatment (supra-and subgingival scaling, tooth polishing, and daily rinsing with 0.12% chlorhexidine gluconate). Those receiving immediate periodontal treatment also received maintenance therapy plus oral hygiene instructions every 2–3 weeks until delivery. Accordingly, the incidence of preterm low birthweight in the immediate treatment group was 2.14% versus 6.71% for the control group (OR = 3.26, 95% CI 1.56–6.83). After adjusting for other known risk factors, women with gingivitis receiving delayed intervention were almost three times more likely to deliver preterm as compared to women who received periodontal treatment (OR = 2.76, 95% CI 1.29–5.88). One trial did not find an effect of scaling and root planing on adverse pregnancy outcomes (Michalowicz _et al_. 2006). Overall, these clinical trials suggest that mechanical intervention in pregnant mothers with gingivitis or periodontitis can reduce the incidence of preterm low birthweight.
Clinicians and investigators working with patients who have diabetes mellitus have studied whether periodontal treatment can improve glycemic control. Several investigators have sought to answer this question using periodontal mechanical treatment as the intervention (Seppala & Ainamo 1994; Aldridge _et al_. 1995; Smith _et al_. 1996; Christgau _et al_. 1998; Stewart _et al_. 2001). Some of these studies have failed to detect an improvement in glycated hemoglobin level with scaling and root planing alone, while others have shown an improvement.
Kiran and co-workers conducted a study of patients with well controlled type 2 diabetes who had gingivitis or mild periodontitis. Prophylaxis and scaling and root planing, without systemic antibiotic therapy, was examined for the effect on periodontal disease and glycemic control. Control diabetic subjects with periodontal disease received no treatment. The treated subjects had a 50% reduction in the prevalence of gingival bleeding 3 months after treatment. In addition these subjects had a significant improvement in glycemic control, with a reduction in the mean HbAlc value of 0.8%. The control subjects who were not treated had no change in periodontal status or glycemic control (Kiran _et al_. 2005).
Grossi _et al_. (1997) reported positive findings from an intervention trial featuring 113 Pima Indians with type 2 diabetes and periodontitis who received both mechanical and antimicrobial treatment. At baseline, participants were treated with scaling and root planing plus one of five antimicrobial regimens: (1) water (placebo) rinse and peroral doxycycline (100 mg qid for 2 weeks), (2) 0.12% chlorhexidine rinse and peroral doxycycline, (3) povidone–iodine rinse and peroral doxycycline, (4) 0.12% chlorhexidine rinse and peroral placebo, or (5) povidone–iodine rinse and peroral placebo. Subjects were evaluated using clinical, microbiologic, and laboratory parameters prior to therapy and at 3 and 6 months. All treatment groups on average demonstrated clinical and microbiological improvements; however, those groups treated with adjunctive peroral tetracycline exhibited significant and greater reductions in pocket depth and subgingival detection rates for _P. gingivalis_ as compared to the groups receiving peroral placebo.
Most strikingly, diabetic subjects receiving mechanical therapy plus peroral tetracycline demonstrated significant, 10% reductions in their glycated hemoglobin levels. Two small, uncontrolled cohort studies with type 1 diabetic–periodontitis patients each similarly reported improvements in glycemic control with combination mechanical–antimicrobial therapy (Williams & Mahan 1960; Miller _et al_. 1992).
At present it is still not clear what can be expected from treating or reducing periodontal disease in diabetic subjects on glycemic control. There are enough available data to at least say that the effect of periodontal disease treatment on reducing HbAlc levels in subjects with diabetes has promise. There is such great variability among patients in the studies to date that it appears that some diabetic subjects had little change in glycemic control while others had major improvement. Nonetheless, it is very clear that periodontal health is a major goal for subjects with diabetes (Mealey & Oates 2006).
Last, the evidence for the effect of periodontal intervention on bacterial pneumonia shows promise. There are a number of studies which examine the effect of treating oral infection in reducing the risk of pneumonia in high-risk populations. DeRiso and colleagues (1996) studied subjects admitted to a surgical intensive care unit. When subjects received a chlorhexidine rinse twice a day compared to control subjects receiving a placebo rinse, the incidence of pneumonia was reduced 60% in the chlorhexidine treated group compared to the control group. Fourrier and colleagues (2000) found a similar 60% reduction in pneumonia with the use of a 0.2% chlorhexidine gel.
In a landmark study, Yoneyama and co-workers (2002) examined the role of supervised toothbrushing plus providone–iodine on the incidence of pneumonia in a group of elders living in nursing homes in Japan. When these subjects had their mouths cleaned, with supervision, there was a 39% reduction in pneumonia over a 2-year period compared to the control group. Recent reviews of the evidence clearly indicate that when bacterial plaque is reduced in the mouth in at-risk subjects, the risk of pneumonia is reduced. These findings are limited at present to special-care populations. Little evidence exists that poor oral hygiene and periodontal disease increase the risk for community-acquired pneumonia (Azarpazhooh & Leake 2006; Scannapieco _et al_. 2003b).
Dentistry has come a long way since 1900 when Willoughby Miller and William Hunter proclaimed that oral disease caused most systemic disease. A century later we are developing a scientifically based understanding of how in fact periodontitis may be a risk for certain systemic diseases. As these more recent observations are confirmed and clarified, dentistry will have a new responsibility in caring for patients who may develop or who have periodontitis. It is no longer just teeth that are at risk.
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# Chapter 22
# The Periodontal Abscess
Mariano Sanz, David Herrera, and Arie J. van Winkelhoff
* * *
Introduction
Classification
Prevalence
Pathogenesis and histopathology
Microbiology
Diagnosis
Differential diagnosis
Treatment
Complications
Tooth loss
Dissemination of the infection
* * *
# Introduction
Odontogenic abscesses include a broad group of acute infections that originate from the tooth and/or the periodontium. Such abscesses are associated with an array of symptoms, including a localized purulent inflammation in the periodontal tissues that causes pain and swelling. Abscesses are one of the main causes for patients to seek emergency care in the dental clinic. Depending on the origin of the infection the lesions can be classified as periapical, periodontal, and pericoronary abscesses.
# Classification
Different classifications have been suggested for periodontal abscesses: chronic or acute; single or mul tiple; gingival or periodontal; occurring in the supporting periodontal tissues or in the gingiva. A classification has been proposed (Meng 1999) and includes _gingival abscesses_ (in previously healthy sites and caused by impactation of foreign bodies), _peri-odontal abscesses_ (either acute or chronic, in relation to a periodontal pocket), and _pericoronal abscesses_ (at incompletely erupted teeth). This classification was included at the revised classification system for periodontal diseases developed at _The International Workshop for a Classification of Periodontal Diseases and Conditions_ organized by the American Academy of Periodontology in 1999, and for the first time, peri-odontal abscesses were included as an independent entity.
The most rational classification of periodontal abscesses is, however, the one based on its aetiology. Depending on the cause of the acute infectious process, two types of abscesses may occur:
* _Periodontitis-related abscess_ , when the acute infection originates from bacteria present at the subgingival biofilm in a deepened periodontal pocket
* _Non-periodontitis-related abscess_ , when the acute infection originates from bacteria originating from another local source, such as a foreign body impaction or from alterations in the integrity of the root leading to bacteria colonization.
In a periodontitis patient a periodontal abscess represents a period of active tissue breakdown and is the result of an extension of the infection into the still intact periodontal tissues. This abscess formation is usually due to the marginal closure of a deep peri-odontal pocket and lack of proper drainage. Therefore, the existence of deep, tortuous pockets and deep concavities associated with furcation lesions favors the development of these acute conditions. Once the acute inflammatory process is started, there is a local accumulation of neutrophils, formation of pus, and tissue breakdown. The retention of pus in the pocket may further compromise the drainage and the lesion may progress rapidly.
There are different mechanisms behind the formation of a _periodontitis-related abscess_ :
* _Exacerbation of a chronic lesion_. Such abscesses may develop in a deepened periodontal pocket without any obvious external influence, and may occur in: (a) an untreated periodontitis patient, or (b) as a recurrent infection during supportive periodontal therapy.
* _Post-therapy periodontal abscesses_. There are various reasons why an abscess may occur during the course of active therapy:
* Post-scaling periodontal abscess (Dello Russo 1985). When these lesions occur immediately after scaling or after a routine professional prophylaxis they are usually related to the presence of small fragments of remaining calculus that obstruct the pocket entrance once the oedema in the gingiva has disappeared (Dello Russo 1985; Carranza 1990). This type of abscess formation can also occur when small fragments of calculus have been forced into the deep, previously uninflamed portion of the periodontal tissues (Dello Russo 1985).
* Post-surgery periodontal abscess. When an abscess occurs immediately following perio-dontal surgery, it is often the result of an incomplete removal of subgingival calculus or to the presence of foreign bodies in the periodontal tissues, such as sutures, regenerative devices, or periodontal pack (Garrett _et al._ 1997).
* Post-antibiotic periodontal abscess. Treatment with systemic antibiotics without subgingival debridement in patients with advanced periodontitis may also cause abscess formation (Helovuo & Paunio 1989; Helovuo _et al._ 1993; Topoll _et al._ 1990). In such patients, the subgingival biofilm may protect the residing bacteria from the action of the antibiotic, resulting in a super-infection leading to an acute process with the ensuing inflammation and tissue destruction. Helovuo _et al._ (1993) followed patients with untreated periodontitis who were given broad-spectrum antibiotics (penicillin, erythromycin) for non-oral reasons. They showed that 42% of these patients developed marginal abscesses within 4 weeks of antibiotic therapy.
_Non-periodontitis-related abscess_ formation may also occur in relation to a periodontal pocket, but in such cases, there is always an external local factor that explains the acute inflammatory process. Such factors may include:
* Impaction of foreign body in the gingival sulcus or periodontal pocket (Gillette & Van House 1980; Abrams & Kopczyk 1983). It may be related to oral hygiene practices (toothbrush, toothpicks, etc.) (Gillette & Van House 1980; Abrams & Kopczyk 1983), orthodontic devices, food particles, etc.
* Root morphology alterations. In this instance local anatomic factors, such as an invaginated root (Chen _et al._ 1990), a fissured root (Goose 1981), an external root resorption, root tears (Haney _et al._ 1992; Ishikawa _et al._ 1996) or iatrogenic endodontic perforations (Abrams _et al._ 1992), may be the cause of the abscess formation.
# Prevalence
The prevalence of periodontal abscesses was studied in emergency dental clinics (Ahl _et al._ 1986; Galego-Feal _et al._ 1996), in general dental clinics (Lewis _et al._ 1990), in periodontitis patients before treatment (Gray _et al._ 1994), and in periodontitis patients during sup-portive periodontal therapy (SPT) (Kaldahl _et al._ 1996; McLeod _et al._ 1997).
Among all dental conditions in need of emergency treatment, periodontal abscesses represent between 8% and 14% (Ahl _et al._ 1986; Galego-Feal _et al._ 1996). Gray _et al._ (1994) monitored periodontal patients in a military clinic and found that periodontal abscesses had a prevalence of 27.5%. In this population, 13.5% of the patients undergoing active periodontal treatment had experienced abscess formation, while untreated patients showed a higher figure, 59.7%. McLeod _et al._ (1997) followed 114 patients in SPT and identified 42 patients (27.5%) that had suffered from acute episodes of periodontal abscess.
In a prospective longitudinal treatment study, by Kaldahl _et al._ (1996), the occurrence of periodontal abscesses during 7 years of periodontal maintenance was also studied. From the 51 patients included, 27 abscesses were detected. Twenty-three of the abscesses occurred at teeth in quadrants treated only by coronal scaling, three in areas treated by root planing, and only one in areas treated by surgical therapy. Sixteen out of 27 abscess sites had an initial probing pocket depth >6 mm, while in eight sites the probing depth was 5–6 mm.
Abscesses often occur in molar sites, representing more than 50% of all sites affected by abscess formation (Smith & Davies 1986; McLeod _et al._ 1997; Herrera _et al._ 2000a). The most likely reason for this high prevalence of abscesses in molars could be presence of pockets involving the furcation and the complex anatomy and root morphology of such teeth. However, in a recently published study in Colombian patients, the lower anterior incisors were the most frequently affected teeth (Jaramillo _et al._ 2005).
The occurrence of a periodontal abscess may be important not only due to its relatively high prevalence, but also on how these acute infections may influence the prognosis of the affected teeth. Since abscesses sometimes develop during SPT in teeth with remaining deep periodontal pockets and a reduced periodontal support, the additional periodontal destruction occurring during the acute periodontal process may be the main indication for its extraction (Chace & Low 1993; McLeod _et al._ 1997).
# Pathogenesis and histopathology
The periodontal abscess lesion contains bacteria, bacterial products, inflammatory cells, tissue breakdown products, and serum. The precise pathogenesis of this lesion is still obscure. It is hypothesized that the occlusion of the periodontal pocket lumen, due to trauma or tissue tightening, will prevent drainage and result in extension of the infection from the pocket into the soft tissues of the pocket wall, resulting in the formation of the abscess. The entry of bacteria into the soft tissue pocket wall could be the event that initiates the formation of a periodontal abscess, however it is the accumulation of leukocytes and the formation of an acute inflammatory infiltrate what will be the main cause of the connective tissue destruction, encapsulation of the bacterial mass, and formation of pus. The inflammatory cells and their extracellular enzymes are, therefore, the main cause of this destruction of connective tissue. Both the lowered tissue resistance and the virulence and number of bacteria will determine the course of this acute infection.
**Fig. 22-1** Schematic drawing showing the histopathology of a periodontal abscess.
The histopathology of this lesion demonstrates, in its first phases, the central area of the abscess filled with neutrophils, in close vicinity with remains of tissue destruction and soft tissue debris. At a later stage, a pyogenic membrane, composed of macro-phages and neutrophils, is organized. The rate of tissue destruction within the lesion will depend on the growth of bacteria inside the foci and their virulence, as well as on the local pH. An acidic environment will favor the activity of lysosomal enzymes and promote tissue destruction (DeWitt _et al._ 1985).
De Witt _et al_. (1985) studied biopsies sampled from 12 abscesses. The biopsies were taken immediately apical to the centre of the abscess and processed for histologic examination. They observed that the sites examined had a normal oral epithelium and lamina propria, but an inflammatory cell infiltrate resided lateral to the pocket epithelium. There were foci of neutrophil and lymphocyte accumulations in areas characterized by massive tissue destruction and a mass of granular, acidophilic, and amorphous debris present in the pocket (Fig. 22-1). Gram-negative bacteria were seen invading both the pocket epithelium and the compromised connective tissue in seven out of nine biopsies evaluated by electron microscopy.
# Microbiology
In review articles and textbooks it is usually cited that that purulent oral infections are polymicrobial, and mainly caused by endogenous bacteria (Tabaqhali 1988). However, very few studies have investigated the specific microbiota of periodontal abscesses. Newman & Sims (1979) studied nine abscesses and
found that 63.1% of the microbiota was comprised of strict anaerobes. Topoll _et al._ (1990) analysed 20 abscesses in 10 patients who had taken antibiotics prior to the study. They reported that 59.5% of the microbiota was made up of strict anaerobes. Herrera _et al._ (2000a) reported that 45.1% of the bacteria in the abscess material included anaerobes.
These studies have shown that the microbiota of periodontal abscess is not different from the microbiota of chronic periodontitis lesions. This microflora is polymicrobial and dominated by non-motile, Gram-negative, strict anaerobic, rod-shaped species. From this group, _Porphyromonas gingivalis_ is probably the most virulent and relevant microorganism. The occur-rence of _P. gingivalis_ in periodontal abscesses ranges from 50–100% (Newman & Sims 1979; van Winkelhoff _et al._ 1985; Topoll _et al._ 1990; Hafström _et al._ 1994; Herrera _et al._ 2000a; Jaramillo _et al._ 2005). Using a poly-merase chain reaction technique, Ashimoto _et al_. (1998) found _P. gingivalis_ in all of the seven cases of abscesses they investigated. Other anaerobic species that are usually found include _Prevotella intermedia_ , _Prevotella melaninogenica_ , _Fusobacterium nucleatum_ , and _Tanner-ella forsythia_. Spirochetes ( _Treponema_ species) are also found in most cases (Ashimoto _et al._ 1998). The major-ity of the Gram-negative anaerobic species are non-fermentative and display moderate to strong proteolytic activity. Strict anaerobic, Gram-positive bacterial species in periodontal abscesses include _Micromonas micros_ , _Actinomyces_ spp., and _Bifidobacterium_ spp. Facultative anaerobic Gram-negative bacteria that can be isolated from periodontal abscesses include _Campylobacter_ spp., _Capnocytophaga_ spp., and _Aggregatibacter actinomycetemcomitans_ (Hafström _et al._ 1994). The presence of Gram-negative enteric rods has also been reported (Jaramillo _et al._ 2005).
# Diagnosis
The diagnosis of a periodontal abscess should be based on the overall evaluation and interpretation of the patient´s chief complaint, together with the clinical and radiological signs found during the oral examination (Corbet 2004).
**Fig. 22-2** Periodontal abscess associated with a lower right first molar. Observe the association between the abscess formation and the furcation lesion in this molar.
**Fig. 22-3** Periodontal abscess associated with a mandibular second molar. There is diffuse swelling affecting all the buccal surface of the molar.
**Fig. 22-4** Periodontal abscess associated with a lower right first molar. Observe the spontaneous suppuration expressed through the gingival margin.
**Fig. 22-5** Periodontal abscess associated with an upper right third molar. This lesion is associated with tooth extrusion and mobility.
The most prominent symptom of a periodontal abscess is the presence of an ovoid elevation of the gingival tissues along the lateral side of the root (Fig. 22-2) _._ Abscesses located deep in the periodontium may be more difficult to identify by this swelling of the soft tissue, and may present as diffuse swellings or simply as a red area (Fig. 22-3). Another common finding is suppuration, either from a fistula or, most commonly, from the pocket (Fig. 22-4). This suppuration may be spontaneous or occur after applying pressure on the outer surface of the gingiva.
The clinical symptoms usually include pain (from light discomfort to severe pain), tenderness of the gingiva, swelling, and sensitivity to percussion of the affected tooth. Other related symptoms are tooth elevation and increased tooth mobility (Fig. 22-5).
During the periodontal examination, the abscess is usually found at a site with a deep periodontal pocket. Signs associated with periodontitis such as bleeding on probing, suppuration and sometimes increased tooth mobility are also present (Smith & Davies 1986; Hafström _et al._ 1994; Herrera _et al._ 2000a). The radiographic examination may reveal either a normal appearance of the interdental bone or evident bone loss, ranging from just a widening of the peri-odontal ligament space to pronounced bone loss involving most of the affected root (Fig. 22-6).
In some patients the occurrence of a periodontal abscess may be associated with elevated body temperature, malaise, and regional lymphadenopathy (Smith & Davies 1986; Carranza 1990; Ibbott _et al._ 1993; Herrera _et al._ 2000a). Herrera _et al._ (2000a) reported laboratory data from blood and urine in patients immediately after the diagnosis of a peri-odontal abscess and reported that in 30% of the patients there was an elevated number of blood leukocytes. The absolute number of blood neutrophils and monocytes was also increased in 20–40% of the patients.
## Differential diagnosis
The differential diagnosis of periodontal abscesses should always be made with other abscesses that can occur in the oral cavity. Acute infections, such as periapical abscesses, lateral periapical cysts, vertical root fractures, endo-periodontal abscesses, may have a similar appearance and symptomatology as a periodontal abscess, although with a clearly different aetiology. Signs and symptoms indicating a more likely periodontal origin include: a history of peri-odontal disease or previous periodontal therapy; clinical signs of deep periodontal pockets releasing pus; frequently a vital pulp response; and radiographic findings of crestal bone loss, frequently associated with angular bone defects and furcations. On the contrary signs and symptoms indicating a more likely periapical (endodontal) origin will include: a history of caries, restorative or endodontic therapy; clinical signs of questionable or lack of response to pulp tests; presence of advanced caries lesions or restorations and the presence of a sinus tract; the radiographic findings will usually evidence the presence of a periapical radiolucency associated with either a carious or restored tooth or an endodontically treated tooth showing more or less endodontic filling or endodontic or post perforations.
**Fig. 22-6** (a) Periodontal abscess associated with a lower left canine. The fistulous tract opening is demonstrated with a guttapercha point. (b) Radiologic image of the lower canine from (a). The differentiation from a periapical abscess was by the positive tooth vitality and absence of caries or restoration in the canine and the presence of a deep periodontal pocket in the lingual aspect of this tooth.
Other lesions may appear in the oral cavity with a similar appearance as a periodontal abscess. Parrish _et al._ (1989) described three cases of osteomyelitis in periodontitis patients, initially diagnosed as peri-odontal abscesses. Different tumors may also have the appearance of a periodontal abscess. Such tumors include gingival squamous cell carcinoma (Torabinejad & Rick 1980; Kirkham _et al._ 1985), a metastatic carcinoma from pancreatic origin (Selden _et al._ 1998), a metastatic head and neck cancer (Elkhoury _et al._ 2004), and an eosinophilic granuloma diagnosed by rapid bone destruction after periodontal therapy (Girdler 1991). In cases where the abscess does not respond to conventional therapy, a biopsy and pathologic diagnosis are recommended (see also Chapter 16).
# Treatment
The treatment of the periodontal abscess usually includes two stages: (1) the management of the acute lesion, and (2) the appropriate treatment of the original and/or residual lesion, once the emergency situation has been controlled _._
For the treatment of the acute lesion, different alternatives have been proposed ranging from: (1) incision and drainage, (2) scaling and root planing,
(3) periodontal surgery, and (4) the use of different systemically administered antibiotics. Some authors have recommended a pure mechanical treatment with either surgical drainage through the pocket, or scaling and planing of the root surface and compression and debridement of the soft tissue wall (Ahl _et al._ 1986; Ammons 1996). This mechanical therapy may cause irreversible damage to healthy periodontal tissues adjacent to the lesion. Such damage may particularly occur when the swelling is diffuse or is associated with marked tissue tension. In order to avoid this damage to healthy periodontal tissue other authors recommend the use of systemically administered antibiotics as the only initial treatment in abscesses with marked swelling, tension, and pain. In such instances, once the acute condition has receded, mechanical debridement, including root planing, should be performed.
The clinical evidence of the efficacy of these different therapeutic approaches is scarce, since only few clinical studies have assessed the efficacy of abscess therapy. Smith and Davies (1986) studied 62 abscesses in 55 patients. Their proposed treatment included incision, drainage, and systemic metronidazole (200 mg, tid for 5 days) and after the acute phase, regular periodontal treatment. Hafström _et al._ (1994) recommended supragingival debridement, together with systemic tetracycline therapy for 2 weeks, and reported good clinical outcomes when drainage and irrigation were added to the protocol. Similar good results were obtained in a controlled parallel study in which two systemic antibiotic regimes (amoxicillin/clavulanate, 500 + 125 mg, tid for 8 days; and azithromycin, 500 mg, once per day for 3 days) were used as the only treatment during the phase of initial therapy. This was followed by regular periodontal treatment once the acute phase was resolved (Herrera _et al._ 2000b). The study showed that the short-term clinical outcome with the use of both antibiotics regimens was successful and the infectious process and abscess symptomatology was controlled just by using systemic antibiotics without concomitant or prior debridement (Fig. 22-7). There was a rapid reduction of the pain, significant resolution of the oedema, redness, and swelling, and the suppuration almost entirely disappeared. Periodontal outcome measurements, such as bleeding and periodontal probing depth, were also significantly reduced. Short-term microbiological results demonstrated a reduction of the microbiota in the abscess, as well as the number of selected periodontal pathogens (Herrera _et al._ 2000b). However, none of the antibiotic therapies were able to resolve the infection entirely. This implies that mechanical debridement, sometimes including a surgical approach, is an essential measure in the definitive treatment of this lesion. Moreover, two different studies have provided information on the antibiotic susceptibility profiles of periodontal pathogens isolated from periodontal abscesses and have reported the presence of resistant strains (Herrera _et al._ 2000b; Jaramillo _et al._ 2005).
**Fig. 22-7** (a) Treatment of a periodontal abscess with systemic antibiotics (azithromycin, 500 mg for 3 days) without any mechanical therapy. Baseline situation. (b) 5 days after antibiotic therapy. (c) 12 days after antibiotic therapy, just before the final periodontal instrumentation.
Table 22-1 shows a number of different antibiotics that may be used in the treatment of a periodontal abscess. Doses and regimes recommended may differ between different countries. In principle, a high dose of the antibiotic delivered during a short period of time, is recommended. If the patient is recovering properly, the antibiotic should not be given for more than a 5-day period.
# Complications
## Tooth loss
Periodontal abscesses have been suggested as the main cause for tooth extraction during the phase of supportive periodontal therapy (SPT) (Chace & Low 1993). A tooth with a history of repeated abscess formation is considered to be a tooth with a questionable prognosis (Becker _et al._ 1984). In a retrospective study, 45% of teeth with periodontal abscesses in a SPT population were extracted (McLeod _et al._ 1997). Another retrospective study including 455 of teeth with a questionable prognosis showed that 55 (12%) were lost after a mean of 8.8 years, and that the main reason for tooth extraction was periodontal abscess formation (Chace & Low 1993). Smith and Davies (1986) evaluated 62 teeth with abscesses; 14 (22.6%) teeth were extracted as initial therapy, and 9 (14.5%) after the acute phase. Out of the 22 teeth treated and subsequently monitored, 14 had to be extracted during the following 3 years.
Table 22-1 Antimicrobial agents that may be used in the treatment of periodontal abscesses
## Dissemination of the infection
A number of publications, mainly case reports, have described different systemic infections in different parts of the body, in which the suspected source of infection was a periodontal abscess. Two possible sources of dissemination have been described:
* Dissemination of the bacteria inside the tissues during therapy. A case of pulmonary actinomycosis was related to the treatment of a periodontal abscess, which was ultrasonically scaled 1 month earlier (Suzuki & Delisle 1984). A case of brain abscess was observed in a healthy patient with a periodontal abscess who was treated with drainage and curettage without systemic antibiotic 2 weeks earlier. The microbiology of the lesions demonstrated, among other bacteria, _Prevotella melaninogenica_ and other _Bacteroides_ sp. (Gallaguer _et al._ 1981). A retrospective study on total knee arthroplasty infections (Waldman _et al._ 1997) discovered that 9 out of 74 infections had been previously treated for an oral infection, including the drainage of a periodontal abscess.
* Bacterial dissemination through the blood stream due to bacteremia from an untreated abscess. Cellulitis in breast cancer patients have been reported following gingivitis or an abscess (Manian 1997), due to transient bacteremia and reduced host defenses (radiation therapy and axillary dissection). A periodontal abscess was associated with the development of a cervical necrotizing fasciitis (Chan & McGurk 1997). A necrotizing cavernositis was thought to be related to a severe periodontal infection, including three periodontal abscesses (Pearle & Wendel 1993).
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# Chapter 23
# Lesions of Endodontic Origin
Gunnar Bergenholtz and Domenico Ricucci
* * *
Introduction
Disease processes of the dental pulp
Causes
Progression and dynamic events
Accessory canals
Periodontal tissue lesions to root canal infection
Effects of periodontal disease and periodontal therapy on the condition of the pulp
Influences of periodontal disease
Influence of periodontal treatment measures on the pulp
Root dentin hypersensitivity
* * *
# Introduction
In the study of pathogenesis and causality of peri-odontal disease processes, lesions of endodontic origin are significant as they frequently extend and manifest themselves in the attachment apparatus. Not only do these lesions produce signs and symptoms of inflammation in apical areas of teeth, they may also induce tissue destruction along the lateral aspects of roots and in furcations of two- and multi-rooted teeth. In either instance, the lesions are main-tained by noxious elements that derive from the pulpal space along openings to the periodontal tissues. Channels connecting the two tissue compartments include foramina at the apex and lateral ramifications termed accessory canals.
Microorganisms residing in necrotic areas of a more or less broken down pulp usually maintain these lesions. Lesions of endodontic origin may also appear or prevail following endodontic treatment. In these cases, treatment measures, aimed at either preventing the establishment of a root canal infection or getting rid of an already manifest infection, have been unsuccessful. As root canal infections have been assumed to have an impact on both the progression of periodontitis and the potential to achieve optimal results of periodontal therapy, the first part of this chapter describes the specific features and dynamic events that are associated with lesions of the pulp and the manner by which they may interfere with the periodontium.
The fact that the periodontium and the dental pulp are anatomically interconnected also implies that exchange of noxious agents may also occur in the opposite direction, that is from the external environment to the pulp. A prerequisite for this is that those communication pathways that are normally secured by healthy periodontal tissue have been uncovered. This will occur as periodontal disease advances. The lesion of the pulp that may follow may involve both pain and tissue destruction. Resorptive processes and treatment measures aimed at managing periodontal disease enhance this potential as the accompanying exposure of dentinal tubules, by loss of cementum, establishes yet another passage across the body of the tooth structure. In fact, a common complication to periodontitis and periodontal therapy is an ailment commonly termed root dentin hypersensitivity, a condition associated with the direct exposure of root dentin to the oral environment (Gillam & Orchardson 2006).
The second part of this chapter is concerned with the consequences for the vital pulp of root surface exposure by periodontal disease and periodontal therapy. It also covers aspects of the mechanisms and management of root dentin hypersensitivity.
# Disease processes of the dental pulp
## Causes
The dental pulp is normally well protected from injurious influences by an intact hard tissue encasement and by a healthy periodontium. The healthy condition of the pulp, however, is regularly challenged under clinical conditions. While some adverse influences are of minor significance and cause only negligible tissue injury and minimal discomfort to the patient, others threaten the pulp's vital functions and can result in infectious complications, with effects both locally and systemically. Lesions of the pulp may have either a direct infectious background or may be induced by non-infectious injury. Both causes will be covered here in some detail.
Of non-infectious impairments, accidental trauma causing rupture of the neurovascular supply at the apex and major internal bleeding represents a distinct threat to the vitality of the pulp. Hence, concussions, subluxations, and various forms of tooth displacements may result in widespread ischemia leading to complete necrosis of the tissue. As the potential for tissue regeneration is slim in the fully developed tooth (Kristerson & Andreasen 1984), such pulp tissue necrosis, although not primarily infected, acts as a target for microbial invasion. The infecting microorganisms usually originate from the oral cavity. Following their penetration of cracks in the enamel and the dentinal tubules, multiplication in the necrotic pulp results in the development of inflammatory lesions of the periodontal tissues (Bergenholtz 1974; Sundqvist 1976).
Most pulpal conditions are initiated and maintained by infectious elements that access the pulp following loss of hard tissue integrity. Tooth destruction by caries is by far the most common source of bacterial exposure and is especially threatening when the lesion has reached the vicinity of the pulp tissue proper (see further below). Also fractures of teeth and dental restorative work bring an inherent risk for detrimental bacterial effects, should a restoration fail to seal completely the defect in the tooth substance (see review by Bergenholtz 2000). Most risky are extensive restorative works like full coverage crowns, which often require substantial sacrifice of healthy tooth tissue. Clearly in the short term, before the permanent restoration is cemented, the tissue exposure is subject to bacterial leakage along the margins of the temporary restoration, especially if it is poorly adapted to the remaining tooth substance. Yet, even though the pulp may have survived the initial stress of the cutting trauma and the leakage of bacterial elements, the injury induced usually results in considerable repair phenomena (scars). Such tissue changes involve hard tissue depositions and soft tissue fibrosis, which occur at the expense of vascularity and nerve tissue support (Bender & Seltzer 1972). Tissue alterations of this nature logically result in impaired immune defense function and, thus, reduce the potential for the pulp to resist future bacterial challenges.
Clinical followups of teeth supplied with single crowns or included as abutments in bridge works have indeed demonstrated that pulp tissue necrosis is not a rare complication and may affect 10–20% of the observed teeth over a 10–15-year period (Bergen-holtz & Nyman 1984; Karlsson 1986; Saunders & Saunders 1998; Cheung _et al_. 2005). In fact, the incidence of loss of pulpal vitality has been reported to increase over the course of time (Bergenholtz & Nyman 1984; Cheung _et al_. 2005). A similar increasing rate of pulpal infections has also been reported for young permanent teeth suffering traumatic ischemic injuries where pulps have been partly or completely replaced by hard tissue repair (Jacobsen & Kerekes 1977; Robertson _et al_. 1998).
### Conclusion
Injurious elements that may put the vital functions of the pulp at risk include deep caries, accidental trauma, and dental restorative procedures. A single insult, such as a traumatic injury, may cause an immediate breakdown of the tissue by severing the neurovascular supply. In other instances tissue breakdown is preceded by a direct bacterial exposure or following tissue repair to non-infectious and infectious insults.
## Progression and dynamic events
Although any injury may have serious implications for the vitality of the pulp, its ability to withstand insults, especially of a microbial nature, is far better if an intervening layer of dentin remains than if the tissue is directly exposed through the hard tissue barrier. In the former case even a thin dentin wall, although permeable, usually allows the pulp to mount an appropriate inflammatory response to offset bacterial threats. The common observation that the pulp rarely suffers breakdown underneath a caries lesion confined to dentin is strong evidence of the pulp's defense potential (Reeves & Stanley 1966; Massler 1967; Kamal _et al_. 1997; see also review by Björndal & Mjör 2001). The mechanisms involved relate both to innate and adaptive immune responses (Hahn _et al_. 2003; Dommisch _et al_. 2005; Durand _et al_. 2006; for a review see also Jontell _et al_. 1997) as well as to changes in dentin that constrict its permeability (for reviews see Pashley 1996; Bergenholtz 2000).
Experimental evidence to this effect derives from observations in both humans (Lundy & Stanley 1969; Warfvinge & Bergenholtz 1986) and animals (Lervik & Mjör 1977; Warfvinge & Bergenholtz 1986; Taylor _et al_. 1988). In some of these studies test cavities were prepared deep into dentin and were left unrestored to the oral environment (Lundy & Stanley 1969; Taylor _et al_. 1988). In other experimental series, similar cavities were challenged with soft carious dentin (Mjör & Tronstad 1972; Lervik & Mjör 1977) or components of dental plaque bacteria (Bergen-holtz & Lindhe 1975; Warfvinge & Bergenholtz 1986). Reflecting the permeability of dentin to microbial elements, inflammatory sequels consisting of increased vascular permeability, migration of polymorphonuclear leukocytes (PMNs) (Bergenholtz & Lindhe 1975; Warfvinge & Bergenholtz 1986), and nerve fiber sproutings (Taylor _et al_. 1988) rapidly emerged in the pulp adjacent to the exposed dentinal tubules. The adapative immune defense is also activated at very early stages as indicated by an increased presence of antigen-presenting cells (Jontell _et al_. 1997). Indeed, dendritic cells appear soon in an area of the pulp next to both cavity preparations (Ohshima _et al_. 1995) and superficial caries (Kamal _et al_. 1997) (Fig. 23-1). Yet, over the course of time, these responses subside and reparative dentin and soft tissue repair emerge, along with a reduction of immunocompetent cells, at the site of the previous inflammatory event (Lundy & Stanley 1969; Lervik & Mjör 1977; Warfvinge & Bergenholtz 1986; Kamal _et al_ 1997). In the experiments involving unrestored human teeth (Lundy & Stanley 1969), patients experienced pain and increased sensitivity of the exposed dentin along with the initial inflammatory episode. As repair and healing progressed the pain symptoms disappeared.
**Fig. 23-1** (a) Defense response of a human dental pulp to superficial caries in dentin (defect and dark stain at upper right hand corner) as represented by increased accumulation of Class II molecule-expressing cells of a dendritic morphology. (b) Extensions of cytoplasmatic processes into the dentinal tubules are numerous. Images kindly provided by Dr. Takashi Okiji.
An important point is that although inflammatory responses develop rapidly and early to bacterial challenges, microorganisms _per se_ are rarely able to penetrate the dentinal barrier and enter the pulp tissue, so long as it retains vital functions. Staining for bacteria in the histologic analysis of Lundy and Stanley (1969), for example, revealed that in no case, observed after 2–240 days, were organisms traced in the pulp tissue proper, while the exposed dentinal tubules were invaded to a varying extent. This finding once again demonstrates that dentin and pulp in concert are able to oppose bacterial threats.
By contrast, direct exposure of the pulp to the oral environment puts its vital functions at risk as bacteria in the oral cavity now may gain direct access to the tissue. Even a minuscule exposure is critical, unless properly treated, as there is little self-healing capacity by virtue of epithelium that can bridge the defect. Defense mechanisms may therefore prevent bacterial invasion of the pulpal space for only a limited period of time.
Three clinical cases, displayed in Figs. 23-2 to 23-4, demonstrate how pulpal inflammatory processes may typically develop and progress to the adjoining periodontal tissues. In these cases, caries has advanced to expose the tissue at an earlier point in time.
In the first example (Fig. 23-2) an inflammatory lesion is present at the site where caries has exposed the pulpal tissue. A rather thick layer of reparative dentine has formed at the roof of the pulp chamber next to the exposure indicating a repair response to previous irritation (Fig. 23-2a). Note that, except for the lesion area, the pulp displays normal tissue morphology with intact odontoblast layers lining the periphery of the tissue. Bacteria have accumulated (blue stains in dentin) near the exposure site (Fig. 23-2). The high magnification in Fig. 23-2d reveals numerous bacterial profiles in the pulp as well, where they are opposed by infiltrating PMNs in the lesion area. In this particular case the inflammatory process was clearly localized and both radiographic (Fig. 23-2a) and histologic examination gave no indication of interference with the periodontium.
A more advanced pulpal lesion is demonstrated in Fig. 23-3, where the inflammatory response to the distally located caries process in the lower molar has extended to the furcation area along a wide accessory canal (23-3b). Intrafurcal alveolar bone is resorbed and has been replaced by inflammatory tissue displaying proliferating epithelium (23-3). There is also an apical radiolucency at the distal root, while the apical region of the mesial root seems unaffected (23-3).
A third case (Fig. 23-4) shows necrosis of the coronal pulp following what has obviously been a rather long-standing caries process in a lower first molar. There are radiographic signs of apical periodontitis on both the distal and the mesial roots and a widened periodontal ligament space in the furcation (Fig. 23-4A). At the mesial aspect of the tooth, gingival tissue has proliferated into the pulp chamber (Fig. 23-4B). Figure 23-4C displays an area of the pulpal space at the entrance of the distal root canal, where the pulp is necrotic and where bacterial organisms have aggregated on the canal walls in a biofilm structure. Further down in the middle portion of the root, numerous PMNs meet the bacterial front and are engaged in phagocytic activities (Fig. 23-4D and inset). In more apical portions of the canal, numerous widened blood vessels are seen along with an infiltrated pulp connective tissue (Fig. 23-4E). The most apical portion of the pulp shows normal tissue structure (Fig. 23-4G), which also applies to the soft tissue attached to the root tip (Fig. 23-4F and inset) representing the apical radiolucency at the distal root in Fig. 23-4A.
**Fig. 23-2** (a) Second lower molar from a 30-year-old man with deep caries at the mesial aspect. Before extraction of the tooth the patient had presented with typical signs of pulpitis including percussion sensitivity and radiating pain. (b) A localized inflammatory response is present in the pulp adjacent to the site of caries penetration without spreading. In a section stained for bacteria (c) organisms are seen at the exposure site (blue stain) as well as in the inflammatory tissue lesion _per se_ (d) (see also text).
### Conclusion
The cases selected demonstrate an important function of the inflammatory defense in general that also applies to the dental pulp, which is to confine infectious elements and limit spread to other body compartments. The cases also demonstrate that a pulpal lesion has its prime focus at the source of the bacterial exposure. Hence, it is only following extension due to breakdown of the pulp and advancement of the bacterial front that periodontal tissue involvement is imminent. In some cases this may occur at a rather early stage of the pulp tissue lesion if an accessory canal is open to the marginal periodontium such as in the case in Fig. 23-3. In the absence of accessory canals extensive breakdown of the pulp is first required before the periodontal tissues may become engaged.
## Accessory canals
Accessory canals are lateral ramifications off the root canal system that connect the neurovascular system of the pulp with that of the periodontal ligament. Such anastomoses are formed during the early phases of tooth development, but may become blocked or reduced in width during the completion of root formation. Patent communications of varying sizes, numbers and locations, however, may remain in the fully developed tooth and serve as additional pathways for the neurovascular supply of the pulp beyond that of the main apical foramen.
Accessory canals can be observed in all groups of teeth. In fact, careful examinations of large numbers of extracted teeth, rendered transparent and injected with contrasting medium in the pulp chamber to allow three-dimensional visualizations, have revealed accessory canals in cervical and middle-root areas as well as in the apical root portions (DeDeus 1975; Vertucci 1984). Clearly the majority is found apically, whereas the prevalence tapers off in the middle and cervical root segments (DeDeus 1975; Vertucci 1984). In a study of 1140 extracted human teeth from adult subjects, De Deus (1975) reported accessory canals in 27% of the examined teeth. These canals were distributed at various levels of the root as depicted in Fig. 23-5.
Molars harbor accessory canals more frequently than premolars and anterior teeth. Patent canals are especially common in the furcation areas, where they have been found in between 20% and 60% of examined teeth (Lowman _et al_. 1973; Vertucci & Williams 1974; Gutmann 1978; Vertucci 1984). Vertucci (2005) has distinguished between different directions of entry by which accessory canals go into the furcation of mandibular molars. In some cases they run more or less vertically from the pulpal chamber. They may also extend off either root canal in a horizontal direction of which 80% derive from the distal root canal (Vertucci 2005) (Fig. 23-6).
**Fig. 23-3** Tooth specimen of a 48-year-old man, who presented with spontaneous pain, pain on mastication, percussion, and tooth mobility. An extensive inflammatory tissue destruction of the coronal pulp extends into the furcal area along an accessory canal. More apically, the pulp of the mesial root has retained normal tissue structures. There was no clinical swelling or remarkable pocket probing depth in this case indicating periodontal involvement (see text).
When accessory canals do occur, the potential dissemination of inflammatogenic elements from a diseased pulp to the periodontium is obvious. There is no documentation yet available to indicate how often such lesions develop. Although clinical observations demonstrate occurrence (Figs. 23-3, 23-7, 23-8, the rate at which endodontic lesions appear in the marginal periodontium from accessory and furcation canals seems to be low, as indicated by lack of reports of this being a significant clinical problem. It is to be expected that the wider accessory canals are, the greater is the likelihood for overt lesions to develop. Diameters of furcation canals in mandibular molars for example have been reported to vary from just a few microns to 720 microns (Vertucci 2005). Consequently, thin accessory canals, with the potential to mediate some release of infectious substances, may not cause more than a minor periodontal reaction that goes clinically undetected.
**Fig. 23-4** Tooth specimen of a 19-year-old female with extensive caries in a 1st lower molar that has led to partial pulp tissue breakdown, bacterial invasion, and establishment of an inflammatory defense line inside the pulpal space (see text). From Ricucci & Bergenholtz (2004), images appeared in _Endodontic Topics_ 2004, **8** , 68–67.
**Fig. 23-5** Frequency of accessory canals at different levels of the root. The data are average values obtained from DeDeus (1975). Observations were made after teeth had been rendered transparent and the root canal system filled with India ink. The figures given for the coronal portion include those of bi- and trifurcations of two- and multi-rooted teeth.
**Fig. 23-6** Furcal canals of two- and multirooted teeth, when present, may extend into the periodontium from the pulpal space either in a horizontal or vertical direction or both. Drawing adapted from Vertucci (2005).
### Conclusion
Although they occur, the large majority of teeth lack accessory canals in their cervical and middle root regions. This fact may explain why pulpal inflammatory lesions rarely are seen extended to the marginal periodontium. Most often they become centered around root apices only. When present with a diameter similar to that of the apical foramen, accessory canals can certainly mediate lesions of endodontic origin in the marginal periodontium. In endodontically treated teeth iatrogenic root perforations, carried out in conjunction with root canal instrumentation or post preparations, may serve as yet another pathway for dissemination of noxious elements to the periodontium (see Chapter 40).
## Periodontal tissue lesions to root canal infection
The ultimate outcome of an inflammatory break-down of the pulp is microbial take over of the pulpal space (Fig. 23-9). As host defense mechanisms are unable to reach far into root canals of necrotic pulps in order to combat the infection and pave the way for regeneration of pulpal tissue, an inflammatory defense zone is established in the periodontal tissues at exits of accessory canals and apical foramina. Hence, lesions of this nature remain as chronic processes unless subjected to treatment. Because the inflammatory process most frequently becomes positioned near root apices, the term apical periodontitis is commonly employed. As lesions may also develop along the lateral aspects of roots, the expression endodontic lesion will be used throughout this text to denote a periodontal lesion in any position that is sustained by noxious elements of endodontic origin.
**Fig. 23-7** (a) A lateral, alveolar bone destruction is observed between the roots of teeth #31 and #32. (b) The lesion in this case turned out to be associated with an accessory canal (filled in conjunction with the root filling procedure) emanating from an infected root canal in tooth #32. (c) Two-year recall of the endodontic treatment demonstrates near complete resolution of the bone lesion. Courtesy of Dr. Conrad Jacobsson.
The bacterial organisms that are able to initiate prevalent and which can be linked to more or less and maintain endodontic lesions have been studied aggressive forms of apical periodontitis (see below). in great detail over the years, primarily by sampling In recent years molecular identification methods, infected root canals followed by laboratory processing and phenotypic identification. The purpose of such studies has been to identify organisms that are prevalent and which can be linked to more or less aggressive forms of apical periodontitis (see below). In recent years molecular identification methods, including the polymerase chain reaction (PCR), have been used to supplement the picture (for reviews see Siqueira & Rocas 2005a; Spratt 2004). Indeed it has been demonstrated that many more species are involved than previously anticipated and the concept that only a limited group of 20–30 common isolates are associated with these lesions is currently being reassessed (Siqueria & Rocas 2005a,b; Siqueria _et al_. 2005). Yet, the microbiota in primary endodontic infections show features similar to that of deep periodontal pockets (Kerekes & Olsen 1990) and anaerobes usually have a dominant role. Spirochetes (Dahle _et al_. 1996; Rocas & Siqueria 2005; Foschi _et al_. 2005) and fungi (Waltimo _et al_. 1997; Peciuliene _et al_. 2001; Egan _et al_. 2002) may also reside in infected root canals and may contribute to the maintenance of these lesions. By contrast persistent infections subsequent to endodontic treatments seem less dominated by anaerobes and cultivation studies have demonstrated high prevalences of Gram-positive facultatives (Molander _et al_. 1998; Sundqvist _et al_. 1998; Chavez de Paz _et al_. 2003; Gomes _et al_. 2004; Forschi _et al_. 2005).
**Fig. 23-8** (a) prior to endodontic treatment, (b) prior to extraction due to extensive caries 11 years after endodontic treatment. (c, d) Cleared specimens show numerous accessory canals filled with root filling material. (e) Histologic examination shows that accessory canals are only partially filled (black material interspersed with inflammatory tissue).
Although not comprehensively studied, root canal infections most likely involve attachment of bacterial organisms to the root canal walls and the development of microbial communities in biofilms (Fig. 23-9) (Svensäter & Bergenholtz 2004). Organization in biofilms affords these organisms better protection against host defense mechanisms in comparison to their planktonic counterparts, but they are detached from such sites and dispersed for colonization at other body sites. Root canal bacteria usually have limited potential to survive in the periodontal tissue lesion _per se_ although bacterial organisms can be found in acute abscesses (Oguntebi _et al_. 1982; Williams _et al_. 1983; Lewis _et al_. 1986). It should also be mentioned that case reports have indicated that _Actinomyces_ -related species occasionally may invade the tissue lesion and aggregate in clusters or nests that elude host tissue elimination (Sundqvist & Reuterving 1980; Happonen _et al_. 1986). Yet in most instances bacteria are confined to the root canal space (Nair 1987). While the front line may be established at the orifice of the canal (Fig. 23-10), the host tissue–bacterial interface zone usually becomes localized well inside the root canal exits (Nair 1987) (Fig. 23-11). In what may be a rare situation (Siqueira & Lopes 2001), bacterial organisms in primary endodontic infections may overcome the host defense and aggregate as a biofilm on the outer root surface (Lomcali _et al_. 1996) (Fig. 23-12). Such structures have also been observed on root ends of teeth which have not responded favorably to endodontic treatment (Tronstad _et al_. 1990).
**Fig. 23-9** (a) Tooth specimen with complete absence of pulp tissue. (b) Filaments and coccoid organisms are seen attached in a biofilm to the root canal walls. From Dr Ricucci's collection, images previously published by Svensäter & Bergenholtz (2004).
The shape and character of the periodontal tissue response to a root canal infection may vary. Often lesions assume a limited and stable extension around root apices and/or at orifices of accessory canals. The inflammatory process may then remain unchanged in size for years, although cyst transformation can result in substantial destruction of alveolar bone (Fig. 23-13). However, the initial expansion of an emerging lesion or acute exacerbation of a chronic lesion, can result in rapid and extensive destruction of the attachment apparatus. In certain cases the periodontal tissue support can be lost to an extent that the gingival sulcus is involved, from where drainage of pus occurs to the oral environment (Fig. 23-14). Such an apical marginal communication along the root surface may later become a permanent pathway for pus that will be released periodically along what is simply a fistulous tract.
The character of the infecting microbiota, its metabolic activity, and the virulence factors it produces, together with the capacity of the host defense to confine and neutralize the bacterial elements, are important parameters that decide the course of the inflammatory process. Hence, growing and multiplying organisms with capacities to invade the periodontal tissues and evade host defense mechanisms mediate acute manifestations of endodontic lesions. Single organisms are normally unable to cause these lesions, which are maintained by groups of organisms; virulent strains of _Porphyromonas_ , _Prevotella_ , _Fusobacterium_ and _Peptostreptococcus_ spp. have been implicated by culture studies (Dahlén 2002). Recent reports utilizing PCR methodology have inferred that a variety of other species, unrecognized by culture, may be of prime importance (Rocas & Siqueria 2005; Sakamoto _et al_. 2006). Given the recent surge in use of molecular methods to map the structure of the endodontic microbiota, it is likely that, in the future, a clearer understanding will be gained of the key organisms which cause acute manifestations of endodontic infections.
**Fig. 23-10** (a) Demonstration of bacterial front (blue stain) near the root canal exit of a root tip with attached periapical tissue lesion (low magnification in (b)). From Ricucci & Bergenholtz (2004).
**Fig. 23-11** (a) Display of bacterial masses (blue stain) attached to the walls of a root canal well inside the apical foramen. A band of inflammatory cells appear to be in combat with the infection. (b) A low magnification overview of the root with attached periapical tissue lesion. From Ricucci & Bergenholtz (2004).
The endodontic microbiota associated with asymptomatic lesions is apparently less aggressive. This condition is likely to be linked to the harsh nutritional supply that usually prevails in root canals and which puts the organisms in a low state of metabolic activity. Nutrients are available primarily from tissue components of the necrotic pulp. In the absence of inflammatory exudate entering the root canal along apical foramina and accessory canals, organisms will consequently have little drive to grow, multiply, and invade the periodontal tissue compartment. When this condition of relative starvation is broken by increase of the nutritional supply, an acute endodontic lesion may occur. Suppressed virulent strains can then be revived and become the dominant organisms at the expense of the less virulent members of the microbial community. Consequently, acute exacerbations of asymptomatic endodontic lesions may occur, for example, when saliva and gingival exudates gain access to the root canal space following a direct exposure of root canals to the oral environment. Similarly during endodontic treatment, inadvertent enlargement of the apical foramen increases the passageway for protein-rich inflammatory exudate into the root canal space.
**Fig. 23-12** Accumulation of bacterial mass (blue stain) at the external root surface of a tooth with an infected necrotic pulp. From Ricucci & Bergenholtz (2004).
While acute manifestations of endodontic lesions are characterized by expanding bone resorption, exudation and influx of phagocytic cells, a balanced host–parasite relationship will be established sooner or later (Stashenko 1990; Nair 1997; Stashenko _et al_.1998). Microscopically, the established lesion is characterized by a richly vascularized granulation tissue, which is infiltrated, to a varying degree, by inflammatory cells (Fig. 23-15). PMNs play a most important role in confining the infection to the pulpal space (Stashenko _et al_. 1995) and constitute an important cellular front line (Fig. 23-11). The remainder of the lesion will be composed of a mixed cellular response (Fig. 23-15c) typical of a longstanding infectious process where various immunocompetent cells ( _viz_. dendritic cells, macrophages, T and B cells) are prevalent (Torabinejad & Kettering 1985; Babal _et al_. 1987; Okiji _et al_. 1994; Stashenko _et al_. 1998; Marton & Kiss 2000). With increasing distances from the root canal apertures, the established lesion harbors a decreasing number of inflammatory cells and an increasing amount of fibrovascular elements representing attempts at repair. More peripherally there is a much stronger expression of fibroblastic activity and formation of new vessels. In the most peripheral portions of the lesion, a collagen-rich connective tissue normally separates it from the surrounding bone tissue (Bergenholtz _et al_. 1983) (Fig. 23-15a,d).
**Fig. 23-13** Extensive destruction of alveolar bone as a result of cyst transformation of a periapical lesion emanating from tooth #31. (a) Note root resorption of neighboring teeth. (b) Buccal protrusion of the process was non-painful to palpation. All teeth responded vital to pulp testing except for the root filled teeth #31 and #41. The latter tooth, however, had a vital pulp as revealed on accessing the root canal. Treatment, carried out in collaboration with Dr. Ulf Lekholm, included placement of an oburator for drainage, decompression, and saline irrigation of the cyst cavity over 6 months. Following its reduction, teeth #31 and #41 received completion of endodontic treatment and a residue of the process was excised surgically. (c–e) Complete resolution of the process 10 months post surgery.
**Fig. 23-14** Drainage of pus upon periodontal probing from a lesion of endodontic origin associated with an upper molar.
**Fig. 23-15** Series of images demonstrating features of apical inflammatory lesions caused by root canal infection. (a) A soft lesion attached to the tip of the palatal root of an extracted upper molar. (b) The longitudinally cut tissue section through the root tip shows an overview of the lesion. The outer collagen-rich connective tissue confines the soft tissue lesion and attaches it to the root surface. (c) A typical mixed inflammatory cell infiltrate at the center of a lesion. (d) In the most peripheral portion the connective of an established lesion is rich in collagen and devoid of inflammatory cells. Microphotograph in (c) is from an apical lesion in a monkey.
In non-symptomatic endodontic lesions, the relative distribution of cellular and tissue elements may show great variation and some, but far from every lesion, may also contain proliferating epithelial cells (Nair 1997). The origin of epithelial strands is thought to be the epithelial rests of Malassez (Ten Cate 1972) that are stimulated to divide and proliferate by the release of pro-inflammatory cytokines and growth factors during the process of inflammation (Thesleff 1987; Lin _et al_. 1996; Suzuki _et al_. 2002). In the lesion, they appear to take a random course, but sometimes they may also attach to the root surface (Fig. 23-16) and eventually block the root canal exit for bacterial advancement into the periapical tissue compartment (Nair & Schroeder 1985). Their contribution to periodontal pocket formation upon an endodontic lesion, developing in close proximity to the epithelial sulcus of the marginal periodontium, remains obscure.
### Conclusion
Inflammatory processes of the periodontium associated with necrotic dental pulps have an infectious etiology similar to periodontal disease. An essential difference between the two disease entities is their different source of infection. While periodontal disease is maintained by bacterial accumulations in the dentogingival region, endodontic lesions are directed towards infectious elements released from the pulpal space. The bacterial organisms in endodontic infections are usually confined to the root canal space. They may also be found in the soft tissue lesion _per se_ either as clusters or as bacterial aggregations on the external root surface. Endodontic lesions rarely involve the marginal periodontium, unless abscessed. Cyst transformation may occur but even then marginal involvement is not common. In its established form, the endodontic lesion is clearly localized and constitutes an immunologically active protection zone which is important in preventing the dissemination of endodontic pathogens to the surrounding tissues (Stashenko 1990).
**Fig. 23-16** Display of a periapical inflammatory process with proliferating epithelium partially attached to the root surface.
# Effects of periodontal disease and periodontal therapy on the condition of the pulp
## Influences of periodontal disease
The formation of bacterial plaque on detached root surfaces following periodontal disease has the potential to induce inflammation in the pulp along the very same pathways as an endodontic infection can affect the periodontium in the opposite direction. Thus, bacterial products and substances released by the inflammatory process in the periodontium may gain access to the pulp via exposed accessory canals and apical foramina, as well as dentinal tubules.
A clear association between progressive periodontal disease and pulpal involvement, however, does not exist. While inflammatory alterations as well as localized inflammatory cell infiltrates and necrosis of pulp tissue have been observed adjacent to accessory canals in teeth exposed by periodontal disease (Seltzer _et al_. 1963; Rubach & Mitchell 1965), a number of clinical studies has failed to confirm a direct relationship between progression of periodontitis and pulp tissue changes (Mazur & Massler 1964; Czarnecki & Schilder 1979; Torabinejad & Kiger 1985). In the cases in these studies, the pulp was observed to remain fully functional without overt inflammatory changes even though the periodontal tissue breakdown was severe. As already pointed out, an important reason for the lack of pulp tissue involvement, is that patent accessory canals are not invariably present and especially not in the cervical root portions. Another is that cementum obviously exerts protection. It is only when the cementum layer has been damaged, by, for example, instrumentation in periodontal therapy, wear from tooth cleaning, external root resorption, and root surface caries, that dentinal tubules can serve as pathways for microbial elements to the pulp (Figs. 23-17 to 23-19).
**Fig. 23-17** Histologic section of a monkey tooth exposed to experimental periodontal tissue breakdown. Beneath resorptive defects in the external root surface a minor inflammatory cell infiltrate and a small rim of reparative dentin have been formed in the pulp. From Bergenholtz & Lindhe (1978).
**Fig. 23-18** Histologic section of a human tooth with bacterial accumulations on the external root surface. There are obvious defects in the root surface. Pulp tissue is minimally affected, however, except for numerous mineralization processes both in the tissue proper and at the inner root canal wall.
**Fig. 23-19** (a) Tooth with extensive caries in the furcation region of a lower molar. (b) Note the overall normal tissue morphology of the pulp except for an area at the mid-root portion of the distal root, where caries process has reached the pulp (c).
The fact that tissue changes develop infrequently and even so only locally in the pulp of teeth subjected to periodontitis was underscored by an experimental study in monkeys (Bergenholtz & Lindhe 1978). Following a ligature-induced breakdown of the attachment apparatus, it was found that the majority of the root specimens examined (70%) exhibited no inflammatory changes, despite the fact that approximately 30–40% of the periodontal attachment was lost. The remaining roots (30%) displayed only small inflammatory cell infiltrates and/or formations of reparative dentin in the pulp subjacent to root areas exposed by the periodontal tissue destruction. These tissue changes were associated with root surface resorption (Fig. 23-17), supporting the view that dentinal tubules have to be uncovered before external irritants can be transmitted to the pulp. Consequently, the lack of correlation found in clinical observations between periodontal disease and pulp tissue alterations, may simply depend on the fact that few open pathways exist to the pulp in many periodontally involved teeth. Furthermore, as described above, once the dentin/pulp complex has been exposed to bacterial elements, repair and healing will often be instituted soon after the initial inflammatory events, leaving the remaining tissue unaffected.
In the study by Bergenholtz and Lindhe (1978), destructive periodontal disease was produced experimentally during a comparatively short period (5–7 months), while in humans a similar degree of destruction of periodontal tissue normally requires several years. It has been reported that the pulp of teeth with longstanding periodontal disease develops fibrosis and various forms of intra-pulpal mineralizations (Bender & Seltzer 1972; Lantelme _et al_. 1976) (Fig. 23-18). If there is an association, it seems reasonable to assume that tissue changes of this nature represent the accumulated response of the pulp to the relatively weak, but repeatedly occurring, insults to the tissue over time, for example by microbial elements reaching the pulp over root surface exposures. Nonetheless the pulp can obviously remain healthy for as long as periodontal disease has not arrived at a terminal stage, when plaque accumulation and associated inflammatory lesions interfere with the neurovascular supply of the tissue through the main apical foramen (Fig. 23-20).
### Conclusion
Available documentation suggests that the vital functions of the pulp are rarely threatened by periodontal disease influences. In teeth with moderate break-down of the attachment apparatus, the pulp usually remains healthy. Breakdown of the pulp presumably does not occur until the periodontal disease process has reached a terminal stage, i.e. when plaque and the periodontal inflammatory process have progressed to the main apical foramina, whereby a retrograde destructive inflammatory pulpal lesion is initiated (Langeland _et al_. 1974) (Fig. 23-20). Consequently, as long as the blood supply through the apical foramen remains intact, the pulp is usually capable of withstanding injurious elements released by the lesion in the periodontium.
## Influence of periodontal treatment measures on the pulp
Pocket/root debridement in periodontal therapy by hand instrumentation (scaling and root planing, S/ RP) or ultrasonics is indispensable in the treatment of periodontal disease. However, this treatment is associated with a number of undesired side effects. Except for recession of gingival tissues resulting in exposures of root surfaces, the instrumentation _per se_ may also inadvertently remove root cementum and the superficial parts of dentin. Thereby a large number of dentinal tubules will become exposed to the oral environment as treated root surfaces are normally left unprotected. Subsequent contact with microbial elements in the oral cavity is potentially harmful to the pulp as bacterial invasion of the exposed dentinal tubules may occur (Adriaens _et al_. 1988). While localized inflammatory lesions may be initiated in the pulp, the experimental study by Bergenholtz and Lindhe (1978) did not observe increased incidence of pulpal lesions in teeth subjected to S/RP in comparison to non-treated teeth subjected to periodontal tissue breakdown alone. In the study, root surfaces denuded of root cementum were left open to the oral environment for up to 30 days. The finding that plaque accumulation on root dentin exposed by one session of S/RP does not seriously threaten the vitality of the pulp has been confirmed in similarly designed experimental studies (Nilvéus & Selvig 1983; Hattler & Listgarten 1984). Yet, root dentin hypersensitivity may follow such treatment measures, causing an uncomfortable problem which is difficult to manage (see below).
During the maintenance phase of periodontal therapy, there are reasons to restrict repeated instrumentations, as some additional dentin always will be removed. Such therapy can result in weakening of the tooth structure and also in extensive reparative dentin formation in the pulp (Fig. 23-21).
### Conclusion
Results of clinical observations and animal experiments support the view that pocket/root debridement procedures normally do not threaten the vitality of the pulp. Localized inflammatory alterations may occur adjacent to instrumented root surfaces followed by tissue repair in the form of hard tissue depositions on the root canal walls.
## Root dentin hypersensitivity
### Symptoms and incidence
Patients who have received pocket/root debridement in periodontal therapy may frequently experience sensitivity of the treated teeth to evaporative, tactile, thermal, and osmotic stimuli (Fischer _et al_. 1991; Kontturi-Närhi 1993; Chabanski _et al_. 1996; Tammaro _et al_. 2000; for review see Gillam & Orchardson 2006). Usually, the symptoms, when they occur, develop and peak during the first week, and then subside or disappear within the subsequent weeks; they are, although uncomfortable, most often a temporary and sustainable problem (Schuurs _et al_. 1995; Chabanski _et al_ 1996; Gillam _et al_. 1999; Fardal _et al_. 2002). Occasionally, the condition may become a chronic pain problem and may persist for months or years. Patients appear to be especially at risk after periodontal surgery. In a comprehensive questionnaire survey, severe painful symptoms were reported to prevail in 26% of the subjects 6 months to 5 years after the completion of treatment, while 16%, treated non-surgically, reported pain symptoms (Kontturi-Närhi 1993). In a clinical trial comprising 35 patients, Tammaro _et al_. (2000) observed that the incidence of sensitive teeth increased following non-surgical periodontal instrumentation in comparison to non-instrumented teeth after initiating a self-performed oral hygiene program in patients with moderate to advanced periodontal disease. While affecting a majority of the patients, pain was generally reported to be minor. Only a few teeth in a small number of the patients developed highly sensitive root surfaces.
**Fig. 23-20** (A) Extensive periodontal tissue breakdown circumscribing the distal root of a lower molar. (B, F) Plaque and calculus cover the root surface to the apical foramen. (C–G) The pulp is necrotic and infected all the way to the extensive hard tissue deposition in the coronal pulp (to arrow in E). Microphotographs enlarging marked area in (E) (H, I) indicate that the pulp tissue of the mesial root is completely unaffected and displays normal tissue morphology. Tooth responded vital to pulp testing.
**Fig. 23-21** (a) Clinical photograph of a patient, who has been in the maintenance phase for periodontal disease. While there are excellent gingival conditions and no pocket probing depths, there is substantial loss of cervical root dentin. (b) One of the lower incisors later had a horizontal fracture, but without a pulpal exposure due to fill of reparative dentin in the coronal portion of the pulp chamber. Courtesy of Dr. Sture Nyman.
The main initial symptom is sharp pain of rapid onset that disappears once the stimulus is removed. In more severe, long-standing cases, shorter or longer periods of lingering, dull or aching pain may be provoked. These symptoms of a pulpitis character may not only be localized to the tooth (teeth) in question but to both quadrants of the jaw. Even a minimal contact with a toothbrush may elicit intense pain – a condition which is not only uncomfortable but one that is likely to hinder proper oral hygiene measures.
### Mechanisms
The painful condition has been given many names, including dentine sensitivity, cervical dentine hypersensitivity, root dentine sensitivity, and root dentine hypersensitivity, reflecting some of the confusion that still exists regarding its etiologic background (Gillam & Orchardson 2006). The fact that root surfaces become sensitive to a variety of externally derived stimuli after periodontal instrumentation is not surprising as dentinal tubules become uncovered to the oral environment and subject to hydrodynamic forces. Hence, a variety of pain-evoking stimuli including evaporative, tactile, thermal, and osmotic stimuli may elicit sudden fluid shifts in the exposed tubules, thereby inducing a painful sensation according to the hydrodynamic theory of dentin sensitivity (Brännström 1966; Pashley 1996). This mechanism alone can certainly explain the sensitivity patients experience immediately after the instrumentation procedure and during a short period afterwards, while it does not make clear why the symptoms increase over time and why pain may prevail in certain patients and in certain teeth.
The increase in pain intensity may have one or both of the following two explanations. Firstly, the smear layer formed on the root surface by the S/RP procedure will be dissolved within a few days (Kerns _et al_. 1991). This in turn will increase the hydraulic conductance of the involved dentinal tubules (Pashley 1996) and thus decrease the peripheral resistance to fluid flow across dentin. Thereby pain sensations are more readily evoked. Secondly, open dentinal tubules serve as pathways for diffusive transport of bacterial elements in the oral cavity to the pulp, which may cause a localized inflammatory pulpal response (Bergenholtz & Lindhe 1975, 1978). Indeed, experiments in dogs have shown that dentin exposures left unprotected greatly enhance the sensitivity of responding nerve fibers (Närhi _et al_. 1994). A large number of intradental A-delta fibers, normally inactive, then become able to respond (Närhi _et al_. 1996). It has furthermore been shown that the receptive field of each individual fiber gets wider (Närhi _et al_. 1996). In addition, sprouting of new terminal branches from pulpal axons may occur in the area subjacent to the root surface defect (Taylor _et al_. 1988). As already stated, sprouting of nerves is a temporary event and will subside if inflammation disappears; a feature which is consistent with their involvement in root dentin hypersensitivity (Byers & Närhi 1999). In other words, an essential component of the increasing root sensitivity patients experience after an instrumentation procedure is likely to be related to a peripheral sensitization of pulpal nociceptors leading to what is termed primary hyperalgesia.
**Fig. 23-22** Scanning electron microscopic images of root surface biopsies of hypersensitive (a, b) and of non-sensitive root dentin areas of human teeth (c, d). Numerous wide tubular apertures are seen in (a). These tubules show no evidence of hard tissue deposition after being opened longitudinally (b). By contrast, most tubules are occluded in (c) and below the surface rhombohedral crystals of from 0.1–0.3 μm are present. Images kindly provided by Dr. Masahiro Yoshiyama and published with permission of the _Journal of Dental Research_.
The fact that root dentin hypersensitivity often disappears a few weeks after the instrumentation procedure is best explained by the development of a natural occlusion of the exposed dentinal tubules. The deposition of mineral crystals in the tubular lumen may play an important role (Yoshiyama _et al_. 1989, 1990) (Fig. 23-22), firstly by inactivating the hydrodynamic mechanism for dentinal pain and secondly, by restricting the potential for an inward diffusion of bacterial elements to the pulp. The observation of few open tubules in non-sensitive root dentin (Hiatt & Johansen 1972; Absi _et al_. 1987; Yoshiyama _et al_. 1989; Cuenin _et al_. 1991; Oyama & Matsumoto 1991; Kontturi-Närhi 1993), while hypersensitive root areas show large numbers of tubular apertures on their surfaces (Absi _et al_. 1987; Yoshiyama _et al_. 1989; Cuenin _et al_. 1991; Oyama & Matsumoto 1991; Kontturi-Närhi 1993), supports this view.
The fact that only certain individuals become seriously affected may be related to local factors in the oral cavity, as well as to the level of the subjects' pain perception. Certain dietary factors, in particular fruit juices, yoghurt, and wines, have been implicated in the causation of root dentin hypersensitivity (Addy _et al_. 1987). By their acidity and ability to etch dentin these substances may dissolve the occlusions of the dentinal tubules or prevent them from forming. It needs be recognized that pain is not only an expression of injury and noxious stimuli, but also a psychobiologic phenomenon having both a physiologic and psychologic basis for its perception and reaction to it. Indeed, a variety of emotional elements may influence the subjective interpretation of pain. Anxiety, fear, and depression are factors that are known to affect pain perception as well as the subject's ability to identify coping methods (Eli 2003).
An important consideration in the deliberation of the mechanisms behind enhanced and lingering pain symptoms of root dentin hypersensitivity is the potential of central nervous system sensitization (for review see Sessle 2006). It is now well documented that frequent and repeated pain stimulations result in structural and functional changes that allow the brain to respond more rapidly and more effectively to the same stimuli. Such an increase of the excitability of central neurons has a downside in that pain may continue as a memory function even if the peripheral cause has been eliminated. Thus, it is possible that central sensitization phenomena explain failure of treatment attempts in some patients.
### Principles for management
In patients suffering from severe root dentin hypersensitivity, active treatment is urgent. However, the methods presently available provide an unpredictable remedy and at best only temporary relief is attained (Ikola 2001; Gillam & Orchardson 2006). Since tubular patency of the exposed dentin seems to play a crucial role in the pathogenesis of root dentin hypersensitivity most procedures hitherto attempted are logically aimed at inducing blockage of the peripheral openings. Some agents commonly employed, primarily for dentist-applied treatment, act by causing an astringent or coagulating effect on the tubular content. Such chemicals include strontium chloride, sodium monofluorophosphate, sodium fluoride, calcium hypophosphate, calcium hydroxide, potassium nitrate, potassium oxalates, glutaraldehyde, ferric oxalate, and stannous fluoride. Other methods aim to produce a physical block for example by the use of grafting procedures and laser applications (for reviews see Zappa 1994; Gangarosa 1994; Ikola 2001; Gillam & Orchardson 2006).
There may be several explanations why such treatments sometimes fail to remedy the problem. One is likely to be of a technical nature in that it is often difficult to attain a completely dry dentin surface during the application of, for example, an astringent solution. Hence, the release of gingival fluid from the sulcus is not easily restrained by compressed air or other methods. Consequently, upon application of the agent, protein from the gingival exudate might primarily be brought to coagulation rather than the tubular content. The precipitate is then easily removed upon subsequent tooth cleaning measures leaving the tubules unoccluded. Most agents furthermore may only cause a superficial block that may be dissolved over the course of time. Also topical applications do not address the pain mechanisms associated with either peripheral or central sensitization of nociceptors. Agents able to decrease the excitability of intradental nerves have, therefore, been proposed based on the assumption that potassium ions released from formulations containing potassium salts (e.g. chlorides, nitrates, citrate, and oxalates) may penetrate dentinal tubules and temper intradental nerve activity (Markowitz & Kim 1992; Orchardson & Peacock 1994). Toothpastes with potassium-containing preparations as active ingredients have indeed shown promise in clinical trials by giving better relief of pain in selected teeth in comparison to toothpastes without active substance (Sowinski _et al_. 2001; Wara-Aswapati _et al_. 2005). Experiments employing electrophysiological recordings in dogs, however, have shown that the effect of topical application of potassium salt is weak and becomes abolished after irrigation (Ikola 2001). More research appears necessary to confirm a clear treatment effect of potassium salts in gels, mouthwashes, and toothpastes (Orchardson & Gillam 2000). This also applies to any other treatment mode. It needs be recognized that demonstrating a significant treatment effect of a given compound in clinical trials is fraught with several difficulties. One is to assemble a sufficient number of patients that are reasonably identical in terms of duration and level of pain. Another is that the pain condition may go into natural remission at any time. A large placebo effect also operates in studies of this nature (Holland _et al_. 1997; Yates _et al_. 1998; Orchardson & Gillam 2000).
Any treatment approach to root dentin hypersensitivity should be preceded by a careful analysis of conditions that may be the cause of, or contributory to, the symptoms. Cracked teeth including cusp fractures, fractured or leaky restorations, caries, as well as a variety of other exposures of dentin to the oral environment may cause pulpal pain sensations to the very same stimuli which elicit root dentin hypersensitivity. An area of exposed dentin may be more sensitive if there is irritation of the pulp from other areas of the tooth, for example from the margin of a restoration that is not sealed from the oral environment (Närhi _et al_. 1994). Particular care should be taken to eliminate traumatic occlusion to alleviate any activation of pulpal nociceptors. Furthermore, dietary counseling should be given to patients who admit excessive consumption of citrus fruits, apples, or any other food or drinks that are acidic in nature.
Self-performed plaque control is important for the prevention and treatment of root dentin hypersensitivity. It has been observed clinically that, with time, teeth in patients with excellent oral hygiene habits develop hard, smooth, and insensitive root surfaces. Electron microscopic examination of the dentin of such root surfaces has revealed that mineral deposits obliterate the tubular openings (Hiatt & Johansen 1972). However, when severe symptoms of root hypersensitivity have emerged, it is difficult to motivate the patient to maintain the degree of plaque control that is necessary to allow for a natural occlusion of the dentinal tubules. In such situations, an agent which has a capacity to block the tubular openings, may be beneficial at least temporarily, so that proper oral hygiene measures can be reinforced. In severe cases, where no remedy is achieved with any advice or treatment approach, pulpectomy and root filling are a last resort.
Any pain treatment should take into consideration the potential of preventing the condition from emerging in the first place. However, no well proven protocol has as yet been established whereby root dentine hypersensitivity can be effectively prevented. Attempts to block the exposed dentinal tubules immediately following S/RP should be an obvious approach. In fact a couple of placebo-controlled studies have shown promise in that significantly fewer sensitive teeth were attained subsequent to instrumentation when 6% ferric oxalate (Wang _et al_. 1993) and 3% potassium oxalate (Pillon _et al_. 2004) were applied topically. The long-term outcome of such procedures awaits confirmation.
### Conclusion
Root dentin hypersensitivity frequently develops as an uncomfortable and sometimes difficult ailment to treat subsequent to scaling and root planing procedures in periodontal therapy. Although the exact mechanism is not well established, the condition is clearly related to open dentinal tubules that allow hydrodynamic mechanisms to elicit painful sensations upon external stimulation. Both peripheral and central sensitizations are likely to contribute to the more intense and lingering pain symptoms some patients experience after root dentin exposure.
Diagnosis and treatment planning should consider contributory etiologic factors including over-consumption of acidic food items. Root dentin hypersensitivity should also be checked against other conditions causing similar pain symptoms and rule out cracked teeth, leaky restoration margins, caries in the tooth or in neighboring teeth, as well as trauma from occlusion. A large number of treatment methods are available for both in-office and over-the-counter applications. Some aim to block tubular patency of the exposed root dentin and others attempt to decrease excitability of intradental nerves for reduced pain transmission. Unpredictable treatment results are to be expected and only temporary relief may be attained.
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# Part 7: Peri-implant Pathology
24 Peri-implant Mucositis and Peri-implantitis
_Tord Berglundh, Jan Lindhe, and Niklaus P. Lang_
# Chapter 24
# Peri-implant Mucositis and Peri-implantitis
Tord Berglundh, Jan Lindhe, and Niklaus P. Lang
* * *
Definitions
Ridge mucosa
Peri-implant mucosa
Peri-implant mucositis
Clinical features
Prevalence
Histopathology
Peri-implantitis
Clinical features
Prevalence
Histopathology
* * *
# Definitions
## Peri-implant disease
Inflammatory processes in the tissues surrounding an implant (Albrektsson & Isidor 1994).
## Peri-implant mucositis
Reversible inflammatory process in the soft tissues surrounding a functioning implant.
## Peri-implantitis
Inflammatory process additionally characterized by loss of peri-implant bone.
See Fig. 24-1.
# Ridge mucosa
The edentulous, hard tissue portion of the alveolar process is covered by a mucosa that is about 2–4 mm thick (see also Chapter 3). The mucosa is lined by a keratinized epithelium and is comprised of a connective tissue that is rich in fibroblasts, collagen fibers, and vascular structures (e.g. Türk 1965; Krajicek _et al_. 1984; Liljenberg _et al_. 1996). The connective tissue is continuous with the cortical bone crest via the peri-osteum. A few scattered inflammatory cells can be observed adjacent to the basement membrane in the connective tissue papillae between the rete pegs of the epithelium.
# Peri-implant mucosa
Following implant installation, a transmucosal passage is formed around the abutment portion of the device. The ridge mucosa at such sites adapts to the new functional demands and a peri-implant mucosa becomes established. The mucosa surrounding implants and the gingiva surrounding teeth have many features in common. Both types of tissues are lined with a keratinized oral epithelium; at clinically healthy sites this is continuous with a thin non-keratinized barrier or junctional epithelium that faces the implant or the tooth surface. In the connective tissue immediately lateral to these thin epithelial linings small infiltrates of inflammatory cells (neutrophils, macrophages, T cells, B cells) are frequently seen (Liljenberg _et al_. 1997). The inflammatory cells represent the host's defense against bacterial products and hence they may be considered as one important component of the biological seal that separates the peri-implant and periodontal attachment tissues from the oral cavity (see also Chapters 3 and 11).
**Fig. 24-1** Schematic drawing illustrating healthy peri-implant mucosa, peri-implant mucositis, and peri-implantitis.
# Peri-implant mucositis
## Clinical features
The clinical features of peri-implant mucositis are in many respects similar to those of in gingivitis at teeth and include classical symptoms of inflammation, such as swelling and redness (see Chapter 17). Differences in the morphology of the peri-implant mucosa and the lack of light transmission through the metal of the device, however, may mask visible signs of inflammation. Assessment of peri-implant mucositis must therefore always include assessment of bleeding following probing (Fig. 24-2).
## Prevalence
Bleeding on probing (BoP) is a good discriminating indicator of peri-implant mucositis. The prevalence of this disease remains difficult to estimate since data on BoP at implants are infrequently reported (Berglundh _et al_. 2002). In a study on 25 subjects treated with implant-supported fixed prosthesis, Lekholm _et al_. (1986) reported that BoP occurred at 80% of the implants. Roos-Jansåker _et al_. (2006a,b,c) examined 987 implants in 216 patients and reported that more than 73% of all implants exhibited BoP. Higher frequencies of BoP at implants were presented by Fransson _et al_. (2007) in a study on 82 subjects. It was reported that BoP occurred in more than 90% of implant sites.
## Histopathology
### Response to early plaque formation
The response of the gingiva and the peri-implant mucosa to early and more long-standing periods of plaque formation was analyzed both in studies in man and in experiments in animals. Pontoriero _et al_. (1994) engaged 20 partially edentulous human subjects in a clinical "Experimental gingivitis in man" (Löe _et al_. 1965) study. All subjects had been treated for advanced periodontal disease and thereafter had been restored with implants in one or several segments of the dentition. During a 6-month period following the prosthetic rehabilitation, the subjects were enrolled in a meticulous maintenance program that included regularly repeated supportive measures. A baseline examination was subsequently performed including assessment of plaque, soft tissue inflammation, probing pocket depth (PPD), soft tissue recession, and composition of oral biofilms. The participants refrained from all oral hygiene measures for 3 weeks. It was observed that during this interval plaque build-up (amount and composition) and the soft tissue response to the microbial challenge, e.g. inflammation and PPD change, developed in a similar manner in the tooth and implant segments of the dentition.
Zitzmann _et al_. (2001) studied the response to plaque formation in the soft tissues at implant and tooth sites in humans. Twelve subjects with healthy periodontal and peri-implant conditions were asked to refrain from tooth/implant cleaning for a period of 3 weeks (Fig. 24-3). Clinical examinations were performed and soft tissue biopsies were harvested prior to and at the end of the plaque accumulation period. The tissues were examined using histologic techniques. It was demonstrated that plaque build-up was associated with clinical signs of soft tissue inflammation. Furthermore, the initially minute lesions in the gingiva and in the peri-implant mucosa markedly increased in size after 3 weeks of plaque build-up: from 0.03 mm2 at baseline to 0.3 mm2 (gingiva) and 0.2 mm2 (peri-implant mucosa). In addition, the proportion of B cells and neutrophils increased more in the lesion in the gingiva than in its counterpart in the peri-implant mucosa.
#### Experimental model
In a carefully supervised experiment in the dog, Berglundh _et al_. (1992) compared the reaction of the gingiva and the peri-implant mucosa to 3 weeks of _de novo_ plaque formation. The mandibular premolars in one side of the mandible were extracted, leaving the premolars on the contralateral side as controls. After 3 months of socket healing, implants were inserted in the edentulous ridge. The animals were placed in a plaque-control program to allow for ideal healing of the mucosa at the implants and to prevent gingivitis from occurring in the tooth segments of the dentition. After this healing period, the dogs were examined and samples from the minute biofilms that were present on the implant and the tooth surfaces were harvested. The plaque-control program was terminated and the animals given a soft diet, that allowed gross plaque formation. Re-examinations, including clinical assessment (Fig. 24-4), sampling of plaque from teeth and implants as well as biopsy, were performed after 3 weeks.
**Fig. 24-2** (a) Clinical symptoms of peri-implant mucositis including varying signs of redness and swelling. (b) Probing resulted in bleeding from the margin of the mucosa.
**Fig. 24-3** (a) Clinical photograph from sites with healthy gingiva and peri-implant mucosa. (b) The sites illustrated in (a) following 3 weeks of plaque formation.
**Fig. 24-4** A clinical view illustrating 3 weeks (3 W) and 3 months (3 M) of undisturbed plaque formation on the implants and the teeth of a beagle dog.
During the course of the study, it was observed that similar amounts of plaque formed on the tooth and implant segments of the dentition. The composition of the two developing plaques was also similar. It was therefore concluded that early microbial colonization on titanium implants followed the same pattern as that on teeth (Leonhardt _et al_. 1992).
Both the gingiva and the peri-implant mucosa responded to this microbial colonization with the establishment of overt inflammatory lesions, i.e. infiltrates of leukocytes in the connective tissue. The lesions in the gingiva and in the peri-implant mucosa were matched both with respect to size and location. Hence, both lesions were consistently found in the marginal portion of the soft tissues and between the keratinized oral epithelium and the junctional or barrier epithelium (Fig. 24-2).
Response to long-standing plaque formation
With increasing duration of plaque build-up (3 months) in the dog model described above, the lesions in the peri-implant mucosa seemed to have expanded and to have progressed further "apically" while the gingival lesions remained unchanged (Ericsson _et al_. 1992) (Fig. 24-5). Furthermore, the lesion in the peri-implant mucosa contained a much smaller number of fibroblasts than the corresponding infiltrate in the gingiva. In any inflammatory lesion of long standing, periods of breakdown and periods of repair interchange. It was suggested, therefore, that in the gingival lesion, the amount of tissue breakdown that occurred during the 3 month interval was more or less fully compensated by tissue build-up that took place during a subsequent phase of repair. In the lesion within the peri-implant mucosa, the tissue breakdown was not fully recovered by reparative events. This reduced build-up may have been the reason for the resulting additional propagation and spread of the lesion in the peri-implant mucosa.
In a similar dog experiment Abrahamsson _et al_. (1998) studied soft tissue lesions after 5 months of plaque formation at three different implant systems. They observed that the response of the peri-implant mucosa to long-standing plaque formation appeared to be independent of the implant system that harbored the biofilm.
**Fig. 24-5** Microphotographs illustrating the establishment of inflammatory cell infiltrates (ICT) in the peri-implant mucosa (a) and the gingiva (b) (3 W = 3 weeks; 3 M = 3 months). Note, in the microphotographs representing 3 months, the infiltrate in the peri-implant mucosa extends much deeper into the tissue than is the case in the gingiva.
# Peri-implantitis
## Clinical features
Peri-implantitis represents a clinical condition that includes the presence of (1) an inflammatory lesion in the peri-implant mucosa and (2) loss of peri-implant bone. The assessment of the diagnosis _peri-implantitis_ must consequently require detection of both bleeding on probing (BoP) as well as bone loss in radiographs. Peri-implantitis initially affects the marginal part of the peri-implant tissues and the implant may remain stable and in function for varying periods of time. Implant mobility is therefore not an essential symptom for peri-implantitis but may occur in a final stage of disease progression and indicates complete loss of integration.
As pointed out for the clinical characteristics of peri-implant mucositis, various factors such as the morphology of the peri-implant mucosa and position of the implant may also influence the clinical appear-ance of inflammation in peri-implantitis. Probing is therefore a prerequisite in the examination of peri-implant tissues and should include assessment of both BoP and probing pocket depth (PPD).
The clinical appearance of peri-implantitis may, hence, vary and may not always be associated with overt signs of pathology. Two different cases are illustrated in Figs. 24-6 and 24-7. While plaque and calculus together with clinical signs of inflammation are present in the case in Fig. 24-6, the case in Fig. 24-7a does not reveal such symptoms. Probing the site in Fig. 24-7a, however, resulted in a PPD of about 10 mm and BoP (Fig. 24-7b).
Crater-formed defects around implants are frequently found in radiographs obtained from sites with peri-implantitis (Fig. 24-8). Bone loss in such sites appears also to be symmetric, i.e. similar amount of bone loss occur at mesial, distal, buccal, and lingual aspects of the implants. On the other hand, the mor-phology of the osseous defect may vary depending on the horizontal dimension of the alveolar ridge. Thus, in sites where the buccal–lingual width of the ridge exceeds that of the peri-implantitis lesion, a buccal and lingual bone wall may remain. Conversely, in sites with a narrow ridge the buccal and lingual bone will be resorbed and lost during progression of peri-implantitis.
**Fig. 24-6** Clinical symptoms of peri-implantitis. Note the large amounts of plaque and calculus and visible signs of inflammation in the peri-implant mucosa.
### Conclusion
Symptoms of peri-implantitis relate to the infectious/ inflammatory nature of the lesion. Thus, there is radiographic evidence of bone loss and the bone loss often has the shape of a crater. Swelling and redness of the mucosa as well as bleeding on gentle probing occur. Suppuration is also a frequent finding. The implant may remain stable over long periods.
## Prevalence
Previous estimates of the prevalence of periimplantitis were based on reports describing varying frequencies of implant failures that were associated with high plaque scores or severe signs of inflammation (van Steenberge _et al_. 1993; Weyant & Burt 1993; Weyant 1994; Esposito _et al_. 1998). Other criteria were used by Mombelli and Lang (1998) and Brägger _et al_. (2001) and it was suggested that the prevalence of peri-implantitis may vary between 5 and 10% among implants.
**Fig. 24-7** Clinical photograph from two implant-supported crowns in the lateral (12) and central (11) incisor positions. (a) No or minor signs of inflammation in the surrounding mucosa. (b) Probing resulted in bleeding and suppuration from the implant site in the lateral incisor position.
**Fig. 24-8** Clinical (a) and radiographic (b) characteristics of two implant sites with peri-implantitis in the left side of the mandible. Note the presence of swelling and suppuration in the peri-implant mucosa (a) and the crater-formed bone destruction around the implants in the radiograph (arrows) (b).
The difficulty of retrieving information on the prevalence of peri-implantitis was confirmed in a systematic review by Berglundh _et al_. (2002). They evaluated the incidence of biologic and technical complications in implant therapy reported in prospective longitudinal studies of at least 5 years. From the 1310 titles and abstracts provided by the search in databases, 159 studies were selected for full-text analysis, out of which 51 studies were used for meta-analysis. Implant loss was the most frequently reported type of complication, while information regarding peri-implantitis and pronounced bone loss was only provided in 40–50% of the studies. The limited information on the incidence of peri-implantitis was explained by the fact that the term periimplantitis, with the definition by Albrektsson and Isidor (1994) referred to above, was included in only a few studies. The inability to use information on the incidence of peri-implantitis and the occurrence of pronounced bone loss at implants was also due to the lack of data describing frequency distributions of various probing depths and amount of radiographic bone loss.
It is important to use appropriate terms in clinical reports to avoid confusion. Peri-implantitis is a clinical condition and should not be mistaken for implant failure. If left untreated, however, peri-implantitis may progress and lead to implant loss. The term failure should thus be avoided and terms referring to peri-implant disease (peri-implant mucositis and peri-implantitis) should be used for implants in function. Implant loss is consequently the term to use for implants that were lost or removed. In a consensus report from the 4th European Workshop on Periodontology, Lang _et al_. (2002) suggested that authors should avoid the terms implant success and failure and report data on implant survival in combination with incidence of complications. It was also recommended that data should be provided on a subject basis. The majority of publications in implant dentistry, however, describe results based on number or proportions of implants. This information is of limited value for the clinician and, hence, data that relate the outcome of treatment for the patient under examination should be required.
Recently subject-based data on peri-implantitis were presented. Fransson _et al_. (2005) evaluated the prevalence of subjects with progressive bone loss at implants with a function time of at least 5 years. Radiographs of 1346 patients who had attended annual follow-up visits at the Brånemark Clinic, Göteborg, Sweden were retrieved. 662 subjects ful-filled the inclusion criteria. Implants that had suffered bone loss amounting to three or more threads of an implant were identified. Progressive bone loss at implants in the study was defined as bone loss occurring between the 1-year examination and the 5 or more years of follow-up examination. It was reported that 27.8% (184) of the 662 included subjects had one or more implants with "progressive" bone loss. A logistic regression analysis revealed that the individuals in this group carried a significantly larger number of implants than the subjects in whom no implants with progressive loss were detected (6 vs. 4.8). Furthermore, >30% of the subjects in the group with progressive bone loss had three or more identified implants and about 33% of all such implants in this group exhibited extensive bone loss. Out of the total 3413 implants included in the study, 423 implants (12.4%) demonstrated progressive bone loss. Fransson _et al_. (2005) concluded that the prevalence of progressive bone loss at implants assessed from subject-based data is higher than that evaluated from implant-based data. In a subsequent clinical study Fransson _et al_. (2007) reported that about 94% of the implants with "progressive" bone loss exhibited BoP. Thus, according to the definition of peri-implantitis presented in this chapter, the findings in the study by Fransson _et al_. (2005) suggest that the prevalence of subjects with peri-implantitis within this implant population was about 28%.
Roos-Jansåker _et al_. (2006b) examined 216 implant-treated patients (Brånemark System®) after 9–14 years of function and reported that 16% of the subjects and 6.6% of the implants had peri-implantitis. Roos-Jansåker _et al_. (2006b), however, used a modified defi-nition of peri-implantitis and suggested that a certain amount of bone loss (≥1.8 mm compared with the 1-year data) together with the finding of BoP was required for the diagnosis _peri-implantitis_. It should be pointed out, however, that the prevalence of implants with peri-implantitis in the study by Roos-Jansåker _et al_. (2006b) would be >43% if normal criteria for peri-implantitis, i.e. bone loss and BoP, were applied.
### Conclusion
The majority of clinical studies reported in the literature did not provide sufficient data on the prevalence of peri-implant mucositis and peri-implantitis. Results from recent publications, however, indicate that both peri-implant mucositis and peri-implantitis are common disorders. The prevalence of subjects with peri-implantitis in more recent studies varied between 25 and 45%.
## Histopathology
Microscopic examinations of tissues harvested from peri-implantitis sites in humans consistently revealed that the mucosa contained large inflammatory cell infiltrates. Sanz _et al_. (1991) analyzed soft tissue biopsies from six patients with peri-implantitis and reported that 65% of the connective tissue portion was occupied by an inflammatory lesion. Piattelli _et al_. (1998) described some pathological features of tissues harvested from 230 retrieved implants. It was reported that at sites where implants were removed due to peri-implantitis, "an inflammatory infiltrate, composed of macrophages, lymphocytes and plasma cells, was found in the connective tissue around the implants". In a study including 12 human peri-implantitis lesions, Berglundh _et al_. (2004) found that the mucosa contained very large lesions in which numerous plasma cells, lymphocytes, and macrophages were present (Fig. 24-9). It was furthermore observed that the inflammatory cell infiltrate consistently extended to an area apical to the pocket epithelium and that the apical part of the soft tissue lesion frequently reached the bone tissue. Berglundh _et al_. (2004) also reported that numerous neutrophil granulocytes (PMN cells) were present in the lesions. Such cells occurred not only in the pocket epithelium and associated areas of the lesions, but also in perivascular compartments in the center of the infiltrate,
i.e. distant from the implant surface. In the apical part of the lesion the inflamed connective tissue appeared to be in direct contact with the biofilm on the implant surface. Gualini and Berglundh (2003) included six subjects in a study and used immunohistochemical techniques to analyze the composition of peri-implantitis. PMN cells were found in large numbers in the central portions of the infiltrate. This finding was in agreement with observations made by Hultin _et al_. (2002). They analyzed the exudate that could be harvested from implant sites in 17 patients with peri-implantitis and reported the presence of large numbers of PMN cells.
### Experimental models
In order to study the ability of the peri-implant mucosa to respond to long-standing plaque exposure and to manage the associated inflammatory lesions, an experimental periodontitis/peri-implantitis model was developed in the dog (Lindhe _et al_. 1992) and in the monkey (Lang _et al_. 1993; Schou _et al_. 1993). Although the experiments had somewhat varying design, the outcome of the studies was almost identical and, hence, only the result from the dog model will be reported.
**Fig. 24-9** (a) Microphotograph illustrating a human peri-implantitis lesion. Note the large inflammatory infiltrate lateral to the pocket epithelium. The implant was positioned to the left. (b) Arrows indicate vascular units illustrated in a larger magnification.
**Fig. 24-10** (a) A clinical view describing features of experimental peri-implantitis in the beagle dog. (b) A clinical view describing features of experimental periodontitis in the beagle dog.
In the _dog model_ , the premolars were extracted in one side of the mandible, fixtures (Brånemark system®) were inserted and abutment connection performed 3 months later as described above (Berglundh _et al_. 1991). During the healing phase a strict plaque control regimen was maintained and healthy tissue conditions were thereby established in all tooth and implant sites to be monitored. On a given day, the periodontitis and peri-implantitis lesions were induced. This was accomplished by (1) terminating the plaque control regimen and (2) placing cotton floss ligatures around the neck of both the premolar teeth and the implants. The ligatures were forced into a position apical to the soft tissue margins. A "pocket" between the tooth/gingiva and implant/ mucosa was thereby created, a submarginal micro-biota rapidly formed, and inflammatory lesions developed in the neighboring tissues. Radiographs obtained after 6 weeks of the experiment revealed that a substantial amount of bone tissue had been lost at both teeth and implant sites. The ligatures were removed. After another 4 weeks, the animals were re-examined (Fig. 24-10), radiographs obtained, bacteria sampled, and biopsies of tooth and implant sites harvested.
It was observed that the plaque that had formed in the deep "pockets" was similar at tooth and implant sites and was dominated by Gram-negative and anaerobic species (Leonhardt _et al_. 1992). This observation is consistent with findings indicating that, in humans, the microbiota at teeth and implants has many features in common but also that the micro-biota at healthy and diseased sites – tooth sites as well as implant sites – is very different. Thus, implants and teeth that are surrounded by healthy soft tissues are associated with biofilms including small amounts of Gram-positive coccoid cells and rods. Sites with extensive periodontal and peri-implant inflammation harbor biofilms with large numbers of Gram-negative anaerobic bacteria (for review see Mombelli 1999).
The histopathologic examination of the biopsy samples from the dog study (Lindhe _et al_. 1992) revealed that there were marked differences in the size and location of the inflammatory lesions of the two sites. Thus, while the lesions in the periodontal sites (Fig. 24-11) para were consistently separated from the alveolar bone by a zone, about 1 mm high, of unin-flamed connective tissue, the lesion in the peri-implant tissue in most situations extended into and involved the marrow spaces of the alveolar bone. It was concluded that the pattern of spread of inflam-mation was different in periodontal and peri-implant tissues. The lesions in plaque-associated periodontitis were limited to the connective tissue, while in the peri-implant tissues the lesions extended to the alveolar bone (Fig. 24-12).
**Fig. 24-11** Microphotograph (buccal–lingual section) illustrating a periodontitis lesion. Note the apical extension of the infiltrate (arrow) but also the presence of a zone of normal connective tissue between the infiltrate and the bone crest (arrow).
It was suggested that the peri-implant tissues, in variance with the periodontal tissues, are poorly organized to resolve progressive, plaque-associated lesions. The validity of this conclusion was substanti-ated in subsequent studies (Marinello _et al_. 1995; Ericsson _et al_. 1996; Persson _et al_. 1996; Gotfredsen _et al_. 2002), using similar models but allowing for different periods of tissue breakdown.
It was also reported that peri-implantitis lesions, which initially were experimentally induced by ligatures as reported above, could spontaneously progress after the removal of the ligatures. Thus, Zitzmann _et al_. (2004) prepared 21 sites with ligature-induced experimental peri-implantitis in five Labrador dogs. After the lesions had become established, the ligatures were removed and the sites were monitored for an additional 12-month interval. It was observed that in 16 sites the aggressive peri-implantitis conditions persisted and caused continuous bone loss. In the remaining five sites, however, the lesions became encapsulated and no further breakdown of peri-implant bone took place. Using a similar model, Berglundh _et al_. (2007) evaluated progression of peri-implantitis at implants with different surface roughness. Experimental peri-implantitis was induced at implants with either a sandblasted acidetched surface (SLA) or a polished surface. The ligatures were removed when about 40% of the height of the supporting bone had been lost and plaque accumula-tion continued during an additional 5 months. It was reported that following ligature removal the progression of bone loss was larger at SLA than at polished sites. The histologic examination revealed that both bone loss and the size of the inflammatory lesion in the connective tissue were larger in SLA than in polished implant sites. The area of plaque was also larger at implants with a SLA surface than at implants with a polished surface. It was concluded that the progression of peri-implantitis, if left un-treated, is more pronounced at implants with a moderately rough surface than at implants with a polished surface.
**Fig. 24-12** (a) Ground section illustrating a peri-implantitis lesion. The implant is positioned to the left and the apical portions of the infiltrate (arrows) extend into contact with the bone. (b) Close-up of (a) illustrating the presence of inflammatory cells and osteoclasts (arrow) on the bone surface.
### Conclusion
Peri-implantitis lesions are poorly encapsulated, extend to the marginal bone tissue and may, if they are allowed to progress, lead to the loss of the implant. The large numbers of neutrophils in the peri-implantitis lesion and the absence of an epithelial lining between the lesion and the biofilm, indicate that the peri-implantitis lesions have features that are different from those of periodontitis lesions. Progression of peri-implantitis is more pronounced at implants with rough than at smooth surfaces.
### Summary
Studies in man and experiments in animals have documented that _de novo_ formation of a biofilm on the implant surface initiates a host response that involves the establishment of an inflammatory lesion in the peri-implant mucosa (peri-implant mucositis). This lesion is initially located in the connective tissue immediately lateral to the barrier epithelium and is, in many respects, similar to that which develops in the gingiva when plaque forms on adjacent tooth surfaces. In the continued presence of a submarginal biofilm, the lesion in the marginal mucosa around implants may occasionally spread in an "apical" direction to involve the hard tissue, compromise osseointegration, cause varying degrees of marginal bone loss (peri-implantitis), and eventually the loss of the implant.
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# Part 8: Tissue Regeneration
25 Concepts in Periodontal Tissue Regeneration
_Thorkild Karring and Jan Lindhe_
# Chapter 25
# Concepts in Periodontal Tissue Regeneration
Thorkild Karring and Jan Lindhe
* * *
Introduction
Regenerative periodontal surgery
Periodontal wound healing
Regenerative capacity of bone cells
Regenerative capacity of gingival connective tissue cells
Regenerative capacity of periodontal ligament cells
Role of epithelium in periodontal wound healing
Root resorption
Regenerative concepts
Grafting procedures
Root surface biomodification
Growth regulatory factors for periodontal regeneration
Guided tissue regeneration (GTR)
Assessment of periodontal regeneration
Periodontal probing
Radiographic analysis and re-entry operations
Histologic methods
* * *
# Introduction
At risk assessment in periodontal patients, the presence of sites with a residual pocket depth ≥6 mm after active treatment plays a significant role in predicting future periodontal destruction (Haffajee _et al_. 1991; Grbic & Lamster 1992; Claffey & Egelberg 1995). Thus, an important goal of periodontal therapy is to obtain a reduced pocket depth after treatment in order to prevent further disease progression. Usually, this goal can be accomplished by non-surgical therapy in patients with moderate periodontitis, whereas in severe cases, particularly in the presence of intrabony defects and furcations, the treatment must be supplemented with periodontal surgery. A fundamental objective of periodontal surgery is to provide access for proper instrumentation and cleaning of the root surface; in addition, most surgical procedures result in the elimination or the reduction of the soft tissue component of the periodontal pocket. Generally, the elimination of deep pockets is achieved by gingivectomy or apical displacement of raised tissue flaps, sometimes associated with bone contouring. In recent years, however, the use of regenerative procedures aimed at restoring the lost periodontal support has become more common.
Periodontal treatment, both surgical and non-surgical, results in recession of the gingival margin after healing (Isidor _et al_. 1984). In severe cases of periodontitis, this may lead to poor esthetics in the front areas of the dentition, in particular when applying surgical procedures including bone contouring for the eradication of bone defects. Treatment of such cases without bone contouring, on the other hand, may result in residual pockets inaccessible to proper cleaning during post-treatment maintenance. These problems can be avoided or reduced by applying regenerative surgical procedures by which the lost periodontal attachment in the bone defects can be restored. Thus, the indication of applying regenerative periodontal therapy is often based on esthetic considerations, besides the fact that the function or long-term prognosis of the treated teeth may be improved.
Localized gingival recession and root exposure may represent an esthetic problem to the patient, and it is often associated with root sensitivity. Such a situation is an indication to apply regenerative periodontal therapy to obtain root coverage in order to improve esthetics and reduce root sensitivity. Successful root coverage implies regeneration of the attachment apparatus on the exposed root surface including cementum with inserting collagen fibers, as well as an esthetically acceptable restoration of the anatomy of the mucogingival complex.
Another indication for regenerative periodontal therapy is furcation-involved teeth. The furcation area is often inaccessible to adequate instrumentation and frequently the roots present concavities and furrows which make proper cleaning of the area after resective surgery impossible. Considering the long-term results and complications reported following treatment of furcation involvements by traditional resective therapy (Hamp _et al_. 1975; Bühler 1988), it is reasonable to anticipate that the long-term prognosis of furcation-involved teeth can be improved considerably by successful regenerative periodontal therapy.
Case reports also exist demonstrating that "hopeless" teeth with deep vertical defects, increased tooth mobility or through-and-through furcations can be successfully treated with regenerative periodontal therapy (Gottlow _et al_. 1986). However, controlled clinical trials or serial case reports presenting a reasonable predictability of treating such advanced cases are not available.
# Regenerative periodontal surgery
Regenerative periodontal therapy comprises procedures which are specially designed to restore those parts of the tooth-supporting apparatus which have been lost due to periodontitis. Regeneration is defined as a reproduction or reconstruction of a lost or injured part in such a way that the architecture and function of the lost or injured tissues are completely restored (Glossary of Periodontal Terms, 1992). This means that the attachment of the tooth has been regenerated when new cementum with inserting collagen fibers has formed on the detached root surface, while regeneration of the periodontal supporting apparatus (periodontium) also includes regrowth of the alveolar bone. Procedures aimed at restoring lost periodontal support have also been described as "reattachment" or "new attachment" procedures.
The term "reattachment" was used to describe the regeneration of a fibrous attachment to a root surface surgically or mechanically deprived of its periodontal ligament tissue, whereas the term "new attachment" was preferred in the situation where the fibrous attachment was restored on a root surface deprived of its connective tissue attachment due to the progression of periodontitis. Research findings, however, indicate that there is no difference regarding the possibility of restoring a connective tissue attachment, whether this has been lost because of periodontal disease or mechanically removed (Nyman _et al_. 1982; Isidor _et al_. 1985). Therefore, it was suggested that the term "new attachment" should be used to describe the formation of new cementum with inserting collagen fibers on a root surface deprived of its periodontal ligament tissue, whether or not this has occurred because of periodontal disease or by mechanical means, and that the term "reattachment" should be confined to describing the reunion of surrounding soft tissue and a root surface with preserved periodontal ligament tissue (Isidor _et al_. 1985).
Periodontal regeneration has been reported following a variety of surgical approaches involving root surface biomodification, often combined with coronally advanced flap procedures, the placement of bone grafts or bone substitute implants, or the use of organic or synthetic barrier membranes (guided tissue regeneration). However, many cases that clinically are considered successful, including cases with significant regrowth of alveolar bone, may histologically show an epithelial lining along the treated root surface instead of deposition of new cementum (Listgarten & Rosenberg 1979).
Successful regeneration is assessed by periodontal probing, radiographic analysis, direct measurements of new bone, and histology. Although histology remains the ultimative standard in assessing true periodontal regeneration, periodontal probing, direct bone measurements, and radiographic measurements of osseous changes are used in the majority of studies of regenerative therapy (Reddy & Jeffcoat 1999).
At the American Academy of Periodontology World Workshop in Periodontics in 1996, the fulfillment of the following criteria was required in order for a periodontal regenerative procedure to be considered as a therapy which can encourage regeneration:
* Human histologic specimens demonstrating formation of new cementum, periodontal ligament, and bone coronal to a notch indicating the apical extension of the periodontitis-affected root surface.
* Controlled human clinical trials demonstrating improved clinical probing attachment and bone.
* Controlled animal histologic studies demonstrating formation of new cementum, periodontal ligament, and bone.
In addition, however, it seems reasonable to require that a regenerative procedure is based on a biological concept which can explain why the treatment results in periodontal regeneration on the basis of current knowledge about periodontal wound healing.
# Periodontal wound healing
Regeneration of the periodontium must include the formation of new cementum with inserting collagen fibers on the previously periodontitis-involved root surfaces and the regrowth of the alveolar bone. However, whether regrowth of alveolar bone should always be considered a requirement for success following regenerative periodontal surgery is a matter of discussion. The basis for this discussion is that a fibrous attachment may exist without opposing bone in a normal dentition, not affected by periodontitis, in the presence of bone dehiscenses and fenestrations (see Fig. 1-74).
In 1976, Melcher suggested in a review paper that the type of cell which repopulates the root surface after periodontal surgery determines the nature of the attachment that will form. After flap surgery the curetted root surface may be repopulated by four different types of cell (Fig. 25-1):
1. Epithelial cells
2. Cells derived from the gingival connective tissue
3. Cells derived from the bone
4. Cells derived from the periodontal ligament.
Previously, in most attempts to restore lost tooth support, particular attention was directed towards the regeneration of the alveolar bone. An investigation was carried out in dogs in order to examine the relationship between the re-establishment of a connective tissue attachment to the root surface and the regrowth of alveolar bone (Nyman & Karring 1979). After elevation of mucoperiostal flaps, the marginal 5–7 mm of the buccal alveolar bone of each experimental tooth was removed (Fig. 25-2). During this procedure, care was taken to minimize the mechanical injury to the connective tissue attachment on the root surface. Prior to flap closure, a notch, serving as a landmark for the histologic measurements, was prepared in the root surface at the level of the surgically reduced bone crest. After 8 months of healing, the animals were sacrificed. Histologic analysis demonstrated that although a connective tissue attachment was re-established consistently on the roots, the amount of bone regeneration varied widely. In some roots, bone regrowth was negligible (Fig. 25-3), whereas in others the bone had regenerated to its normal level. These results demonstrated that the amount of bone regrowth is unrelated to the re-establishment of a connective tissue attachment.
Another experiment was carried out in monkeys (Lindhe _et al_. 1984), in order to examine whether the presence of bone may stimulate the formation of a new connective tissue attachment. Mandibular and maxillary incisors were extracted and re-implanted in their own sockets under the following four experimental conditions (Fig. 25-4):
**Fig. 25-1** Following flap surgery, the curetted root surface may be repopulated by (1) epithelial cells, (2) gingival connective tissue cells, (3) bone cells, or (4) periodontal ligament cells.
**Fig. 25-2** Following flap elevation, the buccal bone, including a part of the inter-radicular and interproximal alveolar bone, is removed without injuring the connective tissue attachment on the root surface.
**Fig. 25-3** (a) Microphotograph of specimen 8 months following bone removal. A connective tissue attachment is re-established (arrows). Bone regeneration is negligible and is confined to the notch (N) in the root surface. (b) Higher magnification of the newly formed bone in the notch area (N).
**Fig. 25-4** Schematic drawing showing the four experimental conditions (a–d) under which experimental teeth were extracted and re-implanted in their own sockets.
1. Non-root-planed teeth were re-implanted into sockets with normal bone height.
2. Teeth, root planed in their coronal portion, were re-implanted into sockets with normal bone height.
3. Non-root-planed teeth were re-implanted into sockets with a reduced bone height.
4. Teeth, root planed in their coronal portion, were re-implanted into sockets with reduced bone height.
Histologic examination after 6 months of healing revealed that a fibrous reunion was established in areas where the periodontal connective tissue attachment was retained at the time of re-implantation. However, in areas, where the periodontal ligament tissue was removed, the epithelium had always migrated to the apical extension of root instrumentation (Fig. 25-5). These results of healing occurred irrespective of the presence or absence of bone, indicating that the establishment of a connective tissue attachment is unrelated to the presence of alveolar bone.
Using orthodontic appliances, Karring _et al_. (1982) tilted maxillary second and third incisors in labial direction in dogs. Subsequently, these teeth were moved back to their original position. During the same period the contralateral incisors were moved to a labially deviated position. The orthodontic appliances were then used to retain the teeth in these positions for a period of 5 months before sacrifice of the animals. Histologic analysis demonstrated that in all experimental teeth, the apical termination of the junctional epithelium was at the cemento-enamel junction. In the teeth which were retained in their labially displaced position, the level of the alveolar bone was reduced to a position about 4.5 mm apical to the cemento-enamel junction (Fig. 25-6a), while in the teeth which were moved back to their original position, the alveolar bone crest was located at a normal level relative to the cemento-enamel junction (Fig. 25-6b). This experiment demonstrated that bone resorption or bone regeneration may be induced by orthodontic forces on teeth with a pristine connective tissue attachment. The experiments described above indicate that the re-establishment of a connective tissue attachment to the root surface and the regeneration of the alveolar bone are not related to each other.
The use of bone grafts in regenerative periodontal therapy is based on the assumption that the promotion of bone regrowth may also induce cells in the bone to produce a new cementum layer with inserting collagen fibers on previously periodontitis-involved root surfaces. However, histologic studies in both humans and animals have demonstrated that grafting procedures often result in healing with a long junctional epithelium rather than a new connective tissue attachment (Caton & Zander 1976; Listgarten & Rosenberg 1979; Moscow _et al_. 1979).
Ellegaard _et al_. (1973, 1974, 1975, 1976) and Nielsen _et al_. (1980) reported that grafting materials in periodontal bony defects may be:
1. Osteoproliferative (osteogenetic), which means that new bone is formed by bone-forming cells contained in the grafted material.
2. Osteoconductive, which means that the grafted material does not contribute to new bone formation _per se_ but serves as scaffold for bone formation originating from adjacent host bone.
3. Osteoinductive, which means that bone formation is induced in the surrounding soft tissue immediately adjacent to the grafted material.
**Fig. 25-5** Microphotographs showing the histological features after 6 months of healing, under the four experimental conditions (a–d) illustrated in Fig. 25-4. The teeth in (b) and (d) are those root planed in their coronal portion, and the teeth (a) and (b) are those re-implanted in sockets with normal bone height. A fibrous reunion was established in areas where the connective tissue attachment was retained (a and c) while the epithelium has migrated to the apical extension of root instrumentation (a RP) where the attachment was removed (b and d). CEJ = cemento-enamel junction.
**Fig. 25-6** Microphotograph of a tooth retained in its labially displaced position (a) and a tooth (b) moved back to its original position. The level of alveolar bone (arrow) is reduced in (a) while it has regenerated to its normal level (arrow) in (b). The apical termination of the junctional epithelium is at the cemento-enamel junction (CEJ) in both situations.
**Fig. 25-7** (a) Microphotograph of furcation 6 weeks after grafting with iliac crest marrow. The furcation is completely filled with bone (B), but ankylosis (AN) and root resorption (RS) can be seen. (b) Higher magnification of the area in (a) showing ankylosis and resorption. OC = osteoclasts.
**Fig. 25-8** (a) Microphotograph of a healed bifurcation defect following transplantation of non-vital bone grafts. The grafts (G) have not been reached by bone formation from the inter-radicular septum (S), but occur as isolated particles surrounded by "cementum". Cementum (C) and new connective tissue attachment formation have taken place along the entire circumference of the bifurcation. (b) High magnification of isolated bone grafts (G) with newly formed "cementum" on the surface.
These studies, where various types of bone graft were placed in intrabony defects or inter-radicular lesions, revealed that cells survived transplantation only in iliac bone marrow grafts. Transplantation of iliac bone marrow grafts almost consistently resulted in bone fill in the experimental defects, but healing was frequently accompanied by ankylosis and root resorption (Fig. 25-7). The iliac bone marrow grafts exerted an osteogeneic effect, and it was suggested that this was responsible for the induction of root resorption (Ellegaard _et al_. 1973, 1974). Jaw bone grafts and xenografts did not actively contribute to bone formation but served as a scaffold for bone regeneration (i.e. osteoconductive effect). Often, however, these bone grafts were not reached by the new bone growing out from the host bone, but occurred as isolated particles surrounded by a bone-like or cementum-like substance (Fig. 25-8). It was found that the treated bifurcation defects became filled mainly with granulation tissue derived from the periodontal ligament (Fig. 25-9). The authors (Nielsen _et al_. 1980) suggested that this invasion of ligament tissue inhibited bone formation and that the new cementum on the root surface in the bifurcation defects, including the cementum-like substance observed around the implanted bone particles, was formed by periodontal ligament cells (Fig. 25-8). Thus, it appeared from these studies that the key cells in periodontal regeneration are periodontal ligament cells rather than bone cells.
**Fig. 25-9** Cleared specimen from a 1-week-old bifurcation defect treated with bone grafts. Judged from the course of the blood vessels, the granulation tissue in the defect has developed mainly from the periodontal ligament (arrows) and only to a minor extent from the inter-radicular septum (IS).
## Regenerative capacity of bone cells
The ability of newly formed tissue originating from bone to produce a new connective tissue attachment was examined in a study by Karring _et al_. (1980). Roots of periodontitis-affected teeth were extracted and placed in surgically created sockets in edentulous areas of dogs. The implanted roots were covered with tissue flaps (submerged) and the results of healing were examined histologically after 3 months. A periodontal ligament was re-established in the apical portion of the re-implanted roots where, at the time of implantation, remnants of periodontal ligament tissue were preserved. In the coronal portion of the roots which were previously exposed to peri-odontitis and then scaled and planed, healing had consistently resulted in ankylosis and root resorption (Fig. 25-10). On the basis of this finding, it was concluded that tissue derived from bone lacks cells with the potential to produce a new connective tissue attachment.
## Regenerative capacity of gingival connective tissue cells
Another experiment (Nyman _et al_. 1980) was carried out in order to examine the potential of gingival connective tissue to produce a new connective tissue attachment. The teeth were treated as described in the experiment above but were not transplanted into sockets. Instead they were placed in bone concavities prepared on the buccal aspect of the jaw and subsequently covered by tissue flaps. Thus, half the circumference of the roots was in contact with bone while the remaining part was facing the gingival connective tissue at the subsurface of the flaps. Histologic examination after 3 months of healing showed areas with periodontal ligament in the apical portion of the roots where, at the time of implantation, periodontal ligament tissue was preserved. In the coronal, previously exposed part of the roots, no signs of new connective tissue attachment were present. The root portion located in contact with gingival connective tissue demonstrated a connective tissue with fibers oriented parallel to the root surface and without attachment to the root. However, root resorption occurred at the majority of the surfaces (Fig. 25-11). On the basis of this result it was concluded that gingival connective tissue also lacks cells with the potential to produce a new connective tissue attachment.
**Fig. 25-10** (a) Microphotograph of a re-implanted root after 3 months of healing. A periodontal ligament (PL) has become re-established in the apical portion of the root whereas ankylosis (A) and root resorption (R) is the predominant feature in the coronal portion. (b) High magnification of the ankylosis seen in (a).
**Fig. 25-11** Microphotograph of root (R) which has been reimplanted with its surface facing the gingival connective tissue (GCT). The surface exhibits extensive resorption.
## Regenerative capacity of periodontal ligament cells
In the experiments described above, root resorption was also observed occasionally in the apical portion of the extracted and re-implanted roots (Karring _et al_. 1980; Nyman _et al_. 1980). It was suggested that this occurred because the periodontal ligament tissue retained on this part of the root had become injured during extraction, thereby allowing bone or gingival connective tissue to contact the root surface during healing and induce resorption. It was assumed that this damage of the retained periodontal ligament tissue had also restricted its potential of proliferating in the coronal direction along the root surface. Indeed, in a later study (Karring _et al_. 1985), where periodontitis-involved roots were retained in their sockets and subsequently submerged, significant amounts of new connective tissue attachment formed on the coronal portion of the roots (Fig. 25-12). The finding of new attachment only on the roots with a non-impaired periodontal ligament, but never on the extracted and re-implanted roots with an impaired ligament, indicates that periodontal ligament tissue contains cells with the potential to form a new connective tissue attachment on a detached root surface.
**Fig. 25-12** Microphotograph showing new attachment formation (between the arrows) on a submerged root with a non-impaired periodontal ligament. Coronal to the cementum, root resorption is the predominant feature.
Active root resorption occurred consistently at the root surfaces above the coronal extension of new attachment (Fig. 25-12). It was suggested that this resorption was induced by gingival connective tissue which had proliferated apically from the covering tissue flap. Thus, only cells in the periodontal ligament seem capable of regenerating lost periodontal attachment.
The final evidence that the progenitor cells for new attachment formation reside in the periodontal ligament was provided in studies in which titanium dental implants were placed in contact with retained root tips whose periodontal ligament served as a source for cells which could populate the implant surface during healing (Buser _et al_. 1990a,b; Warrer _et al_. 1993). Microscopic analysis revealed that a distinct layer of cementum with inserting collagen fibers had formed on the surfaces of the implants (Fig. 25-13a), and that these fibers, often oriented perpendicularly to the surface, were embedded in the opposite bone (Fig. 25-13b). Control implants (Fig. 25-14) placed without contact with retained roots healed with the characteristic features of osseointegration (i.e. direct contact between bone and the implant surface).
Further proof of the ability of periodontal ligament cells to produce a new connective tissue attachment was recently provided by Parlar _et al_. (2005) using a novel and unique experimental model in dogs. After resection of the crowns of the canine teeth in the dogs, the roots were hollowed to a depth of 5 mm. leaving a thin dentinal wall. Slits were then prepared in the cavity wall to create passages from this chamber to the surrounding periodontal ligament. A titanium implant was placed into the center of each chamber, and finally a collagen barrier was placed over the chamber before the roots were submerged. Histologic analysis after 4 months of healing revealed that a periodontal ligament, bone, and root cementum had formed between the implant and the dentinal wall of the chamber. Due to the invasion of periodontal ligament tissue through the slits into the chamber, cementum had formed on the implant as well as the dentinal wall, and a periodontal ligament was consistently interposed between the implant and the bone and between the bone and the dentinal wall. Thus, there is strong evidence that the progenitor cells for periodontal attachment formation reside in the periodontal ligament and not in the alveolar bone as previously assumed (Melcher _et al_. 1987).
**Fig. 25-13** (a) Microphotograph of a titanium implant placed in contact with retained root tips. A distinct cementum layer (arrows) and periodontal ligament (PL) in continuity with that on the roots (R) is visible on the implant surface. (b) High magnification in polarized light of the periodontal ligament formed around the implant seen in (a). A cementum layer (arrows) with Sharpey's fibers is present at the implant surface. Principal fibers, oriented perpendicular to the surface, are running across the ligament space (LS) and are inserting in the opposing bone (B) as in natural teeth (see Fig. 1-71).
**Fig. 25-14** Microphotograph of a titanium implant placed without contact with retained roots (control). This implant has healed with a direct contact between the bone and the implant surface (osseointegration).
## Role of epithelium in periodontal wound healing
Some of the roots in the experiment described above (Karring _et al_. 1985) penetrated the covering mucosa at early stages of healing, thereby allowing the epithelium to grow apically along the root surface. The amount of new connective tissue attachment on these roots was considerably smaller than that formed on the roots which remained submerged throughout the study. This finding and those of other investigators (Moscow 1964; Kon _et al_. 1969; Proye & Polson 1982) indicate that the apical migration of epithelium reduces the coronal gain of attachment, evidently by preventing periodontal ligament cells from repopulating the root surface (Fig. 25-15).
Downgrowth of epithelium into the periodontal lesion has most likely occurred to a varying extent during healing following most flap and grafting procedures applied in regenerative periodontal therapy, which may explain the varying results reported. This view is supported by the results of the monkey study by Caton _et al_. (1980). These investigators examined healing in ligature-induced periodontal lesions following treatment with four different modalities of regenerative surgical procedures:
1. Root planing and soft tissue curettage
2. Widman flap surgery without bone grafting
3. Widman flap surgery with the placement of frozen autogeneous red bone marrow and cancellous bone
4. Beta-tricalcium phosphate in intrabony defects.
**Fig. 25-15** Microphotograph illustrating an intrabony defect after regenerative treatment. New bone (NB) has formed in the defect but epithelium has migrated apically along the root surface to the notch (arrow) in the root surface indicating the bottom of the defect before treatment.
Healing following all treatment modalities resulted in the formation of a long junctional epithelium extending to or close to the same level as before treatment.
## Root resorption
In the experimental studies described previously, granulation tissue, derived from gingival connective tissue or bone, produced root resorption when contacting the curetted root surface during healing following surgery (Karring _et al_. 1980, 1985; Nyman _et al_. 1980). It should be expected, therefore, that this phenomenon would occur as a frequent complication to periodontal surgery, particularly following those procedures which include the placement of grafting materials to stimulate bone formation. The reason why root resorption is rarely seen is most likely that post-operatively, the dentogingival epithelium migrates apically along the root surface, forming a protective barrier towards the root surface (Fig. 25-15). This view is supported by the results of an experimental study in monkeys (Karring _et al_. 1984) in which roots, which previously had been subjected to ligature-induced periodontitis, were extracted and re-implanted in contact with bone and connective tissue and covered with a tissue flap (submerged). After varying time intervals the submerged roots were exposed to the oral cavity by a second incision (wounding) through the covering mucosa, thereby permitting the epithelium to migrate into the wound. In specimens where the wounding occurred within 2 weeks (Fig. 25-16), the previously diseased part of the roots was covered by epithelium and showed no signs of resorption. With increasing intervals between implantation of the roots and the wounding, a steadily diminishing part of the diseased root surface was covered by epithelium, and root resorption and ankylosis became progressively pronounced (Fig. 25-17). This observation concurs with results presented by Björn _et al_. (1965) who treated 11 periodontally diseased teeth in seven human volunteers, using the submerging technique which prevented apical migration of the dentogingival epithelium. The authors reported that root resorption was indeed a common complication following this kind of therapy.
**Fig. 25-16** Microphotograph of an implanted root (R) where epithelium was allowed to migrate into the wound after 2 weeks. The epithelium has migrated along the coronal, previously periodontitis-involved root surfaces down to the level indicated by the arrows. In the areas covered by epithelium, there are no signs of resorption. Apical to this level the root surfaces demonstrate root resorption.
# Regenerative concepts
One of the first methods used in attempts to obtain new attachment was scaling and root planing combined with soft tissue curettage (i.e. mechanical removal of the diseased root cementum and the pocket epithelium). Studies in humans (e.g. McCall 1926; Orban 1948; Beube 1952; Waerhaug 1952; Schaffer & Zander 1953; Carranza 1954, 1960) and in animals (e.g. Beube 1947; Ramfjord 1951; Kon _et al_. 1969) showed that this type of periodontal therapy resulted not only in the establishment of gingival health but also in a reduction of the initially recorded pocket depth. This decrease in the depth of the peri-odontal pocket was assumed to be partly the result of shrinkage of the initially inflamed gingiva, but partly also the effect of the formation of a new connective tissue attachment in the apical part of the pocket.
**Fig. 25-17** Microphotograph of an implanted root (R) where epithelium was allowed to migrate into the wound after 4 weeks. The epithelium (arrows) covers only the coronal cut root surface. Extensive resorption is seen on the surface facing the gingival connective tissue (GCT) and resorption and ankylosis are seen on the surface facing the bone tissue (B).
The possibility of obtaining new attachment became widely accepted with the work of Prichard (1957a,b), in which new attachment formation in intrabony periodontal lesions was reported as a predictable outcome of treatment. Seventeen cases were presented out of which four were subjected to a re-entry surgical procedure, revealing that these defects were filled with bone. The technique of Prichard (1957b, 1960) was only used for the treatment of three-wall intrabony defects, and the results obtained suggested that the morphology of the periodontal bony defect was essential for the establishment of a predictable prognosis. Goldman and Cohen (1958) introduced a classification of periodontal intrabony defects which was based on the number of osseous walls surrounding the defect, being either three-wall, two-wall or one-wall defects or a combination of such situations (Fig. 25-18).
The technique of Prichard (1957a,b, 1960) included the elevation of tissue flaps in order to get access to the defect. All granulation tissue in the defect was removed and the root surface was scaled and planed. In order to enhance regeneration of bone, small per-forations were made with a bur at several sites of the bone walls. The flaps were sutured to accomplish complete coverage of the defect. Many clinical investigators have claimed that new attachment resulted following this type of treatment but there is little quantitative or qualitative documentation (Patur & Glickmann 1962; Wade 1962, 1966; Ellegaard & Löe 1971). Patur and Glickmann (1962) reported a clinical study including 24 intrabony defects treated according to the Prichard technique (1957a,b). The outcome was evaluated by comparing pre-operative and post-operative radiographs, measurements of the alveolar bone level adjacent to the root and study casts taken during operation and post-operatively after reflecting buccal and lingual flaps. The authors reported that new attachment had occurred in two-wall and three-wall intrabony defects but not in one-wall defects. Results from a study by Ellegaard and Löe (1971) comprising 191 defects in 24 patients with periodontal disease indicated that complete regeneration, determined radiographically and by periodontal probing, had occurred in around 70% of the three-wall defects, in 40% of the combined two-wall and three-wall defects, and in 45% of the two-wall defects.
In a later study by Rosling _et al_. (1976), 124 intrabony defects in 12 patients were treated by means of the modified Widman flap procedure (Ramfjord & Nissle 1974). Following treatment the patients were recalled twice per month for professional tooth cleaning. Re-examination performed clinically and on radiographs 2 years after therapy demonstrated bone fillin of two-wall as well as three-wall defects. The authors suggested that this regrowth of bone was also associated with the formation of new connective tissue attachment and ascribed the successful healing mainly to the optimal standard of oral hygiene which was maintained in all patients during healing. A clinical study with almost identical results was presented by Polson & Heijl (1978). The results of several histologic studies in animals and humans, on the other hand, indicate that formation of new periodontal attachment is by no means predictable following subgingival curettage or flap surgery (Listgarten & Rosenberg 1979; Caton & Nyman 1980; Caton _et al_. 1980; Steiner _et al_. 1981; Stahl _et al_. 1983; Bowers _et al_. 1989a).
## Grafting procedures
In a number of clinical trials and animal experiments, the flap approach was combined with the placement of bone grafts or implant materials into the curetted bony defects with the aim of stimulating periodontal regeneration. The various graft and implant materials used so far can be placed into four categories:
**Fig. 25-18** Progression of periodontitis at a different rate on neighboring tooth surfaces results in the development of intrabony defects. Based on the number of surrounding bone walls such defects are classified as one-wall (a), two-wall (b) or three-wall (c) defects.
1. _Autogenous grafts_ : grafts transferred from one position to another within the same individual. This type of graft comprises (i) cortical bone or (ii) cancellous bone and marrow, and is harvested either from intraoral or extraoral donor sites.
2. _Allogeneic grafts_ : grafts transferred between genetically dissimilar members of the same species. (i) Frozen cancellous bone and marrow, and (ii) freeze-dried bone have been used.
3. _Xenogeneic grafts_ : grafts taken from a donor of another species.
4. _Alloplastic materials_ : synthetic or inorganic implant materials which are used as substitutes for bone grafts.
The rationale behind the use of bone grafts or allo-plastic materials is the assumption that both the regrowth of alveolar bone and the formation of new attachment would be stimulated because these materials may either (1) contain bone-forming cells (osteo-genesis), or (2) serve as a scaffold for bone formation (osteoconduction), or because (3) the matrix of the bone grafts contains bone-inducing substances (osteo-induction) (Urist 1980; Brunsvold & Mellonig 1993). Such complete regeneration of the periodontal attachment apparatus following grafting procedures would imply, however, that cells derived from bone possess the ability to form new cementum with inserting collagen fibers on a previously periodontitis-involved root surface (Melcher _et al_. 1987). This assumption is in conflict with current knowledge about the biology of periodontal wound healing, that repopulation of the detached root surface with cells from the peri-odontal ligament is the prerequisite for new attachment formation. This means that all therapeutic procedures involving the placement of bone grafts or bone substitute implants are based on a biologic concept which cannot explain how such treatment should result in regeneration of the periodontium.
The effect of using bone grafts or alloplastic materials for periodontal regeneration has mainly been examined in case reports, while histologic evidence of new attachment and controlled clinical studies is limited. The results from such reports vary and the documentation presented usually consists of pre-operative and post-operative probing attachment levels, radiographic interpretations or re-entry procedures.
### Autogenous grafts
Autogenous grafts (autografts) may retain some cell viability and are considered to promote bone healing mainly through osteogenesis and/or osteoconduction. They are gradually resorbed and replaced by new viable bone. In addition, potential problems of histocompatibility and disease transmission are eliminated with autogenous grafts. Autogenous grafts can be harvested from intraoral or extraoral sites.
#### __Intraoral autogenous grafts__
Intraoral autogenous grafts obtained from edentulous areas of the jaw, healing extraction sites, maxillary tuberosities or the mandibular retromolar area were commonly used in periodontal regenerative surgery (Mann 1964; Ellegaard & Löe 1971; Rosenberg 1971a,b; Dragoo & Sullivan 1973a,b; Hiatt & Schallhorn 1973; Froum _et al_. 1983; Stahl _et al_. 1983). Generally cancellous bone is preferred as graft material but cortical bone, applied as small chips (Rosenberg _et al_. 1979), or mixed with blood prior to the placement in the defects (Robinson 1969; Froum _et al_. 1976), was also reported to be effective in producing regeneration in periodontal intrabony defects.
The effect of intraoral autogenous grafts has been evaluated in both animals and humans. In a study in monkeys, Rivault _et al_. (1971) observed that intrabony defects filled with intraoral autogenous bone chips mixed with blood (osseous coagulum) healed with new bone formation, but no more bone was found in such experimental defects than was observed in similar control defects treated with surgical curettage. Other studies in monkeys and dogs also failed to demonstrate significant differences in bone formation between grafted and non-grafted intrabony or furcation defects (Ellegaard _et al_. 1974; Coverly _et al_. 1975; Nilveus _et al_. 1978).
In clinical case series where intraoral autogenous grafts were used for the treatment of intrabony periodontal defects, a mean bone fill ranging from 3.0–3.5 mm was reported (Nabers & O'Leary 1965; Robinson 1969; Hiatt & Schallhorn 1973; Froum _et al_. 1975). Hiatt and Schallhorn (1973) treated 166 intrabony lesions with intraoral autogenous cancellous bone. They reported a mean increase in bone height of 3.5 mm, evaluated by clinical measurements. One-wall, two-wall, and three-wall defects were included, and the largest bone fill was observed in defects with the highest number of bone walls. A block section obtained from a patient treated in this study presented histologic evidence of new cementum, bone, and periodontal ligament formation. In controlled clinical studies, intraoral autogenous grafts were found superior to surgical debridement alone in terms of bone fill (Froum _et al_. 1976), or probing attachment (PAL) gain (Carraro _et al_. 1976) in two-wall defects. However, there are controlled studies that demonstrate more modest results regarding bone fill or PAL gain after intraoral grafting when compared to ungrafted controls (Ellegaard & Löe 1971; Renvert _et al_. 1985).
Ross and Cohen (1968) reported new bone and cementum formation in a human histologic specimen from an intrabony defect retrieved 8 months following debridement and placement of intraoral autogenous grafts. They also found that the grafts were without osteocytes and that the deposition of new alveolar bone had taken place around the grafts. Nabers _et al_. (1972) observed that new cementum and functionally oriented periodontal ligament fibers were present in half the length of a defect which was biopsied about 4.5 years after treatment with intra-oral autogenous bone grafts. In other human Histologic reports, bone fill and new attachment were observed coronal to reference notches placed on the treated roots at the apical termination of root planing (Hiatt _et al_. 1978) or at the most apical level of previously existing calculus (Froum _et al_. 1983; Stahl _et al_. 1983). Other investigators, however, observed an epithelial lining which occupied a varying portion of the previously diseased part of the root (Hawley & Miller 1975; Listgarten & Rosenberg 1979; Moscow _et al_. 1979). The results from these studies and those from a recent meta-analysis (Trombelli 2005) indicate that the treatment of periodontal osseous defects with intraoral bone grafts may result in periodontal regeneration, but not predictably.
#### __Extraoral autogenous grafts__
Schallhorn (1967, 1968) introduced the use of autogeneous hip marrow grafts (iliac crest marrow) in the treatment of furcation and intrabony defects. Later several studies were published demonstrating the osteogenic potentials of this material (Schallhorn _et al_. 1970; Schallhorn & Hiatt 1972; Patur 1974; Froum _et al_. 1975), and as much as 3–4 mm gain in crestal bone was reported following the treatment of intra-bony defects with hip marrow grafts. The effect of iliac crest marrow and of intraoral cancellous bone grafts in one-wall, two-wall, and three-wall bony defects in humans was evaluated by Patur (1974). He reported that bone fill occurred to a varying extent with both types of graft. The amount of bone fill in one-wall bony defects was larger with iliac crest marrow than with cancellous bone or when no grafts were used. Some defects within all three groups showed bone fill, and no difference was observed between the control defects and those treated with intraoral cancellous bone grafts. The author stated that even with fresh iliac crest marrow, bone regeneration is variable and unpredictable.
Healing of inter-radicular and intrabony lesions following placement of iliac crest marrow was evaluated in monkeys by Ellegaard _et al_. (1973, 1974). Regeneration occurred more frequently with the use of grafts, but iliac crest marrow frequently resulted in ankylosis and root resorption (Fig. 25-19).
Histologic evidence of periodontal regeneration in humans following the use of iliac crest marrow grafts was provided by Dragoo and Sullivan (1973a,b). At 8 months following therapy a mature periodontal ligament was present at the grafted sites and about 2 mm supracrestal new attachment had also formed. Clinical evidence of root resorption was noted in seven of the 250 grafted sites.
**Fig. 25-19** Photomicrograph illustrating an intrabony defect 2 months following grafting with iliac crest marrow. The defect is completely filled with bone, but new cementum (c) is lacking on the root surface except for the most apical part (n) of the defect. Note that ankylosis and root resorption (arrows) are occurring in the coronal part of the defect.
Due to the morbidity associated with the donor site and the fact that root resorption sometimes results, iliac crest marrow grafts are not used in regenerative periodontal therapy today.
### Allogeneic grafts
Allogeneic grafts (allografts) were utilized in attempts to stimulate bone formation in intrabony defects in order to avoid the additional surgical insult associated with the use of autogenous grafts. However, the use of allogeneic grafts involves a certain risk regarding antigenicity, although the grafts are usually pretreated by freezing, radiation or chemicals in order to suppress foreign body reactions.
The types of allogeneic grafts used are frozen iliac cancellous bone and marrow, mineralized freezedried bone allogeneic grafts (FDBA), and decalcified freeze-dried alogeneic bone grafts (DFDBA). The need for cross matching to decrease the likelihood of graft rejection as well as the risk of disease transmission virtually eliminated the use of frozen iliac allogeneic grafts in periodontics.
FDBA is a mineralized bone graft, which loses cell viability through the manufacturing process and, therefore, is supposed to promote bone regeneration through osteoconduction/osteoinduction (Goldberg & Stevenson 1987). The freeze drying also markedly reduces the antigenicity of the material (Turner & Mellonig 1981; Quattlebaum _et al_. 1988). The efficacy of FDBA was evaluated in a study which included 89 clinicians (Mellonig 1991). At re-entry surgery it was found that 67% of the sites treated with FDBA alone and 78% of the sites treated with FDBA plus autogenous bone grafts demonstrated complete or more than 50% bone fill. Thus, FDBA plus autogenous bone appeared more effective than FDBA alone. In split-mouth studies where FDBA was combined with autogenous grafts or tetracycline powder (Sanders _et al_. 1983; Mabry _et al_. 1985), a defect fill of 60% and 80% of the initial lesion was reported. In a split-mouth study it was also shown that FDBA implantation had a similar effect on defect resolution as that achieved by DFDBA (Rummelhart _et al_. 1989) or granular porous hydroxyapatite (Barnett _et al_. 1989). However, the only controlled clinical trial comparing treatment of intrabony defects with FDBA implantation versus flap surgery failed to demonstrate any difference in terms of clinical attachment gain and bone fill between test and control sites at 1 year re-entry examination (Altiere _et al_. 1979). In addition, human histologic specimens demonstrated that implantation of FDBA in intrabony defects yielded no periodontal regeneration but resulted in a long epithelial attachment on the previously diseased root surface (Dragoo & Kaldahl 1983).
Several animal studies suggested that demineralization of a cortical bone allograft (DFDBA) enhances its osteogenic potential by exposing bone morphogenic proteins (BMPs) which presumably have the ability to induce host cells to differentiate into osteo-blasts (Urist & Strates 1970; Mellonig _et al_. 1981). Several case reports presented clinical improvements and bone fill after implantation of DFDBA into intra-bony defects (Quintero _et al_. 1982; Werbitt 1987; Fucini _et al_. 1993; Francis _et al_. 1995), and controlled clinical studies documented considerable gain of attachment and bone fill in sites treated with DFDBA as compared with non-grafted sites (Pearson _et al_. 1981; Mellonig 1984; Meadows _et al_. 1993). However, no statistical differences regarding attachment level changes and bone fill were found when comparing sites treated with FDBA and sites treated with DFDBA (Rummelhart _et al_. 1989).
Histologic evidence of regeneration following grafting with DFDBA was provided by Bowers _et al_. (1989b,c). Complete regeneration with new cementum, periodontal ligament, and bone amounting to 80% of the original defect depth was reported at sites treated with DFDBA, which was considerably more than that observed in defects treated with surgical debridement alone. However, animal experiments failed to confirm the regenerative potential of DFDBA grafting (Sonis _et al_. 1985; Caplanis _et al_. 1998).
The controversial results regarding the effect of DFDBA on the regeneration of periodontal intra-osseous defects along with great differences in the osteoinductive potential (ranging from high to no osteoinductive effect) of commercially available DFDBA (Becker _et al_. 1994, 1995; Shigeyama _et al_. 1995; Schwartz _et al_. 1996; Garraway _et al_. 1998), and the (although minute) risk for disease transmission have raised concern about the clinical applicability of DFDBA. In EU countries, commercially available DFDBA is not granted a CE mark permitting distribution of the material within the community.
### Xenogeneic grafts
The use of xenogeneic bone grafts (xenografts) in regenerative periodontal surgery was examined several years ago. Nielsen _et al_. (1981) treated 46 intrabony defects with Kielbone® (i.e. defatted and deproteinized ox bone) and another 46 defects with intraoral autogenous bone grafts. The results, which were evaluated by periodontal probing and radiographically, showed no difference between the amount of clinical gain of attachment and bone fill obtained in the two categories of defect. A study in monkeys also demonstrated that the two types of bone graft displayed similar histologic features and were frequently seen in the connective tissue of the healed defects as isolated bone particles surrounded by a cementum-like substance (Nielsen _et al_. 1980).
Recently, new processing and purification methods have been utilized which make it possible to remove all organic components from a bovine bone source and leave a non-organic bone matrix in an unchanged inorganic form (e.g. Bio-Oss®, Geistlich AG, Switzerland; Lubboc®/Laddec®, Ost Development SA, France; Endobone®, Biomet Inc. Dordrecht, The Netherlands; OsteoGraf®/N, DENTSPLY, Friadent Cera-Med, Lakewood, CO, USA; Cerabone®, aap Implantate AG, Berlin, Germany). However, differences in the purification and manipulation methods of the bovine bone have lead to commercially available products with different chemical properties and possibly different biologic behavior. These materials are available in different particle sizes or as block grafts.
To date, no controlled human study has compared the effect of such graft materials in periodontal defects with flap surgery alone, but a clinical study has demonstrated that implantation of Bio-Oss®resulted in pocket reduction, gain of attachment, and bone fill in periodontal defects to the same extent as that of DFDBA (Richardson _et al_. 1999). There are, on the other hand, several controlled clinical studies reporting about the outcome of treatment of periodontal intrabony defects with Bio-Oss used as an adjunct to guided tissue regeneration (GTR). In one of these studies, including 124 patients, the combined treatment had an added benefit of 0.8 mm PAL gain over that with flap surgery alone (Tonetti _et al_. 2004). However, conflicting results have been reported following the combined Bio-Oss and GTR treatment of intrabony defects versus GTR alone. In a recent study, significantly more PAL gain was found after the combined treatment than after GTR treatment with a collagen membrane (5.1 mm versus 4.0 mm) (Paolantonio 2002), while in another study, the clinical improvements obtained following the two treatments were similar (Stavropoulos _et al_. 2003b). This latter finding is in agreement with the results of a recent systematic review evaluating various bone grafts and bone graft substitutes as adjuncts to GTR (Murphy & Gunsolley 2003). Studies in experimental animals have also failed to show an added effect of Bio-Oss combined with GTR (Carmagnola _et al_. 2002, 2003). However, human histology (Camelo _et al_. 1998; Nevins _et al_. 2003; Sculean _et al_. 2003) and a study in dogs (Clergeau _et al_. 1996) have suggested that the placement of bovine bone-derived biomaterials in periodontal bone defects may enhance both the regeneration of a new connective tissue attachment and bone. The results of several experimental studies in animals, on the other hand, have questioned whether Bio-Oss encourages bone formation (Stavropoulos _et al_. 2001, 2003a, 2004; Aghaloo _et al_. 2004; Cardaropoli _et al_. 2005). In fact, the results of some of these studies suggest that grafting of Bio-Oss may compromise bone formation.
The use of coral skeleton as a bone graft substitute was proposed some decades ago (Holmes 1979; Guillemin _et al_. 1987). Depending on the pretreatment procedure, the natural coral turns into non-resorbable porous hydroxyapatite (e.g. Interpore 200, Interpore International, Irvine, US) or to a resorbable calcium carbonate (e.g. Biocoral, Inoteb, St Gonnery, France) skeleton (Nasr _et al_. 1999). Implantation of coralline porous hydroxyapatite in intra-bony periodontal defects in humans produced more probing pocket depth reduction, clinical attachment gain, and defect fill than non-grafting (Kenney _et al_. 1985; Krejci _et al_. 1987; Yukna 1994; Mora & Ouhay-oun 1995; Yukna & Yukna 1998), and similar results were found when compared with grafting of FDBA (Barnett _et al_. 1989). When porous hydroxyapatite was compared with DFDBA for the treatment of intraosseous defects, similar results were also obtained (Bowen _et al_. 1989), but another study reported clinical results in favor of this material (Oreamuno _et al_. 1990). However, both animal (West & Brustein 1985; Ettel _et al_. 1989) and human studies (Carranza _et al_. 1987; Stahl & Froum 1987) have provided only vague histologic evidence that grafting of natural coral may enhance the formation of true new attachment. In most cases, the graft particles were embedded in connective tissue with minimal bone formation.
### Alloplastic materials
Alloplastic materials are synthetic, inorganic, bio-compatible and/or bioactive bone graft substitutes which are claimed to promote bone healing through osteoconduction. There are four kinds of alloplastic materials, which are frequently used in regenerative periodontal surgery: hydroxyapatite (HA), beta-tricalcium phosphate (β-TCP), polymers, and bioactive glasses (bio-glasses).
#### _Hydroxyapatite_
The HA products used in periodontology are of two forms: a particulate non-resorbable ceramic form
(e.g. Periograf®, Miter Inc., Warsaw, IN, US; Calcitite®, Calcitek Inc., San Diego, US) and a particulate, resorbable non-ceramic form (e.g. OsteoGraf/LD®, CeraMed Dental, Lakewood, CO, US). In controlled clinical studies, grafting of intrabony periodontal lesions with HA resulted in a PAL gain of 1.1–3.3 mm and also in a greater bone defect fill as compared with non-grafted surgically debrided controls (Meffert _et al_. 1985; Yukna _et al_. 1985, 1986, 1989; Galgut _et al_. 1992). In these studies, improvement of clinical parameters (i.e. PPD reduction and PAL gain) was more evident in the grafted sites than in the sites treated only with debridement, especially for initially deep defects. However, animal studies (Barney _et al_. 1986; Minabe _et al_. 1988; Wilson & Low 1992) and human histologic data (Froum _et al_. 1982; Moskow & Lubarr 1983; Ganeles _et al_. 1986; Sapkos 1986) showed that bone formation was limited and that a true new attachment was not formed consistently after grafting of intrabony periodontal defects with HA. The majority of the HA particles were embedded in connective tissue and new bone was only observed occasionally around particles in close proximity to host bone. A junctional epithelium lined the major part of the roots.
#### __Beta-tricalcium phosphate (β-TCP)__
β-TCP (Ca3(PO4) 2) (e.g. Synthograft®, Johnson and Johnson, New Brunswick, NJ, US) has been used in a series of case reports for the treatment of periodontal osseous lesions (Nery & Lynch 1978; Strub _et al_. 1979; Snyder _et al_. 1984; Baldock _et al_. 1985). After variable time intervals, a significant gain of bone was observed by means of re-entry or radiographs. However, there is no controlled study comparing the result of β-TCP grafting with that of open-flap debridement, and histologic data from animal (Levin _et al_. 1974; Barney _et al_. 1986) and human studies (Dragoo & Kaldahl 1983; Baldock _et al_. 1985; Bowers _et al_. 1986; Stahl & Froum 1986; Froum & Stahl 1987; Saffar _et al_. 1990) showed that β-TCP is rapidly resorbed or encapsulated by connective tissue, with minimal bone formation and no periodontal regeneration.
#### __Polymers__
There are two polymer materials that have been used as bone graft substitutes in the treatment of periodontal defects: a non-resorbable, calcium hydroxide coated co-polymer of polymethylmeth-acrylate (PMMA) and polyhydroxylethylmethacrylate (PHEMA), which is often referred to as HTR (hard tissue replacement) (e.g. HTRTM, Bioplant Inc., New York, NY, US), and a resorbable polylactic acid (PLA) polymer (Driloc®, Osmed Corp., Costa Mesa, CA, US).
In controlled clinical studies, implantation of HTR polymer grafts in intrabony defects resulted in a defect fill of approximately 2 mm, representing about 60% of the initial defect depth, but the improved clinical response with grafting was not significantly better than that following solely flap operation (Yukna 1990; Shahmiri _et al_. 1992). Human histologic data from an experimental study (Plotzke _et al_. 1993), and from two case reports (Stahl _et al_. 1990b; Froum 1996) also revealed that grafting of osseous periodontal defects with HTR does not promote periodontal regeneration. The HTR particles were most frequently encapsulated by connective tissue with only scarce evidence of bone formation. Healing resulted in a long junctional epithelium along the root surface, and true new attachment formation was not observed.
When PLA particles were implanted into intra-bony defects in humans and compared with DFDBA or surgically debrided controls, it was found that the healing results were less favorable than after flap operation alone, both in terms of clinical parameters (PPD and PAL gain), and in terms of bone fill (Meadows _et al_. 1993).
#### _Bioactive glasses (bio-glasses)_
Bio-glasses are composed of SiO2, Na2O, P2O5 and are resorbable or not resorbable depending on the relative proportion of these components. When bio-glasses are exposed to tissue fluids, a double layer of silica gel and calcium phosphate is formed on their surface. Through this layer the material promotes absorption and concentration of proteins used by osteoblasts to form extracellular bone matrix which theoretically may promote bone formation (Hench _et al_. 1972). Commercially available bio-glasses in particulate form, and theoretically resorbable, have been proposed for periodontal treatment (e.g. PerioGlass®, US Biomaterials Corp., Alachua, FL, US; BioGran®, Orthovita, Malvern, PA, US).
A human case report demonstrated that implantation of bio-glass in periodontal osseous defects resulted in a gain of clinical attachment of 2.0–5.3 mm and a radiographic bone fill of 3.5 mm, and in a controlled study, the treatment of intrabony defects with bio-glass also resulted in greater clinical improvements than surgical debridement alone (Froum _et al_. 1998). However, other controlled studies (Zamet _et al_. 1997) and split-mouth studies on grafting of intra-bony defects with bio-glass (Ong _et al_. 1998) failed to demonstrate statistically significant better clinical results than surgery alone or DFDBA grafting (Lovelace _et al_. 1998). Although experimental studies in monkeys have suggested that bio-glass grafting of periodontal intrabony defects (Karatzas _et al_. 1999) may favor new cementum formation and inhibit epithelial downgrowth, there is no histologic evidence in humans that bio-glass may promote true peri-odontal regeneration. In a histologic evaluation of bio-glass implanted in intrabony defects in humans it was observed that, although clinically satisfactory results were produced, healing had most frequently occurred with a junctional epithelium along the previously diseased part of the root, and new cementum with inserting collagen fibers was found in only one out of five treated teeth. Bone formation was limited in all specimens (Nevins _et al_. 2000).
#### _Evaluation of alloplastic materials_
There are no controlled clinical studies demonstrating that grafting with tricalcium phosphate or polymers results in significant clinical improvements beyond that of flap surgery, whereas several reports have indicated that grafting with hydroxyapatite or bioactive glasses may produce more gain of attachment than open-flap debridement (Galgut _et al_. 1992; Zamet _et al_. 1997; Froum _et al_. 1998) or a gain similar to that obtained following grafting with DFDBA (Lovelace _et al_. 1998). Histologic evidence that the use of alloplastic or synthetic graft materials may lead to periodontal regeneration in humans is lacking, and animal experiments have failed to demonstrate regeneration of a functional periodontium following implantation of hydroxyapatite, tricalcium phos-phate or polymers in periodontal lesions (Barney _et al_. 1986; Shahmiri _et al_. 1992). It was reported, however, that treatment with bioactive glasses in experimental animals produced significantly more bone fill and new attachment compared with that in non-grafted controls (Fetner _et al_. 1994; Karatzas _et al_. 1999) or in sites grafted with hydroxyapatite or tricalcium phosphate (Wilson & Low 1992). Although some bone formation has been reported following the use of alloplastic materials, there is no evidence that these materials may stimulate the formation of new cementum with inserting collagen fibers. At the 1996 American Academy of Periodontology World Workshop, it was concluded that synthetic graft materials function primarily as defect fillers.
## Root surface biomodification
Much research has been directed to altering the peri-odontitis-involved root surface in a manner that will promote the formation of a new connective tissue attachment. Removal of bacterial deposits, calculus, and endotoxins from the cementum is generally considered essential for the formation of a new connective attachment (Garrett 1977). However, it was suggested by Stahl _et al_. (1972) that demineralization of the root surface, exposing the collagen of the dentin, would facilitate the deposition of cementum by inducing mesenchymal cells in the adjacent tissue to differentiate into cementoblasts. The biologic concept is that exposure of collagen fibers of the dentin matrix may facilitate adhesion of the blood clot to the root surface and thereby favor migration of the fibroblasts. However, it is doubtful whether this concept is in accordance with current knowledge about periodontal wound healing since there is no evidence that the exposure of collagen fibers of the dentin matrix may facilitate repopulation of the root surface with cells derived from the periodontal ligament. As mentioned previously, periodontal ligament cells are required for the accomplishment of a new connective tissue attachment.
Several studies using various animal models demonstrated an improved healing response histologically following citric acid and tetracycline root surface demineralization (Register & Burdick 1976; Crigger _et al_. 1978; Polson & Proye 1982; Claffey _et al_. 1987). However, in a study in dogs where naturally occurring furcations were treated with citric acid, several specimens demonstrated ankylosis and root resorption (Bogle _et al_. 1981). This finding corroborates that of Magnusson _et al_. (1985) in monkeys, where citric acid conditioning was evaluated in combination with coronally displaced tissue flaps after 6 months. These investigators found root resorption on 28 out of 40 surfaces examined and 21 of these also presented ankylosis.
New connective tissue attachment following citric acid demineralization of root surfaces has been demonstrated histologically in humans (Cole _et al_. 1980; Frank _et al_. 1983; Stahl _et al_. 1983; Stahl & Froum 1991a). Cole _et al_. (1980) showed histologic evidence of a new connective tissue attachment and bone formation coronal to reference notches placed in the apical extent of calculus identified on the root surface at the time of surgery. However, despite histologic evidence of regeneration following root surface bio-modification with citric acid, results of controlled clinical trials failed to show any improvements in clinical conditions compared to controls not treated with acid (Moore _et al_. 1987; Fuentes _et al_. 1993).
In recent years, biomodification of the root surface with enamel matrix proteins (Emdogain®) during surgery and following demineralization with EDTA has been introduced to encourage periodontal regeneration. The biologic concept is that the application of enamel matrix proteins (amelogenins) may promote periodontal regeneration because it mimics events that took place during the development of the periodontal tissues (Hammarström 1997; Gestrelius _et al_. 2000). This view is based on the finding that the cells of the Hertwigs epithelial root sheath deposit enamel matrix proteins on the root surface prior to cementum formation and that these proteins are the initiating factor for the formation of cementum. The commercially available product, Emdogain®, a purified acid extract of porcine origin, contains enamel matrix derivatives (EMD), supposed to be able to promote periodontal regeneration. However, it is not quite clear how this concept is in accordance with current knowledge about periodontal wound healing since no evidence has been provided that it is cells derived from the periodontal ligament that are encouraged to repopulate the root surface after treatment. In fact, a study in dogs (Araùjo _et al_. 2003) where reimplanted roots that had been extracted and deprived of vital cementoblasts and subsequently treated with EMD failed to prevent ankylosis and root resorption, indicating that the root surfaces did not become repopulated with cells with the capacity to form cementum. A recent study in vitro has also failed to confirm that EMD has any significant effect on periodontal ligament cell proliferation (Chong _et al_. 2006).
In case series reports, 4–4.5 mm gain of clinical attachment, and about 70% bone fill in intrabony defects were reported following treatment with EMD (Heden _et al_. 1999; Heden 2000). In a multicenter clinical study involving 33 subjects with 34 paired intrabony defects, application of EMD resulted in larger amounts of PAL gain (2.2 mm) and statistically significantly more bone gain (2.6 mm) than open-flap debridement after 36 months, evaluated clinically and radiographically (Heijl _et al_. 1997). Similar results were reported in another split-mouth clinical trial (23 patients) published more recently (Froum _et al_. 2001). In that study a PPD reduction of 4.9 mm, a PAL gain of 4.3, and a bone gain of 3.8 mm (evaluated by re-entry surgery) were observed after EMD application in 53 intrabony defects. These values were statistically significantly larger than those obtained by flap surgery (2.2 mm, 2.7 mm, and 1.5 mm, respectively, in 31 defects).
In a more recent prospective multicenter randomized controlled clinical trial, the clinical outcomes of papilla preservation flap surgery (simplified papilla preservation flap, SPPF) with or without the application of enamel matrix proteins, were compared (Tonetti _et al_. 2002). A total of 83 test and 83 control patients with similar baseline periodontal conditions and defect characteristics were treated with either SPPF and Emdogain® or with SPPF alone. The test defects exhibited significantly more clinical attachment level (CAL) gain than the controls (3.1 ± 1.5 mm and 2.5 ± 1.5 mm, respectively).
When application of EMD was compared with GTR treatment, it was found that similar clinical improvements were obtained. In a randomized controlled clinical study, Pontoriero _et al_. (1999) compared EMD application with GTR with resorbable (two kinds: Guidor and Resolut) and non-resorbable (e-PTFE) membranes in intrabony defects. After 12 months, there were no significant differences among the groups, and EMD application resulted in a PPD reduction of 4.4 mm and a PAL gain of 2.9 mm, while the corresponding values from the membrane-treated sites (both GTR groups combined) were 4.5 mm and
3.1 mm, respectively. Silvestri _et al_. (2000) reported a PPD reduction of 4.8 mm and a PAL gain of 4.5 mm after EMD application in intrabony defects versus 5.9 mm and 4.8 mm, respectively, after GTR with non-resorbable membranes. Similar results were reported by other investigators (Sculean _et al_. 1999a,b; Silvestri _et al_. 2003; Sanz _et al_. 2004). There are studies indicating that following the application EMD in intrabony defects, clinical improvements can be achieved by the additional use of some bone graft materials (Zucchelli _et al_. 2003; Gurinsky _et al_. 2004; Trombelli _et al_. 2006), although others have failed to demonstrate a beneficial effect of this combined treatment (Sculean _et al_. 2005).
Histologic evidence of new cementum formation with inserting collagen fibers on a previously peri-odontitis-affected root surface and the formation of new alveolar bone in human specimens have been demonstrated following EMD treatment (Mellonig 1999; Sculean _et al_. 1999b). However, while in the study of Mellonig (1999) healing had occurred with acellular cementum on the root surface, the newly formed cementum in the study of Sculean _et al_. (1999b) displayed a predominantly cellular character. The ability of EMD to produce regeneration has been confirmed in controlled animal experiments (Fig. 25-20), following the treatment of intrabony, furcation, and dehiscence defects (Hammarström _et al_. 1997; Araújo & Lindhe 1998; Sculean _et al_. 2000). In a later study it was shown in monkeys that the combined application of EMD and autogenous bone grafts may improve periodontal regeneration in periodontal defects compared to flap surgery alone (Cochran _et al_. 2003).
**Fig. 25-20** (a) Photomicrograph of a grade III furcation defect in a dog following root surface biomodification with enamel matrix proteins and subsequently covered with a resorbable membrane. The defect has healed completely with bone (NB), a periodontal ligament (p) and new cementum (NC). The arrows indicate the apical extension of the lesion. (b) The cementum (NAC) formed on the root surface in the apical portion of the defect was acellular with inserting extrinsic collagen fibers (ECF) while (c) new cellular cementum (NCC) had formed in the coronal portion. cc = cells.
## Growth regulatory factors for periodontal regeneration
Growth factor is a general term to denote a class of polypeptide hormones that stimulate a wide variety of cellular events such as proliferation, chemotaxis, differentiation, and production of extracellular matrix proteins (Terranova & Wikesjö 1987). Proliferation and migration of periodontal ligament cells and synthesis of extracellular matrix as well as differentiation of cementoblasts and osteoblasts is a prerequisite for obtaining periodontal regeneration. Therefore, it is conceivable that growth factors may represent a potential aid in attempts to encourage regeneration of the periodontium.
The effects of various growth factors were studied _in vitro_ , and a significant regeneration potential of growth factors was also demonstrated in animal models. Lynch _et al_. (1989, 1991) examined the effect of placing a combination of platelet-derived growth factors (PDGF) and insulin-like growth factors (IGF) in naturally occurring periodontal defects in dogs. The control sites treated without growth factors healed with a long junctional epithelium and no new cementum or bone formation, while regeneration of a periodontal attachment apparatus occurred at the sites treated with growth factors. Similar results were reported by other investigators following application of a combination of PDGF and IGF in experimentally induced periodontal lesions in monkeys (Rutherford _et al_. 1992; Giannobile _et al_. 1994, 1996). One study examined the effect of PDGF and IGF in periodontal intrabony defects and grade II furcations in humans (Howell _et al_. 1997). At re-entry after 9 months, significantly increased bone fill was only observed at the furcation sites treated with growth factors. Considerable clinical improvements were also observed following a combined treatment of grade II furcations with GTR, a bone graft substitute and PDGF compared to open-flap debridement (Lekovic _et al_. 2003). It can be concluded that growth factors seem to have a positive effect on periodontal regeneration, but several important questions need to be resolved before this type of regenerative treatment can be used in humans (Graves & Cochran 1994).
Bone morphogenetic proteins (BMPs) are osteo-inductive factors that may have the potential to stimulate mesenchymal cells to differentiate into bone-forming cells (Wozney _et al_. 1988). Sigurdsson _et al_. (1995) evaluated bone and cementum formation following regenerative periodontal surgery using recombinant human BMP in surgically created supra-alveolar defects in dogs. Following application of BMP the flaps were advanced to submerge the teeth and sutured. Histologic analysis showed significantly more cementum formation and regrowth of alveolar bone on BMP-treated sites as compared to the controls. Significant amounts of bone regeneration in periodontal defects have also been reported by other investigators following application of BMPs combined with various carrier systems or space-providing devices in different animal models (Ripamonti _et al_. 1994; Selvig _et al_. 2002; Wikesjö _et al_. 2003a,b). Further experimentation is needed to evaluate a possible role of BMP in periodontal regeneration.
## Guided tissue regeneration (GTR)
The experimental studies (Karring _et al_. 1980; Nyman _et al_. 1980; Buser _et al_. 1990a,b; Warrer _et al_. 1993) described previously have documented that the progenitor cells for the formation of a new connective tissue attachment reside in the periodontal ligament. Consequently, it should be expected that a new connective tissue attachment would be predictably achieved if such cells populate the root surface during healing. This view was confirmed in a study in monkeys in which both gingival connective tissue and gingival epithelium were prevented from contacting the root surface during healing by the use of a barrier membrane (Gottlow _et al_. 1984). After reduction of the supporting tissues around selected experimental teeth, the root surfaces were exposed to plaque accumulation for 6 months. Soft tissue flaps were then raised and the exposed root surfaces were curetted. The crowns of the teeth were resected and the roots were submerged. However, prior to complete closure of the wound, a membrane was placed over the curetted root surfaces on one side of the jaws in order (1) to prevent gingival connective tissue contacting the root surface during healing, and (2) to provide a space for in-growth of periodontal ligament tissue. No membranes were placed over the contralateral roots. The histologic analysis after 3 months of healing demonstrated that the roots covered with membranes exhibited considerably more new attachment than the non-covered roots (Fig. 25-21). In four of the nine test roots, new cementum covered the entire length of the root. In all control specimens, the surface coronal to the newly formed cementum presented multinucleated cells and resorption cavities. In one control specimen virtually half the root was resorbed. Coronal regrowth of alveolar bone had occurred to a varying extent in test and control roots, and no relationship was found between the amount of new cementum formation and the degree of bone regrowth. The results of this study strongly suggested that the exclusion of epithelial and gingival connective tissue cells from the healing area by the use of a physical barrier may allow (guide) periodontal ligament cells to repopulate the detached root surface. This observation provided the basis for the clinical application of the treatment principle termed "guided tissue regeneration" (GTR). Thus. GTR treatment involves the placement of a physical barrier to ensure that the previous periodontitis-affected root surface becomes repopulated with cells from the periodontal ligament (Fig. 25-22).
Treatment of the first human tooth with GTR was reported by Nyman _et al_. (1982). Due to extensive periodontal destruction, the tooth was scheduled for extraction. This offered the possibility of obtaining histologic documentation of the result of the treatment. Following elevation of full thickness flaps, scaling of the root surface, and removal of all granulation tissue, an 11 mm deep periodontal lesion was ascertained. Prior to flap closure, a membrane was adjusted to cover parts of the detached root surfaces, the osseous defect, and parts of the surrounding bone. Histologic analysis after 3 months of healing revealed that new cementum with inserting collagen fibers had formed on the previously exposed root surface (Fig. 25-23). In a later study (Gottlow _et al_. 1986), 12 cases treated with GTR were evaluated clinically, and in five of these cases histologic documentation was also presented. The results showed that considerable but varying amounts of new connective tissue attachment had formed on the treated teeth. Frequently, however, bone formation was incomplete. The varying results were ascribed to factors such as the amount of remaining periodontal ligament, the morphology of the treated defect, technical difficulties regarding membrane placement, gingival recession, and bacterial contamination of the membrane and the wound during healing.
**Fig. 25-21** (a) Microphotograph of membrane (M) covered root. Newly formed cementum is visible on the entire length of the buccal root surface coronal to the notch (N) and also on part of the coronal cut surface (arrow). (b, c) Higher magnifications of the areas at the upper and lower triangles in (a), showing that collagen fibers are inserted into the newly formed cementum. AR = artifact.
**Fig. 25-22** Drawing illustrating the placement of the physical barrier which prevents the epithelium and gingival connective tissue from contacting the root surface during healing. At the same time the membrane allows cells from the periodontal ligament (arrow) to repopulate the previously periodontitis-involved root surface.
In the last decades, GTR has been applied in a number of clinical trials for the treatment of various periodontal defects such as intrabony defects (for review see Cortellini & Bowers 1995), furcation involvements (for review see Machtei & Schallhorn 1995; Karring & Cortellini 1999), and localized gingival recession defects (Pini-Prato _et al_. 1996). The efficiency of GTR in producing periodontal regeneration in these defects has been documented in animal studies (Gottlow _et al_. 1990; Araùjo _et al_. 1998; Laurell _et al_. 2006) and in several controlled clinical trials (see Chapter 43).
The clinical outcomes of GTR are most frequently evaluated by changes in clinical attachment levels (CAL), bone levels (BL), probing pocket depths (PPD), and the position of the gingival margin. In some of the studies on grade II and III furcations, horizontal changes in clinical attachment, bone level, and pocket depth were also measured. However, evidence of true regeneration of periodontal attachment can only be provided by histologic means.
# Assessment of periodontal regeneration
In most studies on the effect of regenerative peri-odontal surgery, the outcomes are evaluated by probing attachment level measurements, radio-graphic analysis or re-entry operations. However, such methods do not provide proof of a true gain of attachment (i.e. formation of cementum with inserting collagen fibers coronal to the attachment level before treatment).
## Periodontal probing
The inability of periodontal probing to determine accurately the coronal level of the connective tissue attachment has been demonstrated by several investigators (Listgarten _et al_. 1976; Armitage _et al_. 1977; Van der Velden & de Vries 1978). It is known from these studies that, in the inflamed periodontium, the probe does not stop precisely at the coronal level of the connective tissue attachment. Usually it penetrates 0.5 mm or more into the connective tissue, surpassing the transition between the apical extension of the dentogingival epithelium and the coronal level of connective tissue attachment. After therapy, when the inflammatory lesion is resolved, the probe tip tends to stop coronal to the apical termination of the epithelium. Following treatment of intrabony defects, new bone may form so close to the tooth surface that the probe cannot penetrate (Caton & Zander 1976). Thus, a gain of probing attachment level (PAL) following therapy does not necessarily mean that a true gain of connective tissue attachment was accomplished. More likely it is a reflection of improved health of the surrounding soft tissues which offer increased resistance to probe penetration.
**Fig. 25-23** (a) Microphotograph of a human tooth 3 months following GTR treatment using a Millipore filter (F). New cementum with inserting collagen fibers (about 5 mm) has formed from the notch (N) to the level of the arrow. Bone formation underneath the filter is lacking, probably due to the inflammatory infiltrate seen in the tissues adjacent to the filter. (b) Higher magnification of the area indicated by the arrowhead in (a) showing newly formed cementum with inserting collagen fibers. AR = artifact.
## Radiographic analysis and re-entry operations
Healing of intrabony defects following regenerative surgery is often documented by measurements made on radiographs obtained in a standardized and reproducible manner and/or assessed in conjunction with a re-entry operation. Analysis of radiographs before and after therapy and inspection of the treated area during a re-entry operation can certainly provide evidence of new bone formation. However, such "bone fill" does not prove formation of new root cementum with inserting collagen fibers (i.e. a new periodontal ligament). In fact, it was demonstrated by Caton and-Zander (1976) and Moscow _et al_. (1979) that despite the fact that bone regeneration had occurred adjacent to the root in intrabony defects, a junctional epithelium was interposed between the newly formed bone and the curetted root surface. This means that radio-graphic analysis and assessments of bone formation by re-entry operations are unreliable methods for the documentation of new attachment formation.
## Histologic methods
In several studies healing is analyzed in histologic sections of block biopsies obtained after various forms of regenerative periodontal therapy. Histologic analysis is the only valid method to assess the formation of a true new attachment, but it requires that the location of the attachment level prior to therapy can be assessed with a reasonable accuracy. In a few studies histologic reference notches were placed in the apical extent of calculus deposits, identified on the root surface at the time of surgery (Cole _et al_. 1980; Bowers _et al_. 1989b,c). Usually, however, a reference is obtained by producing a notch in the root surface at the level of the reduced bone height. Although such a notch may not reflect the exact extent of the periodontitis-involved root surface prior to treatment, it is considered an adequate landmark for the assessment of new attachment (Isidor _et al_. 1985). It was also suggested that clinical signs of probing attachment gain and bone fill can be accepted as evidence of periodontal regeneration in the evaluation of GTR procedures (Lindhe & Echeverria 1994). This suggestion was based on evidence of a new attachment apparatus in histologic specimens from human biopsies harvested following GTR treatment (Nyman _et al_. 1982; Gottlow _et al_. 1986; Becker _et al_. 1987; Stahl _et al_. 1990a; Cortellini _et al_. 1993) and on the biologic concept of GTR (Karring _et al_. 1980, 1985, 1993; Nyman _et al_. 1980; Gottlow _et al_. 1984).
### Conclusions
There is evidence that the progenitor cells for reformation of lost periodontal attachment are present in the periodontal ligament. Consequently, a periodontal regenerative procedure needs to encourage repopulation of the previous periodontitis-affected root surface with cells from the periodontal ligament.
GTR and conditioning of the root surface with enamel matrix proteins represent the best documented regenerative procedures for obtaining peri-odontal regeneration in periodontal lesions, although there is some uncertainty whether enamel matrix proteins in fact stimulate the proliferation of peri-odontal ligament cells.
Placement of bone grafts or bone substitute implants are based on a biologic concept which cannot explain how such treatment should result in regeneration of the periodontium. There are some studies indicating that bone grafting in periodontal intrabony defects may produce clinical improvements beyond that achieved with only flap surgery, but generally bone grafts or bone substitute implants are considered as primarily defect filler materials.
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# Volume 2
# CLINICAL CONCEPTS
_Edited by_
Niklaus P. Lang
Jan Lindhe
# Part 9: Examination Protocols
26 Examination of Patients with Periodontal Diseases
_Giovanni E. Salvi, Jan Lindhe, and Niklaus P. Lang_
27 Examination of the Candidate for Implant Therapy
_Hans-Peter Weber, Daniel Buser, and Urs C. Belser_
28 Radiographic Examination of the Implant Patient
_Hans-Göran Gröndahl and Kerstin Gröndahl_
29 Examination of Patients with Implant-Supported Restorations
_Urs Brägger_
30 Risk Assessment of the Implant Patient
_Gary C. Armitage and Tord Lundgren_
# Chapter 26
# Examination of Patients with Periodontal Diseases
Giovanni E. Salvi, Jan Lindhe, and Niklaus P. Lang
* * *
History of periodontal patients
Chief complaint and expectations
Social and family history
Dental history
Oral hygiene habits
Smoking history
Medical history and medications
Signs and symptoms of periodontal diseases
The gingiva
The periodontal ligament and the root cementum
The alveolar bone
Diagnosis of periodontal lesions
Oral hygiene status
Additional dental examinations
* * *
# History of periodontal patients
The history of the patient is a revealing document as a basis for comprehensive treatment planning and understanding of the patient's needs, social and economic situation, as well as general medical conditions. In order to expedite history taking, a health questionnaire may be filled out by the patient prior to the initial examination. Such a questionnaire should be constructed in a way that the professional immediately realizes compromising or risk factors that may modify the treatment plan and, hence, may have to be discussed in detail with the patient during the initial visit. The assessment of the patient's history requires an evaluation of the following six aspects: (1) chief complaint, (2) social and family history, (3) dental history, (4) oral hygiene habits, (5) smoking history, and (6) medical history and medications.
## Chief complaint and expectations
It is essential to realize the patient's needs and desires for treatment. If a patient has been referred for specific treatment, the extent of the desired treatment has to be defined and the referring dentist should be informed of the intentions for treatment.
Patients reporting independently, however, usually have specific desires and expectations regarding treatment outcomes. These may not be congruent with the true assessment of a professional with respect to the clinical situation. Optimal treatment results may only be achieved if the patient's demands are in balance with the objective evaluation of the disease and the projected treatment outcomes. Therefore, the patient's expectations have to be taken seriously and must be incorporated in the evaluation in harmony with the clinical situation.
## Social and family history
Before assessing the clinical condition in detail, it is advantageous to elucidate the patient's social environment and to get a feeling for his/her priorities in life, including the attitude to dental care. Likewise, a family history may be important, especially with respect to aggressive forms of periodontitis.
## Dental history
These aspects include an assessment of previous dental care and maintenance visits if not stated by a referring dentist. In this context, information regarding signs and symptoms of periodontitis noted by the patient, such as migration and increasing mobility of teeth, bleeding gums, food impaction, and difficulties in chewing have to be explored. Chewing comfort and the possible need for tooth replacement is determined.
## Oral hygiene habits
In addition to the exploration of the patient's routine dental care, including frequency and duration of daily tooth brushing, knowledge about interdental cleansing devices and additional chemical supportive agents, and regular use of fluorides should be assessed.
## Smoking history
Since cigarette smoking has been documented to be the second most important risk factor after inadequate plaque control (Kinane _et al_. 2006) in the etiology and pathogenesis of periodontal diseases, the importance of smoking counseling cannot be overestimated. Hence, determination of smoking status, including detailed information about exposure time and quantity, has to be gathered. Further aspects of smoking cessation programs are presented in Chapter 33.
## Medical history and medications
General medical aspects may be extracted from the health questionnaire constructed to highlight the medical risk factors encountered for routine periodontal and/or implant therapy. The four major complexes of complications encountered in patients may be prevented by checking the medical history with respect to: (1) cardiovascular and circulatory risks, (2) bleeding disorders, (2) infective risks, and (4) allergic reactions. Further aspects are presented in Chapters 30 and 33.
In light of the increasing consumption of medications in the aging population, an accurate assessment of the patient's prescribed medications and their potential interactions and effects on therapeutic procedures has to be made. It may be necessary to contact the patient's physician for detailed information relevant to the planned dental treatment.
# Signs and symptoms of periodontal diseases
Periodontal diseases are characterized by color and texture alterations of the gingiva, e.g. redness and swelling, as well as an increased tendency to bleeding upon probing in the gingival sulcus/pocket area (Fig. 26-1). In addition, the periodontal tissues may exhibit reduced resistance to probing perceived as increased probing depth and/or tissue recession. Advanced stages of periodontitis may also be associated with increased tooth mobility as well as drifting or flaring of teeth (Fig. 26-2).
In radiographs, periodontitis may be recognized by moderate to advanced loss of alveolar bone (Fig. 26-3). Bone loss is defined either as "horizontal" or "angular". If bone loss has progressed at similar rates in the dentition, the crestal contour of the remaining bone in the radiograph is even and defined as being "horizontal". In contrast, angular bony defects are the result of bone loss that developed at different rates around teeth/tooth surfaces and, hence, that type is defined as being "vertical" or "angular".
In a histological section, periodontitis is characterized by the presence of an inflammatory cell infiltrate within a 1–2 mm wide zone of the gingival connective tissue adjacent to the biofilm on the tooth (Fig. 26-4). Within the infiltrated area there is a pronounced loss of collagen. In more advanced forms of periodontitis, marked loss of connective tissue attachment to the root and apical downgrowth of the dentogingival epithelium along the root are important characteristics.
Results from clinical and animal research have demonstrated that chronic and aggressive forms of periodontal disease:
1. Affect individuals with various susceptibility at different rates (Löe _et al_. 1986)
2. Affect different parts of the dentition to a varying degree (Papapanou _et al_. 1988)
3. Are site specific in nature for a given area (Socransky _et al_. 1984)
4. Are sometimes progressive in character and, if left untreated, may result in tooth loss (Löe _et al_. 1986)
5. Can be arrested following proper therapy (Rosling _et al_. 2001).
For effective treatment planning, the location, topography, and extent of periodontal lesions must be recognized in all parts of the dentition. It is, therefore, mandatory to examine all sites of all teeth for the presence or absence of periodontal lesions. This, in turn, means that single-rooted teeth will have to be examined at least at four sites (e.g. mesial, buccal, distal, and oral) and multi-rooted teeth at least at six sites (e.g. mesio-buccal, buccal, disto-buccal, distooral, oral, and mesio-oral) with special attention to the furcation areas.
Since periodontitis includes inflammatory al terations of the gingiva and a progressive loss of periodontal attachment and alveolar bone, the comprehensive examination must include assessments describing such pathologic alterations. Figure 26-1 illustrates the clinical status of a 59-year-old patient diagnosed with advanced generalized chronic periodontitis. The examination procedures used to assess the location and extension of periodontal disease will be demonstrated by using this case as an example.
## The gingiva
Clinical signs of gingivitis include changes in color and texture of the soft marginal gingival tissue and bleeding on probing.
Various index systems have been developed to describe gingivitis in epidemiologic and clinical research. They are discussed in Chapter 7. Even though the composition of the inflammatory infiltrate can only be identified in histologic sections, the correct clinical diagnosis for inflamed gingival tissue is made on the basis of the tendency to bleed on probing. The symptom "bleeding on probing" (BoP) to the bottom of the gingival sulcus/pocket is associated with the presence of an inflammatory cell infiltrate. The occurrence of such bleeding, especially in repeated examinations, is indicative for disease progression (Lang _et al_. 1986), although the predictive value of this single parameter remains rather low (i.e. 30%). On the other hand, the absence of bleeding on probing yields a high negative predictive value (i.e. 98.5%) and, hence, is an important indicator of periodontal stability (Lang _et al_. 1990; Joss _et al_. 1994). Since trauma to the tissues provoked by probing should be avoided to assess the true vascular permeability changes associated with inflammation, a probing pressure of 0.25 N should be applied for assessing "bleeding on probing" (Lang _et al_. 1991; Karayiannis _et al_. 1992). The identification of the apical extent of the gingival lesion is made in conjunction with pocket probing depth (PPD) measurements _._ In sites where "shallow" pockets are present, inflammatory lesions in the overt portion of the gingiva are distinguished by probing in the superficial marginal tissue. When the infiltrate is in sites with attachment loss, the inflammatory lesion in the apical part of the pocket must be identified by probing to the bottom of the deepened pocket.
**Fig. 26-1** (a–g) Buccal–labial and palatal–lingual views of a 59-year-old male patient diagnosed with advanced generalized chronic periodontitis with furcation involvement.
**Fig. 26-2** Buccal migration of tooth 13 as a sign of advanced periodontitis.
**Fig. 26-3** Periapical radiographs of the patient presented in Fig. 26-1.
**Fig. 26-4** Schematic drawing (a) and histologic section (b) illustrating the characteristics of periodontal disease. Note the zone of infiltrated connective tissue (ICT) lateral to the junctional epithelium (JE). CEJ = cemento-enamel junction; JE = junctional epithelium.
## Bleeding on probing (BoP)
A periodontal probe is inserted to the "bottom" of the gingival/periodontal pocket applying light force and is moved gently along the tooth (root) surface ( **Fig. 26-5** ). If bleeding is provoked by this instrumentation upon retrieval of the probe, the site examined is considered "bleeding on probing" (BoP) -positive and, hence, inflamed.
**Figure 26-6** illustrates the chart used to identify BoP-positive sites in a dichotomous way at the initial examination. Each tooth in the chart is represented and each tooth surface is indicated by a triangle. The inner segments represent the palatal/lingual gingival units, the outer segments the buccal/labial units and the remaining fields the two approximal gingival units. The fields of the chart corresponding to the inflamed gingival units are marked in red. The mean BoP score (i.e. gingivitis) is given as a percentage. In the present example, 104 out of a total number of 116 gingival units bled on probing, amounting to a BoP percentage of 89%. This method of charting not only serves as a means of documenting areas of health and disease in the dentition but similar charting during the course of therapy or maintenance will disclose sites which become healthy or remain inflamed. The topographical pattern will also identify sites with consistent or repeated BoP at various observation periods.
## The periodontal ligament and the root cementum
In order to evaluate the amount of tissue lost in periodontitis and also to identify the apical extension of the inflammatory lesion, the following parameters should be recorded:
1. Probing pocket depth (PPD)
2. Probing attachment level (PAL)
3. Furcation involvement (FI)
4. Tooth mobility (TM).
## Assessment of probing pocket depth
The probing depth, i.e. the distance from the gingival margin to the bottom of the gingival sulcus/pocket, is measured to the nearest millimeter by means of a graduated periodontal probe with a standardized tip diameter of approximately 0.4–0.5 mm (Fig. 26-7). The pocket depth should be assessed at each surface of all teeth in the dentition. In the periodontal chart (Fig. 26-8), PPD <4 mm are indicated in black figures, while deeper PPD (i.e. ≥4 mm) are marked in red. This allows an immediate evaluation of diseased sites (i.e. red figures) both from an extent and severity point of view. The chart may be used for case presentation and discussion with the patient.
**Fig. 26-5** Probing pocket depth (PPD) in conjunction with bleeding on probing (BoP). A graduated periodontal probe is inserted to the "bottom" of the gingival/periodontal pocket applying light force and is moved gently along the tooth (root) surface.
Results from pocket depth measurements will only give proper information regarding the extent of loss of probing attachment in rare situations (when the gingival margin coincides with the cementoenamel junction, CEJ). For example, an inflammatory edema may cause swelling of the free gingiva resulting in coronal displacement of the gingival margin without a concomitant migration of the dentogingival epithelium to a level apical to the CEJ. In such a situation, a pocket depth exceeding 3–4 mm represents a "pseudopocket". In other situations, an obvious loss of periodontal attachment may have occurred without a concomitant increase of probing pocket depth. A situation of this kind is illustrated in Fig. 26-9, where multiple recessions of the gingiva can be seen. Hence, the assessment of the probing depth in relation to the CEJ is an indispensable parameter for the evaluation of the periodontal condition (i.e. PAL).
## Assessment of probing attachment level
PAL may be assessed to the nearest millimeter by means of a graduated probe and expressed as the distance in millimeters from the CEJ to the bottom of the probeable gingival/periodontal pocket. The clinical assessment requires the measurement of the distance from the free gingival margin (FGM) to the CEJ for each tooth surface. After this recording, PAL may be calculated from the periodontal chart (i.e. PPD – distance CEJ to FGM). In cases with gingival recession, the distance FGM–CEJ turns negative and, hence, will be added to the PPD to determine PAL.
## Errors inherent in periodontal probing
The distances recorded in a periodontal examination using a periodontal probe have generally been assumed to represent a fairly accurate estimate of the PPD or PAL at a given site. In other words, the tip of the periodontal probe has been assumed to identify the level of the most apical cells of the dentogingival (junctional epithelium) epithelium. Results from research, however, indicated that this is seldom the case (Saglie _et al_. 1975; Listgarten _et al_. 1976; Armitage _et al_. 1977; Ezis & Burgett 1978; Spray _et al_. 1978; Robinson & Vitek 1979; van der Velden 1979; Magnusson & Listgarten 1980; Polson _et al_. 1980). A variety of factors influencing measurements made with periodontal probes include: (1) the thickness of the probe used, (2) angulation and positioning of the probe due to anatomic features such as the contour of the tooth surface, (3) the graduation scale of the periodontal probe, (4) the pressure applied on the instrument during probing, and (5) the degree of inflammatory cell infiltration in the soft tissue and accompanying loss of collagen. Therefore, a distinction should be made between the histologic and the clinical PPD to differentiate between the depth of the actual anatomic defect and the measurement recorded by the probe (Listgarten 1980).
**Fig. 26-6** Chart used to identify BoP-positive sites in a dichotomous way at the initial examination and during maintenance care.
**Fig. 26-7** Examples of graduated periodontal probes with a standardized tip diameter of approximately 0.4–0.5 mm.
**Fig. 26-8** Periodontal chart indicating PPD <4 mm in black figures and PPD ≥4 mm in red figures. This allows an immediate evaluation of diseased sites (i.e. red figures) both from an extent and severity point of view.
**Fig. 26-9** Periodontal attachment loss has occurred without a concomitant increase of probing pocket depth. Multiple buccal/labial as well as palatal/lingual gingival recessions can be seen.
Measurement errors depending on factors such as the thickness of the probe, the contour of the tooth surface, incorrect angulation, and the graduation scale of the probe can be reduced or avoided by the selection of a standardized instrument and careful management of the examination procedure. More difficult to avoid, however, are errors resulting from variations in probing force and the extent of inflammatory alterations of the periodontal tissues. As a rule, the greater the probing pressure applied, the deeper the penetration of the probe into the tissue. In this context, it should be realized that in investigations designed to disclose the pressure (force) used by different clinicians, the probing pressure was found to range from 0.03–1.3 N (Gabathuler & Hassell 1971; Hassell _et al_. 1973), and also, to differ by as much as 2:1 for the same dentist from one examination to another. In order to exclude measurement errors related to the effect of variations in probing pressure, so-called pressure-sensitive probes have been developed. Such probes will enable the examiner to probe with a predetermined pressure (van der Velden & de Vries 1978; Vitek _et al_. 1979; Polson _et al_. 1980). However, over- and underestimation of the "true" PPD or PAL may also occur when this type of probing device is employed (Armitage _et al_. 1977; Robinson & Vitek 1979; Polson _et al_. 1980). Thus, when the connective tissue subjacent to the pocket epithelium is infiltrated by inflammatory cells (Fig. 26-10), the periodontal probe will most certainly penetrate beyond the apical termination of the dentogingival epithelium. This results in an overestimation of the "true" depth of the pocket. Conversely, when the inflammatory infiltrate decreases in size following successful periodontal treatment, and a concomitant deposition of new collagen occurs within the previously inflamed tissue area, the dentogingival tissue will become more resistant to penetration by the probe. The probe may now fail to reach the apical termination of the epithelium using the same probing pressure. This, in turn, results in an underestimation of the "true" PPD or PAL. The magnitude of the difference between the probing measurement and the histologic "true" pocket depth (Fig. 26-10) may range from fractions of a millimeter to a couple of millimeters (Listgarten 1980).
**Fig. 26-10** (a) In the presence of an inflammatory cell infiltrate (ICT) in the connective tissue of the gingiva, the periodontal probe penetrates apically to the bottom of the histologic pocket. (b) Following successful periodontal therapy, the swelling is reduced and the connective tissue cell infiltrate is replaced by collagen. The periodontal probe fails to reach the apical part of the dentogingival epithelium. CEJ = cemento-enamel junction; PPD = probing pocket depth; PAL = probing attachment level; R = recession; Gain PAL = recorded false gain of attachment ("clinical attachment").
From this discussion it should be understood that reductions in PPD following periodontal treatment and/or gain of PAL, assessed by periodontal probing, do not necessarily indicate the formation of a new connective tissue attachment at the bottom of the previous lesion. Rather, such a change may merely represent a resolution of the inflammatory process and may thus occur without an accompanying histologic gain of attachment (Fig. 26-10). In this context it should be realized that the terms "probing pocket depth" (PPD) and "probing attachment level" (PAL) have replaced the previously used terms "pocket depth" and "gain and loss of attachment". Likewise, PAL is used in conjunction with "gain" and/or "loss" to indicate that changes in PAL have been assessed by clinical probing.
Current knowledge of the histopathology of periodontal lesions and healing thereof has thus resulted in an altered concept regarding the validity of periodontal probing. However, despite difficulties in interpreting the significance of PPD and PAL measurements, such determinations still give the clinician a useful estimate of the degree of disease involvement, and particularly so, when the information obtained is related to other findings of the examination procedure such as BoP and changes in alveolar bone height.
In recent years, periodontal probing procedures have been standardized to the extent that automated probing systems such as, e.g. the Florida ProbeTM, have been developed, yielding periodontal charts with PPD, PAL, BoP, furcation involvement (FI) and tooth mobility (TM) at one glance (Gibbs _et al_. 1988). Also, repeated examinations allow the comparison of parameters, and, hence, an assessment of the healing process (Fig. 26-11).
## Assessment of furcation involvement
In the progression of periodontitis around multi-rooted teeth, the destructive process may involve the supporting structures of the furcation area (Fig. 26-12). In order to plan treatment for such involvement, a detailed and precise identification of the presence and extension of periodontal tissue breakdown within the furcation area is of importance for proper diagnosis.
**Fig. 26-11** Periodontal chart using an automated probing system (Florida ProbeTM). Reproduced with permission, © Copyright 1996–2005 Florida Probe Corporation.
Furcation involvement is assessed from all the entrances of possible periodontal lesions of multi-rooted teeth, i.e. buccal and/or lingual entrances of the mandibular molars. Maxillary molars and premolars are examined from the buccal, disto-palatal, and mesio-palatal entrances. Owing to the position of the first maxillary molars within the alveolar process, the furcation between the mesio-buccal and the palatal roots is best explored from the palatal aspect (Fig. 26-13).
**Fig. 26-12** Superficial (tooth 46) and deep (tooth 16) periodontal tissue destruction in the buccal furcation areas.
**Fig. 26-13** (a,b) Anatomic locations for the assessment of furcation involvement (FI) in the maxilla and in the mandible.
**Fig. 26-14** (a,b) Furcation involvement (FI) is explored using a curved periodontal probe graduated at 3 mm (Nabers furcation probe).
**Fig. 26-15** The FI degree is illustrated in the periodontal chart. Open circles represent a superficial FI (i.e horizontal probe penetration ≤3 mm) whereas filled black circles represent a deep FI (i.e. horizontal probe penetration >3 mm).
Furcation involvement is explored using a curved periodontal probe graduated at 3 mm (Nabers furcation probe) (Fig. 26-14). Depending on the penetration depth, the FI is classified as "superficial" or "deep":
* Horizontal probing depth ≤3 mm from one or two entrances is classified as a degree I FI.
* Horizontal probing depth >3 mm in at the most one furcation entrance and/or in combination with a degree I FI is classified as degree II FI.
* Horizontal probing depth >3 mm in two or more furcation entrances usually represents a "through-and-through" destruction of the supporting tissues in the furcation and is classified as degree III FI.
The FI degree is presented in the periodontal chart (Fig. 26-15) together with a description of which tooth surface the involvement has been identified on. A detailed discussion regarding the management of furcation-involved teeth is presented in Chapter 39.
## Assessment of tooth mobility
The continuous loss of the supporting tissues during periodontal disease progression may result in increased tooth mobility. However, trauma from occlusion may also lead to increased tooth mobility. Therefore, the reason for increased tooth mobility as being the result of a widened periodontal ligament or a reduced height of the supporting tissues or a combination thereof should be elaborated. Increased tooth mobility may be classified according to Miller (1950).
* Degree 0: "physiological" mobility measured at the crown level. The tooth is mobile within the alveolus to approximately 0.1–0.2 mm in a horizontal direction.
* Degree 1: increased mobility of the crown of the tooth to at the most 1 mm in a horizontal direction.
* Degree 2: visually increased mobility of the crown of the tooth exceeding 1 mm in a horizontal direction.
* Degree 3: severe mobility of the crown of the tooth both in horizontal and vertical directions impinging on the function of the tooth.
It must be understood that plaque-associated periodontal disease is not the only cause of increased tooth mobility. For instance, overloading of teeth and trauma may result in tooth hypermobility. Increased tooth mobility can frequently also be observed in conjunction with periapical lesions or immediately following periodontal surgery. From a therapeutic point of view it is important, therefore, to assess not only the degree of increased tooth mobility but also the cause of the observed hypermobility (see Chapters 14 and 57).
All data collected in conjunction with measurements of PPD, PAL, as well as from the assessments of FI and tooth mobility are included in the periodontal chart (Fig. 26-8). The various teeth in this chart are denoted according to the two-digit system adopted by the FDI in 1970.
## The alveolar bone
The height of the alveolar bone and the outline of the bony crest are examined in radiographs (Fig. 26-3). Radiographs provide information on the height and configuration of the interproximal alveolar bone. Obscuring structures such as roots of the teeth often make it difficult to identify the outline of the buccal and lingual alveolar bony crest. Analysis of radiographs must, therefore, be combined with a detailed evaluation of the periodontal chart in order to come up with a correct estimate concerning "horizontal" and "angular" bony defects.
**Fig. 26-16** The use of a Rinn filmholder and a long-cone paralleling technique yield reproducible radiographs.
As opposed to the periodontal chart that represents a sensitive diagnostic estimate of the lesions, the radiographic analysis is a specific diagnostic test yielding few false-negative results and, hence, is confirmatory to the periodontal chart (Lang & Hill 1977).
To enable meaningful comparative analysis, a radiographic technique should be used which yields reproducible radiographs. In this context, a long-cone paralleling technique (Updegrave 1951) is recommended (Fig. 26-16).
# Diagnosis of periodontal lesions
Based on the information regarding the condition of the various periodontal structures (i.e. the gingiva, the periodontal ligament, and the alveolar bone) which has been obtained through the comprehensive examination presented above, a classification of the patient as well as a diagnosis for each tooth regarding the periodontal conditions may be given (Table 26-1). Four different tooth-based diagnoses may be used:
* _Gingivitis_. This diagnosis is applied to teeth displaying bleeding on probing. The sulcus depth usually remains at levels of 1–3 mm irrespective of the level of clinical attachment. "Pseudopockets" may be present in cases of slightly increased probing depth without concomitant attachment and alveolar bone loss and presence/absence of bleeding on probing. The diagnosis of gingivitis usually characterizes lesions confined to the gingival margin.
* _Parodontitis superficialis_ (mild–moderate periodontitis). Gingivitis in combination with attachment loss is termed "periodontitis". If the PPD does not exceed 6 mm, a diagnosis of mild–moderate periodontitis is given irrespective of the morphology of periodontal lesions. This diagnosis may, therefore, be applied to teeth with "horizontal" loss of supporting tissues, representing suprabony lesions, and/or to teeth with "angular" or "vertical" loss of supporting tissues, representing infrabony lesions. "Infrabony" lesions include "intrabony one-, two- and three-wall defects" as well as "craters" between two adjacent teeth.
* _Parodontitis profunda_ (advanced periodontitis). If the PPD does exceeds 6 mm, a diagnosis of advanced periodontitis is given irrespective of the morphology of periodontal lesions. As for mild–moderate periodontitis, angular as well as horizontal alveolar bone loss are included in this diagnosis. The distinction between mild–moderate and advanced periodontitis is only based on increased PPD.
* _Parodontitis interradicularis_ (periodontitis in the furcation area). Adjunctive diagnoses may be attributed to multi-rooted teeth with FI (see above) : superficial FI if horizontal PPD ≤3 mm (parodontitis interradicularis superficialis) and deep FI for horizontal PPD >3 mm (parodontitis interradicularis profunda).
**Fig. 26-17** Chart of the individual tooth diagnosis of the patient presented in Fig. 26-1.
**Table 26-1** The diagnosis of the periodontal tissue conditions around each tooth in the dentition is given using main criteria (i.e. periodontal chart and radiographic analysis) and additional criteria (i.e. bleeding on probing)
In the presence of necrotizing and/or ulcerative lesions, these terms may be added to tooth-related diagnoses of both gingivitis and periodontitis (Chapter 20). Acute lesions including gingival and periodontal abscesses are diagnosed as indicated in Chapter 22.
The various teeth of the patient whose clinical status is shown in Fig. 26-1, the radiographs in Fig. 26-3 and the periodontal chart in Fig. 26-8 have received the diagnoses described in Fig. 26-17.
# Oral hygiene status
In conjunction with the examination of the periodontal tissues, the patient's oral hygiene practices must also be evaluated. Absence or presence of plaque on each tooth surface in the dentition is recorded in a dichotomous manner (O'Leary _et al_. 1972). The bacterial deposits may be stained with a disclosing solution to facilitate their detection. The presence of plaque is marked in appropriate fields in the plaque chart shown in Fig. 26-18. The mean plaque score for the dentition is given as a percentage in correspondence with the system used for BoP (Fig. 26-6).
Alterations with respect to the presence of plaque and gingival inflammation are illustrated in a simple way by the repeated use of the combined BoP (Fig. 26-6) and plaque (Fig. 26-18) charts during the course of treatment. Repeated plaque recordings alone (Fig. 26-18) are predominantly indicated during the initial phase of periodontal therapy (i.e. infection control) and are used for improving self-performed plaque control. Repeated BoP charts alone (Fig. 26-6), on the other hand, are predominantly recommended during maintenance care.
**Fig. 26-18** The presence of bacterial deposits is marked in the appropriate fields in the plaque chart.
# Additional dental examinations
In addition to the assessment of plaque, retentive factors for plaque, such as supra- and subgingival calculus and defective margins of dental restorations, should also be identified. Furthermore, the assessment of tooth sensitivity is essential for comprehensive treatment planning. Sensitivity to percussion may indicate acute changes in pulp vitality and lead to emergency treatment prior to systematic periodontal therapy. It is obvious that a complete examination and assessment of the patient will have to include the search for carious lesions both clinically as well as radiographically.
Screening for functional disturbances may be performed using a short (i.e. 1/2 minute) test according to Shore (1963). In this test, harmonious function of the jaws with simultaneous palpation of the temporomandibular joints during opening, closing, and excursive movements is verified. Maximal mouth opening is assessed and finally, the lodge of the lateral pterygoid muscles is palpated for muscle tenderness. Further morphologic characteristics of the dentition as well as occlusal and articulating contacts may be identified.
### Conclusion
The methods described above for the examination of patients with respect to periodontal disease provide a thorough analysis of the presence, extent and severity of the disease in the dentition. The classification of the patient and the correct diagnosis for each individual tooth should form the basis for a pretherapeutic prognosis and the treatment planning of the individual patient (see Chapter 31).
References
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# Chapter 27
# Examination of the Candidate for Implant Therapy
Hans-Peter Weber, Daniel Buser, and Urs C. Belser
* * *
Dental implants in periodontally compromised patients
Patient history
Chief complaint and expectations
Social and family history
Dental history
Motivation and compliance
Habits
Medical history and medications
Local examination
Extraoral
General intraoral examination
Radiographic examination
Implant-specific intraoral examination
Patient-specific risk assessment
Risk assessment for sites without esthetic implications
Risk assessment for sites with esthetic implications
* * *
# Dental implants in periodontally compromised patients
Modern comprehensive dental care for patients with periodontally compromised dentitions has to include the consideration of dental implants. Since the initial description of osseointegration experimentally (Branemark _et al_. 1969; Schroeder _et al_. 1976, 1981), scientific evidence has been established through human clinical studies that dental implants will serve as long-term predictable anchors for fixed and removable prostheses in fully and partially edentulous patients and that patient satisfaction with dental implant therapy is high (Adell _et al_. 1990; Fritz 1996; Buser _et al_. 1997; Lindh _et al_. 1998; Moy _et al_. 2005; Pjetursson _et al_. 2005). Furthermore, substantial scientific and clinical evidence has become available to help the understanding of factors enhancing or compromising treatment success with regard to esthetic concerns (Belser _et al_. 2004a,b; Buser _et al_. 2004, 2006; Higginbottom _et al_. 2004; Martin _et al_. 2006). Overall, the pool of information on contributing factors enhancing or compromising treatment success with dental implants continues to grow and is becoming more and more valuable despite its diversity and scientific inconsistency. This is possible through a focused interpretation of the published information via systematic reviews.
The decision whether to use remaining natural teeth as abutments for conventional fixed prostheses or to add dental implants for the replacement of diseased natural teeth is influenced by a number of factors, such as location in the dental arches, strategic value and treatment prognosis for such teeth, subjective and objective need for tooth replacement, dimensions of the alveolar process, esthetic impact, as well as access for treatment. Indications for dental implants in the periodontally compromised dentition include the replacement of single or multiple "hopeless" or missing teeth within or as distal extensions to partially dentate maxillary and mandibular arches (Fig. 27-1).
In the edentulous jaw, implants supporting fixed or removable prostheses will more frequently be inserted in the anterior regions where there are more favorable alveolar bone dimensions and quality. In partially edentulous patients, implants are more likely indicated in posterior regions with less favorable anatomic conditions. The volume of the alveolar process may be substantially reduced, especially in dentitions where teeth have been lost due to periodontal disease (Fig. 27-2). This introduces a number of concerns related to the longevity of implant anchorage, function, and esthetics.
In the posterior areas of the jaw, such concerns may primarily be of biomechanical nature due to the resulting unfavorable "crown–root ratios" in the region of the greatest masticatory forces. Treatment alternatives include the use of multiple short implants splinted together with the fixed partial denture they support (Fig. 27-3), external or internal sinus floor elevation (Fig. 27-4), vertical ridge augmentation with various bone grafting techniques or distraction osteogenesis, nerve repositioning, distal extension fixed prostheses anchored on remaining natural teeth or premolar occlusion without replacement of the failed molars (shortened dental arch concept) (Fig. 27-5).
**Fig. 27-1** (a) Intraoral image of a 77-year-old female patient with multiple dental problems including severe adult periodontitis after several years of neglect. At the initial examination on 12/6/06, the patient states that she does not want removable prostheses and asks for dental implants to replace the teeth, which may require extraction. (b) Full-mouth set of periapical radiographs of the same patient.
Prior to the availability of dental implants and bone augmentation techniques for the replacement of posterior teeth lost to periodontal disease, cantilevered fixed partial dentures were a widely used alternative to extend dental arches distally where indicated and to spare the patient from removable partial dentures (Nyman and Lindhe 1976). Whereas this type of periodontal prosthesis performed admirably when designed and maintained properly (Fig. 27-5), the biological and biomechanical risks associated with such reconstructions have been shown to be considerable (Hammerle _et al_. 2000; Pjetursson _et al_. 2004). In the patient with advanced _generalized_ periodontal disease and a lack of sufficient posterior bone volume for dental implants, the extraction of the remaining compromised anterior dentition for the purpose of placing implants in combination with cantilevered full-arch prostheses as originally described by Brånemark _et al_. (1985) may prognostically be the most favorable treatment approach (Adell _et al_. 1990).
**Fig. 27-2** Typical example of patient with reduced alveolar bone volume in the posterior areas of the upper right and lower left quadrant due to preceding severe periodontal bone loss. The lower left quadrant reveals a failed _alio loco_ attempt for implant restoration of the lower left quadrant. According to the patient, one of the two short implants originally placed failed shortly after delivery of the fixed partial denture.
This generally supportive evidence for implant therapy has to be weighed against the long-term performance of dental implants in patients with a history of periodontal disease. This issue has recently received increased attention in the peer-reviewed dental literature (Ellegaard _et al_. 1997; Baelum & Ellegaard 2004). Whereas after 5 years of function no difference was observed between implants in patients free of periodontal disease versus those with disease, a somewhat increased risk for peri-implantitis with bone loss and subsequent implant failure was found for certain implants after 10 years of follow-up. Despite this finding, the authors concluded that dental implants remain a good treatment alternative for patients with periodontal disease. In this context, the outcome with implants placed in sinus grafts in periodontitis patients was not different from subjects free of periodontal disease (Ellegaard _et al_. 2006).
**Fig. 27-3** (a) Intraoral clinical image of the same patient after prosthodontic reconstruction of the lower left quadrant with three short implants and a three-unit fixed partial denture. Note the resulting extensive crown heights. (b) Panoramic radiographic image of the implant restoration in the lower left quadrant using three 6 mm long implants. Five-year follow-up. The patient decided to wait with any prosthodontic treatment of the upper right quadrant, where a vertical ridge augmentation combined with external sinus elevation is required.
**Fig. 27-4** (a) Reduced alveolar bone height in area of second premolar and first molar in the upper right quadrant. Teeth lost due to endodontic complications and periodontal disease combined. (b) Area restored with implant-supported, splinted restorations after internal sinus augmentation procedure at time of implant placement. Four-year follow-up.
A potential correlation of interleukin-1 (IL-1) gene polymorphism and susceptibility to severe periodontal disease has been reported by Kornman _et al_. (1997). Furthermore, the risk associated with IL-1 polymorphism, smoking and peri-implant bone loss was assessed in a study by Feloutzis _et al_. (2003). The results suggested that in heavy cigarette smokers, the presence of a functionally significant IL-1 gene complex polymorphism is associated with an increased risk for peri-implant bone loss following prosthetic reconstruction and during the supportive periodontal care phase of the treatment. More recently, Laine _et al_. (2006) found that IL-1 gene polymorphism is associated with peri-implantitis (odds ratio = 2.6!). The authors conclude that this has to be considered a long-term risk factor for implant therapy.
**Fig. 27-5** Radiographic documentation of periodontal prostheses with distal cantilevers in all four quadrants as used prior to the availability of dental implants. The patient tolerated the shortened dental arches without difficulty.
In the anterior region, the loss of periodontal hard and soft tissues and the subsequent 'lengthening' of teeth brings along esthetic concerns, which can become complex, especially in patients with high expectations and smile lines as will be discussed later in this chapter. It is important to envision such problems and analyze local conditions carefully at the time of examination so that expected outcomes can be appropriately discussed with the patient prior to the initiation of therapy.
# Patient history
Implant therapy is part of a comprehensive treatment plan. This is especially true for patients with a history of periodontal disease and tooth loss. An understanding of the patient's needs, social and economic background, general medical condition, etc., is a pre-requisite for successful therapy. In order to expedite history taking, the patient should fill out a health questionnaire prior to the initial examination visit. As discussed in Chapter 26, such questionnaires are best constructed in a way that the professional immediately realizes compromising factors that may modify the treatment plan and may have to be discussed in detail with the patient during the initial visit or may require medical consultations to enable proper treatment planning. The assessment of the patient's history should include (1) chief complaint and expectations, (2) social and family history, (3) dental history, (4) motivation and compliance (e.g. oral hygiene), (5) habits (smoking, recreational drugs, bruxism), and (6) medical history and medications.
## Chief complaint and expectations
To facilitate a successful treatment outcome, it is of critical importance to recognize and understand the patient's needs and desires for treatment. Patients usually have specific desires and expectations regarding treatment procedures and results. These may not be in tune with the attainable outcome projected by the clinician after assessment of the specific clinical situation. Optimal individual treatment results may only be achieved if the patient's demands are in balance with the objective evaluation of the condition and the projected treatment outcomes. Therefore, the patient's expectations have to be taken seriously and must be incorporated in the evaluation. A clear understanding of the patient's views is essential, especially in regard to dentofacial esthetics. Esthetic compromises need to be made often when implant restorations are performed in the periodontally compromised dentition because of the loss of hard and soft tissues. If a patient has been referred for specific treatment, the extent of the desired treatment has to be defined and the referring dentist informed of the intentions for treatment and the expectations regarding outcomes.
## Social and family history
Before assessing the clinical condition in detail, it is helpful to interview the patient on her/his professional and social environment and on his/her priorities in life, especially when extensive, time-consuming, and costly dental treatment is envisioned as it is often the case with dental implant treatment. Likewise, a family history may reveal important clues with respect to time and cause of tooth loss, systemic or local diseases such as aggressive forms of periodontitis or other genetic predispositions, habits, compliance, and other behavioral aspects.
## Dental history
It is important that previous dental care, including prophylaxis and maintenance, is explored with the patient if not stated by a referring dentist. As described in Chapter 26, information regarding cause of tooth loss, signs and symptoms of periodontitis noted by the patient such as migration and increasing mobility of teeth, bleeding gums, food impaction, and difficulties in chewing have to be explored in this context. Patient comfort with regard to function and esthetics and the subjective need for tooth replacement is assessed at this time.
## Motivation and compliance
In this part of the communication, an assessment is made of the patient's interest and motivation for extended and costly therapy. The patient's view on oral health, her/his last visit to a dentist and/or hygienist, frequency and regularity of visits to the dentist, and detailed information on home care procedures are helpful pieces of information in this regard.
## Habits
Cigarette smoking has been shown to be a risk factor for implant failure (Bain & Moy 1993; Chuang _et al_. 2002; McDermott _et al_. 2003). In the patient with (severe) periodontal disease, smoking has to be of even greater concern when combined with IL-1 gene polymorphism as discussed earlier in this chapter (Feloutzis _et al_. 2003; Laine _et al_. 2006). The patient's smoking status including details on exposure time and quantity should be assessed as part of a comprehensive examination of the implant candidate. Furthermore, testing for IL-1 gene polymorphism is strongly recommended. In this context, the importance of smoking counseling cannot be overestimated. Further aspects of smoking cessation programs are presented in Chapter 33.
Whereas the scientific evidence for a correlation of bruxism and implant failure is lacking, prosthetic complications, such as fractures of the veneering material, appear to be more frequent. Reports in the literature support the value of including precautionary measures in the implant treatment plan such as the use of implants of sufficient length and diameter, splinting of multiple implants, and use of retrievable restorations and occlusal guards. Whereas early recognition of bruxism or clenching is beneficial for appropriate treatment planning (Lobbezoo _et al_. 2006), it often cannot be diagnosed at the outset of treatment.
## Medical history and medications
A thorough review of the patient's medical history is important. Certain medical conditions may contra indicate dental implant therapy. Any condition which has the potential to negatively affect wound healing has to be considered at least a conditional contra indication. This includes chemotherapy and radiation therapy for the treatment of cancers, bisphosphonate therapy, antimetabolic therapy for the treatment of arthritis, uncontrolled diabetes, seriously impaired cardiovascular function, bleeding disorders including medication-induced anticoagulation, active drug addiction including alcohol, and heavy smoking. Patients with psychiatric conditions may not be good candidates for implant therapy. Such conditions are often difficult to identify at time of initial examination. If identified, these patients should be thoroughly examined by medical specialists before they are accepted for implant treatment (Hollender _et al_. 2003).
In light of the increasing need for medications in the aging population, an accurate assessment has to be made of the patient's prescribed and over-the-counter medications with their potential interactions and effects on therapeutic procedures. Most frequent in this context are anticoagulants, such as coumadin and aspirin. Also the need for antibiotic prophylaxis for dental surgical procedures should be recognized. Recently, the occurrence of ostoenecrosis of the jaw in patients on current long-term bisphosphonate therapy or a history thereof has been described. The occurrence of osteonecrosis has primarily been observed after oral surgical procedures in patients on long-term intravenous bisphosphonate therapy as used in the treatment of cancers, but has also been observed in patients taking oral drugs of this kind (Marx _et al_. 2005). According to the American Dental Association (online member information), the risk for osteonecrosis translates into about seven cases per year for every million people taking oral bisphosphonates. In the most recent article addressing this issue, Mortensen _et al_. (2007) conclude that the increasing number of reports about bisphosphonate-associated osteomyelitis and the difficulty in treating these patients require further investigation to identify those patients who are at increased risk. Also, the optimal and safe duration of treatment with bisphosphonates remains to be determined. Due to the existing uncertainty in this area, recognition of patients on bisphosphonate therapy, communication with the treating physician(s), and a risk:benefit assessment have to be made for such patients who are being considered for implant therapy.
In summary, while most of this medical information can be extracted from a health questionnaire as mentioned earlier (see example in Chapter 26), it is important for the clinician to ask specific questions related to the patient's answers in the questionnaire to clarify their potential impact on treatment with dental implants. In many instances it will be necessary to contact the patient's physician for detailed information relevant to the planned treatment. Further aspects are presented in Chapters 30 and 33.
# Local examination
## Extraoral
An extraoral examination should form part of any initial patient examination. The clinician should look for asymmetries, lesions or swellings of the head and neck areas. Observation of function and palpation of the head and neck musculature and temporomandibular joints are performed. Assessment of the opening amplitude of the mandible is especially important, since instrumentation involved with dental implant therapy requires that the patient is able to open sufficiently wide (Fig. 27-6). This is also the perfect time to take note of esthetic characteristics such as smile line, lip line, gingival line, and facial and dental midline (Fig. 27-7).
**Fig. 27-6** Examination of patient's mouth-opening ability. The width of at least two of the patient's fingers placed vertically between upper and lower incisors is necessary to allow proper access for implant placement in posterior sites.
**Fig. 27-7** Smile characteristics of patient introduced in Fig. 27-1.
## General intraoral examination
The general intraoral examination includes the assessment of the condition of soft and hard tissues of the oral cavity. This also entails a careful cancer screening. Soft or hard tissue lesions will most likely require treatment prior to the placement of dental implants. Pathological soft tissue conditions include herpetic stomatitis, candidiasis, prosthesis-induced stomatitis, tumors, hyperplasia, etc. Hard tissue pathologies, which most likely require treatment prior to implant therapy, include tooth impactions, bone cysts, root fragments, residual infections in the alveolar bone, e.g. caused by failed endodontic treatment, or tumors.
Dental hard tissues are equally carefully examined to determine the need for restorative treatment in the remaining dentition, most importantly those teeth directly adjacent to edentulous spaces. The need for restoration of the latter may influence the treatment plan in terms of choosing a conventional fixed partial denture over an implant-supported restoration to replace a missing tooth. Pathologies such as caries, fractures, attrition, abrasion, abfraction, tooth mobility, or tooth misalignment are noted. Existing restorations are recorded and deficiencies such as open margins, open contacts, or fractures identified. Testing for vitality of teeth, especially of those adjacent to potential implant sites, will point to possible endodontic pathologies, which should be treated prior to implant placement. The examination of periodontal tissues including the assessment of the patient's oral hygiene is described in detail in Chapter 26.
Finally, static and dynamic aspects of the patient's occlusion are determined, including the adequacy of the patient's vertical dimension of occlusion, maxillo-mandibular relationship (angle classification), overbite, overjet, stability in habitual occlusion, centric relation, slide in centric, and lateral and anterior excursive contacts (canine guidance, group function, anterior guidance).
## Radiographic examination
The initial patient evaluation will include a radiographic survey. For the implant candidate with a history of periodontal disease and, hence, comprehensive treatment needs, a full-mouth set of periapical radiographs is needed to supplement the intraoral examination (Fig. 27-1b). A panoramic view will often be required as well, to reveal structures apical to the remaining teeth such as the infra-alveolar nerve canal, the mental foramina, the floor of the maxillary and nasal sinuses, and pathologic findings in the jaws (Fig. 27-8). Minimal radiographic bone height requirements for implant placement depend on a number of factors such as recommended implant length for a single implant restoration, single vs. multiple adjacent implants, jaw location, and ease and predictability of ridge augmentation in that location. For detailed planning of implant placement, additional radiographs such as occlusal views, cephalometric images, conventional or computer tomograms may be indicated. Implant-specific radiographic studies and their indications are described in Chapter 28, and treatment planning details are discussed in Chapter 32.
## Implant-specific intraoral examination
### Sites without esthetic implications
An implant-specific intraoral examination, emphasizing the local characteristics of potential implant sites, is important. Different locations in the oral cavity have varying requirements in this regard, primarily due to differing esthetic impacts of implant treatment. They are, therefore, addressed separately in this text.
**Fig. 27-8** Panoramic radiograph supporting the full-mouth radiographs shown in Fig. 27-1b.
**Fig. 27-9** Examination of alveolar ridge in lower left edentulous area. The ridge appears narrow in the area of the missing second premolar. Further radiographic information (lateral tomograms, computer tomograms) are recommended if dental implants are being considered.
**Fig. 27-10** Area of local soft tissue hyperplasia. Bone mapping is applied to explore the soft tissue thickness and the location of the underlying bone.
Although esthetic concerns are overall of lesser importance in mandibular and posterior maxillary sites, the evaluation of the condition of the local mucosa needs to be part of the examination in these areas as well. The clinical width and height of the alveolar process in potential implant areas is examined (Fig. 27-9). At the same time, pathologic changes are noted including mucosal hyperplasia or hypertrophy (Fig. 27-10). Probing of the local tissues may be indicated to assess tissue thickness and confirm the presence of sufficient alveolar bone. This can be done with a bone mapping procedure using a fine needle or explorer after local anesthesia has been applied (Fig. 27-10).
Besides the above, local assessment of sites with low esthetic impact consists primarily of a three-dimensional space assessment and evaluation of the condition of the adjacent teeth and their surrounding hard and soft tissues. A detailed and accurate space assessment is often difficult intraorally. Thus, it is strongly recommended to obtain diagnostic impressions and adequate bite records to produce articulator-mounted casts, on which these critical diagnostic steps can be properly performed, including a diagnostic tooth set-up or wax-up. This is especially important when multiple teeth need to be replaced (Fig. 27-11).
From a comprehensive restorative point of view, edentulous spaces to be restored with implant restorations should ideally have the mesio-distal width of the natural tooth (teeth) that would normally be there. In the patient with a history of periodontal disease, tooth movements occur frequently and space assessment becomes important. Orthodontic pretreatment may be desirable or even required (Fig. 27-12).
From the perspective of implant placement, a mesio-distal width of 7 mm will allow the insertion of a regular-platform or regular-neck implant (3.75– 5 mm). For spaces only 5–6 mm wide, narrow-platform or narrow-neck implants of approximately 3.5 mm diameter are available. For single-tooth spaces larger than 7 mm, wide-platform or wide-neck implants with a platform diameter of 6–7 mm may be the choice.
**Fig. 27-11** Mounted diagnostic casts of patient introduced in Fig. 27-1: (a) right lateral view; (b) frontal view; (c) left lateral view; (d) maxillary occlusal view; (e) mandibular occlusal view.
**Fig. 27-12** Patient with severe periodontitis and resulting tooth movement in addition to pre-existing malocclusion.
It is important to note that wide-neck or -platform implants generally will also have a wider screw diameter. Thus, sufficient buccal–lingual bone width for the placement of a wider diameter implant is important so as to avoid perforation of the alveolar bone buccal or lingual to the implant. The buccolingual width of the alveolar process at an implant site is assessed either by bone mapping or cross-sectional radiographs (see Chapter 28).
A minimum vertical distance from the crestal mucosa of the potential implant site(s) to the opposing dentition is needed for implant restorations. This space requirement may vary depending on the design of the restoration, including the choice of abutments. As a general guideline, a vertical distance of at least 4 mm from the top of the mucosa to the opposing tooth (teeth) is required for straightforward implant placement and restoration. In the patient with tooth loss due to periodontal disease, this usually does not pose a problem. In contrast, due to concomitant bone loss, the distance is generally greater than the original height of a natural tooth (teeth) so that the potential esthetic and biomechanical impacts of the resulting overlong implant restoration have to be taken in consideration as documented earlier (Fig. 27-3).
### Sites with esthetic implications
#### _Definition of the problem_
In the specific context of implant therapy in the _periodontally_ compromised dentition with esthetic implications, which is primarily the anterior (maxillary) dentition, the local, implant-related examination will have to focus particularly on the esthetic consequences of periodontal disease in this area of the jaw. The most common visible sequels of generalized periodontal disease which may have a direct impact on esthetic appearance, depending on the patient's smile line, comprise (over-)long clinical crowns and flattening of the originally scalloped course of the gingival line, including loss of papillary tissue leading to unsightly, "black interdental triangles". This is particularly pronounced in patients with an originally " _scalloped thin_ " _gingival morphotype_ , in contrast to a rather " _flat thick_ " _phenotype_ (Seibert & Lindhe 1989; Olsson & Lindhe 1991; Olsson _et al_. 1993). Not infrequently, vertical and/or lateral migration of teeth may also have occurred which, in turn, can significantly affect esthetic parameters. Furthermore, in case of more localized periodontal disease and loss of attachment, abrupt changes in vertical tissue height between neighboring teeth can be present.
The resulting major shortcomings from an esthetic point of view mainly consist of an altered length-to-width ratio of the involved clinical crowns ( _long teeth syndrome_ ) on the one hand and of interdental spaces that are not completely filled-out with gingival tissue on the other hand (Fig. 27-13). The latter may not only affect esthetics, but also lead to food retention and phonetic disturbances. As a consequence, reconstructive measures generally, and in implant therapy in particular, have not only to aim at a predictable and long-lasting functional rehabilitation, but need also to re-establish harmony from an esthetics and phonetics perspective. In general, fixed prosthodontic measures have somewhat limited potential of correcting length-to-width discrepancies of clinical crowns and to diminish open inter-proximal embrasures. Furthermore, the clinician should be aware of the additional specific limitations associated with current implant therapy (as described in Chapter 53), particularly when it comes to esthetic parameters, and therefore include this notion while proceeding to the local examination. In this context, the importance of assessing the height of the patient's smile line and his individual treatment expectations, should be once more underlined.
**Fig. 27-13** (a) Frontal view of a 60-year-old female patient. During unforced smiling the transition between the clinical crowns and the artificial gingival epithesis is completely exposed. (b) The view without gingival epithesis displays long clinical crowns and open embrasures, both affecting the esthetic appearance. (c) The occlusal close-up view of the maxillary incisor region highlights the anchorage mechanism of the epithesis in the region of the open embrasures. (d) The gingival epithesis made of pink silicone is characterized by its regular scalloped occlusal course, compensating for the missing interproximal soft tissue. (e) The clinical view in centric occlusal reveals an average inter-arch relationship, but an altered length-to-width ratio of the clinical crowns of the four maxillary incisors as a consequence of periodontal tissue loss. (f) The corresponding radiographs document the advanced interproximal bone loss, indicating in particular that tooth #21 cannot be maintained.
In the scope of this chapter and specifically addressing the local, pre-implant examination, two distinct clinical conditions can be theoretically encountered:
* One or several elements (teeth) of the anterior maxillary segment are periodontally compromised to such an extent (degree) that they can not be maintained and thus require replacement.
* One or several elements (teeth) of the anterior maxillary segment have already been lost due to periodontal disease.
This distinction is of importance, as the removal of a tooth consistently leads to horizontal and vertical tissue loss which includes soft and underlying bone tissue and which has been reported to vary between 2 and 3 mm vertically (Kois 1996; Araujo & Lindhe 2005; Araujo _et al_. 2005, 2006). This means that in the case of teeth still being present, but considered _irrational to treat_ , an additional esthetic aggravation has to be expected. In this context, the beneficial potential of a slow orthodontic _"forced eruption"_ procedure prior to tooth extraction, has to be mentioned (Salama & Salama 1993). Furthermore, as described in more detail in Chapter 53, one has to keep in mind that single-tooth replacement is significantly more predictable when it comes to long-term esthetic treatment outcome, than multiple adjacent implant restorations in the anterior maxilla (Belser _et al_. 2004a,b; Buser _et al_. 2004, 2006; Higginbottom _et al_. 2004). Clearly, single-tooth implant restorations benefit from tissue support provided by the adjacent natural teeth. As a consequence, the currently recommended _extraction strategy_ for this area of the jaw should try to avoid, whenever feasible, ending up with _two-unit_ tooth gaps. In other terms, one should either aim for _single-tooth gaps_ or, if this is not possible, for _more extended edentulous segments_ (three or more missing adjacent teeth). The latter concept, on the one hand, permits one to replace part of the missing teeth with pontics and thus benefit from their inherent superior esthetics (eventually enhanced by connective tissue grafting procedures), and, on the other hand, to avoid adjacent implant restorations.
**Table 27-1** Elements of the local, implant-specific examination of the periodontally compromised dentition in the esthetic zone
• Patient's smile line (high, medium, low)
---
• Periodontal examination (including gingival index, plaque index, probing pocket depth, clinical attachment level, bleeding on probing, width of the keratinized mucosa, gingival recessions, tooth mobility, tooth migrations)
• Inter-proximal bone height (as assessed on radiographs)
• Bone anatomy of the existing and/or anticipated (in case of inevitable tooth extractions) edentulous ridge
• Soft tissue anatomy (course of the gingival line in relation to the cemento-enamel junction of existing teeth and/or the osseous ridge)
• Gingival phenotype ("flat thick" vs. "scalloped thin")
• Shape of anatomic tooth crowns ("square" vs. "triangular")
• Length-to-width ratio of clinical crowns
• Overbite, overjet, malposition of teeth, occlusal parafunctions (wear facets, bruxism)
• Restorative/endodontic status of remaining teeth
• Width of existing and/or prospective edentulous spaces (single-tooth vs. multiple-unit gaps; identification of edentulous spaces that do not correspond to the volume of the respective missing teeth)
#### _Clinical and radiographic examination_
A structured comprehensive examination of the periodontally compromised anterior maxillary dentition (Table 27-1) should logically start with the assessment of the height of the patient's smile line. This will immediately indicate if the major esthetic shortcomings associated with an implant rehabilitation under such conditions, i.e. _long clinical crowns and open embrasures_ , will become visible during unforced smiling. The examination will then focus on the detailed periodontal status, aiming at determining the prognosis of each individual unit of the respective dentition from a primarily periodontal perspective. As it is anticipated in the scope of this chapter that either one or several teeth cannot be maintained for periodontal reasons, or that one or several teeth have already been lost due to periodontal disease, the examination will have to assess whether implant therapy represents the adequate treatment solution or not. This means that additional parameters, directly related to implant therapy, have to be included in the examination process. These parameters comprise the localization of interproximal bone height assessed on radiographs, the bone anatomy of the existing or prospective (after additional tooth extractions) edentulous ridge, the course of the gingival (mucosal) line in relation to the cemento-enamel junction, as well as the width of the edentulous spaces. Furthermore, the general shape of the anatomic crowns (square or triangular) and the length-to-width ratio of the clinical crowns have to be assessed. Finally, the restorative and endodontic status of the remaining teeth and the overall occlusal conditions such as overbite, overjet, and the presence of occlusal parafunctions (wear facets, bruxism) have to be registered. In other words, all additional information which refers directly to implant therapy (e.g. bone volume) is a prerequisite for the decision-making process, to determine if implant therapy is feasible under these specific circumstances.
# Patient-specific risk assessment
Summarizing the above mentioned aspects of a comprehensive preoperative examination, an individual risk profile is recommended for every candidate for implant therapy. Two different risk assessment forms are routinely used by the authors when examining potential implant patients, one for implant sites without esthetic priority, generally those in the mandible or in the posterior maxilla depending on the patient's smile profile, and a more detailed version for sites where esthetic aspects play a dominant role, primarily those in the (anterior) maxilla.
## Risk assessment for sites without esthetic implications
The risk assessment in partially edentulous patients without or with low objective and subjective esthetic concerns is less complex. It should include the patient's health status, periodontal disease susceptibility, smoking history, interleukin-1 phenotype, history of bruxism, patient compliance including oral hygiene, and presence and type of alveolar bone deficiencies at potential implants sites (Table 27-2). In most patients, it takes less than 5 minutes to complete the proposed risk assessment form. Utilizing the obtained information, each implant candidate is categorized as low, medium or high risk. In patients with a 'high risk' mark in multiple areas, the appropriateness of implant therapy must be questioned. For example, heavy smokers with advanced or refractory periodontal disease and a positive IL-1 test have to be considered overall high risk when extended bone augmentation procedures are needed to enable sufficient bony implant anchorage. It is important to discuss the individual risk situation with the patient prior to therapy and obtain the patient's consent based on the given circumstances.
## Risk assessment for sites with esthetic implications
Risk assessment for implant sites with esthetic importance is much more detailed and complex. The risk assessment form contains additional surgical and prosthetic parameters, which are critical for an esthetic treatment outcome (Table 27-3). These parameters have been outlined in detail by Martin _et al_. (2006) in the first ITI Treatment Guide. In periodontally compromised patients, clinicians are often confronted with medium- to high-risk situations, since vertical bone and soft tissue deficiencies are a frequent clinical finding.
### Conclusion
Modern comprehensive dental care for patients with a periodontally compromised dentition has to include the consideration of dental implants. Implant-assisted replacement of teeth that are missing or need to be extracted due to periodontal disease is an overall predictable treatment alternative in this type patient. A meticulous comprehensive examination of implant candidates is crucial and should include a patient and indication-specific risk assessment to achieve favorable short- and long-term treatment outcomes with regard to function and esthetics.
**Table 27-2** Risk assessment for patients/sites without esthetic treatment implications
**Table 27-3** Risk assessment for patients/sites with esthetic treatment implications
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# Chapter 28
# Radiographic Examination of the Implant Patient
Hans-Göran Gröndahl and Kerstin Gröndahl
* * *
Introduction
Radiographic examination for implant planning purposes – general aspects
The clinical vs. the radiologic examination
What is the necessary radiographic information?
Radiographic methods for obtaining the information required for implant planning
Radiographic examination for implant planning purposes – upper jaw examination
Radiographic examination for implant planning purposes – lower jaw examination
Radiographic monitoring of implant treatment
Radiation detectors for intraoral radiography
Image-guided surgery
* * *
# Introduction
In 1965, Brånemark installed the first dental implants made of titanium in the mandible of a 35-year-old male who, due to a cleft palate and loss of most of his teeth, could neither speak nor eat properly (Brånemark _et al_. 2005). The era of osseointegration, as a means to restore oral function compromised as a result of missing teeth, had begun.
The foundation for the use of titanium as the metal of choice for prostheses placed in the bone was laid many years earlier. In 1940, Bothe, Beaton and Davenport published the results of a study in which they had inserted pegs of different metals, among them titanium, in cat femurs. They found that ". . . the response to titanium was as good as, if not better, than that to the non-corrosive alloys in that there was more tendency for the bone to fuse with it". In 1951, Leventhal inserted screws made of titanium into the femurs of rats. He describes that "At the end of six weeks, the screws were slightly tighter than when originally put in; at twelve weeks the screws were more difficult to remove; and at the end of sixteen weeks, the screws were so tight that in one specimen the femur was fractured when an attempt was made to remove the screw". He continues: "In the past, the use of some prostheses has not become popular because it has been felt that these would remain separate from the bone and eventually loosen. Since titanium adheres to bone, it may prove to be an ideal metal for such prostheses".
Brånemark realized that screw-shaped titanium implants placed in the human jawbone could serve as substitutes for teeth that had been lost or never developed. In 1977, results from a 10-year study period were published (Brånemark _et al_. 1977) that demonstrated the clinical usefulness of what would become known as osseointegrated implants.
In the beginning of the osseointegration era limited numbers of people, and practically only those with no teeth left, were treated with dental implants. Gradually the indications were widened until partially edentulous and the patient missing just a single tooth also became candidates for implant treatment. From having been a treatment modality offered by a small number of specialists, it has emerged as a treatment mode provided by more and more dentists worldwide. It seems to grow exponentially and many more years probably remain before the vertex of its diffusion curve has been reached (Fig. 28-1a).
From a radiological point of view this must give us pause because it means that more people will undergo more extensive radiographic examination than people who receive conventional prosthetic treatment do. Consequently, we must try to use radiographic methods that do not unnecessarily increase the radiation burden to the population whilst providing us with all the information that is necessary for successful long-term treatment results.
In this chapter we will show how radiographic examinations for implant treatment purposes can be made so that they yield all necessary information at a reasonable cost both in terms of radiation dosage and economical resources. We will, in other words, adhere to the very important principle in radiography, the ALARA principle. This states that all radiographic information should be obtained with radiation doses that are As Low As Reasonably Achievable. This principle may well be broadened so that it is also understood as stating that the monetary costs should be as low as reasonably achievable (Fig. 28-1b).
**Fig. 28-1** (a, b) With the increasing use of implant treatment, it becomes increasingly important to adhere to the ALARA principle and keep radiation doses and monetary costs as low as possible.
# Radiographic examination for implant planning purposes – general aspects
## The clinical vs. the radiologic examination
Too often a distinction is made between the clinical and the radiographic examination. The latter depends on the former and a meticulous clinical examination, including a thorough patient history, is the foundation upon which any radiologic examination must be based. Without it one can neither decide whether radiographic information is necessary, nor where and how it must be sought. The clinical examiner, whether or not he or she plans to make the radiographic examination her/himself, or refer the patient to a radiologist, thereby plays a decisive role when it comes to keeping radiation doses as low as reasonably achievable whilst obtaining the radiographic information that is necessary for a successful treatment planning. According to the International Commission on Radiation Protection, ICRP 60 (1991) all radiographic examinations should be justified and optimized. It is the clinical need of radiographic information that can make the radiographic examination justified. It is then the responsibility of the person, who will plan and perform the latter, to make certain that it will be made optimally.
## What is the necessary radiographic information?
Before any radiographic technique can be chosen for any type of clinical problem one needs to clarify what radiographic information that is needed to enable a proper diagnosis and treatment plan. As regards the prospective implant patient, the necessary radiographic information is that which allows the clinician to determine:
* Whether implant treatment is the treatment option that offers the best long-term prognosis
* Whether pathological conditions are present in the jaws or remaining teeth that must be taken into account before implant treatment can be contemplated
* Where and how implants can be placed so that they have the best possibilities to become integrated with the surrounding bone and the associated crown/bridge can come into best clinical use
* How to place the implant(s) so that the surgical procedure becomes as safe as possible and the risk for post-operative failures as small as possible
A pre-operative radiographic examination is essential for all implant patients but how much of the jawbones that need to be examined and in what way will vary from patient to patient. Therefore, different radiographic techniques have to be used for different patients.
The pre-operative radiographic examination has several roles to play in respect to the clinician's needs. More specifically, the clinician needs to know the height of the bone that can be used for implant placement. One must then bear in mind that the bone height that can be used for implant placement is not necessarily the same as the total bone height (Fig. 28-2). The bone must also preferably be of a width which allows the implant to be surrounded by bone around its entire circumference. It is not only the available height that is of interest. When planning for implants to be placed adjacent to teeth or other implants one should try to ensure that they do not become positioned too close to each other (Fig. 28-3). Hence, the horizontal dimension of a potential implant site also needs to be assessed. When an implant will be placed adjacent to a tooth one should make certain that it does not become inserted too close to the tooth. Should this happen there is an increased risk of bone loss at the adjacent tooth or implant at least in the immediate period after implant surgery (Esposito _et al_. 1993; Andersson _et al_. 1995; Cardaropoli _et al_. 2003).
**Fig. 28-2** An apparent height, as seen in the cropped panoramic image to the left, does not necessarily correspond to a bone volume useful for implant placement, as revealed by a tomogram (right image) representing a layer indicated by the dotted line.
**Fig. 28-3** Two implants placed very close to each other. A control radiograph taken 1 year after bridge connection (on right) demonstrates, by the thin radiolucent lines around the implants, that they have not become integrated with the surrounding bone.
It is of great importance that the implant can be placed so that it will remain stable during the healing phase. The marginal bone crest may be used as a supporting bone cuff and a bony border in which the "apical" part of the implant can be placed will render some support. This can also be provided by the lingual and/or buccal cortical bone plate(s). The lower borders of the nasal cavity and the maxillary sinuses can give support to an implant (Fig. 28-4), but the upper border of the mandibular canal must not be used as anchorage of the implant tip (Worthington 2004).
A crucial aspect is that which concerns the location of anatomic structures that must not be damaged during implant surgery. In the lower jaw the mandibular canal, with its nerve bundle and blood vessels, is the most important. In the upper jaw placement of the implants so that they come in conflict with the nasopalatine canals should be avoided.
To make the placing of the implant(s) as safe a procedure as possible the radiographic examination must also enable a description of the outer contours of the jawbones so that, for example, tilting of the alveolar bone as well as the presence and depth of bony fossae will be observed and accounted for.
From the above it can be concluded that it is important to evaluate different aspects of the bone in which one intends to place an implant and that accurate and precise measurements of different distances are essential.
The pre-operative radiographic examination serves more purposes than those described above. When implants are to be placed in jaws with remaining teeth, the condition of those and their surrounding bone must be thoroughly evaluated. Inflammatory lesions in the vicinity of an implant site may compromise the implant treatment result. Careful assessment of the remaining teeth may also lead to the choice of an alternative treatment modality. The preoperative radiographic examination thus serves to:
* Ascertain that implant treatment is an appropriate treatment given the condition of the remaining teeth
* Make certain that bone height and width are sufficient for implant placement
* Provide measurements so that implants can be inserted without damaging neighboring structures
* Make implant insertion a safe procedure.
**Fig. 28-4** The lower border of the nasal cavity and the maxillary sinus can provide support to an implant.
**Fig. 28-5** A panoramic image of poor quality can give rise to serious problems. In this one it was not noticed that the bone in the upper right anterior region was not suitable for implant placement. Nevertheless, implants were placed (see inlay in upper left corner), soon to be lost.
Needless to say, none of these objectives can be obtained without a radiographic examination of the best possible quality.
## Radiographic methods for obtaining the information required for implant planning
In this chapter we will not discuss the examination of totally edentulous patients, only of those who have lost one or several teeth in jaws where some teeth still remain. As already mentioned one must then take into account the conditions of the remaining teeth in order not to jeopardize the implant treatment. A comprehensive examination, clinical as well as radiologic, of the dentition should therefore be made prior to a decision about where and how to insert implants. Depending upon the result of the clinical examination, the primary radiographic examination can be made with a combination of panoramic and intraoral radiography or by one or the other. One should not hesitate to take intraoral radiographs in regions where the panoramic radiograph has not been able to provide a clear view of the anatomic structures.
An adage well worth remembering, when determining whether an image is good enough for diagnosis and treatment planning, is that optimal diagnostic quality is only present when all diagnostically important structures are clearly visualized. Figure 28-5 illustrates a case when a panoramic radiograph was considered of good enough quality to be used for implant planning purposes. However, implants were lost, even before being subjected to occlusal loads, due to the poor bone conditions in the region that could have been observed had a better pre-operative radiographic examination been made.
**Fig. 28-6** Horizontal distortions are common in panoramic radiographs, especially in the upper premolar area, and give a false impression of available horizontal bone dimensions. Compare the distance between the second premolar and the cuspid in the two images.
**Fig. 28-7** The panoramic radiograph does not provide information about the width of the alveolar bone. A sagittal tomographic image reveals the true conditions in the lower anterior region.
_Intraoral radiography_ should be performed according to the paralleling technique and radiographs taken so that there will be some overlapping between adjacent image fields. Most teeth will then be seen from two different angulations allowing for a better appreciation of the location of different structures.
_Panoramic radiography_ may seem easy to perform but is a technique where many mistakes are made, not least in patient positioning. Panoramic radiographs taken on incorrectly positioned patients may provide a severely distorted view of the patient's jaws (Tronje 1982). This can cause large overlapping of neighboring teeth that can prevent a proper diagnosis. In regions where teeth are present the distortions are evident due to the overlapping of tooth surfaces (Fig. 28-6). In edentulous areas, however, distortions may not be that apparent which can lead to misjudgement of distances within the jaws. The panoramic technique can be used to provide a quick estimate of the bone height. A tomographic examination needs to be carried out in many cases to determine whether it is sufficient for implant placement (Fig. 28-7). The magnification in panoramic images varies between different types of panoramic machines. Some units also permit various types of radiographic images to be taken, that differ in magnification. It is thus important that one makes certain what magnification is indicated in the image to be evaluated.
_Tomography_ can be used to obtain cross-sectional images, that is, images that are perpendicular to the curvature of the jawbones in the intended implant site. This is the best way in which to assess the width of the jawbone, and thereby the height available for implant placement, as well as other important aspects of the jawbone anatomy. Equipment for tomographic examinations shows much more variation than does that for panoramic and intraoral radiography. Widely different imaging principles are used resulting in different types of images.
The implant treatment spectrum varies from the single implant case to that where large parts of the facial skeleton are missing, and making an implant-anchored facial prosthesis necessary. Ideally, a clinic for oral and maxillofacial radiology is therefore equipped with a spectrum of X-ray machines for tomography capable of satisfying different demands and providing high-quality tomographic examinations. There is a difference between what different machines are best suited for. Three main groups of tomographic techniques are used for pre-implant tomography: motion (conventional) tomography, computed tomography (CT), and digital volume tomography (DVT), also known as cone beam CT. This is not the place to present these techniques in any detail but a little will be said about each of them as it relates to the examination of the implant patient.
**Fig. 28-8** Conventional spiral tomography of the lower jaw. Contiguous, 4 mm wide slices with the most anterior one taken in the region of the mental foramen (image to far right) that serves as an anatomic landmark.
**Fig. 28-9** By selecting just a few tomographic layers the dose can be minimized. Images taken distal to the upper right cuspid (see cropped) panoramic image.
_Conventional tomography_ as applied for dental purposes underwent a profound development in the end of the 1980s when tomographic X-ray machines dedicated for the examination of the jawbones entered the market. Units such as the Scanora (Soredex Co, Helsinki, Finland) later to be followed by Cranex Tome from the same company meant that, most of the time, a comprehensive pre-implant examination of the patient could be made in the same unit and with the patient in the same position (Gröndahl _et al_. 1996, 2003). From a panoramic image one determines where in the jaw(s) one needs information that can only be found in cross-sectional, tomographic images. The tomographic examination of the selected region is then accomplished by means of a synchronized, spiral, movement of the X-ray tube and the detector (film or image plate) permitting image layers of 2–4 mm width to be obtained containing a minimum of spurious contours from adjacent structures.
One to four images of contiguous tomographic layers can be taken during the same examination, that is, without changing patient position or detector. They will then appear on the same film, or within the same digital image frame (Fig. 28-8). By selecting just a few layers to be exposed, radiation doses can be minimized (Fig. 28-9).
By means of multimodality units, conventional spiral tomography provides the possibility of tomographic examinations of limited regions selected from a panoramic view of the entire jaw or a part of it. It has the advantage of being done with a small unit that can also be used for many other radiographic examinations of the oromaxillofacial regions. Spiral tomography can be made with film or image plates but not with CCD or CMOS solid-state detectors: these are not yet available for use with the dental multimodality-type of X-ray machines.
_Computed tomography_ is widely used for pre-implant tomography, often because other techniques are not available (Ekestubbe _et al_. 1997). In the overwhelming majority of cases a stack of axial tomographic layer images is first taken. The height of the stack should be such that it covers a distance from just outside the marginal bone crest down to and including the base of the mandible or, for the upper jaw, up to and including the hard palate. In the upper jaw the slices should be parallel to the hard palate, in the lower jaw to the base of the mandible (Fig. 28-10). The information in the axial slices can be used for image reformatting so that cross-sectional views of the jawbone will be displayed (Fig. 28-11). These are perpendicular to a curve corresponding to the shape of the jaw as seen in a representative axial view.
Computed tomography is easily performed but can also be associated with high radiation doses (Dula _et al_. 1996, 1997; Frederiksen _et al_. 1995; BouSerhal _et al_. 2001). Doses can, however, be significantly reduced by adhering to so-called low-dose protocols which are well suited for studies where the primary interest lies in examining bony structures (Ekestubbe _et al_. 1996, 1999). When using computed tomography it is also important that the height of the examined volume is kept as small as possible. Computed tomography is not ideal for tomographic examinations of partially dentate patients. This is because the volume of diagnostic interest, even when the height of the exposed volume is small, constitutes only a small fraction of the latter. Exposing as small a volume as diagnostically feasible is one of the best ways of adhering to the ALARA principle. Should several edentulous regions within the same jaw need to be tomographically examined, computed tomography may be justified (Buser _et al_. 2002).
_Digital volume tomography_ ( _DVT_ ) is becoming exceedingly popular as a tool for maxillofacial imaging not least for pre-implant planning purposes. With the midpoint of the region of interest as a centre, the X-ray tube moves along the periphery of a circle, on the other side of which is positioned the detector. During this movement a cone-shaped X-ray beam, the diameter of which differs between different types of equipment, exposes the region of interest either continuously or in short bursts. From the X-ray detector a signal is sent to a computer where the electronic signal is converted into a digital one. Based on this information images can be reconstructed so that layer images (axial, sagittal, and coronal) of the exposed volume will appear on the screen. It is possible to travel in either direction within the volume so that the entire volume can be easily searched. Many DVT units make it possible to display curved layers of varying width so that something similar to a conventional panoramic view, although with thinner layer thickness, is obtained.
**Fig. 28-10** Orientation of the axial tomographic slices differs between jaws. The height of the stack should be kept to a minimum.
**Fig. 28-11** Some reformatted cross-sectional images from the right side of the mandible.
**Fig. 28-12** Images (except the panoramic view) taken with 3DX Accuitomo DVT unit (J. Morita Co., Kyoto, Japan). The upper row images show the conditions in the right upper lateral incisor region. In the lower row the coronal and the sagittal tomographic images show the mandibular canal that is barely visible in the panoramic image.
Equipment for digital volume tomography comes in many different shapes (Frederiksen 2004), and they vary with regard to size of the volume that can be examined, geometric resolution, ease of use etc. They also differ as regards the radiation dose to the patient due to, above all, differences in volume size, resolution, and type of detector (Ludlow _et al_. 2006). Digital volume tomography could very well become the technique with which most partially dentate patients in need of implant treatment will be examined. The examination is easily done and radiation doses can be kept low, especially when machines that permit different sized volumes are used. An excellent way of reducing radiation dose is to expose the smallest possible volume. An advantage with digital volume tomography is its applicability in many areas of clinical dentistry. Figures 28-12 and 28-13 provide examples of images taken with DVT units.
Realizing that far from everybody has access to a wide spectrum of X-ray machines we will present various types of commonly seen cases. We will describe how they can be radiographically examined by means of different techniques but not include the totally edentulous patient or the patient in need of facial prosthetic constructions.
# Radiographic examination for implant planning purposes – upper jaw examination
Depending upon where in the upper jaw implant treatment is to be planned one must take different anatomic factors into account. A common denominator is of course that the width and height of the bone must be evaluated. The available height depends on the bucco-palatal width of the bone because, ideally, the implant should be covered by bone both on its buccal and palatal aspects. The length of implants that can be used thus depends on the distance between the inferior border of the nasal cavity, or the maxillary sinus, and that part of the alveolar bone where it is sufficiently wide for implant placement (Fig. 28-14). When implants are to be placed in the vicinity of the midline one must evaluate the width of the incisive foramen and the nasopalatine canal. One must assess the height and width of the alveolar bone on the buccal and distal side of these structures to determine whether and where an implant can be placed (Fig. 28-15).
In the upper frontal region it is not uncommon for a single tooth be missing as a result of previous trauma. In these cases the radiographic examination can be done in a simple, yet comprehensive, way by one or two intraoral radiographs and a single tomographic image (Fig. 28-16).
**Fig. 28-13** Lower jaw tomography performed by i-CAT cone beam CT machine (Imaging Sciences International, Hatfield, PA, USA). Courtesy of Dr. Allan Farman, University of Louisville, Kentucky, USA.
**Fig. 28-14** The height of the bone available for implant placement depends on its width. It may therefore be less than the height as it appears in e.g. intraoral or panoramic radiographs.
**Fig. 28-15** Cross-sectional, 1 mm thick image layers in places indicated by the broken lines in an axial image of the upper anterior region. Such images can be used to assess the available bone volume and the state of neighboring teeth.
Should the available bone lack the dimensions needed for the placement of an implant, the patient may be willing to accept that bone augmentation is performed to provide for sufficient height and width of the bone. In the latter case tomographic images will be of help when determining exactly where the bone is of less than sufficient width or height and the extent to which it needs to be augmented. Tomographic images can also be used to observe the results after healing (Figs. 28-17 and 28-18).
In areas where teeth have been extracted and it is uncertain how much of the alveolus has become filled with new bone, digital volume tomography is a helpful tool. This is illustrated in Fig. 28-19, where it is also apparent how well this technique is able to demonstrate the conditions anterior and inferior to the frontal border of the maxillary sinus.
**Fig. 28-16** Two cases of missing upper incisors in which the pre-operative radiographic examination was made by intraoral radiographs and conventional spiral tomography. In the lower row case an implant could be placed buccal to the nasopalatine canal.
**Fig. 28-17** Pre-operative (upper row) and post-operative images of a patient in whom a bone substitute was placed both buccally and in the nasopalatine canal to enable insertion of an implant in an optimal position.
**Fig. 28-18** A sagittal (left) and an axial tomographic image (middle) after a bone substitute has been placed on the buccal surface. The dotted line indicates the position of the sagittal slice. To the right is a three-dimensional image reconstructed from the volume data.
**Fig. 28-19** Digital volume tomography in the upper first premolar area. Notice the lack of complete bone filling of the extraction socket and the relation of the alveolar bone to the nasal and maxillary sinus cavity.
In some patients in whom the available bone height below the maxillary sinus is too small one can occasionally find bone suitable for implant placement on the palatal side of the sinus. Tomography must be performed so that this can be determined (Fig. 28-20).
In the posterior parts of the upper jaw the maxillary sinus may extend so far down into the alveolar bone that there is not enough bone available in which to insert an implant. By entering the sinus through a buccal window, bone substitutes can be placed under the mucosal lining. Digital volume tomography is an ideal method to evaluate how the bone substitute is positioned and its relation to the adjacent bone (Fig. 28-21).
When implants are intended to be placed in more than one region, the use of computed tomography may be justified (Buser _et al_. 2002) provided that low-dose protocols are applied (Rustemeyer _et al_. 2004). A panoramic radiograph and, when remaining teeth are not well displayed in it, complementary intraoral radiographs are nevertheless important. Figure 28-22 describes how the results of such an examination can look. From the stack of axial images a representative image is chosen in which the curvature of the jaw is drawn. A dedicated computer program then makes new tomographic images at chosen distances. These images describe layers that are perpendicular to the curve and in which measurements of bone height and width can be made.
Computed tomography is mostly performed in medical radiology departments and images considered relevant for the purpose are sent to the clinician. Sometimes these are limited to the axial image describing the curvature of the jaw and the reconstructed cross-sectional images. We recommend that the referring dentist should also receive the scout image and the stack of axial images. In the scout image it is possible to see what reference plane that was used and, if needed, make the appropriate adjustment of the measurements taken in the cross-sectional views. In the axial images one may be able to pick up information about the remaining teeth not displayed in the panoramic or intraoral radiographs (Huumonen _et al_. 2006).
# Radiographic examination for implant planning purposes – lower jaw examination
In the lower jaw there is a distinction between implant placement in the region anterior to the mental foramina and in regions posterior to the foramina. The height of the anterior region is usually well preserved if teeth have not been missing for a long time. This is rarely the case in the partially dentate patient. Its width, however, may be a limiting factor. One can get an indication that the alveolar bone is thinner than normal from periapical radiographs or from panoramic images, provided that the anterior region is well reproduced. This is often the case when one can see vertically running radiolucent structures corresponding to the blood vessel canals in the inner walls of the cortex. They become visible when the bone is thin or has fewer and thinner bone trabeculae than normal. In such cases a tomographic examination may be advisable so that one can determine beforehand whether a thin upper ridge will be removed or a bone augmentation procedure applied.
**Fig. 28-20** From the panoramic image (left) it is not possible to determine that bone for implant placement is available on the palatal side of the maxillary sinus, as is clearly seen in the tomographic image (right). Notice the soft tissue swelling in the sinus.
**Fig. 28-21** A coronal and a sagittal tomographic layer of the lower part of the maxillary sinus in which a bone substitute has been placed.
When implants are to be placed posterior to the mental foramina one must not only take into account the factors one had to consider in the frontal regions. One must also be able to identify the path of the mandibular canal and accurately assess the distance between the upper level of the alveolar bone, where it is sufficiently wide, to the upper border of the canal. To do this before surgery requires that tomography is performed, so that the jawbone anatomy can be evaluated in image layers that correspond to cross sections of the mandible. Estimating this distance in panoramic radiographs, as many seem to do (Worthington 2004), requires so many assumptions of unknown variables that mistakes can easily be made (Fig. 28-23). These can result in temporary or permanent damage to the inferior alveolar nerve. These problems "are more frequent than expected" (Worthington 2004). We are convinced that careful presurgical planning, including the use of tomography, will keep the incidence of nerve damage to an absolute minimum.
The entire distance from where sufficient width of the mandible is found to the upper border of the mandibular canal cannot be used for implant surgery. One reason is that the drill used for preparing the implant site will go deeper than the implant itself. Another is that one cannot always measure distances in radiographs with absolute accuracy and precision. Therefore, prudent clinicians make use of at least a 2 mm safety zone between the upper border of the mandibular canal, as seen in the radiograph, and the planned level of the tip of the implant (Fig. 28-24).
**Fig. 28-22** Computed tomography of the upper jaw where implants are planned to be installed on both sides. To the lower right are cross-sectional views from one side to the other, perpendicular to the curve seen in the axial view to the left.
**Fig. 28-23** In this case implant treatment planning was based on a panoramic radiograph only. One of the implants was placed with its tip into the mandibular canal as seen in a subsequent CT image. The positioning of the implant into the canal may have been caused by a misinterpretation of the panoramic radiograph. It is the lingual part of the upper alveolar bone that gives rise to the upper contour in the panoramic image.
Among other factors that must be considered in the planning process is the outer shape of the mandible. Both concavities and the lingual tilt differ in extension between patients and between different parts of the jaw (Figs. 28-25 and 28-26). Accidental penetration of the lingual wall of the mandible can more easily occur under those conditions than when they are not present. Severing of arteries in the underlying soft tissues can cause severe, even fatal, bleeding (Darriba & Mendonca-Caridad 1977; Niamtu 2001).
Sometimes the mandibular canal, before it ends at the mental foramen, continues a little bit in an anterior direction before going upwards and distally toward the foramen making a so-called anterior loop (Arzouman _et al_. 1993). Therefore it is recommended not to place an implant immediately anterior to the foramen. In other cases there can be a relatively wide anterior continuation of the canal, as indicated by Fig. 28-27. It is then recommended that a radiographic evaluation is performed to determine its position relative to potential implant positions.
**Fig. 28-24** How measurements can be made in tomographic images to ensure that the tip of the implant will not enter the mandibular canal. (a) Measure the entire height from the upper border of the canal to the marginal bone crest. (This value can be used as a reference during surgery.) (b) Assess where the bone is wide enough for the implant. (c) Measure from this level to the canal. (d) Subtract 2 mm from the latter value. From Gröndahl _et al_. (2003).
**Fig. 28-25** Lingual concavity and a small bucco-lingual width just distal to the mental foramen and a different shape and width in a more distal position.
**Fig. 28-26** The shape and angulation of the mandibular jawbone can be very different just a short distance apart. The dotted lines in the sagittal tomograms indicate the positions of the cross-sectional tomographic layers. This information can only be obtained pre-operatively by means of tomography.
**Fig. 28-27** An anterior continuation of the mandibular canal from the mental foramen as seen in tomographic images (same patient as in Fig. 28-26) and as it may appear in a panoramic view (different patient).
**Fig. 28-28** Large local differences in bone density and architecture. The much denser bone in the most distal tomographic layer most probably is due to the inflammatory conditions at the adjacent molar.
This is not the place to discuss factors related to general health that may have an influence on bone structure and architecture. In can be noted however, that in tomographic images, given that their resolution is sufficiently high, the cancellous bone pattern in intended implant sites can be studied and the thickness of the cortical bone evaluated. Local factors can contribute to local variations in bone density. In Fig. 28-28 large differences in bone density can be seen in tomographic images less than 1 cm apart. The higher density in the more distal region is most likely a reaction to the inflammatory conditions seen at an adjacent tooth.
# Radiographic monitoring of implant treatment
Meticulous planning of the implant treatment together with gentle surgical technique for the insertion of the implants make immediate post-operative radiographic examination superfluous unless something unexpected occurs during surgery. Under normal conditions, however, there is simply nothing, apart from the expected, to be found. Should the patient experience symptoms before the first post-operative radiographic examination is scheduled, one should of course not hesitate in taking radiographs if information from them is considered essential for a proper diagnosis.
The radiographs in Fig. 28-29 are from a patient who presented with severe pain very soon after implants were inserted. The images show unevenly demarcated radiolucent areas around the implants, especially the most distally and the most mesially placed. This is a strong indication of bone infection. In addition, the most mesially placed implant appears to have its tip in close proximity to the anterior loop of the mandibular canal. This is confirmed by a tomographic examination. The affected implants were removed and the symptoms soon subsided.
When implants are inserted in dense bone heat necrosis can occur around the "apical" part of the implants, particularly when the implants are long and effective cooling during their insertion has not been applied. Usually this is accompanied by pain. In the radiograph one can see a radiolucent area surrounding the apical part of the implant. A radiolucent area just beneath the apical part and caused by the drill should not be confused with the radiolucency that is a result of heat necrosis. Heat necrosis is most commonly seen in the lower jaw (Fig. 28-30).
**Fig. 28-29** A scanogram (upper left image) indicates an inflammatory reaction around the most distal and the most mesial implant and that the tip of the latter may interfere with the anterior loop of the mandibular canal. This is confirmed by the tomographic examination (upper right images) and after removal of the two implants, the symptoms disappeared.
**Fig. 28-30** Soon after implant insertion the patient presented with slight pain. A radiograph (left image) was interpreted as showing normal conditions. Two weeks later the pain had increased in intensity and a radiolucency could now be seen around the tip of the most mesial implant (middle image). The right image, taken some months later shows completely normal conditions.
Often it is not possible to take radiographs of implants using standard intraoral techniques. One either has to take radiographs more from below or use panoramic radiography or, better yet, so-called scanograms (Fig. 28-31).
Implants that have not been correctly placed in the bone may cause symptoms as well. Should an intraoral examination fail to show the cause of the problem a tomographic examination may be needed (Fig. 28-32). It should preferably be performed with digital volume tomography, as it is less prone to cause artifacts from the implants than computed tomography.
Depending upon the implant system used there may or may not be a need for a radiographic examination when abutments are placed. To examine whether abutments are correctly positioned on top of the implant pillar the X-rays need to pass at right angles to the implant. If not, gaps between the abutment and implant pillar may go unnoticed and uncorrected for (Fig. 28-33). The occlusal load will then not be optimally distributed which can later cause component fractures. Marginal bone loss has also been attributed to gaps between the abutment and the implant pillar (Hermann _et al_. 2001; King _et al_. 2002).
**Fig. 28-31** A so-called scanogram by which even deeply seated implants can be displayed in their entirety.
**Fig. 28-32** An intraoral radiograph (left) failed to reveal the cause of the problem in a patient with pain in the region of a newly placed implant A DVT image demonstrated that most of the implant was not placed in the bone.
**Fig. 28-33** Small gaps between abutment and implant pillar (most mesial implant) may go unnoticed in radiographs taken with less than perfect geometry (left image).
Reference radiographs, with which later radiographs can be compared to monitor the interaction between implant and bone, are preferably taken when crowns or bridges are placed. Little can come out of such comparisons if the quality of the radiographs is not high. It must be possible to notice small marginal bone level differences over time as well as the condition of the bone–implant interface. This requires radiographs to be taken with the X-rays being directed perpendicular to the longitudinal axis of the implant and the surface of the detector. When threaded implants are used the radiographic appearance of the threads provides useful information about the irradiation geometry used and how to change it should it not be correct to start with. One must be able to get a clear picture of the inner parts of the threads on either side of the implant (Fig. 28-34).
Intraoral radiography is the method of choice for monitoring of implant treatment. Irradiation geometry and exposure can be individualized for different implants or group of implants. Panoramic radiography cannot provide the same detailed information and should be reserved for the few cases when intraoral radiography cannot be tolerated. A better alternative can be used by those who have access to multimodality units able to provide multiple exposures of selected small areas using slightly different irradiation geometry.
With high-quality intraoral radiography it is possible to follow the course of events in the marginal and peri-implant bone over time. A fairly typical course of events for lower jaw implants, from abutment placement via bridge installation to a 5-year follow-up examination, can be seen in Fig. 28-35. With well trained and motivated personnel it is possible to get high-quality and comparable radiographs over long periods of time even without going to the effort of using particular film-holding devices. The images in Fig. 28-36 are taken over a 5-year period by different radiographers.
High-quality radiographs make it possible to detect, observe, and quantify bone level changes over time. In the majority of patients the bone level remains at the position it had after the post-surgical remodeling over as long periods that it has been hitherto possible to cover in longitudinal studies (Adell _et al_. 1990; Snauwert _et al_. 2000; Ekelund _et al_. 2003). In other patients one can find loss of bone at the marginal bone crest that affects all implants or, more often, one or a few. It is important to detect those so that the cause of the bone loss can be identified (Figs. 28-37 and 28-38).
**Fig. 28-34** The appearance of the threads of an implant provides useful information about how to change the direction of the X-ray beam so that it can become directed perpendicular to the implant. From Gröndahl _et al_. (1996).
**Fig. 28-35** From abutment connection via bridge installation to a 5-year follow-up examination.
**Fig. 28-36** Intraoral radiographs taken with a free-hand technique and by different radiographers at bridge installation (upper left corner) and at follow-up examinations (1, 3, and 5 years later) demonstrate excellent possibilities of monitoring the postoperative course of events.
**Fig. 28-37** In radiograph (b), the mesial implant has marginal bone loss that was not evident a year before. In radiograph (c), the most distal implant has marginal bone loss involving about a third of the implant length.
**Fig. 28-38** Both implants show marginal bone loss exceeding one third of the implant length. The implant to the right is also surrounded by a thin radiolucent zone. This indicates that the implant is not osseointegrated. At a clinical examination it was found to be mobile and consequently removed.
In high-quality radiographs it is possible to identify implants that are not osseointegrated with an accuracy that is on a par with what one can find when radiography is used for other dental diagnostic purposes (Sundén _et al_. 1995; Gröndahl & Lekholm 1997). Since the first radiographic signs are very subtle, as seen in the radiographs in Fig. 28-39, it is very helpful if one is able to compare radiographs with ones taken previously. Most implants that have not become integrated are found during the first year after bridge installation, or even before that. This stresses the importance that radiographs taken at abutment connection and at bridge installation are of the highest possible quality. Radiographs should be of a quality so that it is possible to evaluate not only the conditions in the surrounding bone and the marginal bone level but also the conditions of all the technical implant components. Such conditions are, for example, fractures of the centre screw or of the implant pillar itself and gaps between abutment and implant pillar, or between bridgework and abutment (Figs. 28-40, 28-41 and 28-42).
## Radiation detectors for intraoral radiography
Although a correctly exposed and optimally processed film, in our opinion, provides the best quality images for implant monitoring we have to accept that digital imaging techniques are gaining wider and wider acceptance among dentists. There are some advantages of digital images over film-based ones, in that they can be subjected to image processing algorithms that can enhance their diagnostic quality and adapt them to various diagnostic tasks (Analoui 2001a,b). This can of course be of value when the diagnostic tasks are so varied as they are in implant monitoring when one must be able to evaluate both thin marginal bone and the metal components of the implant construction.
As we have pointed out several times in this chapter the irradiation geometry is essential when implants are to be monitored. The X-rays should come perpendicular to the longitudinal axis of the implant and to the detector plane. Therefore one must have a digital detector that can be placed in the mouth, and relative to the implants, as easily as can film. When the X-ray beam has passed through a jaw in which implants have been inserted, the transmitted radiation consists of a wide spectrum of X-rays of different intensity. Thus, the detector has to be able to respond to a wide range of exposure differences; its exposure latitude must be wide. Image plate systems possess a wider exposure latitude than most solid-state systems (Farman & Farman 2005). With solid-state systems it is therefore easier that thin bone structures become over-exposed and not visible in the radiograph (Fig. 28-43). For this reason, and because image plates are as easy to use as films, we have chosen image plate systems for implant monitoring purposes. Image plates are, however, not without problems. They can easily get scratched if not handled with extreme care.
**Fig. 28-39** Notice the very subtle sign, a thin radiolucent zone around the implants, indicating that the implants marked by arrows are not osseointegrated. Comparison of the radiographs with those taken earlier, the ones to the left in each image pair, makes the detection of subtle signs much easier.
**Fig. 28-40** In the implant marked by an arrow normal conditions were found at bridge installation (left image). One year later, a fracture of the centre screw went unnoticed (middle image) resulting in a gap between abutment and implant pillar seen in an image taken another year later. Notice that the irradiation geometry was not optimal at the second occasion.
**Fig. 28-41** In this case the conical abutment was not correctly placed (left image). After correction for this, the crown was remade but a later control then found a gap between crown and abutment. Notice the difference in marginal bone height on the distal side.
**Fig. 28-42** Fracture of the implant pillar seen in radiographs taken 2 years after bridge installation. Neither the image from the latter occasion, nor the one taken at a 1-year control examination show any sign of fracture. Notice the inflammatory reaction along both sides of the implant.
**Fig. 28-43** Images taken with an image plate system, exposure times: 0.25 sec, 0.40 sec and 0.63 sec (upper row) and a CMOS system, exposure times: 0.25 sec, 0.32 sec, 0.40 sec, 0.50 sec and 0.63 sec (lower row). In the upper images the marginal bone is seen at the same level. In the lower ones it seems lower with increasing exposure. Compare with the horizontal reference line.
**Fig. 28-44** Images describing the use of a system for surgical planning and image-guided surgery. Courtesy of Matts Andersson and Andreas Pettersson, Nobel Biocare, Göteborg, Sweden.
# Image-guided surgery
Due to the three-dimensional information offered by computed tomography and digital volume tomography it is possible to use those techniques to play a more direct role in the surgical placement of the implants (BouSerhal 2001; Guerrero 2005). The exact placement and angulation of implants are determined by means of the radiographs. Guiding templates are then constructed and applied during surgery so that the implants will be positioned as intended, so-called image-guided surgery. It is also possible to build up images in which the result of the treatment, with specific implants and the final prosthesis "in place". Development in this area is rapid with implant companies, manufacturers of radiographic equipment, and software companies all working to develop and refine these techniques. For that reason we will do no more than mention the possibility and show just a few images that can shed some light on how these techniques can be used (Fig. 28-44). We strongly recommend that radiographic techniques that limit the radiation dose to the patient as much as possible are used. We also recommend that a careful scrutiny for diagnostic purposes is made of all radiographs before they are used for surgical implant planning and guiding.
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# Chapter 29
# Examination of Patients with Implant-Supported Restorations
Urs Brägger
* * *
Identification of the presence of implants and implant systems
Screening
Implant pass
Questionnaire for new patients
Anamnestic information from patients on maintenance
The development of implant recognition software
Clinical inspection and examination
Characteristics of implant-supported restorations
Characteristics of prosthetic components and components of implant systems
Technical failures/complications
Function
Functional analysis
Articulation, phonetics
Implant
Clinical test of mobility
Electronic tools to assess the quality of osseointegration
Bacterial deposits
Soft tissues
Mucosa
Palpation/sensitivity
Recession, pocket probing depth, probing attachment level, bleeding on probing
Esthetics
Papillae, interdental space and type of mucosa
Condition of adjacent teeth
Color shades
* * *
# Identification of the presence of implants and implant systems
## Screening
With the growing use of dental implants, the number of patients with implant-supported restorations seeking dental care will soon affect most dentists on a regular basis (Österberg _et al_. 2000; Berge 2000; Zitzmann & Hagmann 2007). Cohorts with fixed or removable implant-supported restorations demonstrated considerable amounts of technical and biological failures and complications over 5- and 10-year observation periods (Berglund _et al_. 2002; Pjetursson _et al_. 2004; Brägger _et al_. 2005; Widbom _et al_. 2005; Fransson _et al_. 2005; Roos-Jansaker _et al_. 2006). In the coming decades, the profession will be challenged to prevent, diagnose, and treat technical and biological problems of implant-supported restorations. Screening of all new patients, identification of the implants, and assessment of the condition of the implants, the restoration, and the surrounding structures are therefore mandatory. Aspects related to general health, smoking, etc, which may affect the quality of implant integration and function, are discussed in Chapters 27 and 30.
## Implant pass
Information gathered by means of questionnaires can often be incorrect or incomplete. After a few years, patients may not be aware of how many implants were placed or even where exactly they are located. In addition, patients cannot be expected to remember and list brand names, names of biomaterials or complex interventions.
Several professional associations and manufacturers of implant systems have therefore developed an implant pass for patients (Fig. 29-1). All implant-related information can be filled out on the pass, avoiding the loss of important data. Furthermore, tracking of components back to their origin is possible applying the corresponding lot numbers in the patient chart as well as in an implant pass. Patients with implant-supported restorations would benefit from this document whenever a dental service needs to be provided, including emergency situations, maintenance, repairs or even a new restoration. Just a simple tightening of a screw-retained implant-supported prosthesis might be tedious if the dental team is unable to identify the components and if no corresponding screwdriver is available.
**Fig. 29-1** Proposal for an implant pass developed by the Swiss Society of Implantology. Copyright © Schweizerische Gesellschaft für orale Implantologie.
## Questionnaire for new patients
The most straightforward way to obtain information on the presence of implants and implant-supported restorations in new patients is to ask questions related to any past implant experiences. The following comprehensive list of questions can be added to currently used questionnaires in educational programs, clinics, and private practices:
* Do you carry an implant pass?
* Did your dentist ever place implants into your jaw bones (name, address of the dentist, surgeon)?
* How many implants were placed?
* When were these implants placed (if remembered)? (How old were you when implants were placed?)
* Where are they located?
* Why were these implants placed or what were the reasons for the loss of teeth?
* Do you wear a prosthesis/crown supported by an implant (name of the dentist, prosthodontist, technician)?
* Did you have enough bone to have the implant placed?
* Were there additional treatments performed before implants could be placed?
* Did the surgeon perform a bone augmentation, sinus lift procedure?
* What was the brand name of the implants (if remembered)?
* Were bone graft particles used (if remembered)?
* What was the brand name of the biomaterials used (if remembered)?
* Have you ever experienced failures/complications with the implants?
* Have you ever experienced failures/complications with the prostheses/crowns?
* How often has this occurred?
* Are you satisfied with the way you can function with the implant-supported prosthesis/crown?
* Are you satisfied with the esthetic situation?
* Did you have to pay for the implants and prosthesis or was there insurance involved?
* How do you clean the neck portion of the implant/ abutment?
* How do you clean the prosthesis/crowns?
* Do you use any special aids/disinfectants to carry out the cleaning?
* Does the mucosa/do the gums around your implant bleed?
* Do you notice a bad taste coming from underneath the prosthesis/crown?
* Is your implant mobile?
* Have you recently noticed a change with the implant-supported restorations?
## Anamnestic information from patients on maintenance
Before starting to examine the oral conditions at maintenance visits, questions related to implant-supported restorations should include:
* Have you noticed a change with your implant-supported restorations?
* Are your implants stable?
* Do the gums around your implant(s) bleed?
* Are you able to clean the area around the neck portion of the implant(s) easily?
* Do you still have enough cleaning aids/disinfectants to perform daily plaque control?
In addition, general questions related to patient's satisfaction with the implant-supported reconstruction should be part of a quality management concept (Vermylen _et al_. 2003; Pjetursson _et al_. 2005).
## The development of implant recognition software
Sahiwal _et al_. (2002a,b,c) collected implants from more than 50 manufacturers and divided them into threaded and non-threaded, as well as tapered and non-tapered categories. Radiographs were then taken at different angulations. Using tables and flow charts, test implants could be correctly identified in radiographs taken within ±10 degrees, according to their identifying features.
A very recent method to assist in identifying unknown implant systems applies an implant recognition software (IRS) (Michelinakis _et al_. 2006). The internet was searched for implant manufacturing companies worldwide in all languages. Relevant information on the implant designs was collected. A program was devised using key design factors for the identification of specific implants. The search revealed 87 implant manufacturers with 231 different designs. A valuable adjunct to the identification of implant systems was thus introduced for both general dental practice use and forensic identification.
# Clinical inspection and examination
## Characteristics of implant-supported restorations
Following the conventional extraoral and intraoral examination, the distribution of implants in the dental arch is marked in a dental record. A detailed description of the implant-borne restoration, the prosthetic components, and the components of the respective implant system may include material and design aspects.
* Restorations:
* Crown
* FDP, number of units
* Extension prosthesis
* Telescopic restoration
* Removable partial denture
* Bar device
* Overdenture
* Defect prosthesis
* Other
* Material of:
* Veneer
* Framework
* Denture teeth
* Fixation:
* Cemented
* Removable by the patient/dentist
* Screw retained: transocclusal, transversal, access closed, access free, type of screw head, component of what system
* Friction
* Via attachments
* Connection to teeth: one piece, detachable, attachments
* Material.
## Characteristics of prosthetic components and components of implant systems
* Prosthetic components:
* Telescopic or conus crowns
* Bar device
* Riders
* Matrices, patrices
* Mesostructures
* Individualized components
* Material
* Components of implant systems:
* Abutments for cementation
* Abutments for transocclusal screw retention
* Abutments for transversal screw retention
* Angulated abutment
* Anchors: ball anchor, magnets, locator system
* Mesostructures
* Material
* CAD/CAM components
* Connection of abutments to the implants:
* Localization of microgaps
* How many gaps
* Platform
* Internal, external
* Morse taper, butt joint
* Geometry
* Abutment screw: access free, closed, type of screwhead, components of what system.
# Technical failures/complications
Until the first European Workshop on evidence-based reconstructive dentistry, held in Hünigen, Switzerland, 4–7 November 2006, there was no generally accepted definition for success and survival for reconstructions. Zöllner and Belser (2007) therefore suggested the following definitions:
* Success of abutment-reconstruction complex ("reconstruction"): survival without any biologic and/or technical complication
* Survival of abutment-reconstruction complex ("reconstruction"):
* On abutment level: abutment is still _in situ_
* On reconstruction level: reconstruction remaining _in situ_ with or without modification
* Alternatively: reconstruction remaining _in situ_ in its original extension with or without modification.
In addition, factors regarded as biological or technical failures were listed but not further defined:
* Biological complications of abutment-reconstruction complex ("reconstruction"):
* Natural abutment tooth: caries, loss of sensitivity, apical periodontitis, periodontitis
* Implant: peri-implant diseases, implant mobility, loss of sensitivity of adjacent tooth
* Technical complications of abutment-reconstruction complex ("reconstruction"):
* Tooth supported reconstruction: loss of retention, fracture of abutment, fracture of framework, fracture of veneering material
* Implant supported reconstruction: loss of retention/screw loosening/abutment loosening, loss of access hole restoration, fracture of implant, fracture of abutment, screws, fracture of framework, fracture of veneering material.
While describing the above-mentioned detailed characteristics of the implant-supported restorations, any defects and irregular observations are marked.
The suprastructures are inspected for signs of loosening, loss of retention, loss of friction, wear, attrition, fractures of frame work, of denture teeth, of porcelain, of veneers, discolorations, bacterial deposits, precision or misfit at margins, cement rests (Figs. 29-2 and 29-3).
**Fig. 29-2** Fractures of porcelain veneer at the distal aspects 35 and 46 as well as a porcelain chip off at 33. The patient was restored with three screw-retained porcelain fused to metal FDPs (I46 × I44/I43xxxxI33/I35I35). Three repairs within 3 years were needed. In the opposing jaw, the patient still had all his natural teeth. At night the patient wears an occlusal protective splint on an irregular basis.
The torque of occlusal screws can be checked where corresponding equipment is available. Obviously, loose screw-retained suprastructures are removed for further inspection, cleaning and retightening. Stable fixed restorations do not need to be disassembled if there were no complications reported by the patient and if the clinical examination did not reveal any technical problems.
**Fig. 29-3** Fracture of the denture tooth 13 as well as part of the veneer from a screw-retained extension prosthesis on five implants. In the lower jaw, the patient was restored with a fixed partial denture with bilateral distal extensions. The prosthesis could be removed and repaired.
Defective screw heads might complicate the removal of the suprastructure since screw drivers might not catch anymore. Occlusal screws that were tightened together with cementation might as well be very difficult to be removed with the regular instruments. In such cases, repair sets are needed to remove defective screws in a controllable standardized manner (Fig. 29-4). Repair sets might also be very helpful in cases with fractured abutment screws that are completely blocked in the implant (Luterbacher _et al_. 2000a) (Fig. 29-5). Abutments are also checked for their torque, the presence of bacterial deposits, corrosion products, cement rests, fractures, and deformations.
If replacement of a component is needed, the corresponding brand name and ordering number should be identified; a task that can be very tedious in the light of numerous implant producers and, in addition, a long list of copycat products (Jokstad _et al_. 2003).
Some manufacturers of implant components offer a complaint system to protect their customers from undue costs arising because of a potential error in production. Forms are completed with all the relevant information related to the loss of implants or a damaged component of the respective implant system. The defective components are sent in and exposed to a metallurgic evaluation and other tests. If the components were applied for the correct indications and a possible production error has been confirmed, the manufacturer will replace components and may even help to finance part of a new restoration as decided case by case.
**Fig. 29-4** (a) Removal of a screw-retained FDP using a screwdriver was impossible since the head of the occlusal screw was completely worn down due to attrition. The components of the repair set developed for the Straumann Dental Implant System® include an extraction bolt which can be tightened into a hole prepared with drills into the head of the occlusal screw. (b) Applying sufficient torque, the segmented part of the FDP is being removed together with the occlusal screw, the abutment, and the abutment screw. The implant was then used again for the support and fixation of a new extension prosthesis shown in Fig. 29-3.
**Fig. 29-5** (a) Application of the assembled components of the repair system developed for the Straumann Dental Implant System® for the removal of fractured abutment screws. The conical insert at the end of the handle secures the centered guidance of the drill. (b) After counter-clockwise drilling with ample cooling, the fractured portion of the abutment screw is removed. The threads are then recut by hand instruments with conical and cylindrical configurations.
**Fig. 29-6** (a,b) Screw-retained defect prosthesis on three implants in a fibula graft after excision of a malignant tumor. Function and phonetics are acceptable considering the severity of the defect. (c,d) After 5 years, some of the grafted bone has been resorbed. The soft tissues receded, leaving a large space underneath the pontics. Articulation and phonetics became more and more difficult. In addition, loss of saliva during speaking became intolerable. The FDP was removed and reshaped to fill out the missing soft tissues.
If the abutment was individualized, it may also be impossible to just replace the component and use the existing suprastructure. In such cases, a new impression at the implant level will be needed to replace the abutment; a remake of the entire restoration may be necessary.
# Function
## Functional analysis
A functional analysis of the dentition with fixed and/or removable dental prostheses on implants needs to be carried out according to standard protocols in prosthodontics and includes parameters assessing articulation, occlusion, phonetics, denture stability, etc.
## Articulation, phonetics
Disturbed articulation after placement of implant supported restorations may be very difficult to assess without the use of objective parameters (Fig 29-6). Heydecke _et al_. (2004) recorded test words articulated by 30 patients having adjusted to different implant-supported maxillary restorations for 2 months. Lay judges were asked to rate the quality of the articulation. This within-subjects crossover trial demonstrated that overdentures with or without palate enabled patients to produce better speech quality than with fixed prostheses on the implants.
# Implant
Cases with removable implant-borne restorations allow direct access for clinical inspection and examination of the implant components and the periimplant soft tissue conditions. Cemented or screw-retained crowns or fixed dental prostheses may complicate the access for visual inspection and probing.
**Fig. 29-7** (a) After removal of a screw-retained crown on an octa abutment, the amount of submucosal biofilm was impressive (3 years after placement of the crown). The epithetical lining of the emergence profile was ulcerated which led to bleeding after removal of the crown. (b) In a similar case, there were no obvious bacterial deposits detectable. The peri-implant soft tissues appeared epithelialized with few signs of inflammation.
## Clinical test of mobility
Presence or absence of mobility is checked manually/digitally or with the help of instruments trying to move the implants. A perceived mobility of the restoration _per se_ does not necessarily mean that the implant is loose. The connection suprastructure/abutment and/or abutment/implant might be loose leading to the mobility. Implant mobility can only be confirmed after disassembling all the components.
In the case of a multi-unit fixed restoration, the absence of mobility does not necessarily mean that the implants are all well integrated. Actual mobility might be obscured by the splinting effect.
## Electronic tools to assess the quality of osseointegration
Resonance frequency analyses and Periotest® readings were part of numerous study protocols to quantitate the stability of implants. Changes in the readings were interpreted to reflect biological processes such as bone apposition, bone remodeling, bone maturation or, in a negative sense, deterioriation of the firmness of the bone to implant connection. Recent evidence from the literature was condensed to the following consensus statements (Hobkirk & Wiskott 2006): stability may be confirmed by performing repeated Periotest® measurements of the same implant over time. Increases of these measurements, however, became evident, when the implants are clinically obviously loose. Implants with high implant stability quotient (ISQ) values during maintenance appear to stay firmly integrated, while decreasing ISQ values may be indicative of developing instability. For both biomechanical testing methods, however, the lack of normative values and the wide range of reported values for stable implants and potentially failing implants would not justify their routine clinical use.
## Bacterial deposits
The amount and distribution of visual bacterial deposits are evaluated at the emerging portion of the implant-borne restorations (implant neck, abutment, mesostructures, patrices) (Fig. 29-7). A _yes_ or _no_ for presence of bacterial deposits may be noted or marked in a scheme. In clinical studies, a gradual index such as the mPl (by Mombelli _et al_. 1987) has often been used.
# Soft tissues
## Mucosa
The inspection of the soft tissues will include the detection and description of visual signs of infection and/or other pathologic conditions, such as swelling, edema, redness, irregular keratinization, tattoos, pigmentation, hyperplasia, ulceration, soft tissue dehiscencies, or fistula. All soft tissues of the oral cavity, not only the peri-implant tissues, need to be examined (Fig. 29-8).
## Palpation/sensitivity
Palpation at the buccal aspects of the implants may assist in the detection of loose implants (osseo-disintegration). Palpation furthermore reveals pus, swelling and pain, and the exudation of grafting particles. During palpation and sensitivity testing any morbidity due to, for example, grafting procedures (Clavero & Lundgren 2003) or side effects of implant placement, e.g. close to the mandibular nerve, may be detected.
## Recession, pocket probing depth, probing attachment level, bleeding on probing
Measuring the localization of the margin of the mucosa in relation to a fixed reference point such as the connection suprastructure/abutment, abutment/implant, suprastructure/implant, suprastructure/mesostructure as well as the pocket probing depth (PPD) reflects the anatomic situation after implant placement and reconstructive rehabilitation. Clinical parameters assessed by means of probing were first described around the neck of a one-piece transmucosal implant and included the distance between the implant shoulder and the mucosal margin (DIM), and the pocket probing depth (PPD). By adding PPD and DIM, the probing attachment level was calculated (PAL) (Buser _et al_. 1990).
**Fig. 29-8** (a) This 55-year-old female patient is wearing a palate free overdenture. Signs of denture stomatitis are an alarming signal to reinforce plaque control using chlorhexidine gel and rinses. (b) The base of the overdenture as well as the locator® matrices appear to be kept clean.
Applying similar force, the insertion depth of a periodontal probe is usually deeper at implants compared to contralateral natural teeth. In addition, it seems to be easier to provoke bleeding after probing at implants compared to teeth (Brägger _et al_. 1997; Karoussis _et al_. 2004). Repeated probing using similar direction, localization, force, and the same references reveals stable conditions or increasing probing depths and/or increasing recession as signs of continuous loss of tissue or osseointegration.
With increasing PPD, the accuracy of repeated probing will decrease (Christensen _et al_. 1997). Precise readings of tissue destruction in deeper lesions are hindered by blocked access for probing and the lack of a continuous smooth surface to guide the probe tip apically. This occurs mostly at screw threads no longer covered by bone or horizontal steps between implants and abutments (Mombelli _et al_. 1997).
Similarly to periodontal disease, the absence of bleeding on probing (BoP) may reflect a stable condition, while repeated BoP may be indicative of a higher chance to develop tissue disintegration. Clinical and microbiological tests for monitoring tissue conditions during supportive periodontal therapy were performed in 19 patients, and the results indicated statistically significant better diagnostic characteristics of both tests at implants compared to teeth. The inclusion of an additional microbiologic test significantly enhanced the diagnostic characteristics of BoP alone at teeth as well as at implants (Luterbacher _et al_. 2000b).
Increased PPD combined with BoP and/or pus secretion may indicate various stages of mucositis or peri-implantitis.
According to one of the proposed concepts for the prevention and treatment of mucositis and periimplantitis (cumulative interceptive supportive therapy), a cascade of anti-infective and corrective treatment modalities is applied depending on the severity of the findings (Lang _et al_. 2000). The treatment decisions are based on the clinical findings described above. In case of a suspected peri-implantitis, radiographic evaluation may be required to visualize bone levels or changes in bone levels in relation to reference points. If antibiotics are considered, information on the microbiologic composition of plaque samples as well as resistance testing will assist in decision making.
# Esthetics
## Papillae, interdental space and type of mucosa
A comprehensive assessment and documentation of the soft tissue condition may be of importance, especially for fixed restorations in esthetically critical areas (Fig. 29-9). The appearance of papillae and interdental spaces can be evaluated objectively using various indices, possibly including metric measurement (Jemt 1997). When linear measurements and stable reference points were used, valuable parameters for the long-term observation of changes in the papilla characteristics could be obtained (Jemt & Lekholm 2005). This also required that no changes to the crown contour were made (Klinge & Meyle 2006).
Some factors, such as the thickness of the periimplant soft tissues, the amount of the available keratinized mucosa, the space between implants or between teeth and implants, and the underlying bone levels, may influence the esthetic appearance of the papilla/interdental space complex (Tarnow _et al_. 2000; Choquet _et al_. 2001; Gastaldo _et al_. 2004; Lee _et al_. 2005). In some cohorts reformation of papillae was also described (Jemt 1997; Chang _et al_. 1999). Metallic markers can be used to indicate the tip of the papilla in a radiograph in order to assess the distance between the underlying bone level and a papilla (Tarnow _et al_.1992). Assessment of the width of the keratinized mucosa can be facilitated by staining the lining nonkeratinized mucosa with Schiller's (IKI) solution (Fasske & Morgenroth 1958; Brägger _et al_. 1997).
**Fig. 29-9** A porcelain fused to metal crown was cemented on an implant of the Straumann Dental Implant System®. The clinical slides document the situation after cementation and after 1, 5, and 10 years. After 1 year, soft tissue seems to cover the implant shoulder and fill the interdental space: a result that was completely maintained over 5 and 10 years.
**Fig. 29-10** Fifteen years ago, implants were sometimes not correctly placed to fulfill today's esthetic expectations. As a disappointing result, implant margins as well as the implant body were shining through the thin mucosa of this 20-year-old female patient. Due to the continuous eruption of the neighboring teeth, soft tissues now cover the dark implants. The crowns on I13 and I22, however, are no longer in occlusion.
## Condition of adjacent teeth
Implants placed too closely to adjacent teeth might lead to unfavorable periodontal conditions. In some studies, alveolar bone loss was observed if distances were chosen below a minimum distance (Krennmair _et al_. 2003). Adjacent teeth might have been damaged while preparing the implant bed. Delayed loss of sensitivity (vitality) may lead to endodontic interventions.
Long-term vertical changes of anterior maxillary teeth adjacent to implants in 14 young and 14 mature adults were measured in radiographs. In both groups, the tooth eruption process resulted in considerable changes ranging between 0.1 mm and 1.65 mm and 0.12 mm to 1.86 mm (Bernard _et al_. 2004) after an average observation period of about 4 years.
The lack of an implant eruption may result in the formation of steps related to adjacent teeth, incisal edges, etc. Occlusal contacts may still be present, however, due to the different eruption in the opposing jaw; step formation can also be observed (Zachrisson 2006) (Fig. 29-10).
**Fig. 29-11** In this 25-year-old female patient, a full ceramic crown and mesostructure were placed on an implant of the Straumann Dental Implant System®. After only 3 years, a step appeared in relation to the adjacent incisal edges. In addition, the color shade of the full ceramic crown appears to be too dark due to the fact that the patient had been bleaching her teeth.
## Color shades
For a complete documentation of implant-supported restoration, a set of intraoral images of the area of interest may be desirable. In addition, an assessment of color shades based on visual or digital/electronic measurements are helpful. Of special concern are changes in color shade due to aging or bleaching of the adjacent natural teeth leading to noticeable unpleasant shade differences (Fig. 29-11).
Receding margins of the peri-implant mucosa result in visible implant components, potentially interfering with esthetics in visible zones. Even white ceramic components may result in an esthetically unfavorable situation if color matching over a wider range is not possible (Zachrisson 2006). Coverage of recessions or enlargement of the thickness of the mucosa can technically be achieved by means of free mucosa transplants. The predictability and the long-term success of such interventions remains to be assessed.
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# Chapter 30
# Risk Assessment of the Implant Patient
Gary C. Armitage and Tord Lundgren
* * *
Principles of risk assessment
Clinical information required for risk assessment
Technical procedures to help minimize risk
Local risk factors and conditions
Presence of ongoing oral infections
Systemic risk factors
Age
Smoking
Medication history
Immunosuppression
History of radiation therapy to the jaws
Diabetes mellitus
Metabolic bone disease
Connective tissue and autoimmune disorders
Xerostomia
Hematologic and lymphoreticular disorders
Genetic traits and disorders
Importance of behavioral considerations in risk assessment
Dental history of compliance behaviors
Substance use/abuse
Psychiatric/psychological issues
Lack of understanding or communication
Patient's expectations
Interest and commitment to post-treatment care and maintenance program
* * *
In the past few decades the widespread availability and successful use of dental implants have greatly expanded the treatment options for replacement of missing teeth. Data from numerous follow-up studies of the retention rates of implants indicate that well over 90% of the fixtures are functional for 5–10 years after insertion (Lindh _et al_. 1998; Berglundh _et al_. 2002; Weng _et al_. 2003; Fugazzotto _et al_. 2004; Pjetursson _et al_. 2004; Romeo _et al_. 2004). It is clear, however, that some implants fail. In addition, the risk for implant failures and complications is not evenly distributed among all people in a given population since implant problems tend to cluster in certain subsets of patients (Weyant & Burt 1993). There are many possible reasons for failure but it is generally acknowledged that biological, mechanical, or behavioral causes can be important. In general, any factor that increases the risk of developing periodontitis also increases the risk of implant failure. Therefore, in clinical practice it is essential that practitioners understand the possible reasons for implant failures so these threats to implant survival can be minimized. Risk assessment for endosseous implants is an evolving field and it is essential that clinicians have a working knowledge of the current literature dealing with risk factors for the development of implant complications and failure. Without this knowledge an intelligent assessment of risk cannot be conducted.
# Principles of risk assessment
Risk assessment is the deliberate and thoughtful evaluation of all circumstances that can affect the outcome of a therapeutic intervention. In the case of dental implants the assessment is intended to identify variables that increase the risk of complications leading to implant loss. In many cases, early identification of these variables makes it possible to avoid or eliminate them. At the very least, knowledge of the risk-altering variables allows the clinician to discuss with the patient circumstances that might affect implant survival. Risk assessment should be performed: (1) before placement of implants (designed to avoid high failure rates by identifying suitable candidates for implant treatment), (2) during the phase of implant placement and osseointegration (designed to identify and avoid technical issues that can affect implant survival), (3) during the phase of implant maintenance (designed to minimize failure by heading off problems), and (4) after an implant has failed and been removed. This "post-mortem" analysis tries to identify the causes of failure and incorporates the experience into future risk-assessment analyses of other patients.
In the literature the therapeutic outcomes of implant placement are usually described in terms of the fixture's survival, success, or its failure. A detailed discussion of these terms has been reviewed by others and will not be repeated here (Mombelli 1994; Esposito _et al_. 1998a). Criteria for these outcomes have not been consistently used in the literature. Success is often difficult to define since it implies that a large number of criteria have been met, such as stability, functionality, little or no change in bone support, radiographic evidence of osseointegration, absence of infection, lack of paresthesia, comfort, acceptable esthetics, and overall patient satisfaction. However, the criteria for "success" as presented by Albrektsson _et al_. (1986) over 20 years ago are still useful (Table 30-1).
**Table 30-1** Criteria for implant success, as suggested by Albrektsson _et al_. (1986)
1. That an individual, unattached implant is immobile when tested clinically
---
2. That a radiograph does not demonstrate any evidence of periimplant radiolucency
3. That vertical bone loss be less than 0.2 mm annually following the implant's first year of service
4. That individual implant performance be characterized by an absence of persistent and/or irreversible signs and symptoms such as pain, infections, neuropathies, paresthesia, or violation of the mandibular canal
5. That, in the context of the above, a successful rate of 85% at the end of a 5-year observation period and 80% at the end of a 10-year period be a minimum criterion for success
Many authors simply use the outcome of implant "survival" which implies that at least some criteria for overall success have been met. An implant can, of course, survive and meet all of the criteria for success except those dealing with patient satisfaction. If the patient regards the implant as a failure, it is a failure since a major criterion for success has not been met (i.e. patient satisfaction). Since implant failure is often the end result of a gradual accumulation of unwanted events, most studies use surrogates for failure such as the development of implant mobility, abscess formation, and loss of function. Therefore in many papers, failure is defined as the appearance of failure-associated complications such as the development of peri-implantitis.
There are very few _absolute_ or unequivocal contraindications to the placement of dental implants. Depending on a number of patient-centered circumstances, dental implants can be considered even in individuals who are at an elevated risk for implant failure. Like most situations in clinical practice, the potential benefits of an intervention need to be weighed against the morbidity of potential adverse outcomes.
A _risk factor_ is an environmental, behavioral, or biological factor that, if present directly increases the probability of a disease (or adverse event) occurring and, if absent or removed, reduces that probability. Risk factors are part of the causal chain, or expose the host to the causal chain (Genco _et al_. 1996). In the case of risk assessment for implant failure, risk factors can be broadly categorized as local, systemic, or behavioral factors (Table 30-2). In general, risk factors for implant failure make outcomes of implant treatment less predictable. A _risk indicator_ is a probable risk factor that has not been confirmed by carefully conducted longitudinal studies. A _risk predictor_ is a characteristic that is associated with an elevated risk for a disease (or adverse event), but may not be part of the causal chain (Genco _et al_. 1996). In the case of dental implants, a good risk predictor might be a documented history of the failure of previously inserted implants. In the risk assessment process for multifactorial conditions, such as implant failure, it is important to remember that the presence of several risk factors is required to result in implant loss. One or two risk factors are rarely sufficient to cause implant failure.
**Table 30-2** Potential risk factors for peri-implantitis and implant failure that should be considered in the risk-assessment process
## Clinical information required for risk assessment
The process of risk assessment begins with taking thorough medical/dental histories and conducting a complete examination of the prospective candidate for dental implants. Details of these procedures are discussed in Chapters 27–29 and will not be repeated here. However, items that are required for risk assessment include anything that helps identify individuals who might be at an increased risk of implant complications and failure.
A comprehensive evaluation of the patient should contain a review of past dental history including earlier periodontal treatment, reasons for tooth loss, how extraction sockets were treated at the time of extraction, history of increased susceptibility to infection, and awareness of parafunctional habits such as clenching and grinding. It should also include an evaluation of the patient's socioeconomic status and willingness to adjust to an often long treatment process. Dissatisfaction with earlier dental treatment may indicate an increased risk for complications during implant therapy.
The comprehensive medical history should include past and present medications and any substance use or abuse. A standard medical history form filled out and signed by the patient is an efficient way to collect basic information. This should always be followed by a verbal interview to explore in more depth any potential medical risks of implant therapy. If any uncertainties remain regarding the patient's health after the interview, a written medical consultation should be obtained from the patient's physician.
### Components of a complete examination
A complete intraoral examination should be performed to determine the feasibility of placing implants in desired locations. This examination includes oral hygiene status, periodontal status, jaw relationships, occlusion, signs of bruxism, temporomandibular joint conditions, endodontic lesions, status of existing restorations, presence of non-restored caries, crown–root ratio, interocclusal space, available space for implants, ridge morphology, soft and hard tissue conditions, phonetics, and prosthetic restorability.
An appropriate radiographic evaluation of the quality and quantity of available bone is required in order to determine the optimal site(s) for implant placement. Assessments from periapical radiographs, panoramic projections, and tomographic cross-sectional imaging can individually or in combination be helpful diagnostic tools. It is important to understand that accurate estimations of bone height and width cannot be made without a comprehensive clinical examination followed by cross-sectional tomographic images. A comprehensive radiographic evaluation minimizes the risk of injuring vital anatomic structures during the surgical procedure and is also helpful in determining which cases require bone augmentation surgery before implants can be placed. A custom-made stent with radiopaque markers worn by the patient during the radiographic imaging can help locate the proper position for implant placement and also help in evaluation of the relationship between the planned implant location and available bone.
An evaluation of the quality and quantity of peri-implant soft tissues at the proposed implant site will help determine how closely this tissue will mimic the appearance of gingival tissue once the implant has been inserted. The presence of keratinized mucosa around a dental implant is an important part of an esthetically successful dental implant. It is important to evaluate the patient's perception of esthetics prior to implant placement. This is especially true in situations with compromised hard and soft tissues where esthetics can be a real challenge. Diagnostic casts and intraoral photographs can be helpful in evaluating potential esthetic outcomes as well as in the overall treatment-planning process. In general, to minimize the risk of implant complications and failure, any diseases of the soft or hard oral tissues should be treated before implant therapy.
## Technical procedures to help minimize risk
### Minimizing post-surgical infection
Post-operative infections increase the risk of early implant failure. It is important to perform implant surgeries with a strict hygiene protocol to minimize bacterial contamination of the surgical site. Although the incidence of post-operative infection associated with implant placement is only about 1% (Powell _et al_. 2005), some clinicians attempt to reduce this risk by prescribing pre-operative systemic antibiotics (Dent _et al_. 1997; Laskin _et al_. 2000). However, the value of pre-operative antimicrobial treatment has not been established in randomized placebo-controlled clinical trials (Lawler _et al_. 2005). In addition, the results of several case–control studies indicate that there is no advantage in using antibiotics in conjunction with implant placement (Gynther _et al_. 1998; Morris _et al_. 2004; Powell _et al_. 2005).
### Minimizing tissue damage
Surgical techniques that are designed to avoid unnecessary tissue damage should be used whenever possible. Thermal damage to bone can be caused during the drilling sequence if dull drills are used or if osteotomy is performed without using enough liquid coolant. It is important to follow the manufacturer's guidelines and change the drills in the surgical kit accordingly.
### Achieving early stability of implant
An important goal of the osteotomy is to prepare a site for the implant that will allow good stability of the implant during the healing process (Sennerby _et al_. 1992). Post-insertion stability lowers the risk of implant complications or failure. The presence of good-quality bone with a sufficient amount of cortical bone at the implant site is desirable to achieve this objective. In situations where there are less than optimal bone conditions (i.e. thin cortex, low trabecular density), increased initial stability can still be established by using implants with rough surfaces, parallel walls, and optimal height and width. In a study of implants placed in rabbit tibias it was found that good initial stability could be achieved by bicortical placement of an implant that engages two cortical layers of bone (Ivanoff _et al_. 1996). However, the same authors found that in a 15-year retrospective study in humans, bicortically anchored implants failed nearly four times more often than the monocortical ones (Ivanoff _et al_. 2000). They speculated that the overambitious fixation of the bicortical anchorage increased the likelihood of implant fractures that accounted for 80% of the failures in the study.
### Avoiding anatomic structures
Anatomic structures that are at risk of serious collateral or accidental damage during the placement of implants include: nerves, blood vessels, floor of the mouth, nasal cavity, maxillary sinuses, and adjacent teeth. The risks to these structures can be minimized by careful assessment of radiographs and meticulous treatment planning. It is important to remember that the drills used for osteotomies penetrate further than the depth indicators on the drills. In certain situations radiographic indicator methods should be performed during surgery to help determine direction of the implant and its proximity to vital structures.
For implants that are to be placed in the mandible, the distance from the edentulous alveolar crest to the upper border of the inferior alveolar canal should be assessed from cross-sectional tomographic radiographs. The safety zone between the tip of the implant and the border of the canal should be at least 1–2 mm. Patients with compromised vertical bone dimension can sometimes be treated by placing multiple shorter implants of optimal width followed by splinting the prosthetic crowns together during the restorative phase of therapy.
The position of the mental foramen should be identified and located when implant surgeries in the premolar and molar areas of the mandible are performed. In some situations a loop of the nerve can be found to extend mesially. In one report the anterior loop of the mental neurovascular bundle extended mesially from 1.1–3.3 mm and a safety zone of 4 mm was recommended to avoid damaging the nerve during implant placement (Kuzmanovic _et al_. 2003). When placing an implant in the anterior part of the maxilla the size and location of the incisive papilla need to be determined. In addition, it must be established if there is enough bone in the area to place an implant or if the area needs to be grafted.
Anatomic concavities are frequently found on the lingual side of the mandible. It is important to avoid perforating the lingual plate during preparation of the implant site since perforations in this location can result in extensive and even life-threatening bleeding (Bruggenkate _et al_. 1993). A safe way of performing surgery in this area is to reflect a lingual flap at least to a level corresponding to the length of the implant to be placed. If this precaution is taken, any perforation that might occur is detected before any extensive damage and serious bleeding occur.
Some of the challenges of treating the partially edentulous patient are related to biological and functional differences between teeth and implants. If these differences are ignored there is an increased risk for complications. For example, in cases where there are compromised hard and soft tissues a few implants may not be able to withstand heavy occlusal forces associated with extensive posterior reconstructions (Albrektsson _et al_. 1988). Differences in morphology between implants and teeth can present another challenge. In the anterior part of the mouth an implant should blend in with the neighboring natural teeth. To accomplish this, an implant with the correct diameter must be selected and then placed in the optimal position in order to mimic a tooth esthetically and functionally.
After tooth extractions in the maxillary anterior region the alveolar ridge resorbs in a palatal direction. This will affect the position in which the anterior implants need to be placed since the relation of the implants to the lip and opposing dentition is critically important for a successful outcome (Jansen & Weisgold 1995). Where to place anterior implants in patients with a high smile line and thin periodontal tissues should be carefully evaluated to achieve acceptable esthetic and functional results.
# Local risk factors and conditions
## Presence of ongoing oral infections
There are abundant data showing that poor oral hygiene and microbial biofilms are important etiologic factors leading to the development of peri-implant infections and implant loss (Mombelli _et al_. 1987; Jepsen _et al_. 1996; Salcetti _et al_. 1997; Esposito _et al_. 1998a,b; Lindquist _et al_. 1988; Listgarten & Lai 1999; van Winkelhoff _et al_. 2000; Heydenrijk _et al_. 2002; Quirynen & Teughels 2003; Fugazzotto _et al_. 2004). Therefore any risk assessment for implant survival should include an evaluation of the patient's ability to perform oral hygiene procedures (Salvi & Lang 2004).
### Periodontitis
There are several reasons to believe that untreated or incompletely treated periodontitis increases the risk for implant failure. First, there are case reports that suggest an association (Malmstrom _et al_. 1990; Fardal _et al_. 1999). Second, a similar subgingival microbiota has been found in pockets around teeth and implants with similar probing depths (Papaioannou _et al_. 1996; Sbordone _et al_. 1999; Hultin _et al_. 2000; Agerbaek _et al_. 2006). Third, evidence exists that periodontal pockets might serve as reservoirs of pathogens (Apse _et al_. 1989; Quirynen & Listgarten 1990; Papaioannou _et al_. 1996) that hypothetically can be transmitted from teeth to implants (Quirynen _et al_. 1996; Sumida _et al_. 2002).
Studies dealing with the microbiota of failing or failed implants clearly indicate the presence of multiple periodontal pathogens (Table 30-3). However, one of the striking features of the microbiota associated with implant failures is its extensive diversity. It would be naïve to assume that infections around implants are due to a narrow range of microorganisms. A more realistic view is that peri-implant infections are caused by a consortium of multiple microorganisms living on the implant surface in a biofilm. Contrary to the view of some (Heydenrijk _et al_. 2002), peri-implant infections are not simply caused by Gram-negative anaerobic bacteria. Certainly this group of bacteria is important, but yeasts and Gram-positive bacteria such as _Micromonas micros_ and _Staphylococcus_ species are often implicated in peri-implant infections (Table 30-3). Furthermore, in the implant literature the methods used to examine subgingival biofilms have primarily relied on microscopic (morphologic), cultural, and DNA probe analyses to characterize the microbiota. Culture-independent molecular analyses (e.g. studies of 16S ribosomal RNA gene sequences) have not been used to characterize the microbiota associated with implant failures. Application of such techniques to the subgingival microbiota associated with periodontitis has revealed the existence of a more diverse and complex microbial community than can be detected by conventional methods (Paster _et al_. 2001; Brinig _et al_. 2003; Lepp _et al_. 2004). In the case of periodontitis it is estimated that only about 50% of the subgingival flora can be characterized using conventional methods (Wilson _et al_. 1997) and therefore culture-independent analyses are required to get a more complete picture. This will probably also be true of the peri-implant subgingival microbiota once culture-independent molecular methods of analyses are applied to this ecosystem. Based on the documented diversity of the microbiota associated with failing implants, it is unlikely that testing for the presence of a small number of suspect bacteria for risk assessment purposes would have any clinical value.
**Table 30-3** Components of the subgingival microbiota frequently (≥10%) detected around failed or failing implants
Subgingival sites are micro-ecosystems that are preferentially colonized by oral bacteria well adapted to thriving in such environments. Indeed, subgingival sites are the natural or preferred habitat of a diverse group of oral microorganisms. In an interesting study of 15 patients, Devides and Franco (2006) sampled mucosa-associated biofilms of edentulous sites with paper points and analyzed the specimens using polymerase chain reaction (PCR) methods to detect certain periodontal pathogens. At the edentulous sites _Aggregatibacter actinomycetemcomitans_ was detected in 13.3% of subjects, _Prevotella intermedia_ was detected in 46.7% of subjects, and _Porphyromonas gingivalis_ was not detected. Six months after placement of endosteal implants at the same sites, subgingival plaque samples taken from around the implants were positive for _A. actinomycetemcomitans_ in 73.3% of subjects, _Pr. intermedia_ in 53.3% of subjects, and _P. gingivalis_ in 53.3% of subjects. None of the implants showed any clinical signs of either failure or peri-implantitis. These results indicate that healthy subgingival sites around implants are readily colonized by periodontal pathogens without any concomitant development of clinically detectable disease. The mere presence of PCR-detected pathogens is not a valid surrogate for peri-implant disease.
It is important to remember that the microbiota adjacent to failing implants will differ depending on the cause of the failure. For example, Rosenberg _et al_. (1991) demonstrated that the microbiota associated with implants failing because of traumatic loads was different to that found around implants failing because of infection.
There are several reports that the survival rate of implants is decreased when the patient has a history of periodontitis (Hardt _et al_. 2001; Evian _et al_. 2004; Karoussis _et al_. 2004; Wagenberg & Froum 2006). One implication of these observations is that patients who have had periodontitis might also be more susceptible to peri-implant infections. However, this is clearly not always the case since it has also been demonstrated that periodontally compromised patients who have lost a considerable amount of alveolar bone can be successfully treated with dental implants (Nevins & Langer 1995; Ellegaard _et al_. 1997; Sbordone _et al_. 1999). Since there is no clear-cut consensus in the literature on this topic, in risk-assessment discussions with patients it is a good idea to emphasize that based on their history of periodontitis they might be at an increased risk of developing peri-implantitis and therefore should be extra diligent in adhering to a rigorous post-insertion implant maintenance program.
### Endodontic infections
The presence of untreated or insufficiently treated endodontic infections adjacent to the site of implant placement can adversely affect the outcome (Sussman & Moss 1993; Shaffer _et al_. 1998). There are numerous reports of retrograde peri-implantitis in which it is hypothesized that a periapical infection on a tooth spreads to an adjacent implant (Ayangco & Sheridan 2001; Chaffee _et al_. 2001; Jalbout & Tarnow 2001; Quirynen _et al_. 2005b). However, successful retention of implants has been reported when implants were inserted immediately after extraction of endodontically infected teeth (Villa & Rangert 2005).
Based on the strength of existing data discussed above, it is highly recommended that any existing periodontal or endodontic infections should be controlled before dental implants are placed. Although the presence of ongoing oral infections does not guarantee that implants will fail, such infections appear to increase the risk of failure. Finally, since it has been documented that some peri-implant infections may be associated with _Candida_ spp. (Table 30-3) it is probably wise to control and treat any existing candidiasis before implants are inserted.
# Systemic risk factors
## Age
In adult patients, age is usually not considered an important risk factor for implant loss. Indeed, most longitudinal studies of survival rates of implants include some subjects who are well over 75 years of age (Dao _et al_. 1993; Hutton _et al_. 1995; Nevins & Langer 1995; Davarpanah _et al_. 2002; Becktor _et al_. 2004; Fugazzotto _et al_. 2004; Karoussis _et al_. 2004; Fransson _et al_. 2005; Herrmann _et al_. 2005; Quirynen _et al_. 2005a; Mundt _et al_. 2006; Wagenberg & Froum 2006). An upper age limit is usually not listed as an exclusion criterion in such studies. It is clear that implants can be quite successful when placed in patients who are in their eighth and ninth decades of life. Several reports indicate that there is not a statistically significant relationship between age of the patient and implant failure (Dao _et al_. 1993; Hutton _et al_. 1995; Bryant & Zarb 1999; Fransson _et al_. 2005; Herrmann _et al_. 2005; Mundt _et al_. 2006; Wagenberg & Froum 2006). However, a thorough risk-assessment process involves evaluation of multiple possible risk factors. It is possible that there may have been some selection bias in the above studies since some older patients might have been excluded for medical reasons. Older individuals included in the above studies may be atypical in that they were healthy enough to be good candidates for implant placement.
In one retrospective study of the success of 4680 dental implants placed by a single surgeon over a 21-year period in 1140 patients, it was reported that increasing age was strongly associated with implant failure (Moy _et al_. 2005). A univariate analysis of the data indicated that compared to patients younger than 40 years (n = 181), patients in the 60–79-years age group (n = 499) had a significantly higher risk of implant failure (relative risk = 2.24; P < 0.05). However, in a multivariate analysis of the data from the entire study population, age was not a significant predictor of implant failure (Moy _et al_. 2005).
At the other end of the spectrum, a potential problem associated with the placement of dental implants in still-growing children and adolescents is the possibility of interfering with growth patterns of the jaws (Op Heij _et al_. 2003). Osseointegrated implants in growing jaws behave like ankylosed teeth in that they do not erupt and the surrounding alveolar housing remains underdeveloped. Dental implants can be a superb service to young people who have lost teeth due to trauma or have congenitally missing permanent teeth. However, because of the potential deleterious effects of implants on growing jaws it is highly recommended that implants not be placed until craniofacial growth has ceased or is almost complete (Thilander _et al_. 2001).
## Smoking
Based on data generated by several follow-up studies of implant survival, cigarette smoking is often identified as a statistically significant risk factor for implant failure (Bain & Moy 1993; Lindquist _et al_. 1997; Wilson & Nunn 1999; Feloutzis _et al_. 2003; Gruica _et al_. 2004; Karoussis _et al_. 2004; Levin _et al_. 2004; Galindo-Moreno _et al_. 2005; Moy _et al_. 2005; Nitzan _et al_. 2005; Mundt _et al_. 2006). In addition, smoking has been associated with increased post-operative complications after sinus-lift operations and placement of onlay bone grafts (Levin _et al_. 2004).
Smoking is now generally accepted as an important modifiable risk factor for the development and progression of periodontitis (Johnson & Hill 2004). The reasons that smokers are more susceptible to both periodontitis and peri-implantitis are complex, but usually involve impairment of innate and adaptive immune responses (Kinane & Chestnutt 2000; Johnson & Hill 2004) and interference with wound healing (Johnson & Hill 2004; Labriola _et al_. 2005). Smoking is such a strong risk factor for implant failure that some clinicians highly recommend smoking-cessation protocols as part of the treatment plan for implant patients (Bain 1996; Johnson & Hill 2004).
Nevertheless, it should be emphasized that smoking is not an absolute contraindication for the placement of dental implants. Indeed, there are reports indicating that smoking did not adversely affect the rate of implant survival (Peleg _et al_. 2006; Wagenberg & Froum 2006). For multifactorial problems such as peri-implantitis and implant failure, the presence of one risk factor alone is usually insufficient to cause the adverse outcome.
## Medication history
### Bisphosphonates
Bisphosphonates are a widely prescribed class of drugs used for the treatment of osteoporosis and to reduce the bone-lytic effects of certain malignancies such as multiple myeloma and metastatic breast cancer (Woo _et al_. 2006). These pyrophosphate drugs are potent inhibitors of osteoclast activity that also have anti-angiogenic effects. The drugs have a high affinity for hydroxyapatite and are rapidly incorporated into all parts of the skeleton and have a very long half-life (i.e. decades). Relative potencies of the agents depend on their formulation (Table 30-4). An uncommon complication associated with the use of bisphosphonates is the increased risk of developing osteochemonecrosis or osteonecrosis of the jaws (ONJ) (Ruggiero _et al_. 2004; Marx _et al_. 2005; Braun & Iacono 2006). The vast majority of cases of ONJ occur in cancer patients who have received high-potency aminobisphosphonates (e.g. zoledronate, pamidronate) given intravenously to decrease the osteolytic effects of multiple myeloma or malignancies that have metastasized to bone (e.g. breast or prostate cancer).
Of major concern to the prospective implant patient who has been taking an oral bisphosphonate for osteoporosis is the possible risk of developing ONJ after implant placement. Oral bisphosphonates have been reported to be associated with implant failure (Starck & Epker 1995) and ONJ (Ruggiero _et al_. 2004; Marx _et al_. 2005). Although rare, the risk is real. Since bisphosphonates tightly bind to hydroxyapatite and have a very long half-life, it is likely that the length of time a patient has been taking oral bisphosphonates is important in determining the level of risk. Since oral bisphosphonates slowly accumulate in bone with time, an osteoporosis patient who has been taking the drug for 1 year is at a lower risk of developing ONJ or implant failure than someone who has been on the drug for many years. In general, it is not recommended that implants be placed in patients who have been on the drug for more than 3 years. It has been suggested by some that prolonged use of bisphosphonates is a contraindication to implant placement (Scully _et al_. 2006).
**Table 30-4** Relative potency for inhibition of osteoclast activity of various bisphosphonates, adapted from Braun & Iacono (2006)
**Drug**| **Manufacturer**| **Potency factor**
---|---|---
Etidronate (Didronel®)| Procter & Gamble| 1
Tiludronate (Skelid®)| Sanofi| 10
Clodronate (Bonefos®)| Schering| 10
Clodronate (Loron®)| Roche| 10
Neridronate (Nerixia®)| Abiogen| 100
Pamidronate (Aredia®)| Novartis| 100
Alendronate (Fosamax®)| Merck| 500
Ibandronate (Bondronat®)| Roche| 1 000
Risedronate (Actonel®)| Procter & Gamble| 2 000
Zoledronate (Zometa®)| Novartis| 10 000
It is important to remember that bone-remodeling processes are severely inhibited in patients who have been chronically taking oral bisphosphonates for osteoporosis. Because of this such patients are poor candidates for bone-grafting procedures and sinus-lift operations. Therefore, many ridge-augmentation procedures that often make implant placement possible are ill advised in these individuals.
### Drug-influenced gingival enlargement
It is well known that one of the side effects of phenytoin, calcium-channel antagonists, and cyclosporin is gingival enlargement in about 25–50% of the individuals who take one or more of these drugs (Peñarrocha-Diago _et al_. 1990; Hassell & Hefti 1991). Gingival enlargement has also been reported around dental implants in individuals taking either phenytoin (Chee & Jansen 1994) or a calcium-channel antagonist (Silverstein _et al_. 1995). When there is significant gingival enlargement around teeth or implants, oral hygiene and maintenance procedures can become quite difficult. Therefore, medications associated with gingival enlargement should be considered in the overall risk assessment prior to implant placement.
### Cancer chemotherapy
Oral cancer patients are frequently candidates for the placement of endosteal dental implants since prostheses designed to replace missing portions of the jaws need to be anchored to implants. Since anti-mitotic drugs used as chemotherapy for cancer might affect wound healing and suppress certain components of the immune system, it is important to know if these drugs interfere with osseointegration and success of dental implants. In a retrospective study, implant success was compared in 16 oral cancer patients who had no chemotherapy with the success in 20 patients who received postsurgical adjuvant chemotherapy with either cis- or carboplatin and 5-fluorouracil (Kovács 2001). It was found that these drugs did not have any detrimental effects on the survival and success of implants placed in the mandible.
It has also been reported that some cancer patients who received cytotoxic antineoplastic drugs experienced infections around existing transmucosal or endosteal dental implants (Karr _et al_. 1992). Therefore, it is important to recognize that many anticancer drugs suppress or kill cells necessary for optimal innate and adaptive immunity. Patients who are receiving cancer chemotherapy should have thorough periodontal and implant maintenance care to minimize the development of adverse events.
### Anticoagulants
Patients who have blood-coagulation disorders or are taking high doses of anticoagulants are at an elevated risk of experiencing post-operative bleeding problems after implant surgery. Some patients with coagulation disorders may be at an elevated risk of implant failure (van Steenberghe _et al_. 2003) whereas other patients who chronically take oral anticoagulants can safely receive dental implants (Weischer _et al_. 2005). Patients who are on continuous oral anticoagulant therapy (e.g. coumarin derivatives) to reduce the risk of thromboembolic events and require dental implants for optimal restorative care should be evaluated on a case-by-case basis. Most of these patients can safely continue their warfarin or other anticoagulant therapy when they have their dental implant surgery (Wahl 1998, 2000). In such patients, local bleeding after the placement of dental implants can usually be well controlled by conventional hemostatic methods. The risk of developing life-threatening bleeding or bleeding that cannot be controlled using local measures following placement of dental implants is so low that there is no need to stop oral anticoagulant therapy (Beirne 2005).
Therapeutic levels of an anticoagulant drug such as warfarin are measured by the international normalized ratio (INR) which is the patient's prothrombin time (PT) divided by the mean normal PT for the laboratory (i.e. PTR). The PTR is then adjusted for the reagents used to arrive at a standardized INR value that will be comparable anywhere in the world. A higher INR reflects a higher level of anticoagulation with an attendant increased risk of hemorrhage (Herman _et al_. 1997). Although there are insufficient data to draw any evidence-based conclusions, placement of single implants is regarded as safe when the INR target values are 2.0–2.4 (Herman _et al_. 1997).
### Immunosuppressive agents
Any medication that interferes with wound healing or suppresses components of innate and adaptive immunity can theoretically increase the risk of implant failure. Corticosteroids are a good example. They are potent anti-inflammatory agents that are widely used for the management of a wide variety of ailments. These drugs can interfere with wound healing by blocking key inflammatory events needed for satisfactory repair. In addition, through their immunosuppressive effects on lymphocytes, they can increase the rate of post-operative infections. In general, these undesirable effects are greatest in patients who take high doses of the drugs for long periods of time.
## Immunosuppression
In the early years of the AIDS epidemic placement of dental implants was ill advised since affected patients developed major life-threatening oral infections. With the advent of effective HAART (highly active anti-retroviral therapy) regimens, most HIV-positive patients who take their medications live for many years without developing severe opportunistic infections. There have been no controlled studies dealing with the risk of dental implant failures in HIV-positive individuals. However, several case reports suggest that placement of dental implants in HIV-positive patients is not associated with elevated failure rates (Rajnay & Hochstetter 1998; Baron _et al_. 2004; Shetty & Achong 2005; Achong _et al_. 2006). Low T-helper (CD4) cell counts (i.e. <200/μL) do not appear to predict increased susceptibility to intraoral wound infections or elevated failure rates of dental implants (Achong _et al_. 2006). Although more studies are needed, it appears that it is safe to place dental implants if the patient's HIV disease is under medical control.
## History of radiation therapy to the jaws
Patients who have received radiation (i.e. absorbed dose of ≥60 Gy) to the head and neck as part of the treatment for malignancies are at an increased risk of developing osteoradionecrosis (ORN). Most cases of this complication of cancer treatment are triggered by the extraction of teeth or other oral surgery procedures such as insertion of implants. Implant failure rates of up to 40% have been reported in patients who have had a history of radiation therapy (Granström _et al_. 1993, 1999; Beumer _et al_. 1995; Esposito _et al_. 1998a,b; Lindquist _et al_. 1988). At one time it was believed that ORN was due to vascular derangement and hypoxia of bone cells caused by the tissue-damaging effects of radiation (Teng & Futran 2005). Based on this hypothesis, it has been recommended that oral surgical procedures in patients at risk of ORN be performed in conjunction with hyperbaric oxygen (HBO) therapy. Indeed, Granström _et al_. (1999) reported that use of HBO therapy improved implant survival rates. However, the value of HBO therapy for the management of ORN has been called into question partly based on a placebo-controlled, randomized clinical trial (Annane _et al_. 2004) and other reports showing no advantage to HBO interventions (Maier _et al_. 2000; Gal _et al_. 2003). In addition, a systematic review by Coulthard _et al_. (2003) indicated that there is no high-quality evidence that HBO therapy improves implant survival in irradiated patients.
It is now believed that the pathogenesis of ONR is much more complex than a simple hypoxia-related phenomenon related to poor vascularity of irradiated tissues. Current evidence supports the view that ONR is a fibroatrophic process (Teng & Futran 2005). From the perspective of risk-assessment procedures for implant placement, patients who have a history of irradiation to the jaws should be considered at high risk for implant failure and HBO interventions will probably not lower that risk.
## Diabetes mellitus
Although there is a slight tendency for more failures of implants in a diabetic compared to a non-diabetic population, the increased risk is not substantial in patients who are under good metabolic control (Shernoff _et al_. 1994; Kapur _et al_. 1998; Balshi & Wolfinger 1999; Fiorellini _et al_. 2000; Morris _et al_. 2000; Olson _et al_. 2000). In the general population the 5-year overall success rate for implants is approximately 95% (Buser _et al_. 1997; Weber _et al_. 2000; Davarpanah _et al_. 2002; Fugazzotto 2005), whereas in a diabetic population the rate is approximately 86% (Fiorellini _et al_. 2000).
Diabetics under suboptimal metabolic control often experience wound-healing difficulties and have an increased susceptibility to infections due to a variety of problems associated with immune dysfunctions (Geerlings & Hoepelman 1999). In the risk evaluation of diabetics it is important to establish the level of metabolic control of the disease. A useful test to determine the level of control over the last 90 days is a blood test for glycosylated hemoglobin (HbA1c). This is a test for the percentage of hemoglobin to which glucose is bound. Normal values for a non-diabetic or a diabetic under good metabolic control are HbA1c <6–6.5% and fasting blood glucose <6.1 mmol/L (110 mg/dL). Diabetics with HbA1c values of ≥8% are under poor control and have an elevated risk of encountering wound healing problems and infection if dental implants are placed.
## Metabolic bone disease
### Osteoporosis
Osteoporosis is a complex group of systemic skeletal conditions characterized by low bone mass and microarchitectural deterioration of bone tissue. Osteoporotic bone is fragile and has an increased susceptibility to fracture. Primary osteoporosis is a common condition and is diagnosed when other disorders known to cause osteoporosis are not present. Secondary osteoporosis is diagnosed when the condition is related to, or occurs as a consequence of, osteoporosis-inducing circumstances. These might include diet (e.g. starvation, calcium deficiency), congenital conditions (e.g. hypophosphatasia, osteogenesis imperfecta), drugs (e.g. alcohol abuse, glucocorticoids), endocrine disorders (e.g. Cushing's syndrome), and certain systemic diseases (e.g. diabetes mellitus, rheumatoid arthritis). Osteoporosis is assessed using bone densitometry in which a patient's bone mass or bone mineral density (BMD) is determined. BMD refers to grams of bone mineral per square centimeter of bone cross-section and is expressed in units of g/cm2.
There are multiple case reports that conclude that osteoporosis alone is not a significant risk factor for implant failure (Dao _et al_. 1993; Friberg 1994; Fujimoto _et al_. 1996; Friberg _et al_. 2001). Implants placed in individuals with osteoporosis appear to successfully osseointegrate and can be retained for years. However, in cases of secondary osteoporosis there are often accompanying illnesses or conditions that increase the risk of implant failure (e.g. poorly controlled diabetes mellitus, corticosteroid medications). Therefore, in the risk-evaluation process the presence of osteoporosis should alert the clinician to the possible presence of osteoporosis-associated circumstances that are known to increase the risk of implant failure.
In the implant literature the concept of "poor bone quality" was introduced by Lekholm and Zarb (1985). This is something quite different to osteo porosis. Poor bone quality refers to the subjective appraisal of the presence and amount of compact and trabecular bone as visualized in radiographs. The radiographic appraisal of bone quality is reassessed during explorative drilling at the fixture-preparation site. The assessment system uses the following four groups:
* Type 1 = almost the entire jaw is comprised of homogenous compact bone
* Type 2 = a thick layer of compact bone surrounds a core of dense trabecular bone
* Type 3 = a thin layer of cortical bone surrounds a core of dense trabecular bone of favorable strength
* Type 4 = a thin layer of cortical bone surrounds a core of low density trabecular bone.
The system has serious reproducibility problems that limit its usefulness in the risk-assessment process. Nevertheless, there are reports indicating that jaw bone quality is significantly related to implant failure especially when there is type 4 bone (Jaffin & Berman 1991; Hutton _et al_. 1995; Herrmann _et al_. 2005).
## Connective tissue and autoimmune disorders
### Scleroderma
Systemic sclerososis or scleroderma is a chronic autoimmune disease that targets the skin, lungs, heart, gastrointestinal tract, kidneys, and musculoskeletal system. The disease is characterized by widespread tissue fibrosis, endothelial dysfunction of small blood vessels, and formation of auto-antibodies against a number of tissue components. The skin loses much of its flexibility and becomes leatherlike. Patients often experience stiffening of the finger joints making it almost impossible to grasp items such as a toothbrush and other oral hygiene devices. The lips become so stiff and taut that opening the mouth is restricted to only a few centimeters. As a result of these access problems, all types of dental care (i.e. self-administered and professionally delivered) become extraordinarily difficult. The overall effect is long-standing poor oral hygiene leading to the inevitable loss of multiple teeth due to caries and periodontal disease.
There are no well controlled studies on the success rates of dental implants in patients with scleroderma. However, there are some case reports showing that patients with this disease can have implants successfully placed and maintained for several years (Jensen & Sindet-Pedersen 1990; Patel _et al_. 1998; Hodgson _et al_. 2006). If the decision is made to place dental implants in patients with scleroderma, it is critical that a rigorous maintenance program be incorporated into the treatment plan.
### Systemic lupus erythematosus
Systemic lupus erythematosus (SLE) is an autoimmune disease that affects many organ systems, with the joints, kidneys, heart, and lungs being the most commonly affected. It is well established that SLE patients have increased susceptibility to many opportunistic infections (Zandman-Goddard & Shoenfeld 2003; Bosch _et al_. 2006). The reasons for this increased susceptibility are not well understood but SLE-associated abnormalities of both humoral and cellular immunological responses and use of immunosuppressive therapy (e.g. corticosteroids) are undoubtedly important. If implants are absolutely required for a patient with SLE, it should be emphasized that bacteremias from oral surgery procedures increase the risk of developing infections of SLE-affected joints. In such cases it is recommended that antibiotic coverage be considered to minimize this potential problem (Fitzgerald _et al_. 2003). There are no well controlled studies, or even a well documented case series, of the success rates of implants placed in patients with SLE.
## Xerostomia
Xerostomia or dry mouth can be caused by a wide range of factors, including certain medications, aging, and damage to salivary glands (Beikler & Flemmig 2003). Sjögren syndrome (SS) is a group of autoimmune diseases that may be limited to lacrimal and salivary glands leading to xerostomia and keratoconjunctivitis (primary SS). In secondary SS the xerostomia and keratoconjunctivitis occur along with a number of connective tissue disorders such as rheumatoid arthritis and scleroderma. One of the main oral problems associated with SS is severe xerostomia that often leads to severe dental caries, burning sensations of the oral mucosa, oral candidiasis, and difficulty in swallowing. In many cases all of the teeth are lost because of rampant root and coronal caries. Patients with severe xerostomia find wearing artificial dentures to be a difficult and very unpleasant experience because of the lack of lubrication ordinarily supplied by saliva. Based on a few case reports it appears that dental implants can be successfully used in patients with SS (Payne _et al_. 1997; Isidor _et al_. 1999; Binon 2005). However, since SS often accompanies other conditions that increase the risk of implant failure (e.g. scleroderma, lupus erythematosus), it is important that implant candidates with SS be carefully evaluated for numerous other risk factors that might be present.
## Hematologic and lymphoreticular disorders
A number of hematologic and lymphoreticular disorders carry with them an increased susceptibility to periodontitis and other infections (Kinane 1999). Among these disorders are: agranulocytosis, acquired neutropenias, cyclic neutropenias, leukocyte adherence deficiency, and aplastic anemia (e.g. Fanconi's syndrome). Since patients with these diseases frequently lose teeth early in life they often have extensive prosthetic needs that can be met by the placement of dental implants. In the risk-assessment process prior to implant placement the major concern to be considered is the increased susceptibility to infections that could occur around any implants that might be placed. There are no well controlled studies of the success rates of implants placed in patients with these disorders. However, implants can be placed if the patient's disease is under control or in remission and a rigorous post-insertion implant maintenance program is an integral part of the overall treatment plan.
## Genetic traits and disorders
### Polymorphisms (IL-1 and MMP)
Polymorphisms are small variations in base-pair components of DNA that occur with a frequency of approximately 1–2% in the general population (Kornman & Newman 2000). These small variations in genes are biologically normal and do not cause disease. However, gene polymorphisms can affect in subtle ways how different people respond to environmental challenges. Within the context of risk assessment for implant failure, they affect how people respond to a microbial challenge and how efficiently their wounds heal.
Polymorphisms in the interleukin-1 (IL-1) gene cluster on chromosome 2q 13 have been associated with a hyper-responsive inflammatory reaction to a microbial challenge. A specific composite genotype of _IL-1A_ and _IL-1B_ polymorphisms, consisting of allele 2 of both IL-1A −889 (or the concordant +4845) and _IL-1B_ +3954 has been associated with an increased risk of severe chronic periodontitis in non-smokers (Kornman _et al_. 1997). Several investigators have attempted to determine if this composite IL-1 genotype can serve as a risk factor for complications associated with implants such as bone loss or their eventual failure (Wilson & Nunn 1999; Rogers _et al_. 2002; Feloutzis _et al_. 2003; Gruica _et al_. 2004; Jansson _et al_. 2005). All of these reports found that being positive for the composite IL-1 genotype was not associated with an increased risk of bone loss or other implant-related problems. However, in some populations there appears to be a synergistic effect between a positive IL-1 genotype and smoking that puts dental implants at a higher risk of developing peri-implant bone loss (Feloutzis _et al_. 2003; Gruica _et al_. 2004).
Matrix metalloproteinases (MMPs) are a family of at least 15 zinc-dependent endopeptidases that function extracellularly. They are important in both normal and pathologic remodeling of tissues and differ in some of their substrate specificities. For example, MMP-1 is an interstitial collagenase capable of cleaving collagen types I, II, III, VII, and X. While another enzyme called MMP-9 or gelatinase B cleaves collagen types IV, V, VII, and XIV. In a pilot study of 46 patients it was found that a polymorphism in the promoter region of the _MMP-1_ gene was associated with early implant failure, whereas a polymorphism in the promoter region of the _MMP-9_ gene had no relationship with implant loss (Santos _et al_. 2004). Further studies in this general area are warranted since a validated genetic risk factor for implant failure would have immense clinical utility.
### Genetic disorders
A number of genetic disorders such as those associated with chromosomal defects (e.g. Down syndrome) or those transmitted as Mendelian traits (e.g. Papillon-Lefèvre syndrome) often lead to tooth loss due to increased susceptibility to infections. An important question in the restorative care of these individuals is, will the increased susceptibility to periodontal infections also increase the risk of implant failure? In the risk-evaluation process it is probably best to assume that the answer to this question is "yes". However, with good post-operative and effective long-term maintenance care, implants can be successfully placed and retained in high-risk patients. For example, Papillon-Lefèvre syndrome is due to loss-of-function mutations in the cathepsin C gene that impairs innate immune responses (Toomes _et al_. 1999). Even in patients with this genetic disorder dental implants can be successful (Ullbro _et al_. 2000).
# Importance of behavioral considerations in risk assessment
In the examination and evaluation of a candidate for dental implants, one of the most difficult tasks is to analyze the behavioral aspects of risk assessment. This area has not been well studied and falls within the realm of the art, rather than the science, of clinical practice. Important behavioral issues that need to be assessed include compliance history, substance use/abuse habits, psychiatric/psychological issues, practitioner–patient communications, and expectations of the patient.
## Dental history of compliance behaviors
Long-term success of dental implants requires that the patient is able and willing to comply with the recommended post-insertion maintenance procedures required for long-term survival and success of implants. Since poor oral hygiene is a documented risk factor associated with failure of implants, it is critically important that patients understand this and are taught the skills necessary to perform plaque removal on a daily basis (Mombelli _et al_. 1987; Lindquist _et al_. 1988; Jepsen _et al_. 1996; Salcetti _et al_. 1997; Esposito _et al_. 1998a,b; Listgarten & Lai 1999; van Winkelhoff _et al_. 2000; Heydenrijk _et al_. 2002; Fugazzotto _et al_. 2004; Quirynen & Teughels 2003). The teaching of oral hygiene is not a trivial task and often requires a considerable investment of time over multiple visits. In addition, since patient-performed oral hygiene does not adequately remove or disrupt dental plaque biofilms at subgingival locations, periodic maintenance visits are needed so the oral healthcare provider can deliver this care. It is recommended that these visits be at 3-month intervals until it can be established that a less intense schedule is sufficient. The patient's compliance with the recommended maintenance schedule is a major key to long-term success.
## Substance use/abuse
Cigarette smoking as a risk factor for peri-implantitis and implant loss has been discussed earlier in this chapter. Smoking is a well documented risk factor that has both local and systemic effects on implant success. In addition, smoking is a powerful addiction with many complex behavioral components. In the consultation visit with the patient it is important that the clinician explain that smoking can contribute to complications after implant insertion. Referral to experts who conduct smoking-cessation programs is often helpful.
Patients who have addictions to alcohol and drugs are usually poor candidates for dental implants. Since the success of implant therapy requires a considerable amount of patient cooperation at all stages of care, individuals with substance-abuse problems should receive prosthetic care that does not depend on implants.
## Psychiatric/psychological issues
In general, patients who have severe mental health problems or exhibit psychotic behavior are not good candidates for dental implants. As in the case of individuals with substance-abuse problems, the cooperation needed for successful implant therapy is missing. However, people with medically controlled mental health problems, such as depression, can be successfully treated with implants. In cases where there is uncertainty regarding how well the problem is under medical control, a consultation with the patient's physician is advisable.
## Lack of understanding or communication
Most practitioners explain to their patients what the proposed dental care involves. However, in many cases patients do not understand what has been explained to them. It is important that the practitioner determine if the information they tried to convey was understood. One of the best ways to do this is to convey the information in easily understood (non-technical) language and in small increments. A common mistake is to rapidly present too much information. It is highly recommended that the patient be encouraged to give some feedback showing that they actually understand what they have been told. Patients who understand what is being done are usually quite cooperative and this cooperation leads to the increased probability of successful therapeutic outcomes.
## Patient's expectations
It is important to remember that the practitioner's and patient's perspectives may be somewhat different regarding the primary criteria used to measure implant success. From the patient's point of view the successful implant should be esthetically acceptable, comfortable, low-cost, and functional. Practitioners usually discuss implant success in terms of extent of osseointegration, level of alveolar bone, probing depths, and stability. Although the two sets of criteria are not in conflict, they emphasize different things. During the consultation visit, before any care is delivered, the practitioner should discuss, using patient-centered outcomes, what can be expected from placement of the implant.
A final comprehensive treatment plan should be presented to the patient that includes all recommended dental therapy and alternative treatment options. The patient should also be informed about the sequencing of the clinical procedures, risks and costs involved, and the anticipated total treatment time. This discussion between practitioner and patient is critically important in lowering the overall risk of treatment problems. Patients who understand what will be done, and why, are more likely to cooperate with the recommended treatment.
# Interest and commitment to post-treatment care and maintenance program
As discussed above, daily self-care (oral hygiene) and adherence to a maintenance-recall schedule is absolutely required for long-term success. This is best discussed and conveyed to the patient at the consultation visit. Long-term success of both periodontal and implant therapy depends on an effective partnership between the patient and practitioner. Many patients play a passive role when it comes to oral care. They place themselves in the hands of the therapist and expect most of the care to be done for them. An effective way to reduce the risk of implant complications and failure is to stress the importance of the patient's role as an active participant in the overall therapeutic program.
### Summary and conclusions
A key part of implant therapy is the risk-assessment process in which an attempt is made to identify variables that increase the risk of complications leading to implant failure. In many cases, early identification of these variables makes it possible to avoid or eliminate them, thereby increasing the chances of long-term implant survival. Risk factors for implant failure are environmental, biologic, or behavioral factors that are part of the causal chain leading to implant complications. For multifactorial problems, such as peri-implantitis and implant failure, the presence of one risk factor alone is usually insufficient to cause the adverse outcome. It is the combination of multiple risk factors that has clinical importance.
To minimize the risk of implant complications clinicians can use a number of technical procedures, such as adhering to a strict hygienic surgical protocol, performing the osteotomies with sharp drills, achieving early implant stability, and avoiding damage to vital anatomic structures during surgery. Since ongoing oral infections can lead to implant complications it is highly recommended that any endodontic, periodontal, and other oral infections be treated prior to implant placement. Conventional microbiologic methods have revealed that a large number of microorganisms are associated with peri-implant infections. Because of this microbial diversity, it is unlikely that testing for the presence of a small number of suspect bacteria for risk-assessment purposes will have any clinical value. Existing evidence does not support the routine use of pre-operative systemic antibiotics in implant therapy.
Most of the systemic risk factors for implant complications are those that increase the patient's susceptibility to infections or those that interfere with wound healing. Particularly important risk factors that suppress or alter neutrophil function are cigarette smoking, poor metabolic control of diabetes mellitus, and certain hematologic disorders. Factors that can significantly suppress adaptive immune functions are chronic use of corticosteroid medications and the presence of systemic lupus erythematosus. Important risk factors that can interfere with healing around implants are long-term use of bisphosphonates, history of radiation therapy to the jaws, and poor metabolic control of diabetes mellitus.
An effective risk-assessment process includes thorough medical and dental histories, a complete clinical examination, and an appropriate radiographic survey. Important behavioral issues that need to be assessed include compliance history, substance use/abuse habits, psychiatric/psychologic issues, effectiveness of practitioner–patient communication, and expectations of the patient. Depending on a number of circumstances, dental implants can be considered even in individuals who are at an elevated risk for implant complications. Risk assessment of the implant patient is a critically important pre-amble to treatment planning and if properly done can minimize the complications associated with endosseous implants.
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# Part 10: Treatment Planning Protocols
31 Treatment Planning of Patients with Periodontal Diseases
_Giovanni E. Salvi, Jan Lindhe, and Niklaus P. Lang_
32 Treatment Planning for Implant Therapy in the Periodontally Compromised Patient
_Jan L. Wennström and Niklaus P. Lang_
33 Systemic Phase of Therapy
_Niklaus P. Lang and Hans-Rudolf Baur_
# Chapter 31
# Treatment Planning of Patients with Periodontal Diseases
Giovanni E. Salvi, Jan Lindhe, and Niklaus P. Lang
* * *
Screening for periodontal disease
Basic periodontal examination
Diagnosis
Treatment planning
Initial treatment plan
Pre-therapeutic single tooth prognosis
Case presentation
Case report
Patient S.K. (male, 35 years old)
* * *
Caries and periodontal diseases represent opportunistic infections associated with biofilm formation on the surfaces of teeth. Factors such as bacterial specificity and pathogenicity as well as the disposition of the individual for disease, e.g. local and general resistance, may influence the onset, the rate of progression, and clinical characteristics of plaque-associated dental disorders. Findings from animal experiments and longitudinal studies in humans, however, have demonstrated that treatment, including the elimination or the control of the biofilm infection and the introduction of careful plaque control measures, in most, if not all, cases results in dental and periodontal health. Even if health cannot always be achieved and maintained, the arrest of disease progression following treatment must be the goal of modern dental care.
The treatment of patients affected by caries and periodontal disease, including symptoms of associated pathologic conditions such as pulpitis, periapical periodontitis, marginal abscesses, tooth migration, etc., may from a didactic point of view be divided into four different phases:
1. Systemic phase of therapy including smoking counseling
2. Initial (or hygiene) phase of periodontal therapy, i.e. cause-related therapy
3. Corrective phase of therapy, i.e. additional measures such as periodontal surgery, and/or endodontic therapy, implant surgery, restorative, orthodontic and/or prosthetic treatment
4. Maintenance phase (care), i.e. supportive periodontal therapy (SPT).
### Treatment goals
In every patient diagnosed with periodontitis, a treatment strategy, including the elimination of the opportunistic infection, must be defined and followed. This treatment strategy must also define the clinical outcome parameters to be reached through therapy. Such clinical parameters include:
* Reduction or resolution of gingivitis (bleeding on probing; BoP). A patient full mouth mean BoP ≤25% should be reached.
* Reduction in probing pocket depth (PPD). No residual pockets with PPD >5 mm should be present.
* Elimination of (through-and-through) open furcations in multi-rooted teeth. Initial furcation involvement should not exceed 3 mm.
* Absence of pain.
* Individually satisfactory esthetics and function.
In this context it must be emphasized that risk factors for periodontitis that can be controlled must be addressed as well. The three main risk factors for chronic periodontitis are (1) improper plaque control, (2) cigarette smoking, and (3) uncontrolled diabetes mellitus (Kinane _et al._ 2006).
### Systemic phase
The goal of this phase is to eliminate or decrease the influence of systemic conditions on the outcomes of therapy and to protect the patient and the dental care providers against infectious hazards. Contact with a physician or specialist should enable appropriate preventive measures to be taken, if necessary. Efforts must be undertaken to stimulate a smoker to enroll in a smoking cessation program. Additional aspects are discussed in Chapter 33.
### Initial (hygiene) phase
This phase represents the cause-related therapy. The objective of this phase is the achievement of clean and infection-free conditions in the oral cavity through complete removal of all soft and hard deposits and their retentive factors. Furthermore, this phase should aim at motivating the patient to perform optimal plaque control. The initial phase of periodontal therapy is concluded by re-evaluation and planning of both additional and supportive therapies.
### Corrective phase (additional therapeutic measures)
This phase addresses the sequelae of the oportunistic infections and includes therapeutic measures, such as periodontal and implant surgery, endodontic therapy, restorative and/or prosthetic treatment. The amount of corrective therapy required and the selection of the type of restorative and prosthetic therapy can be determined only when the degree of success of the cause-related therapy can be properly evaluated. The patient's willingness and ability to cooperate in the overall therapy must determine the type of corrective treatment. If this cooperation is inadequate, it may not be worth initiating treatment procedures: permanent improvement of oral health, function and esthetics may therefore not be achieved. The validity of this statement can be exemplified by the results of studies aimed at assessing the relative value of different types of surgical methods in the treatment of periodontal disease. A number of clinical trials (Lindhe & Nyman 1975; Nyman _et al._ 1975, 1977; Rosling _et al._ 1976a,b; Nyman & Lindhe 1979) have demonstrated that gingivectomy and flap procedures performed in patients with proper plaque control levels often result in gain of alveolar bone and clinical attachment, while surgery in plaque-contaminated dentitions may cause additional destruction of the periodontium.
### Maintenance phase (supportive periodontal therapy)
The aim of this treatment is the prevention of reinfection and disease recurrence. For each individual patient a recall system must be designed that includes (1) assessment of deepened sites with bleeding on probing, (2) instrumentation of such sites, and (3) fluoride application for the prevention of dental caries. In addition, this treatment involves the regular control of prosthetic restorations incorporated during the corrective phase of therapy. Tooth sensitivity testing should be applied to abutment teeth as loss of vitality is a frequently encountered complication (Bergenholtz & Nyman 1984; Lang _et al._ 2004; Lulic _et al._ 2007). Based upon the individual caries activity, bitewing radiographs should be incorporated into SPT at regular intervals.
# Screening for periodontal disease
A patient seeking dental care is usually screened for the presence of carious lesions by means of clinical and radiographic tools. Likewise, it is imperative that such a patient is screened for the presence of periodontitis as well, using a procedure termed the basic periodontal examination (BPE) (or periodontal screening record; PSR).
## Basic periodontal examination
The goal of the BPE is to screen the periodontal conditions of a new patient and to facilitate treatment planning. BPE scoring will allow the therapist to identify:
* A patient with reasonably healthy periodontal conditions, but in need of long-term preventive measures
* A patient with periodontitis and in need of periodontal therapy.
In the BPE the screening of each tooth or implant is evaluated. For this purpose, the use of a thin graduated periodontal probe is recommended. At least two sites per tooth/implant (i.e. mesio-buccal and disto-buccal) should be probed using a light force (i.e. 0.2 N). Each dentate sextant within the dentition is given a BPE code or score, whereby the _highest_ individual site score is used.
### BPE system code
* Code 0 = probing pocket depth (PPD) ≤3 mm, BoP negative, no calculus or overhanging fillings (Fig. 31-1a)
* Code 1 = PPD ≤3 mm, BoP positive, no calculus or overhanging fillings (Fig. 31-1b)
* Code 2 = PPD ≤3 mm, BoP positive, presence of supra- and/or subgingival calculus and/or overhanging fillings (Fig. 31-1c)
* Code 3 = PPD >3 mm but ≤5 mm, BoP positive (Fig. 31-1d)
* Code 4 = PPD >5 mm (Fig. 31-1e).
If an examiner identifies a single site with a PPD >5 mm within a sextant, the sextant will receive a code of 4, and no further assessments are needed in this particular sextant. Patients with sextants given codes of 0, 1 or 2 belong to the relatively periodontally healthy category. A patient exhibiting a sextant with codes of 3 or 4 must undergo a more comprehensive periodontal examination (for details see Chapter 26).
**Fig. 31-1** Clinical illustration of the basic periodontal examination scores. (a) BPE code 0. (b) BPE code 1. (c) BPE code 2. (d) BPE code 3. (e) BPE code 4.
**Fig. 31-2** (a–d) Clinical status of a 27-year-old female patient (S.B.) diagnosed with generalized aggressive periodontitis with furcation involvement.
The aim of the following text is to explain the overall objectives of the treatment planning of patients with BPE codes of 3 and 4 undergoing a comprehensive diagnostic process.
# Diagnosis
The basis for the treatment planning described in this chapter is established by the clinical data collected from the patient's examination (see Chapter 26). This patient (Ms. S.B., 27 years of age) was systemically healthy and a non-smoker. She was examined with respect to her periodontal conditions, i.e. gingival sites displaying signs of _bleeding on probing_ were identified, _probing pocket depths_ were measured, the _periodontal attachment level_ was calculated, _furcation involvements_ were graded, _tooth mobility_ was assessed, and the radiographs were analyzed to determine the _height_ and _outline_ of the _alveolar bone crest_.
The clinical characteristics of the dentition of this patient are shown in Fig. 31-2. The periodontal chart and the radiographs are presented in Figs. 31-3 and 31-4, respectively. Based on these findings, each tooth in the dentition was given a diagnosis (Fig. 31-5) and a pre-therapeutic prognosis (Fig. 31-6). In addition to the examination of the periodontal condition, detailed assessments of primary and recurrent caries were made for all tooth surfaces in the dentition. Furthermore, the patient was examined with respect to endodontic and occlusal problems as well as temporomandibular joint dysfunction.
**Fig. 31-3** Periodontal chart of the patient presented in Fig. 31-2.
# Treatment planning
## Initial treatment plan
Provided that the patient's examination has been completed (see Chapter 26) and a diagnosis of all pathologic conditions has been made, an initial treatment plan can been established. At this early stage in the management of a patient, it is, in most instances, impossible to make definite decisions regarding all aspects of the treatment sequence, because:
**Fig. 31-4** Radiographs of the patient presented in Fig. 31-2.
**Fig. 31-5** Single tooth diagnosis of the patient presented in Fig. 31-2.
**Fig. 31-6** Pre-therapeutic single tooth prognosis of the patient presented in Fig. 31-2.
1. _The degree of success of initial therapy is unknown_. The re-evaluation after initial, cause-related therapy forms the basis for the selection of means for additional therapy. The degree of disease elimination that can be reached depends on the outcome of subgingival instrumentation, but also on the patient's ability and willingness to exercise proper plaque control and to adopt adequate dietary habits.
2. _The patient's "subjective" need for additional (periodontal and/or restorative) therapy is unknown_. When the dentist has completed the examination of the patient and an inventory has been made regarding periodontal disease, caries, pulpal disease, and temporomandibular joint disorders, the observations are presented to the patient (i.e. "the case presentation"). During the case presentation session it is important to find out if the patient's subjective need for dental therapy coincides with the dentist's professional appreciation of the type and amount of therapy that is required. It is important that the dentist understands that the main objective of dental therapy, besides _elimination of pain_ , is _to satisfy the patient's demands regarding chewing function (comfort) and esthetics_ , demands that certainly vary considerably from one individual to another.
3. _The result of some treatment steps cannot be predicted._ In patients exhibiting advanced forms of caries and periodontal disease it is often impossible to anticipate whether or not all teeth that are present at the initial examination can be successfully treated, or to predict the result of certain parts of the intended therapy. In other words, critical and difficult parts of the treatment must be performed first, and the outcome of this treatment must be evaluated before all aspects of the definitive corrective treatment can be properly anticipated and described.
## Pre-therapeutic single tooth prognosis
Based on the results of the comprehensive examination, including assessments of periodontitis, caries, tooth sensitivity, and the resulting diagnosis, as well as considering the patient's needs regarding esthetics and function, a pre-therapeutic prognosis for each individual tooth (root) is made. Three major questions are addressed:
1. Which tooth/root has a " _good_ " (secure) prognosis?
2. Which tooth/root is " _irrational-to-treat_ "?
3. Which tooth/root has a " _doubtful_ " (unsecure) prognosis?
Teeth with a _good_ prognosis will require relatively simple therapy and may be regarded as secure abutments for function.
Teeth that are considered "irrational-to-treat" should be extracted during initial, cause-related therapy. Such teeth may be identified on the basis of the following criteria:
* Periodontal:
* Recurrent periodontal abscesses
* Combined periodontal–endodontic lesions
* Attachment loss to the apex
* Endodontal:
* Root perforation in the apical half of the root
* Dental:
* Vertical fracture of the root
* Oblique fracture in the middle third of the Root
* Caries lesions that extend into the root canal
* Functional:
* Third molars without antagonists and with periodontitis/caries.
Teeth with a _doubtful_ prognosis are usually in need of comprehensive therapy and must be brought into the category of teeth with a _good_ prognosis by means of additional therapy. Such teeth may be identified on the basis of the following criteria:
* Periodontal:
* Furcation involvement
* Angular (i.e. vertical) bony defects
* "Horizontal" bone loss involving more than two thirds of the root
* Endodontal:
* Incomplete root canal therapy
* Periapical pathology
* Presence of voluminous posts/screws
* Dental:
* Extensive root caries.
## Case presentation
The "case presentation" is of the initial treatment plan and must include a description for the patient of different therapeutic goals and the modalities by which these may be reached. At the case presentation for Ms. S.B. the following treatment plan was described:
* The teeth in the dentition from 12 to 22 and from 45 to 35 will probably not confront the dentist with any major therapeutic challenges. For the remaining teeth in the dentition, however, the treatment plan may involve several additional measures.
Expected benefits inherent to a certain treatment plan versus obvious disadvantages should always be explained to and discussed with the patient. His/her attitude to the alternatives presented must guide the dentist in the design of the overall treatment plan.
Based on the pre-therapeutic single tooth prognosis (Fig. 31-6), the following detailed treatment plan was presented to the patient.
### Systemic phase
Owing to the fact that the patient was systemically healthy and a non-smoker, no medical examination and smoking cessation counseling were required.
### Initial phase (cause-related therapy)
The treatment was initiated and included the following measures to eliminate or control the bacterial infection:
1. _Motivation_ of the patient and _instruction_ in oral hygiene measures with subsequent checkups and re-instruction
2. _Scaling and root planing_ under local anesthesia in combination with removal of plaque-retentive factors
3. _Excavation and restoration_ of carious lesions (16 and 26)
4. _Endodontic treatment_ of tooth 46.
**Fig. 31-7** (a–c) Clinical front and lateral views of the patient presented in Fig. 31-2 at re-evaluation after initial periodontal therapy.
#### _Re-evaluation after initial phase_
The initial phase of therapy is completed with a thorough analysis of the results obtained with respect to the elimination or degree of control of the dental infections. This implies that a re-evaluation of the patient's periodontal conditions and caries activity must be performed. The results of this re-evaluation (Figs. 31-7 and 31-8) form the basis for the selection, if necessary, of additional corrective measures to be performed in the phase of definitive treatment (i.e. corrective phase). In order to provide time for the tissues to heal, the re-evaluation should be performed no earlier than 6–8 weeks following the last session of instrumentation.
#### _Planning of the corrective phase (i.e. additional definitive therapy)_
If the results from the re-evaluation, made 6–8 weeks after the termination of the initial treatment phase, show that periodontal disease and caries have been brought under control, the additional treatment may be carried out. The main goal of this phase is to correct the sequelae caused by oral infections (i.e. periodontal disease and caries). The following procedures may be performed:
* _Additional endodontic treatment with/without post-and-core build-ups_
* _Periodontal surgery_. The type (i.e. open-flap debridement, regenerative or resective surgery) and extent of surgical treatment should be based on probing depth measurements, degree of furcation involvement and BoP score assessed at re-evaluation. Periodontal surgery is often confined to those areas of the dentition where the inflammatory lesions were not resolved by root instrumentation and in areas with angular bony defects or in furcation-involved molars.
* _Installation of oral implants_. In regions of the dentition where tooth abutments are missing, implant therapy for esthetic and functional reasons may be considered. It is essential to realize that implant therapy must be initiated once all dental infections are under control, i.e. after successful periodontal therapy.
* _Definitive restorative and prosthetic treatment_ including fixed or removable dental prostheses.
### Corrective phase (additional therapy)
After initial therapy the patient (Ms. S.B.) exhibited low plaque and gingivitis scores (i.e. 5–10%) and no active carious lesions. The corrective phase therefore included the following components:
1. _Periodontal surgery_ (i.e. open-flap debridement) in the maxillary left and right quadrants as well as in the mandibular molar regions (Fig. 31-9)
2. _Guided tissue regeneration_ (GTR) for tooth 36
3. _Re-evaluation_ after periodontal surgery (Figs. 31-10 and 31-11)
4. _Orthodontic therapy_ in the maxillary front area (Fig. 31-12)
5. _Restorative therapy_ in the maxillary front area for esthetic reasons (Fig. 31-13).
**Fig. 31-8** Periodontal chart of the patient presented in Fig. 31-2 at re-evaluation after initial periodontal therapy.
#### _Re-evaluation after corrective phase_
The corrective phase of therapy is completed with a thorough analysis of the results obtained with respect to the elimination of the sequelae of periodontal tissue destruction (Figs. 31-14, 31-15 and 31-16). This implies that a re-evaluation of the patient's periodontal and peri-implant conditions must be performed. The results of this re-evaluation form the basis for the assessment of the residual periodontal risk. The out-comes of the periodontal risk assessment (PRA), in turn, will determine the recall frequency of the patient during maintenance phase.
### Maintenance phase (care)
Following completion of cause-related therapy, the patient must be enrolled in a recall system aiming at preventing the recurrence of oral infections (i.e. periodontitis, caries, and peri-implantitis). Supportive periodontal therapy (SPT) should be scheduled at the re-evaluation after initial therapy and independently of the need for additional therapy. The time interval between the recall appointments should be based on a periodontal risk assessment established at the re-evaluation after the corrective phase. It is well established that self-performed plaque control combined with regular maintenance care visits following active periodontal treatment represents an effective means of controlling gingivitis and periodontitis and limiting tooth mortality over a 30-year period (Axelsson _et al._ 2004). It is important to emphasize, however, that the recall program must be designed to meet the individual needs of the patient. According to a PRA performed after completion of active therapy, some patients should be recalled every 3 months, while others may have to be checked only once a year (Lang & Tonetti 2003).
**Fig. 31-9** (a–c) Clinical intrasurgical views of the mandibular and maxillary left quadrants. The angular bony defect mesial of tooth 36 was treated according to the principles of guided tissue regeneration (GTR) using a resorbable barrier membrane.
**Fig. 31-10** (a,b) Clinical lateral views of the patient presented in Fig. 31-2 at re-evaluation after periodontal surgery.
**Fig. 31-11** Periodontal chart of the patient presented in Fig. 31-2 at re-evaluation after periodontal surgery.
At the various recall visits the following procedures should be carried out:
1. Update of the medical and smoking history
2. Soft tissue examination as cancer screening
3. Recording of the full-mouth PPD ≥5 mm with concomitant BoP
4. Re-instrumentation of bleeding sites with PPD ≥5 mm
5. Polishing and fluoridation for the prevention of dental caries.
The patient (Ms. S.B.), presented to describe the guiding principles of treatment planning, was recalled twice during the first 6 months after active treatment (i.e. every 3 months) and subsequently only once every 6 months based on the individual PRA.
### Concluding remarks
The overall treatment plan and the sequence of the different treatment procedures used in this case were selected for presentation in order to illustrate the following principle: _in patients exhibiting a generalized advanced breakdown of the periodontal tissues, but with an intact number of teeth, considerable efforts should be made to maintain all teeth_. Extraction of a single tooth in such a dentition will frequently also call for the extraction of several others for "prosthetic reasons". The end result of such an approach thus includes a prosthetic rehabilitation that, if the treatment planning had been properly done, would have been unnecessary.
The large variety of treatment problems that different patients present may obviously require deviations from the sequence of treatment phases (i.e. systemic phase, initial cause-related therapy, corrective therapy, and maintenance care) discussed above. Such deviations may be accepted as long as the fundamental principles characterizing the treatment phases are understood.
**Fig. 31-12** (a–c) Clinical front and lateral views of the patient presented in Fig. 31-2 during orthodontic therapy of the maxillary front teeth.
**Fig. 31-13** (a–c) Clinical front and lateral views of the patient presented in Fig. 31-2 at the final re-evaluation. To improve the esthetic outcome, the maxillary front teeth were restored with composite fillings.
**Fig. 31-14** Periodontal chart of the patient presented in Fig. 31-2 at the final re-evaluation.
**Fig. 31-15** Radiographs of the patient presented in Fig. 31-2 at the final re-evaluation.
**Fig. 31-16** (a,b) Radiographs of tooth 36 of the patient presented in Fig. 31-2 before and after regenerative periodontal therapy according to the principles of GTR.
**Fig. 31-17** (a–c) Clinical front and lateral views of patient S.K. at initial examination.
# Case report
A patient will be presented below together with a brief description of his specific dental problems and the treatment delivered in order to demonstrate the rationale behind such treatment phases.
## Patient S.K. (male, 35 years old)
### Initial examination
The chief complaint of the patient was the slightly increased mobility of tooth 21. The periodontal conditions (i.e. probing pocket depths, furcation involvements, tooth mobility, and periapical radiographs) from the initial examination are shown in Figs. 31-17, 31-18, and 31-19.
The data obtained from the initial examination disclosed the presence of an advanced destruction of the supporting tissues in most parts of the dentition (Fig. 31-18) and the presence of several angular bony defects (Fig. 31-19). The full-mouth plaque score (FMPS) and full-mouth bleeding score (FMBS) were 32% and 86%, respectively. The patient was systemically healthy and a former smoker.
### Diagnosis
The patient was diagnosed with generalized chronic periodontitis with furcation involvement.
**Fig. 31-18** Periodontal chart of the patient presented in Fig. 31-17.
**Fig. 31-19** Radiographs of the patient presented in Fig. 31-17.
### Etiology
The supra- and subgingival bacterial deposits were identified as the main etiologic factors. Past cigarette smoking was considered a modifying factor.
### Pre-therapeutic single tooth prognosis
Teeth 28, 38, and 48 were missing. Tooth 18 was impacted and considered irrational-to-treat. Teeth 13, 12, 11, and 23 in the maxilla and from 45 to 35 in the mandible were classified as secure. A doubtful prognosis was assigned to 17, 16, 15, 14, 21, 22, 24, 25, 26, and 27 in the maxilla and to 36, 37, 46, and 47 in the mandible (Fig. 31-20).
### Treatment planning
In the treatment planning of this young patient, it seemed reasonable to anticipate the retention of all teeth of his periodontally compromised dentition. The prerequisites for a good long-term prognosis after therapy included (1) optimal self-performed plaque control, (2) proper healing of the periodontal tissues following non-surgical and surgical therapy, and (3) a carefully monitored maintenance care program. As stated above, tooth 21 displayed increased mobility. This mobility, however, did not disturb the chewing comfort of the patient.
In such a young patient, extensive efforts were made to treat inflammatory periodontal disease properly in the entire dentition, in order to avoid tooth extraction and subsequent prosthetic rehabilitation.
**Fig. 31-20** Pre-therapeutic single tooth prognosis of the patient presented in Fig. 31-17.
**Fig. 31-21** (a–c) Clinical front and lateral views of the patient presented in Fig. 31-17 at re-evaluation after initial therapy.
**Fig. 31-22** Periodontal chart of the patient presented in Fig. 31-17 at re-evaluation after initial therapy.
### Treatment
Subsequent to initial examination, the patient was given a detailed "case presentation" and information regarding alternative goals of and prerequisites for the overall treatment. This information included a description of the role of dental biofilms in the etiology of periodontal disease and the significance of optimal plaque control for a successful outcome of therapy. A treatment program was subsequently planned which aimed at maintaining all teeth. The overall treatment was performed in the sequence described below.
### _Initial cause-related therapy_
The patient was counseled not to start smoking again. After thorough motivation, the patient was instructed in the toothbrushing technique according to Bass and in the use of interdental brushes. Scaling and root planing of all teeth were performed under local anesthesia. The front and lateral views as well as the periodontal chart at re-evaluation after initial therapy are presented in Figs. 31-21 and 31-22, respectively.
**Fig. 31-23** (a-c) Intra- and postsurgical views of the upper front area of the patient presented in Fig. 31-17.
**Fig. 31-24** (a–c) Clinical front and lateral views of the patient presented in Fig. 31-17 at the final examination.
#### _Additional therapy_
The need for additional therapy was based on the re-evaluation after initial therapy (Fig. 31-22). Periodontal surgery in conjunction with regenerative procedures was deemed necessary in all quadrants. During access flap surgery in the first quadrant extending from 13 to 17, tooth 18 was extracted.
Between the upper front teeth 11 and 21, the modified papilla preservation technique (Cortellini _et al._ 1995) was incorporated in the surgical procedure to gain access to the angular bony defect of tooth 21 (Fig. 31-23). In this area, the application of enamel matrix derivatives (i.e. Emdogain®) aimed at regenerating the lost periodontal tissues on the mesial aspect of 21.
In the third quadrant, the surgical access flap extended from 35 to 37. In the fourth quadrant, flap surgery in conjunction with the simplified papilla preservation technique (Cortellini _et al._ 1999) was used to gain access to the angular bony defect on the distal aspect of 46. In this area, the application of enamel matrix derivatives (i.e. Emdogain®) aimed at regenerating the lost periodontal tissues. Six months after completion of the corrective phase (Fig. 31-24), a re-evaluation of the periodontal conditions (Fig. 31-25), including radiographs (Figs. 31-26 and 31-27) followed by a PRA, were performed.
**Fig. 31-25** Periodontal chart of the patient presented in Fig. 31-17 at the final examination.
**Fig. 31-26** Radiographs of the patient presented in Fig. 31-17 at the final examination.
**Fig. 31-27** Radiographs before (a) and after (b) periodontal regeneration of the angular bony defect on the distal aspect of tooth 46.
#### _Supportive periodontal therapy_
After completion of initial and corrective therapy, the patient was recalled for maintenance care every 3 months. During recall appointments, sites bleeding on probing and with a PPD ≥5 mm were re-instrumented. If necessary, the patient was remotivated and re-instructed in oral hygiene procedures. Fluoride was regularly applied in order to prevent the onset of dental caries.
**References**
Axelsson, P., Nyström, B. & Lindhe, J. (2004). The long-term effect of a plaque control program on tooth mortality, caries and periodontal disease in adults. Results after 30 years of maintenance. _Journal of Clinical Periodontology_ **31** , 749–757.
Bergenholtz, G. & Nyman, S. (1984). Endodontic complications following periodontal and prosthetic treatment of patients with advanced periodontal disease. _Journal of Periodontology_ **55** , 63–68.
Cortellini, P., Pini-Prato, G.P. & Tonetti, M.S. (1995). The modified papilla preservation technique. A new surgical approach for interproximal regenerative procedures. _Journal of Periodontology_ **66** , 261–266.
Cortellini, P., Pini-Prato, G.P. & Tonetti, M.S. (1999). The simplified papilla preservation flap. A novel surgical approach for the management of soft tissues in regenerative procedures. _International Journal of Periodontics and Restorative Dentistry_ **19** , 589–599.
Kinane, D.F., Peterson, M. & Stathoupoulou, P.G. (2006). Environmental and other modifying factors of the periodontal diseases. _Periodontology 2000_ **40** , 107–119.
Lang, N.P., Pjetursson, B.E., Tan, K., Brägger, U., Egger, M. & Zwahlen, M. (2004). A systematic review of the survival and complication rates of fixed partial dentures (FPDs) after an observation period of at least 5 years. II. Combined tooth-implant supported FPDs. _Clinical Oral Implants Research_ **15** , 643–653.
Lang, N.P. & Tonetti, M.S. (2003). Periodontal risk assessment (PRA) for patients in supportive periodontal therapy (SPT). _Oral Health and Preventive Dentistry_ **1** , 7–16.
Lindhe, J. & Nyman, S. (1975). The effect of plaque control and surgical pocket elimination on the establishment and maintenance of periodontal health. A longitudinal study of periodontal therapy in cases of advanced disease. _Journal of Clinical Periodontology_ **2** , 67–79.
Lulic, M., Brägger, U., Lang, N.P., Zwahlen, M. & Salvi, G.E. (2007). Ante's (1926) law revisited. A systematic review on survival rates and complications of fixed dental prostheses (FDPs) on severely reduced periodontal tissue support. _Clinical Oral Implants Research_ **18** (Suppl 3), 63–72.
Nyman, S. & Lindhe, J. (1979). A longitudinal study of combined periodontal and prosthetic treatment of patients with advanced periodontal disease. _Journal of Periodontology_ **50** , 163–169.
Nyman, S., Lindhe, J. & Rosling, B. (1977). Periodontal surgery in plaque-infected dentitions. _Journal of Clinical Periodontology_ **4** , 240–249.
Nyman, S., Rosling, B. & Lindhe, J. (1975). Effect of professional tooth cleaning on healing after periodontal surgery. _Journal_ _of Clinical Periodontology_ **2,** 80–86.
Rosling, B., Nyman, S. & Lindhe, J. (1976a). The effect of systematic plaque control on bone regeneration in infrabony pockets. _Journal of Clinical Periodontology_ **3,** 38–53.
Rosling, B., Nyman, S., Lindhe, J. & Jern, B. (1976b). The healing potential of the periodontal tissues following different techniques of periodontal surgery in plaque-free dentitions. A 2-year clinical study. _Journal of Clinical Periodontology_ **3,** 233–250.
# Chapter 32
# Treatment Planning for Implant Therapy in the Periodontally Compromised Patient
Jan L. Wennström and Niklaus P. Lang
* * *
Prognosis of implant therapy in the periodontally compromised patient
Strategies in treatment planning
Treatment decisions – case reports
Posterior segments
Tooth versus implant
Aggressive periodontitis
Furcation problems
Single-tooth problem in the esthetic zone
* * *
The use of dental implants for replacement of missing teeth is a viable option in the rehabilitation of the periodontally compromised patient, and certainly the availability of this treatment option may also influence our decisions regarding the preservation of teeth with varying degrees of periodontal tissue destruction.
# Prognosis of implant therapy in the periodontally compromised patient
Global data on survival rates of dental implants indicate a rather low incidence of implant loss. The question is, however, whether the long-term prognosis for implants is better than that for teeth. In a systematic review by Berglundh _et al._ (2002), including 16 studies reporting data on implant-supporting fixed partial dentures (FPDs), the overall 5-year failure rate was calculated as about 5%. In the few studies that included a follow-up of 10 years the figure for implant loss was about 10%. It should be noted, however, that these studies did not specifically address the prognosis of implant therapy in periodontally compromised patients. Hardt _et al._ (2002) reported from a 5-year study that 8% of the implants were lost in patients who at time of implant placement presented advanced loss of periodontal support at their natural teeth. The corresponding figure in patients without periodontal tissue destruction was only 3% (Table 32-1). In the periodontally compromised patients most of the implants that were lost were so-called late failures. Furthermore, after 5 years 64% of the periodontally compromised patients showed a mean bone loss at the implants of >2 mm compared to only 24% among the non-compromised patients. Karoussis _et al._ (2003) found a failure rate of 10% after 10 years in patients that had been treated for periodontitis before implant placement, compared to 4% in patients who had received implant therapy because of tooth loss for reasons other than periodontal disease. The data reported above indicate that there is an increased risk for implant failure in individuals susceptible to periodontitis.
**Table 32-1** Proportion (%) of implants lost in relation to experience of destructive periodontal disease
A question of concern in relation to treatment decisions in a periodontally compromised patient is whether the failure rate of implants is different from that of teeth. In order to give an answer to this question we have to know the incidence of tooth loss in periodontally treated patients. Based on data from studies involving patients that have been treated for advanced periodontal disease and thereafter been provided with regular supportive periodontal therapy (SPT), the average incidence of tooth loss during a 10-year period can be estimated to be between 2 and 5% (Table 32-2). These figures, in comparison with the data for implant loss presented above, indicate that the prognosis for long-term survival of implants is not better than that of properly treated periodontitis-affected teeth. Furthermore, evidence is accumulating that suggests that longitudinal bone loss at implants is positively correlated with periodontal disease susceptibility and that implant therapy in the periodontally compromised patient may not be as successful as the global data for implant therapy in general has indicated.
**Table 32-2** Proportion (%) of teeth lost in patients treated for advanced destructive periodontal disease and maintained in supportive care programs
# Strategies in treatment planning
A comprehensive clinical and radiographic examination forms the basis for the treatment planning of the periodontally compromised patient. In relation to implant therapy, careful risk assessments should also be made (see Chapter 30) and additional radiographic examinations may be required (see Chapter 28). The goal of the treatment is to satisfy the patient's demands regarding chewing comfort and esthetics, with a favorable long-term prognosis of the restoration. The use of implants as a means to restore chewing function and esthetics in the periodontitis-susceptible patient has to be carefully evaluated in relation to the patient's standard of infection control. In partially dentate patients with remaining periodontal lesions, implants are rapidly colonized by periodontal pathogens, which indicates that periodontal pockets may act as reservoirs for microbial colonization of implants (see Chapter 10). Since there is no evidence that the host response to the microbial challenge is altered when a tooth is substituted with an implant, it should be anticipated that a periodontitis-susceptible individual with improper infection control will face similar risk for disease-induced bone loss at implants and teeth.
Elimination of periodontitis lesions before implant placement and the establishment of a high standard of infection control are consequently decisive factors for the success of implant therapy. Regular recalls for supportive care should be scheduled after the completion of the therapy (see Chapter 59). Provided such a treatment program is adhered to, the long-term success of implant therapy in the periodontally compromised patient may not deviate from that in a non-susceptible patient (Baelum & Ellegaard 2004; Wennström _et al._ 2004).
# Treatment decisions – case reports
## Posterior segments
In the periodontally compromised patient the posterior segments of the dentition are usually those that are most severely affected by the disease and tooth loss. Figure 32-1 shows the clinical and radiographic status of a 53-year-old male following the completion of basic periodontal therapy for the establishment of infection control. Following periodontal treatment, the patient, originally diagnosed with severe chronic periodontitis, demonstrated a high standard of self-performed infection control and all lesions in the periodontal tissues have now been resolved. Because of the severity of the periodontal destruction, remaining teeth posterior to the canines in the maxilla as well as one remaining mandibular molar had to be removed. Hence, the dentition is markedly reduced, not only with regard to the number of teeth but also in terms of the amount of remaining periodontal support. From a chewing comfort point of view the patient is in need of prosthetic rehabilitation, particularly in the posterior segments of the maxilla. The treatment options available include (1) a removable prosthesis or (2) implant-supported FPDs. Considering that the remaining teeth show slightly increased mobility, the treatment alternative involving implant-supported FPDs seems most appropriate. In addition, the patient would if possible prefer to have fixed prosthetic reconstructions.
Clinical and radiographic evaluation of the posterior jaw segments of the maxilla revealed that two implants might be placed in quadrant 1 between the canine and the anterior border of the maxillary sinus, while the dimension of the bone inferior of the sinus was judged inadequate for placement of implants (Fig. 32-1b,c). If the implant in position 15 was placed along the anterior wall of the sinus cavity and was angulated slightly distally, space might be available to insert a pontic between the two implants and to provide the patient with a three-unit FPD. In the quadrant 2, the bone dimensions were more favorable and it was judged feasible to install three implants. Hence, by providing the patient with two three-unit implant-supported FPDs in the posterior segments of the maxilla a premolar occlusion could be established. The patient considered this treatment solution to be satisfactory with regard to his demands for improved chewing function. He had no requests for improved esthetics in the anterior segments, most likely because of a low lip line and because he only exposed the incisial half of the crown when smiling.
**Fig. 32-1** (a–c) A 53-year-old male patient (H.L.) with periodontally compromised dentition. Clinical and radiographic status after periodontal treatment and establishment of infection control.
**Fig. 32-1** (d–f) Clinical and radiographic status of patient H.L. after completion of the implant treatment.
**Fig. 32-1** (g,h) Clinical and radiographic status of patient H.L. 10 years after completion of the implant treatment. Note that there is no loss of bone support at the implants.
Figure 32-1d–f shows the outcome of the restorative treatment. In order to further improve the patient's chewing comfort a single implant was inserted in the left side of the mandible, after the second premolar had been tilted mesially. After completion of the restorative treatment the patient was enrolled in a maintenance care program, including recalls once every 6 months to secure a high standard of infection control and to provide preventive means to reduce the risk for development of root caries. The 10-year follow-up status (Fig. 32-1g–h) reveals healthy marginal tissues and no loss of supporting structures, neither at the implants nor at the teeth. The standard of self-performed infection control has been excellent throughout the follow-up period.
_In conclusion:_ The treatment outcome in this case clearly illustrates that the periodontitis-susceptible patient can be successfully treated with the use of implants and without signs of peri-implant bone loss over time, provided proper infection control is established and maintained. The recall visits for supportive therapy must include careful evaluation of both the periodontal and the peri-implant tissues for detection of signs of pathology, and proper decisions regarding indicated treatment (see Chapter 59).
## Tooth versus implant
Our treatment decisions regarding implant therapy or advanced periodontal therapy often relate to a single tooth. Figure 32-2(a,b) illustrates such a case. A 67-year-old woman presents with a localized advanced periodontal lesion at an abutment tooth in a three-unit FPD. The FPD is about 15 years old and the patient has no esthetic or functional complaints with regard to the FPD. Tooth 15 has a 10 mm deep pocket at the mesial aspect. The pocket is associated with a wide angular bone defect, and the tooth is positioned with its root in close proximity to the anterior wall of the maxillary sinus. If the tooth is extracted one may anticipate a marked remodeling of the ridge in the area, and the amount of bone available in the region might become insufficient for implant placement to support a new FPD, unless sinus elevation and bone grafting procedures are performed.
The question in the treatment planning with regard to tooth 15 is whether there is a reasonable chance to save 15 and maintain the FPD with periodontal therapy, or should the tooth be extracted and implants placed to support a new FPD? Considering the great functional value of the tooth, it was decided to perform flap elevation and to evaluate the potential for tissue regeneration. Following debridement (Fig. 32-2c), it was observed that the defect was wide and had the morphology of a combined one-/two-/three-wall defect. A regenerative approach (application of enamel matrix proteins; see Chapter 43) was selected. The healing resulted in 6 mm gain in clinical attachment level and radiographic bone fill. The amount of soft tissue recession was minimal as seen from the 6 year follow-up documentation (Fig. 32-2d, e).
_In conclusion_ , considering that implant therapy in this case most likely would have required sinus elevation and bone grafting to satisfy the patient's demands for esthetics and chewing function, the maintenance of 15 through proper periodontal therapy was of great benefit for the patient.
**Fig. 32-2** A 67-year-old female patient with a localized advanced periodontal defect at tooth 15. (a–c) Clinical and radiographic status at the initial examination. (d) Flap elevated and the morphology of the defect can be determined as a wide combined one-/two-/three-wall defect. (e,f) Clinical and radiographic status 6 years after active treatment. Courtesy of Dr. G. Heden, Sweden.
## Aggressive periodontitis
Figure 32-3 shows a 22-year-old female patient diagnosed as a case of aggressive periodontitis. The first molar in the maxillary right quadrant and in the mandibular left quadrant have already been lost due to advanced periodontal destruction. The patient is asking for prosthetic replacement of the missing teeth. The clinical examination also disclosed the presence of deep angular defects at the first molar in the mandibular right quadrant and at the second premolar in the maxillary right quadrant. It seems reasonable to plan for implant-supported restorations to replace the missing 16 and 36. The more difficult question, however, is related to the treatment of the periodontally compromised 15 and 46 (Fig. 32-3c,d).
**Fig. 32-3** A 22-year-old female patient (A.A.) diagnosed as a case of aggressive periodontitis. (a–e) Clinical and radiographic status at the initial examination. Localized advanced periodontal lesions are diagnosed at teeth 15 and 46. (f) Radiographic view after periodontal and implant treatment. (g–j) Clinical and radiographic status 12 years after active treatment.
Is it possible to successfully eliminate the periodontal lesions at 15 and 46 with a good long-term prognosis for the teeth? Or should the teeth be removed and replaced with implant-supported restorations? For tooth 15 extraction may be seen as a rational decision since implant therapy is planned in the region of 16. However, from an esthetic perspective it would be preferable to maintain 15 because the crown is intact and there is no loss of attachment or soft tissue height at the mesial aspect of the tooth (Fig. 32-3b).
Patients with aggressive periodontitis can be successfully treated, and this is well documented in the literature. Further, by applying a regenerative method in the surgical treatment of deep angular defects like those at 15 and 46, the chance of attachment gain of a magnitude of >4 mm is markedly increased (Giannobile _et al._ 2003; Murphy & Gunsolley 2003). Hence, the treatment decisions made in this case were to first establish proper infection control and then to apply a regenerative surgical approach (guided tissue regeneration) in the periodontal treatment of the lesions at 15 and 46.
Evaluation of the periodontal healing revealed closure of the pockets and _de novo_ bone tissue formation. Single implant-supported restorations were subsequently performed to restore for the loss of teeth 16 and 36 (Fig. 32-3e). After completion of the active treatment the patient was assigned to a supportive care program with recall appointments once every 6 months. Fig. 32-3f–i illustrates the outcome at 12 years post treatment. The regained height of the periodontal tissue support at 15 and 46 following the active treatment was maintained over the years, and optimal bone height is seen around the single implants. The good long-term prognosis in this case is attributed to a high quality of infection control and careful monitoring during the maintenance period.
## Furcation problems
Even if the goal of the treatment of patients with periodontitis should be to preserve the teeth, there may be situations when this goal seems less meaningful in relation to the patient's need for prosthetic rehabilitation. Such a situation is illustrated in Fig. 32-4(a–d). The patient is missing the two premolars in the first quadrant and the molars present with advanced periodontal destruction and through-and-through furcation involvement (grade III). The patient requests a fixed restoration to substitute for the missing premolars. A possible treatment solution following periodontal therapy could include root separation of the molars, after proper endodontic therapy, and the maintenance of, for example, the palatal roots of the molars to be used as posterior abutments in a fixed tooth-supported prosthesis 17... 13. However, advanced interradicular periodontal destruction was identified by furcation probing, indicating that the palatal roots might not have enough remaining periodontal support in order to provide functional stability of a straight FPD (17... 13). The clinical and radiographic examination reveals that the alveolar process in the premolar–molar region has proper dimensions for implant placement. An alternative treatment solution to satisfy the patient's demands for improved function and esthetics could therefore include implant placement to support a FPD.
**Fig. 32-4** A 52-year-old male patient with advanced periodontal destruction at remaining molars in the maxillary right quadrant. (a–d) Clinical and radiographic status at the initial examination. (e,f) Clinical and radiographic status 2 years after active treatment.
The decision made in this case was to extract the two molars and, following proper periodontal treatment of the remaining dentition and establishment of adequate infection control, provide the patient with a three-unit implant-supported FPD and a single-crown restoration on tooth 13 (Fig. 32-4e,f). After completion of active treatment this patient was enrolled in a maintenance care program including recall appointments once every 4 months.
## Single-tooth problem in the esthetic zone
Figure 32-5(a–e) illustrates the maxillary front tooth region of a 45-year-old female patient diagnosed with generalized chronic periodontitis. The right central incisor has severe periodontal destruction with probing pocket depths of 10–11 mm and obvious signs of inflammation at its distal and palatal surfaces. The tooth responded positively to sensibility testing. Interdental black triangles can be seen in the entire anterior tooth region because of approximal loss of periodontal attachment and soft tissue recession. Based on the results of the comprehensive examination, tooth 11 was judged to have a questionable prognosis, whereas it would be possible to resolve the periodontal lesions at the other anterior teeth by non-surgical means and improved self-performed infection control. Since the patient had a high lip line, potential recession of the soft tissue margins as a consequence of the treatment was a factor that had to be considered, particularly in relation to the treatment decision for the severely affected right central incisor. By regenerative therapy it might be possible to maintain the tooth, but will the treatment result in acceptable esthetics? The fact that the defect had a wide extension (buccally–lingually) and that the adjacent teeth presented with approximal attachment loss indicated that there was an obvious risk for loss of tissue height during healing following a surgical intervention. An alternative treatment approach could include the extraction of tooth 11 and to perform installation of a single implant. This alternative solution would also offer the possibility of correcting the position of the crown of 11. In discussing the different treatment alternatives and their consequences with the patient, it was apparent that she preferred to have the position of the tooth corrected as part of the treatment. Hence, based on the careful analysis of the esthetic problems associated with the treatment of the tooth, the decision made was to extract the tooth and make an implant-supported restoration. By the use of the crown together with a portion of the root as a pontic, support to the surrounding soft tissues during initial healing of the extraction socket was provided (Fig. 32-5f).
Evaluation of the outcome of the cause-related phase of therapy, which included oral hygiene instructions, plaque control evaluations, and full-mouth pocket/root debridement, disclosed no remaining pathologically deepened pockets in the front tooth region (Fig. 32-5g). The radiographic evaluation of the extraction site 2 months after the removal of 11 (Fig. 32-5h) showed a preserved bone height at the neighboring approximal tooth sites and gain of bone in the extraction socket. Clinically only minor changes had taken place in the position of the soft tissue margin at the extraction site. A single implant was installed and after 3 months the prosthetic therapy was completed.
Following the completion of the active treatment, the patient was scheduled for supportive care every 6 months. Figure 32-5(i–k) shows the clinical and radiographic status at the 1-year follow-up examination. The position of the soft tissue margin is located at a similar level at the implant-supported crown and the contralateral incisor. Compared to the pre-treatment conditions (Fig. 32-5a), only minimal changes in the position of the soft tissue margins at the implant-borne restoration are evident. Overall some recession of the soft tissue margin has occurred as a consequence of the establishment of healthy marginal tissues.
_In conclusion:_ Although it may be possible to maintain a tooth with severe local periodontal destruction by regenerative periodontal surgery, soft tissue recession as a consequence of the treatment may render the treatment outcome unsatisfactory from an esthetic perspective. Selection of a treatment approach involving tooth extraction and implant therapy instead of periodontal therapy should be based on a careful evaluation of the potential of the various treatment approaches to satisfy the patient's demands for esthetics.
### Conclusions
* The prognosis for the properly treated periodontitis-affected tooth is at least as good as that for the implant.
* An increased risk of failure of implant therapy has been reported for periodontitis-susceptible patients.
* Proper infection control is a critical factor for the long-term success of implant therapy in the periodontally compromised patient.
**Fig. 32-5** A 45-year-old female patient with generalized chronic periodontitis. (a–e) Clinical and radiographic status of the maxillary anterior teeth at the initial examination. The right central incisor has severe periodontal destruction with probing pocket depths of 10–11 mm. (f) Tooth 11 was extracted and the tooth was reshaped and fixed to the neighboring teeth to support the soft tissues during the initial healing of the extraction socket. (g,h) Clinical and radiographic status 2 months post extraction when the implant placement surgery was performed. (i–k) Clinical and radiographic status 1 year after completion of the periodontal and implant treatment.
References
Baelum, V. & Ellegaard, B. (2004). Implant survival in periodontally compromised patients. _Journal of Periodontology_ **75** , 1404–1412.
Berglund, T., Persson, L. & Klinge, B. (2002). A systematic review of the incidence of biological and technical complications in implant dentistry reported in prospective longitudinal studies of at least 5 years. _Journal of Clinical Periodontology_ 29 (Suppl 3), 197–212.
Giannobile, W.V., Al-Shammari, K.F. & Sarment, D.P. (2003). Matrix molecules and growth factors as indicators of periodontal disease activity. _Periodontology 2000_ **31** , 125–134.
Hardt, C.R.E., Gröndahl, K., Lekholm, U. & Wennström, J.L. (2002). Outcome of implant therapy in relation to experienced loss of periodontal bone support. A retrospective 5-year study. _Clinical Oral Implants Research_ **13** , 488–494.
Karoussis, I.K., Salvi, G.E., Heitz-Mayfield, L.J.A., Hämmerle, C.H.F. & Lang, N.P. (2003). Long-term implant prognosis in patients with and without a history of chronic periodontitis: a 10-year prospective cohort study of the ITI® Dental Implant System. _Clinical Oral Implants Research_ **14** , 329–339.
Karoussis, I.K., Müller, S., Salvi, G.E., Heitz-Mayfield, L.J.A., Brägger, U. & Lang, N.P. (2004). Association between periodontal and peri-implant conditions: a 10-year prospective study. _Clinical Oral Implants Research_ **15** , 1–7.
König, J., Plagmann, H.C., Ruuhling, A. & Kocher, T. (2002). Tooth loss and pocket probing depths in compliant periodontally treated patients: a retrospective analysis. _Journal of Clinical Periodontology_ **29** , 1092–1100.
Lindhe, J. & Nyman, S. (1984). Long-term maintenance of patients treated for advanced periodontal disease. _Journal of Clinical Periodontology_ **11** , 504–514.
Murphy K.G. & Gunsolley, J.C. (2003). Guided tissue regeneration for the treatment of periodontal intrabony and furcation defects. A systematic review. _Annals of Periodontology_ **8** , 266–302.
Rosling, B., Serino, G., Hellström, M.K., Socransky, S.S. & Lindhe, J. (2001). Longitudinal periodontal tissue alterations during supportive therapy. Findings from subjects with normal and high susceptibility to periodontal disease. _Journal of Clinical Periodontology_ **28** , 241–249.
Wennström, J.L., Ekestubbe, A., Gröndahl, K., Karlsson, S. & Lindhe, J. (2004). Oral rehabilitation with implant-supported fixed partial dentures in periodontitis-susceptible subjects. A 5-year prospective study. _Journal of Clinical Periodontology_ **31** , 713–724.
Yi, S.W., Ericsson, I., Carlsson, G.E. & Wennström, J.L. (1995). Long-term follow-up of cross-arch fixed partial dentures in patients with advanced periodontal destruction. Evaluation of the supporting tissues. _Acta Odontologica Scandinavica_ **53** , 242–248.
# Chapter 33
# Systemic Phase of Therapy
Niklaus P. Lang and Hans-Rudolf Baur
* * *
Introduction
Protection of the dental team and other patients against infectious diseases
Protection of the patient's health
Prevention of complications
Infection, specifically bacterial endocarditis
Bleeding
Cardiovascular incidents
Allergic reactions and drug interactions
Systemic diseases, disorders or conditions influencing pathogenesis and healing potential
Control of anxiety and pain
Smoking counseling
* * *
# Introduction
The systemic phase of periodontal therapy should be concerned with general health implications of periodontal diseases and periodontal treatment. While the former aspects are described in Chapters 12, 13, 16, and 21, the latter aspects are presented in this chapter.
The systemic phase of periodontal therapy is designed to protect the patient against unforeseen systemic reactions, to prevent complications affecting the general health of the patient and to protect the health care providers from (predominantly infectious) hazards in conjunction with the treatment of risk patients.
In order to adequately plan the systemic phase, results from a health questionnaire (Chapter 26) filled in by the patient in the waiting area, the family and social history, the general medical and, in particular, the smoking history have to be evaluated. Also, any extra- and intraoral findings pertinent to the patient's systemic health have to be considered.
The systemic phase of periodontal therapy encompasses:
* Precautions for protecting the general health of the dental team and other patients against infectious and contagious diseases
* Protection against potentially harmful systemic effects of routine therapy
* Making allowances for systemic diseases or disorders that may influence the etiology of the patient's periodontal conditions, the healing potential, and the systemic response to therapy
* Controlling anxiety and low pain threshold
* Risk assessment and considerations of systemic supportive therapy
* Smoking counseling and instituting tobacco use cessation programs.
# Protection of the dental team and other patients against infectious diseases
As a rule, routine periodontal therapy should be postponed in a patient with an active contagious state of a disease until the patient has received adequate medical treatment. Given the fact that patients may not always be aware of such a state or that all manifestations of disease may have abated, but the patient may still be carrier of infectious agents, routine dental treatment should be carried out under special precautions against transmission of the most serious diseases being transmitted orally. These include infectious hepatitis (Levin _et al_. 1974), HIV infection, and venereal diseases (Chue 1975). Hygiene in the dental office, therefore, has to address the most contagious level of infective agents, the hepatitis virus, and cope with the prevention of the transmission of these infections. As a minimal precaution, the wearing of rubber gloves and mouth masks is strongly recommended for all dental therapy in all patients. Also protective glasses for both the therapist and the patient should be worn during procedures generating aerosols.
Herpes simplex virus (Nahmias & Roizman 1973) and tuberculosis are other infectious diseases with a high transmission potential. Special precautions should be observed in patients with a recent history (2–3 years) of infectious hepatitis, although the dental team may be vaccinated against hepatitis. If the medical history and the oral examination reveal that the patient may have overt or hidden systemic disease, she/he should be referred for medical examination prior to enrolling the patient into comprehensive periodontal therapy.
# Protection of the patient's health
A number of systemic conditions may affect treatment planning, although there may be no direct relevance in the pathogenesis and healing potential of periodontal lesions. Since over 50% of all patients over 40 years of age may have systemic conditions or take medications affecting periodontal therapy, these aspects have to be carefully appraised prior to instituting therapy.
For patients with life-threatening systemic conditions, such as coronary insufficiency or hypertensive heart disease, the patient's physician should be consulted about appropriate patient management and whether treatment should be performed in a hospital or clinic rather than a private practice setting. If the dental office is considered to be the adequate environment for treating these patients, short appointments should be planned and treatment performed with complete pain control using local anesthesia without any or with minimal vasoconstrictive drugs.
# Prevention of complications
The complications most commonly encountered in the dental office are:
* Infection
* Bleeding
* Cardiovascular incidents
* Allergic reactions.
These may be prevented if appropriate precautions are taken. Hence, gaining awareness of possible complications from a medical history is an important step for treatment planning and total patient care.
## Infection, specifically bacterial endocarditis
Patients with cardiac disease or disorders involving the endocardium are susceptible to endocarditis as a result of blood-borne infection. Such conditions include rheumatic heart disease, congenital valvular heart defects, aortic valvular diseases, and collagen diseases involving the endocardium. In addition, patients wearing prosthetic heart appliances belong to this risk group.
The major procedures thought to be the cause of bacterial endocarditis are extractions and scaling and/or root planing leading to significant bleeding and possible bacteremia (Durack 1995). Hence, it is not surprising that national societies have issued guidelines for antibiotic prophylaxis against bacterial endocarditis (USA: Dajani _et al_. 1997; UK: Gould _et al_. 2006; FDI, 1987). The common belief is that a bacteremia occurs only when dental procedures cause bleeding and does not occur when there is no bleeding. Hence, procedures such as extractions, root instrumentation, and periodontal and implant surgical procedures would require antibiotic prophylaxis, while for example the placement of fillings does not. This hypothesis was addressed in a study in children in which 14 various dentogingival manipulative procedures were evaluated (Roberts _et al_. 1997). It was clearly demonstrated that no relationship existed between the existence of bleeding and bacteremia. However, the number of oral organisms isolated from the blood where bleeding was present was statistically significantly higher than when there was no bleeding. It was concluded that the cumulative exposure to bacteremia is significantly greater from "everyday" procedures, when compared to dental procedures and hence, the cause of bacterial endocarditis may be attributable to such cumulative everyday exposures that are often thousands to millions of times greater than that occurring following surgical procedures, such as extractions of teeth (Roberts 1999).
Antibiotic prophylaxis to prevent bacterial endocarditis is predominantly based on anecdotal and circumstantial evidence suggesting a causal association between various procedures and bacteremia (Baltch _et al_. 1982). A case study, however, did not identify a link between endocarditis and dental treatment (Guntheroth 1984; Strom _et al_. 1998). Moreover, accumulating evidence suggests that bacteremia may easily be produced, e.g. by toothbrushing or chewing, rather than by single procedures causing bleeding. Hence, endocarditis causation has shifted from procedure-related bacteremia to cumulative or "everyday" bacteremia (Gould _et al_. 2006).
Indeed, a recent systematic review of the Cochrane Collaboration (Oliver _et al_. 2004) concluded that there was no conclusive evidence to support the use of prophylactic penicillin to prevent bacterial endocarditis in invasive dental procedures. This review did not find any randomized controlled clinical trials, any controlled clinical trials or any cohort studies. From a total of three case–control studies (Imperiale & Horowitz 1990; Van der Meer _et al_. 1992; Lacassin _et al_. 1995), only one study (Van der Meer _et al_. 1992) complied with the inclusion criteria. Details of 349 individuals who developed definite native-valve endocarditis in the Netherlands within a 2-year period were collected. Controls had not been diagnosed with endocarditis, but had one of the cardiac conditions and were outpatients of one of five hospitals. Controls were matched for age and had undergone dental procedure within 180 days of their interview. No significant protective effect of antibiotic prophylaxis was seen against endocarditis.
It has to be realized, however, that clinicians feel bound by guidelines and medico-legal considerations to provide antibiotic prophylaxis rather than by the best scientific evidence available. Ethically, practitio ners need to discuss the potential benefits and harms of antibiotic prophylaxis with the patients and their cardiologists before the decision is made about administration (Oliver _et al_. 2004). Considering the change in paradigms regarding bacterial endocarditis, a task force of the British Society for Antimicrobial Chemotherapy has recently published new guidelines (Gould _et al_. 2006) (Table 33-1). According to these, the practice of giving patients antibiotics is reserved for those patients with a history of healed bacterial endocarditis, prosthetic heart valves, and surgically constructed conduits, while patients with cardiac abnormalities should no longer receive antibiotic prophylaxis before dental procedures. A patient information form has also been published (Table 33-2).
Table 33-1 Recommendations of the British Society for Antimicrobial Chemotherapy (BSAC) for prophylaxis of bacterial endocarditis
From Gould _et al_. (2006).
Where a course of treatment involves several visits, the antibiotic regimen should alternate between amoxicillin and clindamycin.
Pre-operative mouth rinse with chlorhexidine gluconate 0.2% (10 ml for 1 minute).
Table 33-2 British Society for Antimicrobial Chemotherapy (BSAC) Prevention of Infective Endocarditis Guidelines Information for Patients and Parents February 2006
A BSAC group of experts has spent a lot of time carefully looking at whether dental treatment procedures are a possible cause of infective endocarditis (IE) (sometimes called bacterial endocarditis (BE)), which is infection of the heart valve.
---
After a very detailed analysis of all the available evidence they have concluded that there is no evidence that dental treatment procedures increase the risk of these infections.
Therefore, it is recommended that the current practice of giving patients antibiotics before dental treatment be stopped for all patients with cardiac abnormalities, except for those who have a history of healed IE, prosthetic heart valves and surgically constructed conduits.
The main reasons for this are the lack of any supporting evidence that dental treatment leads to IE and the increasing worry that administration of antibiotics may lead to other serious complications such as anaphylaxis (severe allergy) or antibiotic resistance.
The advice from the BSAC is that patients should concentrate on achieving and keeping a high standard of oral and dental health, as this does reduce the risk of endocarditis. Help for this will be provided by your Dental Professional.
British Society for Antimicrobial Chemotherapy (BSAC), 2 February 2006
## Bleeding
Due consideration must be given to patient on anticoagulant medication or patients on preventive anticoagulant drugs such as salicylates. For the first group of patients, a consultation with the patient's physician is indispensable. Especially prior to periodontal or implant surgical procedures, temporary adjustment of the intake of anticoagulant medication may have to be initiated in cooperation with the physician. Careful planning and timing of these procedures is mandatory.
Preventive anticoagulant therapy does not generally create problems for routine dental therapy, including surgical procedures, although consultation with the patient's physician still is advisable.
Individuals with known cirrhosis of the liver, or even patients with high alcohol consumption over many years without diagnosed cirrhosis, are at a potential risk for bleeding complications during periodontal and/or implant surgery, as their clotting mechanisms may be affected (Nichols _et al_. 1974). Again, medical consultation is recommended prior to periodontal treatment of such patients.
Extra precautions against bleeding should be taken when treating patients with any kind of blood dyscrasia or hemophilia. Following mandatory consultation with the patient's physician, it is recommended to render treatment in small segments (only a few teeth being instrumented at each visit) and to apply periodontal dressings over the treated area, even if the treatment only consisted of root instrumentation. With systematic periodontal treatment and institution of efficacious oral hygiene measures, the annoying symptom of oral bleeding can often be controlled irrespective of the patient's bleeding disorder.
## Cardiovascular incidents
Cardiac patients are often treated with anticoagulants and, hence, may develop bleeding problems (as indicated above), especially if given drugs (e.g. aspirin, indomethacin, sulfonamide, tetracycline) that interact with coagulation. Other cardiovascular drugs (antihypertensive, antiarrhythmic, diuretic) are often used in these patients which may increase the danger of hypotensive episodes during dental treatment.
Stress associated with dental procedures may precipitate anginal pain or congestive heart failure in patients with cardiovascular disease. Therefore, every effort should be made to keep procedures short and control anxiety and pain in this patient population.
## Allergic reactions and drug interactions
Full knowledge of the patient's known allergies and the medications administered is essential before any drug is prescribed, administered or used during treatment. The most common allergic reactions encountered in the dental office are allergies to some local anesthetics (Novocain®), penicillins, sulfa derivatives, and disinfectants, such as iodine. In case of known allergies, such drugs have to be avoided. A consultation with the patient's physician is advisable to discuss the possible administration of replacement drugs.
Many patients – over 90% over the age of 60 years – regularly take medications for various systemic conditions, special attention has to be devoted to possible drug interactions, especially in the elderly. Drugs prescribed as part of periodontal therapy or used during treatment may interfere with the effectiveness of drugs the patient is already taking or create hazardous or synergistic action with such drugs. Hence, no new drugs should be prescribed without fully understanding their possible interaction with drugs already in use. Dentists should never change an existing drug therapy without prior discussion and preferably written consent of the physician.
Many patients regularly take tranquilizers and antidepressant drugs that have the potential for summation and synergistic effects with drugs that may be used during periodontal therapy. Moreover, the interaction with and potentiation of these drugs with alcohol should be discussed with the patient.
# Systemic diseases, disorders or conditions influencing pathogenesis and healing potential
All possible attempts should be made to alleviate the effects of systemic diseases, such as blood disorders and diabetes mellitus, as much as possible before definitive periodontal treatment is initiated. However, cause-related therapy may easily be carried out and generally results in remarkable success even during active stages of these systemic conditions. How far the treatment plan should progress with respect to pocket reduction and/or regenerative procedures depends on the seriousness of the patient's systemic involvement and likewise, to a great extent, on the potential threat to the patient's health from incomplete periodontal therapy.
Diabetes control, as an example, may be facilitated by successful control of the periodontal infection (Grossi _et al_. 1997; Genco _et al_. 2005). Thus, periodontal treatment may have a beneficial effect on the systemic health of the patient (see Chapter 21). Palliative treatment of advanced periodontitis with furcation involvement and residual deep pockets that cannot be reduced should not be undertaken for such patients. Rather the involved teeth with repeated abscesses and pus formation should be extracted if needed to accomplish infection control.
Clinical experience indicates that the healing response of the periodontal tissues is as good in diabetic as in non-diabetic patients provided that the diabetes is fairly well controlled. However, juvenile diabetics may have angiopathic changes associated with a lowered resistance to infection that may require the use of antibiotics following periodontal or implant surgery. With controlled diabetes, premedication with antibiotics is not indicated. Hypoglycemia may become aggravated by the stress of periodontal surgery and, hence, precautions have to be taken to avoid hypoglycemic reactions in such patients.
Patients taking therapeutic doses of cortisone over a long period of time may yield considerable metabolic effects with systemic manifestations of a reduced rate of fibroblastic activity and hence, a lowered resistance to infection during wound healing. Nevertheless, such patients can be treated successfully by regular cause-related therapy with no significant delay in healing. The use of antibiotics is not recommended for these patients, unless there is a serious infectious condition in the mouth associated with the development of fever.
# Control of anxiety and pain
Many patients interested in maintaining a healthy dentition do not regularly seek dental care because of anxiety and apprehension related to such treatment. Since modern dentistry offers a variety of effective means for controlling pain and apprehension, patients should no longer suffer from dental treatment. During history taking and the oral examination, the patient's profile regarding anxiety and pain thresholds should be explored.
Prior to therapy, it may be advisable to premedicate an apprehensive patient using diazepams (Benzodiazepine, Valium®, 2–5 mg) to be taken the night before, in the morning and half an hour before an extensive and/or surgical procedure. Painless dental care can be achieved by carefully applying local anesthetics.
Post-operative analgesic medication, such as non-steroidal anti-inflammatory drugs (NSAIDs) with analgesic and antipyretic properties are recommended. Diclofenac potassium, the active ingredient of Voltaren® Rapide, inhibits prostaglandin synthesis by interfering with the action of prostaglandin synthetase. Following any kind of periodontal and implant surgery, 50 mg twice daily of Voltaren® Rapide is administered for 3 days. In addition, further adjunctive pain killers (Mefenaminic acid, e.g. Ponstan®, 500 mg not more than every 6–8 hours) may be prescribed depending on the individual patient's need and pain threshold.
Favorable personality interactions between the patient, the therapist, and the entire office staff may contribute to the control of anxiety, but may require more time and consideration than that allocated to the routine patient.
# Smoking counseling
Cigarette smoking constitutes the second most important risk factor in the etiology and pathogenesis of periodontal diseases after poor oral hygiene standards. A careful assessment of the patient's smoking history is therefore indispensable. Depending on the duration of the exposure to tobacco smoking, daily consumption, and the patient's periodontal status, smoking counseling has to be undertaken as one of the primary measures. In all patients that smoke, the contributory role of tobacco consumption to the pathogenesis of periodontitis has to be addressed. Depending on the patient's response, smoking cessation programs may be instituted. Short-term interventions lasting 3–5 minutes using motivational interviewing techniques (Chapter 34) may be included during the initial phase of periodontal therapy. If a heavy smoker is ready to quit the habit, professional cessation programs may be the appropriate measures to take. Smoking counseling is further discussed in Chapter 34.
### Conclusions
The goals of the systemic phase of periodontal therapy are to appraise the aspects that may require protection of both the dental team and the systemic health of the patient. Infection control in the dental office plays a central role. Protecting the patient against presumptive complications, such as infection, especially bacterial endocarditis, bleeding, cardiovascular incidences, and allergies, requires in-depth knowledge of the patient's medical history and oral examination.
Bacterial endocarditis prophylaxis is nowadays reserved for those patients with a history of a healed bacterial endocarditis, prosthetic heart valves or surgically constructed conduits, while the use of antibiotics before dental treatment is not necessary for patients with cardiac abnormalities. Patients with systemic diseases such as diabetes mellitus or cardiovascular diseases usually are treated with a number of medications that may interact with drugs prescribed during periodontal therapy. Precautions should be taken, and consultation with the patient's physician prior to systematic periodontal therapy is recommended.
It has to be realized that periodontal treatment may have a beneficial effect on the systemic health of the patient as well. Glycemic control may be facilitated in diabetics if proper periodontal therapy is rendered.
Finally, smoking counseling is part of modern periodontal treatment owing to the fact that, after inadequate oral hygiene standards, cigarette smoking constitutes the second most important risk factor for periodontitis.
References
Baltch, A.L., Schaffer, C., Hammer, M.C., Sutphen, N.T., Smith, R.P., Conroy, J. & Shayegani, M. (1982). Bacteraemia following dental cleaning in patients with and without penicillin prophylaxis. _American Heart Journal_ **104** , 1335–1339.
Chue, P.W.Y. (1975). Gonorrhoea – its natural history, oral manifestations diagnosis, treatment and prevention. _Journal of the American Dental Association_ **90** , 1297–1301.
Dajani, A.S., Taubert, K.A., Wilson, W., Bolger, A.F., Bayer, A., Ferrieri, P., Gewitz, M.H., Shulman, S.T., Nouri, S., Newburger, J.W., Hutto, C., Pallasch, T.J., Gage, T.W., Levison, M.E., Peter, G. & Zuccaro, G. Jr. (1997). Prevention of bacterial endocarditis. Recommendations by the American Heart Association. _Journal of the American Medical Association_ **227** , 1794–1801.
Durack, D.T. (1995). Prevention of infective endocarditis. _New England Journal of Medicine_ **332** , 38–44.
Federation Dentaire Internationale (1987). Guideline for antibiotic prophylaxis of infective endocarditis for dental patients with cardiovascular disease. _International Dental Journal_ **37** , 235–236.
Genco, R.J., Grossi, S.G., Ho, A., Nishimura, F. & Murayama, Y. (2005). A proposed model linking inflammation to obesity, diabetes, and periodontal infections. _Journal of Periodontology_ 76 (Suppl), 2075–2084.
Gould, F.K., Elliott, T.S.J., Foweraker, J., Fulford, M., Perry, J. D., Roberts, G.J., Sandoe, J.A.T. & Watkin, R.W. (2006). Guidelines of the prevention of endocarditis: report of the Working Party of the British Society of Antimicrobial Chemotherapy. _Journal of Antimicrobial Chemotherapy_ **57** , 1035–1042.
Grossi, S.G., Skrepcinski, F.B., DeCaro, T., Robertson, D.C., Ho, A.W., Dunford, R.G. & Genco, R.J. (1997) Treatment of periodontal disease in diabetics reduces glycated hemoglobin. _Journal of Periodontology_ **68** , 713–719.
Guntheroth, W. (1984). How important are dental procedures as a cause of infective endocarditis? _American Journal of Cardiology_ **54** , 797–801.
Imperiale, T.F. & Horowitz, R.I. (1990). Does prophylaxis prevent post dental infective endocarditis? A controlled evaluation of protective efficacy. _American Journal of Medicine_ **88** , 131–136.
Lacassin, F., Hoen, B., Leport, C., Selton-Suty, C., Delahaye F., Goulet, V., Etienne, J. & Briancon, S. (1995). Procedures associated with infective endocarditis in adults – a case control study. _European Heart Journal_ **16** , 1968–1974.
Levin, M.L., Maddrey, W.C., Wands, J.R. & Mendeloff, A.L. (1974). Hepatitis B transmission by dentists. _Journal of the American Medical Association_ **228** , 1139–1140.
Nahmias, A.J. & Roizman, B. (1973). Infection with herpes simplex viruses 1 and 2. Parts I, II, III. _New England Journal of Medicine_ 289, 667–674, 719– **725** , 781–789.
Nichols, C., Roller, N.W., Garfunkel, A. & Ship, I.I. (1974). Gingival bleeding: the only sign in a case of fibrinolysis. _Oral Surgery, Oral Medicine, Oral Pathology_ **38** , 681–690.
Oliver, R., Roberts G.J. & Hooper, J. (2004). Penicillins for the prophylaxis of bacterial endocarditis in dentistry (Review). _The Cochrane Database of Systematic Reviews._ Issue 2. Art. No.: CD003813.pub2. DOI: 10.1002/14651858.CD003813.pub2. New York: John Wiley & Sons Ltd, 1–20.
Roberts, G.J., Holzel, H., Sury, M.R.J., Simmons, N.A., Gardner, P. & Longhurst, P. (1997). Dental bacteraemia in children. _Pediatric Cardiology_ **18** , 24–27.
Roberts, G.J. (1999). Dentists are innocent! "Everyday" bacteraemia is the real culprit: a review and assessment of the evidence that dental surgical procedures are a principal cause of bacterial endocarditis in children. _Pediatric Cardiology_ **20** , 317–325.
Strom, B.L., Abrutyn, E., Berlin, J.A., _et al_. (1998). Dental and cardiac risk factors for infective endocarditis. A population based, case-control study. _Annals of Internal Medicine_ **129** , 761–769.
Van der Meer, J.T.M., van Wijk, W., Thompson, J., Valkenburg, H.A. & Michel, M.F. (1992). Efficacy of antibiotic prophylaxis for the prevention of native-valve endocarditis. _Lancet_ **339** , 135–139.
# Part 11: Initial Periodontal Therapy (Infection Control)
34 Motivational Interviewing
_Christoph A. Ramseier, Delwyn Catley, Susan Krigel, and Robert A. Bagramian_
35 Mechanical Supragingival Plaque Control
_Fridus Van der Weijden, José J. Echeverría, Mariano Sanz, and Jan Lindhe_
36 Chemical Supragingival Plaque Control
_Martin Addy and John Moran_
37 Non-surgical Therapy
_Noel Claffey and Ioannis Polyzois_
# Chapter 34
# Motivational Interviewing
Christoph A. Ramseier, Delwyn Catley, Susan Krigel, and Robert A. Bagramian
* * *
The importance of behavioral change counseling in periodontal care
What is motivational interviewing?
Development of motivational interviewing
History of motivational interviewing
What is motivational interviewing?
Evidence for motivational interviewing
Implementation of motivational interviewing into the periodontal treatment plan
Key principles of motivational interviewing
Basic communication skills
Giving advice
Case examples for oral hygiene motivation
Oral hygiene motivation 1
Oral hygiene motivation 2
Case example for tobacco use cessation
* * *
# The importance of behavioral change counseling in periodontal care
Periodontal health is supported by appropriate behaviors such as regularly self-performed plaque control, avoidance of tobacco, and consumption of a healthy diet. Inadequate oral hygiene, tobacco use, and uncontrolled diet in type 2 diabetes mellitus, on the other hand, are shown to have a destructive impact on periodontal tissues. The prevention and control of periodontal disease needs to be addressed on both the population and the individual level. Efficient public health approaches consider the entire population and focus on health issues that present the largest burden within a community. The dental community involved with oral health care should gain an understanding of the health effects of inappropriate behaviors in order to successfully target prevention and disease control. As a consequence, services for primary and secondary prevention on an individual level oriented towards the change of inappropriate behavior become a professional responsibility for all oral health care providers.
Data from epidemiologic studies consistently reveal the prevalence of periodontal disease in more than 50% of the adult population (Albandar _et al_. 1999; Albandar 2002). In addition to the causal relationship with dental biofilms, a positive association with tobacco use has been documented (Bergstrom 1989; Haber _et al_. 1993; Tomar & Asma 2000). Tobacco use contributes to the global burden of public health with almost one third of the adult population using various forms of tobacco and an increasing number of annual deaths from tobacco-related diseases. Moreover, dietary excess has been shown to significantly impact chronic diseases including obesity, cardiovascular diseases, type 2 diabetes, cancer, osteoporosis, and oral diseases (Petersen 2003).
There is growing evidence that the patient's individual behavior is seen to be influential or even critical for the success of periodontal therapy; since the results of periodontal therapy appear to be limited in patients who especially lack appropriate behavior. In a recent literature review by Ramseier (2005) it was shown that second to plaque control, smoking cessation was the most important measure for the management of chronic periodontitis. Therefore, it appears to be reasonable in clinical concepts for periodontal care to (1) include assessments of patient behavior, and (2) if necessary apply effective behavior change counseling methods.
Traditional periodontal care includes the instruction of proper oral hygiene methods. In practice, as an example, a demonstration of a suitable tooth-brushing method is given to the patient, followed by recommendations of both the frequency and the time spent per brushing. Past and recent studies on the effectiveness of oral hygiene instructions consistently revealed that the patient adherence to a proper daily oral hygiene regime generally remains poor (Johansson _et al_. 1984; Schuz _et al_. 2006). The reinforcement of oral hygiene habits through additional appointments can compensate somewhat for the ineffectiveness of one-time or repeated oral hygiene instructions. However, due to weak patient adherence, visits for supportive periodontal care are often cancelled, resulting in a lack of professional maintenance care and the potential recurrence of periodontal disease (Wilson _et al_. 1984; Demetriou _et al_. 1995; Schuz _et al_. 2006).
Unfortunately, many health education approaches seem to be inefficient in accomplishing long-term change, potentially leading to frustration of both the patient and the clinician. The following hypothetical dialogue between a clinician (Dr) and a patient (P) illustrates how using a directive advice-oriented method for behavior change counseling can lead to an unproductive conversation and little likelihood of change by the patient:
Dr | Are you flossing regularly?
---|---
P | Yes, but not as often as I should.
Dr | I strongly recommend that you floss every day. There are serious consequences if you don't floss frequently enough.
P | I know I should do it more often, but...
Dr | It is really important!
P | I know...... but I don't have the time!
Since the clinician doesn't offer the patient a chance to discuss the reasons to floss as well as the patient's perceived barriers to flossing, the conversation reaches an impasse and behavior change will be unlikely. In certain cases, the patient may even be blamed for poor compliance and further oral health education may be seen to be pointless.
There is a shortage of evidence in both the dental and behavioral literature on effective methods for behavior counseling in periodontal care, in particular regarding:
* Individual oral hygiene instructions for optimal oral hygiene
* Effective tobacco use prevention and cessation counseling to help abstain from tobacco
* Appropriate dietary counseling for a healthy diet.
In order to get reliably effective outcomes in periodontal care, it may be necessary to apply different behavior change counseling methods for each individual behavior. According to the best available evidence for oral hygiene instructions, the repeated demonstration of a cleaning device may be applied, while for tobacco use cessation, in addition to pharmacotherapy, the method of the five As (ask, advise, assess, assist, arrange) may be used (Fiore 2000). Additionally, type 2 diabetic patients or patients with a high carbohydrate diet may be referred to nutritionists for dietary counseling. From a practical point of view, however, it may be complicated and even discouraging to approach the periodontal patient with a variety of different methods targeting the same purpose: establishing appropriate behavior to improve the outcomes of both periodontal therapy and long-term supportive periodontal care.
Hence, aiming for simplicity, it may be preferable to apply one single method for behavior change counseling in periodontal care that is shown to be effective in both primary and secondary prevention of oral diseases. This method should be:
* Based on the best available evidence
* Applicable to oral hygiene behavior, tobacco use prevention and cessation, and dietary counseling
* Suitable for implementation by the dental practice team in a cost-effective way.
# Development of motivational interviewing
As discussed, health _education_ efforts provided by practitioners are frequently ineffective in changing patient behavior. Considerable behavioral research suggests that the root of this common problem can be traced back to a false assumption inherent in the health education approach. Specifically, that behavior change is simply a function of a patient having the requisite knowledge or understanding, and that it is up to the practitioner to provide the relevant information. Motivational interviewing (MI), in contrast, is based on a different assumption of human behavior change. It assumes that the knowledge is insufficient to bring about behavior change and that, instead, sustained behavior change is much more likely when change is connected to something the individual values. In other words, motivation is elicited "from within the patient" rather than externally imposed upon the patient by a practitioner. In MI, the assumption is that individuals have "within them" their own reasons for changing and that the role of the practitioner is to elicit and reinforce these reasons.
### Motivational Interviewing 697
MI originated in the field of addictive behavior but has increasingly been applied to a wide variety of other behavior change problems, including health behaviors such as tobacco use and diet and exercise (Burke _et al_. 2004; Hettema _et al_. 2005). MI principles and methods have also been specifically adapted for brief interventions in medical settings (Butler _et al_. 1999; Rollnick _et al_. 1999) and have recently been tested in a dental setting (Weinstein _et al_. 2006).
## History of motivational interviewing
William Richard Miller, the originator of MI, developed the method in response to his observations regarding the treatment of patients with alcohol problems in the 1970s. The standard approach to the treatment of alcoholic patients was confrontational, and failure of treatment was attributed either to "denial", seen as a personality deficit on the part of the client, or the failure of the client to engage with the program (Miller 1983). In contrast, he observed that the research literature suggested that positive outcomes were mostly related to a strong bond or "therapeutic alliance" between the counselor and the patient. Miller began to test his empathy-centered treatments on problem drinkers and found that change was occurring more quickly than with traditional methods (Moyers 2004). This brief treatment which used the _therapeutic alliance_ and _empathy_ to engender the client's inherent motivation to change was first described in an article by Miller in Behavioural Psychotherapy (1983). Subsequently Miller met Stephen Rollnick, the co-founder of the MI method, who had been concentrating on ambivalence, or the extent to which the client envisioned the pros and cons of changing. Miller and Rollnick began to explore the use of language during MI, concentrating on the elicitation of client "change talk" to promote behavior change. In 1991, Miller and Rollnick published the first edition of " _Motivational Interviewing: Preparing People to Change Addictive Behaviors_ " in which they provided a detailed description of the approach. Since then there has been an explosion in the research and application of MI with many researchers addressing the applicability of the method to addressing health behavior change (Resnicow _et al_. 2002).
## What is motivational interviewing?
MI has been defined as "a client-centered, directive method for enhancing intrinsic motivation to change by exploring and resolving ambivalence" (Miller & Rollnick 2002). The client-centered element refers to the emphasis that is placed on understanding and working from the perspective of the patient and their view of what it means to make a behavior change. For example, rather than a clinician simply telling a patient about the benefits of quitting smoking (from the practitioner perspective), the practitioner invites the patient to describe _his or her own view_ of the advantages and disadvantages of quitting continuing to smoke. Although the patient's perspective is central, because MI is also directive, the practitioner takes deliberate steps to facilitate a particular behavioral outcome. For example, without ignoring patient concerns about changing, the practitioner selectively reinforces and encourages elaboration of any patient statements that are oriented toward the possibility or benefits of making a change. By eliciting and elaborating upon the patient's own reasons for change the motivation for change that is fostered is intrinsic or internal, rather than externally imposed. This approach rests on the assumption that individuals are almost always ambivalent about changing their behavior (i.e., it is almost always the case that individuals can identify both pros and cons of changing). MI practitioners therefore attempt to enhance intrinsic reasons for change by facilitating an exploration and resolution of the patient's underlying ambivalence.
# Evidence for motivational interviewing
Because MI was initially developed for the treatment of addictive behavior, particularly alcohol addiction, the bulk of empirical studies has been conducted in this area. Nevertheless, the explosion in the application (Hettema _et al_. 2005) of MI to other areas of behavior change has been sufficient that there are now four published meta-analyses (Burke _et al_. 2003, 2004; Hettema _et al_. 2005; Rubak _et al_. 2005), the more recent of which include more than 70 clinical trials. Generally, the meta-analyses indicate that MI-based interventions are at least equivalent to other active treatments and superior to no-treatment or placebo controls for problems involving addictive behavior (drugs, alcohol, and gambling), adoption of water purification/safety technology, diet and exercise, and treatment engagement, retention, and adherence. Effect sizes are on average in the small to medium range but are highly variable (Hettema _et al_. 2005). Of particular relevance to dental settings where only brief counseling is feasible, is that MI-based interventions are just as efficacious as alternative active interventions despite involving significantly less contact time, suggesting that MI may be a particularly efficient method of counseling (Burke _et al_. 2004). Rubak _et al_. (2005) report that in brief encounters of 15 minutes, 64% of studies showed an effect. In addition, when the intervention was delivered by physicians an effect was observed in approximately 80% of studies suggesting that it is feasible for professionals who are not counseling experts to deliver effectively MI in brief encounters.
Studies of MI for tobacco use cessation are also of particular relevance. Although fewer studies were available, the meta-analyses cited above did not find MI to be efficacious for smoking cessation. Nevertheless, most of the smoking cessation studies can be criticized for various reasons, including not having procedures to ensure and document fidelity to MI principles by the interventionists (Colby _et al_. 1998; Butler _et al_. 1999; Stotts _et al_. 2002; Wakefield _et al_. 2004), testing the intervention with smokers who are already motivated to quit which may be counterproductive (Smith _et al_. 2001; Ahluwalia _et al_. 2006), and not providing sufficient guidance on _how_ to quit once participants were motivated by MI (Butler _et al_. 1999; Okuyemi _et al_. 2007). On the positive side, these studies also show that MI leads to significantly more quit attempts (Wakefield _et al_. 2004; Borrelli _et al_. 2005); greater reductions in smoking level (Borrelli _et al_. 2005); greater advances in readiness to quit (Butler _et al_. 1999); greater self-reported abstinence in the previous 24 hours (Butler _et al_. 1999); and a lower rate of increased smoking among pregnant women who were smoking early in pregnancy (Tappin _et al_. 2005). Importantly, a recent study (published subsequent to the meta-analyses) of primary care patients has shown that three 20-minute sessions of MI delivered by family physicians can increase smoking cessation more than five-fold compared to brief advice (Soria _et al_. 2006). This study addressed many of the limitations of prior studies by recruiting a large proportion of smokers not necessarily ready to quit, and incorporating procedures to ensure fidelity to MI principles.
Another particularly relevant target behavior for oral health is dietary habits. As indicated, meta-analyses have found significant effects of MI for changing diet. Specifically, these studies have documented changes due to MI in overall dietary intake (Mhurchu _et al_. 1998), fat intake (Mhurchu _et al_. 1998; Bowen _et al_. 2002), carbohydrate consumption (Mhurchu _et al_. 1998), cholesterol intake (Mhurchu _et al_. 1998), body mass index (BMI) (Mhurchu _et al_. 1998), weight (Woollard _et al_. 1995), salt intake (Woollard _et al_. 1995), alcohol consumption (Woollard _et al_. 1995), and consumption of fruits and vegetables (Resnicow _et al_. 2001; Richards _et al_. 2006).
At the time of writing, there was only one published study focused on oral health. This study examined the effect of using MI compared to traditional health education for motivating 240 mothers of young children with high risk for developing dental caries to use dietary and non-dietary behaviors for caries prevention (Weinstein _et al_. 2004, 2006). An MI session and six follow-up phone calls over a year in addition to an educational pamphlet and video was more effective than the pamphlet and video alone in preventing new dental caries among the children after 2 years. This result is consistent with the results of the meta-analyses that have found MI to be efficacious for dietary change (Burke _et al_. 2003; Hettema _et al_. 2005).
In summary, there is generally a wealth of support for MI as an effective method of counseling for behavior change. MI has also been shown to be relatively efficient and has been successfully delivered by medical practitioners. In areas of specific relevance to oral health practitioners, MI has either already been shown to be efficacious or offers significant promise. Given the extraordinary explosion in the application of MI we anticipate that it will not be long before there will be many more studies specific to dental settings.
# Implementation of motivational interviewing into the periodontal treatment plan
## Key principles of motivational interviewing
Although MI methods and techniques provide a wealth of guidance of what to do and what not to do when counseling patients, Miller and Rollnick have emphasized that to be an effective MI practitioner it is more important to embody the underlying philosophy than to be able to apply the collection of techniques. They have identified four general principles that capture the underlying philosophy of the method. First, a practitioner should _express empathy_ for the patient's behavior change dilemma. In other words, the practitioner should communicate acceptance of the patient's perspective, providing and _expressing_ full acknowledgement of the patient's feelings and concerns. The second principle is to _develop discrepancy_ between the patient's current behavior and how they would ideally like to behave to be consistent with their broader goals and values. For example, the goal of being strong or responsible, or a good spouse or parent, can often be linked to being healthy and suggest the need for improved health behaviors. The third principle is to _roll with resistance_. When patients argue against change there is a strong tendency to fall into the trap of providing counter arguments. As a result the patient expends all of their energy arguing against change which is precisely the opposite of what is desired, perhaps making them even less likely to change. MI practitioners therefore avoid arguing and instead use MI methods to "roll with resistance". The fourth principle is to _support self-efficacy_ or the patient's confidence in their ability to make a change. Patients are unlikely to succeed in making a change even if they are motivated, when they don't know how or don't believe they can. MI practitioners therefore make efforts to enhance their patients' confidence through such means as expressing their belief in the patient's ability to change or pointing out past successes or steps in the right direction.
## Basic communication skills
Implementing MI in a dental setting requires consideration of how to ensure the collaborative and empathic spirit of the method. Even such basic matters as how the patient and practitioner are seated can contribute to the patient feeling like they are truly being invited to engage in a dialogue as a partner (Fig. 34-1), rather than feeling they are simply to be the recipient of expert advice (Fig. 34-2).
**Fig. 34-1** Appropriate position for a conversation: the clinician is facing the patient on the same seating level.
**Fig. 34-2** Inappropriate position for a conversation: the clinician is wearing a face mask and is at a higher level than the supine patient.
There are four primary activities for the beginning stages of a brief MI session. These can be summarized with the acronym OARS, for open-ended questions, affirm the patient, reflect, and summarize.
* _Ask open-ended questions_. Approaching the patient with multiple closed-ended questions (question that will be answered with "yes" or "no") sets the patient's role to be a rather passive one. In contrast, open-ended questions invite thought, collaboration, and effort on the part of the patient. Example: "How do you feel about your smoking?"
* _Affirm the patient_. It is human nature to presume a negative attitude, particularly when one's own behavior is coming under scrutiny. Acknowledging the patient's strengths and appreciation of his or her honesty will decrease defensiveness, increase openness, and the likelihood of change. Example: "You're telling me clearly why you're not very concerned about your toothbrushing and I appreciate that honesty."
* _Reflect what the patient is communicating_. Reflection is the primary way to demonstrate empathy (ability to understand another person's perspective). Appropriate reflection includes the genuine effort to understand the patient's perspective. It (1) captures the underlying meaning of the patient's words, (2) is concise, (3) is spoken as an observation or a comment, and (4) conveys understanding rather than judgment. Example: "You really seem to have lost hope that you can ever really quit smoking."
* _Summarize_. Summarizing the patient demonstrates interest, organizes the interview, and gets things back on track if necessary. It involves the compilation of the patient's thoughts on change mentioned during the counseling. Example: "So there's a big part of you that doesn't feel ready to change right now. You really enjoy smoking, but you have been a little worried by the way some people react when they find out that you smoke. Is that about right?"
## Giving advice
Although we have highlighted the distinction between advice-oriented health education and MI in this chapter, it is important to recognize that at times it is appropriate to provide information to address patient's questions, misapprehensions, or lack of knowledge. The Motivational Interviewing Skill Code (Moyers _et al_. 2003), which is used to assess practitioner's adherence to principles of MI distinguishes between giving advice _without_ permission, which is proscribed, and giving advice _with_ permission, which is consistent with MI principles. In essence, it is consistent with MI to provide information when the patient is willing and interested in receiving it. Practitioners commonly err by providing advice too soon in an encounter with a patient, resulting in patients perceiving the practitioner as having an agenda that they are trying to "push". In contrast, it is common in MI practice to find that the process of eliciting the patient's perspective reveals gaps in knowledge, questions and concerns, and misapprehensions that the patient would appreciate receiving more information about. The practitioner can then provide particularly relevant information that is much more likely to be well received. Rollnick _et al_. (1999) have outlined a three-step process that serves as a useful framework for providing advice in an MI consistent style:
* Step 1: _elicit_ the patient's readiness and interest in hearing the information. For example a practitioner might say to a patient "I have some information related to (that topic) that you may be interested in. Would you be interested in hearing more about that?"
* Step 2: _provide_ the information in as neutral a fashion as possible. For example, a practitioner might say "Research indicates that... ." or "Many of my patients tell me that..." This allows factual information to be presented in a manner that supports the patient's autonomy.
* Step 3: _elicit_ the patient's reaction to the information presented. Following up will often facilitate the patient to integrate the new information in a way that brings about a new perspective and increases motivation to change. Alternatively, following up may reveal further gaps in knowledge or misunderstandings that can be addressed. If a patient "rejects" the information it is important not to get into a debate. It is generally better to simply acknowledge the patient's perspective with statements such as "This information doesn't fit with your experience" or "This information doesn't seem relevant to your situation" and then move on to a more productive area of conversation.
# Case examples for oral hygiene motivation
## Oral hygiene motivation 1
Using the following case example, MI is demonstrated in a dialogue for oral hygiene motivation between a periodontist (Dr) and a patient (P) diagnosed with chronic periodontitis at the beginning of periodontal therapy.
Dr| Would you mind if we talk about methods to improve your oral hygiene during and after your gum treatment?
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P| No, I don't mind.
Dr| Good. Let me know a little bit about how you usually clean your teeth.
P| I usually brush once or twice a day.
Dr| So you brush your teeth regularly. What are you using when you clean your teeth?
P| I use a toothbrush and toothpaste.
Dr| Very good. Could you let me know how you use your toothbrush?
P| I brush all upper and lower teeth on the outside and the inside as I was shown a long time ago.
Dr| And how do you feel about brushing your teeth that way?
P| I generally feel quite good about it. But since I have been told I have gum disease, I'm wondering if I haven't been brushing enough?
Dr| So you have been making efforts to keeping your teeth clean but you're worried that maybe you haven't been brushing enough. It can be difficult to get to all the areas of your teeth and gums to remove the plaque that causes gum disease. I have some information related to prevention of gum disease that you might be interested in. Would you like to hear about it?
P| Yes.
Dr| The chronic gum or periodontal disease you are diagnosed with was caused by bacterial plaque attached to your teeth over time.Plaque has to be entirely removed from all the tooth surfaces on a daily basis in order to prevent and control this disease.
| How confident are you that you were cleaning all the surfaces on a regular basis?
P| Not very, although I thought that I was doing enough.
Dr| Well actually, research indicates that using a toothbrush alone is not sufficient to clean between the teeth. In order to clean these areas, an interdental device is needed such as a dental floss, a toothpick, or an interdental brush. Are you using any one of these devices?
P| Yes, I've tried using dental floss.
Dr| How did you find the use of dental floss?
P| I had some trouble getting to some of the spaces between my teeth. In other areas, the floss used to rip up too, so I quit using it.
Dr| I am sorry to hear that you had trouble using the dental floss. The floss can rip up at the edges of dental fillings or crowns. In spaces with extensive tartar built-up, the gap between your teeth may even be blocked out with tartar. Are you using anything else for cleaning?
P| Yes, I use a toothpick whenever I have something stuck between my teeth.
Dr| So in addition to your regular brushing with toothpaste you are also using a toothpick from time to time to clean your teeth?
P| That's right.
Dr| Good. During gum treatment, fillings and crowns with rough edges will be smoothed over and tartar can be removed which should make it easier to use things like dental floss or a toothpick between your teeth. Thinking of a 10-point scale where 0 is not at all important and 10 is extremely important, how important is it to you to floss or use a toothpick every day to clean the gaps between your teeth?
P| Probably a 7.
Dr| That sounds quite important. What makes this so important to you?
P| I want to do everything needed to keep my teeth. However, I am not quite sure if I will be able to keep doing it over time.
Dr| So you are quite motivated now because you want to look after your teeth, but you are worried about the long term. If you were to use the same 10-point scale to rate how confident you are that you can do it over the long-term, where would rate yourself?
P| I would be at a 6.
Dr| That sounds fairly confident. What gives you that level of confidence?
P| Well, taking care of my teeth and gums is part of my routine already so this would just need to be added to it. But it does take extra effort, so it's a matter of realizing that it's really that important for my gums.
Dr| So the fact that it can be part of your existing routine will help. But perhaps I can help you remain motivated in the long run by showing you at your follow-up visits the benefits you are achieving with your treatment by doing it regularly. How do you think that might help you to stick with it over time?
P| Well, yes I think that would probably help a lot to see or learn from you that it really is making a difference to the success of my treatment.
Dr| Great! So let me summarize what we have discussed. You plan to keep brushing on a regular basis with toothbrush and toothpaste and you will start to use a device for cleaning the gaps between your teeth after the issues with the rough filling and crown margins have been resolved. Then, each time you visit we'll see how you are progressing with your cleaning at home and see if we need to find any other ways to help. Does that sound like it would work for you?
P| Yes, that sounds like it would work.
## Oral hygiene motivation 2
In this second case example dialogue, MI is used in a conversation about oral hygiene at a visit for supportive periodontal therapy (SPT).
Dr| From looking at your plaque index, I noticed today that compared to your visit 3 months ago there is more plaque around the areas between your teeth. I was wondering if you could tell me a little bit about how you find the cleaning between your teeth.
---|---
P| Oh... I guess that I don't do it as often as I should. I barely have time now to do it every day, you know.
Dr| I understand. It takes time to clean all the areas between your teeth, you are right. May I ask you a few questions about your current oral hygiene habits so I could understand your situation better?
P| Sure you can.
Dr| Good. So what do you use to clean your teeth currently?
P| I am using an electric toothbrush and the interdental brushes you showed me.
Dr| OK. How often do you use these?
P| I use the electric toothbrush every day and I use the interdental brushes from time to time.
Dr| So you are using the toothbrush on a regular basis, but only occasionally using the interdental brushes. What is prompting you when you do decide to use the interdental brushes?
P| Well, sometimes I just feel guilty that I haven't been using them and sometimes I can see the tartar on my teeth and am reminded to use them again.
Dr| So you sometimes worry that you are not using them enough and sometimes you can see on your teeth that you are not using them enough.
P| Right, I suppose I should be doing better.
Dr| Well let me ask you this. If you had to rate how important it is for you to use the interdental brushes every day on a scale from 0 to 10, 0 being not important at all and 10 being very important, where would you place yourself?
P| I guess the use of these brushes is pretty important. I'd say an 8.
Dr| Well that sounds very motivated. What makes it that important for you?
P| Well I don't want to have a lot of problems with my teeth – I hate having fillings and of course I don't want to lose any teeth in the long run.
Dr| So avoiding pain and discomfort and keeping your teeth is important to you. So how confident are you that you can use the brushes on a daily basis? Where would you rate yourself on that 0 to 10 scale?
P| As I said, I know that I should use them more often, but finding the time is hard and I even just forget sometimes. I'd give it a 3.
Dr| Using them daily seems quite hard for you. Out of curiosity, though, it seems you do have a little bit of confidence in doing this – may I ask you why a 3 instead of a 0 or a 1?
P| Well, I just think that I would use them more often if they would become a part of my routine tooth cleaning, you know? I used to have toothpicks on my dinner table too and so I used them whenever I saw them sittingthere. I could think about putting my interdental brushes on my sink next to my toothbrush. So I would be reminded to use them after brushing my teeth with the electric toothbrush.
Dr| That sounds like a really good plan. Can you see any problems with doing that?
P| No, not really. Once I have that reminder in place it's just a matter of staying committed to doing it.
Dr| Very good. So if I can summarize, it sounds like you feel quite motivated to use the interdental brushes everyday, and that you think that if you put your interdental brushes on your sink next to your electric toothbrush that would help you remember to actually do it.
P| Yes, that's right.
Dr| Well does that sound like something you want to do?
P| Yes, I'll do that tonight.
# Case example for tobacco use cessation
A brief intervention for tobacco use cessation using MI is presented in a clinical case example dialogue between a periodontist (Dr) and a patient (P) at the beginning of periodontal therapy.
Dr| According to your tobacco use history, you are currently smoking cigarettes. May I ask you a few questions about your smoking?
---|---
P| Yes.
Dr| Tell me how you feel about your smoking.
P| Well I know I should quit. I know it's not good for my health. But I don't want to quit right now.
Dr| So you don't feel that you want to quit right now, but you do have some concern about the health effects.
P| Yes.
Dr| Well, tell me more about what concerns you?
P| Well, mainly that I would get lung cancer or something.
Dr| So you worry a bit about getting cancer because of smoking. Is there anything else that you don't like about smoking?
P| Well if I quit my clothes would stop smelling.
Dr| So the smell of tobacco smoke is something you would like to be rid of?
P| Yes, but I've smoked for many years, you know and I tried to quit once before.
Dr| So even though you would like to be a non-smoker for health and other reasons you haven't had much success quitting.
P| Yes, and right now I'm enjoying smoking so there's not much motivation to try.
Dr| Well it sounds like even though you have some important reasons to quit, you're not very confident you could succeed and you don't feel ready to take on this challenge right now. I wonder if it would be OK for us to talk about this again next time to see where you are with it and whether I could help?
P| Yes that sounds fine.
### Conclusion
Chronic damaging behaviors not only affect general and oral health that individuals face but also impact the burden of disease on a community level. Hence, the services for primary and secondary prevention on an individual level oriented towards the change of inappropriate behavior become a professional responsibility for all oral health care providers. Motivational interviewing, encouraging the modification of all common risk factors for periodontal diseases such as insufficient oral hygiene, tobacco use, unhealthy dietary habits, and alcohol abuse, appears to be suitable for implementation into the periodontal treatment plan.
### Acknowledgment
We are grateful to Dr. Dieter Müller, Bremgarten, Berne, Switzerland, for providing the cartoons of this chapter.
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# Chapter 35
# Mechanical Supragingival Plaque Control
Fridus Van der Weijden, José J. Echeverría, Mariano Sanz, and Jan Lindhe
* * *
Importance of supragingival plaque removal
Self-performed plaque control
Brushing
Interdental cleaning
Adjunctive aids
Side effects
Importance of instruction and motivation in mechanical plaque control
* * *
# Importance of supragingival plaque removal
Dental plaque is a bacterial biofilm that is not easily removed from the surface of teeth. Biofilms consist of complex communities of bacterial species that reside on tooth surfaces or soft tissues. It has been estimated that between 400 and 1000 species may, at some time, colonize oral biofilms. In these microbial communities, there are observable associations between specific bacteria due in part to synergistic or antagonistic relationships and in part to the nature of the available surfaces for colonization or nutrient availability (Chapter 9). The products of biofilm bacteria are known to initiate a chain of reactions leading to host protection but also to tissue destruction (Chapter 11).
The dental biofilm is a complex configuration leading many to speculate that traditional plaque indices are inadequate because they fail to evaluate qualitative features. Furthermore, the term _plaque_ is not precise. Plaque may be supragingival or subgingival and may be adherent or non-adherent to tooth or tissue. In addition the microbial composition of plaque varies from person to person and from site to site within the same mouth (Thomas 2004).
Supragingival plaque is exposed to saliva and to the natural self-cleansing mechanisms existing in the oral cavity. Friction through mastication may have a limiting effect on occlusal and incisal extensions of plaque. However, in most populations natural cleaning of the human dentition appears unimportant (Löe 2000). Therefore, in order to maintain oral health, regular personal plaque removal measures must be undertaken. The most widespread means of actively removing plaque at home is toothbrushing. There is substantial evidence which shows that plaque and gingivitis/periodontitis can be controlled most reliably through toothbrushing supported by other mechanical cleansing procedures. Thus, evidence stemming from large cohort studies demonstrated that high standards of oral hygiene will ensure the stability of periodontal tissue support (Hujoel _et al_. 1998; Axelsson _et al_. 2004).
As meaningful as oral hygiene measures are for disease prevention, they are relatively ineffective when used _alone_ for treatment of moderate and severe forms of periodontitis (Loos _et al_. 1988; Lindhe _et al_. 1989). On the other hand, without an adequate level of oral hygiene in periodontitis-susceptible subjects, periodontal health tends to deteriorate once periodontitis is established and further loss of attachment may occur (Lindhe & Nyman 1984).
Meticulous, self-performed plaque removal measures can modify both the quantity and composition of subgingival plaque (Dahlén _et al_. 1992). The Socransky group (Haffajee 2001) confirmed this finding and reported that a permanent optimal supragingival plaque control regimen can alter the composition of the pocket microbiota and lower the percentage of periodontopathic bacteria.
At present both primary prevention of gingivitis and primary and secondary prevention of periodontitis are based on the achievement of sufficient plaque removal. Almost 50 years of experimental research, clinical trials in different geographical and social settings, have confirmed that effective removal of dental plaque is essential to dental and periodontal health (Löe 2000). The concept of the primary prevention of gingivitis derives from the assumption that gingivitis is the precursor of periodontitis and that maintenance of a healthy gingiva will prevent periodontitis.Consequently, preventing gingivitis could have a major impact on expenditure for periodontal care (Baehni & Takeuchi 2003). Primary prevention of periodontal diseases includes educational interventions on periodontal diseases and related risk factors as well as regular self-performed plaque removal and professional mechanical removal of plaque and calculus. Optimal oral hygiene requires appropriate motivation of the patient, adequate tools, and professional oral hygiene instruction.
# Self-performed plaque control
Personal oral hygiene refers to the effort of the patient to remove supragingival plaque. Procedures used to remove supragingival plaque are as old as recorded history. The earliest record of the chewstick which has been considered the primitive toothbrush dates back in the Chinese literature to about 1600 BC (Carranza & Shklar 2003). In his writings, Hippocrates (460–377 BC) included commentaries on the importance of removing deposits from the tooth surfaces. The observation that self-performed plaque removal is one of the foundations of periodontal health was clearly described by Antonie van Leeuwenhoek in 1683, who wrote (Carranza & Shklar 2003):
"Tis my wont of a morning to rub my teeth with salt and then swill my mouth out with water; and often, after eating, to clean my back teeth with a toothpick, as well as rubbing them hard with a cloth; wherefore my teeth, back and front, remain as clean and white as falleth to the lot of few men of my years, **and my gums never start bleeding**."
The Chinese are given credit for developing the first bristle toothbrush which was introduced in the Western world in the sixteenth century. Currently, toothbrushes of various kinds are important aids for mechanical plaque removal. Furthermore, a fluoridated dentifrice is an integral component of daily home care. The use of toothbrush and dentifrices is almost universal. The use of interdental cleaning devices, mouthrinses, and other oral hygiene aids is less well documented, but available evidence tends to suggest that only a small percentage of the population use such additional measures on a regular basis (Bakdash 1995).
There is an increasing public awareness of the value of good oral health practices. This fact is proven by a recorded increase in both public spending on oral hygiene products (over $3.2 billion a year in the US) and industry spending on consumer-related advertising (over $272 million a year in the US) (Bakdash 1995).
## Brushing
Different cleaning devices have been used in different cultures (toothbrushes, chewing sticks, chewing sponges, etc.). Toothbrushing is currently the most commonly used measure in oral hygiene practice. Toothbrushing alone, however, does not provide adequate interdental cleaning since a toothbrush may only reach the facial, oral, and occlusal tooth surfaces. It was suggested (Frandsen 1986) that the outcome of toothbrushing is dependent on: (1) the design of the brush, (2) the skill of the individual using the brush, and (3) the frequency and (4) duration of brushing.
Dental professionals must become familiar with the variety in shapes, sizes, textures, and other characteristics of available toothbrushes in order to provide their patients with proper advice. From the numerous products present on the market only a few should be selected for the individual patient. It is important that the dental care provider understands the advantages and disadvantages of the various toothbrushes (and other aids) to provide the patient with proper information during the oral hygiene instruction session.
For the most part, studies that have compared the effectiveness of different manual brushes have found relatively little difference among designs (see below). It is quite possible that a given patient may obtain better results with one particular toothbrush than with another. Providing oral hygiene information should therefore be tailored to the individual.
### Motivation
Oral hygiene education is essential in primary prevention of gingivitis. Improvement in a patient's oral hygiene is often accomplished through cooperative interaction between the patient and the dental professional. The role of the patient is to seek education regarding efficient self-performed plaque removal and accept regular check-ups to ensure a high level of oral hygiene. The patient must be interested in maintaining the health of the tissues, interested in a proposed treatment plan, and motivated to participate. Without compliance, which has been described as the degree to which a patient follows a regimen prescribed by a dental professional, a good treatment outcome will not be achieved. In this context it should be realized that compliance with treatment recommendations is generally poor, particularly in patients with chronic diseases in which the risk of complications is not immediate or life threatening. Also compliance with oral hygiene recommendations is generally poor (Thomas 2004).
So, however effective any toothbrushing method is, it will only be of any real value if the patient is prepared to use the technique on a regular basis (Warren & Chater 1996a). Merely the patient's positive attitude to treatment may have a positive longterm effect on her/his tooth cleaning efforts. Thus, well motivated patients who are compliant with professional advice and instruction are likely to achieve and sustain ideal levels of plaque control.
There is an increasing public awareness of the value of personal oral hygiene. Good oral hygiene should form an integral part of overall health practices, such as regular exercise, stress management, diet and weight control, smoking cessation, and moderation in alcohol consumption. If the clinician can establish the link between oral health and general health for the patient, this individual may be more willing to establish proper oral hygiene measures as part of her/his lifestyle.
The issue of changing a patient's lifestyle is the more difficult part of motivational sessions (Chapter 34). The principles of brushing and flossing are easy to learn. Integrating them into one's daily routine is far more difficult. This can form a source of frustration for the clinician who has provided a patient with information about the necessity of personal oral hygiene measures.
### Toothbrush (see Procedure 1)
It is believed that the first toothbrush made of hog's bristles was mentioned in the early Chinese literature. In 1698 Cornelis van Solingen, a doctor from The Hague, published a book in which he presented the first illustration of a toothbrush in Europe (Fig. 35-1). Nylon filaments were introduced in 1938 since complications of World War II prevented the Chinese export of wild boar bristles. Nearly all current toothbrushes are made exclusively of synthetic materials (Wilkins, 1999). Such nylon filaments and plastic handle are easy to manufacture, and therefore more affordable. This has made toothbrushing a common practice in most societies.
During toothbrushing the removal of dental plaque is achieved primarily through direct contact between the filaments of the toothbrush and the surfaces of teeth and soft tissues. At the European Workshop on Mechanical Plaque Control, it was agreed that the features of an ideal manual toothbrush should include (Egelberg & Claffey 1998):
1.Handle size appropriate to user age and dexterity so that the brush can easily and efficiently be manipulated
2.Head size appropriate to the size of the individual patient's requirements
3.Use of end-rounded nylon or polyester filaments not larger than 0.23 mm (0.009 inches) in diameter
4.Use of soft filament configurations as defined by the acceptable international industry standards (ISO)
5.Filament patterns which enhance plaque removal in the approximal spaces and along the gum line.
**Fig. 35-1** Illustration of a toothbrush and tongue scraper from the book of Cornelis van Solingen with special thanks to the University Museum of Dentistry in Utrecht, The Netherlands.
Additional characteristics could be: inexpensive, durable, impervious to moisture, and easily cleaned.
Modern toothbrushes have filament patterns designed to enhance plaque removal from hard-to-reach areas of the dentition, in particular from proximal areas. Cross-placed filaments, crimped, and tapered filaments are the most recent improvements. Such designs are based on the premise that the majority of subjects in any population use a simple horizontal brushing action. In order to improve patient comfort brush head shape, filament shape, and placement of filaments into the handles also have been subject to change over time. Multiple tufts of filaments, sometimes angled in different directions, are currently used (Jepsen 1998). Thus, when the head of the toothbrush is located horizontal to the tooth surface, there are filaments angled in the direction of the approximal tooth surfaces. Toothbrushes with this design facilitate more plaque removal in such difficult-to-reach areas when compared with flatheaded brushes (Cugini & Warren 2006).
Double- and triple-headed toothbrushes have been proposed in order to reach lingual surfaces more easily, especially in molar areas, which are normally the tooth surfaces hardest to reach with a regular toothbrush. Although some studies have indicated that the use of such multi-headed toothbrushes may improve plaque control in lingual areas (Agerholm 1991; Yankell _et al_. 1996), their use is not widespread.
Where handles used to be straight and flat, nowadays round and curved handles are more common. Today, a modern toothbrush has a handle size that is appropriate to the hand size of the prospective user, and much emphasis has been placed on new ergonomic designs (Löe 2002). Several studies have investigated differences in plaque removal between brushes with different handle design. In such studies brushes with long and contoured handles appeared to remove more plaque than brushes with traditional handles (Saxer & Yankell 1997).
When brushes with hard, soft, multi-tufted, and space-tufted filaments were compared, no significant clinical differences were found with respect to plaque removal. It is worth considering that most of such toothbrush studies involved highly motivated participants such as dental students, who do not represent the general population. Most studies on manual brushes are 'single-use' tests. Although such short-term trials may be useful as pilot experiments, they need to be supplemented with studies of longer duration. Numerous manual toothbrushes are available on the market. There is still, however, insufficient evidence that one specific toothbrush design is superior to another. In 1994, two well performed clinical trials which assessed the efficacy of two toothbrushes came to entirely different conclusions (Grossman _et al_. 1994; Sharma _et al_. 1994). In the one trial toothbrush A was more effective than brush B while in the other trial brush B was superior to brush A. The trial which proved that brush A was most effective was sponsored by the manufacturer of brush A. The finances of the other trial which proved that brush B was more effective came from the manufacturer of brush B. As with many other aspects of oral hygiene aids, there is insufficient information to make evidence-based recommendations. Thus, in absence of this evidence, the best toothbrush continues to be the one that is (properly) used by the patient (Cancro & Fischman 1995; Jepsen 1998).
#### _Efficacy of toothbrushing_
The enthusiastic use of the toothbrush is not synonymous with a high standard of oral hygiene. Adults, despite their apparent efforts, appear not to be as effective in their plaque removal as might be expected. Most individuals only remove about 50% of plaque by toothbrushing (Jepsen 1998). De la Rosa and co-workers (1979) studied the pattern of plaque accumulation and removal with daily toothbrushing during a 28-day period following a dental prophylaxis. On average about 60% of the plaque was left after the self-performed brushing. Morris _et al_. (2001) reported on the 1998 UK Adult Dental Health survey and observed that the mean proportion of teeth with plaque deposits was 30% in the 25–34-year age group and 44% in those aged 65 years and above. At the Academic Centre for Dentistry Amsterdam (ACTA) a study was conducted which assessed the efficacy of a single 1-minute brushing exercise in subjects adhering to their customary brushing method (Van der Weijden _et al_. 1998a). It was observed that after 1 minute of brushing, approximately 39% of the plaque had been removed. The results of the studies described above indicate that most subjects are not effective brushers and that they probably live with large amounts of plaque on their teeth, even though they brush once every day.
#### _Methods of toothbrushing_
There is no single oral hygiene method that is correct for all patients. The morphology of the dentition (crowding, spacing, gingival phenotype etc.), the type and severity of the periodontal tissue destruction, as well as the patient's own manual dexterity determine what kind of hygiene aids and cleaning techniques are to be recommended. It should also be realized that during the course of periodontitis therapy, the techniques may have to be changed or adapted to the morphologic situation (longer teeth, open interdental spaces, exposed dentin).
The ideal brushing technique is the one that allows complete plaque removal in the least possible time, without causing any damage to the tissues (Hansen & Gjermo 1971). Different toothbrushing methods have been recommended over time, but also been abandoned. Such methods can be classified based on the position and motion of the brush.
_Horizontal brushing_ is probably the most commonly used toothbrushing method. It is most frequently used by individuals who never had instruction in oral hygiene techniques. Despite the efforts of the dental profession to instruct patients to adopt other more efficient brushing techniques, most individuals use horizontal brushing since it is simple. The head of the brush is positioned perpendicular to the tooth surface and then a horizontal back and forth movement is applied. The occlusal, lingual, and palatal surfaces of the teeth are brushed with open mouth. In order to reduce pressure of the cheek on the brush head the vestibular surfaces are cleaned with the mouth closed.
_Vertical brushing_ (Leonard (1939) technique) is similar to the horizontal brushing technique, but the movement is applied in vertical direction using up and down strokes.
_Circular brushing_ (Fones (1934) method) : with the teeth closed the brush is placed inside the cheek and a fast circular motion is applied that extends from the maxillary gingiva to the mandibular gingiva using light pressure. Back and forth strokes are used on the lingual and palatal tooth surfaces. The _scrubbing method_ includes a combination of horizontal, vertical, and circular strokes.
_Sulcular brushing_ (Bass (1948) technique): this method emphasizes cleaning of the area directly beneath the gingival margin. The head of the brush is positioned in an oblique direction towards the apex. Filament tips are directed into the sulcus at approximately 45º to the long axis of the tooth. The brush is moved in a back and forth direction using short strokes without disengaging the tips of the filaments from the sulci. On the lingual surfaces in the anterior tooth regions the brush head is kept in the vertical direction. The Bass technique is widely accepted as an effective method for removing plaque not only at the gingival margin, but also subgingivally. A few studies have been carried out on teeth affected with periodontal disease and scheduled for extraction, where the gingival margin was marked with a groove and the depth of subgingival cleaning was measured. These studies showed that with the use of this brushing method the plaque removal could reach a depth of approximately 1 mm subgingivally (Waerhaug 1981a).
_Vibratory technique_ (Stillman (1932) method): as originally described by Stillman the method was designed for massage and stimulation of the gingiva as well as for cleaning the cervical areas of the teeth. The head of the brush is positioned in an oblique direction toward the apex, with the filaments placed partly in the gingival margin and partly on the tooth surface. Light pressure together with a vibratory (slight rotary) movement is then applied to the handle, while the filament tips are maintained in position on the tooth surface.
_Vibratory technique_ (Charters (1948) method): this method was originally developed to increase cleansing effectiveness and gingival stimulation in the interproximal areas. It uses a reverse position of the brushhead as compared to the Stillman technique. The head of the brush is positioned in an oblique direction with the filament tips directed towards the occlusal or incisal surfaces. Light pressure is used to flex the filaments and gently force the tips into the interproximal embrassures. A vibratory (slight rotary) movement is then applied to the handle while the filament tips are maintained in position on the tooth surface. This method is particularly effective in cases with receded interdental papillae because the filament tips can easily penetrate the interdental space (Fig. 35-2).
_Roll technique_ : the head of the brush is positioned in an oblique direction toward the apex of the teeth, with the filaments placed partly in the gingival margin and partly on the tooth surface. The sides of the filaments are pressed lightly against the gingiva. Next the head of the brush is rolled over the gingiva and tooth in occlusal direction.
**Fig. 35-2** (a) The Charters method of toothbrushing. The head of the toothbrush is placed in the left maxilla. Note the angulation of the bristles against the buccal tooth surfaces. The bristles are forced into the interproximal areas. (b) The palatal aspect of the incisor region in the maxilla illustrating the penetration of the bristles through the interproximal spaces (arrows).
_Modified Bass/Still-man technique_ : the Bass and Still-man methods were designed to concentrate on the cervical portion of the teeth and adjacent gingival tissues. Each of these methods can be modified to add a roll stroke. The brush is positioned similarly to the Bass/Stillman technique. After activation of the brushhead in a back and forth direction, the head of the brush is rolled over the gingiva and tooth in occlusal direction making it possible for some of the filaments to reach interdentally.
In the 1970s several investigators compared various methods of brushing. Because of varying experimental conditions the outcomes of such studies are difficult to compare. To date no methods of toothbrushing have been shown to be clearly superior to others. As early as 1986, Frandsen commented on this issue by stating: "Researchers have realized that improvement in oral hygiene is not as dependent upon the development of better brushing methods as upon improved performance by the persons using any one of the accepted methods." Therefore, since no particular toothbrushing method has been found to be clearly superior to another, there is no reason to introduce a specific toothbrushing technique in each new periodontal patient. In most cases, small changes in the patient's own method of toothbrushing will suffice, always bearing in mind that more important than the selection of a certain method of toothbrushing is the willingness and thoroughness on the part of the patients to effectively clean their teeth. Implementation of the toothbrushing methods described above must be made according to patient´s needs. For example, since the Bass method has been associated with gingival recession (O'Leary 1980), it would be hardly indicated in individuals with energetic toothbrushing habits who have a thin gingival biotype.
#### _Frequency of toothbrushing_
There is no consensus as to the optimum frequency of toothbrushing. How often and how much plaque has to be removed in order to prevent dental disease from developing is not known. The majority of individuals, including periodontal patients, are usually not able to remove dental plaque completely as a result of daily brushing. However complete plaque removal does not seem to be necessary. A proper level of oral hygiene theoretically is the extent of plaque removal that prevents gingivitis/periodontal disease and tooth decay in the individual patient. Prevention of gingival inflammation is important because the inflammatory condition of soft tissues also favors plaque accumulation (Ramberg _et al_. 1994; Rowshani _et al_. 2004).
Results in cross-sectional studies have been equivocal when the selfreported frequency of tooth cleaning has been related to caries and periodontal disease. Disease appears to be more related to quality of cleaning than to its frequency (Bjertness 1991). Kressin and co-workers (2003) evaluated the effect of oral hygiene practices on tooth retention in a longitudinal study with a 26-year follow-up. They observed that consistent brushing (at least once a day) resulted in a 49% reduction of the risk of tooth loss compared to a lack of consistent oral hygiene habits.
If plaque is allowed to accumulate freely in the dentogingival region, subclinical signs of gingival inflammation (gingival fluid) appear within 4 days (Egelberg 1964). The minimum frequency of tooth cleaning to reverse experimentally induced gingivitis is once every day or every second day. Bosman and Powell (1977) induced experimental gingivitis in a group of students. The signs of gingival inflammation persisted in those students who removed plaque only every third or fifth day. In groups who properly cleaned their teeth once a day or every second day, the gingivae healed within 7–10 days.
Based on the observation that the onset of gingivitis appears to be more related to the maturation and age of the plaque than to its amount, the minimum frequency needed to prevent the development of gingivitis has been investigated in a prospective study. Dental students and young dental faculty members with healthy periodontal conditions were assigned to study groups with different cleaning frequencies over periods of 4–6 weeks. The results showed that that students who thoroughly removed plaque once daily or even every second day, did not develop clinical signs of gingival inflammation over a 6-week period. This tooth cleaning included the use of interproximal aids (dental floss and woodsticks) as well as the toothbrush (Lang _et al_. 1973). Caution should be excercised in extrapolating the results obtained from studies including dentally aware subjects to the average patient.
From a practical standpoint, it is generally recommended that patients brush their teeth at least twice daily, not only to remove plaque but also to apply fluoride through the use of dentifrice in order to prevent caries. This advice is also conceivable based on reasons of practibility and feeling of oral freshness. For most patients, it may be desirable to perform all necessary procedures (e.g. brushing and interdental cleaning) at the same time and in the same manner each day. Unfortunately, with subjects who live busy, stressful lives, this may be difficult to achive (Thomas 2004). Despite the fact that most individuals claim to brush their teeth at least twice a day, it is clear from both epidemiologic and clinical studies that mechanical oral hygiene procedures as performed by most subjects are insufficient to control supragingival plaque formation and to prevent gingivitis and more severe forms of periodontal disease (Sheiham & Netuveli 2002).
#### _Brushing duration_
Patients usually believe that they spend more time on toothbrushing than they actually do (Saxer _et al_. 1998). The least time spent on brushing was observed in a study carried out on English schoolchildren; in the 13 years age group, the children spent approximately 33 seconds on brushing (Macgregor & Rugg-Gunn 1985). About one third of the studies that were reviewed reported an average brushing time of less than 56 seconds whereas two thirds of the studies reported a brushing time of ≥56 seconds and <70 seconds. One investigation which used dental students as study population reported an average of 90 seconds (Ayer _et al_. 1965). The best estimate of actual manual brushing time seems to range between 30 and 60 seconds (Van der Weijden _et al_. 1993).
In reviewing the literature for studies that addressed the question whether in adult patients the duration of toothbrushing is correlated with efficacy of plaque removal five studies were identified. Three of these evaluated the use of electric toothbrushes (Van der Weijden _et al_. 1996a; McCracken _et al_. 2003, 2005). One study compared a manual toothbrush with an electric toothbrush (Preber _et al_. 1991), while one study included only manual toothbrushes (Hawkins _et al_. 1986). Results from all five studies indicate that duration of brushing is consistently correlated with the amount of plaque that is removed. In one study, toothbrushing was delivered by a dentist/dental hygienist. This study compared the effect of brushing time on plaque removal using manual and electric toothbrushes utilizing five different brushing times (30, 60, 120, 180, and 360 seconds).This study showed that 2 minutes of electric toothbrushing can be as effective as 6 minutes of manual toothbrushing. The authors furthermore observed that at 2 minutes an optimum in plaque-removing efficacy was reached with both a manual and electric toothbrushes (Van der Weijden _et al_. 1993). Based on these observations the duration of toothbrushing should also be stressed during the toothbrushing instruction session.
#### _Brushing filaments_
Most current toothbrushes have nylon filaments. The degree of hardness and stiffness of a toothbrush depends on the filament characteristics, such as material, diameter, and length. Also the density of filaments in a tuft influences stiffness, since each filament gives support to the adjacent fiaments and each tuft gives support to adjacent tufts. Toothbrushes with thinner filaments are softer while thicker filament diameters are stiffer and less flexible. This increased stiffness will prevent the filament ends from bending back during brushing, avoiding the potential risk of damaging the gums. However, the filament must be sufficiently stiff so that during brushing enough pressure is exerted to allow proper plaque removal. Consider that a rod represents a filament of a toothbrush. Whilst brushing, a vertical upward load is exerted, which in turn exerts an effect of the same order of magnitude on the oral mucosa. The force of the brush, acting on the individual filament, is thus always as great as the load exercised by the filament on the mucosa. If the load is increased then the load on the mucosa increases to the same extent. Consequently the risk of soft tissue damage increases in that the filament's tip can penetrate into the mucosa. However, elastic rods demonstrate a peculiarity in their behavior. They suddenly fold back laterally when a certain limit load is reached. When folding back, the rod suddenly gives way elastically (without breaking) and the load on the oral mucosa diminishes abruptly. A load higher than this fold-back limit can thus not be transferred to the mucosa by the rod, via its tip. Tapered filaments (Fig. 35-3) have endings with the shape of an extreme rotational ellipsoid instead of a hemisphere. This is suggested to give the filaments very soft endings combined with a good stability of the filament corpus. Curved filaments may be more flexible and less stiff than straight filaments of equal length and diameter.
**Fig. 35-3** Tapered toothbrush filaments.
As late as 1967, most people were buying hard brushes (Fanning & Henning 1967). The shift in preference to soft brushes of specific design paralleled the change that occurred in oral health care when calculus was the prime etiologic agent in periodontal disease (Mandell 1990). The concentration on plaque, especially in the crevicular area and the attention to intrasulcular brushing strongly influenced the change from hard to soft filaments, primarily because of the concern of trauma to the gingival tissues (Niemi _et al_. 1984). The cleaning performance of a toothbrush is influenced by its degree of hardness. The toothbrush must not be too hard, to avoid damaging the gums when positioning the toothbrush. The harder the toothbrush filaments are the greater is risk of gingival abrasion (Khocht _et al_. 1993). But there is no point in using a brush with very thin filaments that merely strokes across the tooth and, as a result of the lack of load, no longer cleans the tooth surface.
#### _Filament end-rounding_
The end of a toothbrush filament can be cut bluntly or rounded. End-rounding has become increasingly common in the manufacturing process to reduce gingival abrasion (Fig. 35-4). The logic that smooth filament tips would cause less trauma than filament tips with sharp edges or jagged projections has been validated with both animal and clinical studies (Breitenmoser _et al_. 1979). Danser _et al_. (1998) evaluated two types of end-rounding, and saw an effect of end-rounding on the incidence of abrasion. The form to which the ends were rounded, however, had no effect on the level of plaque removal.
#### _Toothbrush wear and replacement_
It is generally recommended that toothbrushes be replaced before the first signs of the filaments becoming worn. The useful life of an average toothbrush has been estimated to be 2–3 months. Not all patients take this advice, and evidence indicates that the average age at which a toothbrush is replaced ranges from 2.5–6 months (Bergström 1973). Common sense would suggest that a worn toothbrush with splayed or frayed filaments loses resilience and is less likely to be as effective in removing plaque than a new brush. This is why dental professionals often re commend that toothbrushes are used for a maximum of 3 months before they are they are replaced. Whilst this advice would seem reasonable, there is little actual clinical proof that this recommendation is correct. Because of variability in subjects' brushing techniques and the force applied to the teeth whilst brushing, the degree of wear varies significantly from subject to subject. It is also likely that different brushes, made from various materials, would exhibit differences in longevity. Some commercially available brushes have filaments that change color after a certain amount of use. This serves as a reminder to the patients that it is time to replace the brush.
**Fig. 35-4** Filament end-rounding.
Kreifeldt and co-workers (1980) showed that new brushes were more efficient in removing dental plaque than old brushes. They examined worn toothbrushes and observed that, as a result of wear, the filaments showed a taper, proceeding from the insertion to the free end. For example filaments were seen which tapered from 0.28 mm at one end to 0.020–0.015 mm at the free end. They concluded that among other wear factors, tapering contributed the most to loss of effectiveness. Their explanation for this observation was that as the tapering will result in a reduction of filament diameter, the brush will become softer and remove less plaque.
Since many patients use a brush for periods significantly longer than the recommended time of 3 months, it is important to know whether excessive wear is of clinical relevance. Several studies have examined this question but there is inconclusive evidence about the relationship between toothbrush wear and plaque removal. Studies with laboratoryworn toothbrushes reported that such used toothbrushes had inferior plaque removal efficacy as compared to new brushes (Kreifeldt _et al_. 1980; Warren _et al_. 2002). However, artificially worn toothbrushes may not mimic the characteristics of a naturally worn brush. In a laboratory study of the wear of toothbrushes, wear will inevitably be highly uniform and not reflect the variation in wear seen in normal toothbrush use. Most studies in which naturally worn toothbrushes were used reported no statistically significant decrease in reduction of whole-mouth plaque scores after brushing when compared to using new toothbrushes (Daly _et al_. 1996; Sforza _et al_. 2000; Tan & Daly 2002; Conforti _et al_. 2003; Van Palenstein Helderman _et al_. 2006). From this brief review of the literature it may be concluded that in contrast to what is generally thought, the wear status of a toothbrush might be less critical for maintaining good plaque control.
### Electric toothbrushes (see Procedure 2)
In well motivated and properly instructed individuals who are willing to invest the necessary time and effort, mechanical measures, using traditional toothbrushes and adjunctive manual (interdental) devices, are effective in removing plaque. Maintaining a dentition close to plaque-free is, however, not easy. The electric toothbrush represents an advance that has the potential to both enhance plaque removal and patient motivation. Electric toothbrushes were introduced to the market more than 50 years ago. The first toothbrush powered by electricity was developed by Bemann & Woog in Switzerland and was introduced in the United States in 1960 as the Broxodent. In 1961 a cordless rechargeable model was introduced by General Electric (Darby & Walsh 2003). Studies of the use of these early electric tootbrushes showed that there was no difference in plaque removal when compared with a manual toothbrush and they had mixed effects on gingivitis. The consensus of the research reports on toothbrushing of the World Workshop in Periodontics in 1966 states: " _in non-dentally oriented persons, in persons not high motivated to oral health care, or in those who have difficulty in mastering suitable hand brushing technique the use of an electric brush with its standard movements may result in more frequent and better cleansing of the teeth_ ".
Since the 1980s, tremendous advances have been made in the technology of electrically powered toothbrushes. Various electric toothbrushes have been developed to improve the efficiency of plaque removal using increased filament velocity, brush stroke frequency, and various filament patterns and motions. Where old electric toothbrushes were using a combination of horizontal and vertical movements mimicking closely the back-and-forth motion of the traditional brushing methods, the more recent designs apply rotary motion or oscillating/rotating motion with pulsation, or have brush heads which move at high frequencies.
After reviewing many of the published reports over the past decades, it may be concluded that certain newer types of rechargeable electric toothbrushes have become more effective in removing supragingival plaque and controlling gingivitis. It is also clear that the effectiveness of particularly the low-cost battery-operated brushes are not well documented. To some extent, power brushes have over-come the limitations of the manual dexterity and skill of the user. Modern design features appear to be responsible for this (Fig. 35-5). These newer designed toothbrushes remove plaque in a shorter time than a standard manual brush (Van der Weijden _et al_. 1993, 1996a). The new generation of electric brushes have better plaque removal efficacy and gingival inflammation control in the approximal tooth surfaces (Egelberg & Claffey 1998). This superiority was clearly demonstrated in a study carried out on extracted teeth (Rapley & Killoy 1994). The electric toothbrush should not be considered a substitute for a specific interdental cleaning method, such as flossing, but it may offer advantages in terms of an overall approach to improved oral hygiene.
**Fig. 35-5** Overview of the development of electric toothbrushes from brushes mimicking a manual toothbrush to high-frequency brushhead movement. From left to right: the Braun D3®, Rotadent®, Interplak®, Braun/Oral-B Triumph®, Sonicare Elite®.
Two independent systematic reviews confirmed that oscillating rotating toothbrushes have superior efficacy over manual toothbrushes in reducing plaque and gingivitis (Sicilia _et al_. 2002; Robinson _et al_. 2005). Toothbrushes with this mode of action reduced plaque by 7% and gingival bleeding by 17% when compared with manual brushes (Robinson _et al_. 2005).
One electric toothbrush that has consistently been shown to be more effective than a manual toothbrush, both with respect to plaque removal and improvement of the gingival condition, is the original Braun Oral-B Plaque Remover (D7) (Warren & Chater 1996b). This toothbrush features a small round brush head that makes rotating and oscillating movements at a speed of 2800 oscillating rotations per minute. A further development of this brush, the Braun Oral-B Ultra Plaque Remover (D9) maintained the oscillating rotating action but at an increased speed (3600 rotations per minute). A clinical study with the D9 demonstrated equivalence in safety and a trend towards greater plaque removal when compared with the D7 (Van der Weijden _et al_. 1996b). Newer developments in the oscillating rotating brush technology add the additional high-frequency vibrations in the direction of the bristles creating three-dimensional movements during brushing. This modification was developed to enhance penetration and removal of plaque from approximal spaces of the dentition. Studies have shown the three-dimensional movements carried out by the brush are safe to use and more efficient regarding plaque removal (Danser _et al_. 1998).
Another approach in this technology was the development of sonic toothbrushes that have a high frequency of filament movement in excess of approximately 30 000 strokes per minute. Two recently introduced sonic toothbrushes are the Oral-B Sonic Complete® (SC; Oral-B Laboratories, Boston, MA, USA) rechargeable toothbrush with a side-to-side filament operating at 260 Hz, and the Philips Sonicare® Elite (SE; Philips Oral Healthcare, Snoqualmie, WA, US) based on a different technology, with a side-to-side motion also operating at a frequency of 260 Hz. Some clinical studies have shown sonic technology to be comparable or more effective than a manual toothbrush in removing plaque and reducing gingival inflammation (Johnson & McInnes 1994; Tritten & Armitage 1996; Zimmer _et al_. 2000; Moritis _et al_. 2002). Two studies using the same experimental gingivitis model compared an earlier Sonicare device and the Oral-B oscillating rotating toothbrush. In both studies the oscillating rotating brush was more effective in improving the level of gingival health (Putt _et al_. 2001; Van der Weijden _et al_. 2002a,b). This confirmed the findings of an earlier 6-week crossover study (Isaacs _et al_. 1998) where improvement in gingival condition was 8.6% greater with the oscillating rotating brush. Rosema and co-workers (2005) compared the Sonicare Elite to the Oral-B Professional Care 7000 and again found the oscillating rotating pulsation brush to be more effective. On the other hand, Tritten & Armitage (1996) compared the Sonicare advance to a traditional manual toothbrush in a 12-week parallel group study and concluded that both brushes were equally effective in reducing gingival inflammation.
Modern power toothbrushes are known to enhance long-term compliance. In a study involving periodontitis patients with persistent poor compliance, Hellstadius and co-workers (1993) found that switching from a manual to a power toothbrush reduced plaque levels and that the reduced levels were maintained over a period of between 12 and 36 months. The power brush significantly improved compliance, and patients expressed a positive attitude to the new brush. In a survey carried out in Germany most dentists stated that the time their patients spent on toothbrushing was too small (Warren 1998). Approximately half of the dentists stated that they recommend their patients to use a power toothbrush, and the vast majority of the dentists believed that changing to a power toothbrush would improve the condition of their patients' teeth and gums. Findings from a recent US practice-based study, involving a large number of subjects who switched from a manual toothbrush to the Braun Oral-B Ultra Plaque Remover (D9), confirmed the findings from the German study (Warren _et al_. 2000).
### Electrically active (ionic) toothbrush
Several toothbrushes have been marketed over the years, which are designed to send a small imperceptible electronic current through the brush head, presumedly to enhance the efficacy of the brush in plaque elimination. The electrons should reduce the H+ ions from the organic acid in the plaque which may result in a decomposition of the bacterial plaque (Hoover _et al_. 1992). The first record of a charged toothbrush, the "Dr. Scott's Electric Toothbrush" was found in the February 1886 issue of Harper's weekly magazine. The handle of Dr. Scott's toothbrush was purportedly "charged with an electromagnetic current which acts without any shock, immediately upon the nerves and tissues of the teeth and gums... arresting decay... and restoring the natural whiteness of the enamel."
Short-term clinical studies with the use of these kinds of brushes documented a beneficial effect in terms of plaque reduction and gingivitis resolution (Hoover _et al_. 1992; Weiger 1998). Hotta and Aono (1992) studied an electrically active manual toothbrush that was designed with a piezo-electric element in the handle. This brush generates a voltage potential corresponding to the bending motion of the handle as the teeth are brushed. In this study no difference in the amount of remaining plaque after brushing was observed between the placebo and the electrically active brush. Other toothbrushes, which have a claimed 'electrochemical' effect on dental plaque, have a semiconductor of TiO2 incorporated in the brush handle. In the presence of light, saturated low energy electrons in the wet semiconductor are transformed into high-energy electrons. An electron current of approximately 10 nA was measured to run from the semiconductor to the tooth (Weiger 1988).
## Interdental cleaning
There is confusion in the literature with respect to the definitions of approximal, interproximal, interdental, and proximal sites. Commonly used indices are not suitable for assessing interdental plaque (directly under the contact area), and thereby limit interpretation of interdental plaque removal. The European Workshop on Mechanical Plaque Control in 1999 proposed the following definitions: _approximal_ (proximal) areas are the visible spaces between teeth that are not under the contact area. In health these areas are small, although they may increase after periodontal attachment loss. The terms _interproximal_ and _interdental_ may be used interchangeably and refer to the area under and related to the contact point.
As stated above, the toothbrush does not reach the approximal surfaces of teeth as efficiently as it does for the facial, lingual, and ooclusal aspects nor does it reach into the interproximal area between adjacent teeth. Therefore measures for interdental plaque control should be selected to complement plaque control by toothbrushing (Lang _et al_. 1977; Hugoson & Koch 1979).
The interdental gingiva fills the embrasure between two teeth apical to their contact point. This is a 'sheltered' area, difficult to access, when teeth are in normal position. In populations that use a toothbrush, the interproximal surfaces of the molars and premolars are the predominant sites of residual plaque. The removal of plaque from these surfaces remains a valid objective, since in patients susceptible to periodontal diseases, gingivitis and periodontitis are usually more pronounced in this interdental area than on oral or facial aspects (Löe 1979). Dental caries also occurs more frequently in the interdental region than on oral or facial smooth surfaces. A fundamental principle of prevention is that the effect is greatest where the risk of disease is greatest. Therefore, interdental plaque removal, which cannot be achieved with the toothbrush, is of critical importance for most patients. A number of interdental cleaning methods have been developed, ranging from floss to the more recently introduced electrically powered cleaning aids. Flossing is the most universally applicable method, since it may be used effectively in nearly all clinical situations. However, not all interdental cleaning devices suit all patients or all types of dentitions. Factors such as the contour and consistency of gingival tissues, the size of the interproximal embrasure, tooth position and alignment, and the ability and motivation of the patient should be taken into consideration when recommending an interdental cleaning method. The most appropriate interdental hygiene aids must be selected for each individual patient. The selection made from the numerous commercially available devices is dependent for the most part on the size and shape of the interdental space as well as on the morphology of the proximal tooth surface. In subjects with normal gingival contours and embrasures, dental floss or tape should be recommended. At sites where soft tissue recession has become pronounced, flossing becomes progressively less effective. Then an alternative method (either woodsticks or interdental brushes) should be recommended. A review on interdental cleaning methods (Warren & Chater 1996a) concluded that all conventional devices are effective, but each method should be suited to a particular patient but also to a particular situation in the mouth (Table 35-1).
The use of dental floss, interproximal brushes, and woodsticks may also induce soft tissue damage. In most cases, however, this damage is limited to acute lesions, such as lacerations and gingival erosions (Gillette & Van House 1980). Gingival bleeding during interdental cleaning can be a result of trauma or an indication of inflammation. Patients must be aware that bleeding _per se_ is not a sign that interdental cleaning should be avoided but more likely an indicator of inflammation that needs to be treated.
### Dental floss and tape (see Procedure 3)
Of all the methods used for removing interproximal plaque, dental flossing is the most frequently recommended technique. Levi Spear Parmly, a dentist based in New Orleans, is credited as being the inventor of modern dental floss. As early as 1815 Parmly recommended teeth flossing with a piece of silk thread. Clinical studies clearly show that, when toothbrushing is used together with flossing, more plaque is removed from the proximal surfaces than by toothbrushing alone (Reitman _et al_. 1980; Kinane _et al_. 1992). Dental floss and tape – a type of broader dental floss – are most useful where the interdental papillae completely fill the embrasure space. When properly used, flossing effectively removes up to 80% of proximal plaque. Even subgingival plaque can be removed, since dental floss can be introduced 2–3.5 mm below the tip of the papilla (Waerhaug 1981b). Several types of floss (waxed, unwaxed) are available. Studies have shown no difference in the effectiveness of unwaxed versus waxed dental floss. Unwaxed dental floss is generally recommended for patients with normal tooth contacts because it slides through the contact area easily. It is the thinnest type of floss available, yet when it separates during use it covers a larger surface area of the tooth than waxed floss. Waxed floss is recommended for patients with tight proximal tooth contacts. _Ease of use_ is the most important factor that influences whether patients will use floss on a daily basis. Recently, powered flossing devices have been introduced. In comparison with manual flossing no differences have been found in terms of plaque removal and gingivitis reduction, although patients preferred flossing with the automated device (Gordon _et al_. 1996).
Table 35-1 Interdental cleaning methods recommended for particular situations in the mouth
**Situation**| **Interdental cleaning method**
---|---
Intact interdental papillae; narrow interdental space| Dental floss or small woodstick
Moderate papillary recession; slightly open interdental space| Dental floss, woodstick or small interdental brush
Complete loss of papilla; wide open interdental space| Interdental brush
Wide embrassure space; diastema, extraction diastema, furcation or posterior surface of most distal molar, root concavities or grooves| Single-tufted/end-tufted brush or gauze strip
Frequent reinstruction and reinforcement in the use of floss are necessary because flossing is a difficult skill to master. Flossing is also time-consuming. When a patient is unwilling to use dental floss alternative interdental hygiene aids should be recommended even if these are less efficient. If a patient finds a particular method or device more appealing to use, long-term compliance becomes an achievable goal. Although it is clear that flossing, when properly used, removes plaque in a very efficient manner, there is no evidence that flossing in adult patients with preserved interproximal periodontal tissues should be routinely indicated (Burt & Eklund 1999).
To facilitate flossing a special floss holder may be used. The holder may be reused and is normally made of plastic material, durable, lightweight, and easily cleaned. Research reveals that reductions in bacterial plaque biofilm and gingivitis are equivalent with either the use of a hand flossing or flossholder. A Swedish national dental survey showed that approximately 46% of adults use woodsticks sporadically and only 12% use woodsticks daily. On the other hand, dental floss is used occasionally by 12% of adults and daily by only 2%. In other words, adults use woodsticks as an oral hygiene aid four to six times more frequently than dental floss (Axelsson 1994).
### Woodsticks (see Procedure 4)
Picking our teeth may well be one of humanity's oldest habits and the toothpick one of the earliest tools. The evolution of the primitive toothpick took a second pathway in the more acquisitive societies. It became part of a personal care kit along with a depilatory tweezer and a ear wax scoop (Mandel 1990). In 1872, Silas Noble and J.P. Cooley patented the first toothpick-manufacturing machine.
The key difference between a toothpick and a woodstick (wooden stimulator/cleaner) relates to the triangular (wedge-like) design. Woodsticks should not be confused with toothpicks which are simply meant for removing food debris after a meal (Warren & Chater 1996a). Woodsticks are inserted interdentally with the base of the triangle resting on the gingival side. The tip should point occlusally or incisally and the triangles against the adjacent tooth surfaces. Triangular wedge-like woodsticks have been found to be superior in plaque removal when compared with round or rectangluar woodsticks since they fit the interdental area more snugly (Bergenholtz _et al_. 1980; Mandel 1990). Woodsticks are usually made of soft wood to prevent injury to the gingiva. The tapered form makes it possible for the patient to angle the woodstick interdentally and even clean the lingually localized interdental surfaces. Unlike floss they can be used on the concave surfaces of the tooth root. Some are hand held, while others are designed to be mounted in a handle, which helps gain access to the interdental areas in the posterior region of the mouth (Axelsson 2004).
The wood can store fluoride crystals both on the surface and in the porosities. These crystals readily dissolve when the woodstick is moistened with saliva (Axelsson 2004). During use the soft wood may become splayed. As soon as the first signs of splaying are evident the woodstick should be discarded. As stated above most patients prefer to use woodsticks for the removal of interdental plaque. Woodsticks have the advantage that they are easy to use, and can be used throughout the day without the need for special facilities such as a bathroom or a mirror. Woodsticks may also be used in primary prevention, even in cases of poor manual dexterity, including posterior areas. To use woodsticks there must be sufficient interdental space available and in these cases woodsticks are an excellent substitute to dental floss. Although woodsticks have a good cleansing capacity in the center part of the interproximal surfaces of teeth in contact, their effect is reduced on the lingual side of these surfaces. The woodstick is somewhat difficult to use in the far posterior regions of the jaws because of the lack of accessibility and since the triangular cross section must pass into the embrassure space at a specific angle (Bassiouny & Grant 1981).
When used in healthy dentitions, woodsticks may depress the gingival margin and clean the toothsurface up to 2–3 mm subgingivally (Morch & Waerhaug 1956). Long-term use may cause a permanent loss of the papilla and opening of the embrasure which may have important esthetic implications in the anterior dentition. Woodsticks can clearly be recommended in patients with open interdental spaces as secondary prevention for periodontal diseases.
A review of the literature for studies that have addressed the question whether woodsticks used as adjunct to toothbrushing in adult patients have an effect on plaque and periodontal inflammation identified eight publications. In only one study a significant reduction in plaque scores was reported as result of the use of woodsticks (Schmid _et al_. 1976). In three studies the use of woodsticks resulted in reduction of gingival bleeding (Anaise 1976; Bassiouny & Grant 1981; Bouwsma _et al_. 1992).
### Interdental brushes (see Procedure 5)
Interdental brushes were introduced in the 1960s as an alternative to woodsticks. They are effective in the removal of plaque from the proximal tooth surfaces (Bergenholtz & Olsson 1984). The interdental brush consists of soft nylon filaments twisted into a fine stainless steel wire. This 'metal' wire can prove uncomfortable for patients with sensitive root surfaces. For such patients the use of plastic-coated metal wires may be recommended. The support wire is continuous or inserted into a metal/plastic handle. Interdental brushes are manufactured in different sizes and forms The most common forms are cylindrical or conical/tapered (like a Christmas tree). The length of the bristles in cross section should be tailored to the interdental space. Appropriate interdental brushes are currently available for the smallest to the largest interdental space (Fig. 35-6). Although unconfirmed with scientific documentation, it is believed that the most effcient cleaning is achieved if the brush selected is slightly larger than the embrasure space. The brush is inserted obliquely into the interdental space, from an apical direction. Cleaning is performed with a back-and-forth motion. The interdental brush is the aid of choice when root surfaces with concavities or grooves have been exposed. The interdental brush is also the most suitable cleaning device in "through-and-through" furcation defects. Like woodsticks, interdental brushes are easy to use, although they may have some drawbacks, including the fact that different types may be needed to fit differently sized open interproximal spaces. When not properly used, interdental brushes may elicit dentin hypersensitivity. In order to minimize the risk of hard tissue abrasion interdental brushes should be used without dentifrice except in special cases and then only short-term. They can also be regularly used as a carrier to apply fluoride or antimicrobial agents, e.g. chlorhexidine gel into the interdental space to prevent caries or the recolonization of residual pockets. The brush should be discarded when the filaments become loose or deformed.
**Fig. 35-6** With interdental brushes the diameter of the metal wire core is a detemining factor with respect to access. A close fit of the brushing filaments influences the cleaning ability.
Interdental brushes represent the ideal interdental cleaning tool, especially for periodontitis patients. Waerhaug (1976) showed that individuals who habitually used an interdental brush were able to maintain supragingival proximal surfaces free of plaque and to remove some subgingival plaque below the gingival margin. In a more recent study in patients with moderate to severe periodontitis Christou and co-workers (1998) showed the interdental brush to be more effective than dental floss in the removal of plaque and in promoting pocket reduction. Patients reported that the use of interdental brushes was easier than the use of dental floss. This is in agreement with previous studies (e.g. Wolffe 1976). Also the perception of efficacy was better for the interdental brushes. Significantly less patients reported problems with the use of interdental brushes. Even if efficacy of interdental brushes were not better than that of floss, the long-term use of interdental brushes might be more easily implemented in a patient's routine than that of floss.
### Single-tufted/end-tufted brush (see Procedure 6)
Single-tufted brushes are designed with smaller brush heads that have a small group of tufts or a single tuft. The tuft may be 3–6 mm in diameter and can be flat or tapered. The handle can be straight or contra-angled. Angulated handles permit easier access to lingual and palatal aspects. The filaments are directed into the area to be cleaned and activated with a rotating motion. Single-tufted toothbrushes are designed to improve access to distal surfaces of posterior molars, tipped, rotated or displaced teeth, to clean around and under fixed partial dentures, pontic, orthodontic appliances, or precission attachment, and to clean teeth affected by gingival recession and irregular gingival margin or furcation involvement.
## Adjunctive aids
### Dental water jet
The dental water jet was introduced in 1962. This device, also called an oral irrigator, has been demonstrated to be safe and effective. Oral irrigation has been a source of controversy within the field of periodontology. The daily use of oral irrigation has been shown to reduce dental plaque, calculus, gingivitis, bleeding, probing depth, periodontal pathogens, and host inflammatory mediators (Cutler _et al_. 2000). The strongest and most consistent evidence for the benefit of daily use of a dental water jet is the ability of the device to reduce gingivitis and bleeding. It has been reported that a pulsating stream of water is better than a continuous flow. The pulsating, hydrodynamic forces produced by irrigators can rinse away food debris from interdental spaces and plaque-retentive areas. Irrigation is not, however, a monotherapy but an adjunct designed to supplement or enhance other home care methods (brushing and flossing) intended for mechanical plaque removal (Hugoson 1978; Cutler _et al_. 2000).
Irrigation devices may be used with water or with disinfective ingredients (Lang & Raber 1982). In a study by Flemmig and co-workers (1990) it was observed that the addition of water irrigation to regular oral hygiene reduced bleeding on probing by 50% over a 6-month timeframe. The use of chlorhexidine in suboptimum concentrations (e.g. 0.06%) led to improved plaque inhibition and had an antiinflammatory effect (Lang & Räber 1982; Flemmig _et al_. 1990). The success of pulsating irrigators with regular tips is limited in the subgingival area, and in periodontal pockets (Wennström _et al_. 1987). With specially designed tips (PikPocket: Waterpik Technologies, Inc.; Newport Beach, CA, USA), the pulsating stream of fluid may penetrate more deeply into the pocket areas (Cobb _et al_. 1988).
### Tongue cleaners (see Procedure 7)
The dorsum of the tongue, with its papillary structure and furrows, harbors a great number of microorganisms (Chapter 60). It forms a unique ecologic oral site with a large surface area (Danser _et al_. 2003). The tongue is said to act as a reservoir which permits the accumulation and stagnation of bacteria and food residues (Outhouse _et al_. 2006). The tongue bacteria may serve as a source of bacterial dissemination to other parts of the oral cavity, e.g. the tooth surfaces and may contribute to dental plaque formation. Therefore, tongue brushing has been advocated as part of daily home oral hygiene together with tooth-brushing and flossing (Christen & Swanson 1978). Tongue brushing has also been advocated as a component of the so-called "full-mouth disinfection" approach in the treatment of periodontitis, with the aim of reducing possible reservoirs of pathogenic bacteria (Quirynen _et al_. 2000).
Regular tongue cleaning has been used since ancient times and is still used by natives of Africa, Arabic countries, India, and South America. Many ancient religions emphasized cleanliness of the entire mouth, including the tongue. Indian people's daily ritual of oral hygiene was not only confined to brushing of the teeth but also the tongue was scraped and the mouth was rinsed with concoctions of betel leaves, cardamom, camphor or other herbs.
A large variety of tongue cleaners is commercially available. A modern tonguescraping instrument may consist of a long strip of plastic ribbon. This is held in both hands and bent so that the edge can be pulled down over the dorsal surface of the tongue. Brushing also appears to be an easy method of cleaning the tongue providing that the gagging reflex can be controlled. In a recent systematic review it was concluded that scrapers or cleaners are more effective than toothbrushes for tongue cleaning (Outhouse _et al_. 2006). Patients should be informed that it is most important to clean the posterior portion of the tongue dorsum.
Tongue cleaning is a simple and fast procedure that helps to remove microorganisms and debris from the tongue. When tongue cleaning is practiced on a daily basis, the process becomes easier. Eventually, the patient may indeed feel "unclean" when tongue debris is not removed on a regular basis. In a study by Gross and co-workers (1975) the test group was instructed to brush their tongues as an adjunct to their normal oral hygiene measures. The members of a control group were not instructed to clean the tongue. A reduction in the presence of tongue coating was found of 40% in the test group as compared to the control group.
Some studies have shown that tongue brushing in combination with other methods of oral hygiene is an effective method in reducing the formation of dental plaque. In contrast, Badersten and co-workers (1975) found no difference in _de novo_ plaque accumulation between a 4-day period of tongue brushing and a 4-day period of no oral hygiene procedures. The authors suggested that the majority of the important plaque-forming bacteria might not originate from the tongue. Another reason for not finding an effect of tongue brushing on plaque formation may be that brushing of the posterior part of the dorsum of the tongue is difficult due to inaccesibility and discomfort.
### Dentifrices
The use of a toothbrush is usually combined with a dentifrice (sold as _toothpaste_ ) with the purpose of facilitating plaque removal and applying agents to the tooth surfaces for therapeutic or preventive reasons (Chapter 36). In 1824, a dentist named Peabody was the first person to add soap to toothpaste. John Harris first added chalk as an ingredient to toothpaste in the 1850s. Colgate mass-produced the first toothpaste in a jar. In 1892, Dr. Washington Sheffield of Connecticut manufactured toothpaste into a collapsible tube. The traditional role of dentifrice is primarily cosmetic, in aiding the cleaning of teeth and producing fresh breath. It also makes toothbrushing more pleasant.
The studies by de la Rosa and co-workers (1979) and Stean and Forward (1980) validated the use of dentifrice since they found that there was a reduction in plaque growth after brushing with a dentifrice as opposed to brushing with water. In the course of the years many dentifrice formulations were tested and became well established because of their anti-plaque and/or anti-gingivitis properties. For additional information see Chapter 36.
### Foam brushes, swabs or tooth towelettes
Tooth towelettes are being marketed as a method of plaque removal when toothbrushing is not possible. Their use is not meant to replace a daily toothbrushing regimen. Recently the I-Brush® has been introduced. This swab is mounted on the index finger of the brushing hand. It uses the agility and sensitivity of the finger. Consequently it could permit a better control over the finger pressure because the finger can actually feel the tooth and gingival surfaces and help positioning the brush for more effective scrubbing. During a 3-week clinical trial, no adverse effects were found. The results show that the finger brush removed less plaque than a regular manual toothbrush. In particular approximal plaque reduction was poor in comparison with the manual toothbrush. Based on these results, it is concluded that there is no beneficial effect of the finger brush in comparison with a regular manual toothbrush (Graveland _et al_. 2004).
Foam brushes resemble a disposable soft sponge on a stick and have been dispensed to hospital patients for intraoral cleansing and refreshing as early as the 1970s. They are particularly used for oral care in medically compromised and immunocompromised patients, to reduce the risk of oral and systemic infection (Pearson & Hutton 2002). Lefkoff and co-workers (1995) studied the effectiveness of such a disposable foam brush on plaque. In this study the regular manual toothbrush was found to be significantly more effective in retarding the accumulation of plaque from a plaque-free baseline on both facial and lingual surfaces. The foam brush did, however, show some plaque-preventive capabilities by maintaining plaque formation below 2 mm at the cervical margin of the tooth. Nevertheless, according to most authors, foam brushes should not be considered as a substitute for a regular toothbrush. In a study by Ransier and co-workers (1995) foam brushes were saturated with a chlorhexidine solution. They found the foam brush which had been soaked in chlorhexidine to be as effective as a regular toothbrush in controlling plaque and gingivitis levels. Therefore, if a toothbrush cannot be used in hospitalized patients, an alternative may be the use of chlorhexidine applied with a foam brush.
## Side effects
### Brushing force
Studies have shown brushing force with powered toothbrushes to be lower than that of a manual toothbrush (Van der Weijden _et al_. 1996c). This appears to be a consistent finding. There is an approximately 1.0 N difference between manual and powered toothbrushes. Recently McCracken and co-workers (2003) observed, in a range from 0.75–3.0 N, that the improvement in plaque removal, using a power toothbrush with forces in excess of 1.5 N was negligible. In a feedback study a professional brusher was asked to brush at 1.0 N, 1.5 N, 2.0 N, 2.5 N, and 3.0 N, during which the efficacy in relation of brushing force to brushing was determined. An increase in efficacy was observed with raising brushing force from 1.0 N to 3.0 N (Van der Weijden _et al_. 1996c). Hasegawa and co-workers (1992) evaluated the effect of different toothbrushing forces on plaque reduction by brushing with 100 g intervals on a scale from 100– 500 g. The results of their study corroborate the findings of earlier studies that with increasing force more plaque is removed. In addition they observed that 300 g seems to be the most effective brushing force when using a manual toothbrush for both children and adults. Forces exceeding 300 g caused pain and gingival bleeding in the test patients. As shown in a manual brushing study in which efficacy was plotted against brushing force the relationship between force and efficacy appears not to be linear (Van der Weijden _et al_. 1998a). Using this particular manual toothbrush a positive correlation between efficacy and force up to 4.0 N was found. The more force was used, the more effective was the plaque removal. However efficacy was reduced when forces above 4.0 N were used. Indeed there appeared to be a negative correlation. The hypothesis is that this negative correlation had to do with distortion of the brushing filaments. Above 4.0 N the brushing was no longer performed with the tip of the filament, but due to bending, with its side. This indicates that brushing force is not the sole factor which determines efficacy. Other factors such as action of the brush, size of the brushhead, brushing time, and manual dexterity may be of greater importance.
Excessive brushing force has been mentioned as a factor which is partly responsible for the origin of toothbrush trauma (gingival abrasion). In response to patients that use excessive force, manual and electric toothbrush manufacturers have introduced toothbrush designs, which can limit the amount of force used and thus reduce the chance of damage to soft and hard tissues. However there is no linear correlation between brushing force and abrasion. Mierau and Spindler (1989) performed a quantitative assessment of habit patterns of toothbrushing in 28 subjects and nine sessions. Least variations within each individual were observed with regard to brushing force. Brushing force ranged from 1.0–7.4 N between individuals. They did not observe any (visual) lesions from brushing in those individuals using a brushing force <2 N. If the brushing force was >2 N, co-factors such as brushing time, brushing method, and frequency of brushing appeared to be associated with acute brushing lesions. Burgett & Ash (1974) argued that the potential detrimental effect of brushing is related to the force applied at a particular point, i.e. pressure. it must be recognized that the head of a manual brush is larger than the head of the electric brush. Since the forces are given as a total of the force over the entire brush it may be that the unit pressure was less for the manual than for the electric brushes. They observed no difference in pressure between a soft manual (11.32 g/mm2) and an electric toothbrush (11.29 g/mm2). These data which show that the pressure for the electric and the manual brush are similar are also in agreement with findings presented by Van der Weijden and co-workers (1996c).
### Toothbrush abrasion
Since various mechanical products are used in personal control of supragingival plaque, the possibility exists that some deleterious effects may appear as a consequence of these oral hygiene practices (Echeverría 1998). It has already been known for a long time that toothbrushing may have some unwanted effects on the gingiva and hard tooth tissues (Kitchin 1941). Trauma to hard tissues leads to cervical abrasion of the tooth surface. These lesions have been associated with toothbrush stiffness, the method of brushing, and brushing frequency. Cervical tooth abrasion has a multifactorial etiology, but in most cases it is the consequence of toothbrushing due to an excessive pressure of the brush and an excessive number of toothbrushing episodes/time. Both situations are probably linked to personality traits ( _compulsive brushers_ ). Tooth wear has also been associated with toothbrush characteristics, especially related to the finishing and hardness of the filaments (Fishman 1997). It has been stated that hard tissue damage is mainly caused by the abrasives in the dentifrice, whereas lesions of the gingival tissues are caused by the toothbrush (Axelsson _et al_. 1997; Meyers _et al_. 2000).
In many instances, _tooth abrasion_ is found in combination with _gingival recession_. Whereas gingival recession is associated with different etiologic/risk factors, e.g. periodontal inflammation, smoking, gingival biotype or repeated periodontal instrumentation, inadequate toothbrushing is probably the most significant one (Björn _et al_. 1981). Clinical experience does support the idea that, with improper use, toothbrushing can cause superficial damage to the gingival tissues. Patients with good oral hygiene have been found to have more gingival recession and more dental abrasion than those with poor oral hygiene. Unfortunately there are few studies in the dental literature concerning gingival lesions resulting from toothbrushing. Thus, to what extent oral hygiene procedures may traumatize the gingival tissues is not clear. Gingival abrasions as a result of brushing are often reversible localized superficial lesions. It is unlikely that gingival abrasion is induced by a single factor. One factor which has already been mentioned to be related to gingival abrasion is brushing force. In the literature, other factors have been suggested such as brushing method (e.g. Bass method), abusive toothbrush use, manual or powered toothbrushing, toothbrush grip, brush head shape, stiffness of filaments, end-rounding of toothbrush filaments, and toothbrushing frequency (Van der Weijden & Danser 2000).
Interestingly, there has been little debate on the role of dentifrice in the abrasion of soft tissues. This is somewhat surprising when abrasion of dental hard tissues is almost entirely a function of dentifrice. Detergents in dentifrice, agitated over a mucosal surface, could enhance the removal of the protective salivary glycoprotein layer and exert cytotoxic action on the overlying epithelial cells (Addy & Hunter 2003). No statistically significant difference in the incidence of gingival abrasion was found between brushing with dentifrice or without dentifrice (Versteeg _et al_. 2005) (Fig. 35-7).
# Importance of instruction and motivation in mechanical plaque control
A fundamental principle for all preventive action is that the effect is greatest where the risk of development of disease is greatest. Needs-related instruction in oral hygiene should therefore intensify mechanical plaque removal on those individual teeth and surfaces that are at risk. A prerequisite for establishing needs-related toothcleaning habits is a well motivated, well informed, and well instructed patient (Axelsson 2004). Mechanical plaque control demands active participation of the individual subject, and therefore the establishment of proper oral home care habits is a process that involves and depends on behavioral changes to a great extent. When implementing behavioral changes, dental professionals should try to ensure that the patient recognizes his/ her oral health status and the role of his/her personal oral hygiene procedures in the prevention of caries and periodontal diseases. The patient should be informed about the casual relationship that led to the disease process and should be encouraged to take responsibility for his/her own oral health. The dental team has numerous possibilities to demonstrate soft tissue alterations elicited by inflammation to the patient, and the responsible etiologic factors. Most commonly, as with sports coaching, a one-to-one professional–patient approach should be employed.
Fig. 35-7 (a) Soft tissue damage as a result of extensive toothbrushing. Note gingival recession on the buccal gingival surface of tooth 13. (b) Note multiple ulcerations of the buccal gingival margin in the right maxilla. (c,d) Hard tissue damage has resulted after extensive use of interdental brushes.
Many patients spend too little time brushing or they brush haphazardly. The importance of thorough plaque removal should be stressed. Toothbrushing instruction for a patient involves teaching what, when, where, and how. In addition, instruction should also involve a description of specific toothbrushing methods, the grasp of the brush, the sequence and amount of brushing, the areas of limited access, supplementary brushing for occlusal surfaces and the tongue. The possible detrimental effects from improper toothbrushing and variations for special condition are described (Wilkins 1999). The design of toothbrushes or a specific toothbrushing method are of secondary importance to the skills of the individual in using the brush (Frandsen 1986). The simplest, least time-consuming procedures that will effectively remove bacterial plaque and maintain oral health should be recommended. If a patient prefers a specific oral hygiene strategy the clinician can evaluate this and modify the technique to maximize effectiveness, rather than changing it. Although it is necessary to give all patients honest feedback on their plaque removal efforts, it is also important to reward a positive performance and not entertain unrealistic expectations, so that the patient will not dread each maintenance visit.
Oral hygiene instruction should also include components such as self-assessment, self-examination, self-monitoring, and self-instruction. With this purpose, several devices and chemical agents have been used in order to make dental plaque more evident to the patient. The interested patient can be informed and motivated, for example, through use of disclosing agents to visualize plaque at the gingival margin or in the interdental spaces. Disclosing agents are chemical compounds such as erythrosine, fuchsin or a fluorescein-containing dye that stains dental plaque and thus makes it fully evident to the patient, either with regular or ultraviolet light. Erythrosine has already been used for many years and has received an FDA approval (Arnim 1963) (Fig. 35-8).
Fig. 35-8 (a) Disclosing solution is often used to identify plaque. (b) Note remaining plaque on the buccal tooth surfaces after staining. (c) After self-performed tooth cleaning, remaining plaque can be identified by the patient following rinsing with a disclosing solution.
When applied immediately before toothbrushing, the patient can identify the amount of plaque formed after the last toothbrushing episode, thus receiving an immediate feedback about his/her cleaning performance. This procedure is useful during the early phase of plaque control. Later on, the disclosing agent should be applied after toothbrushing, which allows the patient to identify those areas needing additional cleaning efforts. Disclosing solution is available in either liquid or tablet form. The liquid may offer some advantages in that the operator can ensure that all surfaces are adequately covered. The red disclosing solution remains in the mouth for some time and may temporarily stain the lips and gingiva.
Disclosing of plaque in the patient's mouth is usually not enough to establish good oral hygiene habits, however. Other factors might influence the individual to modify or determine his or her behavior. These factors may be more or less beyond the control of the dental personnel (such as social and personal factors, environmental setting, and past dental experiences) or may lie within the control of dental personnel (such as conditions of treatment, instruction, and education of the patient). All of these should be considered in the design of an individualized oral hygiene program.
A variety of methods can be used to deliver advice and instruction. The effect of various oral hygiene instruction programs, administered individually or in groups, has been evaluated in a number of clinical studies. These studies have evaluated whether instruction given during one visit only is similar to step-by-step instruction provided during several visits, or whether the use of pamphlets or video tapes is superior to self-instruction manuals and to personal instruction given by a dental professional. In a study by Renton-Harper and co-workers (1999) an instructional video for an oscillating rotating electric toothbrush was evaluated. The subjects that followed the instructional video benefited significantly and considerably in terms of plaque removal compared to subjects receiving only written instructions. Different types and amounts of feedback to the patients using disclosed plaque scores and phase contrast demonstrations have also been investigated. These studies have usually reported similar improvements in plaque and gingivitis scores, irrespective of the mode of instruction. However, these results should be interpreted with caution since the subjects participating in these studies were examined at regular intervals, and therefore it is difficult to separate the effect of repeated examinations from the effect of the instructions (Renvert & Glavind 1998).
If oral hygiene motivation, information, and instruction are combined with professional tooth cleaning the effect in terms of reduction of plaque levels and levels of gingival inflammation may persist even after 6 months. A recent systematic review concluded, based on studies ≥6 months of duration, that a single oral hygiene instruction, describing the use of a mechanical toothbrush, in addition to a single professional "oral prophylaxis" provided at baseline, had a significant, albeit small, positive effect on the reduction of gingivitis (Van der Weijden & Hioe 2005).
Rylander and Lindhe (1997) have recommended that oral hygiene instruction be given during a series of visits allowing the possibility of giving the patient immediate feedback and reinforcing the patient in his/her home care activities. The protocol below is based on the one used in several clinical trials by Lindhe and Nyman (1975), Rosling and co-workers (1976), and Lindhe and co-workers (1982), where the role of plaque control in preventing and arresting periodontal diseases was clearly proven.
### First session
1. Apply a plaque-disclosing solution to the teeth and, with aid of a hand mirror, demonstrate all sites with plaque to the patient (Fig. 35-8b). The plaque score should be recorded using a plaque control record (Fig. 35-9).
2. Ask the patient to clean the teeth using his/her traditional technique. With the aid of a hand mirror, demonstrate the results of the toothbrushing to the patient, again identifying all sites with plaque (Fig. 35-8c).
3. Without changing the technique, ask the patient to clean the surfaces with plaque.
Depending on the plaque remaining after this second toothbrushing, the dental professional should either improve the technique or introduce an alternative system of toothbrushing. In order not to overload the patient with too much information during the first session, the use of adjunctive devices for interproximal cleaning can be introduced or improved in the second session.
Fig. 35-9 A chart illustrating the teeth and tooth surfaces in the maxilla and mandible. The distribution of tooth surfaces with dental plaque (shadowed areas) is identified. In this case the plaque score is 17%.
### Second session
1. A few days after the previous session, the disclosing solution is again applied. The results, in terms of plaque deposits, are identified in the mouth, recorded in the plaque control record, and discussed with the patient.
2. The patient is then invited to clean the teeth, according to the directions previously given in the first session, until all staining is removed. In many cases, toothbrushing instructions will need to be reinforced. Reinforcement and positive recognition should be given to the patient at the same time.
If necessary, the use of interproximal cleaning aids can now be introduced or improved.
### Third and following sessions
1. One or two weeks later the same procedure used in the second session is repeated. However, the efficacy of self-performed plaque control should be evaluated and presented to the patient at each appointment. This repeated instruction, supervision, and evaluation aims to reinforce the necessary behavioral changes.
The long-term result of oral hygiene instruction is dependent on behavioral changes. Patients may fail to comply with given instructions for many reasons, ranging from unwillingness to perform oral self-care, poor understanding, lack of motivation, poor dental health beliefs, and unfavorable dental health values, to stressful life events or low socioeconomic status. Although the use of behavior-modification techniques may offer an advantage over traditional instruction techniques, there is limited research in this area to clarify the relationship between health beliefs and compliance.
### Conclusion
* Oral hygiene instruction should be tailored to each individual patient on the basis of his/her personal needs and other factors.
* The patient should be involved in the instructional process.
* An individualized maintenance program should follow the basic oral hygiene instruction.
All the illustrations for the following procedures are used with permission from _Paro Praktijk Utrecht_.
### Procedure 1: Instruction for Manual Toothbrush
It is of utmost importance that in addition to using the correct toothpaste and also brushing for at least 2 minutes to brush the teeth in a set sequence. This prevents missing out certain areas. Areas untouched by the brush allow plaque to continue to grow. Try to choose a brush with medium or soft bristles and a small head.
#### _Instruction_
* Hold the brush firmly and place the bristles at an angle against the edge of your gums (use a 45º angle). Take care to ensure that the bristles are in contact with a small part of the gum margin.
* Place the brush against the molar or tooth at the back of the mouth and make short back and forth scrubbing movements. Brush from the back to the front of the mouth and try to overlap the strokes. Do not brush more than two teeth simultaneously. Always start at the back and work slowly forwards.
* Always hold the brush head horizontal when cleaning the outside surfaces of the teeth. It is easier to hold the head vertically when brushing the inside surfaces of the top and bottom teeth.
* Avoid too much pressure and fast movements and be aware of feeling contact with the gum margin. Also avoid brushing too vigorously thereby preventing damage to the gums.
When cleaning the teeth keep using the same sequence of brushing. For example, inside of bottom jaw left (15 seconds) inside right (15 seconds). Then left on the outside (15 seconds), followed by right on the outside (15 seconds). Repeat the same sequence in the top jaw. Finally, brush the chewing surfaces with small scrubbing movements. Replace the brush when the bristles start to splay.
### Procedure 2: Instruction for the Electric Toothbrush
The importance of using a set sequence of brushing movements is also applicable when using an electric toothbrush. The question as to whether an electric brush is better than a manual one has been asked many times. Both allow to one achieve a high level of oral hygiene. However research has shown that electric toothbrushes are more efficient and many people report that they are easier to use.
#### _Instruction_
* Place the brush firmly on the hand piece. Grip the brush in the palm so that the bristles of the head are somewhat angled toward the gums (at an angle of approximately 70º). Try to allow the longer bristles to penetrate between the teeth and take care that the bristles contact your gums.
* Switch on the brush and place the head on the last tooth in the mouth (check the angle) and move the head gradually (in about 2 seconds) from the back to the front of this tooth.
* Try to follow the contour of both the tooth and the gums. Place the brush head on the next tooth and repeat this process.
* Allow the electric toothbrush to do the work. It is not necessary to press hard or make brushing movements.
* Use a timer! Many brushes will give some form of signal after 30 seconds (the apparatus stops for a moment). This is the point at which to move on to a new part of the mouth.
Remember to thoroughly clean the brush and its head when finished.
### Procedure 3: Use of Dental Floss
The use of dental floss has become part of oral care in addition to correct, more frequent and longer tooth brushing. Floss can be purchased in a variety of thicknesses and types and with or without a layer of wax. If there is sufficient space between the front and back teeth is it advisable to use the somewhat thicker tape than the thinner floss.
#### _Instruction_
* Take approximately 40 cm of floss and wind the ends loosely around the middle finger. Allow for 10 cm between the middle fingers. Then hold the floss between the thumb and first finger so that about 3 cm remains between the thumbs.
* Using a sawing movement, allow the tightly stretched piece of floss to pass between the front and back teeth. This may be difficult where teeth are so close that the space between them is limited. Avoid allowing the floss to slip so fast between the teeth that the gums become damaged.
* Stretch the floss around one of the teeth and carefully allow it to pass just under the gum, once again with a sawing movement.
* Draw the floss up to the contact point with a sawing movement and then repeat the process on the other tooth bordering the space filled with gum tissue.
* Remove the floss from between the teeth, once again with a sawing movement and repeat this process for all the other spaces in the mouth.
* Use a clean piece of floss for each separate space by unwinding part of it from around one middle finger whilst winding it around the other middle finger.
Do not worry if at first your gums bleed slightly. This will stop after using the floss a number of times. Don't give up!
### Procedure 4: Woodsticks
Most adults have sufficient space available between the incisors and molars to allow woodsticks to be used. These come in differing thicknesses and are made from wood and have a triangular cross section, mimicking the shape of the space between the teeth. Woodsticks can only be used once and are ideal when you have a few spare moments – for example when sitting in a traffic queue!
#### _Instruction_
* Hold the woodstick firmly between the thumb and first finger about halfway along its length. When possible place the other fingers for support on the chin. Moisten the tip of the woodstick by sucking on the point of it, thus making it softer and more flexible.
* Place the flat side of the woodstick (i.e. not the sharp side) against the gum. In the upper jaw the flat surface will face upwards and in the lower jaw downwards.
* Push the woodstick firmly from the outer side of the space into it until it becomes just wedged. Then pull it back slightly and push it back once again, using a light sawing motion at right angles to the outer surfaces of the teeth. Light pressure can also be applied simultaneously to the gums. Repeat this a few times, angling the woodstick so as to contact the surfaces of the teeth enclosing the space.
* When using a woodstick between the premolars and molars, close the mouth slightly to reduce tension in the cheeks making the movements easier.
With this method, all spaces between the teeth throughout the mouth can be cleaned. Should the woodstick prick the surface of the gums with the point, angle it a little differently – in the upper jaw the point will face downwards and in the lower jaw upwards. Do not be concerned if your gums bleed a little at first – this will disappear after using the woodsticks repeatedly for a period of time.
### Procedure 5: Interproximal Brushes
Interdental brushes are purchasable in a variety of sizes varying from small to very large. It is of importance to choose the correct diameter of the bristle part of the brush. The size of the space between the teeth determines the size of the diameter of the bristles on the brush. It is often necessary to use different size of brush within one mouth for optimal cleansing. In order to effectively remove dental plaque there should be a slight degree of resistance when the brush is moved back and forth between the teeth.
#### _Instruction_
* Always use the interdental brush _without_ toothpaste
* Hold the interdental brush between the thumb and first finger just behind the bristles. Support can be achieved when necessary by placing your other fingers on your chin. Push, from the outer side of the space, the interdental brush carefully between the teeth, taking care that the brush remains at right angles to the teeth.
* Avoid scraping the centre (metal spiral part) of the brush against the teeth.
* Slide the brush in and out of the space using the full length of the bristle part of the brush. This will remove the dental plaque.
* The area of contact between the brush and the teeth can be somewhat increased by using differing angles of insertion.
* Slight pressure of the brush against the gums should be used as this will allow the bristles to penetrate a little underneath the gum margin.
* By slightly closing the mouth it will be easier to manipulate the brush as the tension in the cheeks is lessened. It may also be of help to slightly bend the brush to ease insertion.
* Cleanse all areas between the teeth where an interdental brush will fit. Rinse the interdental brushes thoroughly after use and allow them to dry out. It is often a good idea to combine the use if interdental brushes and woodsticks.
### Procedure 6: Instruction for Single-Tufted/End-Tufted Brush
The single-tufted toothbrush is a small brush with a small, single tuft of short bristles attached to the end. The end-tufted brush has a number of small tufts attached in a similar manner. These brushes are ideal for cleansing areas of the dentition which cannot be reached with other oral hygiene aids. For example a lone standing tooth, the back surface of the last molar or tooth in the arch, wires and locks of orthodontic braces, grooves or the entrance to areas where roots split apart.
#### _Instruction_
* Hold the single-tufted brush in the same way as a pen. This prevents too much force being applied to the gums.
* Place the single-tufted brush at an angle directed toward the gums (about 45º) – this allows the bristles to reach just under the gum margin.
* Use small, rotational pencil movements.
* The bristles of the brush will then rotate under and along the gum margin. The brush should then be slowly moved along the tooth surface to cover all areas.
### Procedure 7: Use of Tongue Cleaners
Tongue cleaning is a useful addition to the daily oral hygiene routine. Many bacteria can be found within the grooves on the back of the tongue which can cause bad breath. By brushing or scraping the tongue this problem can be markedly helped or prevented entirely. One of the problems associated with tongue cleaning is that it can stimulate a gag reflex, especially when first using this procedure. This occurs more frequently with brushing than when using a scraper. Some people find it less of a problem if they clean their tongue in the evening.
#### _Instruction_
* There are various types of tongue cleaners: the most effective seems to be one having the form of a loop.
* Extend the tongue as far as possible out of your mouth.
* Breathe calmly through your nose.
* Place the tongue cleaner as far as possible on the back of the tongue and press lightly with it so that the tongue becomes flattened.
* Ensure full contact of the tongue cleaner with the tongue.
* Pull the tongue cleaner slowly forward.
* Clean the middle part of the tongue first using the raised edge on one side of the instrument.
* Use the smooth surface of the tongue cleaner on the sides of the tongue.
* Repeat these scraping movements a number of times.
* Rinse the mouth several times.
Remember to clean the tongue cleaner thoroughly after use.
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# Chapter 36
# Chemical Supragingival Plaque Control
Martin Addy and John Moran
* * *
Classification and terminology of agents
The concept of chemical supragingival plaque control
Supragingival plaque control
Chemical supragingival plaque control
Rationale for chemical supragingival plaque control
Approaches to chemical supragingival plaque control
Vehicles for the delivery of chemical agents
Chemical plaque control agents
Systemic antimicrobials including antibiotics
Enzymes
Bisbiguanide antiseptics
Quaternary ammonium compounds
Phenols and essential oils
Natural products
Fluorides
Metal salts
Oxygenating agents
Detergents
Amine alcohols
Salifluor
Acidified sodium chlorite
Other antiseptics
Chlorhexidine
Toxicology, safety, and side effects
Chlorhexidine staining
Mechanism of action
Chlorhexidine products
Clinical uses of chlorhexidine
Evaluation of chemical agents and products
Studies _in vitro_
Study methods _in vitro_
Clinical trial design considerations
* * *
This chapter will consider the past and present status and success of chemical supragingival plaque control in the prevention of gingivitis and thereby the occurrence or recurrence of chronic periodontal diseases. Chlorhexidine, arguably the most studied agent, will be used to consider the possible applications of chemical plaque control in periodontal practice.
# Classification and terminology of agents
Agents that could inhibit the development or maturation of supragingival plaque have been classified according to possible mechanisms of action (for review see Addy & Moran 1997) : (1) anti-adhesive; (2) antimicrobial; (3) plaque removal; and (4) antipathogenic. The majority of agents used to control supragingival plaque are contained in "oral hygiene" products and available to the general public either directly "over the counter" or following recommendation/prescription by a dental or medical professional. Manufacturers of these products and, for that matter, published literature use a variety of terms to describe the action of these chemical agents, often interchangeably, which has tended to cause confusion. In an attempt to clarify the various descriptive terms used the European Federation of Periodontology in the 1996 European Workshop on Periodontology recommended definitions for the terminology employed for agents in chemical supragingival plaque control (Lang & Newman, 1997) as follows:
* Antimicrobial agents: chemicals that have a bacteriostatic or bactericidal effect _in vitro_ that alone cannot be extrapolated to a proven efficacy _in vivo_ against plaque.
* Plaque reducing/inhibitory agents: chemicals that have only been shown to reduce the quantity and/or affect the quality of plaque, which may or may not be sufficient to influence gingivitis and/or caries.
* Antiplaque agents: chemicals that have an effect on plaque sufficient to benefit gingivitis and/or caries (Addy _et al_. 1983).
* Antigingivitis agents: chemicals which reduce gingival inflammation without necessarily influencing bacterial plaque (includes anti-inflammatory agents).
The classification, terminology, and definitions are presented here because of their fundamental importance to understanding the concept of chemical supragingival plaque control. They will be considered in greater detail however under the headings of "Approaches to chemical supragingival plaque control" and "Evaluation of chemical agents and products" and, particularly for the latter, in respect of implied and inferred claims made by manufacturers.
# The concept of chemical supragingival plaque control
Epidemiologic studies revealed a peculiarly high correlation between supragingival plaque levels and chronic gingivitis (Ash _et al_. 1964), and clinical research (Löe _et al_. 1965) led to the proof that plaque was the primary etiologic factor in gingival inflammation. Subgingival plaque, derived from supragingival plaque, is also intimately associated with the advancing lesions of chronic periodontal diseases. On the basis that plaque-induced gingivitis always precedes the occurrence and recurrence of periodontitis (Lindhe 1986; Löe 1986), the mainstay of primary and secondary prevention of periodontal diseases is the control of supragingival plaque (for review see Hancock 1996). Periodontal diseases appear to occur when a pathogenic microbial plaque acts on a susceptible host (for review see Haffajee & Socransky 1994). What constitutes a pathogenic subgingival plaque has been, and continues to be, a much researched area in periodontology. In the 1996 World Workshop on Periodontology a small number of bacteria were confirmed as true pathogens with a longer list considered as putative pathogens (for reviews see Zambon 1996). Much has been learned in the intervening decade, not the least of which is the bacterial diversity of subgingival plaque in health and disease, highlighted in a number of reviews (for review see Socransky & Haffajee 2005). The possibility that viruses may be involved has also been postulated (for review see Slots 2003). If the latter postulate becomes proven an extension of the classification of chemical agents, to include antiviral, will be necessary. Interestingly, and alluded to later in this chapter, some of the antimicrobial agents used in chemical plaque control do have antiviral activity.
Susceptibility to periodontal disease is less well understood and, at this time, certainly difficult to predict and quantify, although risk factors have been identified including genetic markers (for reviews see Kinane _et al_. 2005) (see Chapters 11 and 18). The relationship of plaque levels to pathogenicity and susceptibility is also poorly understood and therefore, for any one individual, what constitutes a satisfactory level of oral hygiene cannot be stated. This aside, there is evidence which demonstrates that improving oral hygiene and gingival health, over several decades, noted in developed countries (Hugoson _et al_. 1998a), has been associated with a decreasing incidence of periodontal disease (Hugoson _et al_. 1998b). Additionally, long-term follow-up of treated periodontal disease patients has shown that success is dependent on maintaining plaque levels compatible with gingival health (Axelsson & Lindhe 1981). Supragingival plaque control is thus fundamental to the prevention and management of periodontal diseases and, with appropriate advice and instruction from professionals, is primarily the responsibility of the individual.
It could be argued that the heavy reliance on mechanical methods to prevent what are microbially associated diseases is outdated. Very few hygiene practices against microorganisms used by humans on themselves, in the home, at the workplace or in the environment rely on mechanical methods alone and some methods are only chemical. The contrary argument must be that the prevention of periodontitis, through the control of gingivitis, would require the discovery of a safe and effective agent. Also, such a preventive agent would have to be applied from an early age to a large proportion of all populations, many of whom would have low or no susceptibility to periodontal disease (for review see Papapanou 1994).
These discussions aside, chemical preventive agents, aimed at the microbial plaque, have been a feature of periodontal disease management for almost a century (for review see Fischman 1997). The consensus appears to be that the use of preventive agents should be as adjuncts and not replacements for the more conventional and accepted effective mechanical methods and only then when these appear partially or totally ineffective alone.
Mechanical tooth cleaning through toothbrushing with toothpaste is arguably the most common and potentially effective form of oral hygiene practiced by peoples in developed countries (for reviews see Frandsen 1986; Jepsen 1998); although, _per capita_ in the world, wood sticks are probably more commonly used. Interdental cleaning is a secondary adjunct and would seem particularly important in individuals who, through the presence of disease, can be retrospectively assessed as susceptible (for reviews see Hancock 1996; Kinane 1998). Unfortunately, it is a fact of life that a significant proportion of all individuals fail to practice a high enough standard of plaque removal such that gingivitis is highly prevalent and from an early age (Lavstedt _et al_. 1982; Addy _et al_. 1986). This, presumably, arises either or both from a failure to comply with the recommendation to regularly clean teeth or lack of dexterity with tooth cleaning habits (Frandsen 1986). Certainly, many individuals remove only around half of the plaque from their teeth even when brushing for 2 minutes (de la Rosa _et al._ 1979). Presumably this occurs because certain tooth surfaces receive little or no attention during the brushing cycle (Rugg-Gunn & MacGregor 1978; MacGregor & Rugg-Gunn 1979). The adjunctive use of chemicals would therefore appear a way of overcoming deficiencies in mechanical tooth cleaning habits as practiced by many individuals.
## Supragingival plaque control
The formation of plaque on a tooth surface is a dynamic and ordered process, commencing with the attachment of primary plaque-forming bacteria. The attachment of these organisms appears essential for initiating the sequence of attachment of other organisms such that, with time, the mass and complexity of the plaque increases (see Chapter 8). Left undisturbed, supragingival plaque reaches a quantitative and qualitative level of bacterial complexity that is incompatible with gingival health, and gingivitis ensues. Even though, as yet, the microbiology of gingivitis is poorly understood, the sequencing of plaque formation highlights how interventions may prevent the development of gingivitis. Thus, any method of plaque control, which prevents plaque achieving the critical point where gingival health deteriorates, will stop gingivitis. Unfortunately, the lack of knowledge of bacterial specificity for gingivitis does not allow targeting or the control of particular organisms except for perhaps the primary plaque formers. Plaque inhibition has, therefore, targeted plaque formation at particular points – bacterial attachment, bacterial proliferation, and plaque maturation – and these will be discussed in more detail in the later section "Approaches to chemical supragingival plaque control".
The mainstay of supragingival plaque control has been regular plaque removal using mechanical methods which, in developed countries, means the toothbrush, manual or electric, and in less well developed countries the use of wood or chewing sticks (for review see Frandsen 1986, Hancock 1996). These devices primarily access smooth surface plaque and not interdental deposits. Interdental cleaning devices include wood sticks, floss, tape, interdental brushes, and, more recently, electric interdental devices (for reviews see Egelberg & Claffey 1998; Kinane 1998). Regular mechanical tooth cleaning is directed towards maintaining a level of plaque, quantitatively and/or qualitatively, which is compatible with gingival health, and not rendering the tooth surface bacteria free. Theoretically, mechanical cleaning of teeth could prevent caries but workshops have concluded that tooth brushing _per se_ and interdental cleaning as performed by the individual do not prevent caries (for review see Frandsen 1986). Clearly, but outside the scope of this chapter, the toothbrush and other mechanical devices do provide a vehicle whereby anticaries agents, such as fluoride, can be delivered to the tooth surface. Under the conditions of clinical experimentation, tooth cleaning performed once every 2 days was shown to prevent gingivitis (Lang _et al_. 1973). The professional recommendation however, has been to brush twice per day, for which there is evidence of a benefit to gingival health over less frequent cleaning with no additional benefit for more frequent brushing (for review see Frandsen 1986). Indeed, recommendations to increase the frequency of brushing more than twice daily may result in more damage to hard and soft tissues (for review see Addy & Hunter 2003). The duration of brushing is somewhat controversial given that most surveys or studies reveal an average brushing time of 60 seconds or less (Rugg-Gunn & MacGregor 1978; MacGregor & Rugg-Gunn 1979). It is worth noting that one study showed less than 50% plaque removal after 2 minutes' brushing (de la Rosa _et al._ 1979). This perhaps highlights that many individuals spend little or no time during the brushing cycle at some tooth surfaces, notably lingually (Rugg-Gunn & MacGregor 1978; MacGregor & Rugg-Gunn 1979).
Oral hygiene, oral hygiene instruction, and the effect of supragingival plaque control alone on subgingival plaque and therefore periodontal disease is the subject of other chapters. Nevertheless, some further comments on mechanical tooth cleaning are pertinent in this chapter, particularly in respect of comparative efficacy of devices. The manual toothbrush as known today, man-made filaments in a plastic head, was invented as recently as the 1930s. Evidence for such devices dates back to China, approximately 1000 years ago, re-emerging in the 1800s in Europe, but too expensive for common usage (for reviews see Fischman 1997). Numerous changes in manual toothbrush design have occurred, particularly recently, and similarly numerous claims have been made for the efficacy of individual designs. Despite this, researchers, workshop reports, and consensus views have repeatedly concluded that there is no best design of manual toothbrush nor an optimal method of tooth cleaning: the major variable being the person using the brush (for reviews see Frandsen 1986; Jepsen 1998). Limited evidence is available comparing the modern toothbrush with chewing sticks but what is available suggests similar efficacy (Norton & Addy 1989), perhaps not surprisingly if indeed the user is the important factor. Interdental cleaning is considered important particularly for those individuals who are known to be susceptible to or have periodontal disease (for reviews see Egelberg & Claffey 1998; Kinane 1998). Here again, there is little evidence supporting one interdental cleaning method over another, leaving patients and professionals to hold subjectively related preferences (for review see Kinane 1998). Electric toothbrushes of the counter-rotation type found prominence for a short time in the 1960s and 1970s but were unreliable and proven of no greater efficacy over manual brushes, except for handicapped individuals (for reviews see Frandsen 1986). More recently, ranges of new electric brushes have appeared with a variety of head, tuft, and filament actions. For these, consensus reports conclude that there is evidence for greater efficacy over manual brushes particularly when professional advice in their use is provided (for reviews see Hancock 1996; Egelberg & Claffey 1998; van der Weijden _et al_. 1998). More recently, a Cochrane systematic review concluded that only oscillating rotating electric toothbrushes could be proven significantly more effective than manual toothbrushes in reducing plaque and gingivitis (Heanue _et al_. 2004). Despite this, there is no clear evidence that any one electric design or head motion is superior and, again, the user appears the major variable. As with manual brushes advice and instruction in the use of electric brushes can result in very high levels of plaque control (Renton Harper _et al_. 2001). Given the speed of head movement for electric versus manual brushes, there must be concerns over potential harmful effect to hard and soft tissues. In this respect, Phaneuf and co-workers (1962) hypothesized that electric brushes would produce the same or less harm, postulating that the users would apply less force. Many years later the application of less pressure to electric compared to manual brushes was proven (for review see van der Weijden _et al_. 1998). Overall, therefore, it has been concluded that the benefits of normal toothbrushing alone and as a vehicle for toothpaste with a variety of active ingredients far outweigh the potential for harm to hard and soft tissues (for review see Addy & Hunter 2003).
## Chemical supragingival plaque control
### History of oral hygiene products
The terminology "oral hygiene products" is recent but there is evidence dating back at least 6000 years that formulations and recipes existed to benefit oral and dental health (for reviews see Fischman 1997). This includes the written Ebers Papyrus 1500 BC containing recipes for tooth powders and mouth rinses dating back to 4000 BC. A considerable number of formulations can be attributed to the writer and scientist Hippocrates (circa 480 BC). By today's standards the early formulations appear strange if not disgusting but they were not always without logic. Thus, bodies or body parts of animals perceived to have good or continuously erupting teeth were used in the belief that they would impart health and strength to the teeth of the user. Hippocrates, for example, recommended the head of one hare and three whole mice, after taking out the intestines of two, mixing the powder derived from burning the animals with greasy wool, honey, aniseeds, myrrh, and white wine. This early toothpaste was to be rubbed on the teeth frequently.
Mouth rinses similarly contained ingredients which would have had some stimulating effect on salivary flow, breath odor masking and antimicrobial actions, albeit not necessarily formulated with all these activities in mind. Alcohol-based mouth rinses were particularly popular with the Romans and included white wine and beer. Urine, as a mouth rinse, appeared to be popular with many peoples and over many centuries. There even appeared differences in opinion, with the Cantabri and other peoples of Spain preferring stale urine, whereas Fauchard (1690–1761) in France recommended fresh urine. The Arab nations were purported to prefer children's urine and the Romans to prefer Arab urine. Anecdotal reports suggest the use of urine as a mouth rinse to this very day with individuals rinsing with their own urine. There could, indeed, be benefits to oral health from rinsing with urine by virtue of the urea content; however this has never been evaluated, and given today's Guidelines for Good Clinical Practice, it is unlikely that study protocols would receive ethical approval.
Throughout the centuries, most tooth powders, toothpastes, and mouth rinses appear to have been formulated for cosmetic reasons including tooth cleaning and breath freshening rather than the control of dental and periodontal diseases. Many formulations contained very abrasive ingredients and/or acidic substances. However, ingredients with antimicrobial properties were used, perhaps not intentionally, and included arsenic and herbal materials. Herbal extracts are, perhaps, increasingly being used in toothpastes and mouth rinses, although there are little data to support efficacy for gingivitis and none for caries. Many agents prescribed well into the twentieth century, usually as rinses, had the potential to cause local damage to tissues, if not systemic toxicity, including aromatic sulfuric acid, mercuric perchloride, carbolic acid, and formaldehyde (Dilling & Hallam 1936).
Perhaps the biggest change to toothpastes came with the chemoparasitic theory of tooth decay of W.D. Miller in 1890. The theory that organic acids were produced by oral bacteria acting on fermentable carbohydrates in contact with enamel led to both the introduction of agents into toothpaste which might influence this process, and the production of alkaline products. Shortly after, and at the beginning of the twentieth century, various potassium and sodium salts were added to toothpaste as a therapy for periodontal disease. The first half of the twentieth century saw numerous claims for toothpastes for oral health benefits, including tooth decay and periodontal disease. For example, with the early recognition that periodontal diseases were associated with microorganisms, emetin hydrochloride was added to toothpaste to treat possible amoebic infections. Perhaps with the exception of the well known essential oil mouth rinse marketed at the end of the nineteenth century, the addition of antimicrobial and/or antiseptic agents to toothpastes and mouth rinses is a relatively recent practice by manufacturers. During the nineteenth and twentieth centuries, toothpastes also became less abrasive. Interestingly, the importance of a level of abrasivity in toothpastes to the prevention of extrinsic dental stain became apparent when one manufacturer marketed a non-abrasive liquid dentifrice. The unsightly brown tooth staining that developed in many users resulted in the early removal of this product from the marketplace. Standard organizations, notably the British Standards Institute (BSI) and the International Standards Organisation (ISO), have written standards for toothpaste (BS5136:1981, ISO11609:1995). The ISO standard for toothpaste is, at this time, under review although, as for the original standard, it is safety rather than efficacy, which is the key issue. Toxicity and abrasivity (see later under Vehicles) are important sections of the toothpaste standard although evaluations for fluoride availability are likely to feature in the next finalized toothpaste standard. An ISO standard for mouth rinses is also under preparation where the hard tissue safety issue of low pH mouth rinses is under consideration. Throughout the ages, and until relatively recently, scientific evaluations of agents and formulations for gum health were not performed and claims for efficacy appear based on anecdotal reports at best. Indeed, given the nature of many ingredients and the recipes recommended in the past for oral hygiene benefits, it is unlikely that efficacy will ever be tested. In the 6000 years history of oral hygiene products, scientific evaluation must be seen as an extremely recent event: an observation which can, of course, be applied to almost all aspects of chemoprevention and chemotherapy of human diseases. Indeed, perhaps the first ever, double-blind, randomized cross-over design clinical trial in dentistry was less than 50 years ago (Cooke & Armitage 1960).
## Rationale for chemical supragingival plaque control
The epidemiologic data and clinical research (Ash _et al_. 1964; Löe _et al_. 1965) directly associating plaque with gingivitis perhaps, unfortunately, led to a rather simplistic view that regular tooth cleaning would prevent gingivitis and thereby periodontal disease. Theoretically correct, this concept did not appear to consider the multiplicity of factors which influence the ability of individuals to clean their teeth sufficiently well to prevent disease, not the least of which are those factors which affect individual compliance with advice, and dexterity in performing such tasks. The need for research into those psychosocial factors which might influence attitude to and performance in oral hygiene, was stated in a workshop report on plaque control and oral hygiene practices (Frandsen 1986) but appears not to have been heeded to this day. Moreover, and as described in other chapters, epidemiologic data suggest that not all individuals are particularly susceptible to periodontal disease. The most severe disease is accounted for by a relatively small proportion of any population and then by only a proportion of sites in their dentition (Baelum _et al_. 1986). Even accepting that a considerable proportion of middle-aged adults will have one or more sites in the dentition with moderate periodontal disease, this will be of the chronic type and a minimal threat to the longevity of their dentition (Papapanou 1994) (see Chapter 7). The prevention of chronic periodontal diseases, through improved oral hygiene practices, will therefore be grossly over-prescribed as the early identification of susceptible individuals is impossible at present.
Host susceptibility is described retrospectively in the already diseased individual but, even here, an explanation for their susceptibility, except for a few risk factors, cannot be made. These risk factors include smoking, diabetes, and polymorph defects, and possibly stress (for review see Chapters 11 and 12). Genetic markers for periodontal disease have been identified but, at present, appear to be applied retrospectively rather than prospectively (Kornman _et al_. 1997; Kinane _et al_. 2005) and the value to early onset disease has been questioned (Hodge _et al_. 2001).
One definition of periodontal disease is chronic gingivitis with loss of attachment. This is a particularly useful definition, since not only does it describe the pathogenic processes occurring but also alludes to the approach to prevent, treat or prevent recurrence of the disease. Therefore prevention through supragingival plaque control still remains the main-stay of controling gingivitis and therefore the occurrence or recurrence of periodontitis. The importance of oral hygiene to outcome and long-term success of therapy for periodontal disease is hampered by the frequent ineffectiveness of mechanical cleaning of specific sites using a toothbrush, and the limited or lack of use of interdental cleaning by many individuals. Despite the encouraging improvements in oral hygiene, gingivitis and, to some extent, periodontitis in developed countries, gingival inflammation is still highly prevalent (see Chapter 7). Taken with the microbial etiology of both gingivitis and periodontitis, this supports the concept of employing agents to control plaque which require minimal compliance and skill in their use. This is the concept that underlies chemical supragingival plaque control, but as with oral hygiene instruction in mechanical methods, it will have to be vastly over-prescribed if periodontal disease prevention is to be achieved in susceptible individuals. Chemical supragingival plaque control has thus been the subject of extensive research using scientific methodologies for 40 years. The question to be addressed here is whether a chemical or chemicals have been discovered and proven efficacious in, firstly, the prevention of gingivitis and, secondly, periodontitis.
### Conclusions
* Gingivitis and periodontitis are highly prevalent diseases and prevention of occurrence or recurrence is dependent on supragingival plaque control.
* Tooth cleaning is largely influenced by the compliance and dexterity of the individual and little by design features of oral hygiene appliances and aids.
* The concept of chemical plaque control may be justified as a means of overcoming inadequacies of mechanical cleaning.
* Gingivitis is highly prevalent and from a young age in all populations, but the proportion of individuals susceptible to tooth loss through periodontal disease is small.
* Prediction of susceptibility to periodontal disease from an early age is at present impossible.
* Mechanical and/or chemical supragingival plaque control measures for prevention of periodontitis will have to be greatly over-prescribed.
* In those individuals with chronic periodontal disease, and therefore considered susceptible, a daily form of interdental cleaning must be essential to long-term treatment success.
## Approaches to chemical supragingival plaque control
The well ordered and dynamic process of plaque formation is summarized in Fig. 36-1. It is apparent that this process can be interrupted, interfered with, reversed or modified at several points and before the plaque mass and/or complexity reach a level whereby gingival health deteriorates. Mechanical cleaning aims to regularly remove sufficient microorganisms to leave a "healthy plaque" present, which cannot induce gingival inflammation. Chemical agents, on the other hand, could influence plaque quantitatively and qualitatively via a number of processes and these are summarized in Fig. 36-1. The action of the chemicals could fit into four categories:
1. Antiadhesive
2. Antimicrobial
3. Plaque removal
4. Antipathogenic.
### Antiadhesive agents
Antiadhesive agents would act at the pellicle surface to prevent the initial attachment of the primary plaque-forming bacteria. Such antiadhesive agents would probably have to be totally preventive in their effects, acting most effectively on an initially clean tooth surface. Antiadhesive agents do exist and are used in industry, domestically, and in the environment. Such chemicals prevent the attachment and development of a variety of biofilms and are usually described as antifouling agents. Unfortunately the chemicals found in such applications are either too toxic for oral use or ineffective against dental bacteria plaques. Nevertheless, the concept of antiadhesives continues to attract research interest (for review see Wade & Slayne 1997). To date, effective formulations or products with antiadhesive properties are not available to the general public, although the amine alcohol, delmopinol, which appears to interfere with bacterial matrix formation and therefore fits some-where between the concepts of antiadhesion and plaque removal, has been shown effective against plaque and gingivitis (Collaert _et al_. 1992; Claydon _et al_. 1996). Were antiadhesive agents to be discovered, a secondary benefit of extrinsic stain prevention of teeth may be expected.
**Fig. 36-1** Bacterial succession plaque formation. There is increasing mass and bacterial complexity as plaque bacteria attach and proliferate. Ideal sites of action for chemicals which might influence plaque accumulation are shown. Acknowledgment to Dr William Wade for permission to publish this diagram.
### Antimicrobial agents
The bacterial nature of dental plaque, not surprisingly, attracted interest in prevention of plaque formation through the use of antimicrobial agents. Antimicrobial agents could inhibit plaque formation through one of two mechanisms alone or combined. The first would be the inhibition of bacterial proliferation and would be directed, as with antiadhesive agents, at the primary plaque-forming bacteria. Antimicrobial agents therefore could exert their effects either at the pellicle-coated tooth surface before the primary plaque formers attach or after attachment but before division of these bacteria. This plaque inhibitory effect would be bacteriostatic in type, with the result that the lack of bacterial proliferation would not allow attachment of subsequent bacterial types on to the primary plaque-forming bacteria. The second effect could be bactericidal, whereby the antimicrobial agent destroys all of the microorganisms either attaching or already attached to the tooth surface. Many antimicrobial agents exist which could produce this effect; however, as will be discussed, to be effective in inhibiting plaque, the bactericidal effect would have to be absolute and/or persistent. If not, other bacteria within the oral environment would colonize the tooth surface immediately following the loss of the bactericidal effect and the biofilm would be re-established. For the most part biofilms in themselves are fairly resistant to total bactericidal effects of antimicrobial agents and, thus far, there does not appear to have been any agent discovered which effectively would sterilize the tooth surface after each application. If such an agent were found it could, of course, have potentially dangerous implications for the oral cavity since it would almost certainly destroy most of the commensal bacteria which normally colonize the oral cavity. This would open up the potential for exogenous microorganisms, with dangerous pathogenic potential, colonizing the oral cavity. In the event, it is probable that antimicrobial agents exert both a bactericidal effect followed by a bacteriostatic action of variable duration. The bactericidal effect will occur when the antimicrobial agent is at high concentration within the oral cavity and usually this will represent the time when the formulation is actually within the oral cavity. This bactericidal effect would be expected to be lost very soon after expectoration.
As will be discussed in respect of chlorhexidine, it is almost certainly the persistence of the bacteriostatic action of antimicrobial agents which accounts for their plaque-inhibitory activity. Calculations by Stralfors (1961) indicated that plaque inhibition through a bactericidal effect would require the immediate killing of 99.9% of the oral bacteria to effect a plaque-inhibitory action of significant duration. Antimicrobial agents for plaque inhibition, to date, are the only agents that have found common usage in oral hygiene products. The efficacy of these agents and products varies at the extremes (for reviews see Addy 1986; Kornman 1986; Mandel 1988; Addy _et al_. 1994; Addy & Renton-Harper 1996; Rolla _et al_. 1997; Eley 1999).
### Plaque removal agents
The idea of employing a chemical agent which would act in an identical manner to a toothbrush and remove bacteria from the tooth surface, is an attractive proposition. Such an agent, contained in a mouth rinse, would be expected to reach all tooth surfaces and thereby be totally effective. For this reason, the idea of chemical plaque removal agents has attracted the terminology of "the chemical toothbrush". As with antiadhesives, there are agents, such as the hypochlorites, which might be expected to remove bacterial deposits and are commonly employed within the domestic environment. Again, such chemicals would likely be toxic were they to be applied within the oral cavity. Perhaps, the nearest success was with enzymes, directed at both pellicle, e.g. proteases, or bacterial matrices, e.g. dextranase and mutanase (for review see Kornman 1986). Again, as will be discussed, these enzymes, albeit potentially effective, lacked substantivity within the oral cavity and had local side effects.
### Antipathogenic agents
It is theoretically possible that an agent could have an effect on plaque microorganisms, which might inhibit the expression of their pathogenicity without necessarily destroying the microorganisms. In some respects antimicrobial agents, which exert a bacteriostatic effect, achieve such results. At present the understanding of the pathogenesis of gingivitis is so poor that this approach has received no attention. Were our knowledge on the microbial etiology of gingivitis to improve, there exists the possibility of an alternative, but related, approach: the introduction into the oral cavity of organisms which have been modified to remove their pathogenic potential to the gingival tissues. This is not a new concept and was an approach experimented with to replace pathogenic staphylococci within the nasal cavities of surgeons with the idea of reducing the potential for wound infection caused by the operator. At present such an approach within the oral cavity for either gingivitis or caries is perhaps within the realms of science fiction.
### Conclusions
* At present most antiplaque agents are antimicrobial and prevent the bacterial proliferation phase of plaque development.
* Plaque formation could be controlled by antiadhesive or plaque removal agents, but these are not, as yet, available or safe for oral use.
* Alteration of bacterial plaque pathogenicity through chemical agents or bacterial modification would require a greater understanding of the bacterial etiology of gingivitis.
## Vehicles for the delivery of chemical agents
The carriage of chemical agents into the mouth for supragingival plaque control has involved a small but varied range of vehicles (for reviews see Addy 1994; Cummins 1997).
### Toothpaste
By virtue of common usage the ideal vehicle for the carriage of plaque-control agents is toothpaste. A number of ingredients go to make up toothpaste and each has a role in either influencing the consistency and stability of the product or its function (for review see Forward _et al_. 1997).
The major ingredients may be classified under the following headings:
1. _Abrasives_ , such as silica, alumina, dicalcium phosphate, and calcium carbonate either alone, or more usually today, in combination. Abrasives affect the consistency of the toothpaste and assist in the control of extrinsic dental staining. The range of abrasivity of toothpaste against dental hard tissues is defined in the BSI and ISO toothpaste standards (presently under review) in an attempt to minimize tooth wear from normal toothbrushing with toothpaste. Dentine abrasion is of prime importance as the majority of abrasives used in toothpastes produce little or no wear to enamel: non-hydrated alumina being the exception. Also, toothpaste detergents produce wear to dentine (Moore & Addy 2005). Abrasivity is calculated by relating the wear of dentine (enamel) by toothpaste to a standard formulation: the relative dentine abrasivity (RDA) value (relative enamel abrasivity (REA)). For the BSI standard a calcium carbonate based abrasive formulation is used whereas for the ISO standard it is calcium pyro-phosphate based. The wear of dentine, measured directly by profilometry or release of P52, by the standard is considered as 100. Toothpastes, according to the two standards, can be up to twice the standard for BSI (RDA range 0–200) and two and a half times for ISO (RDA range 0–250).
2. _Detergents_ : the most common detergent used in toothpaste is sodium lauryl sulfate, which imparts the foaming and "feel" properties to the product. Additionally, detergents may help dissolve active ingredients and the anionic detergent sodium lauryl sulfate has both antimicrobial and plaque inhibitory properties (Jenkins _et al_. 1991a,b). Certain toothpaste products cannot employ anionic detergents as they interact with cationic substances that may be added to the product, such as chlorhexidine, or polyvalent metal salts, such as strontium, used in the treatment of dentine hypersensitivity.
3. _Thickeners_ , such as silica and gums, primarily influence the viscosity of the product.
4. _Sweeteners_ , including saccharine.
5. _Humectants_ , notably glycerine and sorbitol to prevent drying out of the paste once the tube has been opened.
6. _Flavors_ , of which there are many but mint or pep-permint are popular in the western world although rarely found in toothpaste in the Indian subcontinent where herbal flavors are more popular.
7. _Actives_ , notably fluorides for caries prevention; for plaque control triclosan and stannous fluoride and, to a lesser extent, chlorhexidine have been the most studied examples. Other actives relate to different aspects of oral care including anticalculus agents (pyrophosphates), whitening agents (polyphosphates), and desensitizing agents (strontium and potassium salts).
As stated, the addition of cationic antiseptics to toothpastes is difficult but chlorhexidine has been formulated into toothpastes and shown to be effective (Yates _et al_. 1993; Sanz _et al_. 1994), although few products have reached or lasted in the marketplace.
### Mouth rinses
Despite the ideal nature of the toothpaste vehicle, most chemical plaque-control agents have been evaluated and later formulated in the mouth rinse vehicle. Mouth rinses vary in their constituents but are usually considerably less complex than toothpastes. They can be simple aqueous solutions, but the need for products, purchased by the general public, to be stable and acceptable in taste usually requires the addition of flavoring, coloring, and preservatives such as sodium benzoate. Anionic detergents are included in some products but, again, cannot be formulated with cationic antiseptics such as cetylpyridinium chloride or chlorhexidine (Barkvoll _et al_. 1989). Ethyl alcohol is commonly used both to stabilize certain active ingredients and to improve the shelf-life of the product. Several concerns, not always well substantiated, have been expressed over alcohol-containing mouth rinses (for review see Eley 1999). The possible association of alcohol intake with oropharyngeal cancer, has been extended to include alcohol-containing mouth rinses. Whether these concerns are scientifically valid has not been established and separating out the well established role of smoking in these cancers is difficult, if not impossible, as is other sources of alcohol. Also, since at present there seems little support for the long-term use of mouth rinses for gingival health benefits, when mouth rinses are correctly prescribed the risk from contained alcohol is probably minuscule. This, however, does not obviate the possible risk from self-prescription, the chronic use of mouth rinses, or the ingestion of alcoholic mouth rinses by children. In the latter case, toxicity has been reported. Additionally, alcohol may adversely affect the physical properties of some esthetic restoration materials. Sensibly the prescription or recommendation of alcohol-containing mouth rinses would seem inappropriate to known alcoholics or to those individuals whose religion or culture forbids the intake of alcohol. The proportion of alcohol is usually less than 10% but some rinses have in excess of 20% alcohol. Some manufacturers are now producing alcohol-free mouth rinses.
### Spray
Spray delivery of chemical plaque-control agents has attracted both research interest and the development of products by some manufacturers in some countries. Sprays have the advantage of focusing delivery on the required site. The dose is clearly reduced and for antiseptics such as chlorhexidine this has taste advantages. When correctly applied, chlorhexidine sprays were as effective as mouth rinses for plaque inhibition, although there was no reduction in staining (Francis _et al_. 1987a; Kalaga _et al_. 1989a). Chlorhexidine sprays were found particularly useful for plaque control in physically and mentally handicapped groups (Francis _et al_. 1987a,b; Kalaga _et al_. 1989b).
### Irrigators
Irrigators were designed to spray water, under pressure, around the teeth. As such they only removed debris, with little effect on plaque deposits (for review see Frandsen 1986). Antiseptics and other chemical plaque-control agents, such as chlorhexidine, have been added to the reservoir of such devices. A variety of dilutions of chlorhexidine has been employed to good effect (Lang & Raber 1981) but again with the incumbent local side effects of this agent.
### Chewing gum
Over a relatively short period there has been interest in employing chewing gum to deliver a variety of agents for oral health benefits. Also, there appear to be significant benefits to dental health through the use of sugar-free chewing gum. Unfortunately, chewing gums alone appear to have little in the way of plaque-control benefits particularly at sites prone to gingivitis (Hanham & Addy 2001). They can reduce occlusal plaque deposits (Addy _et al_. 1998), but whether this is directly relevant to the prevention of fissure caries has not been proven, indeed is unlikely. Nonetheless, the vehicle has been used to deliver chemical agents such as chlorhexidine and, when used as an adjunct to normal toothbrushing, reduced plaque and gingivitis levels have been shown (Ainamo & Etemadzadeh 1987; Smith _et al_. 1996).
### Varnishes
Varnishes have been employed to deliver antiseptics including chlorhexidine, but the purpose has been to prevent root caries rather than as a reservoir for plaque control throughout the mouth.
### Conclusions
* Many vehicles may be used to deliver antiplaque agents but most information relates to mouth rinses and toothpaste.
* Toothpaste appears the most practical and cost-effective method for chemical plaque control for most individuals.
* In formulating antiplaque agents into toothpaste, potential inactivation by other ingredients must be considered.
* Minority groups, such as the handicapped, may benefit from other delivery systems.
# Chemical plaque control agents
Over a period of nearly four decades there has been quite intense interest in the use of chemical agents to control supragingival plaque and thereby gingivitis. The number and variation of chemical agents evaluated are quite large but most have antiseptic or antimicrobial actions and success has been extremely variable. It is important to emphasize that formulations based on antimicrobial agents provide a considerably greater preventive than therapeutic action. The most effective agents inhibit the development of plaque and gingivitis but are limited or slow to affect established plaque and gingivitis. Were they available, antiadhesive agents would similarly be expected to provide preventive rather than therapeutic effects. Plaque removal agents, on the other hand, would almost certainly provide both preventive and therapeutic actions. Chemical plaque-control agents have been the subject of many detailed reviews since 1980 (Hull 1980; Addy 1986; Kornman 1986; Mandel 1988; Gjermo 1989; Addy _et al_. 1994; Heasman & Seymour 1994; Jackson 1997; Eley 1999). Based on knowledge derived from chlorhexidine (for review see Jones 1997), the most effective plaque-inhibitory agents in the antiseptic or antimicrobial group are those showing persistence of action in the mouth measured in hours. Such persistence of action, sometimes termed substantivity (Kornman 1986), appears dependent on several factors:
1. Adsorption and prolonged retention on oral surfaces including, importantly, pellicle-coated teeth
2. Maintenance of antimicrobial activity once adsorbed primarily through a bacteriostatic action against the primary plaque-forming bacteria
3. Minimal or slow neutralization of antimicrobial activity within the oral environment or slow desorption from surfaces.
The latter concepts will be discussed later under chlorhexidine.
Antimicrobial activity of antiseptics _in vitro_ is not a reliable predictor of plaque-inhibitory activity _in vivo_ (Gjermo _et al_. 1970, 1973). Early studies on a number of antiseptics revealed similar antimicrobial profiles but a large variation in clinical effects. For example, compared to chlorhexidine, the cationic quaternary ammonium compound, cetylpyridinium chloride, has a similar antimicrobial profile _in vitro_ (Gjermo _et al_. 1970, 1973; Roberts & Addy 1981) and is initially adsorbed in the mouth to a considerably greater extent (Bonesvoll & Gjermo 1978). The per-sistence of action of cetylpyridinium chloride is, however, much shorter than chlorhexidine (Schiott _et al_. 1970; Roberts & Addy, 1981), and plaque inhibition is considerably less (for review see Mandel 1988). Several reasons may explain these apparent anomalies, including poor retention of cetylpyridinium chloride within the oral cavity (Bonesvoll & Gjermo 1978), reduced activity once adsorbed, and neutralization in the oral environment (Moran & Addy 1984), or a combination of these factors. Attempts to improve efficacy of cetylpyridinium chloride can, of course, include increasing the frequency of use, but this is likely to incur compliance problems and side effects (Bonesvoll & Gjermo 1978). Alternatively, substantivity could be improved by combining antimicrobials or using agents to increase the retention of antimicrobials (Gaffar _et al_. 1992). Individual groups of compounds, together with the specific agents within the group, are listed in Table 36-1 and discussed below.
**Table 36-1** Groups of agents used in the control of dental plaque and/or gingivitis
## Systemic antimicrobials including antibiotics
(For reviews see Addy 1986; Kornman 1986)
Despite evidence for efficacy in preventing caries and gingivitis or resolving gingivitis, the opinion today is that systemic antimicrobials should not be used either topically or systemically as preventive agents against these diseases. The risk-to-benefit ratio is high and even systemic antimicrobial use in the treatment of adult periodontitis is open to debate (for reviews see Slots & Rams 1990; Addy & Martin 2003) (see Chapter 42). Thus, systemic antimicrobials have their own specific side effects not all of which can be avoided by topical application. Perhaps of greatest importance is the development of bacterial resistance within human populations, for example methicillin-resistant _Staphylococcus aureus_ (MRSA), which causes serious and life-threatening wound infections, particularly within hospitalized patients.
## Enzymes
(For reviews see Addy 1986)
Enzymes fall into two groups. Those in the first group are not truly antimicrobial agents but more plaque removal agents in that they have the potential to disrupt the early plaque matrix, thereby dislodging bacteria from the tooth surface. In the late 1960s and early 1970s enzymes such as dextranase, mutanase and various proteases were thought to be a major breakthrough in dental plaque control that might prevent the development of both caries and gingivitis. Such agents, unfortunately, had poor substantivity and were not without unpleasant local side effects, notably mucosal erosion. The second group of enzymes employed glucose oxidase and amyloglucosidase to enhance the host defense mechanism. The aim was to catalyse the conversion of endogenous and exogenous thiocyanate to hypothiocyanite via the salivary lactoperoxydase system. Hypothiocycanite produces inhibitory effects upon oral bacteria, particularly streptococci, by interfering with their metabolism. This approach is a theoretical possibility and the chemical processes can be produced in the laboratory. A toothpaste product containing the enzymes and thiocyanate was produced but equivocal results for benefits to gingivitis were obtained and there are no convincing long-term studies of efficacy.
## Bisbiguanide antiseptics
(For reviews see Addy 1986; Addy _et al_. 1994; Kornman 1986; Gjermo 1989; Jones 1997; Eley 1999)
Chlorhexidine is thus far the most studied and effective antiseptic for plaque inhibition and the prevention of gingivitis. Consequent upon the original publication (Löe & Schiott 1970), chlorhexidine arguably represents the nearest that research has come to identifying a chemical agent that could be used as a replacement for, rather than an adjunct to, mechanical oral hygiene practices. Other bisbiguanides such as alexidine and octenidine have less or similar activity, respectively, to chlorhexidine but bring with them no improvement in local side effects and have less toxicity data available. Chlorhexidine has thus remained the only bisbiguanide used in a number of vehicles and available in commercial products. In view of the importance of this antiseptic within preventive dentistry, a separate section later in the chapter will be devoted to considering its activity and usage in the mouth.
## Quaternary ammonium compounds
(For reviews see Mandel 1988; Eley 1999)
Benzalconium chloride and, more particularly, cetylpyridinium chloride are the most studied of this family of antiseptics. Cetylpyridinium chloride is used in a wide variety of antiseptic mouth rinse products, usually at a concentration of 0.05%. At oral pH these antiseptics are monocationic and adsorb readily and quantitatively, to a greater extent, than chlorhexidine to oral surfaces (Bonesvoll & Gjermo 1978). The substantivity of cetylpyridinium chloride however appears to be only 3–5 hours (Roberts & Addy 1981) due either to loss of activity once adsorbed or rapid desorption. Cetylpyridinium chloride in mouth rinses has some chemical plaque-inhibitory action but evidence for gingivitis benefits is equivocal, particularly when formulations are used alongside toothbrushing with toothpaste. Home use studies, given the large number of rinse products containing this antiseptic, are surprisingly few. Those available, with one exception, failed to demonstrate any adjunctive benefits to toothbrushing with toothpaste. The one exception (Allen _et al_. 1998) was peculiar in that there was a lack of the expected Hawthorne effect in the control group (see section "Evaluation of chemical agents and prod-ucts" later in this chapter) and the plaque reduction in the active group, 28%, was as great as seen in no brushing chemical plaque inhibition studies. As will be discussed, it is not unusual to find chemicals that provide modest, even moderate, plaque inhibition in no brushing studies but fail to show effects in adjunctive home use studies. This occurs because the range over which to show a benefit of the chemical is limited by the mechanical oral hygiene practices of the study subjects. Additionally, the plaque-inhibitory properties of cetylpyridinium chloride are reduced by toothpaste used before or after the rinse (Sheen _et al_. 2001, 2003). This may explain why a pre-brushing cetylpyridinium mouth rinse offered no adjunctive benefit to mechanical plaque control (Moran & Addy 1991). The efficacy of cetylpyridinium chloride can be increased by doubling the frequency of rinsing to four times per day (Bonsvoll & Gjermo 1978), but this increases local side effects, including tooth staining, and would probably affect compliance. Mouth rinses combining cetylpyridinium chloride with chlorhexidine are available and compare well with established chlorhexidine products (Quirynen _et al_. 2001, 2005). Whether the cetylpyridinium chloride actually contributes to the activity of the chlorhexidine cannot be assessed. A slow-release system and lozenges have been used to deliver cetylpyridinium chloride but provided no greater plaque inhibition than the cetylpyridinium mouth rinse and significantly less than a chlorhexidine rinse (Vandekerchove _et al_. 1995). Interestingly, in this study, the lozenges produced the most dental staining. There is limited information on quaternary ammonium compounds in toothpastes and very few products are available.
## Phenols and essential oils
(For reviews see Mandel 1988; Jackson 1997; Eley 1999)
Phenols and essential oils have been used in mouth rinses and lozenges for many years. One mouth rinse formulation dates back more than 100 years and, although not as efficacious as chlorhexidine, has antiplaque activity supported by a number of short- and long-term home use studies. This mouth rinse product may reduce gingivitis via both a plaque-inhibitory action and an anti-inflammatory action possibly due to an antioxidative activity (Firalti _et al_. 1994). The data from home use studies led the American Dental Association to accept the product as an aid to home oral hygiene measures (for review see Eley 1999). When compared directly with chlorhexidine one 6-month study has demonstrated equivalent effects on plaque and gingivitis but without the inherent side effects of chlorhexidine (Charles _et al_. 2004). Nevertheless, the pH of the product is low (pH 4.3) and has been shown _in vitro_ and _in situ_ to cause erosion of dentine and enamel respectively, albeit to a considerably less degree than orange juice (Addy _et al_. 1991; Pontefract _et al_. 2001). Combining essential oils with cetylpyridinium chloride has been attempted and with promising results from initial studies (Hunter _et al_. 1994).
The non-ionic antimicrobial triclosan, a trichlora-2-hydroxy phenyl ether, is usually considered to belong to the phenol group and has been widely used over many years in a number of medicated products including antiperspirants and soaps. More recently, it has been formulated into toothpaste and mouth rinses and, for the former, has accumulated an impressive amount of literature, some of which is conflicting. In simple solutions, at relatively high concentrations (0.2%) and dose (20 mg twice per day), triclosan has moderate plaque-inhibitory action and antimicrobial substantivity of around 5 hours (Jenkins _et al_. 1991a,b). The dose response against plaque of triclosan alone is relatively flat (Jenkins _et al_. 1993), although significantly greater benefits are obtained at 20 mg doses twice daily compared to 10 mg doses. In terms of plaque inhibition, a 0.1% triclosan concentration (10 mg dose twice per day) was considerably less effective than a 0.01% chlorhexidine mouth rinse (1 mg twice per day) (Jenkins _et al_. 1994).
The activity of triclosan appears to be enhanced by the addition of zinc citrate or the co-polymer, polyvinylmethyl ether maleic acid (for review see Gaffar _et al_. 1992). The co-polymer appears to enhance the retention of triclosan whereas the zinc is thought to increase the antimicrobial activity. Only triclosan toothpastes with the co-polymer or zinc citrate have shown antiplaque activity in long-term home use studies (for review see Jackson 1997). Some home use studies showed little or no effect for one or other of the products on plaque alone, gingivitis alone or both compared to the control paste or conventional fluoride toothpaste (Palomo _et al_. 1994; Kanchanakamol _et al_. 1995; Renvert & Birkhed 1995; Binney _et al_. 1996; Owens _et al_. 1997a). Triclosan toothpastes appear to provide greater gingivitis benefits in some studies than plaque reductions and this could be explained by a possible anti-inflammatory action for this agent (Barkvoll & Rolla 1994).
More recently, long-term studies have suggested that triclosan-containing toothpaste can reduce the progress of periodontitis, although the effects have been considered small (Rosling _et al_. 1997; Ellwood _et al_. 1998). Mouth rinses containing triclosan and the co-polymer are available, with some evidence of adjunctive benefits to oral hygiene and gingival health when used alongside normal tooth cleaning (Worthington _et al_. 1993). This latter study was again interesting with, unusually, no clear Hawthorne effect in the control group. Other studies on the plaque inhibitory properties of a triclosan/co-polymer mouth rinse showed effects significantly less than those of an essential oil mouth rinse product (Moran _et al_. 1997).
## Natural products
(For review see Mandel 1988; Eley 1999)
Herb and plant extracts have been used in oral hygiene products for many years if not centuries. Unfortunately, there are few data available and such toothpaste products provide no greater benefits to oral hygiene and gingival health than do conventional fluoride toothpaste (Moran _et al_. 1991). The plant extract sanguinarine has been used in a number of formulations. Zinc salts are also incorporated, which makes it difficult to evaluate the efficacy of sanguinarine alone. Even when it is combined with zinc, however, data are equivocal for benefits (Moran _et al_. 1988, 1992a; Quirynen _et al_. 1990). Some positive findings were reported for the combined use of sanguinarine/zinc toothpaste and mouth rinses (Kopczyk _et al_. 1991), but the benefit-to-cost ratio must be low. Importantly and very recently, sanguinarine-containing mouth rinses have been shown to increase the likelihood of oral precancerous lesions almost ten-fold even after cessation of mouth rinse use. The manufacturer of the most well known product has replaced sanguinarine in the mouth rinses with an alternative agent. More recently, tea tree oil has been suggested to be of value when topically delivered with positive effects at reducing gingival inflammation (Sookoulis & Hirsch 2004) but as yet no conclusive evidence for effects on plaque accumulation.
## Fluorides
The caries-preventive benefits for a number of fluoride salts are well established but the fluoride ion has no effect against the development of plaque and gingivitis. Amine fluoride and stannous fluoride provide some plaque-inhibitory activity, particularly when combined; however, the effects appear to be derived from the non-fluoride portion of the molecules. A mouth rinse product containing amine fluoride and stannous fluoride is available and there is some evidence from home use studies of efficacy against plaque and gingivitis (Brecx _et al_. 1990, 1992), but less so than chlorhexidine.
## Metal salts
(For reviews see Addy _et al_. 1994; Jackson 1997)
Antimicrobial actions including plaque inhibition by metal salts have been appreciated for many years, with most research interest centered on copper, tin, and zinc. Results have been somewhat contradictory but appear dependent on the metal salt used, its concentration, and frequency of use. Essentially, polyvalent metal salts alone are effective plaque inhibitors at relatively high concentration when taste and toxicity problems may arise. Stannous fluoride is an exception but is difficult to formulate into oral hygiene products because of stability problems, with hydrolysis occurring in the presence of water. Stable anhydrous gel and toothpaste products are available with evidence of efficacy against plaque and gingivitis (Beiswanger _et al_. 1995; Perlich _et al_. 1995). Stannous pyrophosphate at 1% has been added to some stannous fluoride toothpaste to good effect (Svatun 1978). Indeed, it appears that the concentration of available stannous ions is the most significant factor in determining efficacy (Addy _et al_. 1997). Dental staining, however, occurs with stannous formulations and appears to occur by the same mechanism as for chlorhexidine and other cationic antiseptics, involving interaction with dietary chromogens (for reviews see Addy & Moran 1995; Watts & Addy 2001). Combining metal salts with other antiseptics produces added plaque and gingivitis inhibitory effects, for example zinc and hexetidine (Saxer & Muhlemann 1983) and, as already described, zinc and triclosan. Copper also causes dental staining but is not available in oral hygiene products. Zinc, at low concentration, has no side effects and is used in a number of toothpastes and mouth rinses; however, alone it has little effect on plaque (Addy _et al_. 1980) except at higher concentrations. Zinc salts nevertheless, may be of value at reducing volatile sulfur compounds associated with oral malodor (Rosing _et al_. 2002).
## Oxygenating agents
(For review see Addy _et al_. 1994)
Oxygenating agents have been used as disinfectants in various disciplines of dentistry, including endodontics and periodontics. Hydrogen peroxide has been employed for supragingival plaque control and more recently has become important as bleach in tooth whitening. Similarly, peroxyborate may be used in the treatment of acute ulcerative gingivitis (Wade _et al_. 1966). Products containing peroxyborate and peroxycarbonate were, until recently, available in Britain and Europe with evidence of antimicrobial and plaque-inhibitory activity (Moran _et al_. 1995). There are little data from long-term home use studies and such evaluations would seem warranted before conclusions about true antiplaque activity can be drawn.
## Detergents
Detergents, such as sodium lauryl sulfate, are common ingredients in toothpaste and mouth rinse products. Besides other qualities and, for that matter, side effects, detergents such as sodium lauryl sulfate have antimicrobial activity (Jenkins _et al_. 1991b) and probably provide most of the modest plaque-inhibitory action of toothpaste (Addy _et al_. 1983). Alone, sodium lauryl sulfate was shown to have moderate substantivity, measured at between 5 and 7 hours, and plaque-inhibitory action similar to triclosan (Jenkins _et al_. 1991a,b). Detergent-only formulations are not available and no long-term evaluations have been performed.
## Amine alcohols
This group of compounds does not truly fit into an antimicrobial or antiseptic category; indeed they exhibit minimal effects against microbes. Of these morpholinoethenol derivatives, octopinol was the first to be shown effective as an antiplaque agent but was withdrawn for toxicologic reasons. Delmopinol followed and at 0.1% and 0.2% in mouth rinses was shown to be effective against plaque and gingivitis in short-term no oral hygiene and long-term home use studies (Collaert _et al_. 1992; Moran _et al_. 1992b; Claydon _et al_. 1996; Hase _et al_. 1998; Lang _et al_. 1998). Arguably, the short-term no oral hygiene studies showed plaque inhibition closer to chlorhexidine than any other previous agent (Moran _et al_. 1992b). Recently, the data from eight studies from seven independent research groups in five European countries using a 0.2% delmopinol mouth rinse as an adjunct to normal oral hygiene practices were subjected to a meta-analysis. Delmopinol, one of the very few chemical plaque-control agents to be subjected to such analyses, was shown to be a significantly effective adjunct for reducing the plaque burden and severity of gingivitis (Addy _et al_. 2007). The data for gingivitis in several studies met the efficacy criteria for gingivitis reduction of the American Dental Association. The mode of action of delmopinol can be debated but appears to be an interference with plaque matrix formation, reducing the adherence of the primary plaque-forming bacteria of the successional bacteria (Simonsson _et al_. 1991a,b). If correct, delmopinol would closest fit classification as an antiadhesive agent. Side effects include tooth discoloration, transient numbness of the tongue, and burning sensations in the mouth (Claydon _et al_. 1996; Hase _et al_. 1998; Lang _et al_. 1998). Interestingly, the staining was considerably less than with chlorhexidine, rarely reported by study participants and easily removed. In these adjunctive studies discontinuations were considerably less with delmopinol than chlorhexidine. Rinses containing 0.2% delmopinol are available in some countries.
## Salifluor
(For review see Eley 1999)
Salifluor, a salicylanide with both antibacterial and anti-inflammatory properties, has been studied for its effects of plaque inhibition and retardation of onset of gingivitis (Furuichi _et al_. 1996). To improve oral retention and to maximize adsorption, Gantrez (PVM/MA) has been incorporated in salifluor toothpaste and mouth rinse formulations. Perhaps surprisingly, salifluor has not been extensively evaluated, since initial 4-day plaque regrowth studies and 14-day gingivitis studies have suggested equivalent efficacy to a 0.12% chlorhexidine mouth rinse (Furuichi _et al_. 1996). In spite of this evidence to suggest the potential value of the chemical as an antiplaque agent, further long-term studies have yet to be carried out.
## Acidified sodium chlorite
(For review see Yates _et al_. 1997)
This agent does not sit well with any particular group listed in Table 36-1; however, depending on the acid chosen and the conditions of the reaction between the acid and the sodium chlorite, a varied and complex range of reaction products can ensue. Under ideal conditions for antimicrobial benefits sodium chlorite is reacted with a protic acid to produce chlorous acid, which then liberates a range of higher oxidant species but contains minimal amounts of chlorine dioxide. These higher oxidant species have a broad range of antimicrobial action against bacteria, fungi, yeast, and viruses, and products are available in the US within the veterinary and food industry, both as a preventive for mastitis in cows and for the preservation of frozen poultry. Experimental mouth rinses have been tested in short-term plaque regrowth studies and salivary bacterial count investigations (Yates _et al_. 1997). Surprisingly, given that the acid and sodium chlorite are mixed immediately before rinsing, and that the duration of the chemical reaction would be limited to the rinsing time, three experimental formulations were shown to be as good as chlorhexidine against plaque regrowth and showed the same substantivity as chlorhexidine. Although not tested in longer-term studies, side effects, particularly staining and alteration of taste, would appear unlikely with the acidified sodium chlorite mouth rinses. Unfortunately, the low pH of the formulations would be expected to cause some dental erosion and this has been proven in studies _in situ_ (Pontefract _et al_. 2001). Such erosion, which was found comparable to that of orange juice _in situ_ , would tend to obviate the long-term continuous use of such agents. Acidified sodium chlorite mouth rinses, however, could find application in preventive dentistry similar to those to be described for chlorhexidine (see later in this chapter). The erosive effects would not, in short- to medium-term use, reach clinically significant levels. To date no commercial products are available.
## Other antiseptics
(For review see Addy 1986)
A number of antiseptics/antimicrobial agents have been studied for plaque inhibition. Most have been found to have little or no effect _in vivo_ ; a few have been formulated in mouth rinse products including povidone iodine and hexetidine. Povidone iodine at 1% has a substantivity of only 60 minutes (Addy & Wright 1978) and lacks appreciable plaque-inhibitory activity (Addy _et al_. 1977) or action in acute infections such as acute ulcerative gingivitis (Addy & Llewelyn 1978), for which it is recommended. Povidone iodine is largely without side effects but as a rinse has potential to affect thyroid function adversely (Wray _et al_. 1978). Hexetidine, a saturated pyrimidine, at 0.1% was shown to have limited plaque-inhibitory action (Bergenholtz & Hanstrom 1974) and no evidence for antiplaque activity when used as an adjunct for oral hygiene (Chadwick _et al_. 1991). The action of hexetidine against plaque appears enhanced by zinc salts (Saxer & Muhlemann 1983) but data are derived only from short-term studies. Side effects for hexetidine include tooth staining and mucosal erosion, although both are uncommon (Bergenholtz & Hanstrom 1974). Nevertheless, mucosal erosion is markedly increased in incidence if the concentration is raised to 0.14% (Bergenholtz & Hanstrom 1974). A mouth rinse product containing 0.1% hexetidine is available in some European countries. Recent studies have shown favorable effects on plaque and gingivitis (Sharma _et al_. 2003; Ernst _et al_. 2005) and when compared to 0.1% chlorhexidine, less tendency for stain production (Ernst _et al_. 2005).
**Fig. 36-2** Chlorhexidine molecule.
### Conclusions
* Effective antimicrobial antiplaque agents show prolonged persistence of action in the mouth (substantivity). Chlorhexidine is the most effective antiplaque agent to date. Stannous fluoride and triclosan oral hygiene products are available with proven antiplaque activity. The long established mouth rinse, based on essential oils, has some evidence for adjunctive antiplaque activity.
* The limited information on natural products, for example herbal formulations, is not encouraging and the root extract sanguinarine has been withdrawn because of the potential to cause precancerous oral lesions.
* The amine alcohol, delmopinol, is an effective antiplaque agent and products are becoming available.
* Acidified sodium chlorite appears as effective as chlorhexidine against plaque but the acidic nature of the rinse may obviate oral hygiene products ever coming to the marketplace.
* Combinations of agents sometimes provide additive or synergistic action, but with the exception of triclosan, few products are available.
# Chlorhexidine
Chlorhexidine is available in three forms, the digluconate, acetate, and hydrochloride salts. Most studies and most oral formulations and products have used the digluconate salt, which is manufactured as a 20% V/V concentrate. Digluconate and acetate salts are water soluble but hydrochloride is very sparingly soluble in water. Chlorhexidine was developed in the 1940s by Imperial Chemical Industries, England, and marketed in 1954 as an antiseptic for skin wounds. Later, the antiseptic was more widely used in medicine and surgery including obstetrics, gynecology, urology, and presurgical skin preparation for both patient and surgeon. Use in dentistry was initially for presurgical disinfection of the mouth and in endodontics. The first definitive study on chlorhexidine was performed by Löe and Schiott (1970). This study showed that rinsing for 60 seconds twice per day with 10 ml of a 0.2% (20 mg dose) chlorhexidine gluconate solution in the absence of normal tooth cleaning, inhibited plaque regrowth and the development of gingivitis. Numerous studies followed, such that chlorhexidine is one of the most investigated compounds in dentistry (for reviews see Jones 1997; Eley 1998). Chlorhexidine is a bisbiguanide antiseptic, being a symmetrical molecule consisting of four chlorophenyl rings and two biguanide groups connected by a central hexamethylene bridge (Fig. 36-2). The compound is a strong base and dicationic at pH levels above 3.5, with two positive charges on either side of a hexamethylene bridge. Indeed, it is the dicationic nature of chlorhexidine, making it extremely interactive with anions, which is relevant to its efficacy, safety, local side effects, and difficulties with formulation in products.
## Toxicology, safety, and side effects
The cationic nature of chlorhexidine minimizes absorption through the skin and mucosa, including from the gastrointestinal tract. Systemic toxicity from topical application or ingestion is therefore not reported, nor is there evidence of teratogenicity in the animal model. Even in intravenous infusion in animals, chlorhexidine is well tolerated and this has occurred accidentally in humans without serious consequences. Hypersensitivity reactions including anaphylaxis have been reported in fewer than 10 people in Japan and resulted from the application of non-proprietary chlorhexidine products to sites other than the mouth. There was insufficient information to confirm that the reactions were actually due to chlorhexidine. Neurosensory deafness can occur if chlorhexidine is introduced into the middle ear and the antiseptic should not be placed in the outer ear in case the eardrum is perforated. The antiseptic has a broad antimicrobial action, including a wide range of Gram-positive and Gram-negative bacteria (Wade & Addy 1989). It is also effective against some fungi and yeasts including _Candida_ , and some viruses including HBV and HIV. Bacterial resistance has not been reported with long-term, oral use or evidence of super-infection by fungi, yeasts or viruses. Long-term oral use resulted in a small shift in the flora towards the less sensitive organisms but this was rapidly reversible at the end of the 2-year study (Schiott _et al_. 1976).
In oral use as a mouth rinse, chlorhexidine has been reported to have a number of local side effects (Flotra _et al_. 1971). These side effects are:
1. Brown discoloration of the teeth and some restorative materials and the dorsum of the tongue (Figs. 36-3 and Figs. 36-4).
2. Taste perturbation where the salt taste appears to be preferentially affected (Lang _et al_. 1988) to leave food and drinks with a rather bland taste.
3. Oral mucosal erosion (Fig. 36-5). This appears to be an idiosyncratic reaction and concentration dependent. Dilution of the 0.2% formulation to 0.1%, but rinsing with the whole volume to maintain dose, usually alleviates the problem. Erosions are rarely seen with 0.12% rinse products used at 15 ml volume.
4. Unilateral or bilateral parotid swelling (Fig. 36-6). This is an extremely rare occurrence and an explanation is not available.
5. Enhanced supragingival calculus formation. This effect may be due to the precipitation of salivary proteins on to the tooth surface, thereby increasing pellicle thickness and/or precipitation of inorganic salts on to or into the pellicle layer.
**Fig. 36-3** Brown discoloration of the teeth of an individual rinsing twice a day for 3 weeks with a 0.2% chlorhexidine mouth rinse.
**Fig. 36-4** Brown discoloration of the tongue of an individual rinsing twice a day for 2 weeks with a 0.2% chlorhexidine mouth rinse.
**Fig. 36-5** Mucosal erosion occurring following a few days of rinsing twice a day with a 0.2% chlorhexidine mouth rinse.
**Fig. 36-6** Bilateral parotid swelling following a few days of rinsing with a 0.2% chlorhexidine mouth rinse.
Chlorhexidine also has a bitter taste, which is difficult to mask completely.
## Chlorhexidine staining
The mechanisms proposed for chlorhexidine staining can be debated (Eriksen _et al_. 1985; for reviews see Addy & Moran 1995; Watts & Addy 2001) but have been proposed as:
1. Degradation of the chlorhexidine molecule to release parachloraniline
2. Catalysis of Maillard reactions
3. Protein denaturation with metal sulfide formation
4. Precipitation of anionic dietary chromogens.
Degradation of chlorhexidine to release parachloraniline appears not to occur on storage or as a result of metabolic processes. Also, alexidine, a related bisbiguanide, does not have parachloraniline groups, yet causes staining identical to that of chlorhexidine. Non-enzymatic browning reactions (Maillard reactions) catalyzed by chlorhexidine are a theoretical possibility; however, evidence is indirect, circumstantial or inconclusive (Eriksen _et al_. 1985). The theory does not consider the fact that other antiseptics and metals such as tin, iron, and copper also produce dental staining. Protein denaturation produced by chlorhexidine with the interaction of exposed sulfide radicals with metal ions is also theo-retically possible but there is no direct evidence to support this concept. Again, the theory does not take into account similar staining by other antiseptics and metal ions. Laboratory and clinical studies also could not reproduce this process (for reviews see Addy & Moran 1985; Watts & Addy 2001). Precipitation of anionic dietary chromogens by cationic antiseptics, including chlorhexidine and polyvalent metal ions as an explanation for the phenomenon of staining by these substances, is supported by a number of well controlled laboratory and clinical studies (for reviews see Addy & Moran 1995; Watts & Addy 2001). Thus, the locally bound antiseptics or metal ions on mucosa or teeth can react with polyphenols in dietary substances to produce staining. Beverages such as tea, coffee, and red wine are particularly chromogenic, but other foods and beverages will interact to produce various colored stains. These reactions between chlorhexidine and other cationic antiseptics and polyvalent metal ions with chromogenic beverages can be performed within the test tube. Interestingly, most of the precipitates formed between polyvalent metal ions and chromogens have the same color as their sulfide salts. It is for this reason that original theories considered that staining, seen in individuals exposed to these polyvalent metal ions, usually in the workplace, was due to metal sulfide formation. Again, laboratory and clinical experiments have failed to produce such interactions.
It is perhaps the staining side effect that limits long-term use of chlorhexidine in preventive dentistry (Flotra _et al_. 1971) and occurs with all correctly formulated products including gels, toothpastes, and sprays. Indeed, the staining side effect can be used to assess patient compliance in the use and activity of formulations. In the latter case laboratory and clinical studies on staining have revealed a proprietary chlorhexidine mouth rinse product to be inactive (Renton-Harper _et al_. 1995). Interestingly, this particular chlorhexidine product was reformulated in the UK to produce an active formulation (Addy _et al_. 1991), but the manufacturers maintained the original formulation within France when both laboratory and clinical studies confirmed markedly reduced potential of the product to cause staining in the laboratory, and plaque inhibition in the clinic (Renton-Harper _et al_. 1995). Recently, a chlorhexidine product with an anti-discoloration system (ADS) was launched in Europe. A clinical study purporting to show reduced staining had significant drawbacks in design and presentation (Bernadi _et al_. 2004). A laboratory study found no difference in staining potential (Addy _et al_. 2005) and a plaque regrowth study showed significantly reduced plaque inhibition for the ADS rinse (Arweiler _et al_. 2006). The old adage concerning chlorhexidine products appears to still hold true: "If it does not stain it does not work".
## Mechanism of action
(For reviews see Addy 1986; Jenkins _et al_. 1988)
Chlorhexidine is a potent antibacterial substance but this alone does not explain its antiplaque action. The antiseptic binds strongly to bacterial cell membranes. At low concentration this results in increased permeability with leakage of intracellular components including potassium. At high concentration, chlorhexidine causes precipitation of bacterial cytoplasm and cell death. In the mouth chlorhexidine readily adsorbs to surfaces including pellicle-coated teeth. Once adsorbed, and unlike some other antiseptics, chlorhexidine shows a persistent bacteriostatic action lasting in excess of 12 hours (Schiott _et al_. 1970). Radio-labelled chlorhexidine studies suggest a slow release of the antiseptic from surfaces (Bonesvoll _et al_. 1974a,b) and this was suggested to produce a prolonged antibacterial milieu in the mouth (Gjermo _et al_. 1974). The methods used, however, could not determine the activity of the chlorhexidine, which was almost certainly attached to the salivary proteins and desquamating epithelial cells and therefore unavailable for action. Consistent with the original work and conclusions (Davies _et al_. 1970), a more recent study and review suggested that plaque inhibition is derived only from the chlorhexidine adsorbed to the tooth surface (Jenkins _et al_. 1988). It is possible that the molecule attaches to pellicle by one cation leaving the other free to interact with bacteria attempting to colonize the tooth surface. This mechanism would, therefore, be similar to that associated with tooth staining. It would also explain why anionic substances, such as sodium lauryl sulfate based toothpastes, reduce the plaque inhibition of chlorhexidine if used shortly after rinses with the antiseptic (Barkvoll _et al_. 1989). Indeed, a more recent study has demonstrated that plaque inhibition by chlorhexidine mouth rinses is reduced if toothpaste is used immediately before or immediately after the rinse (Owens _et al_. 1997b). These inhibitory effects on chlorhexidine activity by substances such as toothpastes can be modeled using the chlorhexidine tea staining method, which shows reduced staining activity by the chlorhexidine solutions resulting from an interaction with toothpaste (Sheen _et al_. 2001).
Plaque inhibition by chlorhexidine mouth rinses appears to be dose related (Jenkins _et al_. 1994) such that similar effects to that seen with the more usual 10 ml, 0.2% solution (20 mg) can be achieved with high volumes of low-concentration solutions (Lang & Ramseier-Grossman 1981). It is worth noting, however, that not inconsiderable plaque inhibition is obtained with doses as low as 1–5 mg twice daily (Jenkins _et al_. 1994). Also, and relevant to the probable mechanism of action, topically applying 0.2% solutions of chlorhexidine only to the tooth surface, including by the use of sprays, produces the same level of plaque inhibition as rinsing with the full 20 mg dose (Addy & Moran 1983; Francis _et al_. 1987a; Jenkins _et al_. 1988; Kalaga _et al_. 1989a).
## Chlorhexidine products
Chlorhexidine has been formulated into a number of products.
### Mouth rinses
Aqueous alcohol solutions of 0.2% chlorhexidine were first made available for mouth rinse products for twice daily use in Europe in the 1970s. A 0.1% mouth rinse product also became available; however questions were raised over the activity of the 0.1% product and in some countries the efficacy of this product is less than would be expected from a 0.1% solution (Jenkins _et al_. 1989). Later, in the US, a 0.12% mouth rinse was manufactured but to maintain the almost optimum 20 mg doses derived from 10 ml of 0.2% rinses, the product was recommended as a 15 ml rinse (18 mg dose). The studies revealed equal efficacy for 0.2% and 0.12% rinses when used at appropriate similar doses (Segreto _et al_. 1986). More recently alcohol-free chlorhexidine rinses have become available, some formulated with the inclusion of 0.05% CPC. Such formulations have been shown to possess equivalent effects at inhibiting plaque and gingivitis compared to alcohol-containing chlorhexidine rinses but with better taste acceptability with the non-alcoholic rinse (Quirynen _et al_. 2001; Van Strydonck _et al_. 2005)
### Gel
A 1% chlorhexidine gel product is available and can be delivered on a toothbrush or in trays. The distribution of the gel by toothbrush around the mouth appears to be poor and preparations must be delivered to all tooth surfaces to be effective (Saxen _et al_. 1976).
In trays the chlorhexidine gel was found to be particularly effective against plaque and gingivitis in handicapped individuals (Francis _et al_. 1987a). The acceptability of this tray delivery system to the recipients and the carers was found to be poor (Francis _et al_. 1987b). More recently, 0.2% and 0.12% chlorhexidine gels have become available.
### Sprays
Sprays containing 0.1% and 0.2% chlorhexidine are commercially available in some countries. Studies with the 0.2% spray have revealed that small doses of approximately 1–2 mg delivered to all tooth surfaces produces similar plaque inhibition to a rinse with 0.2% mouth rinses (Kalaga _et al_. 1989a). Sprays appear particularly useful for the physically and mentally handicapped groups, being well received by individuals and their carers (Francis _et al_. 1987a,b; Kalaga _et al_. 1989b).
### Toothpaste
(For review see Yates _et al_. 1993)
Chlorhexidine is difficult to formulate into toothpaste for reasons already given and early studies produced variable outcomes for benefits to plaque and gingivitis. More recently, a 1% chlorhexidine toothpaste with and without fluoride was found to be superior to the control product for the prevention of plaque and gingivitis in a 6-month home use study (Yates _et al_. 1993). Stain scores however, were markedly increased as was supragingival calculus formation, and the manufacturer did not produce a commercial product. For a short time a commercial product was available, having been shown to be efficacious for both plaque and gingivitis (Sanz _et al_. 1994). Although effective, chlorhexidine products based on toothpaste and sprays produce similar tooth staining to mouth rinses and gels; taste disturbance, mucosal erosion, and parotid swellings tend to be less or have never been reported.
### Varnishes
Chlorhexidine varnishes have been used mainly for prophylaxis against root caries rather than an antiplaque depot for chlorhexidine in the mouth.
### Slow-release vehicles
A chlorhexidine chip has been produced commercially for placement into periodontal pockets as an adjunct to scaling and root planning. This will be discussed in Chapter 42.
### Conclusions
* Chlorhexidine to date is the proven most effective antiplaque agent, for which commercial products are available to the public.
* Chlorhexidine is free from systemic toxicity in oral use, and microbial resistance and super-infection do not occur.
* Local side effects are reported which are mainly cosmetic problems.
* The antiplaque action of chlorhexidine appears dependent on prolonged persistence of antimicrobial action in the mouth (substantivity).
* A number of vehicles for delivering chlorhexidine are available, but mouth rinses are most commonly recommended.
* Extrinsic dental staining and perturbation of taste are variably the two side effects of chlorhexidine mouth rinse usage, which limit acceptability to users and the long-term employment of this antiseptic in preventive dentistry.
## Clinical uses of chlorhexidine
Despite the excellent plaque inhibitory properties of chlorhexidine, widespread and prolonged use of the agent is limited by local side effects. Moreover, because of the cationic nature of the chlorhexidine and therefore its poor penetrability, the antiseptic is of limited value in the therapy of established oral conditions including gingivitis, and is much more valuable in the preventive mode. A number of clinical uses, some well researched, have been re commended for chlorhexidine (for reviews see Gjermo 1974; Addy 1986; Addy & Renton-Harper 1996; Addy & Moran 1997; Eley 1999).
### As an adjunct to oral hygiene and professional prophylaxis
Oral hygiene instruction is a key factor in the treatment plan for patients with periodontal disease and as part of the maintenance program following treatment. Adequate plaque control by periodontal patients is therefore essential to successful treatment and the prevention of recurrence of the disease. Chlorhexidine should therefore increase the improvement in gingival health through plaque control, particularly following professional prophylaxis to remove existing supra- and immediately subgingival plaque. There is, however, a potential disadvantage of using such an effective chemical plaque-control agent at this stage of the periodontal treatment plan. Thus, following oral hygiene instruction, it is normal, usually by the use of indices, to quantify the improvement in plaque control by patients so instructed and, in particular, the improvement at specific sites, which previously had been missed by individual patients. By virtue of the excellent plaque-control effects of chlorhexidine, the response to oral hygiene instruction cannot be accurately assessed since the antiseptic will overshadow any deficiencies in mechanical cleaning. Indeed, as the original research demonstrated, with chlorhexidine mouth rinse patients could maintain close to zero levels of plaque following a professional prophylaxis without using any form of mechanical oral hygiene (Löe & Schiott 1970). Nevertheless, chlorhexidine mouth rinse may be of value in maintaining oral hygiene following scaling and root planing when adequate tooth brushing may be compromised by post-treatment soreness or sensitivity.
### Post oral surgery including periodontal surgery or root planing
Chlorhexidine may be used post-operatively since it offers the advantage of reducing the bacterial load in the oral cavity and preventing plaque formation at a time when mechanical cleaning may be difficult because of discomfort. In periodontal surgery, periodontal dressings have largely been replaced by the use of chlorhexidine preparations, in particular mouth rinses, since healing is improved and discomfort reduced (Newman & Addy 1978, 1982). Regimens vary but chlorhexidine should be used immediately post treatment and for periods of time until the patient can re-institute normal oral hygiene. Depending on the appointment schedule, chlorhexidine could be used throughout the treatment phase and for periods of weeks after completion of the treatment plan. If dressings are used, chlorhexidine is of limited value to the post-operative site since it does not penetrate beneath the periodontal dressings (Pluss _et al_. 1975). Although chlorhexidine rinses are probably used after root planing by many clinicians, evidence of therapeutic benefit has only recently been published (Faveri _et al_. 2006).
The idea of full-mouth disinfection using chlorhexidine both supra- and subgingivally as an adjunct to scaling and root planing has been assessed by one group in a number of papers since 1995 (for review see Quirynen _et al_. 2006). In the event, few adjunctive benefits could be shown (for review see Apatzidou 2006). It appeared that the more dominant factor was the time over which the non-surgical treatment plan was completed. Thus, root planing performed totally within 24 hours was more effective than root planing completed over more conventional periods of several weeks (Quirynen _et al_. 2006). Similar clinical research however, showed no difference between root planing completed within 24 hours compared to within several weeks (Apatzidou & Kinane 2004).
### For patients with jaw fixation
Oral hygiene is particularly difficult when jaws are immobilized by such methods as intermaxillary fixation. Chlorhexidine mouth rinses have been shown markedly to reduce the bacterial load, which tends to increase during jaw immobilization, and to improve plaque control (Nash & Addy 1979). The more recent trend to use sub-dermal or sub-mucosal plates to stabilize bony fragments probably impedes oral hygiene procedures to a lesser degree, providing there are no oral mucosal lacerations. The influence of these factors on oral hygiene and therefore the role of chlorhexidine formulation has never been investigated.
### For oral hygiene and gingival health benefits in the mentally and physically handicapped
Chlorhexidine has been found particularly useful in institutionalized mentally and physically handicapped groups, improving both oral hygiene and gingival health (Storhaug 1977). Spray delivery of 0.2% solutions was found particularly useful and acceptable to patients and care workers (Francis _et al_. 1987a,b; Kalaga _et al_. 1989b).
### Medically compromised individuals predisposed to oral infections
A number of medical conditions predispose individuals to oral infections, notably candidiasis. Chlorhexidine is effective as an anticandidal agent but is most useful when combined with specific anticandidal drugs, such as nystatin or amphotericin B (Simonetti _et al_. 1988). Indications for chlorhexidine use combined with anticandidal drugs have been for the prevention of oral and systemic infections in the immunocompromised, including those with blood dyscrasias, those receiving chemotherapy and/or radiotherapy, and notably bone marrow transplant patients (Ferretti _et al_. 1987, 1988; Toth _et al_. 1990). The value of chlorhexidine appears greatest when initiated before oral or systemic complications arise. A chlorhexidine spray was also found to produce symptomatic/psychologic oral care benefits in the terminally ill (Jobbins _et al_. 1992).
### High-risk caries patients
Chlorhexidine rinses or gels can reduce considerably the _Streptococcus mutans_ counts in individuals who are caries prone. Additionally, and interestingly, chlorhexidine appears synergistic with sodium fluoride and combining chlorhexidine and fluoride rinses appears beneficial to such at-risk individuals (Dolles & Gjermo 1980). Sodium monofluorophosphate on the other hand, reduces the effect of chlorhexidine and probably _vice versa_ (Barkvoll _et al_. 1988). A chlorhexidine rinse product with sodium fluoride has recently become available.
### Recurrent oral ulceration
Several studies have shown that chlorhexidine mouth rinses and chlorhexidine gels reduce the incidence, duration, and severity of recurrent minor aphthous ulceration (for review see Hunter & Addy 1987). The mechanism of action is unclear but may relate to a reduction in contamination of ulcers by oral bacteria, thereby reducing the natural history of the ulceration. Regimens have included three times daily use of chlorhexidine products for several weeks. Interestingly, one study showed that triclosan rinses reduce the incidence of recurrent mouth ulcers (Skaare _et al_. 1996). There have been no controlled studies of chlorhexidine in the management of major aphthous ulceration or other oral erosive or ulcerative conditions, although anecdotally chlorhexidine appears ineffective. Again, this may reflect the low therapeutic potential of this and other antiseptics, and the considerable amount of proteinacious material associated with these lesions which would both tend to inactivate chlorhexidine and block access to underlying microorganisms (Roberts & Addy 1981). A similar explanation may be propounded for the failure of chlorhexidine mouth rinses in treatment of acute necrotizing ulcerative gingivitis (periodontitis) (Addy & Llewelyn 1978) : further evidence for the lack of absorption into tissues and biofilms of this cationic antiseptic.
### Removable and fixed orthodontic appliance wearers
Plaque control in the early stages of orthodontic appliance therapy may be compromised and chlorhexidine can be prescribed for the first 4–8 weeks. Additionally, chlorhexidine has been shown to reduce the number and severity of traumatic ulcers during the first 4 weeks of fixed orthodontic therapy (Shaw _et al_. 1984).
### Denture stomatitis
Chlorhexidine has been recommended in the treatment of _Candida_ -associated infections; however, in practice even applying chlorhexidine gel to the fitting surfaces of dentures produces, in many cases, slow and incomplete resolution of the condition. Again, chlorhexidine is less effective in the therapeutic mode and it is more advantageous to treat denture stomatitis with specific anticandidal drugs and then employ chlorhexidine to prevent recurrence. The denture itself can be usefully sterilized from _Candida_ by soaking in chlorhexidine solutions (Olsen 1975).
### Oral malodor
Rinsing with chlorhexidine as with other antiseptic mouth rinses containing CPC, triclosan, and essential oils, has been suggested to be of value in reducing halitosis. Reductions in volatile sulphur compounds and morning malodor have been noted with all these chemicals (Carvalho _et al_. 2004).
### Immediate preoperative chlorhexidine rinsing and irrigation
This technique can be used immediately prior to operative treatment, particularly when air polishing, ultrasonic scaling or high-speed instruments are to be used. Such pre-operative rinsing markedly reduces the bacterial load and contamination of the operative area, operator, and staff (Worral _et al_. 1987). Additionally, in susceptible patients, irrigation of chlorhexidine around the gingival margin reduces the incidence of bacteremia (MacFarlane _et al_. 1984). This should be seen, however, only as an adjunct to appropriate systemic antimicrobial prophylaxis. Chlorhexidine mouth rinsing now features as an adjunct to antibiotic prophylaxis in the new UK guidelines.
### Subgingival irrigation
Numerous antimicrobial agents have been used as subgingival irrigants in the management and treatment of periodontal diseases (for reviews see Wennstrom 1992, 1997). Alone, irrigation with antimicrobial agents produces effects little different from using saline, and they are of short duration, suggesting that the action is a washing-out effect. Irrigation combined with root planing appears to provide no adjunctive benefits.
### Conclusions
* There is a significant number of indications for the use of chlorhexidine in preventive dentistry, most of which rely on the antimicrobial properties of the antiseptic and its duration of action.
* The most valuable chemical plaque-control uses of chlorhexidine are in the short to medium term when mechanical tooth cleaning is not possible, difficult or inadequate and during which time local side effects are likely to be minimized.
* Chlorhexidine is more effective as a preventive rather than a therapeutic agent and therefore must be of questionable value as a subgingival adjunct in the treatment of periodontitis (see Chapter 42).
# Evaluation of chemical agents and products
(For reviews see Addy _et al_. 1992; Addy 1995; Moss _et al_. 1995; Addy & Moran 1997)
The number and use of oral hygiene products has grown enormously in recent years and, as an example, hundreds of millions of pounds per year are spent on oral hygiene products in the UK and presumably billions worldwide. There can be no doubt that the oral hygiene industries, through their collaboration and research with the dental profession and their promotion of their products have, in no small way, contributed to the improvement in dental health seen in many countries. Claims for efficacy of oral hygiene products, however, are frequently made and it is essential that these are supported by scientific evidence. Without such evidence the profession and the public may be confused or misled. The dental profession is, however, faced with a large number of oral hygiene products supported by huge quantities of varied promotional literature and media advertising, which makes impossible, in many cases, any valid judgment or assessment of the efficacy or value of individual products to specific patient groups or the public as a whole. Even those with specialized interest, and research experience in specific aspects of oral hygiene product evaluation, must find validation, based on published literature, a daunting task. This is made all the more difficult since what constitutes proof of efficacy is not generally agreed even amongst so-called experts. Few countries of the world have central control over what evidence is required before efficacy claims can be made and there are very few guidelines suggesting requirements for proof of efficacy for oral hygiene products.
The scientific evaluation of dental products, and for that matter, preventive and therapeutic agents in medicine as a whole, is a relatively modern concept but today must be the backbone on which to base claims of efficacy. Anecdotal and case reports, uncontrolled studies and data listed as "held on file" by manufacturers, whilst interesting, should not be used as the basis for efficacy claims. Blind, randomized, controlled clinical and laboratory studies must be the methods used today to obtain data on the activity of agents, formulations, and products. Terminology and phraseology in product claims also needs to be carefully reviewed and assessed. Perhaps the greatest area for criticism must be the implied claim by the manufacturer and/or the inferences left to be drawn, from promotional material, by the dental profession or public. A classic scenario for which there is precedence can be stated as follows: A is the cause of B, C reduces A, leaving the inference to be drawn that C can control B. Perhaps nowhere is this more apparent than in the use of agents which are known to control plaque, and therefore it can be implied, without evidence, they must control gingivitis. The now familiar claim would be "this product reduces plaque, the major cause of gum disease". Similarly, creative arithmetic is not infrequently used to give inflated impressions of efficacy. Proportional differences, rather than actual differences, are not infrequently quoted, as are percentages of percentages giving hundreds of percent improvements over another product or control, yet the actual benefit is a fraction of the scoring index used. Finally, "piggy back" claims are not uncommon, when a known active ingredient is formulated into a new product and equivalent efficacy to established products is assumed. It would seem reasonable here to repeat the definitions for the terminology for oral hygiene products, agreed at the European Workshop on Periodontology in 1996 which defined certain terms (Lang & Newman 1997) :
* _Antimicrobial agents_ : chemicals that have a bacteriostatic or bactericidal effect _in vitro_ that alone cannot be extrapolated to a proven efficacy _in vivo_ against plaque.
* _Plaque reducing/inhibitory agents_ : chemicals that have only been shown to reduce the quantity and/or affect quality of plaque, which may or may not be sufficient to influence gingivitis and/or caries.
* _Antiplaque agents_ : chemicals that have an effect on plaque sufficient to benefit gingivitis and/or caries.
* _Antigingivitis agents_ : chemicals which reduce gingival inflammation without necessarily influencing bacterial plaque (includes antiinflammatory agents).
Thus, the fact that antimicrobial agents such as antiseptics kill or inhibit the growth of bacteria does not necessarily mean they will be effective plaque inhibitors (Gjermo _et al_. 1970). Also, the mere incorporation of a known antiplaque agent into a formulation is not a guarantee of efficacy because inactivation by other ingredients may occur.
This section looks at methods that have been used to test oral hygiene products both in the laboratory and the clinic. No one protocol can provide all the answers, and research and development of agents into products is a step-by-step process, hopefully culminating in a body of evidence proving efficacy, beyond doubt, of a final product. Methods _in vitro_ and _in vivo_ will be summarized but animal testing will not be discussed except to acknowledge that the use of animals is still necessary in drug development, in understanding the mode of action of drugs and, particularly, in evaluating safety from a toxicologic point of view. The evaluation of oral hygiene products on animals, however, particularly for efficacy, must be questioned on a number of scientific and moral grounds.
Most laboratory and clinical methods have been developed to test antimicrobial agents but methodologies are available, or present ones could be modified, to study potential antiadhesive and plaque removal chemicals (for reviews see Addy _et al_. 1992; Addy 1995; Addy & Moran 1997).
## Studies _in vitro_
### Bacterial tests
Antimicrobial tests, including minimum inhibitory concentration (MIC), minimum bactericidal concentration (MBC), and kill curves, can be determined. These tests indicate the antibacterial activity and antimicrobial spectrum of agents and formulations against a range of oral bacteria. Continuous culture techniques can also be used but they may not provide more meaningful data. It is likely that, with technologic advances, laboratory models to accurately replicate the plaque biofilm will become available to test chemical plaque-control agents. At present, antimicrobial tests _in vitro_ primarily only indicate activity, or lack of it, and they are very poor predictors _per se_ of effects on plaque _in vivo_. This is because, so far, methods do not provide particularly reliable information on the substantivity of the antimicrobial agent. Nevertheless, antimicrobial tests are valuable for a variety of reasons. With few exceptions, agents without activity _in vitro_ will not provide activity _in vivo_. The additive or negative effects of ingredient mixtures can be determined. The availability of active ingredients incorporated in the product can be assessed. The adverse influence of the oral environment can be modeled; for example, the influence of saliva or proteins on the antibacterial activity of agents can be tested.
### Uptake measurements
One aspect of substantivity is adsorption of antimicrobials and other potential plaque-inhibitory agents on to surfaces. This can be quantified using a variety of substrates such as hydroxyapatite, dentine, enamel, acrylic, and other polymers. The influence of other factors or agents on the uptake of a particular agent can also be assessed. Such data are of interest but must be interpreted with caution since they only measure uptake, not activity once adsorbed. Nevertheless, desorption of an agent from such surfaces can be measured by a variety of analytical techniques, thereby giving some indication of both the adsorption profile and the subsequent substantivity of the agent to the substrate surface.
### Other methods
Activity or availability of an ingredient in a formulation can be measured or assessed. Methods include chemical analyses; however, some methods chemically extract the agent from the formulation in its entirety and therefore do not necessarily demonstrate that it is freely available and active within the formulation. For the cationic antiseptics and polyvalent metal salts, their potential to bind dietary chromogens from beverages such as tea can be used to assess the possibility that they may cause staining _in vivo_. More usefully, the test method can be employed to determine and compare the availability of the same ingredient in different formulations. Such methods have shown considerable differences in availability of chlorhexidine and cetylpyridinium chloride in apparently similar mouth rinses (Addy _et al_. 1995). Moreover, how other oral hygiene products might interfere with the activity of chemical plaque-control agents, such as toothpaste with chlorhexidine and cetylpyridinium chloride, has given surprisingly accurate predictions of clinical outcome (Owens _et al_. 1997b; Sheen _et al_. 2001, 2003). Again, these methods give little indication of substantivity and therefore the staining method _in vitro_ cannot be used to compare different agents for propensities to cause staining _in vivo_. For example, a 0.05% cetylpyridinium chloride mouth rinse produces comparable tea staining on a substrate surface to a 0.2% chlorhexidine mouth rinse, yet clinically the amount of staining reported for chlorhexidine is considerably greater than that for cetylpyridinium chloride and this can be explained by the fact that the substantivity of the former is greater than that of the latter.
## Study methods _in vivo_
A considerable number of protocols have been developed to evaluate potential antiplaque agents and products. Ideally, because of the number of ingredients and more particularly formulations, a step-by-step pyramid approach is taken. Thus initially, study designs are used which permit, if necessary, the screening of relatively large numbers of agents and formulations and on relatively small numbers of subjects.
### Depot studies
Retention of agents in the mouth may be measured by determining the amount expectorated versus the known dose (the buccal retention test) or by measuring plaque and saliva levels of the agent over time. Such retention assessments can be misleading because retention is only one aspect of substantivity and the measurement techniques do not provide information on the activity of the retained agents. Moreover, the buccal retention test does not distinguish drug absorption from adsorption nor determine how much is swallowed. Thus, for example, studies using radiolabeled chlorhexidine purported to demonstrate slow release from oral surfaces and this occurred over a protracted period of time (Bonesvoll _et al_. 1974a,b). However, saliva derived from subjects following rinsing with chlorhexidine only provided antimicrobial activity for up to 3 hours following rinsing (Addy & Wright 1978). This is clearly markedly less than the known substantivity or persistence of action of chlorhexidine in the mouth of at least 12 hours (Schiott _et al_. 1970). It is likely, therefore, that the initial desorption studies using a radiolabel were merely detecting chlorhexidine adsorbed to desquamating oral surfaces, particularly the mucosa.
### Antimicrobial tests
For antimicrobial agents only, salivary bacterial count assessments are much more indicative of substantivity and are predictive of antiplaque action for the same agents. The method involves measuring salivary bacterial counts before, and at time points, after a single rinse with the agent (Fig. 36-7) and was first described for chlorhexidine (Schiott _et al_. 1970). In the case of toothpaste, the product can be either brushed or rinsed as an aqueous slurry (Addy _et al_. 1983; Jenkins _et al_. 1990). Agents and products produce variable reductions in counts ranging from none, as with water, to greater than 90%, as with chlorhexidine. More importantly, the duration of reduction from baseline varies from minutes to hours. Thus, povidone iodine only reduces counts for approximately 1 hour, cetylpyridinium chloride for 3 hours (Roberts & Addy 1981), whereas chlorhexidine produces such effects for over 12 hours (Schiott _et al_. 1970). Toothpastes generally show reductions in counts between 3 and 5 hours, probably largely due to contained detergents and/or specific ingredients such as triclosan (Addy _et al_. 1989).
**Fig. 36-7** Salivary bacterial counts over time following mouth rinsing with chlorhexidine, saline, sodium lauryl sulfate, and triclosan. Following a single rinse with chlorhexidine, sodium lauryl sulfate, and triclosan there is an immediate large reduction in bacterial counts. This continues and persists to the 420-minute endpoint of the study for chlorhexidine (positive control) with a tendency for counts to revert towards baseline for triclosan and sodium lauryl sulfate. With saline (placebo control), there is little change in counts over time.
### Experimental plaque studies
Short-term plaque regrowth studies are perhaps the most commonly used clinical experiments to screen chemical oral hygiene products. They have the advantage of assessing the chemical action of the formulation divorced from the indeterminate variable of toothbrushing. Typically, plaque regrowth from a zero baseline and the influence of the test agent is recorded. Originally used for mouth rinses, the method has been modified for toothpaste by delivering the formulation in a tray applied to the teeth (Etemadzadeh _et al_. 1985) or as a slurry rinse (Addy _et al_. 1983). Studies are usually cross-over, allowing many formulations to be evaluated against suitable controls. Study periods range from 24 hours to several days, usually 4–5 days (Harrap 1974; Addy _et al_. 1983). A negative control such as water and a positive control such as chlorhexidine may be used (Fig. 36-8). These help to position the activity of the test formulations between the extremes. Also, because the results from these controls can be predicted, their use tends to confirm or otherwise the conduct of these blind, randomized study designs.
### Experimental gingivitis studies
Experimental gingivitis studies (Löe & Schiott 1970) are based on the original experimental gingivitis in man protocol first used to demonstrate the direct etiologic relationship between plaque and gingivitis (Löe _et al_. 1965). This latter original study did not return subjects to zero baseline plaque scores or gingival health, whereas most subsequent methods, to evaluate oral hygiene products, have taken this approach with baseline parameters. Study periods usually range from 12, but more particularly 19–28 days. In the absence of normal tooth cleaning, the development of plaque and gingivitis are recorded under the influence of test and control formulations. Studies may be either cross-over or parallel.
**Fig. 36-8** Plaque area following the use of chlorhexidine, saline, sodium lauryl sulfate, and triclosan mouth rinses after 4-day periods. Considerable plaque inhibition was afforded by chlorhexidine (positive control) when toothcleaning was suspended. Both sodium lauryl sulfate and triclosan show significant plaque-inhibitory action compared to saline (placebo control) albeit significantly less than chlorhexidine.
### Home use studies
For chemical oral hygiene products and usually toothpastes and mouth rinses, the final evaluation requires that they are shown to be effective against plaque and, more particularly, gingivitis, when used along with normal mechanical tooth cleaning. Studies can be over days or weeks but usually, in accordance with guidelines such as those for the American Dental Association (Council of Dental Therapeutics 1985), they need to be 6 months or longer, particularly since safety needs to be assessed (Fig. 36-9). Most studies are parallel in design. Protocols have used two approaches. One is perhaps more therapeutic in concept whereby subjects have to exhibit a certain level of plaque and/or gingivitis before entry (Johansen _et al_. 1975). The other is more preventive in concept and there is a pre-study period in which subjects with gingivitis receive prophylaxis and instruction to improve their gingival health. Those satisfactorily responding are entered, and change in gingival health is monitored in the test and control groups (Stephen _et al_. 1990).
Several factors tend to confound home use studies of oral hygiene products and may mask a proven chemical antiplaque action determined from short-term plaque and experimental gingivitis studies. Most important is the so-called Hawthorne effect where subjects knowingly involved in oral hygiene studies improve their tooth cleaning (Fig. 36-9). Secondly, baseline prophylaxes are commonly given and the influence of this on the subsequent gingivitis levels is not known. In mouth rinse studies used as adjuncts to tooth cleaning, there is the potential of interaction between toothpaste and mouth rinse, which could be additive but in most cases is more likely negative for effects on mouth rinse ingredients (Owens _et al_. 1997b; Sheen _et al_. 2001, 2003). Compliance in home use studies can also be a problem and difficult to determine accurately. In short-term studies compliance can be guaranteed through supervision but this is difficult in home use studies although was achieved, in part, in a series of delmopinol studies (for review see Addy _et al_. 2007). Finally, particularly in toothpaste studies, the control product will have some inherent plaque-inhibitory action consequent upon ingredients such as detergents (Addy _et al_. 1983). If the appropriate control products have been used in the screening plaque inhibitory and experimental gingivitis models this should not pose a problem. However, there is no doubt, and this will be discussed, that the choice of control toothpaste, used to compare an active toothpaste, could considerably influence the outcome and therefore the conclusions concerning a potential antiplaque toothpaste.
**Fig. 36-9** A 6-month study of delmopinol rinses as adjuncts to oral hygiene. Significant improvements in plaque scores are seen in the delmopinol mouth rinse groups at 3 and 6 months compared to placebo. A Hawthorne effect of improved toothcleaning irrespective of the treatment is apparent in the placebo group, particularly at 3 months, although this is still present at 6 months.
## Clinical trial design considerations
Clinical trials involving human patients, subjects or healthy volunteers in many countries must now conform to the Guidelines for Good Clinical Practice (ICH 1996) including the Declaration of Helsinki (World Medical Association 1996). The Declaration of Helsinki was introduced primarily to protect the well-being of the participants. The Guidelines for Good Clinical Practice are broadly concerned with all aspects of a clinical trial and, in particular, the ethical requirements, the design and conduct of the trial, data collection and record keeping, data analysis, and reporting of the findings. As a result, the Guidelines not only also protect the interests of the participants but of those organizing, supporting, and conducting the trials. An important additional purpose of the Guidelines is to limit the possibility of falsification of data. Requirements of ethical committees will vary locally, nationally, and internationally; however, common to all is a need for a detailed protocol covering all aspects of the clinical trial, subject or patient information, and consent. Written indemnification and/or insurance cover from the appropriate source or sources for the subjects or patients is required, although the details may vary both nationally and internationally. For example, in the UK most ethical committees would adopt the indemnification principles as set out by the Association of British Pharmaceutical Industries.
The basic requirements of a clinical trial are that it should be blind, randomized, and suitably controlled. These three aspects of clinical trial design are intimately related and are there to remove, limit or allow adjustment for possible influences that might confound the outcome of a clinical trial and thereby reduce or completely obviate the scientific value of any particular study. These three design features will be discussed individually.
### Blindness
The term "blindness" is for obvious reasons not universally accepted and alternatives include "masking" or "masked". All clinical studies must be, at least, single, examiner blind. Single blindness requires that any investigator collecting data from the patients or subjects should not know the identity of the treatments used by any particular individual. Single blindness should eliminate bias in data collection. Examiner blindness, however, can be compromised to a variable degree if a particular treatment produces changes within the oral cavity, which can be perceived by the examiner. Such an example could be extrinsic staining of the teeth and/or oral mucosa by chlorhexidine formulations. The use of objective measures, which reduce or remove the requirement for subjective judgment, by the examiner, can improve the likelihood of single blindness. Unfortunately, such objective methods are not common to the recording of plaque, gingivitis, and periodontal disease parameters.
Double blindness is the ideal when neither the examiner nor subject or patient is aware of the treatment being used by the individual. Numerous factors will influence whether the subjects or patients can be maintained totally blind to their treatment (s), including whether the study is parallel or cross-over (to be discussed later), prior experience with treatments, and the presentation, taste, and appearance of the treatments, particularly controls. Subject blindness, although ideal, is less important where the treatment outcome measures are out of the immediate control of the subject, e.g. plaque accumulation and gingivitis; assuming, that is, that lack of subject blindness does not influence compliance. Subject blindness becomes highly important where the subject is required to make a valid judgment of the effects of the treatment, for example the effects of treatments on symptoms such as pain. The term "triple blindness" is used by some investigators and relates to the blindness of the individual analyzing the data to the identity of the treatments. Thus, the data are analyzed using the treatment codes e.g. treatments A, B, and C. The identities of A, B, and C are only revealed once the statistical tests have been completed.
### Randomization
The order in which treatments are received by each subject in a cross-over study, or into which treatment group subjects are placed in a parallel study, should be according to a randomized schedule. Randomization provides several important safety aspects to the study design in that firstly it is an essential part of examiner blindness. Secondly, in a cross-over study randomization should remove the potential confounding effects of the order of product use, the so-called period effects. Thirdly, the use of balanced randomization designs allows for potential carry-over effects of treatments in cross-over design studies (Newcombe _et al_. 1995). Finally, where the effects of a treatment on a disease state are to be assessed, randomization improves the chances that parallel treatment groups should be as similar as possible in baseline disease levels and, if relevant, demographic data. Randomization schedules, which use subject matching for demographic and disease status or stratification for level of disease, can be employed to improve balancing of parallel groups.
### Controls
The use of appropriate control treatments is essential to the evaluation of the benefits of a particular agent or product. Without such controls, studies essentially become no more than case report data at best and anecdotal at worst, particularly when specific treatment is evaluated alone for effects on various parameters. The choice of controls, however, can vary depending on the aim of the study and the level of evaluation of an agent or product within a program of research. The choice of controls could therefore be one or more of the following:
* _Placebo control_. Here the control is a substance without any expected pharmacologic action, e.g. water. This is useful when assessing a new agent or positioning an agent or formulation between a positive or benchmark control. Placebo controls are particularly valuable where a condition or symptom may be perceived by the subject or patient to have improved, so-called placebo response, or where a condition appears to improve naturally over time, the so-called regression to the mode. Both of these phenomena are common to studies of the treatment of dentine hypersensitivity where pain is a primary outcome measure, but they are, of course, unlikely to occur in studies where the outcome measure are levels of plaque and gingivitis.
* _Minus active control (negative control)_. This type of control is commonly employed to determine whether an agent provides activity over and above its vehicle. It is particularly useful in the initial assessment of formulations such as toothpastes which have included a new active. In the later stages of development, perhaps at the product level, the use of minus active controls in home use studies is of less value since minus active controls are not normally used by the general public.
* _Bench mark control_. This term is usually used to define a control which is a commercially available product commonly used by the general public. Such controls would appear more sensible for home use studies rather than minus active products when, for example, a new toothpaste product is formulated to promote gingival health benefits. In this case it would seem reasonable to determine whether efficacy is superior to conventional fluoride toothpaste rather than the minus active toothpaste.
* _Positive control_. Positive control is an agent or formulation presently considered the most effective agent available. In this case chlorhexidine mouth rinse is arguably considered the "gold" standard antiplaque agent and is frequently used as the positive control by which to compare and position the efficacy of agents and formulations. Usually a chlorhexidine mouth rinse is used as the positive control in the early no oral hygiene study protocols.
Depending on the aims and constraints of a clinical study, more than one of the aforementioned controls may be used; for example, in the short-term studies it is not unusual to position an agent or formulation for plaque and gingivitis efficacy between a positive control, chlorhexidine, and a placebo, water.
### Study groups
Study designs for oral hygiene products are usually either parallel or cross-over. Parallel group studies require that each individual uses only one of the formulations (active or control) throughout the duration of the study. Parallel designs can be used for any of the previously described oral hygiene study methods; however they are more commonly used when the study duration is protracted to weeks or months. Parallel designs require that the study groups are large in number to provide sufficient power for statistical analysis. Indeed, the power of any particular study to demonstrate a statistically significant difference between treatments should be calculated prior to the study, although this may be compromised by lack of data as to the likely outcome or by difficulty in deciding the clinical relevance of any difference found. Advice from a statistician is important and group sizes can be calculated based on expected differences between test and control formulations. It must be remembered that small differences can be found statistically significant merely by using large group sizes.
Cross-over studies randomly allocate subjects to use all of the agents or formulations under test. Since each individual acts as their own control, paired statistical analytical techniques mean that the power to detect differences is markedly increased compared to parallel designs, and thereby the total study cohort of subjects can be relatively small. Furthermore, a considerable number of formulations can be compared, although this will be limited by the duration of each study period which, in itself, will have a knockon effect on acceptability to and compliance of the subjects. Cross-over studies require a wash-out period between each treatment period and this will depend on the known, or expected, carry-over effect of a treatment or a condition into the next period. Random incomplete block designs can be used, in which each subject only uses so many of the agents under test.
The relationship between statistical significance and clinical significance is always difficult to resolve (for review see Addy & Newcombe 2005). Statistical significance is a mathematical concept which, with varying levels of probability, supports the idea that any difference between treatments is not due to chance. Clinical significance, on the other hand, is conceptual and attempts to define the benefit to the patient of any particular treatment. Unlike some branches of medicine and surgery, in periodontology, clinical significance is particularly difficult to define because the usual outcome variables are not absolute. Thus, treatment effects on plaque and/or gingivitis indices, unless approaching 100%, cannot be translated with any certainty to the initiation or progress of periodontitis and certainly not to tooth loss. Clinical significance could be:
1. _Bench mark equivalent_ : when a formulation performs as well as an established formulation or product.
2. _Bench mark superior_ : when a formulation performs significantly better than an established formulation.
3. _Disease related_ : when a formulation has an effect on an etiologic factor such that the related signs or symptoms of the associated disease are reduced to a significantly greater extent than the control, e.g. plaque reduction which reduced gingivitis to a greater extent than control.
4. _Positive_ : when a formulation produced the effect significantly greater than the most effective agent today, e.g. the antiplaque effect is greater than chlorhexidine.
5. _Proportional superiority_ : when from the outset of a study a minimum percentage improvement over the control group is set down as clinically significant.
### Conclusions
* Terminology concerning oral hygiene products needs to be standardized and defined.
* Efficacy claims, which are implied, or rely on inferences to be drawn, should be avoided.
* Studies _in vitro_ can provide supportive data to clinical investigations but cannot stand alone as proof of efficacy _in vivo_.
* Research and development of oral hygiene products needs to be step-by-step processed, making available a body of knowledge supporting the efficacy of a final formulation.
* Clinical proof should be largely dependent on data from blind, randomized, controlled clinical trials conducted to the Guideline for Good Clinical Practice (GCP).
* In reporting clinical trials the clinical significance of the finding should be considered.
* Statistical significance should not necessarily be taken as proof _per se_ of the benefit of an oral hygiene product to the general public.
* Clinical outcome, when possible, should be evaluated against side effects and the cost–benefit ratio should be determined.
* Where possible, systematic reviews with meta-analyses need to be conducted to prove the efficacy of agents and products for the control of supragingival plaque.
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Zambon, J.J. (1996). Periodontal Diseases: Microbial factors. Proceedings of the 1996 World Workshop in Periodontics. _Annals of Periodontology_ **1** , 879–925.
# Chapter 37
# Non-surgical Therapy
Noel Claffey and Ioannis Polyzois
* * *
Introduction
Detection and removal of dental calculus
Methods used for non-surgical root surface debridement
Hand instrumentation
Sonic and ultrasonic scalers
Reciprocating instruments
Ablative laser therapy
Choice of debridement method
The influence of mechanical debridement on subgingival biofilms
Implication of furcation involvement
Pain and discomfort following non-surgical therapy
Re-evaluation
Interpretation of probing measurements at re-evaluation
Average changes in measurements due to nonsurgical therapy
Interpretation of longitudinal changes at individual sites
Prediction of outcome and evaluation of treatment
Full-mouth disinfection
* * *
# Introduction
It is generally accepted that the goal of the initial periodontal treatment is to restore the biological compatibility of periodontally diseased root surfaces, thus halting the process of the disease. Figure 37-1 illustrates the role and sequencing of non-surgical therapy in the management of most periodontitis patients.
Non-surgical therapy aims to eliminate both living bacteria in the microbial biofilm and calcified biofilm microorganisms from the tooth surface and adjacent soft tissues. Complete elimination of such pathogenic microorganisms is perhaps over-ambitious. However a reduction in inflammation of the periodontium due to a lesser bacterial load leads to beneficial clinical changes. In addition, non-surgical therapy aims to create an environment in which the host can more effectively prevent pathogenic microbial recolonization using personal oral hygiene methods.
This chapter outlines the various methods used in non-surgical therapy, such as hand instrumentation, ultrasonic and sonic scalers, and ablative laser therapy. Their respective merits and shortcomings and their clinical efficacy will be discussed. The chapter will attempt to identify realistic prognostic outcomes of therapy when taking into consideration factors such as different methods of instrumentation, different root surfaces, and varying degrees of periodontitis.
Re-evaluation of the initial clinical response to non-surgical therapy as well as consideration of modifiable risk factors allows the clinician to formulate an ongoing treatment plan tailored to the individual.
# Detection and removal of dental calculus
Periodontitis is strongly associated with the presence of dental calculus on root surfaces. It has been suggested that the rough surface of calculus does not in itself induce inflammation but that the deleterious effect of calculus relates to its ability to provide an ideal surface for microbial colonization (Waerhaug 1952). It has also been demonstrated that epithelial adherence to subgingival calculus can occur following its disinfection with chlorhexidine (Lisgarten & Ellegaard 1973). Thus, a rationale for the removal of calculus relates to eliminating, as far as possible, surface irregularities harboring pathogenic bacteria.
Microbes giving rise to and colonizing the surface of dental calculus have been shown to produce lipopolysaccharides (LPS). These potent triggers of host response mechanisms were thought to be present within calculus and underlying cementum. For this reason it was thought necessary to remove not only calculus but also underlying cementum. However later evidence suggested that removal of tooth substance was not necessary. Ground sections of extracted periodontally involved teeth were examined. LPS was detected on cementum which had been previously exposed to the periodontal pocket. LPS also extended 1 mm into the surrounding connective tissue attachment. On no occasion was LPS seen penetrating into sub-surface cementum (Hughes & Smales 1986). These conclusions were further supported by animal and human studies which demonstrated that removal of superficial plaque on subgingival calculus resulted in the healing of periodontal lesions and the maintenance of health, provided supragingival hygiene was meticulous (Nyman _et al_. 1986, 1988; Mombelli _et al_. 1995). From a clinical standpoint, minimizing the total volume of dental calculus present seems to be desirable. However, aggressive tooth substance removal does not seem warranted.
**Fig. 37-1** Schematic representation of a typical treatment regimen for periodontitis patient management.
Factors that may influence complete calculus removal include the extent of disease, anatomic factors, the skill of the operator, and the instruments used. Waerhaug (1978) suggested that in more than 90% of cases, deposits of plaque and calculus remained in sites with pocket depths (PD) >5 mm following scaling and root planing. Similar conclusions were reported by Rabbani _et al_. (1981) and Magnusson _et al_. (1984). Brayer _et al_. (1989) investigated inter-operator variability performing non-surgical root debridement, comparing operators of two different levels of experience. It was found that the more experienced clinician achieved a superior level of calculus removal.
Although Caffesse _et al_. (1986) found more residual calculus following non-surgical root debridement compared to root debridement as part of a surgical procedure, 50% or more of surfaces with PD >7 mm showed residual calculus irrespective of methodology. Buchanan and Robertson (1987) found more residual calculus following non-surgical treatment on molar and premolar tooth surfaces than non-molar teeth. They also demonstrated that over 60% of molar sites had residual calculus following closed root debridement. These findings may reflect increased difficulty in achieving successful root debridement in posterior areas in the mouth in addition to the more complicated anatomy of multi-rooted teeth.
Matia _et al_. (1986) noted no difference in the quality of root debridement following evaluation of ultra-sonic, sonic or hand instrumentation. However none of the sites treated were totally free of calculus.
The agreement between clinicians in the detection of residual subgingival calculus has been found to be low. Furthermore microscopic studies have demonstrated that even if calculus is not detected clinically it may yet be present on a microscopic level. Nonetheless from a practical standpoint if calculus is detected clinically the site is more likely to display ongoing inflammation (Sherman _et al_. 1990).
# Methods used for non-surgical root surface debridement
Scaling is a procedure which aims at the removal of plaque and calculus from the tooth surface. Depending on the location of deposits, scaling is performed by supragingival and/or subgingival instrumentation. Root planing denotes a technique of instrumentation by which the "softened cementum" is removed and the root surface is made "hard" and "smooth". However, on the basis of evidence already discussed, excessive tooth substance removal is not warranted and so perhaps the term root debridement is more appropriate. Root debridement may therefore be defined as the removal of plaque and/or calculus from the root surface without the intentional removal of tooth structure.
Non-surgical periodontal treatment may be carried out using a variety of methods including hand instruments, sonic and ultrasonic scalers reciprocating instruments, and ablative laser therapy.
## Hand instrumentation
Hand instrumentation allows good tactile sensation while minimizing the risk of contaminated aerosol production. However, it tends to be more time consuming than other methods and, if aggressively performed, hand instrumentation can lead to excessive tooth substance removal. In addition, hand instrumentation is more technique sensitive and requires correct and frequent instrument sharpening.
Access to furcations and the base of deep pockets is limited compared to some machine-driven instruments which have been designed to access narrow apertures and relatively inaccessible areas (Leon _et al_. 1987; Oda & Ishikawa 1989; Dragoo _et al_. 1992; Takacs _et al_. 1993; Yukna _et al_. 1997; Kocher _et al_. 1998, 2001; Beuchat _et al_. 2001). Recently however, modified curettes with extended shanks for deep pockets and mini-bladed curettes for narrow pockets have been developed to improve efficacy of scaling and root planing in difficult areas (Singer _et al_. 1992; Landry _et al_. 1999).
### Hand instruments
A hand instrument is composed of three parts: the working part (the blade), the shank, and the handle (Fig. 37-2). The cutting edges of the blade are centered over the long axis of the handle in order to give the instrument proper balance. The blade is often made of carbon steel, stainless steel or tungsten carbide.
Curettes are instruments used for both scaling and root debridement (Fig. 37-3). The working part of the curette is the spoon-shaped blade which has two curved cutting edges. The two edges are united by the rounded toe. The curettes are usually made "double-ended" with mirror-turned blades. The length and angulation of the shank as well as the dimensions of the blade differ between different brands of instruments.
**Fig. 37-2** A curette demonstrating the handle, shank, and blade.
**Fig. 37-3** (a) Selections of curettes with varying shank configurations to facilitate debridement of different areas of the dentition. (b) The working end of a curette demonstrating rounded toe, face, and cutting edge.
**Fig. 37-4** (a) Sickle scaler. (b) Hoe. (c) File.
**Fig. 37-5** The effect of different angulations of the cutting edge of the curette to the tooth surface. (a) Correct angle of application. (b) Too obtuse angulation resulting in ineffective calculus removal and the possibility of cratering the surface. (c) Too acute angulation resulting in ineffective calculus removal and burnishing of the calculus deposits.
The sickle is manufactured with either a curved or a straight blade which has a triangular cross section and two cutting edges. The "facial" surface between the two cutting edges is flat in the lateral direction but may be curved in the direction of its long axis. The "facial" surface converges with the two lateral surfaces of the blade. Sickles are mainly used for supragingival debridement or scaling in shallow pockets (Fig. 37-4a).
The hoe has only one cutting edge. The blade is turned at a 100º angle to the shank with the cutting edge bevelled at a 45º angle. The blade can be positioned at four different inclinations in relation to the shank: facial, lingual, distal, and mesial. The hoe is mainly used for supragingival scaling (Fig. 37-4b). Periodontal files can be useful for smoothing roots in areas of stubborn deposits (Fig. 37-4c).
### Principles of curette use
Perhaps the most widely used instrument type for subgingival debridement is the curette. The angulation of the cutting edge of the curette to the tooth surface influences the efficiency of debridement. The optimal angle between the cutting edge and the tooth is approximately 80º (Fig. 37-5a). Too obtuse an angle, as shown in Fig. 37-5b, will result in cratering and consequent roughening of the root surface. Too acute an angle, as shown in Fig. 37-5c, will result in ineffective removal and burnishing of subgingival calculus deposits.
Subgingival instrumentation should preferably be performed under local anesthesia. The root surface of the diseased site is explored with a probe to identify (1) the probing depth, (2) the anatomy of the root surface (irregularities, root furrows, open furcation, etc.), and (3) the location of the calcified deposits.
The instrument is held in a modified pen grasp and the blade inserted into the periodontal pocket with the face of the blade parallel to and in light contact with the root surface. It is important that all root surface instrumentation is performed with a proper finger rest. This implies that one finger – the third or the fourth – must act as a fulcrum for the movement of the blade of the instrument. A proper finger rest serves to (1) provide a stable fulcrum, (2) permit optimal angulation of the blade, and (3) enable the use of wrist–forearm motion. The finger rest must be secured as close as possible to the site of instrumentation to facilitate controlled use of the instrument (Fig. 37-6).
**Fig. 37-6** Illustrations of (a) a modified pen grasp and (b) a finger rest in close proximity to the area of instrumentation.
**Fig. 37-7** Illustration of the shank of the curette held parallel to the long axis of the tooth during instrumentation of a posterior site.
After the base of the periodontal pocket has been identified with the lower edge of the blade, the instrument is turned into a proper "cutting" position: i.e. the shank is parallel to the long axis of the tooth (Fig. 37-7). The grasp of the instrument is tightened somewhat, the force between the cutting edge and the root surface is increased, and the blade is moved in a coronal direction. Strokes must be made in different directions to cover all aspects of the root surface (crosswise, back and forth) but, as stated above, strokes should always start from an apical position and be guided in a coronal direction. The probe is inserted in the pocket again and the surface of the root assessed anew for the presence of calculus.
Frequent sharpening of the cutting edge of the instrument is necessary to obtain efficient calculus removal (Fig. 37-8a). The angle between the face and the back of curettes must be maintained at approximately 70º during sharpening (Fig. 37-8b). Any greater angle will result in dulling of the cutting edge. A more acute angle results in a fragile and easily worn cutting edge.
## Sonic and ultrasonic scalers
A common alternative to hand instrumention for non-surgical periodontal therapy is the use of sonic and ultrasonic scalers. Sonic scalers use air pressure to create mechanical vibration that in turn causes the instrument tip to vibrate; the frequencies of vibration ranging from 2000–6000 Hz (Gankerseer & Walmsley 1987; Shah _et al_. 1994). Ultrasonic scalers convert electrical current to mechanical energy in the form of high-frequency vibrations at the instrument tip; the vibration frequencies ranging from 18 000–45 000 Hz. There are two types of ultrasonic scalers, magnetostrictive and piezoelectric. In piezoelectric scalers the alternating electrical current causes a dimensional change in the hand piece which is transmitted to the working tip as vibrations. The pattern of vibration at the tip is primarily linear. In magnetostrictive scalers the generated electrical current produces a magnetic field in the handpiece that causes the insert to expand and contract along its length and in turn causes the insert to vibrate. The pattern of vibration at the tip is elliptical. Modified sonic and ultrasonic scaler tips, e.g. tiny, thin, periodontal probe type, and diamond coated, have been developed for use in deep pockets (Drisko _et al_. 2000).
Recently, ultrasonic instruments using a working frequency of 25 kHz and a coupling at the head of the handpiece to transfer energy indirectly to the working tip have been developed. These instruments are cooled by a water-based medium containing polishing particles of various sizes dependent on therapeutic indication. The amount of contaminated aerosol is said to be reduced compared to other ultrasonic or sonic scalers. This system has been advocated for the treatment of periodontitis and peri-implantitis, as well as minimal invasive preparation of tooth structures. This development has been shown to be equally effective as conventional methods (Sculean _et al_. 2004).
## Reciprocating instruments
Few studies have been carried out to investigate the efficacy of reciprocating instruments. Results demonstrated that they produce an equivalent clinical outcome compared to hand, sonic or ultrasonic scalers. The use of reciprocating instruments is less time consuming than hand instrumentation and results in less root surface loss (Obeid _et al_. 2004; Obeid & Bercy 2005). Further evidence is awaited to support their widespread use.
**Fig. 37-8** (a) The angulation of the sharpening stone in relation to the curette shank. (b) The angle between the flat surface of the sharpening stone and the cutting edge of the curette.
## Ablative laser therapy
Ablative laser therapy targets both the soft and hard tissues of the periodontium. It has bacteriocidal and detoxification effects and can remove the epithelium lining and granulation tissue within the periodontal pocket which may potentially improve healing. Considering the possibility of bacterial invasion into the soft tissues of pockets, this effect could be an important factor in the treatment of moderate to deep pockets. However, studies have shown that curettage of granulation tissues had no added benefit over scaling and root planing (Lindhe & Nyman 1985; Ramfjord _et al_. 1987). Laser therapy is capable of removing plaque and calculus with extremely low mechanical stress and no formation of a smear layer on root surfaces. In addition the use of lasers may allow access to sites that conventional mechanical instruments cannot reach.
Various types of lasers such as carbon dioxide lasers, Er:YAG lasers, and Nd:YAG lasers are currently in use. Carbon dioxide lasers, when used with relatively low energy output in a pulsed and/or defocused mode, have root conditioning, detoxification, and bacteriocidal effects on contaminated root surfaces. However, at low energy outputs they are unable to remove calculus. Er:YAG lasers are capable of effectively removing calculus from the root surface. Er:YAG laser irradiation energy is absorbed by water and organic components of the biological tissues which causes their evaporation resulting in heat generation, water vapour production, and thus an increase in internal pressure within the calculus deposits. The resulting expansion within the calculus causes its separation from the root surface.
## Choice of debridement method
It has been demonstrated that hand, sonic, and ultrasonic scalers produce similar periodontal healing response with respect to probing pocket depths, bleeding on probing, and clinical attachment level (Badersten _et al_. 1981, 1984; Lindhe & Nyman 1985; Kalkwarf _et al_. 1989; Loos _et al_. 1987; Copulos _et al_. 1993; Yukna _et al_. 1997; Kocher _et al_. 2001; Obeid _et al_. 2004; Wennstrom _et al_. 2005; Christgau _et al_. 2006). With respect to time spent, several studies have shown that debridement time spent per tooth may be reduced when ultrasonic or sonic scalers used compared to hand scalers (Copulos _et al_. 1993; Boretti _et al_. 1995; Tunkel _et al_. 2002; Wennstrom _et al_. 2005; Christgau _et al_. 2006). Regarding root surface loss, sonic and ultrasonic scalers have been shown to produce less tooth surface loss compared to hand scalers (Ritz _et al_. 1991; Schmidlin _et al_. 2001).
In contrast to hand instrumentation, the use of sonic and ultrasonic scalers is less technique sensitive, requires less time to complete, and removes less root surface cementum. It has been shown to provide better access to deep pockets and furcation areas (Kocher _et al_. 1998; Beuchat _et al_. 2001). In addition the flushing action of water used in sonic and ultrasonic scalers removes, to a certain extent, debris and bacteria from the pocket area. However, tactile sensation is reduced, and there is production of contaminated aerosols (Harrel _et al_. 1998; Barnes _et al_. 1998; Rivera-Hidalgo _et al_. 1999; Timmerman _et al_. 2004). Some patients may find the vibration, sound, and water spray uncomfortable.
It has been demonstrated that the use of lasers produces results comparable to scaling and root planing (Schwarz _et al_. 2001). However, no adjunctive benefit of the use of lasers over scaling and root planing alone has been demonstrated (Schwarz _et al_. 2003; Ambrosini _et al_. 2005). Inadvertent irradiation and reflection from shiny metal surfaces may cause damage to patient's eyes, throat, and oral tissues other than the targeted area. In addition there is also a risk of excessive tissue destruction by direct ablation and thermal side effects. Also the high cost of the laser apparatus is a drawback for many clinicians.
**Fig. 37-9** Lingual view of mandibular teeth of patient with untreated periodontitis prior to periodontal therapy.
Figures 37-9 and 37-10 demonstrate the effects of non-surgical therapy.
# The influence of mechanical debridement on subgingival biofilms
Supra- and subgingival debridement results in the mechanical disruption of the plaque biofilm and remains the "gold standard" modality for periodontal treatment. Removal of subgingival plaque and calculus deposits through subgingival debridement exposes the cementum, root dentine, and pocket epithelium for novel colonization. Species which may have thrived in the subgingival environment of the diseased pocket may find the new habitat less hospitable. A decreased concentration of microbial products and tissue breakdown products, and a decrease in the flow of gingival crevicular fluid, along with a more neutral subgingival biofilm pH may encourage the growth of less pathogenic bacterial species. Also a decrease in pocket depth as a result of a resolution of inflammation, decreased oedema, and a re-adaptation of apical junctional epithelium favors the recolonization of more aerobic species.
**Fig. 37-10** Lingual view of mandibular teeth of patient 3 months following initial non-surgical therapy.
Following treatment the subgingival habitat may be repopulated by microorganisms which originate from: residual subgingival plaque deposits (Ramberg _et al_. 1994; Dahan _et al_. 2004); radicular dentinal tubules or cementum (Daly _et al_. 1982; Adriaens _et al_. 1988; Giuliana _et al_. 1997); pocket epithelium and connective tissues (Slots & Rosling 1983); supragingival plaque deposits (Magnusson _et al_. 1984; Ximenez-Fyvie _et al_. 2000); subgingival deposits of adjacent teeth and from other intraoral soft tissue sites (von Troil-Linden _et al_. 1996).
Subgingival debridement has been observed to result in a decrease in the total number of microorganisms present in subgingival sites and a shift in the relative proportion of different microbial species within the subgingival plaque biofilm. A decrease in the total bacterial count for sites of 3 mm or greater depth, from 91 ± 11 × 105 to 23 ± 6 × 105, has been observed immediately following subgingival debridement (Teles _et al_. 2006). Although pre-debridement subgingival microbial counts are restored in 4–7 days post debridement (Sharawy _et al_. 1966), the impact of subgingival debridement on the composition of subgingival plaque biofilms, although often transient, is more long lasting.
Subgingival debridement has been observed to result in a decrease in the mean counts and number of sites colonized by _P. gingivalis_ , _A. actinomycetemcomitans_ , _Pr. intermedia_ (Shiloah & Patters 1994), _T. forsythia_ , and _Tr. denticola_ (Darby _et al_. 2005) several weeks following subgingival debridement. The persistence of _A. actinomycetemcomitans_ and _P. gingivalis_ following subgingival debridement is attributed to the ability of these microorganisms to invade the pocket epithelium and connective tissues (Slots & Rosling 1983; Renvert _et al_. 1990; Shiloah & Patters 1994). Haffajee _et al_. (1997) found that the only species to be significantly affected in prevalence and mean counts 3 months following non-surgical periodontal therapy were _B. forsythus_ , _P. gingivalis_ , and _Tr. denticola_.
An increase in the proportions of Gram-positive aerobic cocci and rods following subgingival debridement is associated with health (Cobb 2002). Haffajee _et al_. (2006) reported an increase in proportion of streptococci (including _S. gordonni_ , _S. mitis_ , _S. oralis_ , and _S. sanguinis_ ) and _Actinomyces_ spp., _E. corrodens_ , and _G. morbillarum_ post subgingival debridement.
Microorganisms do not exist in isolation in the subgingival environment, but rather as members of communities. Socransky _et al_. (1998) identified groups of organisms which were commonly found together and subdivided microorganisms into complexes accordingly. Members of the red and orange complexes are most commonly identified at sites displaying signs of periodontitis. A re-emergence of species of the red and orange complex 3–12 months post debridement may be associated with ongoing attachment loss at these sites (Haffajee _et al_. 2006).
In the absence of appropriate home care, the re-establishment of the pretreatment microflora as well as the rebound of clinical improvements due to treatment will occur in a matter of weeks (Magnusson _et al_. 1984; Loos _et al_. 1988; Sbordone _et al_. 1990). In the absence of professional maintenance an increase in the prevalence and counts of periodontopathogens is to be expected (Renvert _et al_. 1990; Shiloah & Patters 1994). Following supra- and subgingival debridement and appropriate home care the re-establishment of a pathogenic subgingival microflora and an associated rebound in clinical parameters may occur in localized sites (Beikler _et al_. 2004).
# Implication of furcation involvement
Once attachment loss has progressed to the furcation area of multi-rooted teeth, patient-performed home care and professionally performed subgingival debridement become more difficult (Wylam _et al_. 1993). Microbial communities may develop relatively undisturbed in this sheltered anatomic site and increasingly anaerobic and virulent microbes may thrive.
Loos _et al_. (1988) observed that while subgingival debridement resulted in improvements in clinical and microbiologic parameters over a 1-year period post debridement, sites with furcation involvement consistently demonstrated higher microbial counts and greater proportions of suspected periodontopathogens. Generally clinical improvement was found to be less pronounced in furcation sites than in other locations (Loos _et al_. 1989). Nordland _et al_. (1987) and Claffey and Egelberg (1994) observed that the frequency of continued probing attachment loss was considerably greater in furcation-involved sites compared with all other sites. Consequently, teeth with furcation involvement may be viewed with some caution with respect to long-term prognosis.
# Pain and discomfort following non-surgical therapy
It has been demonstrated that tissue trauma occurs during non-surgical periodontal therapy (Claffey _et al_. 1988). This trauma can trigger local mechanoreceptors and polymodal nociceptors, the activation of which leads to the release of chemicals, such as prostaglandins, bradykinin, and histamine, and ultimately to the perception of pain in the central nervous system.
Clinical studies referring to pain experience after non-surgical therapy are limited. Quantifying pain is difficult as it cannot be measured directly. Pain perception to a similar stimulus is highly variable from individual to individual. Pain may be measured using visual analogue scales whereby the patient is asked to indicate their level of pain by a mark on a gradated scale from no pain to the most severe pain imaginable.
Pihlstrom _et al_. (1999) reported that patients experienced pain of significant duration and magnitude following scaling and root planning. Pain was reported to peak in intensity between 2 and 8 hours post therapy and on average lasted for 6 hours. Almost 25% of patients self-medicated to relieve pain after treatment.
In addition to pain resulting from soft tissue trauma, patients may also experience root sensitivity following non-surgical therapy. Good oral hygiene measures resulting in low plaque scores prior to commencement of non-surgical periodontal therapy have been shown to decrease root dentin sensitivity.
Despite this, root dentin sensitivity can be a side effect of thorough root planing. Tammaro _et al_. (2000) demonstrated only moderate increases in root dentin sensitivity in most patients with only a small portion of patients experiencing more extreme sensitivity. Patients with sensitive teeth prior to treatment had higher levels of sensitivity following treatment. Although a reduction in the intensity of root dentin sensitivity over 4 weeks was noted, the number of sensitive teeth remained unchanged.
Clinical trials have shown anxiety, depression, and stress to be related to pain perception. Kloostra _et al_. (2006) investigated these factors with regard to non-surgical as well as surgical periodontal therapy and concluded that psychosocial factors may influence pain experience and the need for medication after therapy.
In a further clinical trial concerned with patients' experience of pain during diagnosis and non-surgical treatment of periodontitis it was demonstrated that pain experience during diagnostic instrumentation correlated significantly with pain experience during root instrumentation (van Steenberghe _et al_. 2004). One third of patients took analgesic medication after non-surgical treatment. However approximately half of the total number of patients complained of gingival soreness and pain and two thirds even experienced problems while eating.
Pain during and after periodontal diagnosis and non-surgical therapy seems to be on average mild to moderate and transient in nature. Nevertheless, some patients experience significant pain during treatment. Patients' psychosocial factors such as anxiety may influence the intensity of the pain experienced. Moreover recognition of this anxiety may be the first step in the management of pain in such patients (Chung _et al_. 2003). There is some first evidence that pre-emptive analgesics (ibruprofen arginine) may have some beneficial effect and help the patient to have a much more positive experience during periodontal treatment (Ettlin _et al_. 2006).
# Re-evaluation
Healing following non-surgical therapy is almost complete at 3 months. However a slower ongoing but limited healing can continue for up to 9 or more months following the treatment (Badersten _et al_. 1984). Re-evaluation is a vital stage in a periodontal treatment plan. At re-evaluation the effectiveness of treatment previously carried out is evaluated and the nature of further therapy, if needed, is established.
Measurements are made at baseline and again at 3 months as a method of evaluation of periodontal status and effectiveness of therapy. Measurements include plaque scores, bleeding on probing, suppuration on probing, probing pocket depth, recession, probing attachment level, and assessment of mobility. These are usually recorded at four to six sites around each tooth.
## Interpretation of probing measurements at re-evaluation
Probing depth is defined as the distance from the gingival margin to the base of the periodontal pocket measured in millimeters using a periodontal probe. Probing attachment level change is utilized to assess events occurring at the base of the periodontal pocket. Measurements are made at different times from a fixed point, such as from a stent margin or cemento-enamel junction to the base of the pocket. It is generally accepted that any improvement in probing attachment level is not a result of connective tissue reattachment but due to a re-adaptation of the junctional epithelium at the base of the pocket (Fig. 37-11). Probing depth change is a combination of recession and the change in probing attachment level due to events occurring at the base of the periodontal pocket.
**Fig. 37-11** Schematic illustration of the healing occurring in deep pockets following initial therapy (adapted from Fowler _et al_.1982).
On average the change in pocket depth seen following treatment for deeper pockets is a combination of recession at the gingival margin due to resolution of inflammation and a tightening of the junctional epithelium at the base of the pocket. Moreover the reduced bleeding on probing scores found after treatment may reflect the increased resistance to probe penetration into the connective tissue.
## Average changes in measurements due to non-surgical therapy
Tables 37-1 and 37-2 present mean changes in plaque scores, bleeding scores, probing depths, and probing attachment levels which were generally observed in studies of mean changes from baseline to re-evaluation. However the use of mean results of pooled sites can mask deterioration or improvement at individual sites.
It is important to appreciate that the extent of the initial probing depth has a marked influence on probing depth changes due to treatment. For example, for shallow pockets, non-surgical treatment results in loss of probing attachment, whereas in deep pockets there is a marked gain of probing attachment. It has been shown that there is an initial loss of probing attachment due to instrumentation trauma for pockets of all initial probing depths. However in the deeper sites this loss is reversed upon resolution of inflammation (Claffey _et al_. 1988).
## Interpretation of longitudinal changes at individual sites
Difficulties arise in detecting individual sites with ongoing destruction due to the following reasons:
**Table 37-1** Estimations generally observed in studies, of improvements in plaque and bleeding scores for sites of different initial probing depths after a single episode of supra- and subgingival instrumentation
**Initial probing depth (mm) ≤3.5** | **Plaque ≈ 50% → 10%** | **Bleeding ≈ 55% → 15%**
---|---|---
4–6.5 | ≈ 80% → 15% | ≈ 80% → 25%
≥7 | ≈ 90% → 25% | ≈ 90% → 30%
**Table 37-2** Mean changes (mm) generally observed in studies in probing depth, probing attachment levels, and gingival recession after a single episode of supra- and subgingival instrumentation
* Lack of reproducibility of probing measurements. Factors influencing the reproducibility of probing measurements include: probing force, probe tip diameter, angulation of probe, position in the mouth, probing depth itself and the inflammatory status of the tissues. A similar lack of reproducibility has been reported following recordings made by the same examiner at different time points (intra-examiner) and recordings taken by different examiners at the same time points (interexaminer). Badersten _et al_. (1984) demonstrated that duplicate probing measurements were exactly the same in only 30–40% of cases when looking at both inter-examiner and intra-examiner reproducibility. Differences of 2 mm or more were noted in 5–7% of recordings. Therefore, such probing attachment level changes at individual sites cannot be relied upon to indicate true disease progression.
* As discussed above variations in probing attachment levels may simply reflect changes in the inflammatory status at the base of the pocket rather than true connective tissue loss or gain.
With these points in mind, in order to identify sites with ongoing connective tissue loss, probing measurements should be interpreted with caution. Various methods have been reported in the literature to address this problem. One method is to demand a high threshold of change before indicating a site as deteriorating. Others include the application of statistical methods, such as regression analysis, to a series of longitudinal measurements.
# Prediction of outcome and evaluation of treatment
It would be of great benefit to the clinician to be able to predict the outcome of treatment prior to therapy and also to identify at re-evaluation the sites likely to continue to deteriorate. Prediction and evaluation must be considered both at a patient level and a site level. On a patient level, the extent of baseline bleeding scores, probing attachment loss, and probing depths have been found to relate to future probing attachment loss in untreated patients (Halazonetis _et al_. 1989; Lindhe _et al_. 1989; Haffajee _et al_. 1991). In patients treated with non-surgical therapy without the use of local anesthetic, baseline scores of attachment loss were also seen to relate to the risk of further loss of attachment (Grbic _et al_. 1991; Grbic & Lamster 1992). On a patient level, the number of sites greater then 6 mm at re-evaluation bears a direct relationship to future periodontal breakdown (Claffey & Egelberg 1995).
On a site level, bleeding on probing is, at best, a moderate predictor of future attachment loss (Badersten _et al_. 1990; Claffey _et al_. 1990). On the other hand, absence of bleeding on probing has been demonstrated as a useful indicator of health (Lang _et al_. 1990). Claffey _et al_. (1990) found that deep residual probing depth was of limited predictive value when observed over short periods (Fig. 37-12). However, over the longer term, deep residual sites appeared to be more indicative of further attachment loss, particularly if combined with bleeding on probing. This emphasizes the need for ongoing monitoring to identify such sites and instigate appropriate intervention.
**Fig. 37-12** Diagnostic predictability of residual probing depths at 3 months and 12 months following non-surgical treatment of advanced periodontitis. Diagnostic predictability is the percentage of sites with a certain feature, for instance with a deep probing depth at 3 or 6 months, which show attachment loss at a later time point.
# Full-mouth disinfection
Traditionally non-surgical treatment of periodontitis involves a series of appointments separated by perhaps a week or more. Each appointment typically involves root debridement of a quadrant depending on disease severity. In 1995 Quirynen _et al_. introduced the concept of total mouth disinfection as a new treatment strategy. It involved full-mouth scaling and root debridement within a 24-hour treatment period, subgingival irrigation (repeated three times within 10 minutes) with 1% chlorhexidine gel, tongue brushing with 1% chlorhexidine gel, and mouth rinsing with 0.2% chlorhexidine. This full-mouth disinfection protocol aimed to reduce the bacterial load in pockets and intraoral niches to minimize the risk of reinfection of the treated pockets from areas harboring pathogenic bacteria. Quirynen _et al_. (1995) showed that full-mouth disinfection yielded better periodontal treatment results on a short-term basis compared to conventional treatment.
Subsequent studies (Bollen _et al_. 1996, 1998; Vandekerckhove _et al_. 1996; Mongardini _et al_. 1999; Quirynen _et al_. 1999, 2000; De Soete _et al_. 2001) concluded that the full-mouth disinfection protocol resulted in clinical and microbiologic improvements comparable to the traditional technique of treatment in patients with advanced chronic periodontitis.
Many recent studies report varying degrees of efficacy of full-mouth disinfection protocol (Apatzidou & Kinane 2004). However, the full-mouth disinfection treatment approach has been promoted as a more efficient way of treating chronic periodontitis patients (Koshy _et al_. 2004; Wennstrom _et al_. 2005).
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# Part 12: Additional Therapy
38 Periodontal Surgery: Access Therapy
_Jan L. Wennström, Lars Heijl, and Jan Lindhe_
39 Treatment of Furcation-Involved Teeth
_Gianfranco Carnevale, Roberto Pontoriero, and Jan Lindhe_
40 Endodontics and Periodontics
_Gunnar Bergenholtz and Gunnar Hasselgren_
41 Treatment of Peri-implant Lesions
_Tord Berglundh, Niklaus P. Lang, and Jan Lindhe_
42 Antibiotics in Periodontal Therapy
_Andrea Mombelli_
# Chapter 38
# Periodontal Surgery: Access Therapy
Jan L. Wennström, Lars Heijl, and Jan Lindhe
* * *
Introduction
Techniques in periodontal pocket surgery
Gingivectomy procedures
Flap procedures
Regenerative procedures
Distal wedge procedures
Osseous surgery
Osteoplasty
Ostectomy
General guidelines for periodontal surgery
Objectives of surgical treatment
Indications for surgical treatment
Contraindications for periodontal surgery
Local anesthesia in periodontal surgery
Instruments used in periodontal surgery
Selection of surgical technique
Root surface instrumentation
Root surface conditioning/biomodification
Suturing
Periodontal dressings
Post-operative pain control
Post-surgical care
Outcome of surgical periodontal therapy
Healing following surgical pocket therapy
Clinical outcome of surgical access therapy in comparison to non-surgical therapy
* * *
# Introduction
Since most forms of periodontal disease are plaque-associated disorders, it is obvious that surgical access therapy can only be considered as adjunctive to cause-related therapy (see Chapters 34 to 37). Therefore, the various surgical methods described below should be evaluated on the basis of their potential to facilitate removal of subgingival deposits and self-performed plaque control and thereby enhance the long-term preservation of the periodontium.
The decision concerning what type of periodontal surgery should be performed and how many sites should be included is usually made after the effect of initial cause-related measures has been evaluated. The time lapse between termination of the initial cause-related phase of therapy and this evaluation may vary from 1 to 6 months. This routine has the following advantages:
* Removal of calculus and bacterial plaque will eliminate or markedly reduce the inflammatory cell infiltrate in the gingiva (edema, hyperemia, flabby tissue consistency), thereby making assessment of the "true" gingival contours and pocket depths possible.
* Reduction of gingival inflammation makes the soft tissues more fibrous and thus firmer, which facilitates surgical handling of the soft tissues. The propensity for bleeding is reduced, making inspection of the surgical field easier.
* A better basis for a proper assessment of the prognosis has been established. The effectiveness of the patient's home care, which is of decisive importance for the long-term prognosis, can be properly evaluated. Lack of effective self-performed infection control will often mean that the patient should be excluded from surgical treatment.
# Techniques in periodontal pocket surgery
Over the years, several different surgical techniques have been described and used in periodontal therapy. A superficial review of the literature in this area may give the reader a somewhat confusing picture of the specific objectives and indications relevant for various surgical techniques. It is a matter of historic interest that the first surgical techniques used in periodontal therapy were described as means of gaining access to diseased root surfaces. Such access could be accomplished without excision of the soft tissue pocket ("open-view operations"). Later, procedures were described by which the "diseased gingiva" was excised (gingivectomy procedures).
**Fig. 38-1** Gingivectomy. The straight incision technique (Robicsek 1884).
The concept that not only inflamed soft tissue but also "infected and necrotic bone" had to be eliminated called for the development of surgical techniques by which the alveolar bone could be exposed and resected (flap procedures). Other concepts such as (1) the importance of maintaining the mucogingival complex (i.e. a wide zone of gingiva) and (2) the possibility for regeneration of periodontal tissues have also prompted the introduction of "tailor-made" surgical techniques.
In the following, surgical procedures will be described which represent important steps in the development of the surgical component of periodontal therapy.
## Gingivectomy procedures
The surgical approach as an alternative to subgingival scaling for pocket therapy was already recognized in the latter part of the nineteenth century, when Robicsek (1884) pioneered the so-called _gingivectomy_ procedure. Gingivectomy was later defined by Grant _et al_. (1979) as being "the excision of the soft tissue wall of a pathologic periodontal pocket". The surgical procedure, which aimed at "pocket elimination", was usually combined with recontouring of the diseased gingiva to restore physiologic form.
Robicsek (1884) and, later, Zentler (1918) described the gingivectomy procedure in the following way. The line to which the gum is to be resected is determined first. Following a straight (Robicsek) ( **Fig. 38-1**) or scalloped (Zentler) ( **Fig. 38-2**) incision, first on the labial and then on the lingual surface of each tooth, the diseased tissue should be loosened and lifted out by means of a hook-shaped instrument. After elimination of the soft tissue, the exposed alveolar bone should be scraped. The area should then be covered with some kind of antibacterial gauze or be painted with disinfecting solutions. The result obtained should include eradication of the deepened periodontal pocket and formation of an area which can be kept clean more easily.
**Fig. 38-2** Gingivectomy. The scalloped incision technique (Zentler 1918).
### _Technique_
The gingivectomy procedure as it is employed today was described in 1951 by Goldman.
* When the dentition in the area scheduled for surgery has been properly anesthetized, the depths of the pathological pockets are identified with a conventional periodontal probe (Fig. 38-3a). At the level of the bottom of the pocket, the gingiva is pierced with the probe and a bleeding point is produced on the outer surface of the soft tissue (Fig. 38-3b). The pockets are probed and bleeding points produced at several location points around each tooth in the area. The series of bleeding points produced describes the depth of the pockets in the area scheduled for treatment and is used as a guideline for the incision.
* The primary incision ( **Fig. 38-4**), which may be made by a scalpel (blade No. 12B or 15; Bard-Parker®) in either a Bard-Parker handle or an angulated handle (e.g. a Blake's handle), or a Kirkland knife No. 15/16, should be planned to give a thin and properly festooned margin of the remaining gingiva. Thus, in areas where the gingiva is bulky, the incision must be placed at a level more apical to the level of the bleeding points than in areas with a thin gingiva, where a less accentuated bevel is needed. The beveled incision is directed towards the base of the pocket or to a level slightly apical to the apical extension of the junctional epithelium. In areas where the interdental pockets are deeper than the buccal or lingual pockets, additional amounts of buccal and/or lingual (palatal) gingiva must be removed in order to establish a "physiologic" contour of the gingival margin. This is often accomplished by initiating the incision at a more apical level.
* Once the primary incision is completed on the buccal and lingual aspects of the teeth, the interproximal soft tissue is separated from the interdental periodontium by a secondary incision using an Orban knife (No. 1 or 2) or a Waerhaug knife (No. 1 or 2; a saw-toothed modification of the Orban knife) ( **Fig. 38-5**).
* The incised tissues are carefully removed by means of a curette or a scaler ( **Fig. 38-6**). Remaining tissue tabs are removed with a curette or a pair of scissors. Pieces of gauze packs often have to be placed in the interdental areas to control bleeding. When the field of operation is properly prepared, the exposed root surfaces are carefully scaled and planed.
* Following meticulous debridement, the dentogingival regions are probed again to detect any remaining pockets ( **Fig. 38-7**). The gingival contour is checked and, if necessary, corrected by means of knives or rotating diamond burs.
* To protect the incised area during the period of healing, the wound surface must be covered by a periodontal dressing ( **Fig. 38-8**). The dressing should be closely adapted to the buccal and lingual wound surfaces as well as to the interproximal spaces. Care should be taken not to allow the dressing to become too bulky, since this is not only uncomfortable for the patient, but also facilitates dislodgement of the dressing.
* The dressing should remain in position for 10–14 days. After removal of the dressing, the teeth must be cleaned and polished. The root surfaces are carefully checked and remaining calculus removed with a curette. Excessive granulation tissue is eliminated with a curette. The patient is instructed to clean properly the operated segments of the dentition, which now have a different morphology compared to the pre-operative situation.
**Fig. 38-3** Gingivectomy. Pocket marking. (a) An ordinary periodontal probe is used to identify the bottom of the deepened pocket. (b) When the depth of the pocket has been assessed an equivalent distance is delineated on the outer aspect of the gingiva. The tip of the probe is then turned horizontally and used to produce a bleeding point at the level of the bottom of the probeable pocket.
**Fig. 38-4** Gingivectomy. (a) The primary incision. (b) The incision is terminated at a level apical to the "bottom" of the pocket and is angulated to give the cut surface a distinct bevel.
**Fig. 38-5** Gingivectomy. The secondary incision through the interdental area is performed with the use of a Waerhaug knife.
**Fig. 38-6** Gingivectomy. The detached gingiva is removed with a scaler.
**Fig. 38-7** Gingivectomy. Probing for residual pockets. Gauze packs have been placed in the interdental spaces to control bleeding.
**Fig. 38-8** Gingivectomy. The periodontal dressing has been applied and properly secured.
**Fig. 38-9** Original Widman flap. Two releasing incisions demarcate the area scheduled for surgical therapy. A scalloped reverse bevel incision is made in the gingival margin to connect the two releasing incisions.
**Fig. 38-10** Original Widman flap. The collar of inflamed gingival tissue is removed following the elevation of a mucoperiosteal flap.
## Flap procedures
### The original Widman flap
In 1918 Leonard Widman published one of the first detailed descriptions of the use of a flap procedure for pocket elimination. In his article "The operative treatment of pyorrhea alveolaris" Widman described a mucoperiosteal flap design aimed at removing the pocket epithelium and the inflamed connective tissue, thereby facilitating optimal cleaning of the root surfaces.
### _Technique_
* Sectional releasing incisions were first made to demarcate the area scheduled for surgery ( **Fig. 38-9**). These incisions were made from the mid-buccal gingival margins of the two peripheral teeth of the treatment area and were continued several millimeters out into the alveolar mucosa. The two releasing incisions were connected by a gingival incision, which followed the outline of the gingival margin and _separated the pocket epithelium and the inflamed connective tissue from the non-inflamed gingiva_. Similar releasing and gingival incisions, if needed, were made on the lingual aspect of the teeth.
* A mucoperiosteal flap was elevated to expose at least 2–3 mm of the marginal alveolar bone. The collar of inflamed tissue around the neck of the teeth was removed with curettes ( **Fig. 38-10**) and the exposed root surfaces were carefully scaled. Bone recontouring was recommended in order to achieve an ideal anatomic form of the underlying alveolar bone ( **Fig. 38-11**).
* Following careful debridement of the teeth in the surgical area, the buccal and lingual flaps were laid back over the alveolar bone and secured in this position with interproximal sutures ( **Fig. 38-12**). Widman pointed out the importance of placing the soft tissue margin at the level of the alveolar bone crest, so that no pockets would remain. The surgical procedure resulted in the exposure of root surfaces. Often the interproximal areas were left without soft tissue coverage of the alveolar bone.
**Fig. 38-11** Original Widman flap. By bone recontouring, a "physiologic" contour of the alveolar bone may be re-established.
**Fig. 38-12** Original Widman flap. The coronal ends of the buccal and lingual flaps are placed at the alveolar bone crest and secured in this position by interdentally placed sutures.
**Fig. 38-13** Modified flapoperation (the Kirkland flap). Intracrevicular incision.
The main advantages of the " _original Widman flap_ " procedure in comparison to the gingivectomy procedure included, according to Widman (1918):
* Less discomfort for the patient, since healing occurred by primary intention
* It was possible to re-establish a proper contour of the alveolar bone in sites with angular bony defects.
### The Neumann flap
Only a few years later, Neumann (1920) suggested the use of a flap procedure, which in some respects was different from that originally described by Widman.
### _Technique_
* According to the technique suggested by Neumann, an intracrevicular incision was made through the base of the gingival pockets and the entire gingiva (and part of the alveolar mucosa) was elevated in a mucoperiosteal flap. Sectional releasing incisions were made to demarcate the area of surgery.
* Following flap elevation, the inside of the flap was curetted to remove the pocket epithelium and the granulation tissue. The root surfaces were subsequently carefully "cleaned". Any irregularities of the alveolar bone were corrected to give the bone crest a horizontal outline.
* The flaps were then trimmed to allow both an optimal adaptation to the teeth and a proper coverage of the alveolar bone on both the buccal/lingual (palatal) and the interproximal sites. With regard to pocket elimination, Neumann (1920) pointed out the importance of removing the soft tissue pockets, i.e. replacing the flap at the crest of the alveolar bone.
**Fig. 38-14** Modified flap operation (the Kirkland flap). The gingiva is retracted to expose the "diseased" root surface.
**Fig. 38-15** Modified flap operation (the Kirkland flap). The exposed root surfaces are subjected to mechanical debridement.
**Fig. 38-16** Modified flap operation (the Kirkland flap). The flaps are replaced to their original position and sutured.
### The modified flap operation
In a publication from 1931 Kirkland described a surgical procedure to be used in the treatment of "periodontal pus pockets". The procedure was called the _modified flap operation_ , and is basically an access flap for proper root debridement.
### _Technique_
* In this procedure incisions were made intracrevicularly through the bottom of the pocket ( **Fig. 38-13**) on both the labial and the lingual aspects of the interdental area. The incisions were extended in a mesial and distal direction.
* The gingiva was retracted labially and lingually to expose the diseased root surfaces ( **Fig. 38-14**) which were carefully debrided ( **Fig. 38-15**). Angular bony defects were curetted.
* Following the elimination of the pocket epithelium and granulation tissue from the inner surface of the flaps, these were _replaced_ to their original position and secured with interproximal sutures ( **Fig. 38-16**). Thus, no attempt was made to reduce the pre-operative depth of the pockets.
In contrast to the _original Widman flap_ as well as the _Neumann flap_ , the _modified flap operation_ did not include (1) extensive sacrifice of non-inflamed tissues and (2) apical displacement of the gingival margin. The method could be useful in the anterior regions of the dentition for esthetic reasons, since the root surfaces were not markedly exposed. Another advantage of the _modified flap operation_ was the potential for bone regeneration in intrabony defects which frequently occurred according to Kirkland (1931).
The main objectives of the flap procedures so far described were to:
* Facilitate the debridement of the root surfaces as well as the removal of the pocket epithelium and the inflamed connective tissue
* Eliminate the deepened pockets (the _original Widman flap_ and the _Neumann flap_ )
* Cause a minimal amount of trauma to the periodontal tissues and discomfort to the patient.
**Fig. 38-17** Apically repositioned flap. Following a vertical releasing incision, the reverse bevel incision is made through the gingiva and the periosteum to separate the inflamed tissue adjacent to the tooth from the flap.
**Fig. 38-18** Apically repositioned flap. A mucoperiosteal flap is raised and the tissue collar remaining around the teeth, including the pocket epithelium and the inflamed connective tissue, is removed with a currette.
### The apically repositioned flap
In the 1950s and 1960s new surgical techniques for the removal of soft and, when indicated, hard tissue periodontal pockets were described in the literature. The importance of maintaining _an adequate zone of attached gingiva_ after surgery was now emphasized. One of the first authors to describe a technique for the preservation of the gingiva following surgery was Nabers (1954). The surgical technique developed by Nabers was originally denoted "repositioning of attached gingiva" and was later modified by Ariaudo and Tyrrell (1957). In 1962 Friedman proposed the term _apically repositioned flap_ to describe more appropriately the surgical technique introduced by Nabers. Friedman emphasized the fact that, at the end of the surgical procedure, the entire complex of the soft tissues (gingiva and alveolar mucosa) rather than the gingiva alone was displaced in an apical direction. Thus, rather than excising the amount of gingiva which would be in excess after osseous surgery (if performed), the whole muco-gingival complex was maintained and repositioned apically. This surgical technique was used on buccal surfaces in both upper and lower jaws and on lingual surfaces in the lower jaw, while an excisional technique had to be used on the palatal aspect of maxillary teeth where the lack of alveolar mucosa made it impossible to reposition the flap in an apical direction.
### _Technique_
According to Friedman (1962) the technique should be performed in the following way:
* A reverse bevel incision is made using a scalpel with a Bard-Parker blade (No. 12B or No. 15). How far from the buccal/lingual gingival margin the incision should be made is dependent on the pocket depth as well as the thickness and the width of the gingiva ( **Fig. 38-17**). If pre-operatively the gingiva is thin and only a narrow zone of keratinized tissue is present, the incision should be made close to the tooth. The beveling incision should be given a scalloped outline, to ensure maximal interproximal coverage of the alveolar bone when the flap subsequently is repositioned. Vertical releasing incisions extending out into the alveolar mucosa (i.e. past the muco-gingival junction) are made at each of the end points of the reverse incision, thereby making apical repositioning of the flap possible.
* A full-thickness mucoperiosteal flap including buccal/lingual gingiva and alveolar mucosa is raised by means of a mucoperiosteal elevator. The flap has to be elevated beyond the muco-gingival line in order to be able later to reposition the soft tissue apically. The marginal collar of tissue, including pocket epithelium and granulation tissue, is removed with curettes ( **Fig. 38-18**), and the exposed root surfaces are carefully scaled and planed.
* The alveolar bone crest is recontoured with the objective of recapturing the normal form of the alveolar process but at a more apical level ( **Fig. 38-19**). The osseous surgery is performed using burs and/or bone chisels.
* Following careful adjustment, the buccal/lingual flap is repositioned to the level of the newly recontoured alveolar bone crest and secured in this position ( **Fig. 38-20**). The incisional and excisional technique used means that it is not always possible to obtain proper soft tissue coverage of the denuded interproximal alveolar bone. A periodontal dressing should therefore be applied to protect the exposed bone and to retain the soft tissue at the level of the bone crest ( **Fig. 38-21**). After healing, an "adequate" zone of gingiva is preserved and no residual pockets should remain.
**Fig. 38-19** Apically repositioned flap. Osseous surgery is performed with the use of a rotating bur (a) to recapture the physiologic contour of the alveolar bone (b).
**Fig. 38-20** Apically repositioned flap. The flaps are repositioned in an apical direction to the level of the recontoured alveolar bone crest and retained in this position by sutures.
**Fig. 38-21** Apically repositioned flap. A periodontal dressing is placed over the surgical area to ensure that the flaps remain in the correct position during healing.
To handle periodontal pockets on the palatal aspect of the maxillary teeth, Friedman described a modification of the "apically repositioned flap", which he termed the _beveled flap_ :
* In order to prepare the tissue at the gingival margin to follow the outline of the alveolar bone crest properly, a conventional mucoperiosteal flap is first resected ( **Fig. 38-22**).
* The tooth surfaces are debrided and osseous recontouring is performed ( **Fig. 38-23**).
* The palatal flap is subsequently replaced and the gingival margin is prepared and adjusted to the alveolar bone crest by a secondary scalloped and beveled incision ( **Fig. 38-24**). The flap is secured in this position with interproximal sutures ( **Fig. 38-25**).
Among a number of suggested advantages of the _apically repositioned flap_ procedure, the following have been emphasized:
* Minimum pocket depth post-operatively
* If optimal soft tissue coverage of the alveolar bone is obtained, the post-surgical bone loss is minimal
* The post-operative position of the gingival margin may be controlled and the entire muco-gingival complex may be maintained.
The sacrifice of periodontal tissues by bone resection and the subsequent exposure of root surfaces (which may cause esthetic and root sensitivity problems) were regarded as the main disadvantages of this technique.
### The modified Widman flap
Ramfjord and Nissle (1974) described the _modified Widman flap_ technique that is also recognized as the _open flap curettage_ technique. It should be noted that, while the _original Widman flap_ technique included both apical displacement of the flaps and osseous recontouring (elimination of bony defects) to obtain proper pocket elimination, the _modified Widman flap_ technique is not intended to meet these objectives.
**Fig. 38-22** Bevelled flap. A primary incision is made intracrevicularly through the bottom of the periodontal pocket (a) and a conventional mucoperiosteal flap is elevated (b).
**Fig. 38-23** Bevelled flap. Scaling, root planing, and osseous recontouring are performed in the surgical area.
**Fig. 38-24** Bevelled flap. The palatal flap is replaced and a secondary, scalloped, reverse bevel incision is made to adjust the length of the flap to the height of the remaining alveolar bone.
### _Technique_
* According to the description by Ramfjord and Nissle (1974) the _initial incision_ ( **Fig. 38-26**), which may be performed with a Bard-Parker knife (No. 11), should be parallel to the long axis of the tooth and placed approximately 1 mm from the buccal gingival margin in order to properly separate the pocket epithelium from the flap. If the pockets on the buccal aspects of the teeth are less than 2 mm deep or if esthetic considerations are important, an intracrevicular incision may be made. Furthermore, the scalloped incision should be extended as far as possible in between the teeth, to allow maximum amounts of the interdental gingiva to be included in the flap. A similar incision technique is used on the palatal aspect. Often, however, the scalloped outline of the initial incision may be accentuated by placing the knife at a distance of 1–2 mm from the mid-palatal surface of the teeth. By extending the incision as far as possible in between the teeth, sufficient amounts of tissue can be included in the palatal flap to allow for proper coverage of the interproximal bone when the flap is sutured. Vertical releasing incisions are not usually required.
* Buccal and palatal full-thickness flaps are carefully elevated with a mucoperiosteal elevator. The flap elevation should be limited and allow only a few millimeters of the alveolar bone crest to become exposed. To facilitate the gentle separation of the collar of pocket epithelium and granulation tissue from the root surfaces, an intracrevicular incision is made around the teeth ( _second incision_ ) to the alveolar crest ( **Fig. 38-27**).
* A _third incision_ ( **Fig. 38-28**) made in a horizontal direction and in a position close to the surface of the alveolar bone crest separates the soft tissue collar of the root surfaces from the bone.
* The pocket epithelium and the granulation tissues are removed by means of curettes. The exposed roots are carefully scaled and planed, except for a narrow area close to the alveolar bone crest in which remnants of attachment fibers may be preserved. Angular bony defects are carefully curetted.
* Following the curettage, the flaps are trimmed and adjusted to the alveolar bone to obtain complete coverage of the interproximal bone ( **Fig. 38-29**). If this adaptation cannot be achieved by soft tissue recontouring, some bone may be removed from the outer aspects of the alveolar process in order to facilitate the all-important flap adaptation. The flaps are sutured together with individual interproximal sutures. Surgical dressing may be placed over the area to ensure close adaptation of the flaps to the alveolar bone and root surfaces. The dressing, as well as the sutures, is removed after 1 week.
**Fig. 38-25** Bevelled flap. The shortened and thinned flap is replaced over the alveolar bone and in close contact with the root surfaces.
**Fig. 38-26** Modified Widman flap. The initial incision is placed 0.5–1 mm from the gingival margin (a) and parallel to the long axis of the tooth (b).
**Fig. 38-27** Modified Widman flap. Following careful elevation of the flaps, a second intracrevicular incision (a) is made to the alveolar bone crest (b) to separate the tissue collar from the root surface.
**Fig. 38-28** Modified Widman flap. A third incision is made perpendicular to the root surface (a) and as close as possible to the bone crest (b), thereby separating the tissue collar from the alveolar bone.
The main advantages of the _modified Widman flap_ technique in comparison to other procedures previously described are, according to Ramfjord and Nissle (1974) :
* The possibility of obtaining a close adaptation of the soft tissues to the root surfaces
* The minimum of trauma to which the alveolar bone and the soft connective tissues are exposed
* Less exposure of the root surfaces, which from an esthetic point of view is an advantage in the treatment of anterior segments of the dentition.
### The papilla preservation flap
In order to preserve the interdental soft tissues for maximum soft tissue coverage following surgical intervention involving treatment of proximal osseous defects, Takei _et al_. (1985) proposed a surgical approach called _papilla preservation technique_. Later, Cortellini _et al_. (1995b, 1999) described modifications of the flap design to be used in combination with regenerative procedures. For esthetic reasons, the papilla preservation technique is often utilized in the surgical treatment of anterior tooth regions.
### _Technique_
* According to the description by Takei _et al_. (1985) the _papilla preservation flap technique_ is initiated by an intra-sulcular incision at the facial and proximal aspects of the teeth without making incisions through the interdental papillae (Fig. 38-30a). Subsequently, an intra-sulcular incision is made along the lingual/palatal aspect of the teeth with a semilunar incision made across each interdental area. The semilunar incision should dip apically at least 5 mm from the line angles of the teeth, which will allow the interdental tissue to be dissected from the lingual/palatal aspect so that it can be elevated intact with the facial flap. In situations where an osseous defect has a wide extension into the lingual/palatal area, the semilunar incision may be placed on the facial aspect of the interdental area to have the papillae included with the lingual/ palatal flap.
* A curette or interproximal knife is used to free the interdental papilla carefully from the underlying hard tissue. The detached interdental tissue is pushed through the embrasure with a blunt instrument (Fig. 38-30b).
* A full-thickness flap is reflected with a periosteal elevator on both facial and lingual/palatal surfaces. The exposed root surfaces are thoroughly scaled and root planed and bone defects carefully curetted ( **Fig. 38-31**).
* While holding the reflected flap, the margins of the flap and the interdental tissue are scraped to remove pocket epithelium and excessive granulation tissue. In anterior areas, the trimming of granulation tissue should be limited in order to maintain the maximum thickness of tissue.
* The flaps are repositioned and sutured using cross mattress sutures ( **Fig. 38-32**). Alternatively, a direct suture of the semilunar incisions can be done as the only means of flap closure. A surgical dressing may be placed to protect the surgical area. The dressing and sutures are removed after 1 week.
**Fig. 38-29** Modified Widman flap. (a) Following proper debridement and currettage of angular bone defects, the flaps are carefully adjusted to cover the alveolar bone and sutured. (b) Complete coverage of the interdental bone as well as close adaptation of the flaps to the tooth surfaces should be accomplished.
**Fig. 38-30** Papilla preservation flap. Intracrevicular incisions are made at the facial and proximal aspects of the teeth.
**Fig. 38-31** Papilla preservation flap. (a) An intracrevicular incision is made along the lingual/palatal aspect of the teeth with a semilunar incision made across each interdental area. (b) A curette or a papilla elevator is used to carefully free the interdental papilla from the underlying hard tissue. (c,d) The detached interdental tissue is pushed through the embrasure with a blunt instrument to be included in the facial flap.
**Fig. 38-32** Papilla preservation flap. The flap is replaced and sutures are placed on the palatal aspect of the interdental areas.
## Regenerative procedures
In the 1980s treatment of periodontal pockets was given a new dimension when it was shown that, with specific surgical handling of the periodontal wound, a significant amount of new connective tissue attachment is achievable following surgical treatment (Nyman _et al_. 1982; Bowers _et al_. 1989).
Obtaining periodontal regeneration has always been a major challenge to the periodontist and several approaches to periodontal regeneration have been used throughout the years. The earliest attempts involved various bone-grafting procedures, such as the use of autogenous grafts from both extraoral and intraoral donor sites, allogenic marrow grafts, and non-decalcified/decalcified lyophilized bone grafts, or "implant" procedures utilizing slowly resorbable tricalcium phosphate and non-resorbable, nonporous hydroxyapatite. Other approaches to periodontal regeneration involved the use of citric acid for root surface demineralization or the use of methods for improved root surface biocompatibility or to enhance cellular responses.
The use of physical barriers, such as membranes (non-biodegradable or biodegradable), to retard or prevent apical migration of epithelium as well as exclude gingival connective tissue from the healing wound, formed the basis for the concept known as "guided tissue regeneration" (Gottlow _et al_. 1986). The procedure can be described as a coronally repositioned flap procedure without bone recontouring, with the adjunctive use of a membrane tightened to the tooth to cover the exposed root surface and adjacent intrabony defect before repositioning the soft tissue flaps.
In the late 1990s a new approach to periodontal regeneration was presented, which involves the use of a derivative of enamel matrix proteins (Hammarström 1997; Heijl _et al_. 1997). These proteins are involved in the embryogenesis of cementum, periodontal ligament, and supporting bone, and when applied to the exposed root surface facing an intrabony periodontal defect they mediate regeneration of a new attachment apparatus. The surgical procedure is performed as a coronally repositioned flap procedure without bone recontouring. Before repositioning of the soft tissue flaps, the exposed roots are treated with EDTA for removal of the "smear layer", followed by the application of the derivative of enamel matrix proteins.
Various regenerative procedures for surgical treatment of periodontal lesions, as well as the biologic basis for periodontal regeneration, are discussed in detail in Chapters 25 and 43.
# Distal wedge procedures
In many cases the treatment of periodontal pockets on the distal surface of distal molars is complicated by the presence of bulbous tissues over the tuberosity or by a prominent retromolar pad. The most direct approach to pocket elimination in such cases in the maxillary jaw is the gingivectomy procedure. The incision is started on the distal surface of the tuberosity and carried forward to the base of the pocket of the distal surface of the molar ( **Fig. 38-33**).
However, when only limited amounts of keratinized gingiva are present, or none at all, or if a distal angular bony defect has been diagnosed, the bulbous tissue should be reduced in size rather than being removed _in toto._ This may be accomplished by the _distal wedge procedure_ (Robinson 1966). This technique facilitates access to the osseous defect and makes it possible to preserve sufficient amounts of gingiva and mucosa to achieve soft tissue coverage.
**Fig. 38-33** Distal wedge procedure. Simple gingivectomy incision (broken line) can be used to eliminate a soft tissue pocket and adjacent fibrous tissue pad behind a maxillary molar.
### _Technique_
* Buccal and lingual incisions are made in a vertical direction through the tuberosity or retromolar pad to form a triangular wedge (Fig. 38-34a). The facial and lingual incisions should be extended in a mesial direction along the buccal and lingual surfaces of the distal molar to facilitate flap elevation.
* The facial and lingual walls of the tuberosity or retromolar pad are deflected and the incised wedge of tissue is dissected and separated from the bone (Fig. 38-34b).
* The walls of the facial and lingual flaps are then reduced in thickness by undermining incisions (Fig. 38-34c). Loose tags of tissue are removed and the root surfaces are scaled and planed. If necessary, the bone is recontoured.
* The buccal and lingual flaps are replaced over the exposed alveolar bone, and the edges trimmed to avoid overlapping wound margins. The flaps are secured in this position with interrupted sutures (Fig. 38-34d). The sutures are removed after approximately 1 week.
The original distal wedge procedure may be modified according to individual requirements. Some commonly used modifications of the incision technique are illustrated in Figs. 38-35 to 38-38, all having the goals of eliminating the deep pocket and achieving mucosal coverage of the remaining periodontium.
**Fig. 38-34** Distal wedge procedure. (a) Buccal and lingual vertical incisions are made through the retromolar pad to form a triangle behind a manibular molar. (b) The triangular-shaped wedge of tissue is dissected from the underlying bone and removed. (c) The walls of the buccal and lingual flaps are reduced in thickness by undermining incisions (broken lines). (d) The flaps, which have been trimmed and shortened to avoid overlapping wound margins, are sutured.
**Fig. 38-35** Modified distal wedge procedure. A deep periodontal pocket combined with an angular bone defect at the distal aspect of a maxillary molar (a). Two parallel reverse bevel incisions, one buccal and one palatal, are made from the distal surface of the molar to the posterior part of the tuberosity (b–d), where they are connected with a buccolingual incision (d). The buccal and palatal incisions are extended in a mesial direction along the buccal and palatal surfaces of the molar to facilitate flap elevation.
# Osseous surgery
The principles of osseous surgery in periodontal therapy were outlined by Schluger (1949) and Goldman (1950). They pointed out that alveolar bone loss caused by inflammatory periodontal disease often results in an uneven outline of the bone crest. Since, according to these authors, the gingival contour is closely dependent on the contour of the underlying bone as well as the proximity and anatomy of adjacent tooth surfaces, the elimination of soft tissue pockets often has to be combined with osseous reshaping and the elimination of osseous craters and angular bony defects to establish and maintain shallow pockets and optimal gingival contour after surgery.
**Fig. 38-36** Modified distal wedge procedure. Buccal and palatal flaps are elevated (a) and the rectangular wedge is released from the tooth and underlying bone by sharp dissection and then removed (b).
**Fig. 38-37** Modified distal wedge procedure. Following bone recontouring and root debridement, the flaps are trimmed and shortened to avoid overlapping wound margins and sutured (a,b). A close soft tissue adaptation should be accomplished to the distal surface of the molar. The remaining fibrous tissue pad distal to the bucco-lingual incision line is "levelled" by the use of a gingivectomy incision.
## Osteoplasty
The term _osteoplasty_ was introduced by Friedman in 1955. The purpose of osteoplasty is to create a physiologic form of the alveolar bone _without_ removing any "supporting" bone. Osteoplasty therefore is a technique analogous to gingivoplasty. Examples of osteoplasty are the thinning of thick osseous ledges and the establishment of a scalloped contour of the buccal (lingual and palatal) bone crest ( **Fig. 38-39**). In flap surgery without bone recontouring, interdental morphology may sometimes preclude optimal mucosal coverage of the bone post-surgically, even if pronounced scalloping of soft tissue flaps is performed. In such a situation removal of non-supporting bone by vertical grooving to reduce the facio-lingual dimension of the bone in the interdental areas may facilitate flap adaptation, thereby reducing the risk of bone denudation as well as reducing the risk of ischemic necrosis of unsupported mucosal flaps due to flap margin deficiencies.
**Fig. 38-38** Modified incision techniques in distal wedge procedures. To ensure optimal flap adaptation at the furcation site the incision technique may be modified. The amount of attached keratinized tissue present as well as the accessibility to the retromolar area has to be considered when placing the incision.
Removal of non-supporting bone may sometimes also be required to gain access for intrabony root surface debridement. The leveling of interproximal craters and the elimination (or reduction) of bony walls of circumferential osseous defects are often referred to as "osteoplasty" since usually no resection of supporting bone is required ( **Fig. 38-40**).
## Ostectomy
In _ostectomy_ supporting bone, i.e. bone directly involved in the attachment of the tooth, is removed to reshape deformities caused by periodontitis in the marginal and interdental bone. Ostectomy is considered to be an important part of surgical techniques aimed at pocket elimination. As a general rule, however, care must be exercised when supporting bone is to be removed.
After exposing the alveolar bone by elevation of a flap, buccal and/or lingual crater walls are reduced to the base of the osseous defect using bone chisels and bone rongeurs ( **Fig. 38-41**). A round bur or a diamond stone under continuous saline irrigation can also be used. If bone resection has been carried out in the interdental area, the buccal and lingual/ palatal bone margins may subsequently have to be recontoured to compensate for discrepancies in bone height resulting from the interdental bone resection (Fig. 38-41b). It is considered important to remove the small peaks of bone, which often remain in the area of the line angles. The objective of bone surgery is thus to establish a "physiologic" anatomy of the alveolar bone, but at a more apical level.
**Fig. 38-39** Osteoplasty. Thick osseous ledges in a mandibular molar region area are eliminated with the use of a round bur to facilitate optimal flap adaptation.
**Fig. 38-40** Osteoplasty. Levelling of an interproximal bone crater through the removal of the palatal bone wall. For esthetic reasons the buccal bone wall is maintained to support the height of the soft tissue.
**Fig. 38-41** Ostectomy. (a) A combined one- and two-wall osseous defect on the distal aspect of a mandibular bicuspid has been exposed following reflection of mucoperiosteal flaps. Since esthetics is not a critical factor to consider in the posterior tooth region of the mandible, the bone walls are reduced to a level close to the base of the defect using rotating round burs under continuous saline irrigation. (b) The osseous recontouring completed. Note that some supporting bone has to be removed from the buccal and lingual aspect of both the second bicuspid and the first molar in order to provide a hard tissue topography which allows a close adaptation of the covering soft tissue flap.
# General guidelines for periodontal surgery
## Objectives of surgical treatment
Traditionally, _pocket elimination_ has been the main objective of periodontal therapy. The removal of the pocket by surgical means served two purposes: (1) the pocket, which established an environment conducive to progression of periodontal disease, was eliminated and (2) the root surface was made accessible for scaling and for self-performed tooth cleaning after healing.
While these objectives cannot be entirely discarded today, the necessity for pocket elimination in periodontal therapy has been challenged. During recent years our understanding of the biology of the periodontium, the pathogenesis of periodontal disease and the healing capacity of the periodontium has markedly increased. This new information has thus formed the basis for a more differentiated understanding of the role played by periodontal surgery in the preservation of teeth.
In the past, _increased pocket depth_ was the main indication for periodontal surgery. However, pocket depth is no longer as unequivocal a concept as it used to be. The _probeable depth_ , i.e. the distance from the gingival margin to the point where tissue resistance stops further periodontal probe penetration, may only rarely correspond to the "true" depth of the pocket (see Chapter 26). Furthermore, regardless of the accuracy with which pockets can be measured, there is no established correlation between probeable pocket depths and the presence or absence of active disease. This means that symptoms other than increased probing depth should be present to justify surgical therapy. These include clinical signs of inflammation, especially exudation and bleeding on probing (to the bottom of the pockets), as well as aberrations of gingival morphology. Finally, the fact that proper infection control, maintained by the patient, is a decisive factor for a good prognosis (Rosling _et al_. 1976a; Nyman _et al_. 1977; Axelsson & Lindhe 1981) must be considered prior to the initiation of surgery.
In conclusion, the main objective of periodontal surgery is to contribute to the long-term preservation of the periodontium by facilitating plaque removal and infection control, and periodontal surgery can serve this purpose by:
* Creating accessibility for proper professional scaling and root planing
* Establishing a gingival morphology which facilitates the patient's self-performed infection control.
In addition to this, periodontal surgery may aim at regeneration of periodontal attachment lost due to destructive disease. (New attachment procedures in periodontal therapy are discussed in Chapter 43.)
## Indications for surgical treatment
### Impaired access for scaling and root planing
Scaling and root planing are methods of therapy that are difficult to master. The difficulties in accomplishing proper debridement increase with (1) increasing depth of the periodontal pockets, (2) increasing width of the tooth surfaces, and (3) the presence of root fissures, root concavities, furcations, and defective margins of dental restorations in the subgingival area.
Provided a correct technique and suitable instruments are used, it is usually possible properly to debride pockets up to 5 mm deep (Waerhaug 1978; Caffesse _et al_. 1986). However, this 5 mm limit cannot be used as a universal rule of thumb. Reduced accessibility and the presence of one or several of the above-mentioned impeding conditions may prevent proper debridement of shallow pockets, whereas at sites with good accessibility and favorable root morphology, proper debridement can be accomplished even in deeper pockets (Badersten _et al_. 1981; Lindhe _et al_. 1982a).
It is often difficult to ascertain by clinical means whether subgingival instrumentation has been properly performed. Following scaling, the root surface should be smooth – roughness will often indicate the presence of remaining subgingival calculus. It is also important to monitor carefully the gingival reaction to subgingival debridement. If inflammation persists and if bleeding is elicited by gentle probing in the subgingival area, the presence of subgingival deposits should be suspected ( **Fig. 38-42**). If such symptoms are not resolved by repeated subgingival instrumentation, surgical treatment should be performed to expose the root surfaces for proper cleaning.
**Fig. 38-42** Evaluation following non-surgical instrumentation reveals persistent signs of inflammation, bleeding following pocket probing and probing depth ≥6 mm. Flap elevation to expose the root surface for proper cleaning should be considered.
### Impaired access for self-performed plaque control
The level of infection control that can be maintained by the patient is determined not only by his/her interest and dexterity but also, to some extent, by the morphology of the dentogingival area. The patient's responsibility in an infection-control program must obviously include the cleansing of the supragingival tooth surfaces and the marginal part of the gingival sulcus. This means that the tooth area coronal to the gingival margin and at the entrance to the gingival sulcus should be the target for the patient's home care efforts.
Pronounced gingival hyperplasia and gingival craters ( **Fig. 38-43**) are examples of morphologic aberrations, which may impede proper home care. Likewise, the presence of restorations with defective marginal fit or adverse contour and surface characteristics at the gingival margin may seriously compromise plaque removal.
By the professional treatment of periodontal disease, the dentist prepares the dentition in such a way that home care can be effectively managed. At the completion of treatment, the following objectives should have been met:
* No sub- or supragingival dental deposits
* No pathologic pockets (no bleeding on probing to the bottom of the pockets)
* No plaque-retaining aberrations of gingival morphology
* No plaque-retaining parts of restorations in relation to the gingival margin.
These requirements lead to the following indications for periodontal surgery:
* Accessibility for proper scaling and root planing
* Establishment of a morphology of the dentogingival area conducive to infection control
* Pocket depth reduction
* Correction of gross gingival aberrations
* Shift of the gingival margin to a position apical to plaque-retaining restorations
* Facilitate proper restorative therapy.
**Fig. 38-43** Examples of gingival aberrations, (a) gingival enlargement and (b) proximal soft tissue crater, which favor plaque retention and thereby impede the patient's plaque control.
## Contraindications for periodontal surgery
### Patient cooperation
Since optimal post-operative infection control is decisive for the success of periodontal treatment (Axelsson & Lindhe 1981), a patient who fails to cooperate during the cause-related phase of therapy should not be exposed to surgical treatment. Even though short-term post-operative infection control entails frequent professional treatments, the long-term responsibility for maintaining good oral hygiene must rest with the patient. Theoretically, even the poorest oral hygiene performance by a patient may be compensated for by frequent recall visits for supportive therapy (e.g. once a week), but it is unrealistic to consider larger groups of patients being maintained in this manner. A typical recall schedule for periodontal patients involves professional consultations for supportive periodontal therapy once every 3–6 months. Patients who cannot maintain satisfactory oral hygiene over such a period should normally be considered unsuited for periodontal surgery.
### Cardiovascular disease
_Arterial hypertension_ does not normally preclude periodontal surgery. The patient's medical history should be checked for previous untoward reactions to local anesthesia. Local anesthetics free from or low in adrenaline may be used and an aspirating syringe should be adopted to safeguard against intravascular injection.
_Angina pectoris_ does not normally preclude periodontal surgery. The drugs used and the number of episodes of angina may indicate the severity of the disease. Premedication with sedatives and the use of local anesthesia low in adrenaline are often recommended. Safeguards should be adopted against intravascular injection.
_Myocardial infarction patients_ should not be subjected to periodontal surgery within 6 months following hospitalization, and thereafter only in cooperation with the physician responsible for the patient.
_Anticoagulant treatment_ implies increased propensity for bleeding. Periodontal surgery should be scheduled first after consultation with the patient's physician to determine whether modification of the anticoagulant therapy is indicated. In patients on moderate levels of anticoagulation and only requiring minor surgical treatment, no alteration of their anticoagulant therapy may be required. To keep the prothrombin time within a safety level for hemorrhage control during surgery in patients with higher levels of anticoagulation, adjustments of the anticoagulant drug therapy usually needs to be initiated 2–3 days prior to the dental appointment. Anticoagulation may be safely resumed immediately after the periodontal surgical procedure since several days are needed for full anticoagulation to return. Aspirin and other non-steroidal anti-inflammatory drugs should not be used for post-operative pain control since they increase bleeding tendency. Furthermore, tetracyclines are contraindicated in patients on anticoagulant drugs due to interference with prothrombin formation (Fay & O'Neil 1984).
_Rheumatic endocarditis_ , _congenital heart lesions_ , and _heart/vascular implants_ involve risk for transmission of bacteria to heart tissues and heart implants during the transient bacteremia that follows manipulation of infected periodontal pockets. In patients with these conditions, as well as in patients at risk of hematogenous total prosthetic joint infection (for the first 2 years following joint placement), probing, scaling and root planing (including placement of antimocribial devices and prophylactic cleaning of implants and teeth where bleeding is anticipated), surgery and tooth extraction should be preceded by prescription and administration of an appropriate antibiotic at a high dose (American Dental Association – Position Statement on Antibiotic Prophylaxis 2003) and antiseptic mouth rinsing (0.2% chlorhexidine). According to the recommendations by the American Heart Association (Advisory Statement 1997), 2 grams of amoxicillin administrated orally 1 hour before the treatment is an adequate regimen. If the patient is allergic to penicillin, clindamycin (600 mg) orally 1 hour before the treatment is recommended as alternative. No second doses are recommended for any of the above dosing regimens. Tetracyclines and erythromycin are not recommended for prophylactic cardiovascular antibiotic coverage.
### Organ transplantation
In organ transplantation medications are used to prevent transplant rejection. The drug of choice today is cyclosporine A, a potent immunosuppressant drug. The adverse effects seen following cyclosporine A treatment include an increased risk for gingival enlargement as well as hypertension. In addition, hypertension seen in renal transplant recipients is often treated with calcium channel blockers. These antihypertensive agents have also been associated with gingival enlargement. As in patients on phenytoin therapy, gingival enlargement in patients on cyclosporine A therapy or on antihypertensive therapy with calcium blockers may be corrected by means of periodontal surgery. However, due to the strong propensity for recurrence, the use of intensified conservative periodontal therapy to prevent gingival enlargement in susceptible patients should be encouraged.
Prophylactic antibiotics are recommended in transplant patients taking immunosuppressive drugs, and the patient's physician should be consulted before any periodontal therapy is performed. In addition, antiseptic mouth rinsing (0.2% chlorhexidine) should precede the surgical treatment.
### Blood disorders
If the medical history includes blood disorders, the exact nature of these should be ascertained. Patients suffering from _acute leukemias_ , _agranulocytosis_ , and _lymphogranulomatosis_ must _not_ be subjected to periodontal surgery. _Anemias_ in mild and compensated forms do not preclude surgical treatment. More severe and less compensated forms may entail lowered resistance to infection and increased propensity for bleeding. In such cases, periodontal surgery should only be performed after consultation with the patient's physician.
### Hormonal disorders
_Diabetes mellitus_ entails lowered resistance to infection, propensity for delayed wound healing, and predisposition for arteriosclerosis. Well compensated patients may be subjected to periodontal surgery provided precautions are taken not to disturb dietary and insulin routines.
_Adrenal function_ may be impeded in patients receiving large doses of corticosteroids over an extended period. These conditions involve reduced resistance to physical and mental stress, and the doses of corticosteroid may have to be altered during the period of periodontal surgery. The patient's physician should be consulted.
### Neurologic disorders
_Multiple sclerosis_ and _Parkinson's disease_ may, in severe cases, make ambulatory periodontal surgery impossible. Paresis, impaired muscular function, tremor, and uncontrollable reflexes may necessitate treatment under general anesthesia.
_Epilepsy_ is often treated with _phenytoin_ that, in approximately 50% of cases, may mediate the formation of gingival enlargement. These patients may, without special restrictions, be subjected to periodontal surgery for correction of the enlargement. There is, however, a strong propensity for recurrence of the enlargement, which in many cases can be countered by intensifying plaque control.
### Smoking
Although smoking negatively affects wound healing (Siana _et al_. 1989), it may not be considered as a contraindication for surgical periodontal treatment. The clinician should be aware, however, that less resolution of probing pocket depth and smaller improvement in clinical attachment may be observed in smokers than in non-smokers (Preber & Bergström 1990; Ah _et al_. 1994; Scabbia _et al_. 2001; Labriola _et al_. 2005).
## Local anesthesia in periodontal surgery
Traditional views of pain and discomfort as an inevitable consequence of dental procedures, in particular surgical procedures (including scaling and root planing) and extractions, are no longer accepted by patients. Pain management is an ethical obligation and will improve patient satisfaction in general (e.g. increased confidence and improved cooperation) as well as patient recovery and short-term functioning after oral/periodontal surgical procedures. In order to prevent pain during the performance of a periodontal surgical procedure, the entire area of the dentition scheduled for surgery, the teeth as well as the periodontal tissues, require proper local anesthesia.
### Mechanism of action
Local anesthesia is defined as a loss of feeling or sensation that is confined to a certain area of the body. All local anesthetics have a common mechanism of action. To produce their effect they block the generation and propagation of impulses along nerve fibers. Such impulses are transmitted by rapid depolarization and repolarization within the nerve axons. These changes in polarity are due to the passage of sodium and potassium ions across the nerve membrane through ionic channels within the membrane. Local anesthetics prevent the inward movement of sodium ions, which initiate depolarization, and as a consequence the nerve fiber cannot propagate any impulse. The potassium efflux, on the other hand, is influenced very little and there is no change in the resting potential. The mechanisms behind the activity of the local anesthetics are not fully understood, but the most plausible theory is that the lipid-soluble free base form of the local anesthetic, which is the form that penetrates biologic membranes most easily, penetrates the connective tissue to reach the axons and diffuses across the lipid membrane into the axon. Inside the axon the drug interacts with specific receptor sites on or within the sodium channels to exert an inhibitory effect on sodium influx and, consequently, on impulse conduction.
### Dental local anesthetics
Anesthetics from the chemical group amino-amides, for example lidocaine, mepivacaine, prilocaine, and articaine, are more potent and significantly less allergenic than amino-esters (e.g. procaine and tetracaine) and have therefore replaced esters as the "gold standard" for dental local anesthetics.
Due to the specific need for bone penetration, dental local anesthetics contain high concentrations of the active agent. Although most amide local anesthetics may cause local vasoconstriction in low concentrations, the clinically used concentrations in dental solutions will cause an increase in the local blood flow. Significant clinical effects of this induced vasodilatation are an increased rate of absorption, thus decreasing the duration of anesthesia. Major benefits can therefore be obtained by adding relatively high concentrations of vasoconstrictors (e.g. epinephrine >1 : 200 000 or >5 mg/ml) to dental local anesthetic solutions; the duration is considerably prolonged, the depth of anesthesia may be enhanced, and the peak concentrations of the local anesthetic in blood can be reduced. Furthermore, in periodontal surgery incorporation of adrenergic vasoconstrictors into the local anesthetic is of considerable value to allow for only minimal bleeding during surgery (to avoid considerable blood loss, to visualize the surgical site, and shorten the time spent on the procedure maintaining surgical quality). As a matter of fact, the use of a dental local anesthetic without a vasoconstrictor during a periodontal surgical procedure is counterproductive because the vasodilating properties of such a local anesthetic will increase bleeding in the area of surgery.
### Vasoconstrictors and local hemostasis
Epinephrine is the vasoconstrictor of choice for local hemostasis and is most commonly used in a concentration of 1 : 80 000 (12.5 mg/ml). However, 1 : 100 000 epinephrine also provides excellent hemostasis and most periodontists are unable to detect a clinical difference between the two concentrations. It therefore seems prudent to use the least concentrated form of epinephrine that provides clinically effective hemostasis (i.e. the 1 : 100 000 concentration).
Although the cardiovascular effects of the usually small amounts of epinehrine used during a periodontal surgical procedure are of little practical concern in most individuals, accidental intravascular injections, unusual patient sensitivity and unanticipated drug interactions (or excessive doses), can result in potentially serious outcomes. It must also be understood that the use of epinephrine for hemostasis during periodontal surgery has some potential drawbacks. Epinephrine will produce a rebound vasodilatation after the vasoconstriction has worn off leading to increased risk for bleeding in the immediate postoperative period. There is a greater potential for such undesirable delayed hemorrhage following the use of 1 : 80 000 epinephrine than after the use of 1 : 100 000.
Post-operative pain may increase and wound healing may be delayed when adrenergic vasoconstrictors are used because of local ischemia with subsequent tissue acidosis and accumulation of inflammatory mediators. Furthermore, the possibility of an ischemic necrosis of surgical flaps infiltrated with an adrenergic vasoconstrictor (especially if norepinephrine is used instead of epinephrine) cannot be discounted. For these reasons as well as for the possibility of systemic reactions eluded to above, dental local anesthetics containing adrenergic vasoconstrictors for hemostasis should be infiltrated _only_ as needed and _not_ merely by habit.
Felypressin, another commonly used vasoconstrictor, appears to act preferentially on the venous side of the microcirculation and is not very active in constricting the arteriolar circulation. Felypressin is therefore not nearly as effective as adrenergic vasoconstrictors in limiting hemorrhage during a surgical procedure.
### Individual variability in response to dental local anesthetics
Although it is possible for the periodontist to choose from a broad spectrum of dental local anesthetics to achieve the expected clinical action, there is a number of other factors (i.e. not related to the drug) that can affect the drug action in a single patient. During clinical conditions the variability in response to dental local anesthetics administered can be expected to be great, for example with regard to depth and duration of anesthesia. The reasons for the great variation have not been adequately explained but have to be accepted as the variation may have significant implications in periodontal surgical procedures. A list of possible factors that may cause anesthetic failures include:
* Accuracy in administration of the drug
* Anatomic variation between patients (e.g. in elderly patients with bone resorption)
* Status of the tissues at the site of injection (vascularity, inflammation)
* General condition of patient
* Psychologic factors.
Inaccuracy in administration is a major factor causing anesthetic failures. Although not particularly significant in infiltration anesthesia, the mandibular block is a prime example of a technique in which duration of anesthesia is greatly influenced by accuracy of injection.
The general condition of the patient as well as psychologic factors may also affect the anticipated duration of action. Infection, stress or pain will usually lead to decreased duration of anesthesia, while an increase in the patient's own defense mechanisms against pain perception by, for example, release of endogenous endorphins, may provide for improved depth and/or duration of anesthesia.
### Techniques for anesthesia in periodontal surgery
Injections of dental local anesthetics prior to a periodontal surgical procedure may be routine for the dentist, but is often a most unpleasant experience for the patient. Reassurance and psychologic support are essential and will increase the patient's confidence in his dentist. To create a relaxed atmosphere and to decrease the patient's fear in an unusual situation is of course also a useful way of increasing the patient's own defense mechanisms against pain perception (e.g. release of endogenous endorphins).
Anesthesia for periodontal surgery is obtained by nerve block and/or by local infiltration. In cases of flap surgery, complete anesthesia must be attained before commencing the operation, as it may be difficult to supplement the anesthesia after the bone surface has been exposed. In addition, the pain elicited by needle insertion can be significantly reduced if the mucosa at the puncture site is anesthetized in advance by the use of a suitable topical ointment or spray.
Local infiltration may have a greatly decreased rate of success in areas where inflammation remains in the periodontal tissues, in spite of optimal conservative periodontal therapy and good oral hygiene. The suggested reason being that tissue pH tends to be low in inflamed areas and anesthetic solutions are less potent at low pH because there is a greater proportion of charged cation molecules than of the uncharged base molecules. Because of this, diffusion of the local anesthetic into the axoplasm is slower with subsequent delayed onset and decreased efficacy. Another more recent hypothesis suggests that NGF (nerve growth factor) released during tissue inflammation will induce sprouting or proliferation of sensory nerve endings expressing a different (sub-) type of sodium channel than is expressed in normal tissues. Our presently used dental local anesthetics may not be selective enough for proper interaction with these sodium channel subtypes to induce anticipated anesthesia.
### Local anesthesia in the mandible
As a rule, analgesia of the teeth and the soft and hard tissues of the mandible should be obtained by a mandibular block and/or a mental block. In the anterior region of the mandible, canines and incisors can often be anesthetized by infiltration, but there are often anastomoses over the midline. These anastomoses must be anaesthetized by bilateral infiltration, or by bilateral mental blocks. The buccal soft tissues of the mandible are anesthetized by local infiltration or by blocking the buccal nerve. Local infiltration, performed as a series of injections in the buccal fold of the treatment area, has of course the added advantage of providing a local ischemic effect if a suitable anesthetic is used.
The lingual periodontal tissues must also be anesthetized. This is accomplished by blocking the lingual nerve and/or by infiltration in the floor of the mouth close to the site of operation. If necessary to obtain proper ischemia, and only then, supplementary injections may be made in the interdental papillae (intraseptal injections).
### Local anesthesia in the maxilla
Local anesthesia of the teeth and buccal periodontal tissues of the maxilla can easily be obtained by injections in the muco-gingival fold of the treatment area. If larger areas of the maxillary dentition are scheduled for surgery, repeated injections (in the mucogingival fold) have to be performed, e.g. at the central incisor, canine, second premolar, and second molar. In the posterior maxillary region a tuberosity injection can be used to block the superior alveolar branches of the maxillary nerve. However, because of the vicinity to the pterygoid venous plexus, this type of block anesthesia is not recommended due to the risk of intravenous injection and/or hematoma formation.
The palatal nerves are most easily anesthetized by injections made at right angles to the mucosa and placed around 10 mm apical to the gingival margin adjacent to teeth included in the operation. In cases of advanced bone loss, the pain produced by injecting into the non-resilient palatal mucosa can be minimized if the injections are performed from the buccal aspect, i.e. through the interdental gingiva. Sometimes blocks of the nasopalatine nerves and/or the greater palatine nerves can be applied. Supplementary blocking of the greater palatine nerve should be considered, especially for periodontal surgery involving molars.
## Instruments used in periodontal surgery
### General considerations
Surgical procedures used in periodontal therapy often involve the following measures (instruments):
* Incision and excision (periodontal knives)
* Deflection and re-adaptation of mucosal flaps (periosteal elevators)
* Removal of adherent fibrous and granulomatous tissue (soft tissue rongeurs and tissue scissors)
* Scaling and root planing (scalers and curettes)
* Removal of bone tissue (bone rongeurs, chisels, and files)
* Root sectioning (burs)
* Suturing (sutures and needle holders, suture scissors)
* Application of wound dressing (plastic instruments).
**Fig. 38-44** Set of instruments used for periodontal surgery and included in a standard tray.)
The set of instruments used for the various periodontal surgical procedures should have a comparatively simple design. As a general rule, the number and varieties of instruments should be kept to a minimum. In addition to particular instruments used for periodontal treatment modalities, equipment and instruments generally used in oral surgery are often needed. Within each category of surgical instruments used for periodontal therapy there are usually several brands available, varying in form and quality, leaving ample room for individual preferences.
The instruments should be stored in sterile "readyto-use" packs or trays. Handling, storing, and labeling of surgical instruments and equipment must be managed in such a way that interchanging of sterile and non-sterile items is prevented.
It is also important that the instruments are kept in good working condition. The maintenance routine should ensure that scalers, curettes, knives with fixed blades, etc., are sharp and the hinges of scissors, rongeurs, and needle holders are properly lubricated. Spare instruments (sterile) should always be available to replace instruments found to be defective or accidentally contaminated.
### The instrument tray
Instrument trays for periodontal surgery may be arranged in several ways. Different trays can be used for different procedures or a standard tray can be used for all procedures supplemented with the particular instruments that are needed for a specific procedure.
A commonly used standard tray combines the basic set of instruments used in oral surgery and a few periodontal instruments. The instruments listed below are often found on such a standard tray ( **Fig. 38-44**) :
* Mouth mirrors
* Graduated periodontal probe/explorer
* Handles for disposable surgical blades (e.g. Bard-Parker handle)
* Mucoperiosteal elevator and tissue retractor
* Scalers and curettes
* Cotton pliers
* Tissue pliers ( _ad modum_ Ewald)
* Tissue scissors
* Needle holder
* Suture scissors
* Plastic instrument
* Hemostat
* Burs.
Additional equipment may include:
* Syringe for local anesthesia
* Syringe for irrigation
* Aspirator tip
* Physiologic saline
* Drapings for the patient
* Surgical gloves, surgical mask, surgeon's hood.
### Surgical instruments
#### _Knives_
Knives are available with fixed or replaceable blades. The advantage of the fixed blade versions is that the blade can be given any desired shape and orientation in relation to the handle. A disadvantage is that such instruments need frequent resharpening. Figure 38-45 shows examples of knives with fixed blades.
New disposable blades are always sharp. They can be rapidly replaced if found defective. The cutting edge of the blades normally follows the long axis of the handle, which limits their use. However, knives with disposable blades fitted at an angle to the handle are also available. Disposable blades are manufactured in different shapes ( **Fig. 38-46**). When mounted in ordinary handles (Bard-Parker®), they are used for releasing incisions in flap operations and mucogingival surgery and for reverse bevel incisions where access is obtainable. Special handles ( **Fig. 38-47**) make it possible to mount blades in angulated positions, which facilitate the use of such knives for both gingivectomy excisions and reverse bevel incisions.
**Fig. 38-45** Examples of gingivectomy knives with fixed blades. From left to right: Kirkland 15/16, Orban 1/2, and Waerhaug 1/2.
**Fig. 38-46** Disposable blades which can be mounted in various types of handles. The shape of the blades are from left to right: No. 11, No. 12, No. 12D, No. 15, and No. 15C.
#### _Scalers and curettes_
Scaling and root planing in conjunction with periodontal surgery take place on exposed root surfaces. Access to the root surfaces for debridement may therefore be obtained with the use of comparatively sturdy instruments ( **Fig. 38-48**). Tungsten carbide curettes and scalers with durable cutting edges are often used when "access" is not a problem. Rotating fine-grained diamond stones ( **Fig. 38-49**) may be used within infrabony pockets, root concavities, and entrances to furcations.
**Fig. 38-47** A universal 360º handle for disposable blades, which allows the mounting of the blade in any angulated position of choice.
**Fig. 38-48** Examples of double-ended sickle scalers and curettes useful for root debridement in conjunction with periodontal surgery. From left to right: Curette SG 215/16C Syntette, Sickle 215-216 Syntette, and mini-curette SG 215/16MC.
**Fig. 38-49** A set of burs useful in periodontal surgery. The rotating fine-grained diamond stones may be used for debridement of infrabony defects. The round burs are used for bone recontouring.
**Fig. 38-50** Examples of instruments used for bone recontouring. From left to right: Bone chisels Ochsenbein no. 1 and 2 (Kirkland 13K/13KL), Bone chisel Ochsenbein no. 3, and Schluger curved file no. 9/10.
#### _Instruments for bone removal_
Sharp bone chisels or bone rongeurs ( **Fig. 38-50**) cause the least tissue damage and should be employed whenever access permits. With reduced access, surgical burs or files may be used. The burs should operate at low speed and ample rinsing with sterile physiologic saline should ensure cooling and removal of tissue remnants.
#### _Instruments for handling flaps_
The proper healing of the periodontal wound is critical for the success of the operation. It is therefore important that the manipulations of soft tissue flaps are performed with the minimum of tissue damage. Care should be exercised in the use of periosteal elevators when flaps are deflected and retracted for optimal visibility. Surgical pliers and tissue retractors that pierce the tissues should not be used in the marginal area of the flaps. Needle holders with small beaks and atraumatic sutures should be used.
#### _Additional equipment_
Hemorrhage is rarely a problem in periodontal surgery. The characteristic oozing type of bleeding can normally be controlled by a pressure pack (sterile gauze moistened with saline). Bleeding from small vessels can be stopped by clamping and tying using a hemostat and resorbable sutures. If the vessel is surrounded by bone, bleeding may be stopped by crushing the nutrient canal in which the vessel runs with a blunt instrument.
Sterile physiologic saline is used for rinsing and moistening the field of operation and for cooling when burs are employed. The saline solution may be kept in a sterile metal cup on the instrument tray and may be applied to the wound by means of a sterile disposable plastic syringe and a needle with a blunt tip.
Periodontal Surgery: Access Therapy 805
Visibility in the field of operation is secured by using effective suction. The lumen of the aspirator tip should have a smaller diameter than the rest of the tube, in order to prevent clogging.
The patient's head may be covered by autoclaved cotton drapings or sterile disposable plastic/paper drapings. The surgeon and all assistants should wear sterile surgical gloves, surgical mask, and surgeon's hood.
## Selection of surgical technique
Many of the technical problems experienced in periodontal surgery stem from the difficulties in accurately assessing the degree and type of breakdown that has occurred prior to surgery. Furthermore, at the time of surgery, previously undiagnosed defects may be recognized or some defects may have a more complex outline than initially anticipated. Since each of the surgical procedures described above is designed to deal with a specific situation or to meet a certain objective, it must be understood that in most patients no single standardized technique alone can be applied when periodontal surgery is undertaken. Therefore, in each surgical field, different techniques are often used and combined in such a way that the overall objectives of the surgical part of the periodontal therapy are met. As a general rule, surgical modalities of therapy that preserve or induce the formation of periodontal tissue should be preferred over those that resect or eliminate tissue.
### General indications for various surgical techniques
#### _Gingivectomy_
The obvious indication for gingivectomy is the presence of deep supra-alveolar pockets. In addition, the gingivectomy technique can be used to reshape abnormal gingival contours such as gingival craters and gingival hyperplasias ( **Fig. 38-43**). In such cases the technique is often termed _gingivoplasty_.
Gingivectomy is usually not considered suitable in situations where the incision will lead to the removal of the entire zone of gingiva. This is the case when the bottom of the probeable pocket to be excised is located at or below the mucogingival junction. As an alternative in such a situation, an _internal beveled gingivectomy_ may be performed ( **Fig. 38-51**). Furthermore, since the gingivectomy procedure is aimed at the complete elimination of the periodontal pocket, the procedure cannot be used in periodontal sites where infrabony lesions or bony craters are present.
These limitations, combined with the development in recent years of surgical methods which have a broader field of application, have led to less frequent use of gingivectomy in the treatment of periodontal disease.
**Fig. 38-51** Internal beveled gingivectomy. Schematic illustration of the incision technique in case of the presence of only a minimal zone of gingiva.
#### _Flap operation with or without osseous surgery_
Flap operations can be used in all cases where surgical treatment of periodontal disease is indicated. Flap procedures are particularly useful at sites where pockets extend beyond the muco-gingival border and/or where treatment of bony lesions and furcation involvements is required.
The advantages of flap operations include:
* Existing gingiva is preserved
* The marginal alveolar bone is exposed whereby the morphology of bony defects can be identified and the proper treatment rendered
* Furcation areas are exposed, the degree of involvement and the "tooth–bone" relationship can be identified
* The flap can be repositioned at its original level or shifted apically, thereby making it possible to adjust the gingival margin to the local conditions
* The flap procedure preserves the oral epithelium and often makes the use of surgical dressing superfluous
* The post-operative period is usually less unpleasant to the patient when compared to gingivectomy.
### Treatment decisions for soft and hard tissue pockets in flap surgery
Classifications of different flap modalities used in the treatment of periodontal disease often make distinctions between methods involving the marginal tissues and those involving the muco-gingival area and, further, between tissue-eliminating/resective varieties and tissue-preserving/reconstructive types (access flaps for debridement). Such classifications appear less than precise since several techniques are often combined in the treatment of individual cases, and since there is no clear-cut relationship between disease characteristics and selection of surgical methods. From a didactic point of view it seems more appropriate to discuss surgical therapy with regard to how to deal with (1) the soft tissue component and (2) the hard tissue component of the periodontal pocket at a specific tooth site ( **Fig. 38-52**).
#### _Soft tissue pockets_
The description of the various flap procedures reveals that, depending on the surgical technique used, the soft tissue flap should either be apically positioned at the level of the bone crest (original Widman flap, Neumann flap, and apically repositioned flap) or maintained in a coronal position (Kirkland flap, modified Widman flap, and papilla preservation flap) at the completion of the surgical intervention. The maintenance of the pre-surgical soft tissue height is of importance from an esthetic point of view, particularly in the anterior tooth region. However, long-term results from clinical trials have shown that major differences in the final position of the soft tissue margin are not evident between surgical procedures involving coronal and apical positioning of the flap margin. The reported difference in final positioning of the gingival margin between surgical techniques is attributed to osseous recontouring (Townsend-Olsen _et al_. 1985; Lindhe _et al_. 1987; Kaldahl _et al_. 1996; Becker _et al_. 2001). In many patients it may be of significance to position the flap coronally in the anterior tooth region in order to give the patient a prolonged time of adaptation to the inevitable soft tissue recession. In the posterior tooth region, however, an apical position should be the standard.
Independent of flap position, the goal should be to achieve complete soft tissue coverage of the alveolar bone, not only at buccal/lingual sites but also in proximal sites. It is therefore of utmost importance to carefully plan the incisions in such a way that this goal can be achieved at the termination of the surgical intervention.
**Fig. 38-52** Surgical decisions. Treatment decisions with respect to the soft and the hard tissue component of a periodontal pocket.
#### _Hard tissue pockets_
During conventional periodontal surgery one would usually opt for the conversion of an intrabony defect into a suprabony defect, which then is eliminated by apical repositioning of the soft tissues. Osseous recontouring of angular bony defects and craters are excisional techniques, which should be used with caution and discrimination. However, the therapist is often faced with the dilemma of deciding whether or not to eliminate an angular bony defect. There are a number of factors that should be considered in the treatment decision, such as:
* Esthetics
* Tooth/tooth site involved
* Defect morphology
* Amount of remaining periodontium.
Since alveolar bone supports the soft tissue, an altered bone level through recontouring will result in recession of the soft tissue margin. For esthetic reasons one may therefore be restrictive in eliminating proximal bony defects in the anterior tooth region. For example, in the case of an approximal crater it may often be sufficient to reduce/eliminate the bone wall on the lingual side of the crater, thereby maintaining the bone support for the soft tissue on the facial aspect ( **Fig. 38-40**). In favor of esthetics one may even have to compromise the amount of bone removal and accept that some pocket depth will remain in certain situations. In addition to esthetics, the presence of furcations may limit the extent to which bone recontouring can be performed.
Defect morphology is a variable of significance for repair/regeneration during healing (Rosling _et al_. 1976a; Cortellini _et al_. 1993, 1995a). While two- and, especially, three-wall defects may show great potential for repair/regeneration, one-wall defects and approximal craters will rarely result in such good healing. Further, the removal of intrabony connective tissue/granulation tissue during a surgical procedure will always lead to crestal resorption of bone, especially in sites with thin bony walls. This results in reduction of the vertical dimensions of the bone tissue at the site ( **Fig. 38-53**). Thus, the potential for bone fill following a compromise in regard to osseous surgery is greater in areas with thick, non-supporting bone.
**Fig. 38-53** Illustration of the amount of crestal bone resorption that may take place following a modified Widman flap procedure without bone recontouring. (a) View of the area at time of initial surgical treatment. (b) At the re-entry operation performed after 6 months of healing.
The various treatment options available for the hard tissue defect may include:
* Elimination of the osseous defect by resection of bone (osteoplasty and/or ostectomy)
* Maintenance of the area without osseous resection (hoping for some type of periodontal repair, e.g. bone fill leading to gain of clinical attachment)
* Compromising the amount of bone removal and accepting that a certain pocket depth will remain
* An attempt to improve healing through the use of a regenerative procedure
* Extract the involved tooth if the bony defect is considered too advanced.
After careful consideration, indications for osseous surgery in conjunction with apical repositioning of flaps may also include subgingival caries, perforations or root fractures in the coronal third of the root as well as inadequate retention for fixed prosthetic restorations due to a short clinical crown (crown-lengthening procedures). The "crown lengthening" needed in such cases is performed by removing often significant amounts of supporting bone and by recontouring. A "biologic width" of approximately 3 mm between the alveolar bone crest to be established and the anticipated restoration margin must be ensured for successful results (Brägger _et al_. 1992; Herrero _et al_. 1995; Pontoriero & Carnevale 2001).
## Root surface instrumentation
Before incisions are made to excise or elevate the soft tissue, a careful examination should be carried out to identify at which tooth sites periodontal lesions remain. Only tooth sites with signs of pathology (bleeding following pocket probing) should be subjected to root instrumentation following surgical exposure. Further, at these sites root surface instrumentation should be limited to that part of the root that will be covered by the soft tissue following flap replacement and suturing. This is an important consideration since instrumentation of the supragingival portion of the root may lead to post-surgical root hypersensitivity, which in turn may impede proper oral hygiene measures. Before root instrumentation is executed, therefore, remaining granulation tissue must be removed, bone recontouring is carried out, if indicated, and the post-surgical soft tissue level is determined. If the intention is to reposition the flap apically at the level of the bone crest, only approximately 3 mm of the root surface coronal to the bone crest has to be carefully scaled and root planed, whereas if the flap is to be positioned coronally the entire exposed root has to be instrumented.
The root instrumentation can be performed with hand or ultrasonic instruments according to the operator's preferences. Ultrasonic (sonic) instrumentation offers the additional benefits of improved visibility due to the irrigating effect of the cooling water. For root instrumentation within intrabony defects, root concavities, and entrances to furcations, the use of rotating fine-grained diamond stones may be used.
## Root surface conditioning/biomodification
An important consideration in periodontal surgery is to make the exposed root surface biologically compatible with a healthy periodontium. This so-called conditioning includes removing bacteria, endotoxins, and other antigens found within the cementum–dentin of a pathologically exposed root. In addition to scaling and root planing, agents such as citric acid/orthophosphoric acid, tetracycline, and EDTA are used for root surface conditioning. Root surface conditioning/biomodification by means of an etching procedure may serve several purposes:
* Removal of the smear layer following mechanical debridement
* Demineralization of the root surface (citric acid)
* Selective removal of hydroxyapatite and exposure of the collagenous matrix of the root surface (EDTA)
* Local delivery of antimicrobial compound (tetracycline HCL)
* Inhibition of collagenolytic activity (tetracycline HCL)
* Enhancing cellular responses
* Preventing of epithelial down-growth
* Improving retention of different biomolecules to exposed collagen
* To express a cementoblast phenotype for colonizing cells.
It should be noted that etching of a root surface with an agent operating at a low pH, e.g. citric acid or orthophosphoric acid, might exert immediate necrotizing effects on the surrounding periodontal ligament and other periodontal tissues, whereas agents operating at a neutral pH (e.g. EDTA) do not seem to have this negative effect (Blomlöf & Lindskog 1995a,b).
Although _in vitro_ results have indicated possible benefits of the use of root surface conditioning/ biomodification agents through enhanced cellular responses during wound healing, the usefulness of acids as well as other chemical agents for conditioning of root surfaces in conjunction with conventional periodontal surgery has been questioned (Blomlöf _et al_. 2000). Histologic evidence indicates that healing following root surface conditioning with acids or other chemical agents is generally dominated by a long junctional epithelium or connective tissue attachment without evidence of new cementum formation. However, root surface biomodification must still be regarded as an important method to facilitate regeneration. Thus, in this treatment the root represents one of the wound margins and must provide an appropriate surface for cell attachment, colonization, and proliferation.
## Suturing
When a flap procedure has been employed it is important to ensure that, at the end of surgery, the flaps are placed in the intended position and that the flaps are properly adapted to each other and to the tooth surfaces. Preferably, full coverage of the buccal/ lingual (palatal) and interdental alveolar bone should be obtained by full (primary) closure of the soft tissue flaps. If this can be achieved, healing by first intention results and post-operative bone resorption is minimal. Therefore, prior to suturing, the flap margins should be trimmed to properly fit the buccal and lingual (palatal) bone margin as well as the interproximal areas; excessive soft tissue must be removed. If the amount of flap tissue present is insufficient to cover the interproximal bone, the flaps at the buccal or lingual aspects of the teeth must be recontoured and, in some cases, even displaced coronally.
Following proper trimming, the flaps are secured in the correct position by sutures. Sutures should not interfere with incision lines and must not pass through the tissues near the flap margins or too close to a papilla, because this may result in tearing of the tissues. The use of non-irritating, mono-filamentous materials is recommended. These materials are nonresorbable and extremely inert, do not adhere to tissues, and are therefore easy to pull out. "Wicking", the phenomenon of bacteria moving along or within multi-stranded suture materials, particularly silk, is also avoided. The dimensions usually preferred are 4/0 to 5/0, but even finer suture material (6/0 or 7/0) may be used, particularly in conjunction with periodontal micro- and plastic surgical procedures. Sutures are removed after 7–14 days.
Since the flap tissue following the final preparation is thin, either curved or straight non-traumatic needles (eyeless), with a small diameter, should be used. Such needles are available as rounded (noncutting) or with different cutting edges. In the latter case, a reverse-cutting needle should be selected.
### Suturing technique
The three most frequently used sutures in periodontal flap surgery are:
* Interrupted interdental sutures
* Suspensory sutures
* Continuous sutures.
The _interrupted interdental suture_ ( **Fig. 38-54**) provides a close interdental adaptation between the buccal and lingual flaps with equal tension on both units. This type of suture is therefore not recommended when the buccal and lingual flaps are repositioned at different levels. When this technique of suturing is employed, the needle is passed through the buccal flap from the external surface, across the interdental area and through the lingual flap from the internal surface, or vice versa. When closing the suture, care must be taken to avoid tearing the flap tissues.
In order to avoid having the suture material between the mucosa and the alveolar bone in the interdental area, an alternative technique in the use of the interrupted interdental suture can be used if the flaps have not been elevated beyond the mucogingival line ( **Fig. 38-55**). With the use of a curved needle the suture is anchored in the attached tissue on the buccal aspect of the proximal site, the suture brought to the lingual side through the proximal sites, and anchored in the attached tissue on the lingual side. The suture is then brought back to the starting point and tied (Fig. 38-55b). Hence, the suture will be lying on the surface of the interdental tissue, keeping the soft tissue flaps in close contact with the underlying bone.
**Fig. 38-54** Suturing. Interrupted interdental suture.
**Fig. 38-55** Suturing. Modified interrupted interdental suture. Note that with this suturing technique the suture is laying on the surface of the interdental tissue keeping the soft tissue flaps in close contact with the underlying bone.
In regenerative procedures, which usually require a coronal advancement of the flap, a _modified mattress suture_ may be used to secure close flap adaptation ( **Fig. 38-56**). The needle is passed through the buccal flap from the external surface, across the interdental area and through the lingual flap from the internal surface. The suture is run back to the buccal side by passing the needle through the lingual and buccal flaps. Thereafter, the suture is brought through the approximal site coronally to the tissue, passed through the loop of the suture on the lingual aspect, and then brought back to the starting point on the buccal side and tied.
**Fig. 38-56** Suturing. Modified mattress suture.
**Fig. 38-57** Suturing. Suspensory suture.
**Fig. 38-58** Suturing. Continuous suture.
The _suspensory suture_ ( **Fig. 38-57**) is used primarily when the surgical procedure is of limited extent and involves only the tissue of the buccal or lingual aspect of the teeth. It is also the suture of choice when the buccal and lingual flaps are repositioned at different levels. The needle is passed through the buccal flap from its external surface at the mesial side of the tooth, the suture is placed around the lingual surface of the tooth and the needle is passed through the buccal flap on the distal side of the tooth (Fig. 38-57a). The suture is brought back to the starting point via the lingual surface of the tooth and tied (Figs. 38-57b,c). If a lingual flap has been elevated as well, this is secured in the intended position using the same technique.
The _continuous suture_ ( **Fig. 38-58**) is commonly used when flaps involving several teeth are to be repositioned apically. When flaps have been elevated on both sides of the teeth, one flap at a time is secured in its correct position. The suturing procedure is started at the mesial/distal aspect of the buccal flap by passing the needle through the flap and across the interdental area. The suture is laid around the lingual surface of the tooth and returned to the buccal side through the next interdental space. The procedure is repeated tooth by tooth until the distal/mesial end of the flap is reached. Thereafter, the needle is passed through the lingual flap (Fig. 38-58a), with the suture laid around the buccal aspect of each tooth and through each interproximal space. When the suturing of the lingual flap is completed and the needle has been brought back to the first interdental area, the positions of the flaps are adjusted and secured in their proper positions by closing the suture (Fig. 38-58b). Thus, only one knot is needed.
## Periodontal dressings
Periodontal dressings are mainly used:
* To protect the wound post-surgically
* To obtain and maintain a close adaptation of the mucosal flaps to the underlying bone (especially when a flap has been repositioned apically)
* For the comfort of the patient.
In addition, periodontal dressings can prevent post-operative bleeding during the initial phase of healing and, if properly placed in the operated segment (especially interproximally), prevent the formation of excessive granulation tissue.
Periodontal dressings should have the following properties:
* The dressing should be soft, but still have enough plasticity and flexibility to facilitate its placement in the operated area and to allow proper adaptation.
* The dressing should harden within a reasonable time.
* After setting, the dressing should be sufficiently rigid to prevent fracture and dislocation.
* The dressing should have a smooth surface after setting to prevent irritation to the cheeks and lips.
* The dressing should preferably have bacteriocidal properties to prevent excessive plaque formation.
* The dressing must not detrimentally interfere with healing.
It has been suggested that antibacterial agents should be incorporated in periodontal dressings to prevent bacterial growth in the wound area during healing. Results from clinical studies and _in vitro_ evaluation of the antibacterial properties of various periodontal dressings, however, suggest that the antibacterial activity of most commercial dressings probably is exhausted long before the end of the 7– 14-day period during which the dressing is frequently maintained in the operated segment (O'Neil 1975; Haugen _et al_. 1977).
Mouth rinsing with antibacterial agents such as chlorhexidine does not prevent the formation of plaque _under_ the dressing (Plüss _et al_. 1975) and should therefore not be regarded as a means to improve or shorten the period of wound healing. On the other hand, results from clinical studies as well as clinical experience suggest that a periodontal dressing may often be unnecessary or even undesirable after periodontal flap procedures and may be usefully replaced by rinsing with chlorhexidine only (Sanz _et al_. 1989; Vaughan & Garnick 1989).
A commonly used periodontal dressing is Coe-PakTM (Coe Laboratories Inc., Chicago, IL, USA), which is supplied in two tubes. One tube contains oxides of various metals (mainly zinc oxide) and lorothidol (a fungicide). The second tube contains nonionizing carboxylic acids and chlorothymol (a bacteriostatic agent). Equal parts from both tubes are mixed together immediately prior to insertion. Adding a retarder can prolong the setting time of the dressing.
A light-cured dressing, e.g. BarricaidTM (Dentsply International Inc., Milford, DE, USA), is useful in the anterior tooth region and particularly following muco-gingival surgery, because it has a favorable esthetic appearance and it can be applied without dislocating the soft tissue. However, the light-cured dressing is not the choice of dressing for situations where the flap has to be retained apically, due to its soft state before curing.
Cyanoacrylates have also been used as periodontal dressings with varying success. Dressings of the cyanoacrylate type are applied in a liquid directly on to the wound, or sprayed over the wound surface. Although the application of this kind of dressing is simple, its properties often do not meet clinical demands, which is why its use is rather limited at present.
### Application technique
* Ensure that bleeding from the operated tissues has ceased before the dressing material is inserted.
* Carefully dry teeth and soft tissue before the application for optimal adherence of the dressing.
* Moisten the surgical gloves to avoid the material sticking to the fingertips.
* When using the Coe-PakTM dressing material, the interproximal areas are filled first. Thin rolls of the dressing, adjusted in length to cover the entire field of operation, are then placed against the buccal and lingual surfaces of the teeth. The rolls are pressed against the tooth surfaces and the dressing material is forced into the interproximal areas. Coe-PakTM may also be applied to the wound surfaces by means of a plastic syringe. It is important to ensure that dressing material is never introduced between the flap and the underlying bone or root surface.
* The surface of the dressing is subsequently smoothened and excess material is removed with a suitable instrument. The dressing should not cover more than the apical third of the tooth surfaces. Furthermore, interference of the dressing with muco-gingival structures (e.g. vestibular fold, frenula) should be carefully checked to avoid displacement of the dressing during normal function.
The light-cured dressing (BarricaidTM) is preferably applied with the supplied syringe, adjusted and then cured by light. It is important to dry teeth and soft tissue carefully before application for optimal adherence. Excess of dressing material can easily be removed following curing with a knife or finishing burs in a low-speed handpiece.
## Post-operative pain control
In order to minimize post-operative pain and discomfort for the patient, surgical handling of the tissues should be as atraumatic as possible. Care should be taken during surgery to avoid unnecessary tearing of the flaps, to keep the bone moistened, and to secure complete soft tissue coverage of the alveolar bone at suturing. With a carefully performed surgical procedure most patients will normally experience only minimal post-operative problems. The pain experience is usually limited to the first days following surgery and of a level that in most patients can be adequately controlled with normally used drugs for pain control. However, it is important to recognize that pain threshold level is subjective and may vary between individuals. It is also important to give the patient information about the post-surgical sequence and that uncomplicated healing is the common event. Further, during the early phase of healing, the patient should be instructed to avoid chewing in the area subjected to surgical treatment.
## Post-surgical care
Post-operative plaque control is the most important variable in determining the long-term result of periodontal surgery. Provided proper post-operative infection control levels are established, most surgical treatment techniques will result in conditions that favor the maintenance of a healthy periodontium. Although there are other factors of a more general nature affecting surgical outcome (e.g. the systemic status of the patient at time of surgery and during healing), disease recurrence is an inevitable complication, regardless of surgical technique used, in patients not given proper post-surgical and maintenance care.
Since self-performed oral hygiene is often associated with pain and discomfort during the immediate post-surgical phase, regularly performed professional tooth cleaning is a more effective means of mechanical infection control following periodontal surgery. In the immediate post-surgical period self-performed rinsing with a suitable antiplaque agent, e.g. twice daily rinsing with 0.1–0.2% chlorhexidine solution, is recommended. Although an obvious disadvantage with the use of chlorhexidine is the staining of teeth and tongue, this is usually not a deterrent for compliance. Nevertheless, it is important to return to and maintain good mechanical oral hygiene measures as soon as possible. This is especially important since rinsing with chlorhexidine, in contrast to properly performed mechanical oral hygiene, is not likely to have any influence on subgingival recolonization of plaque.
Maintaining good post-surgical wound stability is another important factor affecting the outcome of some types of periodontal flap surgery. If wound stability is judged an important part of a specific procedure, the procedure itself as well as the postsurgical care must include measures to stabilize the healing wound (e.g. adequate suturing technique, protection from mechanical trauma to the marginal tissues during the initial healing phase). If a mucoperiosteal flap is replaced rather than repositioned apically, early apical migration of gingival epithelial cells will occur as a consequence of a break between root surface and healing connective tissue. Hence, maintenance of a tight adaptation of the flap to the root surface is essential and one may therefore consider keeping the sutures in place for longer than the 7–10 days usually prescribed following standard flap surgery.
Following suture removal, the surgically treated area is thoroughly irrigated with a dental spray and the teeth are carefully cleaned with a rubber cup and polishing paste. If the healing is satisfactory for starting mechanical tooth cleaning, the patient is instructed in gentle brushing of the operated area using a toothbrush that has been softened in hot water. Toothpicks are prescribed for cleaning the interdental area. In this early phase following surgical treatment the use of interdental brushes is abandoned due to the risk of traumatizing the interdental tissues. Visits are scheduled for supportive care at 2-week intervals to monitor the patient's plaque control closely. During this post-operative maintenance phase, adjustments of the methods for optimal self-performed mechanical cleaning are made depending on the healing status of the tissues. The time interval between visits for supportive care may gradually be increased, depending on the patient's plaque control standard.
# Outcome of surgical periodontal therapy
## Healing following surgical pocket therapy
### Gingivectomy
Within a few days following excision of the inflamed gingival soft tissues coronal to the base of the periodontal pocket, epithelial cells start to migrate over the wound surface. The epithelialization of the gingivectomy wound is usually complete within 7–14 days following surgery (Engler _et al_. 1966; Stahl _et al_. 1968). During the following weeks a new dentogingival unit is formed ( **Fig. 38-59**). The fibroblasts in the supra-alveolar tissue adjacent the tooth surface proliferate (Waerhaug 1955) and new connective tissue is laid down. If the wound healing occurs in the vicinity of a plaque-free tooth surface, a free gingival unit will form which has all the characteristics of a normal free gingiva (Hamp _et al_. 1975). The height of the newly formed free gingival unit may vary not only between different parts of the dentition but also from one tooth surface to another due to primarily anatomic factors.
The re-establishment of a new, free gingival unit by coronal regrowth of tissue from the line of the "gingivectomy" incision implies that sites with so-called "zero pockets" only occasionally occur following gingivectomy. Complete healing of the gingivectomy wound takes 4–5 weeks, although by clinical inspection the surface of the gingiva may appear to be healed already after approximately 14 days (Ramfjord _et al_. 1966). Minor remodeling of the alveolar bone crest may also occur post-operatively.
### The apically repositioned flap
Following osseous surgery for elimination of bony defects and the establishment of "physiologic contours" and repositioning of the soft tissue flaps to the level of the alveolar bone, healing will occur primarily by first intention, especially in areas where proper soft tissue coverage of the alveolar bone has been obtained. During the initial phase of healing, bone resorption of varying degrees almost always occurs in the crestal area of the alveolar bone ( **Fig. 38-60**) (Ramfjord & Costich 1968). The extent of the reduction of the alveolar bone height resulting from this resorption is related to the thickness of the bone in each specific site (Wood _et al_. 1972; Karring _et al_. 1975).
**Fig. 38-59** Gingivectomy. Dimensional changes as a result of therapy. (a) The pre-operative dimensions. The black line indicates the location of the primary incision, i.e. the suprabony pocket is eliminated with the gingivectomy technique. (b) Dimensions following proper healing. Minor resorption of the alveolar bone crest as well as some loss of connective tissue attachment may occur during the healing.
**Fig. 38-60** Apically repositioned flap. Dimensional changes. (a) The pre-operative dimensions. The broken line indicates the border of the elevated mucoperiosteal flap. (b) Bone recontouring has been completed and the flap repositioned to cover the alveolar bone. (c) Dimensions following healing. Minor resorption of the marginal alveolar bone has occurred as well as some loss of connective tissue attachment.
During the phase of tissue regeneration and maturation a new dentogingival unit will form by coronal growth of the connective tissue. This regrowth occurs in a manner similar to that which characterized healing following gingivectomy.
### The modified Widman flap
If a "modified Widman flap" procedure is carried out in an area with a deep infrabony lesion, bone repair may occur within the boundaries of the lesion (Rosling _et al_. 1976a; Polson & Heijl 1978). However, crestal bone resorption is also seen. The amount of bone fill obtained is dependent upon (1) the anatomy of the osseous defect (e.g. a three-walled infrabony defect often provides a better mould for bone repair than two- or one-walled defects), (2) the amount of crestal bone resorption, and (3) the extent of chronic inflammation, which may occupy the area of healing. Interposed between the regenerated bone tissue and the root surface, a long junctional epithelium is always found ( **Fig. 38-61**) (Caton & Zander 1976; Caton _et al_. 1980). The apical cells of the newly formed junctional epithelium are found at a level on the root that closely coincides with the presurgical attachment level.
Soft tissue recession will take place during the healing phase following a modified Widman flap procedure. Although the major apical shift in the position of the soft tissue margin will occur during the first 6 months following the surgical treatment (Lindhe _et al_. 1987), the soft tissue recession may often continue for a time period of more than 1 year. Among factors influencing the degree of soft tissue recession as well as the time period for soft tissue remodeling are the initial height and thickness of the supracrestal flap tissue and the amount of crestal bone resorption.
## Clinical outcome of surgical access therapy in comparison to non-surgical therapy
Surgical treatment of periodontal lesions mainly serves the purpose of (1) creating accessibility for proper professional debridement of the infected root surfaces and (2) establishing a gingival morphology that facilitates the patient's self-performed plaque control, in order to enhance the long-term preservation of the dentition. Hence, the amount of tooth loss would be the most relevant criterion in an evaluation of the relative importance of surgical access therapy in the overall treatment of periodontal disease. However, this would require studies with extremely long follow-up periods and, therefore, other criteria are commonly used to evaluate the efficacy of periodontal therapy, even if these may only be considered as surrogate end-points. The most commonly used outcome criteria in clinical research have been resolution of gingivitis (bleeding on probing), probing pocket depth reduction, and clinical attachment level change. An additional variable often of concern is gingival recession, since this outcome variable may affect the patient's overall appreciation of the treatment result. With regard to changes in probing attachment levels, it should be recalled that healing following conventional surgical access therapy consistently results in the formation of a junctional epithelium to a level on the root that closely coincides with the presurgical attachment level. Hence, when evaluating the outcome of various therapeutic approaches the magnitude of _gain_ of clinical attachment may be of less importance since it mainly is a measure of "pocket closure". Instead maintained probing attachment levels or further loss should be focused on as the pertinent outcome variable.
**Fig. 38-61** Modified Widman flap. Dimensional changes. (a) The pre-operative dimensions. The broken line indicates the border of the elevated mucoperiosteal flap. (b) Surgery (including currettage of the angular bone defect) is completed with the mucoperiosteal flap repositioned as close as possible to its presurgical position. (c) Dimensions following healing. Osseous repair as well as some crestal bone resorption can be expected during healing with the establishment of a "long" junctional epithetium interposed between the regenerated bone tissue and the root surface. An apical displacement of the soft tissue margin has occurred.
**Fig. 38-62** Average approximal pocket depth at the initial examination and 6, 12, and 24 months after surgery (top) and alterations in approximal attachment levels from the initial examination immediately prior to surgery to the re-examinations 6, 12, and 24 months post-operatively (bottom). Note that only areas with pockets that at the initial examination had a depth of 3 mm or more are included in the analysis. I = standard error; AFB = apically repositioned flap with bone recontouring; AF = apically repositioned flap; WFB = modified Widman flap with bone recontouring; WF = modified Widman flap; G = gingivectomy including curettage of bone defects. (Data from Nyman _et al_. 1977.)
Pioneering contributions to the understanding of the relative importance of the surgical component of periodontal therapy were generated by the classical longitudinal studies by the Michigan group (Ramfjord and co-workers) and the Gothenburg group (Lindhe and co-workers). Subsequently, several other clinical research centers contributed with important data regarding the efficacy of surgical access therapy in comparison to non-surgical periodontal therapy. The topic has been extensively reviewed in several recent publications (e.g. Kaldahl _et al_. 1993; Palcanis 1996) and some of the general conclusions from these reviews will be highlighted below.
### Plaque accumulation
An important factor to consider in the evaluation of the relative effect of the surgical component of periodontal therapy is the standard of post-operative infection control. Nyman _et al_. (1977) reported on a clinical study in which the patients received only a single episode of oral hygiene instruction before the surgical treatment and no specific post-operative supportive care. As a consequence both plaque and gingival indices remained relatively high during the 2 years of post-operative follow-up. Independent of surgical technique used, the patients showed a rebound of pocket depths to more or less pretreatment levels and further deterioration of clinical attachment levels at both proximal and lingual tooth sites ( **Fig. 38-62**). In contrast, in a parallel study in which the patients received repeated oral hygiene instructions and professional tooth-cleaning once every 2 weeks during the post-operative period (Rosling _et al_. 1976b), the patients maintained the surgically reduced pocket depth throughout the 2-year follow-up period and clinical attachment level gains were observed for most of the surgical procedures evaluated ( **Fig. 38-63**). The fact that the standard of post-operative oral hygiene is decisive for the outcome of surgical pocket therapy is further underlined by data from a 5-year longitudinal study by Lindhe _et al_. (1984), which showed that patients with a high standard of infection control maintained clinical attachment levels and probing depth reductions following treatment more consistently than patients with poor plaque control. On the other hand, professional tooth cleaning, including subgingival scaling every 3 months, may partly compensate for the negative effects of variations in self-performed plaque control (Ramfjord _et al_. 1982; Isidor & Karring 1986).
With regard to post-treatment plaque accumulation, there is no evidence to suggest that differences exist between non-surgical or surgical treatment or between various surgical procedures. In addition, most studies have shown that the magnitude of gingivitis resolution is not influenced by the treatment modality.
**Fig. 38-63** Average approximal pocket depth at the initial examination and 6, 12, and 24 months after surgery (top) and alterations in approximal attachment levels from the initial examination immediately prior to surgery to the re-examinations 6, 12, and 24 months post-operatively (bottom). Note that only areas with pockets that at the initial examination had a depth of 3 mm or more are included in the analysis. I =standard error; AFB = apically repositioned flap with bone recontouring; AF = apically repositioned flap; WFB = modified Widman flap with bone recontouring; WF = modified Widman flap; G = gingivectomy including curettage of bone defects. (Data from Rosling _et al_. 1976b.)
### Probing pocket depth reduction
All surgical procedures result in a decrease in probing pocket depths with greater reduction occurring at initially deeper sites (Knowles _et al_. 1979; Lindhe _et al_. 1984; Ramfjord _et al_. 1987; Kaldahl _et al_. 1996; Becker _et al_. 2001). Furthermore, surgical therapy generally creates greater short-term reduction of probing depth than non-surgically performed scaling and root planing. Flap surgery with bone recontouring (pocket elimination surgery) usually results in the most pronounced short-term pocket reduction. Long-term (5–8 years) results show various outcomes. Some studies reported greater probing depth reduction following surgery while others reported no differences in relation to non-surgical therapy. Also, the magnitude of the initial probing depth reduction shows a tendency to decrease with time, independent of treatment modality.
### Clinical attachment level change
In sites with shallow initial probing depth, both short- and long-term data demonstrate that surgery creates a greater loss of clinical attachment than nonsurgical treatment, whereas in sites with initially deep pockets (≥7 mm), a greater gain of clinical attachment is generally obtained (Knowles _et al_. 1979; Lindhe _et al_. 1984; Ramfjord _et al_. 1987; Kaldahl _et al_. 1996; Becker _et al_. 2001) ( **Fig. 38-64**). When clinical attachment levels following surgery with and without osseous resection were compared, either no difference was found between therapies, or flap surgery without osseous resection produced a greater gain. In addition, there was no difference in the longitudinal maintenance of clinical attachment levels between sites treated non-surgically and those treated surgically, with or without osseous resection.
Based on data generated from a clinical trial comparing non-surgical and surgical (modified Widman flap) approaches to root debridement, Lindhe _et al_. (1982b) developed the concept of _critical probing depth_ in relation to clinical attachment level change. For each treatment approach, the clinical attachment change was plotted against the initial pocket depth and regression lines were calculated ( **Fig. 38-65**). The point where the regression line crossed the horizontal axis (initial probing depth) was defined as the _critical probing depth_ (CPD), i.e. the level of pocket depth below which clinical attachment loss would occur as the result of the treatment procedure performed. The CPD was consistently found to be greater for the surgical approach than for the non-surgical treatment. Furthermore, at incisors and premolars the surgical therapy showed superior outcome only when the initial probing depth was greater than 6–7 mm, while at molars the corresponding cut-off point was 4.5 mm. The interpretation of the latter finding would be that, in the molar tooth regions, the surgical approach to root debridement offers advantages over the non-surgical approach. This interpretation is supported by the observation that inferior results are obtained by non-surgical therapy in molars compared to single-rooted teeth (Nordland _et al_. 1987; Loos _et al_. 1988). Also data generated from studies comparing closed and open root debridement in furcation sites favor surgical access therapy in the treatment of molar tooth regions (Matia _et al_. 1986).
**Fig. 38-64** Longitudinal evaluation of four treatment modalities in the three categories of initial probing depth; 1–3 mm, 4–6 mm and ≥7 mm.
RPL = scaling and root planning;
CUR = subgingival curettage;
MWF = modified Widman flap;
PEL = pocket elimination surgery.
(Data from Ramfjord _et al_. 1987, presented by Egelberg 1995.)
The removal of the pocket epithelium and the soft tissue lesion by curettage (Echeverria & Caffesse 1983; Ramfjord _et al._ 1987) or surgical excision (Lindhe & Nyman 1985) is not a prerequisite for proper healing of the treated periodontal site. In the study by Lindhe and Nyman (1985) three treatment modalities were used, i.e. excision of the soft tissue lesion during flap surgery (modified Widman flap procedure), surgery without removal of the soft tissue lesion (Kirkland flap), and non-surgical scaling and root planing. The 1-year follow-up examination revealed about 1 mm of gain in clinical attachment level for all three procedures. Thus, deliberate excision of the soft tissue lesion did not improve the healing result.
### Gingival recession
Gingival recession is an inevitable consequence of periodontal therapy. Since it occurs primarily as a result of resolution of the inflammation in the periodontal tissues, it is seen both following non-surgical and surgical therapy. Irrespective of treatment modality used, initially deeper pocket sites will experience more pronounced signs of recession of the gingival margin than sites with shallow initial probing depths (Badersten _et al_. 1984; Lindhe _et al_. 1987; Becker _et al_. 2001).
**Fig. 38-65** Diagram illustrating the gain and loss of clinical attachment (Y-axis) at incisors, premolars, and molars, calculated from measurements taken prior to and 6 months after treatment. RPL = scaling and root planning; MWF = modified Widman flap surgery. The non-surgical approach (RPL) consistently yielded lower critical probing depth (CPD) values than the surgical approach. (Data from Lindhe _et al_. 1982b.)
A general finding in short-term follow-up studies of periodontal therapy is that non-surgically performed scaling and root planing causes less gingival recession than surgical therapy, and that surgical treatment involving osseous resection results in the most pronounced recession. However, data obtained from long-term studies reveal that the initial differences seen in amount of recession between various treatment modalities diminish over time due to a coronal rebound of the soft tissue margin following surgical treatment (Kaldahl _et al_. 1996; Becker _et al_. 2001) ( **Fig. 38-66**). Lindhe and Nyman (1980) found that after an apically repositioned flap procedure the buccal gingival margin shifted to a more coronal position (about 1 mm) during 10–11 years of maintenance. In interdental areas denuded following surgery, van der Velden (1982) found an upgrowth of around 4 mm of gingival tissue 3 years after surgery, while no significant change in attachment levels was observed. A similar finding was reported by Pontoriero and Carnevale (2001) 1 year after an apically positioned flap procedure for crown lengthening.
### Bone fill in angular bone defects
The potential for bone formation in angular defects following surgical access therapy has been demonstrated in a number of studies. Rosling _et al_. (1976a) studied the healing of two- and three-wall angular bone defects following a modified Widman flap procedure, including careful curettage of the bone defect and proper root debridement, in 24 patients with multiple osseous defects. Following active treatment, patients assigned to the test group received supportive periodontal care once every 2 weeks for a 2-year period, while the patients in the control group were only recalled once a year for prophylaxis. Re-examination carried out 2 years after therapy demonstrated that the patients who had been subjected to the intensive professional tooth-cleaning regimen had experienced a mean gain of clinical attachment in the angular bone defects amounting to 3.5 mm. Measurements performed on radiographs revealed a marginal bone loss of 0.4 mm, but the remaining portion of the original bone defect (2.8 mm) was refilled with bone ( **Fig. 38-67**). All the 124 bone defects treated were completely resolved. In the control group most of the sites treated showed signs of recurrent periodontitis, including further loss of clinical attachment and alveolar bone. Similar healing results were reported by Polson and Heijl (1978). They treated 15 defects (two- and three-wall) in nine patients using a modified Widman flap procedure. Following curettage of the bone defect and root planing, the flaps were closed to achieve complete soft tissue coverage of the defect area. All patients were enrolled in a professional tooth-cleaning program. The healing was evaluated a re-entry operation 6–8 months after the initial surgery. Eleven of the 15 defects had resolved completely. The healing was characterized by a combination of coronal bone regeneration (77% of the initial depth of the defects) and marginal bone resorption (18%). The authors concluded that intrabony defects might predictably remodel after surgical debridement and establishment of optimal plaque control.
**Fig. 38-66** Longitudinal changes over 7 years in recession (top diagram) and clinical attachment levels (bottom diagram) at sites with initial probing pocket depth of >6 mm following three different periodontal treatment modalities. RPL = scaling and root planning; MWF = modified Widman flap procedure; FO = flap and osseous surgery. (Data from Kaldahl _et al_. 1996.)
**Fig. 38-67** Schematic drawing illustrating alterations in the level of the marginal bone crest and the level of the bottom of the bone defects in the test and control groups of the study by Rosling _et al_. (1976a). Distance A denotes the depth of the bone defects at the initial examination; test group 3.1 mm, control 2.5 mm. Distance B denotes resorption of the alveolar crest (b,c), which amounted to 0.4 mm in the test patients (b) and 1.4 mm in the controls (c). Distance C denotes gain or loss of bone in the apical portion of the defect. There was a refill of bone in the test patients (b) amounting to 2.8 mm, whereas a further 0.7 mm loss of bone occurred in the control patients (c).
The results from the studies referred to demonstrate that a significant bone fill may be obtained in two- and three-wall intrabony defects at single-rooted teeth, provided the post-operative supportive care is of very high quality. Two recent reviews (Laurell _et al_. 1998; Lang 2000), focusing on the outcome of surgical access therapy in angular bone defects, give additional information regarding expected bone regeneration in angular defects following open-flap debridement (modified Widman flap). In the review by Laurell _et al_. (1998) 13 studies were included representing a total of 278 treated defects with a mean depth of 4.1 mm. The weighted mean bone fill in the angular defects amounted to 1.1 mm. Lang (2000) reported an analysis of 15 studies providing data generated from radiographic assessments of the healing of 523 angular bone defects. The analysis yielded a weighted mean of 1.5 mm of bone gain. Since the included studies in these reviews showed great variability in bone fill, one may assume that the standard of post-surgical plaque control varied between the studies. As shown in the study by Rosling _et al_. (1976a), meticulous post-surgical plaque control and close professional supervision of the patients are critical for optimal healing conditions. One also has to consider that the potential for bone fill may differ depending on the morphology of the angular bone defect. Most angular defects appear as combinations of one-, two- and three-wall defects and whereas the two- and three-wall component of an angular bone defect may show great potential for bone fill during healing, the one-wall component will rarely demonstrate this type of healing.
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# Chapter 39
# Treatment of Furcation-Involved Teeth
Gianfranco Carnevale, Roberto Pontoriero, and Jan Lindhe
* * *
Terminology
Anatomy
Maxillary molars
Maxillary premolars
Mandibular molars
Other teeth
Diagnosis
Probing
Radiographs
Differential diagnosis
Trauma from occlusion
Therapy
Scaling and root planing
Furcation plasty
Tunnel preparation
Root separation and resection (RSR)
Regeneration of furcation defects
Extraction
Prognosis
* * *
Detailed knowledge of the morphology of the multi-rooted teeth and their position in the dental arch is a fundamental prerequisite for a proper understanding of problems which may occur when such teeth become involved in destructive periodontal disease. The first part of this chapter therefore includes a brief description of some important anatomic features of the root complexes and related structures of premolars and molars.
# Terminology
_Root complex_ is the portion of a tooth that is located apical to the cemento-enamel junction (CEJ), i.e. the portion that normally is covered with a root cementum. The root complex may be divided into two parts: the _root trunk_ and the _root cone(s)_ (Fig. 39-1).
The _root trunk_ represents the _undivided region_ of the root. The height of the root trunk is defined as the distance between the CEJ and the separation line (furcation) between two root cones (roots). Depending on the position of the separation line the height of the root trunk may vary from one surface to the next in one given molar or premolar.
The _root cone_ is included in the _divided region_ of the root complex. The root cone (root) may vary in size and position and may at certain levels be connected to or separated from other root cones. Two or more root cones make up the _furcated region_ of the root complex (Fig. 39-2a). The _furcation_ is the area located between individual root cones.
**Fig. 39-1** Root complex of a maxillary molar. The root complex is separated into one undivided region: the root trunk, and one divided region: the (three) root cones.
The _furcation entrance_ is the transitional area between the undivided and the divided part of the root (Fig. 39-2a,b). The _furcation fornix_ is the roof of the furcation (Fig. 39-2b).
The d _egree of separation_ is the angle of separation between two roots (cones) (Fig. 39-3a). _Divergence_ is the distance between two roots; this distance normally increases in apical direction (Fig. 39-3a). The _coefficient of separation_ is the length of the root cones in relation to the length of the root complex (Fig. 39-3b).
Fusion between divergent root cones may occur. The fusion may be complete or incomplete. In the case of an incomplete fusion, the root cones may be fused in the area close to the CEJ but separated in a more apical region of the root complex.
**Fig. 39-2** (a) Apical-occlusal view of a maxillary molar where the three root cones make up the furcated region and the three furcation entrances. (b) A buccal view of the furcation entrance and of its roof.
**Fig. 39-3** (a) Photograph illustrating the angle (degree) of separation and the divergence between the mesio-buccal and the palatal roots of a maxillary molar. (b) The coefficient of separation (A/B) of the illustrated mandibular molar is 0.8 (A = 8 mm; B = 10 mm).
# Anatomy
## Maxillary molars
As a general rule the maxillary first molar, in all respects – crown and individual roots – is larger than the second molar, which in turn is larger than the third molar.
The first and second molars most often have three roots; one mesio-buccal, one disto-buccal, and one palatal. The mesio-buccal root is normally vertically positioned while the disto-buccal and the palatal roots are inclined. The disto-buccal root projects distally and the palatal root projects in palatal direction (Fig. 39-4). The cross sections of the disto-buccal and the palatal roots are generally circular. The palatal root is generally wider in the mesio-distal than in the bucco-palatal direction. The distal surface of the mesio-buccal root has a concavity which is about 0.3 mm deep (Bower 1979a,b). This concavity gives the cross section of the mesio-buccal root an "hourglass" configuration (Fig. 39-5).
The three furcation entrances of the maxillary first and second molars vary in width and are positioned at varying distances apical to the CEJ. As a rule, the first molar has a shorter root trunk than the second molar. In the first molar the mesial furcation entrance is located about 3 mm from the CEJ, while the buccal is 3.5 mm and the distal entrance about 5 mm apical to the CEJ (Abrams & Trachtenberg 1974; Rosenberg 1988). This implies that the furcation fornix is inclined; in the mesiodistal plane the fornix is comparatively close to the CEJ at the mesial but closer to the apex at the distal surface. The buccal furcation entrance is narrower than its distal and mesial counterparts.
The degree of separation between the roots and their divergence decreases from the first to the second, and from the second to the third maxillary molar.
The mesio-buccal root of the first molar is frequently located more buccally in the arch than the disto-buccal root. If the buccal bone plate is thin, the mesio-buccal root frequently projects through the outer surface of the alveolar bone and bone fenestrations and/or dehiscences may occur.
**Fig. 39-4** Furcation entrances (a, mesial; b, buccal; c, distal) and the position of the roots of a maxillary first molar.
**Fig. 39-5** Root-shape of a maxillary first molar in a horizontal cut at the level of the coronal third of the cones. Note the circular shape of the palatal root in comparison with the mesio-distally compressed shape of the mesio-buccal root, which also exhibits a concavity in the distal aspect.
## Maxillary premolars
In about 40% of cases the maxillary first premolars have two root cones, one buccal and one palatal, and hence have a mesiodistal furcation. A concavity (about 0.5 mm deep) is often present in the furcation aspect of the buccal root. In many cases the furcation is located in the middle or in the apical third of the root complex (Fig. 39-6). The mean distance between CEJ and the furcation entrance is about 8 mm. The width of the furcation entrance is about 0.7 mm.
**Fig. 39-6** A maxillary first premolar with the furcation located in the apical third of the root complex.
## Mandibular molars
The mandibular first molar is larger than the second molar, which in turn is larger than the third molar. In the first and second molars the root complex almost always includes two root cones, one mesial and one distal. The mesial root is larger than the distal. The mesial root has a position which is mainly vertical while the distal root projects distally. The mesial root is wider in the bucco-lingual direction and has a larger cross-sectional area than the distal root. The cross section of the distal root is circular while the mesial root has an "hour-glass" shape. In addition, furrows and concavities often occur on the distal surface of the mesial root (Fig. 39-7). The distal concavity of the mesial root is more pronounced than that of the distal root (Bower 1979a,b; Svärdström & Wennström 1988).
The root trunk of the first molar is often shorter than the trunk of the second molar. The furcation entrances of the mandibular first molar, similar to those of the maxillary first molar, are located at different distances from the CEJ. Thus, the lingual entrance is frequently found more apical to the CEJ (>4 mm) than the buccal entrance (>3 mm). Thus, the furcation fornix is inclined in the bucco-lingual direction. The buccal furcation entrance is often <0.75 mm wide while the lingual entrance is >0.75 mm in most cases (Bower 1979a,b). The degree of separation and divergence between the roots decreases from the first to the third molar (Fig. 39-8).
**Fig. 39-7** "Hour-glass" shape of the mesial root – with a concavity in the distal aspect – and the circular shape of the distal root (horizontal section at the level of the coronal third of the cones).
**Fig. 39-8** From left to right, differences in degree of separation and in divergence between the root cones from the first to the mandibular third molar.
**Fig. 39-9** Radiographs illustrating morphologic variations represented by two-rooted (a) maxillary lateral incisor and (b) mandibular canine.
It should also be observed that the buccal bone plate is thinner outside the roots of the first than of the second molar. Bone fenestrations and dehiscences are, as a consequence, more frequent in the first than in the second molar region.
## Other teeth
Furcations may be present also in teeth which normally have only one root. In fact, two-rooted incisors (Fig. 39-9a), canines (Fig. 39-9b), and mandibular premolars may exist. Occasionally three-rooted maxillary premolars (Fig. 39-10a) and three-rooted mandibular molars can be found (Fig. 39-10b).
# Diagnosis
The presence of furcation-involved teeth in a periodontal patient will influence the treatment plan (see Chapter 31). The selection of procedures to be used in the treatment of periodontal disease at multi-rooted teeth can first be made when the presence and depth of furcation lesions have been assessed. In this examination traditional measures of periodontal disease are used (see Chapter 26) but special attention is paid to findings from clinical _probing_ and analysis of _radiographs_ from the premolar–molar regions.
The classification description of the involved furcation is based on the amount of periodontal tissue destruction that has occurred in the inter-radicular area, i.e. degree of "horizontal root exposure" or attachment loss that exists within the root complex. Hamp _et al_. (1975) has suggested the following classification of the involved furcation:
**Fig. 39-10** (a) Anatomic variation represented in a radiograph of a three-rooted mandibular first premolar. (b) Clinical photograph illustrating, during surgery, the separation – before extraction – of an "abnormal" second mesial root of a mandibular molar.
**Fig. 39-11** Different degrees of furcation involvement in relation to the probe (penetration/superimposition) in the inter-radicular space of a mandibular molar. (a) Degree I. (b) Degree II. (c) Degree III.
* Degree I: horizontal loss of periodontal support not exceeding one third of the width of the tooth (Fig. 39-11a).
* Degree II: horizontal loss of periodontal support exceeding one third of the width of the tooth, but not encompassing the total width of the furcation area (Fig. 39-11b).
* Degree III: horizontal "through-and-through" destruction of the periodontal tissues in the furcation area (Fig. 39-11c).
It is important to understand that each furcation entrance must be examined and each entrance must be classified according to the above criteria.
**Fig. 39-12** Easily accessible vestibular furcation entrances for probing of a (a) maxillary molar and (b) mandibular molar.
**Fig. 39-13** Common access for probing of a mesial furcation entrance of a maxillary molar. The mesial furcation entrance is generally located at the palatal aspect of the tooth, while the distal entrance is located midway between the buccal and the palatal surface.
## Probing
The buccal furcation entrance of the _maxillary molars_ and the buccal and lingual furcation entrances of the _mandibular molars_ are normally accessible for examination using a curved graduated periodontal probe (Fig. 39-12), an explorer or a small curette. The examination of approximal furcations is more difficult, in particular when neighboring teeth are present. Large contact areas between the teeth further impair access to approximal furcation entrances.
In maxillary molars the mesial furcation entrance is located much closer to the palatal than to the buccal tooth surface. Thus, the mesial furcation should be probed from the palatal aspect of the tooth (Fig. 39-13). The distal furcation entrance of a _maxillary molar_ is generally located midway between the buccal and palatal surfaces and, as a consequence, this furcation could be probed from either the buccal or the palatal aspect of the tooth.
In _maxillary premolars_ the root anatomy often varies considerably. The roots may also harbor irregularities such as longitudinal furrows, invaginations or true furcations, which may open at varying distances from the CEJ. Due to the above variations and limited access, the clinical assessment of a furcation involvement in maxillary premolars is often difficult. In some patients, a furcation involvement may, in such teeth, first be identified after the elevation of a soft tissue flap.
**Fig. 39-14** Radiograph showing the location of the interdental bone level in relation to the furcation entrances of the maxillary first and second molar.
## Radiographs
Radiographs must always be obtained to confirm findings made during probing of a furcation-involved tooth. The radiographic examination should include both paralleling "periapical" and vertical "bite-wing" radiographs. In the radiographs the location of the interdental bone as well as the bone level within the root complex should be examined (Fig. 39-14). Situations may occur when findings from clinical probing and from the radiographs are inconsistent. Thus, the localized but extensive attachment loss which may be detected within the root complex of a maxillary molar with the use of a probe, will not always appear in the radiograph. This may be due to the superimposition in the radiograph of the palatal root and of remaining bone structures (Fig. 39-15a). In such a case, additional radiographs with different angles of orientation of the central beam should be used to identify bone loss within the root complex (Fig. 39-15b).
**Fig. 39-15** (a) Radiographs of the right maxillary molar region where, with a normal bisecting projection, the furcation defect of the first molar is not evident. (b) It is, however, easily identified in a bitewing radiograph.
**Fig. 39-16** (a) Radiograph demonstrating a destruction of inter-radicular bone and the presence of periapical defects at the mesial and distal roots of a maxillary first molar. (b) Radiographic appearance of complete healing of the inter-radicular and periapical lesions after endodontic treatment.
# Differential diagnosis
A lesion in the inter-radicular space of a multi-rooted tooth may be associated with problems originating from the root canal or be the result of occlusal overload. The treatment of a furcation-involved tooth, therefore, should not be initiated until a proper differential diagnosis of the lesion has been made.
_Pulpal pathosis_ may sometimes cause a lesion in the periodontal tissues of the furcation (see Chapter 23). The radiographic appearance of such a defect may have some features in common with a plaque-associated furcation lesion. In order to differentiate between the two lesions the vitality of the affected tooth must _always_ be tested. If the tooth is vital, a plaque-associated lesion should be suspected. If the tooth is non-vital, the furcation involvement may have an endodontic origin. In such a case, proper endodontic treatment must _always_ precede periodontal therapy. In fact, endodontic therapy may resolve the inflammatory lesion, soft and hard tissue healing may occur and the furcation defect will disappear (Fig. 39-16). If signs of healing of a furcation defect fail to appear within 2 months of endodontic treatment, the furcation involvement is probably associated with marginal periodontitis.
## Trauma from occlusion
Forces elicited by occlusal interferences, e.g. bruxers and clenchers (see Chapters 14 and 51), may cause inflammation and tissue destruction or adaptation within the inter-radicular area of a multi-rooted tooth. In such a tooth a radiolucency may be seen in the radiograph of the root complex. The tooth may exhibit increased mobility. Probing, however, fails to detect an involvement of the furcation. In this particular situation, occlusal adjustment must always precede periodontal therapy. If the defects seen within the root complex are of "occlusal" origin, the tooth will become stabilized and the defects disappear within weeks following correction of the occlusal overload (Fig. 39-17).
**Fig. 39-17** (a) Radiographic appearance of a defect in the furcation area caused by occlusal overload. After occlusal adjustment the inter-radicular defect spontaneously healed, as documented 6 months after therapy in a radiograph (b). (Courtesy of M. Cattabriga.)
**Fig. 39-18** Resolution of inflammatory lesions in the gingiva achieved by scaling, root planing and the re-establishment of a correct tissue morphology in the inter-radicular area of degree I furcation-involved mandibular molars. (a) Before therapy. (b) 6 months after therapy.
# Therapy
Treatment of a defect in the furcation region of a multi-rooted tooth is intended to meet two objectives:
1. The elimination of the microbial plaque from the exposed surfaces of the root complex.
2. The establishment of an anatomy of the affected surfaces that facilitates proper self-performed plaque control.
Different methods of therapy are recommended:
* Degree I furcation involvement. Recommended therapy: scaling and root planing; furcation plasty.
* Degree II furcation involvement. Recommended therapy: furcation plasty; tunnel preparation; root resection; tooth extraction; guided tissue regeneration at mandibular molars.
* Degree III furcation involvement. Recommended therapy: tunnel preparation; root resection; tooth extraction.
## Scaling and root planing
Scaling and planing of the root surfaces in the furcation entrance of a degree I involvement in most situations result in the resolution of the inflammatory lesion in the gingiva. Healing will re-establish a normal gingival anatomy with the soft tissue properly adapted to the hard tissue walls of the furcation entrance (Fig. 39-18).
## Furcation plasty
Furcation plasty (Fig 39-19) is a resective treatment modality which should lead to the elimination of the inter-radicular defect. Tooth substance is removed (odontoplasty) and the alveolar bone crest is remodeled (osteoplasty) at the level of the furcation entrance.
Furcation plasty is used mainly at buccal and lingual furcations. At approximal surfaces access is often too limited for this treatment. Furcation plasty involves the following procedures:
**Fig. 39-19** Furcation plasty performed at the buccal aspect of a mandibular molar. (a) Initial degree II furcation involvement. (b) After flap elevation, removal of the granulation tissue and scaling of the exposed root surfaces. (c) After odontoplasty. (d) After osteoplasty. (e) Apical position of the flap managed by periosteal sutures. (f) Healing resulting in the elimination of the furcation defect and in the establishment of a proper soft tissue morphology.
* The dissection and reflection of a soft tissue flap to obtain access to the inter-radicular area and the surrounding bone structures.
* The removal of the inflammatory soft tissue from the furcation area followed by careful scaling and root planing of the exposed root surfaces.
* The removal of crown and root substance in the furcation area (odontoplasty) to eliminate or reduce the horizontal component of the defect and to widen the furcation entrance.
* The recontouring of the alveolar bone crest in order to reduce the buccal–lingual dimension of a bone defect in the furcation area.
* The positioning and the suturing of the mucosal flaps at the level of the alveolar crest in order to cover the furcation entrance with soft tissue. Following healing a "papilla-like" tissue should close the entrance of the furcation.
Care must be exercised when odontoplasty is performed on vital teeth. Excessive removal of tooth structure will enhance the risk for increased root sensitivity.
**Fig. 39-20** Tunnel preparation of a degree III-involved mandibular molar. Radiograph (a) and photograph (b) showing a wide inter-radicular space where self-performed plaque control can be obtained by the use of an interproximal brush.
## Tunnel preparation
Tunnel preparation is a technique used to treat deep degree II and degree III furcation defects in mandibular molars. This type of resective therapy can be offered at mandibular molars which have a short root trunk, a wide separation angle, and long divergence between the mesial and distal root. The procedure includes the surgical exposure and management of the entire furcation area of the affected molar.
Following the reflection of buccal and lingual mucosal flaps, the granulation tissue in the defect is removed and the root surfaces are scaled and planed. The furcation area is widened by the removal of some of the inter-radicular bone. The alveolar bone crest is recontoured; some of the interdental bone, mesial and distal to the tooth in the region, is also removed to obtain a flat outline of the bone. Following hard tissue resection enough space has been established in the furcation region to allow access for cleaning devices to be used during self-performed plaque-control measures (Fig. 39-20). The flaps are apically positioned to the surgically established inter-radicular and interproximal bone level.
During maintenance the exposed root surfaces should be treated by topical application of chlorhexidine digluconate and fluoride varnish. This surgical procedure should be used with caution, because there is a pronounced risk for root sensitivity and for carious lesions developing on the denuded root surfaces within artificially prepared tunnels (Hamp _et al_. 1975).
## Root separation and resection (RSR)
_Root separation_ involves the sectioning of the root complex and the maintenance of all roots. _Root resection_ involves the sectioning and the removal of one or two roots of a multi-rooted tooth. RSR is frequently used in cases of deep degree II and degree III furcation-involved molars.
Before RSR is performed the following factors must be considered:
* _The length of the root trunk_. In a patient with progressive periodontal disease a tooth with a _short_ root trunk may have an early involvement of the furcation (Larato 1975; Gher & Vernino 1980). A tooth with a short root trunk is a good candidate for RSR; the amount of remaining periodontal tissue support following separation and resection is often sufficient to ensure the stability of the remaining root cone. If the root trunk is _long_ , the furcation involvement occurs later in the disease process, but, once established, the amount of periodontal tissue support left apical to the furcation may be insufficient to allow RSR.
* _The divergence between the root cones._ The distance between the root cones must be considered. Roots with a short divergence are technically more difficult to separate than roots which are wide apart. In addition, the smaller the divergence is, the smaller also is the inter-radicular (furcation) space. In cases where the divergence between two roots is small, the possibility of increasing the inter-radicular distance with an orthodontic root movement may be considered (Fig. 39-21). The furcation space may also be increased by odontoplasty performed during surgery. Figure 39-22 illustrates that _odontoplasty_ was performed on (1) the distal part of the mesial root and (2) the mesial part of the distal root and deep finishing lines prepared for the subsequent restoration (Di Febo _et al_. 1985).
* _The length and the shape of the root cones_. Following separation, short and small root cones (Fig. 39-23) tend to exhibit an increased mobility. Such roots, in addition, have narrow root canals which are difficult to ream. Short and small roots consequently should be regarded as poor abutments for prosthetic restorations.
* _Fusion between root cones_. When a decision has been made to perform RSR, it is important that the clinician first determines that the cones within the root complex are not fused. This is generally an uncomplicated diagnostic problem for mandibular molars or for the buccal furcation of maxillary molars (Fig. 39-24). At such teeth the separation area between the roots can easily be identified both with the probe and in a radiograph. It is more difficult to identify a separation line between mesio-buccal (or disto-buccal) and palatal roots of a maxillary molar or maxillary first premolar with a narrow root complex. In such situations, a soft tissue flap must often be raised to allow the operator to get proper access to the approximal tooth surfaces. The mesial (or distal) entrance of the furcation must be probed to a depth of 3–5 mm to ascertain that a fusion does _not_ exist between the roots scheduled for RSR.
* _Amount of remaining support around individual roots._ This should be determined by probing the entire circumference of the separated roots. It should be observed that a localized deep attachment loss at one surface of one particular root (e.g. on the buccal surface of the palatal root, or the distal surface of the mesio-buccal root of a maxillary molar) may compromise the long-term prognosis for an otherwise ideal root.
* _Stability of individual roots_. This must be examined following root separation. Rule of thumb: the more mobile the root cone is, the less periodontal tissue support remains.
* _Access for oral hygiene devices_. After completion of therapy the site must have an anatomy which facilitates proper self-performed tooth cleaning.
**Fig. 39-21** Effect of orthodontic treatment of a separated mandibular molar with a small root divergence. (a) After root separation. (b) 3 months after completion of orthodontic therapy.
**Fig. 39-22** Odontoplasty of a separated mandibular molar performed during surgery to increase the furcation space. After flap elevation and exposure of the alveolar bone, it is evident that the distance between the two roots is small (a). By preparing the inter-radicular surfaces during surgery (b) the furcation space is increased and is sufficient for self-performed plaque control measures (c).
**Fig. 39-23** Radiograph showing maxillary molars with thin, short, and conical roots.
### Maxillary molars
#### _General example_
Several decisions must be made when RSR is planned for a furcation-involved maxillary molar. Since such teeth have three root cones, one or two cones may be retained after separation. Different treatment alternatives exist. They are listed in Table 39-1.
**Fig. 39-24** Radiograph indicating the presence of a degree III involvement of the buccal furcation of the maxillary first molar. This tooth is a candidate for root resection.
Prior to RSR, the morphology of the individual roots as well as the surface area of each root must be carefully analyzed.
The _disto-buccal root_ of a maxillary molar (1) is the shortest of the three roots; (2) the root trunk is comparatively long. Thus, the distal root has a small quantity of bone support and once separated, the cone may exhibit increased mobility. The disto-buccal root is, therefore, often removed as part of RSR (Rosenberg 1978; Ross & Thompson 1980).
The _mesio-buccal root_ has (1) a wide buccopalatal dimension, (2) an hour-glass cross section, and therefore a large root surface area. In fact, the mesio-buccal cone often has a total root surface area that is equal to or greater than that of the palatal root cone. The mesio-buccal root (1) is located centrally in the alveolar process, (2) is properly aligned with the maxillary premolars and is in an ideal position to function as a separate unit (Fig. 39-25). For these reasons, the mesio-buccal root may be preferred for retention when the clinician is selecting between the mesio-buccal or palatal root. It should be remembered, however, that the root canals of the mesio-buccal root are narrow and more difficult to treat than the single and wide canal of the palatal root.
**Fig. 39-25** Occlusal view of a restoration using the mesial root of a maxillary first molar as abutment. Note the alignment of the mesial root and the adjacent premolars.
Table 39-1 Root resective treatment possibilities in molars with furcation involvement
**Furcation involvement**| **Root resection**| **Root resection plus separation of the remaining roots**
---|---|---
1 Buccal| Mesio-buccal, disto-buccal|
Mesial| Mesio-buccal, palatal|
Distal| Disto-buccal, palatal|
2 Buccal & distal| Disto-buccal, mesio-buccal & palatal| Palatal
Buccal & mesial| Mesio-buccal, disto-buccal & palatal| Palatal, disto-buccal
Mesial & distal| Palatal, mesial & disto-buccal| DistoBuccal
3 Buccal, distal & mesial| Disto-buccal & palatal, mesio-buccal & palatal, mesio- & disto-buccal| Palatal, disto-buccal
**Fig. 39-26** (a) Palatal root of a root-resected maxillary molar serving as a single abutment for a crown restoration. (b) A mesio-buccal root was included in the restoration for esthetic reasons.
The tissue destruction in the furcation area often causes deep attachment and bone loss at the distal palatal surface of the mesio-buccal root. In such situations the palatal root remains as the only candidate for retention (Fig. 39-26).
The series of illustrations presented in Fig. 39-27 demonstrates two left maxillary molars (teeth 26 and 27) with degree III involvement of all six furcation entrances. Both teeth were, following a detailed examination and diagnosis, scheduled for treatment with RSR. Note that in this case the second premolar was missing. In cases of advanced periodontal disease at maxillary molars, it is often necessary to separate all three roots of the individual tooth to obtain access to the inter-radicular area for assessment of the height of the remaining bone at (1) the buccal surface of the palatal root and (2) the palatal surfaces of the buccal roots. Figure 39-27b illustrates the two maxillary molars with all six roots separated. Because of anatomic considerations and increased mobility, the distobuccal roots of 26 and 27 were extracted (Fig. 39-27c). The palatal root of the first molar had a deep area of localized attachment loss on its buccal surface, was considered to be a poor candidate for a bridge abutment, and was extracted. The mesio-buccal root of the first molar as well as the mesio-buccal and palatal roots of the second molar (27) were stable and exhibited moderate probing depth. It was anticipated that at all three roots the anatomy would allow proper plaque control following healing after treatment. The three roots were maintained (Fig. 39-27d). Figure 39-27e shows the area after 3 months' healing and Fig. 39-27f illustrates the segment properly restored. Since in this segment one premolar was missing, the mesio-buccal root of the first molar was used as second premolar in the prosthetic reconstruction and the two roots of the second molar served as abutments for a crown restoration in the position of a molar.
### Maxillary premolars
Root resection of maxillary first premolars is possible only in rare instances due to the anatomy of the root complex (Joseph _et al_. 1996) (Fig. 39-28). The furcation of this premolar is often located at such an apical level that the maintenance of one root serves no meaningful purpose. In most cases, therefore, the presence of a deep furcation involvement of degree II or degree III in a maxillary first premolar calls for tooth extraction.
### Mandibular molars
If RSR must be applied in a furcation-involved mandibular molar, three treatment alternatives exist:
1. Separate the two roots, but maintain both roots (premolarization)
2. Separate and extract the mesial root
3. Separate and extract the distal root.
In some situations, both roots may be maintained following separation. If one root is to be removed, the following facts must be considered:
* The _mesial_ root has a significantly greater root surface area than the distal root. The mesial root, however, has an hour-glass-shaped cross section which may be difficult to manage (1) in the self-performed plaque control and (2) in the restorative procedure. In addition, the mesial root frequently has two narrow root canals. The root canals are often close to the external root surface. This may complicate root preparation during the subsequent restorative treatment.
* The _distal_ root has an oval cross section and, as a rule, only one, wide root canal. The distal root is: (1) comparatively large, providing a greater mass of dentin to resist root fracture (Langer _et al_. 1981); and (2) a good candidate for pin or post placement. Further, when the resected mandibular molar is a terminal abutment for a bridge, the retention of the distal root will result in a longer dental arch than would be the case had the mesial root been retained (Fig. 39-29).
**Fig. 39-27** The sequential stages of root resection of two maxillary molars with degree III involvement. (a) Radiograph showing the pre-RSR situation. (b) The roots were separated before flap elevation. (c,d) The distal roots of both molars and the palatal root of the first molar were extracted and the teeth prepared. (e) After 3 months of healing. (f) The final prosthetic restoration of the site.
**Fig. 39-28** Resection of the disto-buccal root of a three-rooted maxillary first premolar.
### Sequence of treatment at RSR
Once anatomic and pathologic characteristics of the root complex(es) of multi-rooted teeth have been documented, treatment should follow a logical plan (see also Chapter 31).
#### _Endodontic treatment_
If the tooth to be resected is vital or if an improper root canal filling was placed in a non-vital tooth, RSR starts with endodontic therapy. Rubber dam can be placed, and optimal conditions thus be established for the important management (cleaning and shaping) of the root canal. The structural integrity of the root must be maintained and minimal amounts of root dentin should be removed (Fig. 39-30a,b). Direct filling with amalgam or chemically cured composite of the endodontically treated tooth should be performed before RSR (Fig. 39-30c). Each root should have individual retention for a restoration which should not break or detach during RSR, removal and relining of the provisional restorations, impressions, and prosthetic try-in. Endocanal posts or endodontic screws are used only if natural retention needs improvement.
**Fig. 39-29** Results of the root resection of a mandibular first molar of which the distal root was retained.
**Fig. 39-30** Combined photograph and radiograph showing the "conservative" approach both regarding the access to the pulp chamber (a) and the shaping and filling of the root canal system (b). (c) Schematic illustration showing the temporary restoration of the endodontically treated tooth.
Occasionally, a furcation involvement may first be identified during periodontal surgery. In this emergency situation RSR may be completed but the root canal entrance(s) of the remaining root(s) must be properly sealed. Definitive root canal therapy must be completed within 2 weeks (Smukler & Tagger 1976).
#### _Provisional restoration_
Alginate impressions of the area to be treated are taken and sent to the laboratory together with a wax record of the intercuspal position. A provisional restoration is prepared.
#### _Root separation and resection_
Root separation and root resection may be performed as part of the preparation of the segment for prosthetic rehabilitation ("prosthetic preparation"), i.e. prior to periodontal surgery (Carnevale _et al_. 1981). During the prosthetic preparation it is important to _avoid_
* Exposing the interradicular bone to undue mechanical trauma (Fig. 39-31)
* Leaving behind parts of the furcation fornix (Fig. 39-32)
* Perforating the root canals
* Preparing the vertical surfaces of the remaining roots with sharp angles (Fig. 39-33).
_Situation 1_ : _mandibular molar_. Following separation, both roots are maintained. The distal surface of the distal root and the mesial surface of the mesial root must be prepared parallel to each other to increase the retention for a subsequent restoration. The mesial surface of the distal root and the distal surface of the mesial root should be prepared with diverging angles to increase the space available between the separated roots (Fig. 39-34).
_Situation 2_ : _maxillary molar_. Following separation, the disto-buccal root was extracted. The distal surface of the crown is prepared with a bevel cut and in such a way that the concave curvature (in apicocoronal direction) is eliminated (Fig. 39-35). If the mesio-buccal and the palatal roots of this molar must be separated but maintained, it is important that the buccal surface of the mesio-buccal root and the palatal surface of the palatal root are prepared parallel to each other. This will enhance the retention of the subsequent restoration. The palatal surface of the mesio-buccal root and the buccal surface of the palatal root must be prepared at diverging angles to increase the space available between the separated roots (Fig. 39-36). At this stage the provisional restoration is relined with cold cured acrylic and cemented after RSR.
**Fig. 39-31** Radiograph illustrating the damage which occurred to the inter-radicular septum during root separation.
**Fig. 39-32** (a) Radiographs of a mandibular first molar to be extracted and of a second molar to be root resected. (b) During hemisection an overhang is left behind as a result of an oblique sectioning of the tooth distal to the furcation. (c) In a radiograph obtained 2 years later, the presence of an angular bony defect can be seen adjacent to the "overhang". The lesion was resolved and the angular defect disappeared following removal of the "overhang". (d) Radiograph after 2 years.
#### _Periodontal surgery_
Following flap elevation, osseous resective techniques are used to eliminate angular bone defects that may exist around the maintained roots. Bone resection may also be performed to reduce the buccolingual dimension of the alveolar process of the extraction site. The remaining root(s) may be prepared with a bevel cut to the level of the supporting bone (Levine 1972; Ramfjord & Nissle 1974; Carnevale _et al_. 1983). This additional preparation may serve the purpose of (1) eliminating residual soft and hard deposits and (2) eliminating existing undercuts to facilitate the final impression (Fig. 39-37). The provisional restoration is relined. The margins of the provisional restoration must end ≥3 mm coronal of the bone crest. The soft tissue flaps are secured with sutures at the level of the bone crest. The relined provisional restoration is cemented and a periodontal dressing is applied to cover the surgical area. The dressing and the sutures are removed 1 week later. The roots are debrided and a new dressing applied. After another week, the dressing is finally removed and the patient instructed in proper plaque-control techniques.
**Fig. 39-33** Maintenance of the two fused buccal roots of a maxillary first molar. The buccal roots were separated from the palatal root. Note the rounded line angles and the wide space created between the separated roots.
**Fig. 39-34** Mandibular molar after root separation. Note the diverging angle of preparation performed to increase the inter-radicular space between the mesial and distal roots and the parallel approximal surfaces.
**Fig. 39-35** (a,b) The sequential stages of root resection and extraction of the distal root of a maxillary molar. In order to minimize the concave outline of the cut surfaces, the sectioning should be performed with a straight line cut. (c, d) After extraction of the distal root, the furcation area of the remaining roots must be re-prepared to eliminate undercuts.
**Fig. 39-36** (a,b) Preparation, during separation, of the mesio-buccal and palatal roots after the disto-buccal root of a maxillary molar had been extracted. The internal (furcation) surfaces of the two roots should be prepared with diverging angles to increase the inter-radicular space, while the external surfaces of the two roots should be prepared parallel to each other to increase the subsequent retention of the restoration. (c) When the palatal surface of the palatal root is not prepared parallel to the buccal surface, the palatal abutment will become shortened and not self-retentive.
**Fig. 39-37** (a,b) Sequential stages of root resection at maxillary first and second molars. The extraction of the distal root of the first molar was performed during tooth preparation and prior to the insertion of the provisional restoration. (c,d,e) During the surgical procedure, after flap elevation, the furcation-involved second molar was separated, the mesial and palatal roots were extracted and the osseous defects were eliminated. (f) Healing with the definitive prosthetic restoration in place.
#### _Final prosthetic restoration_
Since the prosthetic preparation of the roots was completed during surgery, the clinician concerns him-/herself only with minor adjustments. The preparation margins are located supragingivally, which improves the precision of the definitive crown restoration. The framework of the restoration must be rigid to compensate for the compromised abutments (roots) with a compromised periodontal tissue support. The occlusion should be designed to minimize the infliction of lateral deflective forces (see Chapter 51) (Fig. 39-38).
## Regeneration of furcation defects
The possibility of regenerating and closing a furcation defect has been investigated (see Chapter 43). Following an early case report publication (Gottlow _et al_. 1986), where histologic documentation of new attachment formation in human furcation defects (Fig. 39-39) treated by "guided tissue regeneration" (GTR) therapy was provided, the results of several investigations on this form of treatment in furcation-involved teeth have been presented. In these reports, a reasonably predictable outcome of GTR therapy was demonstrated only in degree II furcation-involved mandibular molars, where a clinical soft tissue closure or a decreased probing depth of the furcation defect was recorded (Pontoriero _et al_. 1988; Lekovic _et al_. 1989; Caffesse _et al_. 1990).
**Fig. 39-38** (a) Soft tissue healing at a separated maxillary first molar and at a root-resected second molar. (b) The final prosthetic restoration in place with the occlusion designed to minimize the lateral stresses on the roots left as abutments.
**Fig. 39-39** Histologic mesiodistal section of a previous degree II furcation involvement of a human mandibular molar, treated with GTR. The section demonstrates that the newly formed cementum covers the entire circumference of the furcation defect.
Less favorable results have been reported when GTR therapy was used in other types of furcation defects such as degree III furcation-involved mandibular and maxillary molars (Pontoriero _et al_. 1989; Pontoriero & Lindhe 1995a) and degree II furcations in maxillary molars (Metzeler _et al_. 1991; Pontoriero & Lindhe 1995b).
The reason for the limited predictability of GTR therapy in furcation-involved teeth may be related to several factors:
**Fig. 39-40** Position of the furcation fornix in relation to the level of the supporting bone and attachment apparatus in a lingual degree II furcation-involved mandibular molar.
* The morphology of the periodontal defect, which in the root complex often has the character of a "horizontal lesion". New attachment formation is hence dependent on coronal upgrowth of periodontal ligament tissue (Fig. 39-40).
* The anatomy of the furcation, with its complex internal morphology, may prevent proper instrumentation and debridement of the exposed root surface (Fig. 39-41).
* The varying and changing location of the soft tissue margins during the early phase of healing with a possible recession of the flap margin and early exposure of both the membrane material and the fornix of the furcation (Fig. 39-42).
GTR treatment could be considered in dentitions with isolated degree II furcation defects in mandibular molars. The predictability of this treatment outcome improves following GTR therapy if:
* The _interproximal_ bone is located at a level which is close to the CEJ of the approximal surface. This "key-hole" type of degree II involvement allows for an effective retention of the membrane material and retention also of the position of the coronally placed flap margins (Fig. 39-43).
* The debridement of the exposed root surfaces in the furcation area is comprehensive. Since the width of the furcation entrance and the internal morphology of the inter-radicular area may limit the access of curettes for proper debridement, the removal of hard and soft bacterial deposits from the root surfaces must frequently be made with ultrasonic instruments, rotating, flame-shaped fine diamond burs, and endodontic files (Fig. 39-44).
* The membrane material is properly placed and a "space" between the tooth and the material established. A "primary" wound closure is thereby obtained, blood clot protection will occur, and recession of the soft tissue margin during the early phase of healing will be minimized (Fig. 39-45).
* A plaque-control program is put in place. This should include daily rinsing with a chlorhexidine solution and professional tooth cleaning once a week for the first month, and once every 2–3 weeks for at least another 6 months of healing following the surgical procedure.
**Fig. 39-41** Internal morphology of the furcation of a maxillary molar. Note the invagination of the palatal root.
**Fig. 39-42** Exposure of the membrane and of the furcation entrance as a consequence of recession of the flap margin. The photograph is taken at 3 weeks of healing after GTR treatment of a degree II buccal furcation of a mandibular molar.
**Fig. 39-43** Aspect of a lingual degree II furcation involvement in a mandibular first molar. (a) Note the infrabony component of the defect and the level of the approximal supporting bone in relation to the furcation fornix. (b) The Teflon membrane sutured in position and supported by the interproximal alveolar bone. (c) The flap positioned and sutured over the membrane. (d) At reentry, after 6 months of healing, the previously exposed furcation defect was closed and filled with bone tissue.
**Fig. 39-44** Phase of debridment of a buccal degree II furcation defect by the use of an "extra-fine" ultrasonic tip.
Enamel matrix proteins included in a commercially available product (Emdogain®; Straumann, Basel, Switzerland) were used in the treatment of furcation defects in experimental studies in animals (Araùjo & Lindhe 1998) and in clinical trials in humans (Jepsen _et al_. 2004; Meyle _et al_. 2004). The ability of Emdogain® (EMD), applied to the root surfaces in the furcation area, to stimulate periodontal regeneration in surgically created degree III furcation defects in dogs was documented histologically by Araùjo and Lindhe (1998). In a multicenter randomized controlled clinical trial, including 45 subjects with 45 paired mandibular molars with buccal degree II furcation involvements, Jepsen _et al_. (2004) compared the EMD with GTR therapy. After 14 months of healing, the subjects were re-examined. The authors reported a mean reduction in the open horizontal furcation depth of 2.8 mm for EMD-treated sites and of 1.8 mm for GTR-treated defects. In addition the frequency of complete closed furcation defects was higher for EMD sites (8/45) than for GTR sites (3/45). It was concluded that both treatment modalities resulted in significant clinical improvements although the EMD method provided (1) greater reduction of the furcation depths, (2) a smaller incidence of post-operative pain/swelling, and (3) less gingival recession (Meyle _et al_. 2004) as compared to GTR therapy.
The outcome of the regenerative procedures at furcation-involved molars should result in the complete elimination of the defect within the inter-radicular space in order to establish anatomic conditions which facilitate optimal self-performed plaque-control measures. In fact, partial gain of clinical attachment levels within the furcation defect, although statistically significant, will not necessarily improve the site's accessibility for plaque-control measures.
## Extraction
The extraction of a furcation-involved tooth must be considered when the attachment loss is so extensive that no root can be maintained or when the treatment will not result in a tooth/gingival anatomy which allows proper self-performed plaque-control measures. Moreover, extraction can be considered as an alternative form of therapy when the maintenance of the affected tooth will not improve the overall treatment plan or when, due to endodontic or caries-related lesions, the preservation of the tooth will represent a risk factor for the long-term prognosis of the overall treatment.
The possibility of substituting a furcation-involved tooth with an osseointegrated implant should be considered with extreme caution and only if implant therapy will improve the prognosis of the overall treatment (see Chapter 32). In fact, the implant alternative has obvious anatomic limitations in the maxillary and mandibular molar regions.
# Prognosis
Several studies have evaluated the long-term prognosis of multi-rooted teeth with furcation involvement that were treated in accordance with the principles described in this chapter (Table 39-2). In a 5-year study, Hamp _et al_. (1975) observed the outcome of treatment of 175 teeth with various degrees of furcation involvement in 100 patients. Of the 175 teeth, 32 (18%) were treated by scaling and root planing alone, 49 (28%) were subjected, in addition to scaling and root planing, to furcation plasty which included odonto- and/or osteoplasty. In 87 teeth (50%) root resection had been carried out and in seven teeth (4%) a tunnel had been prepared. At the completion of the active phase of therapy the patients were enrolled in a maintenance program which included a recall visit every 3–6 months. The plaque and gingivitis scores assessed immediately after treatment and once a year during maintenance indicated that the patients' oral hygiene was of high quality. None of the teeth treated was lost during the 5 years of study. Only 16 furcation sites exhibited probing depths exceeding 3 mm. During the observation period carious lesions were detected in 12 surfaces of the 32 teeth which had been treated by scaling and root planing, in three surfaces of the 49 teeth subjected to furcation plasty, in five surfaces of the 78 root-resected teeth, and in four surfaces of the seven teeth where a tunnel was prepared.
**Fig. 39-45** The sequential stages of GTR treatment of a buccal degree II furcation-involved mandibular first molar. (a,b) The clinical appearance and the horizontal probing of the defect. (c,d) Membrane placement and retention. (e) The clinical aspect of the soft tissue at 4 weeks after membrane removal. (f) The clinical aspect after 6 months of healing. During the re-entry procedure the furcation defect appeared completely closed (g) and was not probeable (h).
**Table 39-2** Long-term clinical studies on root resection therapy in molars with furcation involvement
The results of this study were basically confirmed in a more recent investigation (Hamp _et al_. 1992). In this 7-year study, the authors followed 100 patients with 182 furcation-involved teeth. Out of the 182 furcation-involved teeth, 57 had been treated by scaling and root planing only, 101 were treated by furcation plasty, and 24 were subjected to root resection or hemisection. No tunnel preparation was performed. After the active phase of therapy, the patients were enrolled in a meticulous maintenance care program including recall appointments once every 3–6 months. During the course of the study, more than 85% of the furcations treated with scaling root planing alone, or in conjunction with furcation plasty, maintained stable conditions or showed signs of improvement. Only one tooth and one mesial root of a mandibular molar were extracted among the root-resected or hemisected teeth.
Carnevale _et al_. (1998), in a 10-year prospective controlled clinical trial, demonstrated a 93% survival rate of root resected furcation-involved teeth and a 99% survival rate of non-furcation-involved teeth.
More recently, Svärdström (2001) presented the results of a retrospective analysis on factors influencing the decision-making process regarding the treatment for 1313 molars with furcation involvement in 222 patients and the outcome of the treatment decisions after 8–12 years (mean 9.5 years) of regular maintenance care. The treatment options included were: tooth extraction, root separation/resection, and maintenance of the tooth with non-surgically/surgically performed scaling and root planing with or without furcation plasty. Of the 1313 furcation-involved molars, 366 (28%) were extracted during the active phase of therapy. The decision for tooth extraction was primarily influenced by factors such as tooth mobility, tooth position, absence of occlusal antagonism, the degree of furcation involvement, probing depth, and the amount of remaining periodontal support. Out of the 685 molars with furcation involvement and the 160 patients that were available for the follow-up examination 8–12 years after treatment, 47 teeth were root separated/resected and 638 teeth were considered to be maintainable after a nonsurgical or conservative surgical therapy.
The factor found to have the strongest influence for the decision to perform root separation/resection was the degree of furcation involvement (degree II and III). Tooth position, probing depth, and tooth mobility were also factors of statistical significance. The author explained that other factors such as endodontic conditions, root anatomy, and overall treatment strategy may also have influenced the choice of treatment. The long-term outcome of the treatment decisions made for furcation-involved molars showed a favorable survival rate for both root resective (89%) and non-resective (96%) therapy options in patients included in a proper maintenance care program. Of the 47 root separated/resected teeth, only five (11%) were lost during the 9.5 years of follow-up. Of the 638 molars initially considered to be maintainable by a non-resective treatment, 21 teeth (3.5%) were extracted and three teeth were root resected.
Table 39-3 Factors to consider in treatment of furcation-involved molars
**Tooth-related factors**
---
Degree of furcation involvement
Amount of remaining periodontal support
Probing depth
Tooth mobility
Endodontic conditions and root/root-canal anatomy
Available sound tooth substance
Tooth position and occlusal antagonisms
**Patient-related factors**
Strategic value of the tooth in relation to the overall plan
Patient's functional and esthetic demands
Patient's age and health conditions
Oral hygiene capacity
### Conclusion
In treatment decisions for furcation-involved molars, it must be realized that there is no scientific evidence that a given treatment modality is superior to the others (Table 39-3).
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# Chapter 40
# Endodontics and Periodontics
Gunnar Bergenholtz and Gunnar Hasselgren
* * *
Introduction
Infectious processes in the periodontium of endodontic origin
General features
Clinical presentations
Distinguishing lesions of endodontic origin from periodontitis
Endo–perio lesions – diagnosis and treatment aspects
Endodontic treatments and periodontal lesions
Iatrogenic root perforations
Vertical root fractures
Mechanisms
Incidence
Clinical expressions
Diagnosis
Treatment considerations
External root resorptions
Mechanisms of hard tissue resorption in general
Clinical presentations and identification
Different forms
* * *
# Introduction
Inflammatory lesions of the attachment apparatus of teeth involve a variety of etiologies other than plaque accumulations in the dentogingival region; these require attention in diagnosis and treatment planning processes. In fact, signs and symptoms, seen as typical of periodontitis, such as pocket probing depths, loss of attachment, increased tooth mobility, pain, swellings and suppurations, may reflect several tooth-associated infections including infections of endodontic origin (here termed endodontic lesion), infections initiated and maintained by iatrogenic root perforations, vertical root fractures, and external root resorption.
Differentiating between inflammatory disease conditions of the periodontium is not normally a thorny exercise. This is because symptoms of periodontitis usually affect several teeth in the dentition and are confined to the marginal periodontium. Other tooth-associated infections, by contrast, are usually isolated to a single tooth and display rather typical clinical and radiographic signs. These conditions can nevertheless produce confusing clinical expressions and lead to misinterpretation of their cause, especially when affecting teeth in dentitions diseased by periodontitis. Diagnostic difficulties particularly arise when lesions appear deep down the lateral aspects of roots in what can be designated a marginal–apical communication. These so-called "endo–perio lesions" present the clinician with exceptional challenges in that the origin and thus the proper course of treatment are not readily revealed. An "endo–perio lesion", as the term implies, involves a condition where both the pulp and the periodontium are diseased simultaneously in what appears to be a single periodontal lesion. However, a complicating factor is that the process may be of periodontal origin in its entirety and may have caused the death of the pulp in the process or the lesion may just be a representation of a root canal infection alone. Hence, determination of causality is crucial in these cases not only to avoid unnecessary and possibly detrimental treatment, but also to assess whether the disease condition stands a reasonable chance of being successfully treated.
To guide clinical decision making on diagnosis and treatment of inflammatory lesions in the periodontium, the focus of this chapter is on various tooth-associated disorders that display similar signs and symptoms to periodontitis. Specifically addressed are the clinical presentations and the means by which endodontic infections and infections associated with root perforations, root fractures, and root resorptions can be identified and distinguished from manifestations of periodontitis. Management principles will be given where appropriate. Non-infectious processes _viz._ developmental cysts and tumors, which also can interfere with the supporting tissues, will not be discussed in this chapter.
# Infectious processes in the periodontium of endodontic origin
## General features
Disease conditions of the dental pulp are for the most part infectious in nature and involve inflammatory processes. Caries, restorative procedures, and traumatic injuries are common etiologies (see Chapter 23). In fact, any loss of hard tissue integrity of teeth, exposing dentin or the pulp directly to the oral environment, may allow bacteria and bacterial elements to adversely affect the normally healthy condition of the pulp. The resulting inflammatory lesion will then be directed towards the source of irritation and be confined for as long as the inflammatory defense does not collapse and convert into a major destructive breakdown of the pulpal tissue. Consequently, inflammatory alterations in the vital pulp will not normally produce lesions in the adjoining periodontium that can be detected by clinical means. Yet, disruption of the apical lamina dura or widening of the periodontal ligament space can occasionally be observed radiographically (Fig. 40-1a). Teeth, particularly in young individuals with large pulp chambers, may also display minor radiolucent areas either apically or laterally along the root surface at exits of accessory canals and apical foramina or both, in spite of the fact that vital pulp functions prevail (Langeland 1987; Gesi _et al_. 2006). In such cases, typical clinical signs of pulpitis, including spontaneous pain, thermal sensitivity or tenderness to percussion, may or may not be present.
Overt lesions in the periodontium, on the other hand, are common in teeth where the pulp has lost its vitality. In these cases the process is associated either with a non-treated necrotic pulp or a tooth that has been the subject of endodontic treatment. In the latter case, the cause of the lesion is usually to be found in an existing, although not successfully managed, root canal infection (Fig. 40-1b). Extrusion of toxic medicaments and root-filling materials into the periodontium in conjunction with endodontic treatments may also cause periodontal lesions. While severe damage of the periodontal tissue support formerly was a rather common complication following the use of arsenic- or formaldehyde-based preparations to devitalize pulps, medicate, and fill root canals (Fig. 40-2), modern day medicaments for canal irrigation and disinfection as well as materials for root canal filling are comparatively well tolerated (Geurtsen & Leyhausen 1997). However, acute toxic and allergic reactions may be encountered from the use of highly concentrated sodium hypochlorite (Pashley _et al_. 1985) and adverse components of root-filling material (Hensten-Pettersen _et al_. 1985).
**Fig. 40-1** (a) Radiograph of an upper second premolar with caries extending to the vicinity of the pulp. There is loss of lamina dura at the root tip. (b) The 3-year recall radiograph after pulpectomy of the vital pulp and root filling shows a periapical radiolucency suggesting existence of a persistent root canal infection in this case.
### Conclusion
It is important to realize that as long as the pulp maintains vital functions, although inflamed or scarred, it is unlikely to produce irritants that cause overt periodontal tissue lesions. For clinically significant lesions to occur the pulp must have lost its vitality. Consequently no benefit will normally be gained from extirpation of vital pulps (pulpectomy) as an adjunct or alternative to the treatment of teeth for periodontal disease.
## Clinical presentations
Inflammatory lesions in the periodontal tissues, induced and maintained by root canal infection, typically expand around the apex of teeth, where the root canal space interconnects with the periodontium along apical foramina. Lesions develop more seldom in a juxtaposition that is at the lateral aspects of roots (Fig. 40-3) and in furcations of multi-rooted teeth (Fig. 40-4). An important reason is that accessory canals that can mediate the release of bacterial elements from the pulpal chamber are relatively uncommon in cervical and mid-root portions (see Chapter 23). Another important factor is that an intact layer of root cementum blocks potential dissemination of bacteria and their products along the dentinal tubules.
**Fig. 40-2** (a) Clinical photograph showing a periodontal defect at the mesial aspect of tooth #46. The pulp had been subjected to devitalization by the use of a paraformaldehyde-containing paste. (b) Leakage of the agent along the temporary filling margins obviously occurred as suggested by the subsequent loss of proximal bone and the emergence of a bone sequestrum.
The clinical presentation varies. Lesions can either be in a silent, non-symptomatic state or appear with more or less salient signs of acute infection. In the former case a balanced host–parasite interrelationship has usually been established. The only means to diagnose the condition is then by radiography (Fig. 40-1b). Unless transformed to a cyst, the extension of such non-symptomatic lesions may remain limited and stable over many years. This applies in particular to lesions associated with root-filled teeth, where the persisting root canal infection has assumed a relatively low grade of metabolic activity (see Chapter 23).
Lesions associated with untreated infections of a necrotic pulp or with inadequately treated root canals may any time, either soon after pulp tissue break-down or after a period of silence, turn into an exacerbating, acute inflammatory process. Exacerbating lesions may also be induced in conjunction with endodontic treatment from over-instrumentation along with extrusion of bacterial organisms and tissue-irritating medicaments. Exudation and pus production dictate the clinical course. Typical symptoms include throbbing pain, pain on percussion, tenderness to palpation, increased tooth mobility, and apical as well as marginal swellings. The severity of these symptoms may have escalated successively over a period of time, although a single sign may be the only presenting symptom. It should be noted that the very same symptoms occur with some forms of aggressive periodontitis, iatrogenic root perforation, root fracture, and external root resorption (see below).
**Fig. 40-3** Series of radiographs showing endodontic treatment of an upper premolar included as an abutment in a three-unit bridge. The patient, a 78-year-old male, had been treated and maintained for periodontal disease. (a) There are bone lesions both at the apical and at the distal aspect of the tooth. Following endodontic treatment of the necrotic pulp (b) and root filling (c), an accessory canal communicating with the lateral lesion became evident. (d) The 6-month recall radiograph shows substantial reduction of both bone lesions. Case kindly provided by Dr. Peter Jonasson.
**Fig. 40-4** (a) Bone loss of the furcal region in a second left molar in addition to apical bone lesions at both the mesial and the distal roots. (b) Upon endodontic treatment an accessory canal became filled, suggesting that the furcal lesion was of endodontic origin. Case kindly provided by Dr. Pierre Machtou.
The pressure the exudative process exerts results in tissue destruction as a path for drainage is sought. This expansion of the lesion may take a variety of directions. Significant in the context of differential diagnosis to periodontitis are those lesions that drain at or near the gingival margin. The character of the accompanying bone lesion may add to the risk of misdiagnosis, as it may look similar to that of aggressive periodontitis (Fig. 40-5).
Several routes of drainage from an acute endodontic lesion should be recognized (Fig. 40-6) :
1. The suppurative process may drain off along the periodontal ligament space and exit at the bottom of the sulcus (Fig. 40-6a). This usually results in only a narrow opening of the fistula into the gingival sulcus/pocket and may not be detected unless careful probing of the sulcus is carried out at multiple sites. Such a sinus tract may readily be probed down to the apex of the tooth, where no increased probing depth otherwise may exist around the tooth. In multi-rooted teeth a sinus tract along the periodontal ligament can drain into the furcation area as it exits along the root surface. The resulting bone lesion may then resemble a "through-and-through" furcation defect from periodontal disease (Figs. 40-7 and 40-8).
2. A periapical abscess can also perforate the cortical bone close to the apex. In this acute stage the soft tissue including the periosteum may be elevated from the bone surface to the extent that a wide opening for drainage of pus is created in the gingival sulcus/pocket area (extraosseous drainage; Fig. 40-6b). Later this route of drainage may develop into in a chronic sinus tract that may remain in or near the sulcus, often at the buccal aspect of the involved tooth. Such a fistula may also emerge following a less aggressive process. It is important to note that this type of drainage is not associated with loss of bone tissue at the inner walls of the alveolus, and that a periodontal probe cannot penetrate into the periodontal ligament space.
### Conclusion
Endodontic lesions either do not have overt clinical signs or may present with various acute manifestations of root canal infection. The asymptomatic lesions usually assume a limited extension around the apex, while rapid and extensive destruction that may extend marginally along the attachment apparatus may follow acute exacerbations. Exudation and pus formed in the process may drain off in different directions; pathways along the periodontal ligament space or following penetration of the alveolar bone at the apical region with drainage in or near the gingival sulcus/pocket warrant particular attention from a differential diagnostic point of view. In addition to deep pocket probing depths, the accompanying bone lesion may mimic that of periodontitis.
## Distinguishing lesions of endodontic origin from periodontitis
### Pulp vitality testing
Differential diagnosis is important because at times endodontic lesions may produce clinical signs and symptoms similar to those of periodontitis. Tools to distinguish the two disease conditions from each other, however, are limited as neither the patient's disease history, the clinical presentation nor the character of the radiographic signs invariably are clearcut. As an endodontic lesion of clinical significance in this context cannot emerge unless the tissue has turned necrotic and become infected, determination of pulp vitality is a most important measure in cases where an endodontic etiology is suspected. Endodontic lesions associated with root-filled teeth are discussed separately, below.
Pulp vitality implies that the tissue has an intact neurovascular supply to support cell and tissue functions. Although a vital pulp may be inflamed or display a variety of degenerative changes, the vasculature is still functioning in a vital pulp. Most methods of determining pulp vitality act by stimulating the pulp's sensory nerve function and presume that the provocation of a sharp pain sensation indicates a vital pulp. This means that in reality the _sensibility_ of the pulp is tested rather than the _vitality_ of it. However, there is ample documentation to support the concept that a tooth which responds to sensory stimuli has vital pulp functions. Conversely, if a tooth does not respond, the pulp may be non-vital (Petersson _et al_. 1999; Peters _et al_. 1994; Pitt Ford & Patel 2004). Means to detect blood flow within the pulp by non-invasive methods, for example by laser light scattering, have been developed and tested, but have so far gained limited clinical application (see review by Pitt Ford & Patel 2004).
**Fig. 40-5** (a) A radiolucent area along the distal root surface of tooth #45 is combined with horizontal loss of marginal bone. (b) As the pulp was non-vital it was subjected to endodontic treatment. After prosthodontic treatment (c) the 2-year recall radiograph (d) shows bone fill in the previous angular defect. Careful examination of the radiographs in (b) and (c) reveals a filled accessory canal communicating with the lateral bone defect.
**Fig. 40-6** Schematic illustrations demonstrating possible pathways for drainage of a periapical abscess. (a) Drainage along the periodontal ligament with an exit in the sulcus. (b) Extraosseous drainage with exits either in or near the sulcus.
**Fig. 40-7** (a) A large radiolucent area is present in the furcal region of a lower left first molar mimicking a furcation involvement caused by periodontal disease. In this case the lesion was of endodontic origin as indicated by the large caries lesion and necrosis of the pulp. (b) Endodontic treatment resulted in complete resolution of the bone lesion as demonstrated by the 18-month follow-up radiograph (c). Case kindly provided by Dr. Kevin Martin.
**Fig. 40-8** (a) Second molar displaying an apical–marginal communication along the distal root surface. The communication was made visible by a gutta-percha point brought into the sulcus. Endodontic treatment (b) resulted in complete resolution of the bone lesions associated with the distal root (c). At an emergency visit 2 years later the patient complained of pain and tenderness that turned out to be caused by a longitudinal root fracture involving the mesial root. Case kindly provided by Dr. Peter Jonasson.
Caution should be exercised in interpreting sensibility tests as findings can reflect both false-positive and false-negative readings (Mumford 1964; Petersson _et al_. 1989; Peters _et al_. 1994; Pitt Ford & Patel 2004). A combination of different test methods should be employed to ensure correct diagnosis, especially in doubtful cases. Also the equipment and the results should be tested for reliability by comparing results from tests of neighboring and contralateral teeth. No test has so far been advanced, which can identify the disease status of the pulp in other terms than vital or non-vital.
Testing non-restored or minimally restored teeth in dentitions affected by periodontitis can usually be successfully conducted by mechanical, thermal, and electric stimulation. Common methods utilize hydro-dynamic forces to stimulate nociceptive mechano-receptors at the pulp–dentin border, primarily the fast conducting A-delta fibers. Useful techniques include direction of a jet of compressed air against an exposed root surface, scratching such surfaces, use of a rubber wheel to generate frictional heat, and various cold tests; all intended to elicit movement of dentinal fluid. Highly effective and reliable are carbon dioxide snow (Fulling & Andreasen 1976) and dichloro-difluoro-methane sprayed on a cotton pledge. Boiling points of these two agents are at −72ºC and −50ºC, respectively. For this reason patients should be cautioned prior to application that an intense pain response might be elicited. Clues can also be obtained with less potent means such as ice sticks and ethyl chloride as well as heated gutta-percha sticks (for review see Pitt Ford & Patel 2004).
In dubious cases, mechanical and thermal provocation should be supplemented with electric pulp testing. Units are available which provide a read-out value of the voltage or micro-current being applied to generate the pain response. This function is important so that the test result can be repeated and compared for assessment of patient reliability. Electric pulp testing is technique sensitive and therefore warrants extra precaution to avoid leakage of current to the gingiva and neighboring teeth. To avoid this problem, the test should only be carried out on cleaned and dry teeth isolated from saliva and adjacent teeth with pieces of rubber dam placed in the tooth contacts (Fig. 40-9). The test further requires that the tooth electrode be provided with proper conducting medium and applied directly on to enamel or dentin.
**Fig. 40-9** Demonstration of proper tooth isolation to avoid leakage of current during pulp sensibility testing with an electric pulp tester.
Cases with extensive restorations and crowned teeth present special challenges as none of the normal test procedures are useful. Unless tooth substance can be reached underneath the restoration with a good margin to the gingiva, the restoration must be pierced to the extent that the test procedure can be conducted in a so-called test cavity. Even then a false-negative response can be obtained as extensive hard tissue repair may have developed in the pulp from previous disease and cutting traumas thus attenuating the stimulus.
Three cases are described below to illustrate the significance of pulp vitality testing in the process of distinguishing endodontic lesion from periodontitis. The cases demonstrate, in addition, that diagnostic entities such as location, form, and extension of radiolucencies, clinical symptoms of pain or swelling, and increased probing depths may not serve as precise diagnostic signs.
The clinical photograph in Fig. 40-10a shows swelling of the marginal gingiva on the buccal aspect of tooth #11. The swelling had been preceded by severe throbbing pain for a few days. Radiographic examination (Fig. 40-10b) disclosed the presence of an angular bone defect that involved the apical portions of the tooth. In this case the pulp clearly responded sensible on testing, indicating that the pathologic condition was not of endodontic origin. Pocket debridement was combined with irrigation with 0.2% chlorhexidine digluconate solution and systemic administration of an antibiotic. The lesion healed rapidly. Seven months following treatment new bone had formed around the apex and in the defect along the mesial root surface (Fig. 40-10c). In this case, therefore, the periodontal lesion was a manifestation of periodontal disease.
In Fig. 40-11a the radiograph taken of the lower front teeth demonstrates bone loss associated with the apex of tooth #31 in addition to a generalized horizontal loss of alveolar bone in this young individual. The form and extension of the apical radiolucency around tooth #31 suggests an endodontic lesion. Clinically, a deep periodontal pocket could be probed along the disto-buccal aspect of the root. The patient had been on a recall program after treatment for periodontal disease and had previously shown excellent gingival conditions. Sensibility tests by cold and electricity indicated vital pulp. Therefore, endodontic treatment was not performed. On elevating a mucoperiosteal flap an angular bone defect was found at the buccal aspect of the root without involvement of the root tip. The wound area was debrided along with scaling of the root surface. Rapid bone fill followed surgery without undertaking any adjunctive measures to support tissue regeneration (Fig. 40-11b). The pulp maintained its vitality, although later the root canal became obliterated by hard tissue, most likely as a consequence of the surgical trauma (Fig. 40-11c). The apically positioned radiolucency in Fig. 40-11a is explained by superimposition of the buccal loss of alveolar bone on the root tip of tooth #31, which went beyond its most apical level (Fig. 40-12) without interfering with the neurovascular supply of the pulp.
**Fig. 40-10** (a) Gingival swelling at the buccal aspect of tooth #11. (b) There is advanced destruction of alveolar bone along the mesial aspect of the root (arrowheads). Following periodontal treatment bone lesion resolved. Case kindly provided by Dr. Harald Rylander.
**Fig. 40-11** Advanced bone destruction of alveolar bone including an angular bone defect simulating an endodontic periapical lesion around the root tip of tooth #31. The pulp responded vital on testing and the tooth was therefore not subjected to endodontic therapy but to periodontal treatment only. For further case history see the text. Case kindly provided by Dr. Ingvar Magnusson.
Figure 40-13 demonstrates a clinical case where pulp vitality testing was difficult to carry out and which gave inconclusive findings even upon the preparation of a test cavity. A swelling had appeared at the buccal aspect of tooth #46 (Fig. 40-13a) after the patient had experienced pain and tenderness in the area for approximately 1 week. Periodontal probing disclosed a deep facial pocket along the mesial root (Fig. 40-13b). Radiographic examination indicated a lesion that seemed to circumscribe the mesial root with a marginal extension into the furcation (Fig. 40-13c). Frictional heat by drilling, as well as cold and electric tests, failed to give a positive response even in a test cavity preparation. After finding a sensitive and bleeding pulp in the distal root, a necrotic pulp with pus drainage was detected in the mesial root canals confirming an endodontic cause of the lesion. Endodontic treatment with a temporary intracanal dressing with calcium hydroxide over 3 months resulted in an obvious reduction of the bone lesion (Fig. 40-13d). The gingival lesion resolved with no abnormal pocket-probing depth (Fig. 40-13e), although a small bone defect remained in the furcation area (Fig. 40-13d). Treatment was then completed with root canal fillings. The 12-month recall radiograph demonstrates complete resolution of the bone defect (Fig. 40-13f).
**Fig. 40-12** Drawing depicting a potential mechanism for the radiographic lesion in tooth #31, Fig. 40-11. While there was substantial breakdown of alveolar bone there was no interference of the inflammatory lesion with the neurovascular supply of the pulp. The fact that the bone lesion appeared as an apical radiolucency is explained by the superimposition of the bone loss on the root tip. Courtesy of Dr. Mats Joatell.
### Other indications of endodontic lesion
Except for a negative pulp test response, single-tooth lesions in a dentition otherwise free from periodontal disease strongly suggest an endodontic cause, provided other tooth-associated disorders such as external root resorption and root fracture can be excluded. An endodontic etiology should be explored particularly in cases with extensive restoration or a crowned tooth (Figs. 40-8 and Figs. 40-13), bridge abutment (Fig. 40-3), caries (Fig. 40-7), a root-filled tooth, and in patients with a history of a previous dental trauma. The character of the pocket probing depth should also be taken into consideration. Endodontic lesions, when extending marginally, usually do not follow more than one root surface and then exit in a rather narrow area of the sulcus. Pocket probing depth may also be in an area uncharacteristic of periodontitis, for example at the buccal aspect, when all other sites display normal probing depths.
### Conclusion
The clinical presentation and the character of radiographic findings may lead to erroneous diagnosis in cases, where an endodontic lesion emerges in a patient with periodontal disease. The recognition of pulp vitality is crucial because clinically significant lesions of endodontic origin rarely develop in teeth with vital but inflamed pulps. The clinician should always be watchful for false leads and consider features which normally are associated with diseased pulps, such as extensive restoration, previous pulp capping, history of dental trauma, and endodontic treatment.
## Endo–perio lesions – diagnosis and treatment aspects
The potential for an infected, necrotic pulp to cause breakdown of the attachment apparatus with extension into the marginal periodontium has been addressed above, along with the measures to establish the diagnosis. Once confirmed, the mode of treatment in this type of case is simple and should involve only conservative root canal therapy. Following adequate treatment, directed to elimination of the root canal infection, the lesion should be expected to heal without a persistent periodontal defect (Figs. 40-3, Fig. 40-5, Fig. 40-8, and Fig. 40-13). Adjunctive periodontal therapy would have no treatment effect and would be inappropriate.
A more complex situation arises when a periodontal lesion is sustained by both plaque infection and a root canal infection concurrently. This kind of lesion is associated with a deep pocket probing depth and a lateral bone defect that extends to the apex (Fig. 40-8). The problem here is that it is not normally possible to determine how much of the lesion is sustained by one or the other infection. In fact there are three scenarios. Firstly, the entire lesion may be a manifestation of a root canal infection alone. Secondly, the entire lesion may be the result of plaque infection. Thirdly, there are, in fact, two disease processes, one marginal associated with a plaque infection and one apical associated with a root canal infection. It is just that the two soft tissue lesions have merged and there is no longer a clear demarcation zone between the two as a probe can penetrate both soft tissue lesions. This latter condition has been termed a "true endo–perio lesion".
Pulp vitality testing only partly settles the diagnostic quandary in this kind of case. Yet, if distinctly positive, one can exclude contribution of an endodontic infection and the process should be subject to periodontal therapy. Taking the pulp out and replacing it with a root filling is then a meaningless and unnecessary treatment effort. In the case of a negative pulp test, death of the pulp may have occurred as a direct result of the periodontal disease process or it may have developed independently as a separate condition. In the former case, prognosis for any other treatment than extraction must be regarded as bleak. A major reason is that not only may a substantial portion of the attachment apparatus be lost, but the root surface may be bacterially infected close to the root tip as well. In addition, the infection may have entered the root canal after necrosis of the pulp (see Chapter 23). Accessing this kind of infection for treatment is therefore a very challenging task with a questionable outcome.
**Fig. 40-13** Case with an initial unclear etiology of a facial swelling and deep pocket probing depth that turned out to have an endodontic etiology. The case history is given in the text. Diagnosis and treatment of this case was carried out by one of the authors (G.B.) in collaboration with Dr. David Simpson.
If a portion of the lesion is sustained by a root canal infection independent of periodontal disease, the potential for periodontal tissue regeneration is much increased. Because it is not possible to know beforehand how far the endodontic lesion has extended along the root, root canal treatment should be attempted first and periodontal treatment post-poned until the result of the endodontic treatment can be evaluated. The part of the lesion sustained by root canal infection can usually be expected to heal rapidly (Fig. 40-3). Periodontal attachment along with bone healing can then be expected within a few months. The part of the lesion caused by plaque infection may also heal following adequate periodontal therapy. Yet little or no regeneration of the attachment apparatus should be anticipated. Table 40-1 outlines the strategy to be taken for treatment of "endo–perio lesions".
**Table 40-1** Outline of treatment strategies
**Cause**| **Condition of the pulp**| **Treatment**
---|---|---
Endodontic| Non-vital| Endodontic
Periodontal| Vital| Periodontal
Endodontic/periodontal| Non-vital| Endodontic – first observe the result of this therapy and institute periodontal therapy later if necessary
### Conclusion
Deep pocket probing depths associated with angular bone defects may reflect a combined endodontic and periodontal lesion. Yet, the extent to which an endodontic infection has contributed to the attachment loss cannot normally be determined upon a negative sensibility test, as the entire loss might be caused by plaque infection. Therefore, a treatment strategy should be applied which includes endodontics in the first place, but only in cases where an endodontic etiology is reasonably plausible, that is in teeth with large restorations, full-coverage crowns or history of dental trauma. If the tooth is completely intact without major restoration, caries or history of trauma, the potential of an endodontic etiology of the process is remote.
## Endodontic treatments and periodontal lesions
Periodontal lesions, as already stated, may be maintained by infectious elements released from endodontically treated teeth. The lesion may have never resolved or may have developed after the completion of treatment. Several routes for dissemination of bacterial products are possible. Except for apical foramina and accessory canals, another possible pathway is inadvertently produced communication by root perforation (see below). The clinical presentation is no different to the one described above and consequently may involve acute exacerbations with quite extensive breakdowns of the attachment apparatus as well as localized, non-symptomatic lesions, only apparent in radiographs.
A persistent infection in root-filled teeth may also impact on the periodontium along dentinal tubules in areas where cementum has been damaged or lost (Hammarström _et al_. 1986; Blomlöf _et al_. 1988). The potential significance of such an avenue has been highlighted in clinical studies. Comparing teeth with healthy pulps, endodontically treated teeth with periapical pathology, indicating presence of persistent root canal infection, showed increased pocket probing depths (Jansson _et al_. 1993a), more marginal bone loss (Jansson _et al_. 1993b), and retarded or impaired periodontal tissue healing subsequent to periodontal therapy (Ehnevid _et al_. 1993a, b). Although the differences in probing depths and attachment losses in these studies were rather small, the observations suggest that endodontic re-treatment should be considered as an adjunct to periodontal therapy when a root canal filling is defective and/or displays signs of periapical inflammation. In individuals with no or minor evidence of periodontal disease, the root canal condition, whether root filled or not or infected or not, did not seem to affect the periodontal status in a controlled study (Miyashita _et al_. 1998).
### Conclusion
Unfilled spaces in endodontically treated root canals can sustain bacterial growth, and infectious products from these may reach the periodontium along the very same pathways as in an untreated tooth with infected pulp. Endodontic re-treatment may be considered as an adjunct to periodontal therapy when a root canal filling is of poor quality and/or displays signs of periapical inflammation because of the potential that bacterial elements may become disseminated to the periodontium along dentinal tubules exposed by periodontal instrumentation.
# Iatrogenic root perforations
During endodontic treatment, and in conjunction with preparation of root canals for insertion of posts, instrumentation can accidentally result in perforation of the root and wounding of the periodontal ligament (Sinai 1977; Kvinnsland _et al_. 1989; Eleftheriadis & Lambrianidis 2005). Perforations can be made through the lateral walls of the root or through the pulpal floor in multi-rooted teeth. The clinical course from then on depends largely on the extent the wound site becomes infected (Beavers _et al_. 1986). If made in the crestal bone area, a typical feature is epithelial proliferation and periodontal pocket formation (Lantz & Persson 1967; Petersson _et al_. 1985). If the perforation is more apical along the root, a wound site infection process may first lead to an acute pain condition, including abscess formation and drainage of pus, followed by further loss of fibrous attachment and periodontal pocketing (Fig. 40-14).
Early detection is critical for a successful outcome of treatment as long-standing perforations with a manifest infection have poor potential for repair. Successful treatments have, however, been attained in such cases (Tsesis & Fuss 2006).
**Fig. 40-14** Angular bone defect at the distal root surface of a mandibular molar (arrows). The root is perforated as indicated by the misaligned post. Clinical symptoms included drainage of pus from the pocket and increased tooth mobility. The tooth was extracted.
Diagnosis is based on the occurrence of sudden pain and bleeding during preparation of root canals coronal to the working length. Such signs are likely to be less distinct, however, if the perforation occurs during a procedure conducted under local anesthesia. A perforation may also go undetected as bleeding may not invariably be provoked. For example, when post preparations are carried out by means of a machine-driven instrument, a smear layer is formed that may clog up the blood vessels. Thus, in many instances no bleeding will be noticed until the following visit, when granulation tissue has proliferated into the root canal space along the perforation defect. Granulation tissue usually bleeds profusely on attempts to remove it. Electronic apex locators are helpful in the confirmation of a root perforation, when readings obtained are substantially shorter than the root canal length (Fuss _et al_. 1996).
Over the years many therapeutic agents and methods have been proposed for the management of root perforations (reviewed by Tsesis & Fuss 2006). Materials proposed for sealing from the inside of the root canal space include amalgam, zinc oxide and eugenol cements, both chemically cured and light-cured calcium hydroxide-containing pastes, and plaster of Paris. More recently, mineral trioxide aggregate (MTA) based on Portland cement has shown great promise by its ability to permit cementum repair (Arens & Torabinejad 1996; Schwartz _et al_. 1999).
Regardless of the material used, healing of the lesion in the periodontium depends on whether bacterial infection can be excluded from the wound site by a tight seal of the perforation (Beavers _et al_. 1986) (Fig. 40-15). This may be difficult to achieve, particularly if the perforation is made deep into the root canal at an oblique angle giving it an oval-shaped orifice into the periodontium. Nevertheless, for mid-root and cervical perforations, non-surgical approaches, including placement of an internal seal, are preferable to a surgical approach, as the latter often results in persistent pocket formation and furcation involvement. Furthermore, surgical treatment is not always feasible because of the inherent difficulty of accessing many perforation sites. As a last resort, extraction followed by repair and re-implantation of the tooth may be attempted (Tsesis & Fuss 2006). In multi-rooted teeth, hemisection and extraction of one or two roots may be a treatment of choice.
### Conclusion
Inflammatory lesions in the marginal periodontium, as manifested by increased probing depth, suppuration, increased tooth mobility, and loss of fibrous attachment, may result from an undetected or unsuccessfully treated root perforation. If an iatrogenic root perforation occurs during instrumentation of root canals, filling of the artificial canal to the periodontium should be carried out without delay to prevent granulation tissue formation and wound site infection. Outcome of treatment depends on how well the wound site can be sealed. The closer the perforation is to the bone margin, the greater the likelihood is for proliferation of epithelium at the perforation site with a deep, potentially suppurating pocket as a result.
# Vertical root fractures
Clinical symptoms that are typical of tooth-associated infections such as endondontic lesions and plaque-induced periodontitis may also appear at teeth with vertical root fractures. A vertical root fracture is defined as a fracture of a root that is longitudinally oriented at a more or less oblique angle relative to the long axis of the tooth (Fig. 40-16). It can traverse the root in different directions mesially/distally or facially/lingually; it may, but does not always, engage the root canal space. A vertical root fracture can extend the entire length of a root and then involve the gingival sulcus/pocket area. It may also be incomplete and confined to either coronal or apical ends. It should be noted that vertical root fractures although expanding in opposite directions may extend to one root surface only.
**Fig. 40-15** (a) Perforation of the pulpal floor of the mandibular first molar occurred in conjunction with a search for root canal openings. There is also a file fragment in one of the mesial canals. (b) The perforation was immediately sealed with guttapercha. (c) In a radiograph taken 1 month after treatment a slight radiolucency is seen at the site of the perforation (arrow). (d) Follow-up after 2 years showed normal periodontal conditions both clinically and radiographically. Case kindly provided by Dr. Gunnar Heden.
**Fig. 40-16** Vertical root fracture of a root-filled upper canine included as an abutment in a prosthetic reconstruction. Due to inflammatory breakdown of the buccal plate a typical bone dehiscence is seen.
## Mechanisms
Endodontically treated teeth appear over-represented among teeth with vertical root fracture in comparison to teeth with vital pulps (Meister _et al_. 1980; Gher _et al_. 1987; Patel _et al_. 1995). Generally the increased fracture propensity of root-filled teeth has been attributed to loss of tooth structure as a result of endodontic instrumentation and subsequent restorative procedures (Reeh _et al_. 1989; Sedgley & Messer 1992). Loss of fracture resistance increases especially after overzealous root canal preparation leaving thin dentin walls to the periodontium (Tjan & Whang 1985). Notches, ledges, and cracks induced by root canal preparation, root canal filling procedures, and seating of threaded pins and posts also contribute to sites of stress concentration during mastication that eventually may lead to fracture (Kishen 2006). Decrease of moisture content following root canal treatment is another claimed cause of increased fracture susceptibility of root-filled teeth; insignificant moisture differences were found, however, when dentin of teeth with vital pulps and dentin of root-filled teeth were compared (Papa _et al_. 1994). More recent observations have nevertheless demonstrated that biomechanical effects occur in dehydrated dentin that may render endodontically treated teeth prone to fracture (Kishen 2006). Dehydrated dentin _in vitro_ was observed to assume increased stiffness as well as a decrease in toughness (e.g. the total energy a material can absorb before fracturing) in comparison to hydrated dentin (Jameson _et al_. 1994; Kahler _et al_. 2003; Kishen & Asundi 2005). Hence, fluid-filled dentinal tubules as well as a water-rich pulp tissue may give normal teeth better resistance to occlusal loading forces than root-filled teeth. It has also been speculated that, along with loss of vital pulp tissue, mecha-noreceptive functions are lost concomitantly, allowing larger loads to be placed during mastication than the patient normally would feel tolerable (Löwenstein & Rathkamp 1955; Randow & Glantz 1986).
**Fig. 40-17** Crack in an unrestored maxillay molar causing symptoms of pulpitis. The patient, a 47-year-old male, had thought the pain problem originated from the temporo-mandibular joint. Following the preparation of a test cavity, a clear split line was observed at the bottom of the cavity (arrows), confirming the cause of the pain condition. Case kindly provided by Dr. Hideaki Suda.
Vertical root fracture may also occur in clinically intact teeth with no or minor restoration (Fig. 40-17). As posterior teeth are exposed to more heavy occlusal forces, mandibular molars appear to be especially at risk for fracture (Yang _et al_. 1995; Chan _et al_. 1999). Subsequent to fracture of teeth with vital pulps, typical pulpitis symptoms may be initiated, together with pain on percussion and mastication.
## Incidence
Data on the incidence of vertical root fractures are scarce in the literature. While it appears to be low, vertical root fractures probably occur more often than clinicians are able to diagnose (Tamse _et al_. 1999b). Molars and premolars appear more often affected than incisors and canines (Meister _et al_. 1980; Testori _et al_. 1993). In longitudinal clinical follow-up studies of patients treated with fixed prostheses, vertical root fractures were frequent in root-filled teeth with posts and especially so in teeth serving as terminal abutments in cantilever bridges (Randow _et al_. 1986).
It is important to recognize that root fracture of endodontically treated teeth may occur several years after the completion of endodontic therapy and final restoration of the tooth (Fig. 40-18). In a study comprising 32 vertical root fractures, the average time between the completion of endodontic treatment and diagnosis of fracture was 3.25 years, with a range varying between 3 days and 14 years (Meister _et al_. 1980). In another study comprising 36 teeth, symptoms of root fracture developed on average more than 10 years after completion of treatment (Testori _et al_. 1993).
## Clinical expressions
Clinical signs and symptoms associated with vertical root fractures vary hugely. Occasionally, there may be pronounced pain symptoms and abscess formation because of active bacterial growth in the fracture space (Fig. 40-18). In other instances clinical symptoms may be limited to tenderness on mastication, mild pain, and dull discomfort. Sinus tracts may emerge near the gingival margin (Fig. 40-19). A strong indication of a vertical root fracture is sinus tracts occurring at both buccal and lingual/palatal sites (Tamse 2006). In other instances, a narrow, local deepening of a periodontal pocket in an area not typical for periodontal disease may be the only clinical finding (Fig. 40-20).
The osseous defect emanating from the periodontal tissue lesion may take different shapes depending on how the fracture extends. If there is a buccal extension, the thin alveolar bone plate readily resorbs and a typical bone cleft can be seen upon raising a muco-periosteal flap (Fig. 40-16). At palatal or lingual extensions, the lesion may not resorb the entire bone wall. Therefore, the osseous defect may take a U-form shape with the height of the bone margin preserved. On fractures that are limited to the apical portion of the root, the bone defect may center on the root apex, similar to that of a periapical lesion associated with an infected root canal.
In conventional intraoral periapical radiographs these bone lesions may not be readily visible, depending on the location, character, and shape of the bone destruction (Fig. 40-20). Absence of lesion, even when taken at different angles, can also be explained by superimposition of roots and bone structures over the bone dehiscence. In yet other cases radiographic signs may be limited to widening of the periodontal ligament space. Lateral radiolucency along one or both of the lateral root surfaces may be discerned with more pronounced bone lesions. A thin halo-like apical radiolucency is another example of a radio-graphic lesion suggestive of a vertical root fracture (Pitts & Natkin 1983; Testori _et al_. 1993; Tamse _et al_. 1999a). Recent developments of tomographic techniques have brought valuable new diagnostic tools as they can remove interfering anatomic structures and thereby help to visualize presence, location, and extension of bone lesions (Gröndahl & Hummonen 2004) (Fig. 40-20e,f).
**Fig. 40-18** A typical case of a root fracture. (a) The first maxillary premolar had been asymptomatic for 20 years after completion of endodontic treatment and bridge-work. Patient sought treatment because of suddenly appearing pain, tenderness and facial swelling. (b) A deep periodontal pocket could be probed at the buccal aspect of the tooth, while all other sites displayed normal pocket probing depths. (c) Radiographs revealed a radiolucent area along the mesial aspect of the root system. (d) A set of radiographs taken 6 months earlier showed no such lesion. (e) Elevation of a mucoperiosteal flap revealed substantial loss of marginal bone at the buccal aspect of the root. A fracture going in a mesio-distal direction was subsequently confirmed. (f) Following removal of bone tissue, the roots were separated from the crown and extracted.
## **Diagnosis**
The diagnosis of a vertical root fracture is often difficult to ascertain because the fracture is usually not readily detectable by clinical inspection unless there is a clear separation of the root fragments. To give a radiographic appearance of the fracture in the absence of separation, the central X-ray beam has to be parallel to the fracture plane (Fig. 40-21). This is rarely achieved. The suspicion of a vertical root fracture is often inferred from a pocket probing depth in an aberrant position, for example at a buccal or lingual aspect of a tooth, in a dentition which otherwise is free from symptoms of periodontal disease. Another strong indication is the sudden appearance of clinical symptoms and/or radiographic lesion on a root-filled tooth that has remained asymptomatic and without lesion for years (Fig. 40-18).
**Fig. 40-19** (a) Periapical radiolucency associated with an upper second premolar that turned out to be caused by a vertical root fracture. There was a buccal, deep pocket-probing depth and a sinus tract near the gingival margin. (b) A gutta-percha point inserted in the fistulous tract points to the root apex but provided no additional clue in this case. The widely prepared root canal and the use of the tooth as an abutment in a cantilever bridge provided likely contributors to the fracture in this case kindly provided by Dr. Thomas Kvist.
A number of diagnostic procedures can be under-taken to confirm the diagnosis. Application of various dye solutions, e.g. methylene blue or iodine tincture, on to the crown and the root surface can sometimes be indicative. As the dye enters the fracture space, it will show up as a distinct line against the surrounding tooth substance. Indirect illumination of the root, using fiber-optic light, can also be of value. The fiber-optic probe should then be placed at various positions on the crown or the root, whereby the fracture line may clearly present itself. A surgical microscope or an endoscope, providing both enlargement and directed light, are other valuable tools to disclose vertical root fractures.
In premolars and molars the diagnosis may be supported from observation of varying pain sensations elicited by loading facial and lingual cusps. The procedure includes asking the patient to bite down on a rubber wheel or a specially designed plastic stick (FracFinder). Separate loading of either buccal or lingual cusps eliciting pain sensation from one, but not the other loaded cusp indicates the potential of a fracture. Often the diagnosis of a vertical root fracture has to be confirmed by surgical exposure of the root for direct visual examination (Walton _et al_. 1984) at which one may also discover a typical bone dehiscence (Fig. 40-16).
## Treatment considerations
Vertical root fractures that involve the gingival sulcus/pocket area usually have a hopeless prognosis due to continuous bacterial invasion of the fracture space from the oral environment. While there are reports of successful management of fractured teeth by re-attaching the fragments with bonding resin or laser fusing after extraction followed by re-implantation, fractured teeth are normally candidates for extraction. In multi-rooted teeth a treatment alternative is hemisection and extraction of the fractured root.
### Conclusion
Symptoms and signs associated with vertical root fractures vary and may be difficult to distinguish from those prevalent with other tooth-associated infections. A variety of diagnostic procedures should therefore be considered. Except for the leads obtained from anamnestic findings and pocket probing depths in buccal or lingual positions or both, clinical examination should include measures to make fracture lines visible _viz._ application of disclosing solutions, the use of fiber-optic light, inspection by a surgical microscope or endoscope, or by raising a surgical flap. Pain on selective loading of cusps may indicate root fracture. A vertical root fracture should be anticipated in root-filled teeth, which, after a long history of being asymptomatic and without signs of infection, suddenly present with tenderness, pain, and radiographic bone lesion (Fig. 40-18). Roots with vertical root fracture usually have a hopeless prognosis and are clear candidates for extraction.
**Fig. 40-20** Case of vertical root fracture, where ordinary intraoral radiographs failed to provide evidence of the associated bone lesion. (a) Radiograph shows normal periodontal contours. (b) A second radiograph indicates a widened periodontal ligament space. (c) The patient had complained of recurrent pain on occlusal load for several weeks and presented at the clinic with a light swelling on the buccal aspect that had appeared several weeks before. (d) Clinically there was an isolated 9 mm pocket probing depth mid-buccally, suggesting root fracture. (e,f) Limited cone beam computed tomography was helpful to reveal a bone lesion in this case along the palatal aspect of the tooth. (g) After extraction methylene blue staining visualized the fracture line (arrows) that turned out to extend to both the lingual and the buccal root surface (h). Case kindly provided by Dr. Thomas von Arx.
**Fig. 40-21** (a) Mandibular premolar included in a four-unit bridge showing a bone lesion at the mesial aspect of the root. In this projection there is no sign of fracture, while in a radiograph (b) taken with a slight shift of angle, a fracture line is clearly visible. Case kindly provided by Dr. K-G. Olsson.
# External root resorptions
Root surface resorptions, here termed external root resorptions, usually progress without producing clinical symptoms and may therefore go undetected unless observed radiographically. However, in advanced stages, the surface defect may interfere with the gingival sulcus and thereby initiate an infectious process. As such lesions can be associated with increased pocket probing depths as well as drainage of pus upon probing, this section of the chapter addresses various forms of external root resorptions, their mechanism, clinical features, and management.
## Mechanisms of hard tissue resorption in general
The hard tissues of the body consist of two major components, mineral and matrix. While the ratio of these two components varies between bone, cementum, and dentin, the same tools – acids and enzymes – are used by nature to perform the degradation of these tissues. Bone is normally remodeled to adapt to functional changes. Resorption of dental hard tissues of permanent teeth, on the other hand, should be seen as an expression of a pathological process. Clast cells carry out resorption of bone as well as cementum, dentin, and enamel (Hammarström & Lindskog 1992; Suda _et al_. 1996). These cells are large, multi-nucleated, motile cells emanating from hematopoietic precursor cells in the bone marrow (Marks 1983; Vaes 1988; Pierce _et al_. 1991; Suda _et al_. 1996) and termed osteoclasts when involved in bone remodeling processes. Phenotypically the very same kind of clast cells conduct resorption of the hard tissues of the tooth. Mononucleated cells are also involved in the later phase of the resorption process by eliminating the organic matrix that became released following dissolution of the mineral components (Wedenberg & Lindskog 1985; Lindskog _et al_. 1987; Brudvik & Rygh 1993; Lerner 2006).
Under normal, physiologic conditions, hard tissues are protected from resorption by their respective surface layers of blast cells; in the case of cementum by cementoblasts. As long as these blast cell layers remain intact with the unmineralized layer of osteoid or cementoid at the surface of the mineralized tissue, resorption will not occur. It is known that bone resorption is under hormonal regulation and is mediated by osteoblasts (Lerner 2006). Stimulation by parathyroid hormone makes the osteoblasts first degrade the osteoid and then contract to expose the bone surface for osteoclastic demineralization (Jones & Boyde 1976; Rodan & Martin 1981; Lerner 2006). However, parathyroid hormone exerts no influence on cementoblasts (Lindskog _et al_. 1987), which may explain why bone, but not teeth, is remodeled to adapt to functional changes. However, dental trauma, excessive orthodontic forces and aggressive scaling and root planing during periodontal therapy are examples of injuries that can initiate root resorption (Andreasen 1981; Rygh 1977). Subsequent to the injury, the denuded hard tissue surface, without its blast cell layer and cementoid, attracts motile clast cells (Chambers 1981), which seal themselves to the hard tissue surface and excrete acids for demineralization. Concomitantly an acid environment is created that is essential for the degradation of tissue matrix by lysosomal enzymes at low pH optima (Vaes 1988; Kremer _et al_. 1995; Pascoe & Oursler 2001; Czupalla _et al_. 2006; Henriksen _et al_. 2006).
Consequently, a trigger mechanism is required to set off root resorption. For the resorption process to continue, a lasting osteoclast stimulus is required, for example an infection or a continuous mechanical force such as the one elicited by orthodontic treatment. In both instances the resorptive process may be halted if the cause for prolongation can be curbed; in the case of orthodontic tooth movement, by releasing the forces, and in the case of a root canal infection, by root canal therapy.
**Fig. 40-22** Series of radiographs taken at different time intervals showing the appearance of an external root resorption in a young adult patient. (a) At the age of 15 years there is no sign of resorption. (b) Six years later a small radiolucency is seen (arrow). (c) In just 6 months the lesion expanded considerably (arrow). (d) The lesion appeared clinically as a pink spot in the cervical area of the tooth (arrow). Case kindly provided by Dr. Anders Molander.
### Conclusion
Two mechanisms are involved in resorption of a hard tissue: (1) a trigger mechanism and (2) a reason for the resorption to continue. Thus, treatment of active root resorption should be directed to eliminate the cause for its continuance.
## Clinical presentations and identification
Root resorptions _per se_ do not cause painful symptoms. Unless a resorptive process is located coronally and is undermining the enamel, giving it a pinkish appearance (Fig. 40-22), the only way to detect and diagnose dental resorption is by means of radiography (Fig. 40-22b,c). Only in very late stages, as the resorptive process engages the gingival sulcus, may an infectious process emerge with typical features of a periodontal abscess (Fig. 40-23).
A single radiograph is usually not sufficient to define a radiolucent area within the confines of a root as an external resorption. A radiolucency may portray a variety of conditions including a resorptive process inside the root canal (internal root resorption), or a resorptive defect located buccally or lingually as the image of the root is superimposed. It may also be an artifact and reflect a radiolucent bone area superim-posed on the root. Therefore, one should always take more than one radiograph and use different angulations to observe whether the radiolucent area belongs to the root or not (Fig. 40-23). New tomographic techniques can be of great benefit to distinguish external from internal root resorptions.
The initial stage of a resorptive process usually passes undetected as radiographs can only present a resorptive cavity after a certain size has been reached (Andreasen _et al_. 1987) (Fig. 40-23). The location of the lesion is also important for detection. A facial or lingual root resorption defect is more difficult to visualize radiographically than a proximal cavity, unless tomography is used. Be aware that in the cervical region it may be difficult to differentiate radiographically between cavities caused by caries and those caused by resorption. To distinguish caries from resorption it is useful to recognize that bacterial acids that demineralize dentin leave a soft cavity surface. By contrast, clastic resorption removes both the mineral and the organic phases of the hard tissues resulting in a cavity floor that is hard to probing.
## Different forms
There are different forms of external root resorption. The underlying mechanism is understood only for some of them. A genetic link can be seen in certain cases as external root resorptions run in families. There are also instances when only the enamel of an unerupted tooth is resorbed. Furthermore, external resorptions can be caused by precipitation of oxalate crystals in the hard tissues of patients as a result of increased concentration of oxalates in the blood due to kidney failure (Moskow 1989). Malignant tumors close to a tooth can also cause root resorption (Fig. 40-24).
Andreasen (1981) has published a classification of those external root resorptions that have a known etiology:
* Surface resorption
* Replacement resorption associated with ankylosis
* Inflammatory resorption associated with persistent inflammation in the periodontium adjacent to the resorption site.
**Fig. 40-23** Case of peripheral inflammatory root resorption (PIRR). Pain and tenderness of the right maxilla for several weeks prompted the 30-year-old male patient to seek treatment. (a) Clinical inspection revealed no obvious pathology. (b) Periodontal probing, however, released pus drainage from the lingual aspect of tooth #13. Pulp-vitality test of the tooth as well as neighboring teeth gave clear positive responses. (c) An angulated radiograph disclosed the presence of a resorptive defect. (d) The tooth was extracted as successful treatment was deemed unlikely. An extensive resorptive defect had undermined the clinical crown.
**Fig. 40-24** External root resorption of a lower second molar caused by breast cancer metastasis. Case kindly provided by Dr. John Kuo-Hung Yu.
Subforms are:
* Peripheral inflammatory root resorption (PIRR)
* External inflammatory root resorption (EIRR).
### Surface resorption
This type of resorption is common, self-limiting, and reversible (Harding 1878; Andreasen 1981). In a histologic study of human teeth from individuals varying in age from 16–58 years, only 10% of the teeth showed absence of active resorption or signs of healed resorptions (Henry & Weinman 1951). Resorptions were noted twice as often in older than in young subjects. Another study demonstrated up to 88% of teeth with active or, in most instances, healed resorptions (Hötz 1967).
The mechanisms behind surface resorptions are only partly understood. These resorptions are normally initiated in conjunction with a localized injury to the cementoblast cell layer, for example by external trauma (Andreasen 1981) or by trauma from occlusion. As clast cells are attracted to the denuded root surface, hard tissue is resorbed for as long as the activating factors are released at the site of injury (Hammarström & Lindskog 1992). The resorptive process then stops within a few days following the disappearance of clast cells along with the defect becoming populated with hard tissue repairing cells leading to cementum repair (Lindskog _et al_. 1983, 1987). The regulating factors governing this process are virtually unknown.
Surface resorption may also result from orthodontic forces. Light forces produce insignificant cemental cratering (root resorption) with rapid tooth movement. On the other hand, intermediate and heavy forces produce substantial cemental cratering and slower tooth movement (Rygh 1977). Following application of an orthodontic force three main stages for the tooth movement can be identified:
1. _Initial minor movement due to the compression of pliable tissues_. During the initial stage of tooth movement, osteoclasts, macrophages, fibroblasts, and resorption lacunae in bone increase on the pressure side (Kurihara 1977; Brudvik & Rygh 1993, 1995).
2. _Delay period with no movement_. The induced tissue damage to the periodontal ligament is resolved by macrophages and osteoclasts during a delay period (Rygh 1977; Brudvik & Rygh 1993, 1995). If excessive forces are placed on teeth, there is increased damage to the surrounding tissues, which prolongs the delay period (Storey 1973). In this phase, the tissues show signs of hyalinization, i.e. development of a cell-free, structureless zone (Sandstedt 1904; Reitan 1951; Kvam 1967; Brudvik & Rygh 1993) as compressed collagen fibers gradually unite to a more or less cell-free mass (Rygh 1972, 1977).
3. _Rapid tooth movement and extensive bone remodeling_. Elimination of the hyalinized tissue leads to removal of the mature collagen and cementoid layer leaving a raw root surface lacking a protective blast cell barrier. The denuded root surface subsequently attracts clast cells and root resorption continues for as long as the force is present (Storey 1973; Rygh 1977; Brudvik & Rygh 1993, 1995). Major loss of dental hard tissue may follow this kind of iatrogenic injury.
### _Conclusion_
Signs of active or healed surface resorptions or both are common in the large majority of teeth of the adult dentition. It is conceivable that minor traumata caused by unintentional biting on hard objects, bruxism, high fillings, etc., cause localized damage to the periodontal ligament and trigger the initiation of this type of resorption. The process is self-limiting and self-healing and no active treatment is required. During orthodontic treatment caution should be exercised and the forces moderated so that the risk of root foreshortening is minimized. When heavy forces are used the involved teeth should be monitored radiographically.
### Replacement resorption
This type of resorptive process involves replacement of the dental hard tissues by bone, hence the name (Andreasen 1981). When a surface resorption stops, cells from the periodontal ligament will proliferate and populate the resorbed area (Lindskog _et al_. 1983, 1987). If the surface resorption defect is large, it will take some time before periodontal ligament cells have covered the entire surface. In the interim period osteoblasts from the nearby bone tissue may then arrive first and establish themselves at the resorbed surface (Andreasen & Kristerson 1981; Gottlow _et al_. 1986). Bone is thus being formed directly upon the dental hard tissue. This results in a fusion between the bone and the tooth substance, which is known as ankylosis. Note that replacement resorption and ankylosis are often erroneously used as synonyms. While replacement resorption describes the active process during which the tooth is resorbed and replaced by bone tissue, ankylosis is the Greek word for immobile. Thus, it describes the situation of a tooth lacking normal mobility due to the fusion between tooth and bone.
The fusion can be permanent or transient and appears to depend on the size of the resorbed area. If the ankylotic area is small, the bone on the tooth surface can resorb and be replaced with reparative cementum (Andreasen & Skougaard 1972; Andreasen & Kristerson 1981; Andersson _et al_. 1985; Hammarström _et al_. 1986). If the ankylotic area is large, a sufficient amount of bone will be formed on the root surface to make the fusion between bone and tooth permanent (Andreasen 1981; Andreasen & Kristersson 1981; Hammarström _et al_. 1986). It has been shown that long-term rigid splinting following external trauma results in a higher incidence of dento-alveolar ankylosis than with a short-term, less rigid fixation (Andreasen 1975).
Clinically, ankylosis is diagnosed by absence of tooth mobility and by a percussion tone that is higher than in a normal tooth (Andreasen 1975; Andersson _et al_. 1985). Radiographically, a local disappearance of the periodontal ligament contour may show an initial stage of fusion. However, even in non-ankylosed teeth it is not always possible to observe the entire contour of the periodontal ligament. Percussion and tooth mobility testing are therefore more sensitive diagnostic tools than radiography in the early stages of replacement resorption (Andersson _et al_. 1985). When dento-alveolar ankylosis occurs at a young age, the tooth will not erupt resulting in infra-occlusion (Andreasen & Hjörting-Hansen 1966; Malmgren _et al_. 1984; Kürol 1984).
The formation of bone on a dentin surface is not a pathologic process, but one to be regarded as a form of repair. The bone has accepted the dental hard tissue as a part of itself and the tooth becomes involved in the normal skeletal turnover (Löe & Waerhaug 1961; Hammarström _et al_. 1986). The turnover phase is fast in a growing child, but slower in an adult. Hence, the rate of bone replacement follows the pattern of bone remodeling. The detailed mechanism directing the resorptive process is not understood.
### _Conclusion_
Ankylosis caused by apposition of bone to a root surface is a prerequisite for replacement resorption. The condition may be seen as a form of repair of root surface resorptions, albeit not desirable from a clinical standpoint as the root structure will become successively destroyed. No treatment is available for this condition.
### External inflammatory resorption
The term external inflammatory resorption describes the presence of an inflammatory lesion in the periodontal tissues adjacent to a resorptive process (Andreasen 1985). There are two main forms – peripheral inflammatory root resorption (PIRR) and external inflammatory root resorption (EIRR). Both forms are triggered by destruction of cementoblasts and the cementoid. In PIRR the factor maintaining osteoclast activation is thought to be provided by an inflammatory lesion in the adjacent periodontal tissue (Andreasen 1985; Gold & Hasselgren 1992). EIRR, on the other hand, receives its stimulus from an infected necrotic pulp (Andreasen 1985; Andreasen & Andreasen 1992).
### _Peripheral inflammatory root resorption_
The major feature of this type of resorption is its location close to the gingival margin and its invasive nature. In teeth with a normal height of bone crest it usually becomes localized cervically, whereas in cases where the periodontal tissue has receded it can develop more apically. Different names have been proposed, including subosseous resorption (Antrim _et al_. 1982) and (the complete opposite) supraosseous extra-canal invasive resorption (Frank & Bakland 1987) reflecting the confusion that has surrounded the cause of this type of resorptive lesion. As it extends into the peripheral dentin towards the pulp, and as clast-activating factors seem to emanate from an inflammatory lesion in the periodontium, the term peripheral inflammatory root resorption (PIRR) was proposed to reflect the potential etiology of this phenomenon (Gold & Hasselgren 1992).
The clinical features of PIRR include a granulation tissue that bleeds freely on probing. Occasionally, a periodontal abscess may develop due to marginal infection, which may mimic a periodontal or endodontic condition (Fig. 40-23). When the lesion is located more apically or proximally, probing is usually difficult. Radiographically, the lesion may only be seen after a certain size has been reached (Fig. 40-22c). Sometimes the appearance is mottled due to the proliferation of bone tissue into the resorptive defect (Seward 1963) (Fig. 40-25). The outline of the root canal can often be seen within the radiolucent area (Figs. 40-22, 40-25 and 40-26) and this is a diagnostic feature for external root resorption in general. The presence of profuse bleeding upon probing and granulation tissue formation, in combination with a hard cavity bottom confirm the diagnosis of PIRR. Electric pulp test and cold tests are usually positive, but will not distinguish this condition from caries or internal resorption, the two major differential diagnostic options (Frank & Bakland 1987).
**Fig. 40-25** (a,b) Peripheral inflammatory root resorption in a first lower molar showing a mottled appearance. There are pulp stones within the pulp tissue and bone tissue formation within the resorptive defect superimposed on the pulpal space. Following accessing both the pulp and the resorptive process (c) and removing the bleeding tissue, bone tissue appeared at the lingual wall of the cavity, where the resorptive process had entered the tooth (d). Arrow in (d) indicates the orifice of the root canal in the distal root. Case kindly provided by Dr. Magnus Fridjon Ragnarsson.
**Fig. 40-26** Case with external root resorption on the lingual aspect of both central incisors. (a) The patient, a 78-year-old lady, had presented herself to the clinic after an episode of severe pain and development of a lingual periodontal abscess. The medical history was unremarkable. The patient was initially managed by antibiotic treatment. (b) Later, upon flap elevation and accessing the resorbing area and removal of the granulation tissue, exposure to a necrotic pulp of tooth #31 was noted. (c) Endodontic treatment was carried out during the surgery procedure. Tooth #41 was left without any further treatment and the case was followed clinically and radiographically. No recurrence of resorption occurred on either tooth and the patient remained comfortable. (d) Radiograph of the last follow-up is 8 years after treatment. Note that there is no progression of the resorptive process associated with tooth #41.
The mechanism for this form of resorption is far from completely understood. Predisposing factors seem to be orthodontic treatment, trauma, and intracoronal bleaching, while periodontal therapy had a low incidence among 222 analyzed cases (Heithersay 1999). The reason for the low incidence following periodontal treatment could be that, even upon excessive scaling and root planing, the damaged area of the root surface usually becomes covered by junctional epithelium. If a resorptive process is triggered it seems that its continuance has an infectious cause (Brosjö _et al_. 1990; Gold & Hasselgren 1992).
Unmineralized, newly formed tissue in cementum (Gottlieb 1942) and in predentin (Stenvik & Mjör 1970) appears resistant to resorption and explains why PIRR expands laterally without invading the pulp. Yet, this peripheral extension can markedly undermine the tooth structure (Fig. 40-23). If there is a non-vital pulp and thus no resorption inhibition in the form of odontoblast-supported predentin, PIRR may extend to the pulpal space. In root-filled teeth, which have been subjected to intracoronal bleaching, tissue toxic bleaching agents such as hydrogen peroxide have been found to be capable of penetrating through dentin and cementum (Fuss _et al_. 1989). If this occurs during the bleaching process, periodontal tissue injury will be inflicted and a resorptive processs may be initiated (Harrington & Natkin 1979; Montgomery 1984). The ensuing progression is thought to be a function of persisting inflammation as bacteria have colonized the chemically emptied dentinal tubules (Cvek & Lindvall 1985).
Obviously there are also different forms of this kind of resorption, some of which may be associated with a broad opening to the periodontium, as in the cases initiated by bleaching agents. Others may have smaller openings through the cementum layer along which the resorptive process continues inside the tooth structure without causing major peripheral breakdown. The two patterns dictate the choice of treatment attempt. Surgical exposure of the area including removal of the granulation tissue is the only reasonable option in the former case; a dental filling, e.g. a resin composite, is placed in the defect followed by resuturing the flap. Other treatment options include repositioning of the flap apical to the restoration or orthodontic extrusion of the tooth (Gold & Hasselgren 1992). Guided tissue regeneration has also been advocated after surgical removal of the granulation tissue, to promote ingrowth of periodontal ligament cells into the resorbed area (Rankow & Krasner 1996)
### _External inflammatory root resorption_
This type of resorption usually occurs as a complication to luxation injuries in conjunction with dental traumata. It begins as a surface resorption due to damage of the periodontal ligament and the cementum layer. There is good support for the view that the stimulus for continuance is infectious in nature and that the source is an infected pulp that succumbed as a result of the traumatic injury (Bergenholtz 1974; Andreasen 1985; Andreasen & Andreasen 1992). Following the initial surface resorption the often rapid progression is then due to the release of bacterial elements into the periodontal tissue by way of the exposed dentinal tubules. While the inflammatory process is maintained, the resorptive process, aimed at eliminating the irritants in the dentin tubules, moves in the direction of the infected pulp. As dentin is further resorbed, more infectious products are released thus perpetuating the inflammatory reaction with acceleration of the resorptive process as a result (Andreasen 1985).
The earliest stages are not radiographically visible due to the small size of the resorptive cavity and the first radiographic signs following trauma cannot usually be seen for several weeks (Andreasen _et al_. 1987). Treatment is directed towards the cause of the resorption, that is, the root canal infection (Cvek 1993), and the procedure to be carried out is no different to the one applied in normal cases. While a successful halt of the resorption can be anticipated (Cvek 1973) there is always risk of ankylosis after the initial healing phase. The greater the resorbed area, the greater is the risk for this complication (Andreasen & Kristerson 1981; Andersson _et al_. 1985; Gottlow _et al_. 1986).
### _Conclusion_
Peripheral inflammatory root resorption (PIRR) and external inflammatory root resorption (EIRR) are two forms of progressive external root resorption associated with persistent inflammation in the periodontal tissues. While the direct cause for progression is not well understood, infectious elements maintaining periodontal inflammation close to a root surface that is not covered by periodontal ligament or epithelium appear to drive PIRR. To remedy the condition it is necessary to remove all resorbing granulation tissue surgically and fill the resorption cavity. In certain cases it may be possible to carry out the treatment from the pulpal side (Fig. 40-25). Regardless of approach, periodontal tissue complications may ensue, including deep pockets and suppuration from such pockets. Treated cases should therefore be monitored by regular clinical/radiographic follow-ups to observe any signs of recurrence and how the periodontal tissue copes. In advanced cases extraction is the only reasonable treatment option. EIRR is usually seen as a complication to luxation injuries in conjunction with dental traumata. The primary impetus for its progression is an infected pulp that releases bacterial elements to the resorbing area along exposed dentinal tubules by which an inflammatory lesion is also maintained in the periodontium. EIRR can usually be stopped by focusing the treatment on the endodontic infection (Fig. 40-27) although ankylosis and replacement resorption may appear as complications that may not be detected until years later.
**Fig. 40-27** Radiographs from a 27-year-old woman showing the emergence of external inflammatory root resorptions on the left maxillary canine, which had been autotransplanted into a surgically prepared socket 2 months earlier (a). Endodontic treatment of the necrotic pulp (b) halted the resorptive process. (c) Radiograph following root filling shows that the external resorption cavity is rounded. A normal contour of the periodontal ligament space can be seen between the root and bone, which has filled the prepared socket.
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# Chapter 41
# Treatment of Peri-implant Lesions
Tord Berglundh, Niklaus P. Lang, and Jan Lindhe
* * *
Introduction
The diagnostic process
Treatment strategies
Resolution of peri-implantitis lesions
Cumulative Interceptive Supportive Therapy (CIST)
Preventive and therapeutic strategies
Mechanical debridement; CIST protocol A
Antiseptic therapy; CIST protocol A+B
Antibiotic therapy; CIST protocol A+B+C
Regenerative or resective therapy; CIST protocol A+B+C+D
* * *
# Introduction
Inflammatory lesions occurring in the peri-implant tissues were described in Chapter 24. Such processes are the result of opportunistic infections (see Chapter 10) and may, if left untreated, progress deep into the supporting bone and lead to implant loss. It is, therefore, imperative that the tissues around implants be monitored at regular intervals to discover arising biologic complications and to interfere with the disease process at an early stage. The appropriate therapy instituted following diagnosis must be aimed towards the reduction of the submucosal biofilm and the alteration of the ecologic conditions for the bacterial habitat.
# The diagnostic process
The examination of the tissues around implants has many features in common with the periodontal examination and must include parameters relevant to the pathogenic process of the peri-implant lesion. It should be understood that, while advanced peri-implant lesions are easily recognized on radiographs, early alterations in the mucosa are often discrete (see also Chapter 24). Hence, a systematic examination for their detection is required that should include assessments of:
* Bleeding on probing (BoP)
* Suppuration
* Probing depth (PPD)
* Radiographic bone loss
* Implant mobility.
Assessments of BoP, suppuration, and PPD must be made at four surfaces (mesial, buccal, distal, and lingual) of each implant, while radiographic evaluation is limited to mesial and distal aspects.
# Treatment strategies
The decision on treatment strategies is based on the diagnosis and the severity of the peri-implant lesion. Peri-implant mucositis and incipient forms of peri-implantitis require less extensive measures than advanced peri-implantitis lesions with severe bone loss. In all situations of peri-implant disease, however, the treatment strategies must include mechanical cleaning (infection control) procedures. Thus, information and instruction on the use of oral hygiene measures must be provided to the patient in combination with professional mechanical cleaning, including removal of plaque and calculus on implant surfaces. In this context it is important that the design of the implant-supported prosthesis allows access for oral hygiene. Thus, in cases where access for implant cleaning is obstructed, the prosthesis has to be modified to promote self-performed and professional mechanical infection control.
Two cases that illustrate the outcome of self-performed and professional mechanical cleaning are presented in Figs. 41-1 and 41-2. While plaque, calculus, and signs of inflammation are evident at implants in the initial examination, the follow-up visit at 3 months of infection control demonstrates improved oral hygiene and soft tissue conditions.
There are obvious similarities between teeth and implants regarding the strategies in treatment of periodontal and peri-implant infections. One important difference, however, relates to difficulties with instrumentation of the implant surface below the margin of the mucosa. Thus, subgingival scaling and root planing are well known procedures in the treatment of periodontitis, while in peri-implantitis the geometry of the implant with threads of different designs may impede the ability of the clinician to detect and remove calculus located below the mucosal margin. During such "blind" instrumentation at implants there is also a risk that deposits may be dislodged and become displaced into the mucosa. It is thus recommended that non-surgical debridement of implant surfaces, i.e. procedures that aim to remove calculus and plaque, should be restricted the portion of the implant located coronal to or at the level of the mucosal margin. While calculus may be chipped off using carbon fiber (Fig. 41-3) or plastic curettes, plaque is removed by polishing the implant surface with rubber cups and a polishing paste. Carbon fiber curettes do not damage the implant surface. They may be sharpened and are strong enough to remove most accumulations of calculus. Conventional steel curettes or ultrasonic instruments with metal tips should not be used because they may cause severe damage to the implant surface (Matarasso _et al_. 1996).
There are obvious similarities between teeth and implants regarding the strategies in treatment of periodontal and peri-implant infections. One important difference, however, relates to difficulties with instrumentation of the implant surface below the margin of the mucosa. Thus, subgingival scaling and root planing are well known procedures in the treatment of periodontitis, while in peri-implantitis the geometry of the implant with threads of different designs may impede the ability of the clinician to detect and remove calculus located below the mucosal margin. During such "blind" instrumentation at implants there is also a risk that deposits may be dislodged and become displaced into the mucosa. It is thus recommended that non-surgical debridement of implant surfaces, i.e. procedures that aim to remove calculus and plaque, should be restricted the portion of the implant located coronal to or at the level of the mucosal margin. While calculus may be chipped off using carbon fiber (Fig. 41-3) or plastic curettes, plaque is removed by polishing the implant surface with rubber cups and a polishing paste. Carbon fiber curettes do not damage the implant surface. They may be sharpened and are strong enough to remove most accumulations of calculus. Conventional steel curettes or ultrasonic instruments with metal tips should not be used because they may cause severe damage to the implant surface (Matarasso _et al_. 1996).
**Fig. 41-1** Clinical photograph from implant sites in the mandible of a 75-year-old male (a) and a 62-year-old woman (b). Note the large amounts of plaque and calculus and the overt signs of inflammation in the peri-implant mucosa (a).
**Fig. 41-2** Implant sites in Fig. 41-1 after 3 months of self-performed mechanical infection control combined with professional cleaning. Improved oral hygiene and soft tissue conditions.
Peri-implant mucositis and incipient peri-implantitis lesions may be resolved using the cause-related measures described above. A re-examination of peri-implant tissues following initial therapy that reveals absence of BoP and pocket closure indicates resolution of peri-implant lesions. On the other hand, if signs of pathology, i.e. BoP/suppuration in combination with deep pockets remain at the re-examination, additional therapy is required. Surgical procedures are one treatment option which provides access to the implant surfaces harboring biofilms. A prerequisite for surgical therapy in treatment of peri-implantitis is appropriate standards of self-performed infection control.
**Fig. 41-3** Calculus deposits may be chipped off using carbon fiber curettes with the aim of not scratching the implant surface.
Surgical therapy of peri-implantitis lesions is illustrated in Figs. 41-4, 41-5, and 41-6. Clinical signs of inflammation, PPD of about 10 mm in combination with BoP and suppuration were detected at the initial examination (Fig. 41-4). The radiograph revealed crater-formed defects around the two implants. Flap elevation allowed access to the area and granulation tissue in the defects was removed using steel curettes (Fig. 41-5). Mechanical debridement of the implant surface was performed using carbon fiber curettes and small pieces of gauze or pellets soaked in saline. The peri-implantitis associated bone defect may be treated using either resective or regenerative procedures (see also Chapter 46). In this case the morphology of the osseous defect was not suitable for regenerative techniques and, hence, resective procedures were performed to adjust the morphology of the interproximal bone walls. At the 6-month follow-up after surgery, PPD was reduced and clinical signs of inflammation were absent (Fig. 41-6).
**Fig. 41-4** Clinical photograph from implant sites with peri-implantitis. Note the PPD of 10 mm and suppuration (a) and the crater-formed defects in the radiograph (b).
**Fig. 41-5** Implant sites in Fig. 41-3 after flap elevation and removal of granulation tissue. Note the absence of buccal bone walls of the osseous defects. The implant surfaces are accessible for mechanical debridement.
**Fig. 41-6** Implant sites in Fig. 41-3 at 6 months after surgical therapy. Maintenance therapy with supervised infection control is provided. Note the soft tissue recession following the pocket elimination procedure.
Recent reviews on treatment of peri-implant mucositis and peri-implantitis indicated that most articles in the literature consist mainly of case reports (Klinge _et al_. 2002; Roos-Jansåker _et al_. 2003). In addition to mechanical debridement a vast number of different treatment procedures have been suggested including antiseptic agents and local and/or systemic antibiotics. Klinge _et al_. (2002) concluded that there is insufficient evidence to support a specific treatment protocol.
## Resolution of peri-implantitis lesions
In dog experiments by Ericsson _et al_. (1996) and Persson _et al_. (1996, 1999), peri-implantitis lesions were first produced according to the technique previously described (Lindhe _et al_. 1992). The peri-implantitis lesions were subsequently exposed to therapy. Antibiotics (amoxicillin and metronidazole) were administered to the animals via the systemic route but local treatment was provided to only some of the diseased implant sites. Following several months of healing, it was observed that in implant sites also given local therapy, i.e. submarginal debridement, the inflammatory lesions were resolved. In implant sites not exposed to local debridement, however, the inflammatory infiltrate persisted in the mucosa as well as in locations immediately adjacent to the bone tissue.
These observations clearly demonstrate that a treatment regimen that is restricted to systemic administration of antibiotics is not effective in the management of peri-implantitis, but must always be combined with meticulous removal of the biofilm from the contaminated implant surface. In this context it must be remembered that in the treatment of chronic periodontitis administration of systemic antibiotics without local therapy (i.e. scaling and root planing) will not resolve the inflammatory lesion in the gingiva and will also fail to arrest further progression of tissue breakdown (Lindhe _et al_. 1983a,b; Berglundh _et al_. 1998).
# Cumulative Interceptive Supportive Therapy (CIST)
## Preventive and therapeutic strategies
Depending on the clinical, and eventually the radiographic, diagnosis, protocols for preventive and therapeutic measures were designed to intercept the development of peri-implant lesions. This system of supportive therapy is cumulative in nature and includes four steps, which should not be used as single procedures, but rather as a sequence of therapeutic procedures with increasing anti-infective potential depending on the severity and extent of the lesion. Diagnosis, therefore, represents a key feature of this supportive therapy program (Lang _et al_. 2004).
The major clinical parameters to be used have been discussed above and include:
* Presence of a biofilm
* Presence or absence of BoP
* Presence or absence of suppuration
* Increased peri-implant probing depth
* Evidence and extent of radiographic alveolar bone loss.
Oral implants without plaque and calculus and surrounded by healthy peri-implant tissues, as evidenced by (1) absence of BoP, (2) absence of suppuration, and (3) probing depth usually not exceeding 3 mm, should be considered clinically stable. Such sites should not be exposed to therapeutic measures (Fig. 41-7).
**Fig. 41-7** Clinically stable implant with VMK crown (region 21) characterized by absence of bleeding on probing, suppuration, and a peri-implant probing depth not exceeding 3 mm.
**Fig. 41-8** Peri-implant mucositis characterized by presence of bleeding on probing, absence of suppuration, and a periimplant probing depth of 4 mm.
## Mechanical debridement; CIST protocol A
Implants with plaque and calculus deposits and surrounded by a mucosa that is BoP positive but suppuration negative and with a PPD ≤4 mm are to be subjected to mechanical debridement as described above (Fig. 41-8).
## Antiseptic therapy; CIST protocol A+B
At implant sites which are BoP positive, exhibit an increased probing depth (4–5 mm) and may or may not demonstrate suppuration, antiseptic therapy is delivered in addition to mechanical debridement. A 0.2% solution of chlorhexidine digluconate is prescribed for daily rinsing, or a 0.2% gel of the same antiseptic is recommended for application to the affected site (Fig. 41-9). Generally, 3–4 weeks of antiseptic therapy are necessary to achieve positive treatment results.
## Antibiotic therapy; CIST protocol A+B+C
At BoP-positive implant sites with deep pockets (PPD ≥6 mm) (suppuration may or may not be present), there are frequently also radiographic signs of bone loss. Such pockets represent an ecologic habitat which is conducive for the colonization of Gram-negative and anaerobic putative periodontal pathogens (Mombelli _et al_. 1987). Anti-infective treatment must include the use of antibiotics to eliminate or reduce the pathogens in this habitat. This, in turn, will allow soft tissue healing as demonstrated in a clinical study by Mombelli and Lang (1992). Prior to administering antibiotics the mechanical (CIST A) and the antiseptic (CIST B) protocols have to be applied. During the last 10 days of the antiseptic treatment regimen, an antibiotic directed against anaerobic bacteria (e.g. metronidazole or ornidazole) is used. Thus for instance, 350 mg tid of Flagyl® (Rhone-Poulenc) or 500 mg bid of Tiberal® (Roche) is administered via the systemic route. A site treated according to the above protocol is depicted in Fig. 41-10. A fistula can be seen in the buccal aspect of implant site 45 (Fig. 41-10a). The site exhibited BoP and had a probing depth of 7 mm. After therapy the inflammation is resolved (Fig. 41-10b) and some recession of the mucosal margin has occurred. In Fig. 41-10c the bone fill that took place in the angular defect is illustrated in a subtraction radiography image using contrast enhancing. Figure 41-10d presents the site 8 years after active therapy.
**Fig. 41-9** Mechanical and antiseptic cleansing. Application of chlorhexidine gel (Plakout®, 0.2%) to a site with peri-implant mucositis.
An alternative to systemic administration is the controlled, local delivery of antibiotics. It must be realized, however, that only devices with proper release kinetics must be used to assure successful clinical results. The antibiotic must thus remain at the site of action for at least 7–10 days and in a concentration high enough to penetrate the submucosal biofilm (Mombelli _et al_. 2001). An example of such a controlled-release device is the tetracycline-containing periodontal fiber (Actisite®; Alza). The therapeutic effect of this controlled-release device appears to be identical to the effect obtained by the systemic use of antibiotics (Mombelli _et al_. 2001).
**Fig. 41-10** Treatment of peri-implantitis according to the protocol of CIST (cumulative interceptive supportive therapy). (a) Clinical diagnosis of peri-implantitis: presence of bleeding on probing, suppuration, development of a fistula, loss of alveolar bone. Peri-implant probing depth 7 mm. (b) Clinical resolution of the peri-implant infection 1 year after mechanical and antiseptic cleansing, followed by the systemic application of antibiotics (500 mg Tiberal® bid for 10 days). Some recession is visible. (c) Absence of mucositis, reduced peri-implant probing depth to 3 mm, and bone fill of the lesion. (d) Documentation of the healed peri-implant infection by contrast-enhanced subtraction radiography. The intrabony crater has been completely filled 1 year after therapy.
In a more recent development, minocycline microspheres (1 mg Arestin®; Orapharma, Johnson & Johnson) have been used as a controlled-release device in a similar manner to the application of tetracycline fibers (Mombelli _et al_. 2001). These microspheres are easily applied into the peri-implant pocket by means of a syringe. The antibiotic is contained in very small beads that stick to the lateral walls of the pocket and to the implant surface providing enough substantivity (high enough concentration for up to 14 days) to penetrate the biofilm. The principle has been tested in a randomized controlled clinical trial with a 1% chlorhexidine gel as a control (Renvert _et al_. 2006) and a prospective cohort study in patients with peri-implantitis (Persson _et al_. 2006; Salvi _et al_. 2007). Both studies demonstrated reduction in bleeding on probing, pocket depth reduction, and slight recession. Significantly lower bacterial loads were seen after 10 days and up to 180 days for some presumptive pathogens (Persson _et al_. 2006). This indicates that the application of minocycline microspheres adjunctive to the CIST protocols A+B represents a valuable alternative to the administration of systemic antibiotics for the treatment of incipient peri-implant infections.
## Regenerative or resective therapy; CIST protocol A+B+C+D
It is imperative to understand that regenerative or resective therapy is not instituted until the peri-implant infection is under control. Thus, before surgical intervention is planned, the previously diseased site should have become BoP negative, exhibit no suppuration, and have a reduced probing depth. Depending on the extent and severity of the local bone loss, a decision is made whether regenerative or resective measures are to be applied. In this context it must be realized that the goal of regenerative therapy, including the use of barrier membranes, is new bone formation in the crater-like defect around the implant, although _de novo_ osseointegration may occur to a limited extent (Persson _et al_. 1999; Wetzel _et al_. 1999).
### Conclusions
An implant patient must always be enrolled in a supportive therapy program that involves recall visits at regular intervals. Each recall visit must start with an examination to assess whether the implant sites are healthy or exhibit signs of inflammation. Cumulative Interceptive Supportive Therapy (CIST) includes a series of four protocols to be used when the examination and the diagnostic process are completed.
Figure 41-11 outlines (1) the decision process to be used for the peri-implant tissue diagnosis (Lang _et al_. 2004) and (2) the different therapeutic measures that are available to treat and/or prevent peri-implant infections.
**Fig. 41-11** Decision tree for cumulative interceptive supportive therapy (CIST). Depending on the mucosal condition and probing depth, either regime A or regime A+B, regime A+B+C or regime A+B+C+D are performed. A = Mechanical debridement; B = Antiseptic cleansing; C = Antibiotic therapy; D = Resective or regenerative surgery.
**References**
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Ericsson, I., Persson, L.G., Berglundh, T., Edlund, T. & Lindhe, J. (1996). The effect of antimicrobial therapy on peri-implantitis lesions. An experimental study in the dog. _Clinical Oral Implants Research_ 7, 320–328.
Klinge, B., Gustavsson, A. & Berglundh, T. (2002). A systematic review on the effect of anti-infective therapy in the treatment of peri-implantitis. _Proceedings from the 4th European Workshop on Periodontology. Journal of Clinical Periodontology_ 29 (Suppl), 213–225.
Lang, N.P., Berglundh, T., Heitz-Mayfield, L.J., Pjetursson, B.E., Salvi, G.E. & Sanz, M. (2004). Consensus statements and recommended clinical procedures regarding implant survival and complications. _International Journal of Oral and Maxillofacial Implants_ 19, 150–154.
Lindhe, J., Berglundh, T., Ericsson, I., Liljenberg, B. & Marinello, C.P. (1992). Experimental breakdown of periimplant and periodontal tissues. A study in the beagle dog. _Clinical Oral Implants Research_ 3, 9–16.
Lindhe, J., Liljenberg, B. & Adielsson, B. (1983b). Effect of longterm tetracycline therapy of human periodontal disease. _Journal of Clinical Periodontology_ 10, 590–601.
Lindhe, J., Liljenberg, B., Adielsson, B. & Börjesson, I. (1983a). Use of metronidazole as a probe in the study of human periodontal disease. _Journal of Clinical Periodontology_ 10, 100–112.
Matarasso, S., Quaremba, G., Coraggio, F., Vaia, E., Cafiero, C. & Lang, N.P. (1996). Maintenance of implants: an in vitro study of titanium implant surface modifications, subsequent to the application of different prophylaxis procedures. _Clinical Oral Implants Research_ 7, 64– 72.
Mombelli, A., Feloutzis, A., Brägger, U. & Lang, N.P. (2001). Treatment of peri-implantitis by local delivery of tetracycline. Clinical, microbiological and radiological results. _Clinical Oral Implants Research_ 12, 287–294.
Mombelli, A. & Lang, N.P. (1992). Anti-microbial treatment of peri-implant infections. _Clinical Oral Implants Research_ 3, 162–168.
Mombelli, A., van Oosten, M.A.C., Schürch, E. & Lang, N.P. (1987). The microbiota associated with successful or failing osseointegrated titanium implants. _Oral Microbiology and Immunology_ 2, 145–151.
Persson, L.G., Araújo, M., Berglundh, T., Gröhndal, K. & Lindhe, J. (1999). Resolution of periimplantitis following treatment. An experimental study in the dog. _Clinical Oral Implants Research_ 10, 195–203.
Persson, L.G., Ericsson, I., Berglundh, T. & Lindhe, J. (1996). Guided bone generation in the treatment of periimplantitis, _Clinical Oral Implants Research_ 7, 366–372.
Persson, G.R., Salvi, G.E., Heitz-Mayfield, L.J.A. & Lang, N.P. (2006). Antimicrobial therapy using a local drug delivery system (Arestin®) in the treatment of peri-implantitis. I: Microbiological outcomes. _Clinical Oral Implants Research_ 17, 386–393.
Renvert, S., Lessem, J., Dahlén, G., Lindahl, C. & Svensson, M. (2006). Topical minocycline microspheres versus topical chlorhexidine gel as an adjunct to mechanical debridement of incipient peri-implant infections: a randomized clinical trial. _Journal of Clinical Periodontology_ 33, 362–369.
Roos-Jansåker, A-M., Renvert, S. & Egelberg, J. (2003). Treatment of peri-implant infections: a literature review. _Journal of Clinical Periodontology_ 30, 467–485.
Salvi, G.E., Persson, G.R., Heitz-Mayfield, L.J.A. & Lang, N.P. (2007). Antimicrobial therapy using a local drug delivery system (Arestin®) in the treatment of peri-implantitis. I: Clinical outcomes. _Clinical Oral Implants Research_ 18 (in press).
Wetzel, A.C., Vlassis, J., Caffesse, R.J., Hämmerle, C.H.F. & Lang, N.P. (1999). Attempts to obtain re-osseointegration following experimental peri-implantitis in dogs. _Clinical Oral Implants Research_ 10, 111–119.
# Chapter 42
# Antibiotics in Periodontal Therapy
Andrea Mombelli
* * *
Principles of antibiotic therapy
The limitations of mechanical therapy: can antimicrobial agents help?
Specific characteristics of the periodontal infection
Drug delivery routes
Evaluation of antibiotics for periodontal therapy
Systemic antimicrobial therapy in clinical trials
Systemic antibiotics in clinical practice
Local antimicrobial therapy in clinical trials
Local antibiotics in clinical practice
Overall conclusion
* * *
# Principles of antibiotic therapy
Antibiotics are drugs that can kill or stop the multiplication of bacterial cells, at concentrations that are relatively harmless to host tissues, and therefore can be used to treat infections caused by bacteria. The capacity of the drug to reach the infected site, and the ability of targeted bacteria to resist or inactivate the agent determine the effectiveness of therapy. Based on their effect at concentrations tolerated by the host, antibiotics can be categorized as "bactericidal" or "bacteriostatic", and, depending on the range of susceptible bacteria, "narrow-spectrum" or "widespectrum". Antibiotics are just one group of antimicrobial agents, which also comprise antiviral, antifungal, and antiparasitic chemicals. The term was originally applied to substances extracted from fungus or other living organisms, but today also includes synthetic products.
As antibiotics can kill or suppress bacteria, the recognition of periodontitis as an infection – caused or sustained by certain bacteria living and multiplying in diseased sites – is a fundamental issue for any antimicrobial treatment concept. Antibiotics do not remove calculus and bacterial residues, and this is traditionally perceived to be an essential part of periodontal therapy.
## The limitations of mechanical therapy: can antimicrobial agents help?
The continued presence of large masses of bacteria on hard oral surfaces induces inflammation in adjacent soft tissues such as gingiva or mucosa, and the importance of removing bacterial plaque for resolution of gingivitis or mucositis is undisputed. The propensity of sites to undergo further periodontal destruction is felt to be more specific in nature, since not all sites with gingivitis invariably progress to periodontitis, and since increased proportions and detection frequencies of suspected oral pathogens are found in periodontitis lesions. Nevertheless, thorough mechanical cleaning of the root surfaces has also proven to be beneficial in the case of periodontitis, of whatever class, and under whatever clinical circumstances. Furthermore, it has been shown that the ability of the patient to prevent the re-formation of structured bacterial deposits by toothbrushing is crucial for long-term stability (for review see Chapter 59). However, this way of dealing with periodontal disease is time consuming, requires high levels of motivation and manual skills – of both the clinician and the patient – and has unwanted effects. It would be irrational to believe that mechanical instruments are able to completely remove periodontal pathogens from all infected sites (Mombelli _et al_. 2000). Bacteria may be inaccessible to mechanical instruments in concavities, lacunae, and dentin tubules, not to mention invaded soft tissues. Substantial hard tissue trauma may arise from repeated attempts at instrumentation in locally unresponsive sites, or sites with recurrent disease (Fig. 42-1). In addition, successfully treated sites may be recolonized by pathogens persisting in non-dental areas. Although we know that mechanical therapy can be clinically successful in many patients even if all putative pathogens are not completely eradicated, persistence or regrowth of certain microorganisms in treated sites should be considered as a cause of unsatisfactory treatment outcomes.
**Fig. 42-1** Conventional periodontal therapy and maintenance imply repeated treatment of sites with localized unresponsive or recurrent disease, resulting in sometimes substantial hard tissue trauma.
A closer look at the composition of the subgingival microbiota reveals that mechanical treatment is targeted at a variable mixture of different bacteria. The number of different species and subspecies occasionally identified in samples from human plaque by far exceeds 100, but only relatively few show a distinctive pattern of association with disease. While most frequently identified organisms are thought to harm tissues significantly only if present in high numbers over prolonged periods of time, in susceptible individuals certain species may have a negative effect even at relatively low numbers. On the basis of their pathogenicity, demonstrated in animal experiments, and the identification of virulence factors, a few organisms have been suggested to be specific periodontal pathogens (for review see Chapter 9). _Aggregatibacter actinomycetemcomitans_ (formerly known as _Actinobacillus actinomycetemcomitans_ ) (Norskov-Lauritsen & Kilian 2006) and _Porphyromonas gingivalis_ have attracted particular attention because longitudinal and retrospective studies have indicated an increased risk for periodontal breakdown in positive sites and because results of treatment have been better if the organisms could no longer be detected at follow-up (Bragd _et al_. 1987; Wennström _et al_. 1987; Carlos _et al_. 1988; Haffajee _et al_. 1991; Grossi _et al_. 1994; Haffajee & Socransky 1994; Dahlén _et al_. 1996; Rams _et al_. 1996; Chaves _et al_. 2000). If periodontal disease is in fact caused by a limited number of bacterial species, then non-specific continuous plaque removal is not the only possibility for prevention and therapy. Specific suppression of pathogenic bacteria becomes a valid alternative, and antibiotic approaches to regain and maintain periodontal health may have a better efficiency ratio.
In the late 1930s and early 1940s, the appearance of powerful agents selectively active against bacteria – sulfonamides, penicillin, and streptomycin – revolutionized the treatment of bacterial infections. The phenomenal success of these agents in the treatment of formerly life-threatening diseases led many to believe that bacterial infections would never again be a major medical concern. More than six decades of experience with these, and hundreds of additionally developed antimicrobial drugs have shown that, despite all the success, this view was too optimistic. Emerging problems, resulting from the widespread use of antibiotics have modified the general perception of the capabilities of antimicrobial agents. Over the years, many bacteria have developed a remarkable ability to withstand or repel antibiotic agents and are increasingly resistant to formerly potent agents. It has been noted that the use of antibiotics may disturb the delicate ecologic equilibrium of the body, allowing the proliferation of resistant bacteria or non-bacterial organisms. Sometimes this may initiate new infections that are worse than the ones originally treated. In addition, no antibacterial drug is absolutely non-toxic and the use of any antimicrobial agent carries with it accompanying risks. Thus, before we can start to administer antibiotics routinely to our periodontal patients we need to be sure about the specific benefit in comparison to standard treatment approaches. To limit the development of microbial antibiotic resistance in general, and to avoid the risk of unwanted systemic effects of antibiotics for the treated individual, a precautionary, restrictive attitude towards using antibiotics is recommended.
## Specific characteristics of the periodontal infection
The term infection refers to the presence and multiplication of microorganisms in or on body tissues. The uniqueness of plaque-associated dental diseases as infections relates to the lack of massive bacterial invasion of tissues. Although there is evidence for bacterial penetration in severely diseased periodontal tissues, notably in periodontal abscesses and in acute necrotizing ulcerative lesions (Listgarten 1965; Saglie _et al_. 1982a,b; Allenspach-Petrzilka & Guggenheim 1983; Carranza _et al_. 1983), it has not been generally accepted that true bacterial invasion (including multiplication of bacteria within tissues) is crucial for periodontal disease progression. Bacteria in the subgingival plaque obviously interact with host tissues even without direct tissue penetration. Thus, to have an effect, any antimicrobial agent used in periodontal therapy needs to be available at a sufficiently high concentration not only within the periodontal tissues, but also in the environment of the periodontal pocket (Fig. 42-2). Antibiotic resistance always occurs first in sites where penetration of the agent is restricted, and therapeutic concentrations are difficult to achieve. A periodontal pocket may contain very large amounts of bacteria, and the antimicrobial agent may be inhibited, inactivated or degraded by non-target microorganisms.
**Fig. 42-2** Specific conditions for the use of antimicrobial agents in periodontal therapy. The periodontal pocket as an open site is subject to recolonization after therapy (top arrow). The subgingival bacteria are protected from antimicrobial agents in a biofilm (middle arrow). The agent must be available at a sufficiently high concentration not only within, but also in the subgingival environment, outside the periodontal tissues (bottom arrow).
The subgingival microbiota accumulate on the root surface to form an adherent layer of plaque. Accumulation of bacteria on solid surfaces can be observed on virtually all surfaces immersed in natural aqueous environments and is called "biofilm" formation. Extensive bacterial growth, accompanied by excretion of copious amounts of extracellular polymers, is a typical phenomenon in biofilms. Biofilms effectively protect bacteria from antimicrobial agents (Anwar _et al_. 1990, 1992). Bacteria involved in adhesion-mediated infections that develop on permanently or temporarily implanted materials, such as intravascular catheters, vascular prostheses or heart valves, are notoriously resistant to systemic antimicrobial therapy and tend to persist until the device is removed (Gristina 1987; Marshall 1992). Several mechanisms leading to this increased resistance of bacteria in biofilms have been proposed. Due to limited diffusion, antimicrobial agents may simply not reach deeper parts of a biofilm at sufficiently high levels during a given time of exposure. Within biofilms an unequal distribution of electrical charge may develop. Intrusion may thus be further complicated in certain areas of the biofilm depending on the charge of the penetrating molecule. Because of a limited availability of nutrients within the biofilm, bacteria may also reduce their metabolism, rendering them less susceptible to killing by agents interfering with protein, DNA or cell wall synthesis. _In vitro_ experiments indicate that the attachment of bacteria to surfaces can trigger genes, which activate specific resistance mechanisms. Since these mechanisms are switched on upon contact, they may occur already in newly forming, very thin biofilms (Costerton _et al_. 1995).
Recognizing the above described problems there is currently a general consensus that mechanical instrumentation must always precede antimicrobial therapy. First, we should quantitatively reduce the large mass of bacteria, which otherwise may inhibit or degrade the antimicrobial agent. Second, we should mechanically disrupt the structured bacterial aggregates that can protect the bacteria from the agent.
Since the periodontal flora never consists of one single species, synergistic, but also antagonistic, relationships between microorganisms could occur. Based on the concept that the presence of beneficial bacterial species may suppress the activity of pathogens, one can speculate that it may be advantageous specifically to eliminate target bacteria only and to allow the growth of potentially beneficial microorganisms. Such contemplations have been used as an argument to propagate narrow-spectrum antibiotics for periodontal therapy.
## Drug delivery routes
Oral antibiotics ( _per os_ , by mouth, abbreviated "p.o.") are the most common approach for treating bacterial infections. Administration by means other than through the alimentary tract (as by intramuscular or intravenous injection) is usually reserved for serious medical conditions if the oral route is proven ineffective. Some local infections can be treated with topically administered antibiotics, as with eyedrops or ointments. In the therapy of periodontal diseases antibiotics may be delivered via the systemic route or by direct placement into the periodontal pocket. Each method of delivery has specific advantages and disadvantages (Table 42-1). Local therapy may allow the application of antimicrobial agents at levels that cannot be reached by the systemic route and may be suitable for agents, i.e. antiseptics, that are too toxic to be delivered by the systemic route. This form of application seems to be particularly promising if the presence of target organisms is confined to the clinically visible lesions. Systemic administration of antibiotics may be better if the targeted bacteria are distributed wider. Studies have shown that periodontal bacteria may in fact be distributed throughout the whole mouth in some patients (Mombelli _et al_. 1991a, 1994), including non-dental sites, such as the dorsum of the tongue or tonsillary crypts (Zambon _et al_. 1981; van Winkelhoff _et al_. 1988; Müller _et al_. 1993, 1995; Pavicic _et al_. 1994). Disadvantages of systemic antibiotic therapy relate to the fact that the drug is dissolved by dispersal over the whole body, and only a small portion of the total dose actually reaches the subgingival microflora in the periodontal pocket. Adverse drug reactions are a greater concern and more likely to occur if drugs are distributed via the systemic route. Even mild forms of unwanted effects may severely decrease patient compliance (Loesche _et al_. 1993). Local delivery is independent of patient compliance.
Table 42-1 Comparison of local and systemic antimicrobial therapy
**Issue** | **Systemic administration** | **Local administration**
---|---|---
Drug distribution | Wide distribution | Narrow effective range
Drug concentration | Variable levels in different body compartments | High dose at treated site, low levels elsewhere
Therapeutic potential | May reach widely distributed microorganisms better | May act locally on biofilm associated bacteria better
Problems | Systemic side effects | Re-infection from non-treated sites
Clinical limitations | Requires good patient compliance | Infection limited to the treated site
Diagnostic problems | Identification of pathogens, choice of drug | Distribution pattern of lesions and pathogens, identification of sites to be treated
**Fig. 42-3** (a) An antimicrobial gel is applied with a syringe inserted into a residual pocket. (b) For retention of the agent in the site, the viscosity of the carrier should change immediately. A large portion of the product may otherwise be expelled from the pocket quickly.
Local drug delivery systems are means of drug application to confined areas. For the treatment of periodontal disease, local delivery of antimicrobial drugs ranges from simple pocket irrigation, over the placement of drug-containing ointments and gels, to sophisticated devices for sustained release of antibacterial agents. In order to be effective, the drug should not only reach the entire area affected by the disease, including especially the base of the pocket, but should also be maintained there at a sufficiently high local concentration for some time. With a mouth rinse or supragingival irrigation it is not possible to deliver an agent predictably to the deeper parts of a periodontal defect (Eakle _et al_. 1986; Pitcher _et al_. 1980). The crevicular fluid rapidly washes out agents brought into periodontal pockets by subgingival irrigation. Based on an assumed pocket volume of 0.5 ml and a crevicular fluid flow rate of 20 μl/hr, Goodson (1989) estimated that the half-time of a non-binding drug placed into a pocket is about 1 minute. Even a highly concentrated, highly potent agent would thus be diluted below a minimal inhibitory concentration (MIC) for oral microorganisms within minutes. If an agent can bind to surfaces and be released in active form, a prolonged time of antibacterial activity could be expected. Such an effect has in fact been noted for salivary concentrations of chlorhexidine after use of chlorhexidine mouth rinse (Bonesvoll & Gjermo 1978). Although there are indications that this may also occur to a certain extent within the periodontal pocket, for instance after prolonged subgingival irrigation with tetracycline (Tonetti _et al_. 1990), the potential to create a drug reservoir of significant size on the small surface area available in a periodontal pocket is limited. To maintain a high concentration over a prolonged period, the flushing action of the crevicular fluid flow has to be counteracted by a steady release of the drug from a larger reservoir. Considering the small volume of a periodontal pocket and the pressure exerted by the tonus of the periodontal tissues on anything inserted, it appears unlikely that this task can be completed by a carrier that does not maintain its physical stability for some time and that cannot be secured against premature loss. Gels, for instance, rapidly disappear after instillation into periodontal pockets (Fig. 42-3), unless they change their viscosity immediately after placement (Oostervaal _et al_. 1990; Stoltze 1995). Viscous and/or biodegradable devices show an exponential decrease of their concentration in gingival fluid. In order to have sustained control over drug release it is necessary to have a matrix that lasts longer than the drug load. Controlled delivery of an antimicrobial agent over several days has been shown for tetracycline released from non-degradable monolithic ethylene vinyl acetate fibers (Fig. 42-4).
**Fig. 42-4** Mean concentration of tetracycline ( ) in gingival crevicular fluid (GCF) during tetracycline fiber treatment (Tonetti _et al_. 1990), of doxycycline hyclate ( ) after application in a biodegradable polymer (Stoller _et al_. 1998), and of metronidazole ( ) after application of 25% metronidazole dental gel (Stoltze 1992).
# Evaluation of antibiotics for periodontal therapy
In the large range of antimicrobial agents, a limited number have been tested thoroughly for use in periodontal therapy. The drugs more extensively investigated for systemic use include tetracycline, minocycline and doxycycline, erythromycin, clindamycin, ampicillin, amoxicillin, and the nitro-imidazole compounds metronidazole and ornidazole. The drugs investigated for local application include tetracycline, minocycline, doxycycline, metronidazole, and chlorhexidine.
The first antibiotics used in periodontal therapy were mainly systemically administered penicillins. The choice was initially based exclusively on empiric evidence. Penicillins and cephalosporins act by inhibition of cell wall synthesis. They are narrow-spectrum and bactericidal. Among the penicillins, amoxicillin has been favored for treatment of periodontal disease because of its considerable activity against several periodontal pathogens at levels available in gingival fluid. The molecular structure of penicillins includes a β-lactam ring that may be cleaved by bacterial enzymes. Some bacterial β-lactamases have a high affinity for clavulanic acid, a β-lactam molecule without antimicrobial activity. To inhibit bacterial β-lactamase activity, clavulanic acid has been added successfully to amoxicillin. This combination (Augmentin®) has been tested for periodontal therapy in clinical studies.
Tetracycline-HCl became popular in the 1970s due to its broad-spectrum antimicrobial activity and low toxicity. The tetracyclines, clindamycin, and erythromycin are inhibitors of protein synthesis. They have a broad spectrum of activity and are bacteriostatic. In addition to their antimicrobial effect, tetracyclines are capable of inhibiting collagenase (Golub _et al_. 1985). This inhibition may interfere with tissue breakdown in periodontal disease. Furthermore they bind to tooth surfaces, from where they may be released slowly over time (Stabholz _et al_. 1993).
The nitro-imidazoles were introduced into the periodontal field in 1962 when _The Lancet_ published the report of a female patient, who after a week of treatment for trichomonal vaginitis with metronidazole (200 mg tid) declared she had undergone "a double cure". The vaginitis was cured and the "acute marginal gingivitis" she was also suffering from was relieved (Shinn 1962). The nitro-imidazoles (metronidazole and ornidazole) and the quinolone antibiotics (e.g. ciprofloxacin) act by inhibiting DNA synthesis. Metronidazole is known to convert into several short-lived intermediates after diffusion into an anaerobic organism. These products react with the DNA and other bacterial macromolecules, resulting in cell death. The process involves reductive pathways characteristic of strictly anaerobic bacteria and protozoa, but not aerobic or microaerophilic organisms. Thus, metronidazole affects specifically the obligately anaerobic part of the oral flora, including _P. gingivalis_ and other black-pigmenting Gram-negative organisms, but not _A. actinomycetemcomitans_ , a facultative anaerobe.
The concentrations following systemic administration of the most common antimicrobial agents used in the treatment of periodontal disease are listed in Table 42-2. The _in vitro_ susceptibility of _A. actino-mycetemcomitans_ to selected antimicrobial agents is given in Table 42-3 and the susceptibility of _P. gingivalis_ is listed in Table 42-4. The data given in these tables may serve as a base for the choice of an appropriate agent. However, it is important to remember that _in vitro_ tests do not reflect the true conditions found in periodontal pockets. In particular, they do not account for the biofilm effect. One should add that MIC values depend on technical details that may vary between laboratories. As a consequence, demonstration of _in vitro_ susceptibility is no proof that an agent will work in treatment of periodontal disease.
**Table 42-2** Characteristics of antimicrobial agents used in the treatment of periodontal disease (adapted from Lorian 1986; Slots & Rams 1990)
c = concentration; tmax = hours to reach peak serum concentration; ND = not determined.
**Table 42-3** Susceptibility of _A. actinomycetemcomitans_ to selected antimicrobial agents. MIC90: minimal inhibitory concentration for 90% of the strains (adapted from Mombelli & van Winkelhoff 1997)
**Antibiotic** | **MIC90 (μg/ml)** | **Reference**
---|---|---
Penicillin | 4.0 | Pajukanta _et al_. (1993b)
| 1.0 | Walker _et al_. (1985)
| 6.25 | Höffler _et al_. (1980)
Amoxicillin | 1.0 | Pajukanta _et al_. (1993b)
| 2.0 | Walker _et al_. (1985)
| 1.6 | Höffler _et al_. (1980)
Tetracycline | 0.5 | Pajukanta _et al_. (1993b)
| 8.0 | Walker (1992), Walker _et al_. (1985)
Doxycycline | 1.0 | Pajukanta _et al_. (1993b)
| 3.1 | Höffler _et al_. (1980)
Metronidazole | 32 | Pajukanta _et al_. (1993b)
| 32 | Jousimies-Somer _et al_. (1988)
| 12.5 | Höffler (1980)
Since the subgingival microbiota in periodontitis often harbors several putative periodontopathic species with different antimicrobial susceptibility, combination drug therapy may be useful. A combination of antimicrobial drugs may have a wider spectrum of activity than a single agent. Overlaps of the antimicrobial spectrum may reduce the possible development of bacterial resistance. For some combinations of drugs there may be synergy in action against target organisms, allowing a lower dose of the single agents. A synergistic effect against _A. actinomycetemcomitans_ has been noted _in vitro_ between metronidazole and its hydroxy metabolite (Jousimies-Somer _et al_. 1988; Pavicic _et al_. 1991) and between these two compounds and amoxicillin (Pavicic _et al_. 1992). With some drug combinations there may, however, also be antagonistic drug interaction. For instance, bacteriostatic agents such as tetracyclines, which suppress cell division, may decrease the antimicrobial effect of bactericidal antibiotics such as βlactam drugs or metronidazole, which act during bacterial cell division. Combination drug therapy may also lead to increased adverse reactions.
**Table 42-4** Susceptibility of _P. gingivalis_ to selected antimicrobial agents (adapted from Mombelli & van Winkelhoff 1997)
**Antibiotic** | **MIC90 (μg/ml)** | **Reference**
---|---|---
Penicillin | 0.016 | Pajukanta et al. (1993a)
| 0.29 | Baker et al. (1983)
Amoxicillin | 0.023 | Pajukanta et al. (1993a)
| <1.0 | Walker (1992)
Doxycycline | 0.047 | Pajukanta et al. (1993a)
Metronidazole | 0.023 | Pajukanta et al. (1993a)
| 2.1 | Baker et al. (1983)
| 2.0 | Walker (1992)
Clindamycin | 0.016 <1.0 | Pajukanta et al. (1993a)
| <1.0 | Walker (1992)
Table 42-5 lists common adverse reactions to systemic antibiotic therapy (for a detailed overview the reader is referred to Walker 1996). The penicillins are among the least toxic antibiotics. Hypersensitivity reactions are by far the most important and most common adverse effects of these drugs. Most reactions are mild and limited to a rash or skin lesion in the head or neck region. More severe reactions may induce swelling and tenderness of joints. In highly sensitized patients a life-threatening anaphylactic reaction may develop. The systemic use of tetracyclines may lead to epigastric pain, vomiting or diarrhea. Tetracyclines can induce changes in the intestinal flora, and superinfections with nonbacterial microorganisms (i.e. _Candida albicans_ ) may emerge. Tetracyclines are deposited in calcifying areas of teeth and bones where they cause yellow discoloration. Systemic administration of clindamycin may be accompanied by gastrointestinal disturbances, leading to diarrhea or cramps, and may cause mild skin rashes. The suppression of the normal intestinal flora increases the risk for colonization of _Clostridium difficile_ , which may cause a severe colon infection (antibiotic-associated colitis). Although not related to _C. difficile_ , gastrointestinal problems are also the most frequent adverse event of systemic metronidazole therapy. Nausea, headache, anorexia, and vomiting may be experienced. Symptoms may be more pronounced with alcohol consumption, because imidazoles affect the activity of liver enzymes. Because some cases have developed permanent peripheral neuropathies (numbness or paresthesia), patients should be advised to stop therapy immediately if such symptoms occur.
**Table 42-5** Adverse effects of antibiotics used in the treatment of periodontal diseases
**Antibiotic** | **Frequent effects** | **Infrequent effects**
---|---|---
Penicillins | Hypersensitivity (mainly rashes), nausea, diarrhea | Hematologic toxicity, encephalopathy, pseudomembranous colitis (ampicillin)
Tetracyclines | Gastrointestinal intolerance, candidiasis, dental staining and hypoplasia in childhood, nausea, diarrhea, interaction with oral contraceptives | Photosensitivity, nephrotoxicity, intracranial hypertension
Metronidazole | Gastrointestinal intolerance, nausea, antabus effect, diarrhea, unpleasant metallic taste | Peripheral neuropathy, furred tongue
Clindamycin | Rashes, nausea, diarrhea | Pseudomembranous colitis, hepatitis
## Systemic antimicrobial therapy in clinical trials
Although clinical efficacy is not an absolute proof for bacteriologic efficacy (Marchant _et al_. 1992), the ultimate evidence to advocate the use of systemic antibiotics must come from clinical trials in humans with periodontitis. A large number of reports suggesting beneficial effects in various clinical situations have been published. However, many of them score low when evaluated by established study quality criteria, e.g. those proposed by the Oxford Centre for Evidence-based Medicine (<http://www.cebm.net/levels_of_evidence.asp>). Studies may be difficult to interpret due to an unclear status of patients at baseline (treatment history, disease activity, composition of subgingival microbiota), insufficient or non-standardized maintenance after therapy, short observation periods, or lack of randomization and controls. Comparisons may be possible because studies not only vary with regard to the treatment provided, but also in the selection of subjects, sample size, range of study parameters, outcome variables, the duration of the study, and the control to which the test procedure is compared. In most trials, systemic antibiotics have been used as an adjunct to scaling and root planing. Typically, the effect of mechanical therapy plus the antimicrobial agent has been compared to mechanical treatment alone. In studies evaluating the effect of antimicrobial therapy in patients with refractory periodontitis or with recurrent abscess formation, placebo control is often lacking for ethical reasons.
In recent years systematic reviews have become the preferred method of analyzing the medical literature. They use explicit procedures to perform a thorough literature search, critically appraise individual reports, and try to combine valid studies by applying appropriate statistical techniques. Two systematic reviews have been conducted to determine whether systemically administered antibiotics improve the clinical outcome of periodontal therapy (Herrera _et al_. 2002; Haffajee _et al_. 2003). Both have been prepared in the context of structured consensus conferences, where the findings have been translated into consensus statements on periodontal therapy.
Herrera _et al_. (2002) sought studies of at least 6 months' duration, designed as controlled clinical trials, in which systemically healthy subjects with either chronic or aggressive periodontitis had been treated with scaling and root planing, with or without systemic antibiotics. Main outcome variables were changes in clinical attachment level and pocket probing depth. Twenty-five papers were eligible for inclusion, but due to difficulties encountered when pooling the data, only limited metaanalyses could be performed. Overall, antibiotic groups showed better results than control groups. A specific benefit in change of attachment level was found in deep pockets for the combination of metronidazole plus amoxicillin.
Haffajee _et al_. (2003) sought clinical trials in periodontitis patients of more than 1 month duration, comparing systemic antibiotic therapy with nonantibiotic therapy, and using mean attachment level change as primary outcome. A meta-analysis included the data from 27 eligible studies. The authors noted that by and large therapeutic procedures were diverse, although metronidazole, alone or in combination with amoxicillin, was the most frequently used drug. In all studies the antibiotic groups showed significantly better mean attachment level changes than the control groups, and this benefit averaged 0.45 mm. Although tests of heterogeneity were not significant, indicating that the outcomes were consistent, differences in the magnitude of the effect were noted in some patient populations: aggressive periodontitis groups had a larger adjunctive benefit than patients with chronic periodontitis. Results varied more between trials in which antibiotics had been used adjunctively to surgery than in trials where antibiotics had been tested adjunctively to scaling and root planing. Where it was possible to discriminate, sites with deep pockets seemed to show the greatest improvements. The reviews were unable to clarify which agents should be used for which infection, and what the optimal dosage and duration of antibiotic therapy should be. Furthermore it remained open how long the benefit would persist, and to what extent the antibiotics induced resistance or other changes in the oral microbiota. The low level of evidence with regards to the dosing regimen is very regrettable since the amount of drug administered is known to be a critical determinant of antimicrobial efficacy (Craig 1998).
In many trials the antibiotic has not been chosen based on a microbiologic analysis. This approach does not consider the possibility that some pathogens may be resistant to the tested drugs. We have mentioned _A. actinomycetemcomitans_ , which is not susceptible to metronidazole when used as a monotherapy. Therefore, clinical studies including patients for an antibiotic therapy irrespective of their microbiologic status may underestimate the potential of the tested drug. Some studies have in fact indicated that systemic antibiotics were only effective in patients with a specific microbial profile (Flemmig _et al_. 1998; Winkel _et al_. 2001). Others, however, have demonstrated considerable adjunctive benefits to mechanical treatment even in the absence of specific target organisms (e.g. Rooney _et al_. 2002), and one could argue that nobody has ever shown certain patients to be better off, if treated _without_ antibiotics.
In recent years the combination of metronidazole and amoxicillin has become the favorite treatment modality for many practitioners and clinical researchers. Studies corroborating the benefit of this regime, for example in non-surgical treatment of generalized aggressive periodontitis (Guerrero _et al_. 2005), continue to be published. Its remarkable ability to suppress or even eliminate _A. actinomycetemcomitans_ and other subgingival organisms from periodontitis lesions and other oral sites (Christersson _et al_. 1989; Kornman _et al_. 1989; van Winkelhoff _et al_. 1989, 1992; Goené _et al_. 1990; Pavicic _et al_. 1992, 1994) has made it the first choice especially for the treatment of advanced periodontitis associated with _A. actinomy-cetemcomitans_. Gastrointestinal disturbances (diarrhea, nausea, and vomiting) have been noted as the most frequent side effects.
## Systemic antibiotics in clinical practice
Overall, it can be stated that systemic antibiotic therapy can improve the clinical conditions and microbiologic status of periodontal patients. There is evidence to support the use of systemic antibiotics in cases of aggressive forms of periodontitis associated with _P. gingivalis_ and/or _A. actinomycetemcomitans_. Systemic antibiotics are also indicated in generalized refractory periodontitis patients with evidence of ongoing disease despite previous mechanical therapy. Although some studies have shown a certain benefit of antibiotics even when administered without thorough subgingival debridement (Berglundh _et al_. 1998; Lopez & Gamonal 1998; Lopez _et al_. 2000, 2006) there is a general consensus that whenever possible antibiotics should not be administered before completion of root surface debridement (Mombelli 2006). Patients with acute signs of disease such as periodontal abscesses, or acute necrotizing gingivitis, with fever and malaise, may be the exception. Systemic antibiotics, given after scaling and root planing, provide an additional treatment benefit especially in deep pockets, and can reduce the need for further, surgical therapy (Loesche _et al_. 1992). In most cases however, mechanical therapy is initially carried out without antibiotics and evaluated after an appropriate period of time. The original treatment plan is then adapted, to account for the degree of clinical improvement already obtained. Immediately before starting the antibiotic regime the subgingival area should be re-instrumented once more to reduce the bacterial mass as much as possible and to disrupt the subgingival biofilm. This may be accomplished during a surgical intervention but is indicated also if no further mechanical therapy seems necessary from a clinical point of view.
Table 42-6 lists adjunctive systemic antibiotic regimens currently recommended for the therapy of periodontal diseases. Metronidazole alone has proven to be effective against _P. gingivalis_ , _Tannerella forsythia_ , spirochetes, and other strictly anaerobic Gram-negative bacteria. Clindamycin and tetracyclines have also been shown to act on a broad range of periodontal bacteria. Monotherapy with one antibiotic as an adjunct to mechanical instrumentation can change the composition of the subgingival microbiota significantly, but certain periodontal organisms cannot be eliminated predictably. For maximal suppression of subgingival _A. actinomycetemcomitans_ the combination of metronidazole and amoxicillin is recommended. For patients who cannot tolerate amoxicillin it has been suggested to combine metronidazole with cefuroximaxetil or ciprofloxacin (Rams _et al_. 1992; van Winkelhoff & Winkel 2005).
Microbiologic tests can help to choose the appropriate antibiotic regimen. A microbial analysis should be comprehensive and sensitive enough to quantitatively identify the most important periodontal organisms. From the discussion above it follows that data indicating the involvement of _A. actinomycetemcomitans_ and _P. gingivalis_ have the highest practical utility. Microbial samples from the deepest pocket in each quadrant can give a good picture of the presence and relative proportion of these pathogens in the oral flora (Mombelli _et al_. 1991b, 1994). Since the antimicrobial profiles of most putative periodontal pathogens are quite predictable, susceptibility testing is not routinely performed. One should keep in mind, however, that some important microorganisms might demonstrate resistance to tetracyclines, β-lactam drugs or metronidazole.
**Table 42-6** Adjunctive systemic antibiotic regimens currently recommended for the therapy of periodontal diseases (adapted from van Winkelhoff & Winkel 2005)
**Antibiotic** | **Usual dosage** | **Microbiology**
---|---|---
Metronidazole | 250–500 mg, tid | _P. gingivalis_
| 7–10 days | _T. forsythia_
| | _Treponema_ spp.
Clindamycin | 300 mg, qid | Gram-negative anaerobes
| 7–8 days | Absence of _A. actinomycetemcomitans_
Doxycycline | 100–200 mg, sid | Non-specific infection
| 7–14 days |
Metronidazole + Amoxicillin | 250–500 mg, tid | _A. actinomycetemcomitans_ or
| 375–500 mg, tid | _P. gingivalis_ with high numbers of Gram-positive pathogens
| 7 days |
Metronidazole + Cefuroximaxetil | 250–500 mg, tid | _A. actinomycetemcomitans_
| 250–500 mg, bid | Hypersensitivity towards amoxicillin
| 7 days |
Metronidazole + Ciprofloxacin | 250–500 mg, tid | _A. actinomycetemcomitans_
| 500 mg, bid | Hypersensitivity towards β-lactams or presence of susceptible enteric microorganisms
| 7 days |
As mentioned already, suboptimal dosage of antibiotics, caused by either inadequate prescribing or poor patient compliance, favors the spread of antibiotic-resistant bacterial clones. The classical oral dosage for metronidazole, used in most studies, has been 250 mg, three times a day, for 7–10 days. This dosage might not be sufficient in subjects with a high body mass. In addition, it has been proposed to prolong medication in smokers (van Winkelhoff & Winkel 2005), because smoking decreases the gingival blood flow and the amount of crevicular fluid, and hereby the availability of the drug in the subgingival environment (Morozumi _et al_. 2004). The specific conditions of smokers have become the subject of clinical research in recent time. The utilization of azithromycin, a macrolide antibiotic derived from erythromycin, has been advocated specifically for smokers (Mascarenhas _et al_. 2005). More research is however needed to substantiate the specific benefit of particular regimes for distinct groups of patients.
After resolution of the periodontal infection, the patient should be placed on an individually tailored maintenance care program. Optimal plaque control by the patient is of paramount importance for a favorable clinical response (Kornman _et al_. 1994) and long-term stability. Systemic antibiotics should never be applied as a means to compensate for inadequate oral hygiene.
## Local antimicrobial therapy in clinical trials
Various methods to deliver antimicrobial agents into periodontal pockets have been devised and subjected to numerous kinds of experiments. The shortcomings of rinsing, irrigating, and similar forms of drug placement – rapid clearance resulting in inadequate exposure of subgingival bacteria to the drug and lack of significant clinical effects – have already been discussed. This section will deal with clinically tested drug delivery systems that fulfill at least the basic pharmacokinetic requirements of sustained drug release. Much of what has been stated about difficulties in the interpretation of studies dealing with the systemic use of antibiotics applies to the studies conducted with local delivery devices. Again, comparisons are complicated because studies vary with regard to sample size, selection of subjects, range of parameters, controls, duration of the study, and the inclusion of only one form of local drug delivery. Most of the evidence for a therapeutic effect of local delivery devices comes from trials involving patients with previously untreated adult periodontitis. Only few studies have addressed the use of local drug delivery in recurrent or persistent periodontal lesions – the potentially most valuable area for their application. Some protocols compare local drug delivery to a negative control, such as the application of only the carrier without the drug. These studies may be able to show a net effect of the drug, but they are not able to demonstrate a benefit over the most obvious alternative – scaling and root planing – and the question remains as to how much value the procedure has in addition to mechanical treatment. If a study is unable to demonstrate a significant difference between local drug delivery and scaling and root planing, this is not automatically a proof of equivalence of the two treatments (equivalence testing requires statistical testing of the power of the data, taking into account the size of the study sample).
The following paragraphs focus on minocycline ointment and microspheres, doxycycline hyclate in a biodegradable polymer, metronidazole gel, tetracycline in a non-resorbable plastic co-polymer, and chlorhexidine gluconate in a gelatin chip. These are the predominant commercial formulations adequately tested for local antimicrobial periodontal therapy. Unfortunately some of them are currently unavailable in certain regions of the world, or have disappeared completely, while other products without properly evaluated clinical efficacy continue to be introduced and utilized on an empiric basis.
### Minocycline ointment and microspheres
The subgingival delivery of minocycline has been investigated in different forms. The efficacy of a 2% minocycline ointment (Dentomycin; Cyanamid, Lederle Division, Wayne, NJ, US) has been evaluated in a randomized, controlled trial of 103 adults with moderate to severe periodontitis (van Steenberghe _et al_. 1993). All patients were treated by conventional scaling and root planing. In addition, the patients received either the test or a control ointment in four consecutive sessions at baseline and weeks 2, 4, and 6. A significantly greater reduction of probing depths was noted in the test group at week 12. An additional study evaluating the repeated application of minocycline ointment as an adjunct to subgingival debridement in chronic periodontitis, demonstrated better clinical and microbiologic conditions over a 15-month period (van Steenberghe _et al_. 1999). One study assessed the effect of a weekly repeated local application of minocycline ointment for 8 weeks after placement of teflon membranes to guide regeneration of periodontal tissue. Although bacterial colonization of treated sites could not be prevented, the mean clinical attachment gain of the test group was significantly greater than that of the control group (Yoshinari _et al_. 2001).
Currently the major device for local minocycline application is a product with the physical properties of a powder, consisting of resorbable polymer microspheres (Arestin; OraPharma, Warminster, PA, US). The efficacy and safety of locally administered microencapsulated minocycline was shown in a multicenter trial including 748 patients with moderate to advanced periodontitis. Minocycline microspheres plus scaling and root planing provided substantially more probing depth reduction than either scaling and root planing alone or scaling and root planing plus vehicle. The difference reached statistical significance after the first month and was maintained throughout the 9 months of the trial (Williams _et al_. 2001; Paquette _et al_. 2004).
### Doxycycline hyclate in a biodegradable polymer
A two-syringe mixing system for the controlled release of doxycycline (Atridox; Block Drug, Jersey City, NJ, US) has been evaluated in a number of investigations, and has been commercially available for a few years. One syringe contained the delivery vehicle, flowable bioabsorbable poly (DL-lactide) dissolved in _N_ -methyl-2-pyrrolidone, and the other syringe contained doxycycline hyclate powder. The clinical efficacy and safety of Atridox was assessed in two multicenter studies. Each study entered 411 patients who demonstrated moderate to severe adult periodontitis. The treatment was statistically superior to placebo control and oral hygiene, and equally effective as scaling and root planing in reducing the clinical signs of adult periodontitis over a 9-month period (Garrett _et al_. 1999). In a group of patients undergoing supportive periodontal therapy, attachment level gains and probing depth reductions were similar at 9 months after local treatment with doxycycline or traditional scaling and root planing (Garrett _et al_. 2000).
The effect of Atridox, applied after no more than 45 minutes of debridement without analgesia in subjects with moderately advanced chronic periodontitis, was compared to 4 hours of thorough deep scaling and root planing in a study involving 105 patients at three centers. Interestingly, clinical parameters indicated a better result for the pharmacomechanical treatment approach after 3 months, although considerably less time had been invested than for conventional mechanical therapy (Wennström _et al_. 2001).
### Metronidazole gel
Dialysis tubing, acrylic strips, and poly-OHbutyric acid strips have been tested as solid devices for delivery of metronidazole. The most extensively used device for metronidazole application is a gel consisting of a semi-solid suspension of 25% metronidazole benzoate in a mixture of glyceryl mono-oleate and sesame oil (Elyzol Dental Gel; Dumex, Copenhagen, Denmark). The gel is applied with a syringe into the pocket, and should increase its viscosity after placement. The clinical response to subgingival application of the metronidazole gel twice within 1 week was compared to the effect of subgingival scaling in several studies including subjects with untreated adult periodontitis (Ainamo _et al_. 1992; Pedrazzoli _et al_. 1992; Grossi _et al_. 1995). The results indicated no significant difference between metronidazole gel application and scaling and root planing. The fact that no significant difference between the two treatments was observed opened the question of equivalence between the two treatment modalities. Equivalence between scaling and root planing and metronidazole gel therapy has been evaluated using the lower bounds of confidence intervals in a parallel arm, multicenter, controlled clinical trial including 84 subjects (Pihlstrom _et al_. 1995). The estimates provided by this study indicated that metronidazole gel therapy is 82% as good as mechanical debridement at the 95% confidence level.
**Fig. 42-5** Insertion of a chlorhexidine chip into a residual pocket mesial to an upper molar with a furcation involvement.
### Tetracycline in a non-resorbable plastic co-polymer
Hollow devices, such as dialysis tubing, and solid devices, such as acrylic strips, collagen, or poly-OH-butyric acid strips, have been tested for tetracycline delivery in several experiments. Semi-solid viscous media include white petrolatum and poloxamer or carbopol gels. The most extensively tested tetracycline-releasing device is the Actisite periodontal fiber (ALZA, Palo Alto, CA, US). This currently unavailable product consists of a monolithic thread of a biologically inert, non-resorbable plastic copolymer (ethylene and vinyl-acetate) containing 25% tetracycline hydrochloride powder. The fiber is packed into the periodontal pocket, secured with a thin layer of cyanoacrylate adhesive, and left in place for 7–12 days (Goodson _et al_. 1991a, 1983). By continuous delivery of tetracycline, a local concentration of the active drug in excess of 1000 mg/l can be maintained throughout that period (Fig. 42-4). Many clinical studies have been performed with Actisite, among them the following three large multicenter trials. The first showed better clinical results in deep pockets of 107 periodontitis patients 60 days after fiber therapy than control procedures (Goodson _et al_. 1991b). The second, conducted in periodontal maintenance patients needing treatment of localized recurrent periodontitis, demonstrated superiority after 6 months for scaling and root planing plus tetracycline fiber over scaling and root planing alone (Newman _et al_. 1994). The third indicated that the results obtained within 3 months after therapy were maintained over 1 year and that the combined treatment with fiber and scaling had a significantly lower incidence of disease recurrence than any of the other tested treatment modalities (Michalowicz _et al_. 1995).
### Chlorhexidine gluconate in a gelatin chip
Several attempts have been made to develop local delivery devices for the subgingival application of antiseptic, rather than antibiotic agents. Acrylic strips and ethyl-cellulose compounds have been tested for this purpose. PerioChip (Perio Products, Jerusalem, Israel), a degradable gelatin chip containing 2.5 mg chlorhexidine, is the most extensively tested delivery device of this category (Fig. 42-5). Safety and efficacy of PerioChip were evaluated in a multicenter study of 118 patients with moderate periodontitis (Soskolne _et al_. 1997). The average pocket depth reduction in the treated sites with the chip was significantly greater than in the sites receiving mechanical treatment only. The efficacy of the chlorhexidine chip when used as an adjunct to scaling and root planing on reducing probing depth and improving clinical attachment level in adult periodontitis was evaluated in two double-blind, randomized, placebo-controlled multicenter clinical trials. At 9 months significant reductions from baseline were shown with the chlorhexidine chip compared with mechanical control treatments (Jeffcoat _et al_. 1998).
### Comparison of treatment methods
Most studies have tested a single form of local drug delivery or systemic administration, instead of comparing various forms of therapy. Understandably, developers and distributors have the primary interest to register and promote their own product for the broadest possible usage, and not to differentiate specific benefits or shortcomings of various applications. The efficacy of three commercially available local delivery systems as adjuncts to scaling and root planing was tested in two trials including patients with persistent periodontal lesions: Actisite, Dentomycin, Elyzol Dental Gel (Radvar _et al_. 1996; Kinane & Radvar 1999) ; Atridox, Elyzol Dental Gel, PerioChip (Salvi _et al_. 2002). One systematic review has tried to evaluate the combined literature-based evidence to determine the relative effect of local controlled release anti-infective drug therapy in patients with chronic periodontitis (Hanes & Purvis 2003). A meta-analysis including 19 studies, comparing scaling and root planing plus local sustained-release agents with scaling and root planing alone, confirmed the clinical advantages of minocycline gel, microencapsulated minocycline, doxycycline gel, and chlorhexidine chips over scaling and root planing alone. Due to the heterogeneity of the material the authors could not make any firm statements regarding the superiority of one system. A further systematic review looked at the relative adjunctive benefits of various locally applied agents (Bonito _et al_. 2005). Unfortunately data were combined from studies exploring various modes of local treatment, including irrigation, impregnated strips or pastes. Nonetheless, a statistically significant mean advantage resulted for four agents in terms of additional attachment gain, best for minocycline, followed by tetracycline, chlorhexidine, and metronidazole. One cannot exclude, however, that the differences noted between the drugs primarily reflect differences in modes of application and study populations, not the potency of the agent.
Few studies have addressed the problem of incorporating local or systemic antimicrobial therapy into an overall treatment strategy. As little direct evidence for a comparison of various methods of treatment is available so far, well founded decision algorithms to choose specific methods of intervention for distinct clinical situations are not yet available. A key issue requiring clarification refers to the selection of a local or a systemic delivery approach whenever the use of an antibiotic is indicated. One investigation addressed this question in patients with rapidly progressing periodontitis (Bernimoulin _et al_. 1995). Overall, no significant differences were noted between systemic administration of amoxicillin–clavulanic acid and tetracycline fibers as an adjunct to mechanical therapy. For patients with adult periodontitis, two studies reported better results of scaling and root planing supplemented with locally applied metronidazole than adjunctive systemic metronidazole (Paquette _et al_. 1994; Noyan _et al_. 1997).
As different oral distribution patterns can be recognized in periodontitis patients for microorganisms such as _P. gingivalis_ (Mombelli _et al_. 1991a,b), local therapy may be less successful in patients where these organisms are widespread than in patients where the presence of pathogens is confined to isolated areas. This hypothesis was tested in a study comparing two extremes of local therapy. In one group of patients, a combination of measures including full mouth scaling and root planing, application of tetracycline fibers, and chlorhexidine rinse, was applied. In the other group, only two teeth were treated locally and no attempt was made to interfere with the overall conditions of the oral environment. Major clinical differences were found in the local healing response, depending on whether the rest of the dentition was left untreated or was also subjected to therapy (Mombelli _et al_. 1997). How can a clinician be sure that the areas he treats coincide with the sites harboring the pathogens? No diagnostic tool is available presently at a reasonable cost that could give the dentist a detailed distribution map of periodontal pathogens. Provided that such a tool would exist, could _P. gingivalis_ and _A. actinomycetemcomitans_ be eradicated from an infected dentition by microbiologically guided local antimicrobial therapy? A study evaluating the effect of local antibiotic therapy, given to every tooth with cultural evidence of _P. gingivalis_ or _A. actinomycetemcomitans_ after completion of conventional mechanical periodontal therapy demonstrated the limits of this approach (Mombelli _et al_. 2002). Even if a detailed microbiologic assessment provided information about the distribution pattern within the dentition, and all positive teeth were treated, the target organisms could be detected again after therapy in some sites in a considerable number of subjects.
## Local antibiotics in clinical practice
To treat periodontal disease successfully, local delivery devices must provide therapeutic levels of antimicrobial agents in the subgingival area over several days. Clinical trials show the efficacy of local antibiotic therapy under these conditions. The current evidence suggests that local delivery may be most beneficial in the control of localized ongoing disease in otherwise stable patients. Maintenance patients with a few non-responding sites may therefore benefit most from local antimicrobial therapy. Local antibiotic therapy adds flexibility and improves efficacy of periodontal care by providing a non-surgical local treatment alternative with more powerful antibacterial effects than scaling and root planing. Potential uses for locally delivered antibiotics also include the treatment of peri-implant infections (Mombelli _et al_. 2001; Renvert _et al_. 2006). A comment made in the context of systemic antibiotics needs to be reiterated here with regards to local therapy: antibiotics are not a means to compensate for inadequate oral hygiene. For a maximal benefit, and a sustained local effect, patients should receive specific instructions on how to keep the treated sites plaque free with appropriate home care procedures.
## Overall conclusion
Although mechanical periodontal treatment alone improves clinical conditions sufficiently in most cases, adjunctive antibiotics, delivered either systemically or locally, can enhance the effect of therapy. Systemic antibiotics may be a useful adjunct to the mechanical treatment of aggressive forms of periodontitis and for cases with evidence of ongoing disease despite previous mechanical therapy. By providing an additional treatment benefit especially in deep pockets, systemic antibiotics can reduce the need for further, surgical therapy. Localized non-responding sites and localized recurrent disease may be treated with locally delivered antibiotics. Mechanical debridement before the application of antimicrobial agents, and mechanical plaque control after therapy, are essential for treatment success. To limit the development of microbial antibiotic resistance in general, and to avoid the risk of unwanted systemic effects of antibiotics for the treated individual, a precautionary, restrictive attitude towards using antibiotics is recommended.
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# Part 13: Reconstructive Therapy
43 Regenerative Periodontal Therapy
_Pierpaolo Cortellini and Maurizio S. Tonetti_
44 Mucogingival Therapy – Periodontal Plastic Surgery
_Jan L. Wennström, Giovanni Zucchelli, and Giovan P. Pini Prato_
45 Periodontal Plastic Microsurgery
_Rino Burkhardt and Niklaus P. Lang_
46 Re-osseointegration
_Tord Berglundh and Jan Lindhe_
# Chapter 43
# Regenerative Periodontal Therapy
Pierpaolo Cortellini and Maurizio S. Tonetti
* * *
Introduction
Classification and diagnosis of periodontal osseous defects
Clinical indications
Long-term effects and benefits of regeneration
Evidence for clinical efficacy and effectiveness
Patient and defect prognostic factors
Patient factors
Defect factors
Tooth factors
Factors affecting the clinical outcomes of GTR in furcations
The relevance of the surgical approach
Papilla preservation flaps
Modified papilla preservation technique
Simplified papilla preservation flap
Minimally invasive surgical technique
Post-operative regime
Post-operative morbidity
Barrier materials for regenerative surgery
Non-absorbable materials
Bioabsorbable materials
Membranes in intrabony defects
Membranes for furcation involvement
Surgical issues with barrier membranes
Bone replacement grafts
Biologically active regenerative materials
Membranes combined with other regenerative procedures
Root surface biomodification
Clinical strategies
* * *
# Introduction
The advances in the understanding of the biology of wound healing and periodontal regenerative technologies are applied to improve long-term clinical outcomes of teeth which are periodontally compromised by intrabony or inter-radicular defects. The treatment objective is to obtain shallow, maintainable pockets by reconstruction of the destroyed attachment apparatus and thereby also limiting recession of the gingival margin. In general periodontal regeneration is selected to obtain: (1) an increase in the periodontal attachment of a severely compromised tooth; (2) a decrease in deep pockets to a more maintainable range; (3) a reduction of the vertical and horizontal component of furcation defects. Current approaches, however, remain technique sensitive and clinical success requires application of meticulous diagnostic and treatment strategies.
# Classification and diagnosis of periodontal osseous defects
Site-specific periodontal breakdown compromises the long-term prognosis of teeth by producing three types of defects: suprabony (or horizontal) defects, infrabony (or vertical) defects, and inter-radicular (or furcation) defects.
According to the classification by Goldman and Cohen (1958), suprabony defects are those where the base of the pocket is located coronal to the alveolar crest. Infrabony defects, on the other hand, are defined by the apical location of the base of the pocket with respect to the residual alveolar crest. This chapter does not deal with suprabony defects. With regard to infrabony defects, two types of defects can be recognized: intrabony defects and craters. Intrabony defects are bony defects whose infrabony component affects primarily one tooth, while in craters the defect affects two adjacent root surfaces to a similar extent. Intrabony defects (Fig. 43-1) have been classified according to their morphology in terms of residual bony walls, width of the defect (or radiographic angle), and in terms of their topographic extension around the tooth. Three-wall, two-wall, and one-wall defects have been defined on the basis of the number of residual alveolar bone walls. This represents the primary classification system. Frequently, intrabony defects present a complex anatomy consisting of a three-wall component in the most apical portion of the defect, and two- and/or one-wall components in the more superficial portions. Hemiseptal defects, that is, vertical defects in the presence of adjacent roots and where half of a septum remains on one tooth, represent a special case of one-wall defects. Several authors have also used descriptive terms to define special morphological characteristics: funnel-shaped defects, moat-like defects, trenches, etc. Of particular interest is a special morphology: the crater (Fig. 43-1). It is defined as a cup- or bowl-shaped defect in the interdental alveolar bone with bone loss nearly equal on the roots of two contiguous teeth and more coronal position of the buccal and lingual alveolar crest; the facial and lingual/palatal walls may be of unequal height. This defect can be considered as the result of the apical spread of periodontitis along two adjacent roots in a relatively narrow (mesiodistally) interproximal area. Notably, all the definitions above are not based on radiographic assessments but on the actual morphology of the defects after flap elevation. Conditions entailing pathologic resorption of bone within the furcation of a multi-rooted tooth, defined as furcation invasions, are also included in the group of periodontal bony defects; the reader however is referred to Chapter 39 for a discussion of the anatomy and classification of furcations.
**Fig. 43-1** Infrabony defects. (a) One-wall intrabony defect. (b) Two-wall intrabony defect. (c) Three-wall intrabony defect. (d) Interproximal crater. From Papapanou & Tonetti (2000).
The diagnosis of the presence and the morphology of periodontal osseous lesions represents a major clinical challenge. It is primarily performed combining clinical information derived from the evaluation of the attachment level with information derived from diagnostic-quality parallel-technique intraoral radiographs. A precise knowledge of root anatomy and its variations is also an important component for the diagnosis of periodontal osseous defects, and inter-radicular defects in particular. Diagnostic-quality radiographs provide additional information on the morphology of the alveolar bone resorption. In this context, interpretation of the radiographic image of the interdental septum is complicated, since the radiograph provides a two-dimensional illustration of a three-dimensional anatomy consisting of superimposed structures including alveolar bone, hard tooth substances, and soft tissue. This complexity of the visualized structures means that a certain amount of tissue destruction must occur before its radiographic detection becomes possible, often rendering incipient bone lesions obscure. Furthermore, even advanced lesions may be masked by the presence of superimposed structures. It is therefore generally stated that radiographic diagnosis has a high positive predictability (that is, the visualized lesions are indeed there) but a low negative predictability (that is, absence of radiographically detectable bone loss does not exclude the presence of an osseous lesion).
Clinical attachment level, on the other hand, is a highly sensitive diagnostic tool; its combination with radiographs, therefore, confers a higher degree of accuracy to the diagnostic approach (Tonetti _et al_. 1993b). In particular, the site-specific comparison of radiographic bone loss with clinical attachment loss allows the clinician to make a qualified guess of the true osseous architecture, whose exact morphology, however, can only be established after flap elevation. Detection of the defect, its location and extension, along with its major morphologic features, should be performed before flap elevation. A further aid to this end is the use of transgingival probing or bone sounding.
# Clinical indications
Periodontal treatment, either surgical or non-surgical, results in recession of the gingival margin after healing (Isidor _et al_. 1984). In advanced cases of periodontitis, this may lead to poor esthetics in the front areas of the dentition, in particular when applying surgical procedures, including bone contouring, for the eradication of bone defects. Treatment of such cases without bone contouring, on the other hand, may result in residual pockets inaccessible to proper cleaning during post-treatment maintenance. These problems can be avoided or reduced by applying regenerative surgical procedures by which the lost periodontal attachment in the bone defects can be restored. Thus, the indication of applying regenerative periodontal therapy is often based on esthetic considerations, besides the fact that the function or long-term prognosis of the treated teeth may be improved.
Another indication for regenerative periodontal therapy are furcation-involved teeth. The furcation area is often inaccessible to adequate instrumentation and frequently the roots present concavities and furrows that make proper cleaning of the area after resective surgery impossible. Considering the long-term results and complications reported following treatment of furcation involvements by traditional resective therapy (Hamp _et al_. 1975; Bühler 1988), the long-term prognosis of furcation-involved teeth can be improved considerably by successful regenerative periodontal therapy.
Case reports also exist demonstrating that "hopeless" teeth with deep vertical defects, increased tooth mobility or through-and-through furcations can be successfully treated with regenerative periodontal therapy (Gottlow _et al_. 1986). However, controlled clinical trials or serial case reports presenting a reasonable predictability of treating such advanced cases are not available.
# Long-term effects and benefits of regeneration
A pertinent question with respect to regenerative treatment is whether the achieved attachment level gains can be maintained over an extended period of time. In a long-term follow-up study, Gottlow _et al_. (1992) assessed the stability of new attachment gained through guided tissue regeneration (GTR) procedures. Eighty sites in 39 patients, which 6 months after surgery exhibited a gain of clinical attachment of ≥2 mm (2–7 mm), were monitored during additional periods of 1–5 years. Of the 80 sites, 65 were monitored for 2 years, 40 for 3 years, 17 for 4 years, and 9 sites for 5 years. The results of this study and those of other trials indicate that attachment gain obtained following GTR treatment can be maintained on a long-term basis (Becker & Becker 1993; McClain & Schallhorn 1993).
An investigation on intrabony defects demonstrated that the stability of sites treated with GTR was dependent on participation of the patients in a recall program, and on the absence of bacterial plaque, bleeding on probing, and re-infection of the treated sites with periodontal pathogens (Cortellini _et al_. 1994). The susceptibility to disease recurrence at sites treated with non-bioabsorbable barrier membranes was assessed in a study comparing long-term changes in attachment levels at regenerated and non-regenerated sites in the same patient (Cortellini _et al_. 1996a). Results indicated that there was a high degree of concordance in the clinical outcomes (stability vs. recurrence of attachment loss) within the same patient suggesting that patient factors, rather than the site factors, including the specifics of the histologic type of expected wound healing, are associated with disease recurrence. Among patient factors, compliance with oral hygiene, smoking habits, and susceptibility to disease progression were the major determinants of stability of the treated sites, rather than the employed treatment modality.
Support for a limited impact of the histologic type of healing comes from an experimental study. In a study in monkeys (Kostopoulos & Karring 1994), periodontal breakdown was produced by the placement and retention of orthodontic elastics on experimental teeth until 50% bone loss was recorded. The experimental teeth were endodontically treated and subjected to a flap operation, and all granulation tissue was removed. The crowns of the teeth were resected at the level of the cemento-enamel junction and a barrier membrane was placed to cover the roots before they were submerged. Following 4 weeks of healing, the membranes were removed. At the same time the contralateral teeth that served as controls were endodontically treated and subjected to a sham operation during which the crowns were resected at the level of the cemento-enamel junction. Artificial composite crowns were then placed on both the experimental and the control roots. The sites were allowed to heal for 3 months during which period careful plaque control was performed. At the end of this period cotton-floss ligatures were placed on both experimental and control teeth to induce periodontal tissue breakdown. After another 6 months, the animals were sacrificed. With respect to attachment level, bone level, pocket depth, and gingival recession, similar results were recorded in histologic specimens of experimental (Fig. 43-2) and control (Fig. 43-3) teeth. This indicates that the new connective tissue attachment formed with GTR is not more susceptible to periodontitis than the naturally existing periodontium.
**Fig. 43-2** Microphotograph of test specimen with a reformed connective tissue attachment. After 6 months of ligature-induced periodontitis, loss of attachment has occurred from the coronal cut root surface to the level indicated by the arrow.
**Fig. 43-3** Microphotograph of control specimen with a naturally existing periodontium. After 6 months of ligature-induced periodontitis, loss of attachment has occurred from the coronal cut tooth surface to the level indicated by the arrow.
A few studies have evaluated the long-term prognosis for furcation defects treated with regenerative therapy. Sixteen mandibular degree II furcation defects, following coronal flap positioning and citric acid root biomodification with and without implantation of demineralized freeze-dried bone allografts (DFDBA), were determined as completely resolved with bone fill assessed by re-entry surgery. They were re-evaluated after 4–5 years (Haney _et al_. 1997), when 12 of the 16 sites exhibited recurrent degree II furcations and all 16 sites demonstrated probable buccal furcation defects. The investigators concluded that these findings question the long-term stability of bone regeneration in furcations following coronally advanced flap procedures.
The long-term stability of mandibular furcation defects regenerated following GTR alone or in combination with root surface biomodification with citric acid and bone grafting, was also evaluated by McClain and Schallhorn (1993). Out of the 57% of the furcation defects that were assessed as completely filled at 6 and 12 months, only 29% were completely filled after 4–6 years. However, 74% of the furcations treated with GTR in combination with the placement of DFDBA were completely filled at both the short and long-term evaluation, suggesting that the results obtained with the combined procedure were more stable over time. Long-term results of GTR treatment of mandibular degree II furcations with e-PTFE membranes were also reported by Machtei _et al_. (1996). The teeth were followed up to 4 years and compared with non-furcated molars. Improvements assessed in vertical (V-CAL) and horizontal (H-CAL) clinical attachment levels after treatment were also maintained after 4 years, suggesting that changes obtained in degree II furcation defects by GTR are stable. Only 9% of the treated defects were unstable, which was similar to that observed for non-furcated molars. Good oral hygiene, as reflected in low plaque scores and elimination of periodontal pathogens, was closely related to the long-term stability. On the basis of these results, it was concluded that furcation defects treated with membrane barriers can be maintained in health for at least 4 years, provided good oral hygiene and frequent recall visits are established.
In summary, several clinical studies addressing the long-term effects of periodontal regeneration show that, if the patient participates in a professionally delivered supportive periodontal care program and maintains good oral hygiene, the regenerated attachment can be maintained long term (Gottlow _et al._ 1992; MacClain & Schallhorn 1993; Cortellini _et al._ 1994, 1996a; Machtei _et al._ 1996; Christgau _et al_. 1997; Eickholz _et al_. 1997; Sculean _et al_. 2006). Risk factors for attachment loss are those associated with disease recurrence: poor compliance with supportive periodontal care, poor oral hygiene, and cigarette smoking (Cortellini _et al._ 1996a; Cortellini & Tonetti 2004).
Few investigations have looked at the long-term effects of periodontal regeneration on tooth survival. Cortellini and Tonetti (2004) performed a Kaplan Mayer analysis of tooth survival following periodontal regenerative treatment in a sample of 175 patients followed up for 2–16 years (average 8 ± 3.4 years) in a specialist environment. In this study, 96% of teeth treated by periodontal regeneration survived. Of interest was the observation that tooth loss was observed only among the 32% of the population that were smokers (tooth survival was 89% among smokers and 100% among non-smokers). Clinical attachment levels were located at the same level or coronal to the pre-treatment levels in 92% of cases up to 15 years after treatment (Table 43-1, Fig. 43-4).
**Table 43-1** Survival analysis of regenerated periodontal attachment over a 16-year follow-up period in 175 subjects treated with periodontal regeneration. In this survival analysis, the event is represented by clinical attachment level (CAL) loss of 2 mm or more from the level of attachment obtained at completion of healing 1 year after regeneration. No substantial recurrence of periodontitis (CAL loss) was observed in 92% of treated cases who participated in a secondary prevention program. (From Cortellini & Tonetti (2004) with permission)
The potential clinical benefits of periodontal regeneration can be best illustrated in a consecutive case series of strategic abutments severely compromised by the presence of deep intrabony defects with associated deep pockets with up to 8 years' follow-up following regenerative treatment (Tonetti _et al_. 1996a; Cortellini _et al_. 1998). At baseline, the periodontal defect rendered these teeth unsuitable as abutments to be included in a reconstruction. In all cases, periodontal regeneration with barrier membranes was able to change the clinical prognosis by providing both a 30% increase in radiographic bone support and shallow, maintainable probing depths. These outcomes remained stable during the follow-up period (Fig. 43-5). A similar benefit has been recently reported following use of combination therapy (barrier membranes and demineralized freeze-dried bone allograft) in teeth compromised by class II furcation defects (Bowers _et al_. 2003): 92% of class II defects were either closed or transformed into class I and thus at lower risk of tooth loss 1 year after therapy (McGuire & Nunn 1996a,b).
The limitation of recession of the gingival margin observed in controlled clinical trials when comparing a regenerative treatment with a non-regenerative surgical procedure is also an important benefit.
# Evidence for clinical efficacy and effectiveness
Questions of efficacy relate to the added benefit of a treatment modality under ideal experimental conditions (such as those of a highly controlled research center environment). Effectiveness, on the other hand, relates to the benefit that can be achieved in a regular clinical setting where the procedure is likely to be performed in relation to morbidity and adverse events. Besides efficiency considerations, both evidence for efficacy and effectiveness need to be available in order to provide support for adoption of a novel approach in clinical practice.
The clinical efficacy of periodontal regenerative procedures has been extensively evaluated in randomized controlled clinical trials that have compared the regenerative procedure with a standard approach.
To limit sample size and study duration, these trials have utilized surrogate outcomes – clinical attachment level changes, decrease in pocket depths, furcation closure or radiographic measurements – rather than changes in tooth survival. These surrogate outcomes, however, are considered to be adequate proxies of the true outcome represented by tooth survival: persistence of deep pockets or furcation involvement are associated with higher risk of periodontal breakdown and tooth extraction.
The majority of clinical trials were small single-center studies. The evidence of these studies has been recently summarized in meta-analyses performed on data retrieved by systematic reviews of the published literature. In 2002 and 2003, the European Workshop on Periodontology and the Workshop on Emerging Technologies in Periodontics provided much of the systematic assessment of the evidence for currently available technologies. These include the use of barrier membranes (guided tissue regeneration, GTR), the use of bone replacement grafts, and the use of biologically active regenerative materials. The clinical evidence must be interpreted in the context of the biologic mechanisms and evidence for regeneration discussed in Chapter 25.
The evidence of clinical efficacy of barrier membranes has been assessed in the systematic reviews and meta-analyses performed by Needleman _et al_. (2002), Jepsen _et al_. (2002), and Murphy and Gunsolley (2003).
**Fig. 43-4** (a,b) Left maxillary lateral incisor with a deep interproximal intrabony defect on the mesial surface. (c) Flaps are raised according to the modified papilla preservation technique, and a titanium-reinforced barrier membrane is placed over the defect. (d) By coronal displacement of the flap and preservation of the interdental papilla, the membrane is completely covered. (e,f) After 6 weeks of uneventful post-operative healing the membrane was removed, (g) and the newly formed tissue was completely covered. (h) At 1 year, residual probing pocket depth was 2 mm and no buccal or interdental recession had occurred. (i) The baseline radiograph shows radiolucency approaching the apex of the tooth, but after 1 year the intrabony defect is resolved and some supracrestal bone apposition seems to have occurred (j). The radiograph taken at 6 years confirms the supracrestal bone regeneration (k) and the clinical image shows the integrity of the interdental papilla with optimal preservation of the esthetic appearance (l).
For intrabony defects, 26 controlled trials with 867 intrabony defects were included (Murphy & Gunsolley 2003). The application of barrier membranes resulted in an additional clinical attachment level gain of more than 1 mm compared to an access flap approach control (Fig. 43-6).
For class II furcation defects, 15 controlled trials with 376 involved teeth were included (Murphy & Gunsolley 2003). Membrane application resulted in additional vertical and horizontal (depth of the furcation involvement) clinical attachment level gains (Fig. 43-7).
These data alone, however, did not present conclusive evidence of efficacy as the possibility of bias arising from a possible tendency to report studies with positive results could not be ruled out. Multi-center studies were designed to assess efficacy conclusively. These were performed in a private practice environment in order to assess also the generalizability of the benefit to this specific setting (effectiveness). The results of large prospective multi-center studies in private practice settings (Tonetti _et al_. 1998, 2004b; Cortellini _et al_. 2001) conclusively support the additional benefit of membranes in improving clinical attachment levels in intrabony defects and thus their efficacy and effectiveness. More limited evidence is also available for combination therapy (bone replacement grafts and barrier membranes) in furcation defects (Bowers _et al_. 2003).
**Fig. 43-5** Clinical benefits of periodontal regeneration. Patient presented with periodontally compromised mesial abutment of bridge: a 10-mm pocket was associated with a 10-mm intrabony defect extending on three of the four surfaces of the tooth (a–d). A barrier membrane was positioned and secured around the root of the tooth (e). Primary closure with internal mattress sutures was achieved (f) and maintained during the healing period. At 1 year, periodontal probing shows a shallow maintainable pocket (3 mm) (g) and the complete resolution of the defect (h). Clinical and radiographic stability of the outcome is illustrated 8 years following regenerative therapy (i,j): stability of the gingival margin, shallow pockets, good esthetics, and good periodontal support for the abutment are evident.
The efficacy of bone replacement graft materials has been assessed in two systematic reviews (Trombelli _et al_. 2002; Reynolds _et al_. 2003). As these two systematic reviews used significantly different criteria for study inclusion, results did not fully overlap. Trombelli _et al_. (2002), who included only controlled studies that reported changes in clinical attachment level as the primary outcome, concluded that there was insufficient evidence to support clinical use of bone replacement graft materials in intrabony defects, since: (1) there was significant heterogeneity among included studies; (2) the size of the adjunctive effect was small; and (3) there were differences that did not allow pooling of results obtained with different materials. In the other meta-analysis for intrabony defects, 27 controlled trials with 797 intrabony defects were included (Reynolds _et al_. 2003). The application of bone replacement grafts resulted in an additional clinical attachment level gain of 0.5 mm compared to an access flap approach control (Fig. 43-8). Greater additional benefits from the application of bone replacement grafts were observed whenever hard tissue measurements (bone fill or defect resolution) were utilized as outcome measures.
**Fig. 43-6** Meta-analysis of intrabony defect studies examining open flap debridement versus GTR with barrier, using clinical attachment level (CAL) gain as an outcome variable. Bov coll = bovine collagen; e-PTFE = expanded polytetrafluoroethylene; Hum coll = human collagen; PLA = polylactic acid; PLA/PGA = polylactic/polyglycolic acid; TR = titanium-reinforced. From Murphy & Gunsolley (2003) with permission from the American Academy of Periodontology.
**Fig. 43-7** Forest plot of furcation defect studies examining open flap debridement (OFD) versus GTR with barrier, using HOPA gain as an outcome variable. e-PTFE = expanded polytetrafluoroethylene; Mand = mandibula; Max = maxilla. From Murphy & Gunsolley (2003) with permission from the American Academy of Periodontology.
For furcation defects, the lack of consistent comparisons did not allow a meaningful assessment of the potential benefits of the use of bone replacement grafts alone (Reynolds _et al_. 2003). No large multi-center trials have provided definitive support for efficacy and/or effectiveness of the use of bone replacement grafts.
The evidence of clinical efficacy of biologically active regenerative materials has been summarized in meta-analyses only for enamel matrix derivative (Trombelli _et al_. 2002; Giannobile & Somerman 2003) and only for the application to intrabony defects. The outcomes of eight studies including 444 defects have indicated that enamel matrix derivative provides additional benefits of a magnitude of 0.75 mm in terms of clinical attachment level gains (Fig. 43-9). These data have been in accordance with those of a large practice-based multi-center trial that demonstrated both efficacy and effectiveness of enamel matrix derivative in intrabony defects (Tonetti _et al_. 2002).
**Fig. 43-8** Final meta-analysis of clinical attachment level in randomized controlled clinical studies comparing BRG to OFD in the treatment of intrabony defects. ALL = allograft; AUT = autograft; CER = calcium phosphate (hydroxyapatite) ceramic; COR = coralline calcium carbonate; GLA = bioactive glass. From Reynolds _et al_. (2003) with permission from the American Academy of Periodontology.
**Fig. 43-9** Meta-analysis depicting the effectiveness of enamel matrix derivative (EMD) combined with surgery on clinical attachment level (CAL) gain as compared to control flap surgery alone. The use of EMD showed a significant improvement in CAL gain. Heterogeneity: Cohen's D, _P_ = 0.04, Hedge's g, _P_ = 0.16. From Giannobile & Somerman (2003) with permission from the American Academy of Periodontology.
# Patient and defect prognostic factors
The results reported in Table 43-2 indicate that clinical improvements beyond that of flap surgery can be obtained by treating intrabony defects with GTR, but they also suggest a great variability in clinical outcomes among the different studies. In addition, it is apparent from the results that the complete resolution of the intrabony component of the defect is observed in only a minority of sites. A series of prognostic factors associated with the clinical outcomes were identified using multi-variate approaches (Tonetti _et al_. 1993a, 1995, 1996a; Cortellini _et al_. 1994; Machtei _et al_. 1994; Falk _et al_. 1997). Attention has focused on some important patient and defect factors.
**Table 43-2** Clinical outcomes of GTR treatment of deep intrabony defects
## Patient factors
### Periodontal infection
Periodontal regeneration does not treat periodontitis, but rather is an approach for regenerating defects that have developed as a result of periodontitis. Therefore, appropriate periodontal treatment should always be completed before periodontal regeneration is initiated. In this context – i.e. in patients who underwent a cycle of cause-related periodontal therapy to the satisfaction of the treating clinician – evidence suggests that the level of control of periodontitis, achieved before a periodontal regenerative procedure is initiated, is associated with outcomes: the persistence of poor plaque control, high levels of bleeding upon probing in the dentition, as well as the persistence of high loads of total bacteria or of specific microbial pathogens (or complexes of pathogens) have all been associated in a dose-dependent manner with poor clinical outcomes (Tonetti _et al_. 1993a, 1995; Cortellini _et al_. 1994; Machtei _et al_. 1994; Heitz-Mayfield _et al._ 2006).
The level of self-performed plaque control has a great and dose-dependent effect on the outcome of periodontal regeneration. Better clinical attachment level gains were observed in patients with optimal levels of plaque control as compared with those in patients with less ideal oral hygiene (Cortellini _et al_. 1994; Tonetti _et al_. 1995, 1996a). Patients with plaque on <10% of the tooth surfaces (full mouth plaque score, FMPS) had a gain of clinical attachment which was 1.89 mm greater than that observed in patients with FMPS >20% (Tonetti _et al_. 1995).
Although not formally tested for efficacy in randomized trials, achieving high levels of plaque control and suppression of the pathogenic microflora through behavioral intervention and intensive anti-infective periodontal therapy are generally advocated before proceeding with periodontal regeneration. Furthermore, some proof of principle investigations have assessed the adjunctive effect of using an antibiotic locally delivered within the wound area or in the regenerative material (Yukna & Sepe 1982; Sanders _et al_. 1983; Stavropoulos _et al_. 2003). Results showed consistently better outcomes in the groups that received the antibiotic. At present, however, no regenerative device with enhanced antimicrobial activity is commercially available.
### Smoking
A retrospective study found that cigarette smokers displayed significantly impaired regenerative outcomes compared to non-smokers (Tonetti _et al_. 1995). Data showed that cigarette smoking was associated with reduced attachment level gains. The attachment gain in subjects smoking more than ten cigarettes/day was 2.1 ± 1.2 mm versus 5.2 ± 1.9 mm observed in non-smokers (Tonetti _et al_. 1995). Thereafter a series of investigations has confirmed that cigarette smoking displays a dose-dependent detrimental effect on clinical attachment level gains.
Although no formal evidence is available, it is generally suggested that smoking cessation counseling should be initiated in the context of cause-related periodontal therapy and that patients who have been unable to quit the habit should be informed of the possibility of reduced outcomes and of the need to abstain from smoking during the peri-operative and early healing period.
### Other patient factors
It has been suggested that other patient factors, such as age, genetics, systemic conditions or stress levels, may be associated with sub-optimal regenerative outcomes. In the light of the lack of evidence, however, no action is required with the exception of considering the patient characteristics that represent a contraindication to surgery (e.g. uncontrolled diabetes or unstable, severe diseases).
### Clinical relevance of patient factors
The data discussed above indicates that patient factors play an important role in regenerative periodontal therapy (Fig. 43-10). Some of these factors can be modified by appropriate interventions in some patients. These interventions should be performed before periodontal regenerative therapy. Whenever modification is not possible, reduced outcomes in terms of extent and predictability should be considered.
## Defect factors
### Type of defect
With the currently available periodontal regenerative technologies, there is no evidence that suprabony (horizontal) defects, supracrestal components of intrabony defects or class III furcation involvements can be predictably treated with regenerative approaches. This limitation is also true for interdental craters, thus limiting the type of defects that can be treated to intra-bony defects and class II furcation defects.
### Morphology of the defect
Defect morphology plays a major role in healing following periodontal regenerative treatment of intrabony defects. This was demonstrated in studies showing that the depth and width of the intrabony component of the defect influence the amount of clinical attachment and bone gained at 1 year. The deeper the defect, the greater was the amount of clinical improvements, while the wider the defect, the lower were the attachment and bone gains (Garrett _et al_. 1988; Tonetti _et al_. 1993a, 1996a).
**Fig. 43-10** Diagram illustrating patient selection criteria. It can be seen that control of local, behavioral, and systemic patient characteristics may improve the treatment outcomes. FMPS = full mouth plaque score; FMBS = full mouth bleeding score. Modified from Cortellini & Bowers (1995).
In a controlled study, however, it was demonstrated that deep and shallow defects have the "same potential" for regeneration. In this study, deep defects (deeper than 3 mm) resulted in larger linear amounts of CAL gains than shallow defects (3.7 ± 1.7 mm versus 2.2 ± 1.3 mm), but the percentage of CAL gains as related to baseline defect depth was similar in deep (76.7 ± 27.7%) and in shallow (75.8 ± 45%) defects. The width of the intrabony component of the defects is measured as the angle that the bony wall of the defect forms with the long axis of the tooth. In a study on 242 intrabony defects treated with membranes, Cortellini and Tonetti (1999) demonstrated that defects with a radiographic angle of 25º or less gained consistently more attachment (1.6 mm on average) than defects of 37º or more.
Two recent follow-up studies have addressed the significance of the baseline radiographic angle of the intrabony defect following the use of either enamel matrix derivative (Tsitoura _et al_. 2004) or of a combination of bone replacement graft with a barrier membrane (Linares _et al_. 2006). The impact of the width of the baseline radiographic angle was confirmed for the non-space-making biological mediator but not for the more stable combination therapy. These data are consistent with the notion that choice of the regenerative technology may partially overcome negative morphologic characteristics of intrabony defects. An earlier secondary analysis of a controlled clinical trial using titanium-reinforced membranes (Tonetti _et al_. 1996a) indicated that the relevance of defect morphology parameters may be diminished with the use of supported membranes.
It was also shown that the number of residual bony walls was related to the outcomes of various regenerative approaches (Goldman & Cohen 1958; Schallhorn _et al_. 1970). This issue as related to GTR therapy was addressed in three investigations (Selvig _et al_. 1993; Tonetti _et al_. 1993a, 1996a). In one study, the reported 1-year mean clinical attachment level gain was 0.8 ± 1.3 mm. This gain corresponded to the depth of the three-wall intrabony component of the defect (Selvig _et al_. 1993). In the other two investigations, on the contrary, gains in attachment were not related to the defect configuration in terms of one-wall, two-wall, and three-wall subcomponents (Tonetti _et al_. 1993a, 1996a). A total of 70 defects were examined in these two latter studies, utilizing a multi-variate approach. The treatment resulted in mean attachment gains of 4.1 ± 2.5 mm and 5.3 ± 2.2 mm, and it was observed that the most coronal portion of the defects which is most susceptible to negative influences from the oral environment were often incompletely filled with bone, irrespective of whether these were one-wall, two-wall or three-wall defects. Thus, these studies questioned the impact of the number of residual bony walls of the defect on the clinical outcomes of periodontal regeneration with membranes and suggested that location of the one-wall subcomponent (the one most likely to be the most superficial one) may have acted as confounder in other studies and be an important predictor of the outcomes.
## Tooth factors
The endodontic status of the tooth has been suggested as a potential relevant factor in periodontal therapy. Emerging evidence (see Chapter 40) indicates that root canal treated teeth may respond differently to periodontal therapy. A clinical study on 208 consecutive patients with one intrabony defect each demonstrated that properly performed root canal treatment does not negatively affect the healing response and the long-term stability of results of deep intrabony defects treated with membranes (Cortellini & Tonetti 2000b).
Tooth mobility has long been considered an important factor for periodontal regeneration (Sanders _et al_. 1983). Recently, a multi-variate analysis of a multi-center controlled clinical trial demonstrated that tooth hypermobility was negatively and dose-dependently associated with the clinical outcomes of regeneration (Cortellini _et al_. 2001). Though significant, the size of the effect was small within the range of physiologic mobility. Another recent secondary analysis of three previously reported trials assessed the regenerative outcomes of hypermobile teeth (Trejo & Weltman 2004). This report indicated that teeth with baseline mobility amounting to less than 1 mm horizontally could be successfully treated by periodontal regeneration. Although no intervention trial has been performed to date, these results are generally considered supportive of an approach that does not set the prognosis of the tooth or the regenerative procedure based on tooth mobility but rather considers splinting hypermobile teeth before periodontal regenerative surgery.
Based on these results, it can be concluded that deep and narrow intrabony defects at either vital or endodontically treated teeth are the ones in which the most significant and predictable outcomes can be achieved by GTR treatment. Severe, uncontrolled dental hypermobility (Miller class II or higher) may impair the regenerative outcomes.
## Factors affecting the clinical outcomes of GTR in furcations
Significant evidence has demonstrated that treatment of maxillary degree II furcations and maxillary and mandibular degree III furcation involvements with GTR is unpredictable, while clinical improvements can be expected treating mandibular degree II furcations. The great variability in clinical outcomes, following treatment of mandibular degree II furcations with GTR, is probably related to the factors discussed relative to intrabony defects.
Regarding defect factors, it was shown that first and second mandibular molars and buccal and lingual furcations respond equally well to GTR treatment (Pontoriero _et al_. 1988; Machtei _et al_. 1994). It was also demonstrated that the pre-operative horizontal pocket depth is directly correlated with the magnitude of attachment gain and bone formation in the furcation area (Machtei _et al_. 1993, 1994). The deeper the baseline horizontal pocket, the greater was the H-CAL and bone gain. The anatomy of the furcations in terms of height, width, depth, and volume, however, did not correlate with the clinical outcome (Machtei _et al_. 1994). Anderegg _et al_. (1995) demonstrated that sites with a gingival thickness of >1 mm exhibited less gingival recession post surgery than sites with a gingival thickness of <1 mm. The authors concluded that the thickness of the gingival tissue covering a barrier material must be considered if post-treatment recession is to be minimized or avoided.
# The relevance of the surgical approach
At the beginning of the 1980s the need to modify standard periodontal surgical procedures to favor periodontal regeneration became apparent. In particular, the need to preserve soft tissues in order to attempt primary closure of the interdental space to contain grafts or coronally advanced flaps to cover furcation entrances led to the development of specific flap designs for periodontal regeneration (Takei _et al_. 1985; Gantes & Garret 1991).
In fact, graft exfoliation and membrane exposure with consequent bacterial contamination during healing represented the major complications of periodontal regenerative procedures at the time. Membrane exposure was reported to be a major complication with prevalence in the range of 50–100% (Becker _et al_. 1988; Cortellini _et al_. 1990, 1993b; Selvig _et al_. 1992, 1993; Murphy 1995a; DeSanctis _et al_. 1996a,b; Falk _et al_. 1997; Trombelli _et al_. 1997; Mayfield _et al_. 1998). Cortellini _et al_. (1995c,d) reported that the prevalence of membrane exposure could be greatly reduced with the use of access flaps, specifically designed to preserve the interdental tissues (modified papilla preservation technique) (Fig. 43-11).
Many studies have shown that the exposed membranes are contaminated with bacteria (Selvig _et al_. 1990, 1992; Grevstad & Leknes 1992; Machtei _et al_. 1993; Mombelli _et al_. 1993; Tempro & Nalbandian 1993; Nowzari & Slots 1994; Novaes _et al_. 1995; Nowzari _et al_. 1995; DeSanctis _et al_. 1996a,b). Contamination of exposed non-bioabsorbable as well as bioabsorbable membranes was associated with lower probing attachment level gains in intrabony defects (Selvig _et al_. 1992; Nowzari & Slots 1994; Nowzari _et al_. 1995; DeSanctis _et al_. 1996a,b). The impaired clinical results in some studies were associated with high counts of bacteria and with the presence of _P. gingivalis_ and _A. actinomycetemcomitans_ (Machtei _et al_. 1994; Nowzari & Slots 1994; Nowzari _et al_. 1995).
Bacterial contamination of the membrane may occur during surgery, but also during the post-operative healing phase. After placement, bacteria from the oral cavity may colonize the coronal part of the membrane. Frequently, this results in recession of the gingival tissues, which allows colonization of the membrane material further apically. In addition, "pocket" formation may occur on the outer surface of the membrane due to apical migration of the epithelium on the inner surface of the covering gingival tissue. This may allow bacteria from the oral cavity to colonize the subgingival area. The significance of bacterial contamination was addressed in an investigation in monkeys (Sander & Karring 1995). The findings of this study showed that new attachment and bone formation occurred consistently when bacteria were prevented from invading the membrane and the wound during healing.
**Fig. 43-11** (a) Left maxillary central incisor with a 10-mm pocket depth and 11 mm of clinical attachment loss on the mesial surface. A diastema is present between the two central incisors. (b) Full thickness buccal and palatal flaps have been raised and an intrabony defect can be seen. The interdental papilla has been incised on the buccal aspect and elevated with the palatal flap (modified papilla preservation technique). (c) A titanium-reinforced e-PTFE barrier membrane has been placed and fixed close to the level of the cemento-enamel junction. (d) The membrane is completely covered. This primary closure has been obtained by preserving the interdental papilla and by coronal displacement of the buccal tissue flap. (e) At 6 weeks, the membrane is completely covered with healthy tissue. (f) After membrane removal at 6 weeks, dense newly formed tissue is evident in the defect and in the supracrestal space maintained by the titanium-reinforced membrane. (g) The newly formed tissue is completely covered by the raised and well preserved tissue flaps. (h) The photograph after 1 year shows a 4 mm residual pocket depth. A gain of clinical attachment of 6 mm was recorded, and no recession has occurred compared to baseline. (i) Ten year photograph showing the optimal preservation of the interdental tissues.
In order to prevent wound infection, some investigators have administered systemic antibiotics to patients before and during the first weeks after membrane application (Demolon _et al_. 1993; Nowzari & Slots 1994). However, despite the application of systemic antibiotics, occurrence of post-operative wound infection related to implanted barrier membranes was noticed. This indicates that either the drug administered is not directed against the microorganisms responsible for the wound infection, or that the drug does not reach the infected site at a concentration sufficiently high to inhibit the target microorganisms. An improved effect on periodontal healing after GTR in association with local application of metronidazole was reported by Sander _et al_. (1994). Twelve patients with one pair of intrabony defects participated in the study. Metronidazole in a gel form was placed in the defects and on the membrane prior to wound closure, while the controls were treated with a membrane alone. Six months following membrane removal the medium gain in probing attachment level, presented as a percentage of the initial defect depth, was 92% for test defects versus 50% for the control defects. Other clinical parameters, like plaque index, bleeding on probing, pocket depth reduction or recession of the gingival margin, were similar in the test and control sites. Although the use of local or systemic antibiotics may reduce the bacterial load on exposed membranes, it seems ineffective in preventing the formation of a microbial biofilm (Frandsen _et al_. 1994; Nowzari _et al_. 1995). Apart from the erythema and swelling related to such infection of the wound, more severe post-operative complications such as suppuration, sloughing or perforation of the flap, membrane exfoliation, and post-operative pain have been reported (Murphy 1995a,b).
Another important issue associated with the clinical results is the coverage of the regenerated tissue after removal of a non-bioabsorbable membrane. Many authors have reported that the frequent occurrence of a gingival dehiscence over the membrane is likely to result in insufficient protection of the interdental regenerated tissue (Becker _et al_. 1988; Selvig _et al_. 1992; Cortellini _et al_. 1993b; Tonetti _et al_. 1993a). Exposure of the regenerated tissue to the oral environment entails the risks of mechanical and infectious insults that in turn may prevent complete maturation of the regenerated tissue into a new connective tissue attachment. In fact, incomplete coverage of the regenerated tissue was associated with reduced attachment and bone gain at 1 year (Tonetti _et al_. 1993a). Recently, the positioning of a saddle-shaped free gingival graft over the regenerated interdental tissue (Fig. 43-12) was suggested to offer better coverage and protection than a dehiscent gingival flap (Cortellini _et al_. 1995a). In this randomized controlled study, more gain of attachment was observed in the 14 sites where a free gingival graft was positioned after membrane removal (5.0 ± 2.1 mm), than in the 14 sites where conventional protection of the regenerated tissue was accomplished (3.7 ± 2.1 mm).
The systematic assessment of the relevant factors associated with variability of periodontal regenerative outcomes performed at the beginning of the 1990s (Tonetti _et al_. 1993a, 1995, 1996a; Machtei _et al_. 1994; Falk _et al_. 1997) provided further evidence that surgical factors had a great impact on regeneration and led the way to the development of procedures specifically designed for periodontal regeneration.
**Fig. 43-12** Clinical case illustrating the management of the most common complication following application of non-resorbable barrier membrane: membrane exposure and consequent loss of interdental soft tissue. Upon completion of cause-related periodontal therapy, regenerative periodontal surgery was performed to resolve a deep pocket associated with a deep intrabony defect (a,b). The 7-mm intrabony defect was accessed with a modified papilla preservation flap (c) and a non-resorbable barrier membrane was placed (d). Primary closure with multilayered sutures was obtained, but 5 weeks after surgery, the membrane became exposed to the oral cavity (e). Upon membrane removal (f), a newly regenerated tissue completely filled the space below the membrane but inadequate amounts of soft tissue were available to completely cover the regenerated tissue in the interdental space. In order to protect the maturation of this tissue, a saddle-shaped interdental free gingival graft was harvested from the palate and shaped to precisely fit the interdental area (g). The graft healed well on the highly vascularized recipient bed and allowed good healing of the interdental tissues. Six years after completion of therapy, the clinical and radiographic outcomes show healing with shallow probing depths and elimination of the defect (h,i).
In general the development of new procedures was aimed at complete tissue preservation of the marginal tissue in order to achieve and maintain primary closure on top of the applied regenerative material during the critical stages of healing. Specifically, flap designs attempted to achieve passive primary closure of the flap combined with optimal wound stability.
## Papilla preservation flaps
The modified papilla preservation technique (MPPT) was developed in order to increase the space for regeneration, and in order to achieve and maintain primary closure of the flap in the interdental area (Cortellini _et al_. 1995c,d). This approach combines special soft tissue management with use of a self-supporting titanium-reinforced membrane capable of maintaining a supra-alveolar space for regeneration. The MPPT allows primary closure of the interdental space, resulting in better protection of the membrane from the oral environment (Cortellini _et al_. 1995d). The technique involves the elevation of a full-thickness palatal flap which includes the entire interdental papilla. The buccal flap is mobilized with vertical and periosteal incisions, coronally positioned to cover the membrane, and sutured to the palatal flap through a horizontal internal crossed mattress suture over the membrane. A second internal mattress suture warrants primary closure between the flap and the interdental papilla. A representative case is shown in Figs. 43-4 and 43-11. In a randomized controlled clinical study on 45 patients (Cortellini _et al_. 1995c), significantly greater amounts of attachment gain were obtained with the MPPT (5.3 ± 2.2 mm), in comparison with either conventional GTR (4.1 ± 1.9 mm) or flap surgery (2.5 ± 0.8 mm), demonstrating that a modified surgical approach can result in improved clinical outcomes.
In this study 100% of the sites were closed on top of a titanium-reinforced membrane and 73% remained closed for up to 6 weeks, when the barrier membrane was removed. This study provided proof of principle of the benefit of specific flap designs for periodontal regeneration.
A recent meta-analysis (Murphy & Gunsolley 2003) showed the existence of a trend associating better clinical outcomes in studies using flap designs and closing techniques considered conducive to the achievement and maintenance of primary closure of the flap (Figs. 43-13, 43-14). The reported procedure can be successfully applied in sites where the interdental space width is at least 2 mm at the most coronal portion of the papilla.
When interdental sites are narrower, the reported technique is difficult to apply. In order to overcome this problem, a different papilla preservation procedure (the simplified papilla preservation flap) has been proposed for narrower interdental spaces (Cortellini _et al_. 1999). This approach includes an oblique incision across the defect-associated papilla, starting from the buccal angle of the defect-associated tooth to reach the mid-interdental part of the papilla at the adjacent tooth under the contact point. In this way, the papilla is cut into two equal parts of which the buccal is elevated with the buccal flap and the lingual with the lingual flap. In the cited study, 100% of the narrow interdental papillae could be closed on top of bioresorbable barriers, and 67% maintained primary closure over time, resulting in 4.9 ± 1.8 mm of clinical attachment level gains. This approach has been successfully applied in different multi-center randomized clinical trials designed to test the generalizability of the added benefits of using barrier membranes on deep intrabony defects (Tonetti _et al_. 1998; Cortellini _et al_. 2001).
**Fig. 43-13** Means of intrabony defect studies examining the relationship between flap closure technique ranking and the gain in clinical attachment level (CAL) (in mm) considering only e-PTFE barrier types. Groupings were not statistically different from one another. From Murphy & Gunsolley (2003) with permission from the American Academy of Periodontology.
In the cited studies, GTR therapy of deep intrabony defects performed by different clinicians on various patient populations resulted in both greater amounts and improved predictability of CAL gains than access flap alone. The issue of soft tissue manipulation to obtain stable protection of the regeneration site has been further explored, applying a microsurgical approach in the regenerative therapy of deep intrabony defects (Fig. 43-15). In a patient cohort study on 26 patients with 26 intrabony defects treated with papilla preservation techniques, primary closure on the barrier was obtained in 100% of the cases and maintained over time in 92.3% of the sites (Cortellini & Tonetti 2001). Treatment resulted in large amounts of CAL gains (5.4 ± 1.2 mm) and minimal gingival recession (0.4 ± 0.7 mm). Thus, the improved vision and better soft tissue handling improved the predictability of periodontal regeneration.
**Fig. 43-14** Regression analysis of furcation defect studies examining the relationship between flap closure technique ranking and the reduction (in mm) in horizontal probing depth (HPD). Groups 1 and 2 are statistically different from one another. From Murphy & Gunsolley (2003) with permission from the American Academy of Periodontology.
Today, the use of papilla preservation flap designs and closure techniques has become the standard approach for regenerative periodontal surgery.
## Modified papilla preservation technique
The rationale for developing this technique was to achieve and maintain primary closure of the flap in the interdental space over the membrane (Cortellini _et al._ 1995d) (Figs. 43-16 to 43-18). Access to the interdental defect consists of a horizontal incision traced in the buccal keratinized gingiva at the base of the papilla, connected with mesio-distal buccal intrasulcular incisions. After elevation of a full-thickness buccal flap, the residual interdental tissues are dissected from the neighboring teeth and the underlying bone and elevated towards the palatal aspect. A full-thickness palatal flap, including the interdental papilla, is elevated and the interdental defect exposed. Following debridement of the defect, the buccal flap is mobilized with vertical and periosteal incisions, when needed.
This technique was originally designed for use in combination with self-supporting barrier membranes. In fact, the suturing technique requires a supportive (or supported) membrane to be effective (Figs. 43-16, 43-17). To obtain primary closure of the interdental space over the membrane, a first suture (horizontal internal crossed mattress suture) is placed beneath the mucoperiosteal flaps between the base of the palatal papilla and the buccal flap. The interdental portion of this suture hangs on top of the membrane allowing the coronal displacement of the buccal flap. This suture relieves all the tension of the flaps. To ensure primary passive closure of the interdental tissues over the membrane, a second suture (vertical internal mattress suture) is placed between the buccal aspect of the interdental papilla (i.e. the most coronal portion of the palatal flap which includes the interdental papilla) and the most coronal portion of the buccal flap. This suture is free of tension.
An alternative type of suture to close the interdental tissues has been proposed by Dr Lars Laurell. This modified internal mattress suture (see Fig. 38-56) starts from the external surface of the buccal flap, crosses the interdental area and gets through the lingual flap at the base of the papilla. The suture runs back through the external surface of the lingual flap and the internal surface of the buccal flap, about 3 mm apart from the first two bites. Finally, the suture is passed through the interdental area above the papillary tissues, passed through the loop of the suture on the lingual side, and brought back to the buccal side, where it is tied. This suture is very effective in ensuring stability and primary closure of the interdental tissues.
In a randomized controlled clinical study on 45 patients (Cortellini _et al_. 1995c), significantly greater amounts of PAL were gained with the MPPT (5.3 ± 2.2 mm), in comparison with either conventional GTR (4.1 ± 1.9 mm) or access flap surgery (2.5 ± 0.8 mm), demonstrating that a modified surgical approach can result in improved clinical outcomes. The sites accessed with the MPPT showed primary closure of the flap in all but one case, and no gingival dehiscence until membrane removal, in 73% of the cases.
This surgical approach has also been used in combination with non-supported bioresorbable barrier membranes (Cortellini _et al_. 1996c), with positive results. Clinical attachment level gains at 1 year were 4.5 ± 1.2 mm. In all the cases primary closure of the flap was achieved and about 80% of the sites maintained primary closure over time (Fig. 43-19). It should be underlined, however, that the horizontal internal crossed mattress suture most probably caused an apical displacement of the interdental portion of the membrane, thereby reducing the space for regeneration.
**Fig. 43-15** (a) Right first maxillary premolar with a 7-mm pocket on the mesial surface. The interdental space (b) is very narrow (>2 mm), and is accessed with a simplified papilla preservation flap. The 5-mm deep intrabony defect (c) is covered with a bioresorbable barrier membrane (d). Primary closure of the flap over the membrane (e,f) is maintained over time (g,h). After 1 year, the interdental papilla is completely preserved and the residual pocket depth is 3 mm (i,j). The radiograph taken at baseline (k) compared with that taken 1 year after treatment (l) shows that the intrabony defect has healed completely.
The MPPT can be successfully applied in conjunction with a variety of regenerative materials including biologically active materials such as enamel matrix derivative (EMD) (Tonetti _et al_. 2002) (Fig. 43-20) or growth factors and bone replacement grafts (Fig. 43-21) (Tonetti _et al_. 2004b; Cortellini & Tonetti 2005).
The surgical access of the interdental space with the MPPT is technically very demanding, but it has been reported to be very effective and applicable in wide interdental spaces (wider than 2 mm at interdental tissue level), especially in the anterior dentition. In properly selected cases, large amounts of attachment gain, and consistent reduction of pocket depths associated with no or minimal recession of the interdental papilla are consistently expected. It is, therefore, indicated in cases in which esthetics are particularly important.
**Fig. 43-16** Suture to obtain coronal positioning of the buccal flap: schematic illustration of the crossed horizontal internal mattress suture between the base of the palatal papilla and the buccal flap immediately coronal to the muco-gingival junction. Note that the suture crosses above the titanium reinforcement of the membrane. (a) Buccal view; (b) mesio-distal view. From Cortellini _et al_. (1995d) with permission from the American Academy of Periodontology.
**Fig. 43-17** Suture to obtain tension-free primary closure of the interdental space: schematic illustration of the vertical internal mattress suture between the most coronal portion of the palatal flap (which includes the interdental papilla) and the most coronal portion of the buccal flap. (a) Buccal view; (b) mesio-distal view. From Cortellini _et al_. (1995d) with permission from the American Academy of Periodontology.
**Fig. 43-18** Clinical case illustrating the operative procedure of the modified papilla preservation technique used to completely close the interdental space above a barrier membrane. Following completion of initial cause-related therapy, an 8-mm pocket associated with 2 mm of recession of the gingival margin was present on the distal of the central incisor (a). A wide intrabony defect was detectable on the radiograph (b). The defect was accessed with the modified papilla preservation technique keeping the whole interdental tissue connected with the palatal flap. A 7-mm intrabony defect was uncovered (c). Following root debridement, a titanium-reinforced barrier membrane was positioned (d). Primary closure of the interdental space was obtained by suturing back the papilla preservation flap using a multilayered suturing technique aimed at coronal advancement of the flap, complete relief of wound tension, and good flap stability (e). Six weeks thereafter, the same flap was elevated in order to remove the membrane that had remained completely submerged for the whole time. New tissue formed below the membrane was obtained with a shape that filled the space maintained under the membrane (f). Following completion of healing (1 year) a 3-mm probing depth and fill of the intrabony defect were observed. The results were maintained over time as indicated by the clinical and radiographic appearance 6 years after regeneration (g,h).
**Fig. 43-19** Clinical case illustrating the application of the modified papilla preservation technique to a case treated with a resorbable barrier membrane. An 8-mm pocket associated with an intrabony defect persisted on the mesial aspect of the lower first molar following completion of initial cause-related therapy (a,b). The defect was accessed with the modified papilla preservation flap. Please note the papilla preserved attached to the lingual flap (c) as well as the presence of a 7-mm intrabony defect (d). Following root debridement, a bioresorbable barrier membrane was positioned and secured around the root of the tooth with bioresorbable sutures (e). Primary closure of the interdental space was obtained with multilayered sutures (f) and was fully maintained at the 1-week suture removal appointment (g). At 6 years, probing depths were 2–3 mm, the soft tissue profile was conducive to optimal self-performed oral hygiene measures and the radiograph showed elimination of the defect (h–j).
## Simplified papilla preservation flap
To overcome some of the technical problems encountered with the MPPT (difficult application in narrow interdental spaces and in posterior areas, suturing technique not appropriate for use with non-supportive barriers) a different approach (simplified papilla preservation flap, SPPF) (Figs. 43-15, 43-22) was subsequently developed (Cortellini _et al_. 1999).
This different and simplified approach to the interdental papilla includes a first incision across the defect-associated papilla, starting from the gingival margin at the buccal-line angle of the involved tooth to reach the mid-interdental portion of the papilla under the contact point of the adjacent tooth. This oblique incision is carried out keeping the blade parallel to the long axis of the teeth in order to avoid excessive thinning of the remaining interdental tissues. The first oblique interdental incision is continued intrasulcularly in the buccal aspect of the teeth neighboring the defect. After elevation of a full-thickness buccal flap, the remaining tissues of the papilla are carefully dissected from the neighboring teeth and the underlying bone crest. The interdental papillary tissues at the defect site are gently elevated along with the lingual/palatal flap to fully expose the interdental defect. Following defect debridement and root planing, vertical releasing incisions and/or periosteal incisions are performed, when needed, to improve the mobility of the buccal flap. After application of a barrier membrane, primary closure of the interdental tissues above the membrane is attempted in the absence of tension, with the following sutures:
**Fig. 43-20** Clinical case illustrating the application of the papilla preservation technique in conjunction with the application of enamel matrix derivative in gel form. A 10-mm pocket was detectable on the distal aspect of the lower lateral incisor following successful completion of initial cause-related therapy (a). The radiograph showed the presence of a deep intrabony defect extending to the apical third of the root (b). The defect was accessed with the modified papilla preservation technique (c) with limited mesial and distal extension of the flap. Following careful debridement, the root is conditioned with an EDTA gel according to the manufacturer's instructions for the application of enamel matrix derivative (d). After rinsing and drying of the defect and root surface, the enamel matrix derivative gel is applied on the root surface and to fill the defect (e), and flaps are sutured with a multilayer technique to achieve primary closure in the absence of tension (f). One year following regenerative surgery, shallow pockets and radiographic resolution of the defect are apparent (g,h).
1. A first horizontal internal mattress suture (offset mattress suture) is positioned in the defectassociated interdental space running from the base (near to the mucogingival junction) of the keratinized tissue at the mid-buccal aspect of the tooth not involved with the defect to a symmetrical location at the base of the lingual/palatal flap. This suture frictions against the interdental root surface, hangs on the residual interdental bone crest and is anchored to the lingual/palatal flap. When tied, it allows the coronal positioning of the buccal flap. A relevant notation is that this suture, lying on the interdental bone crest, does not cause any compression at the mid-portion of the membrane, therefore preventing its collapse into the defect.
2. The interdental tissues above the membrane are then sutured to obtain primary closure with one of the following approaches: (a) one interrupted suture whenever the interdental space is narrow and the interdental tissues thin; (b) two interrupted sutures, when the interdental space is wider and the interdental tissues thicker; (c) an internal vertical/oblique mattress suture, when the interdental space is wide and the interdental tissues are thick.
**Fig. 43-21** Clinical case illustrating the application of the modified papilla preservation technique in conjunction with a bone replacement graft in combination with a bioresorbable membrane. After completion of initial cause-related therapy, a 9-mm pocket associated with an intrabony defect was present on the distal aspect of the upper second premolar (a,b). The defect reached the apical portion of the root and had a 9-mm intrabony component (c). Following careful root debridement, a bioresorbable membrane was adapted to the local anatomy and was positioned to contain the defect. A bone replacement graft was subsequently inserted under the membrane to provide additional support for the membrane and for the soft tissues (d). Primary closure was achieved with a single internal mattress suture (e). The control radiograph taken upon completion of the surgery shows the presence of the radio-opaque bone replacement graft in the defect (f). At 1-year follow-up, a 3-mm probing depth associated with resolution of the intrabony component of the defect is apparent (g,h). Please note that the radio-opaque bone replacement graft particles are still detectable but appear embedded in newly formed mineralized tissue.
Special care has to be paid to ensure that the first horizontal mattress suture would relieve all the tension of the flaps, and to obtain primary passive closure of the interdental tissues over the membrane with the last suture. When tension is observed, the sutures should be removed and the primary passive closure attempted a second time.
This approach has been preliminarily tested in a case series of 18 deep intrabony defects in combination with bioresorbable barrier membranes (Cortellini _et al_. 1999). The average clinical attachment level gain observed at 1 year was 4.9 ± 1.8 mm. In all the cases it was possible to obtain primary closure of the flap over the membrane, and 67% of the sites maintained primary closure over time. The same approach was then tested in a multi-center controlled randomized clinical trial involving 11 clinicians from seven different countries and a total of 136 defects (Tonetti _et al_. 1998). The average clinical attachment gain observed at 1 year in the 69 defects treated with the SPPF and a resorbable barrier membrane was 3 ± 1.6 mm. More than 60% of the treated sites maintained primary closure over time. It is important to underline that these results were obtained by different clinicians treating different populations of patients and defects, also involving narrow spaces and posterior areas of the mouth. The SPPF was successfully applied in conjunction with a variety of regenerative materials including biologically active materials such as EMD (Tonetti _et al_. 2002) (Fig. 43-23) and bone replacement grafts (Fig. 43-24) (Tonetti _et al_. 2004b; Cortellini & Tonetti 2004).
## Minimally invasive surgical technique
In order to provide even greater wound stability and to further limit patient morbidity, a papilla preservation flap can be used in the context of a minimally invasive, high-power magnification-assisted surgical technique (Cortellini & Tonetti 2007a). Such a minimally invasive approach is particularly suited for treatment in conjunction with biologically active agents such as EMD or growth factors.
The defect-associated interdental papilla is accessed either with the simplified papilla preservation flap (SPPF) (Cortellini _et al_. 1999) or the modified papilla preservation technique (MPPT) (Cortellini _et al_. 1995d). The SPPF is performed whenever the width of the interdental space is 2 mm or narrower, while the MPPT is applied at interdental sites wider than 2 mm. The interdental incision (SPPF or MPPT) is extended to the buccal and lingual aspects of the two teeth adjacent to the defect. These incisions are strictly intrasulcular to preserve all the height and width of the gingiva, and their mesio-distal extension is kept at a minimum to allow the corono-apical elevation of a very small full-thickness flap with the objective of exposing just 1–2 mm of the defect-associated residual bone crest. When possible, only the defect-associated papilla is accessed and vertical releasing incisions are avoided. With these general rules in mind, different clinical pictures can be encountered in different defects.
**Fig. 43-22** (a) Pre-surgical appearance of the area that will be accessed with a simplified papilla preservation flap (SPPF). The defect is located on the mesial aspect of the maxillary right lateral incisor. (b) First oblique incision in the defect-associated papilla begins at the gingival margin of the mesio-buccal line angle of the lateral incisor. The blade is kept parallel to the long axis of the tooth and reaches the midpoint of the distal surface of the central incisor just below the contact point. (c) First oblique incision continues intrasulcularly in the buccal aspect of the lateral and central incisors, extending until the adjacent papillae, and a buccal full-thickness flap is elevated to expose 2–3 mm of bone. Note the defect-associated papilla still in place. (d) Buccolingual horizontal incision at the base of the papilla is as close as possible to the interproximal bone crest. Care is taken to avoid a lingual/palatal perforation. (e) Intrasulcular interdental incisions continue in the palatal aspect of the incisors until the adjacent partially dissected papillae. A full-thickness palatal flap including the interdental papilla is elevated. (f) Intrabony defect following debridement. Note the position of the bone crest on the distal aspect of the central incisor. (g) Membrane is positioned to cover the defect and 2–3 mm of remaining bone and secured to neighboring teeth. A horizontal internal mattress suture runs from the base of the keratinized tissue at the midbuccal side of the central incisor to a symmetric location at the base of the palatal flap. This suture causes no direct compression of the midportion of the membrane, preventing its collapse into the defect. (h) Primary closure and complete coverage of the membrane are obtained. From Cortellini _et al_. (1999) with permission from Quintessence Publishing Co. Inc.
The shortest mesio-distal extension of the incision and the minimal flap reflection occurs when the intrabony defect is a pure three-wall, or has shallow two- and/or one-wall subcomponents allocated entirely in the interdental area. In these instances the mesio-distal incision involves only the defect-associated papilla and part of the buccal and lingual aspects of the two teeth neighboring the defect. The full-thickness flap is elevated minimally, just to expose the buccal and lingual bone crest delineating the defect in the interdental area (Fig. 43-25).
A larger corono-apical elevation of the full-thickness flap is necessary when the coronal portion of the intrabony defect has a deep two-wall component. The corono-apical extension of the flap is kept to a minimum at the aspect where the bony wall is preserved (either buccal or lingual), and extends more apically at the site where the bony wall is missing (lingual or buccal), the objective being to reach and expose 1–2 mm of the residual bone crest (Fig. 43-26).
When a deep one-wall defect is approached, the full-thickness flap is elevated to the same extent on both the buccal and the lingual aspects.
When the position of the residual buccal/lingual bony wall(s) is very deep and difficult or impossible to reach with the above described minimal incision of the defect-associated interdental space, the flap(s) is(are) further extended mesially or distally involving one extra interdental space to obtain a larger flap reflection. The same approach is used when the bony defect also extends to the buccal or the palatal side of the involved tooth, or when it involves the two interdental spaces of the same tooth (Fig. 43-27) or two approximal teeth (Fig. 43-28). In the latter instance a second interdental papilla is accessed, either with a SPPF or a MPPT, according to indications. Vertical releasing incisions are performed when flap reflection causes tension at the extremities of the flap(s). The vertical releasing incisions are always kept very short and within the attached gingiva (never involving the mucogingival junction). The overall aim of this approach is to avoid using vertical incisions whenever possible or to reduce their number and extent to a minimum when there is a clear indication for them. Periosteal incisions are never performed.
**Fig. 43-23** Clinical case illustrating the clinical application of the simplified papilla preservation flap in conjunction with the application of a biologically active regenerative material (enamel matrix derivative in gel form). At re-evaluation following completion of successful initial cause-related therapy, an 8-mm pocket was detected on the mesial palatal aspect of the left central incisor (a). An angular defect was evidenced on a peri-apical radiograph (b). The complex anatomy of the defect is apparent following access to the defect with the modified papilla preservation technique: a buccal fenestration is apparent with the majority of the defect extending palatally to the apical third of the root (c). Following application of the enamel matrix derivative, primary closure of the flap was achieved with a multilayered suture (d). At the 1-week suture removal appointment, excellent maturation of the soft tissue healing is apparent (e). At 6 months, a well represented interdental papilla is present thanks to both the papilla preservation approach and the presence of a bony bridge that assisted in soft tissue support, in spite of the gel formulation of the enamel matrix derivative (f). Clinical and radiographic outcomes at 1 year show preservation of excellent esthetics and elimination of the defect (g,h). Probing depths were in the 2 to 3 mm range.
The defects are debrided with a combined use of mini curettes and power-driven instruments and the roots carefully planed. During the instrumentation the flaps are slightly reflected, carefully protected with periosteal elevators and frequent saline irrigations. At the end of instrumentation the biologically active agent is applied. Then the flaps are repositioned.
The suturing approach in most of the instances consists of a single modified internal mattress suture at the defect-associated interdental area to achieve primary closure of the papilla in the absence of any tension (Cortellini & Tonetti 2001, 2005). When a second interdental space has been accessed, the same suturing technique is used to obtain primary closure in this area. Vertical releasing incisions are sutured with simple passing sutures. The buccal and lingual flaps are re-positioned at their original level, without any coronal displacement to avoid any additional tension in the healing area.
**Fig. 43-24** Clinical case illustrating the application of the simplified papilla preservation flap in combination with a bioresorbable barrier membrane applied in combination with a bone replacement graft. At re-evaluation, a 9-mm pocket is detected on the mesial aspect of the lateral incisor (a). The radiograph shows the presence of a deep intrabony defect (b). Following access with a simplified papilla preservation flap, a predominantly two-wall intrabony defect was exposed (c). After careful root instrumentation, a bioresorbable membrane was placed on top of a bone replacement graft (d). Primary closure of the flap was obtained with a multilayered suture approach (e). At 6 years, shallow probing depths are present (f); note the moderate increase in recession of the gingival margin. The radiograph at 6 years shows elimination of the defect but persistence of mineralized granules of bone replacement graft embedded in the newly formed mineralized tissue (g).
All the surgical procedures can be performed with the aid of an operating microscope or magnifying loops at a magnification of 4× to 16× (Cortellini & Tonetti 2001, 2005). Microsurgical instruments are utilized, whenever needed, as a complement to the normal set of periodontal instruments.
This approach has been preliminarly tested in two case series with a total of 53 deep intrabony defects (Cortellini & Tonetti 2007a,b). One-year results have shown clinically significant improvements (clinical attachment level gains of 4.8 ± 1.9 mm and 88.7 ± 20.7% clinical resolution of the defect) accompanied by greatly reduced morbidity.
## Post-operative regime
The post-operative regime prescribed to the patients is aimed at controlling wound infection or contamination as well as mechanical trauma to the treated sites. A recent meta-analysis indicated that differences in regenerative outcomes are expected based on the post-operative care protocol: more frequent, intensive regimens were associated with better clinical attachment level gains in intrabony defects (Murphy _et al_. 2003) (Fig. 43-29). It generally includes the prescription of systemic antibiotics (doxycycline or amoxicillin) in the immediate post-operative period (1 week), 0.2 or 0.12% chlorhexidine mouth-rinsing two or three times per day, and weekly professional tooth cleaning until the membrane is in place. Professional tooth cleaning consists of supragingival prophylaxis with a rubber cup and chlorhexidine gel. Patients are generally advised not to perform mechanical oral hygiene and not to chew in the treated area.
**Fig. 43-25** Clinical illustration of the use of the minimally invasive surgical technique (MIST) in an isolated interdental three-wall defect. The diagram shows the extent of the incision performed according to the principles of the modified papilla preservation technique in the interdental space associated with the defect. Mesio-distal extension of the flap is limited to the buccal aspect of the teeth adjacent to the defect in order to optimize wound stability (a). The baseline radiograph shows the presence of dental diseases (peri-apical infection and caries) that need to be controlled during the initial cause-related phase of therapy (b). At re-evaluation, an 8-mm pocket associated with the presence of a deep intrabony defect was detected on the mesial aspect of the first molar (c,d). The defect was accessed in a minimally invasive fashion using a modified papilla preservation flap. The three-wall intrabony defect was exposed and carefully debrided (e). After application of enamel matrix derivative, primary closure was obtained with a single modified internal mattress suture (f). The 1-year outcomes show shallow probing depths and almost complete resolution of the defect (g,h).
Non-resorbable membranes are removed 4–6 weeks after placement, following elevation of partial-thickness flaps. Patients are re-instructed to rinse two or three times per day with chlorhexidine, not to perform mechanical oral hygiene and not to chew in the treated area for 3–4 weeks. In this period weekly professional control and prophylaxis are recommended. When bioresorbable membrane, bone replacement grafts or biologically active regenerative materials are used, the period of tight infection control regime is extended for 6–8 weeks. After this period, patients are re-instructed to resume mechanical oral hygiene gradually, including interdental cleaning, and to discontinue chlorhexidine. Patients are then enrolled in a periodontal care program on a monthly basis until 1 year. Probing or deep scaling in the treated area is generally avoided before the 1-year follow-up visit.
## Post-operative morbidity
To date, little consideration has been given to critical elements that could contribute to the patient's assessment of the cost-benefit ratio of GTR procedures. These include post-operative pain, discomfort, complications, and the perceived benefits from the treatment. A parallel group, randomized, multi-center and controlled clinical trial designed to test the efficacy of GTR and flap surgery alone assessed these patient issues (Cortellini _et al_. 2001). During the procedure, 30.4% of the test and 28.6% of the controls reported moderate pain and subjects estimated the hardship of the procedure as 24 ± 25 units on a visual analog scale (VAS in a scale from 0 to 100) in the test group and 22 ± 23 VAS in the controls. Test surgery with membranes required longer chair time than flap surgery (on average 20 minutes longer). Among the post-operative complications, edema was most prevalent at week 1 and most frequently associated with the GTR treatment, while post-operative pain was reported by fewer than 50% of both test and control patients. Pain intensity was described as mild and lasted on average 14.1 ± 15.6 hours in the test patients and 24.7 ± 39.1 hours in the controls. Post-operative morbidity was limited to a minority of subjects: 35.7% of the test and 32.1% of the controls reported that the procedures interfered with daily activities for an average of 2.7 ± 2.3 days in the test group and 2.4 ± 1.3 days in the control group. These data indicate that GTR adds almost 30 minutes to a flap procedure and is followed by a greater prevalence of post-surgical edema, while no difference could be observed between GTR and flap surgery alone in terms of post-operative pain, discomfort, and interference with daily activities.
**Fig. 43-26** Clinical illustration of the use of the minimally invasive surgical technique (MIST) in an isolated interdental defect extending towards the buccal aspect of the tooth. The diagram shows the extent of the incision performed according to the principles of the modified papilla preservation technique in the interdental space associated with the defect. Mesio-distal extension of the flap is limited to the buccal aspect of the teeth adjacent to the defect and to the interdental aspect adjacent to the buccal extension of the defect in order to optimize wound stability (a). Following completion of successful initial cause-related therapy, a 6-mm pocket associated with an intrabony defect was detected on the distal aspect of the lateral incisor (b,c). The attachment loss extended to the buccal aspect of the lateral incisor, suggesting the need to obtain access to the buccal aspect of this tooth. The defect was therefore accessed with a minimally invasive approach using the modified papilla preservation technique to access the interdental area and extending the incision to the papilla between the lateral and central incisors to ensure adequate access to the defect (d). Primary closure was obtained with a modified internal mattress suture and a simple passing suture (e). The 1-year outcomes show shallow probing depths, good preservation of the soft tissue heights, and resolution of the defect (f,g).
To date, no comparative study has reported the morbidity associated with various regenerative approaches. Reports of multi-center trials on application of enamel matrix derivative or barrier membranes using the same methodology, however, show similar results for the application of these two regenerative materials (Tonetti _et al_. 1998, 2004a; Cortellini _et al_. 2001).
**Fig. 43-27** Clinical illustration of the use of the minimally invasive surgical technique (MIST) in intrabony defects involving both interdental spaces of the same tooth. The diagram shows the extent of the incision performed according to the principles of the modified papilla preservation technique in the two interdental spaces associated with the defects. Mesio-distal extension of the flap is limited to the two interdental papillae associated with the defects (a) and reaches the line angle of the two adjacent teeth in order to limit the loss of wound stability while allowing adequate access to the defects. The clinical and radiographic appearance at baseline highlight the good control of inflammation obtained following completion of initial cause-related therapy and the presence of deep mesial and distal pockets with associated intrabony defects (b,c). Both the mesial and distal defects are accessed with papilla preservation flaps, the defects are debrided, and the root surfaces are carefully instrumented (d). Following application of enamel matrix derivative in the well contained defects, primary closure of the flap is achieved by modified internal mattress sutures. At 1-year follow-up, shallow pockets, preservation of soft tissues, and elimination of the defects are apparent (e,f).
Another important issue that has been addressed in a large multi-center trial has been the comparison of surgical complications (such as membrane exposure, flap dehiscence, or occurrence of suppuration) using resorbable barrier membranes or biologically active regenerative materials (EMD in gel form). Sanz _et al_. (2004) showed that all sites treated with membranes presented at least a surgical complication during healing, while this was observed in only 6% of sites treated with EMD. This study indicates that some regenerative materials/procedures may be less technique sensitive than others.
# Barrier materials for regenerative surgery
In the first GTR attempts, a bacterial filter produced from cellulose acetate (Millipore®) was used as an occlusive membrane (Nyman _et al_. 1982; Gottlow _et al_. 1984; Magnusson _et al_. 1985b). Although this type of membrane served its purpose, it was not ideal for clinical application.
## Non-absorbable materials
Later studies have utilized membranes of expanded polytetrafluoroethylene (e-PTFE) specially designed for periodontal regeneration (Gore Tex Periodontal Material®). The basic molecule of this material consists of a carbon–carbon bond with four attached fluorine atoms to form a polymer. It is inert and does not result in any tissue reaction when implanted in the body. This type of membrane persists after healing and must be removed in a second operation. Membranes of e-PTFE have been used successfully in animal experiments and in several clinical studies. From such studies it was found that for a barrier material to function optimally, it has to meet certain essential design criteria:
1. To allow for good tissue acceptance it is important that the material is biocompatible. The material should not elicit an immune response, sensitization or chronic inflammation that may interfere with healing and present a hazard to the patient. Biocompatibility, however, is a relative term since practically no materials are completely inert.
2. The material should act as a barrier to exclude undesirable cell types from entering the secluded space adjacent to the root surface. It is also considered an advantage that the material would allow the passage of nutrients and gases.
3. Tissue integration is another important property of a barrier material. Thus, tissue may grow into the material without penetrating all the way through. The goal of tissue integration is to prevent rapid epithelial downgrowth on the outer surface of the material or encapsulation of the material, and to provide stability to the overlying flap. The importance of tissue integration was demonstrated in a study in monkeys (Warrer _et al_. 1992) in which bioabsorbable membranes of polylactic acid, a synthetic polymer, were used for treatment of circumferential periodontal defects. Due to the lack of tissue integration, the membranes in this study became surrounded by an epithelial layer and were often encapsulated and exfoliated.
4. It is also essential that the barrier material is capable of creating and maintaining a space adjacent to the root surface. This will allow the ingrowth of tissue from the periodontal ligament. Some materials may be so soft and flexible that they collapse into the defect. Other materials are too stiff and may perforate the overlying tissue.
5. Finally, there are clinical needs in the design of a barrier. It should be provided in configurations which are easy to trim and to place.
**Fig. 43-28** Clinical illustration of the use of the minimally invasive surgical technique (MIST) in intrabony defects involving two adjacent teeth. The diagram shows the extent of the incision performed according to the principles of the papilla preservation flaps in the two interdental spaces associated with the defects. Mesio-distal extension of the flap is limited to the two interdental papillae associated with the defects (a) and reaches the line angle of the two adjacent teeth in order to limit the loss of wound stability and limit flap extension. After successful initial cause-related therapy, two defects are present on the mesial aspect of the first molar and second premolar (b,c). Simplified papilla preservation flaps are used to access the defects (d). Incisions are stopped at the distal line angle of the first premolar and on the buccal aspect of the first molar. Root debridement and application of enamel matrix proteins in gel form are performed before primary closure of the flap that was obtained by using two modified internal vertical mattress sutures (e). Excellent early healing in the absence of pain or discomfort is evident at the 1-week suture removal (f). At 1-year follow-up, absence of inflammation, shallow probing depths and resolution of the defects are evident (g,h).
**Fig. 43-29** Regression analysis of intrabony defect studies examining the relationship between post-operative care protocol ranking and the reduction (in mm) in probing depth (PD). Group 3 is statistically different from groups 1 and 2. From Murphy & Gunsolley (2003) with permission from the American Academy of Periodontology.
## Bioabsorbable materials
In recent years, natural or synthetic bioabsorbable barrier materials for GTR have been introduced in order to avoid a second surgery for membrane removal. Barrier materials of collagen from different species and from different anatomic sites have been tested in animals and in humans (Blumenthal 1988, 1993; Pitaru _et al_. 1988; Tanner _et al_. 1988; Paul _et al_. 1992; Wang _et al_. 1994; Camelo _et al_. 1998; Mellonig 2000). Often the collagen used is a cross-linked variety of porcine or bovine origin. When a collagen membrane is implanted in the human body it is resorbed by the enzymatic activity of macrophages and polymorphnuclear leucocytes (Tatakis _et al_. 1999). Successful treatment following the use of such barrier materials has been demonstrated, but the results of the studies vary. Several complications, such as early degradation, epithelial downgrowth along the material, and premature loss of the material, were reported following the use of collagen materials. The varying results are probably due to differences in the properties of the material and the handling of the material at the time of implantation. Although probably very minimal, there is a risk that infectious agents from animal products can be transmitted to humans, and autoimmunization has also been mentioned as a risk.
Barrier materials of polylactic acid or copolymers of polylactic acid and polyglycolic acid were evaluated in animal and human studies and are commonly used (Magnusson _et al_. 1988; Caffesse _et al_. 1994; Caton _et al_. 1994; Gottlow _et al_. 1994; Laurell _et al_. 1994; Hugoson _et al_. 1995; Polson _et al_. 1995a; Hürzeler _et al_. 1997; Sculean _et al_. 1999a). These materials are biocompatible, but by definition they are not inert since some tissue reaction may be expected during degradation. The materials are degraded by hydrolysis and eliminated from the organism through the Krebs cycle as carbon dioxide and water (Tatakis _et al_. 1999).
The types of barrier materials tested in the studies differ regarding configuration and design. It appears that a number of bioabsorbable materials meet to a varying extent the requirements of a good barrier listed above. Indeed, there are several studies (Hugoson _et al_. 1995; Cortellini _et al_. 1996b; Smith _et al_. 1998; Tonetti _et al_. 1998; Cortellini & Tonetti 2000a) indicating that similar satisfactory results can be obtained with bioabsorbable barrier materials of polylactic and polyglycolic acid as with non-bioabsorbable materials.
## Membranes in intrabony defects
Early evidence that GTR treatment of deep intrabony defects may produce clinical improvements in terms of clinical attachment gain was presented in several case reports (Nyman _et al_. 1982; Gottlow _et al_. 1986; Becker _et al_. 1988; Schallhorn & McClain 1988; Cortellini _et al_. 1990). In recent years, a number of clinical investigations have reported on a total of 1283 intrabony defects treated with GTR (Table 43-2). In these studies, the issue of evaluating the predictability of the clinical outcomes following application of GTR procedures was addressed. The weighted mean of the reported results indicates a mean gain in clinical attachment of 3.8 ± 1.7 mm, with a 95% confidence interval ranging from 3.7–4.0 mm (Cortellini & Tonetti 2000a). The reported clinical attachment gains following GTR treatment were significantly larger than the ones obtained from conventional flap surgery. A recent review (Lang 2000) on flap surgery reported a weighted mean of 1172 defects in 40 studies. CAL gains were 1.8 ± 1.4 mm, with a 95% confidence interval ranging from 1.6–1.9 mm.
Different types of non-bioabsorbable (Fig. 43-30) and bioabsorbable (Fig. 43-31) barrier materials were used in the studies summarized in Table 43-2. A subset analysis indicated that cases treated with non-bioabsorbable barrier materials (351 defects) showed a mean gain in clinical attachment of 3.7 ± 1.7 mm which did not differ from that obtained with bioabsorbable barrier materials of 3.6 ± 1.5 mm (592 defects).
Analysis of the results reported in some of the studies in Table 43-2 (i.e. 211 defects in 9 investigations: Proestakis _et al_. 1992; Cortellini _et al_. 1993b, 1995c, 1996b; Cortellini & Pini-Prato 1994; Laurell _et al_. 1994; Mattson _et al_. 1995; Mellado _et al_. 1995; Tonetti _et al_. 1996b) provides important information regarding the predictability of GTR in intrabony defects. Gains of 2–3 mm were observed in 29.2% of the defects, gains of 4–5 mm in 35.4% of the defects, and gains of 6 mm or more in 24.9% of the defects. Only in 10.5% of the treated defects was the gain less than 2 mm, while no change or attachment loss was observed in two cases.
**Fig. 43-30** Intrabony defect on the mesial aspect of a right maxillary canine treated with a non-bioabsorbable barrier membrane. (a) The pocket depth is 9 mm and the loss of clinical attachment is 10 mm. (b) Radiograph showing the presence of an interproximal intrabony defect. (c) After full-thickness flap elevation, defect debridement, and root planing, a 4-mm intrabony defect is evident. (d) An e-PTFE non-bioabsorbable barrier membrane has been tailored, positioned and tightly sutured around the teeth adjacent to the defect. (e) The flap has been repositioned and sutured to cover the membrane. Optimal preservation of the soft tissues has been accomplished with an intrasulcular incision. (f) After removal of the membrane at 5 weeks, the defect appears to be completely filled with newly formed tissue. (g) The treated site has been surgically re-entered after 1 year. The intrabony defect is completely filled with bone. (h) The 1-year radiograph confirms the complete resolution of the intrabony defect.
In some of the investigations, changes in bone levels were also reported (Becker _et al_. 1988; Handelsman _et al_. 1991; Kersten _et al_. 1992; Cortellini _et al_. 1993b,c; Selvig _et al_. 1993). Bone gains ranged between 1.1 and 4.3 mm and correlated with the reported gains in clinical attachment. In a study by Tonetti _et al_. (1993b), 1 year after GTR the bone was found to be located 1.5 mm apically to the position of the attained clinical attachment level.
Another important parameter related to the outcome of regenerative procedures is the residual pocket depth. In the studies reported in Table 43-2, shallow pockets were consistently found at 1 year. The weighted mean of residual pocket depth was 3.4 ± 1.2 mm, with a 95% CI ranging from 2.3–3.5 mm.
The reported outcomes indicate that GTR procedures predictably result in clinical improvements in intrabony defects beyond that of flap surgery. This was further confirmed in 11 controlled randomized clinical trials in which guided tissue regeneration was compared with conventional flap surgery (Table 43-3). A total of 267 defects were treated with flap surgery and 317 with GTR. In 9 of the 11 investigations, GTR resulted in statistically significantly greater probing attachment level gains when compared to flap surgery. Similar results were also observed for residual pocket depth. It should be emphasized that one of the investigations reporting no significant differences between GTR and flap surgery was carried out in only nine pairs of defects (18 defects) located on maxillary premolars (Proestakis _et al_. 1992). In this study the intrabony component of the defects was shallow and 10 of the 18 defects had a furcation involvement. The weighted mean of the results reported in the 11 studies listed in Table 43-3 (Cortellini & Tonetti 2000a) indicated that the gain in clinical attachment in sites treated with GTR was 3.3 ± 1.8 mm (95% CI 2.8–3.6 mm), while the flap surgery resulted in a mean gain of 2.1 ± 1.5 mm (95% CI 1.8–2.4 mm). These clinical results strongly indicate that there is an added beneficial effect of placing a barrier material over an intrabony defect in conjunction with surgery.
**Fig. 43-31** Intrabony defect on the mesial aspect of a left maxillary premolar treated with a bioabsorbable barrier membrane. (a) Clinical attachment loss was 12 mm. (b) Radiograph showing the presence of a deep interproximal intrabony defect approaching the apex of the tooth. (c) A 7-mm interproximal intrabony defect was measured after flap elevation, defect debridement, and root planing. (d) A bioabsorbable barrier membrane has been placed and sutured to cover the defect. (e) At 1 year, a 4-mm pocket depth and 5-mm clinical gain of attachment were recorded. (f) The 1-year radiograph shows that the intrabony defect is almost resolved.
## Membranes for furcation involvement
The invasion of the furcation area of multi-rooted teeth by periodontitis represents a serious complication in periodontal therapy. The furcation area is often inaccessible to adequate instrumentation, and the roots frequently present concavities and furrows which make proper cleaning of the area impossible (see Chapter 39). As long as the pathologic process only extends a small distance (<5 mm; degree I and II involvements) into the furcation area, further progress of the disease can usually be prevented by scaling and root planing, provided a proper oral hygiene program is established after treatment. In more advanced cases (5–6 mm; degree II involvements), the initial cause-related treatment is frequently supplemented with surgery involving contouring of the inter-radicular bone (osteoplasty) or reduction of the tooth prominence at the furcation entrance by grinding (odontoplasty), in order to reduce the horizontal extension of the furcation involvement. In cases where the involvement extends deeper into the furcation area (>5 mm; degree II involvements), or a through-and-through defect (degree III involvements) has developed, tunnel preparation or root resection have been advocated as the choice of treatment. However, both of these latter treatments involve a risk of complications on a long-term basis. Following tunnel preparation, caries frequently develops in the furcation area and root-resected teeth often present complications of non-periodontal nature, although controversial reports exist regarding the long-term results of these treatment modalities (Hamp _et al_. 1975; Langer _et al_. 1981; Erpenstein 1983; Bühler 1988; Little _et al_. 1995; Carnevale _et al_. 1998).
Considering the complexity of current techniques for the treatment of furcation problems, and in view of the long-term results and complications reported following treatment of advanced furcation involvements by traditional resective therapy, predictable regeneration of the periodontium at furcationinvolved sites would represent a considerable progress in periodontics.
**Table 43-3** Controlled clinical trials comparing clinical outcomes of GTR procedures with access flap procedures in deep intrabony defects
### Mandibular degree II furcations
Pontoriero _et al_. (1988) reported a controlled randomized clinical trial in which significantly greater amounts of horizontal clinical attachment (H-CAL) gain (3.8 ± 1.2 mm) were obtained in 21 mandibular degree II furcations treated with e-PTFE membranes compared to those in a control group treated with open flap debridement alone (H-CAL gains of 2.0 ± 1.2 mm). Complete closure of the furcation was observed in 67% of the test sites and in only 10% of the control sites. Other studies, however, have failed to confirm these promising results to the same extent (Becker _et al_. 1988; Lekovic _et al_. 1989; Caffesse _et al_. 1990). Analysis of a series of studies published between 1988 and 1996 demonstrates a great variability in the clinical outcomes (Figs. 43-32, 43-33). Table 43-4 summarizes the outcomes of 21 clinical trials in which a total of 423 mandibular degree II furcations were treated with different types of non-bioabsorbable and bioabsorbable barrier membranes. The weighted mean of the reported results shows a H-CAL gain of 2.3 ± 1.4 mm with a 95% confidence interval ranging from 2.0–2.5 mm in defects with a baseline horizontal probing depth of 5.4 ± 1.3 mm. The reported number of complete furcation closures after GTR range from 0–67%. In three studies none of the treated furcations were closed (Becker _et al_. 1988; Yukna 1992; Polson _et al_. 1995b), in seven studies fewer than 50% were closed (Schallhorn & McClain 1988; Blumenthal 1993; Bouchard _et al_. 1993; Parashis & Mitsis 1993; Laurell _et al_. 1994; Mellonig _et al_. 1994; Hugoson _et al_. 1995), and in only one study were more than 50% of the treated furcations completely resolved (Pontoriero _et al_. 1988).
**Fig. 43-32** (a) Right mandibular first molar presenting with a degree II furcation involvement. (b) Full-thickness buccal flaps have been raised, the defect debrided and the root carefully planed. (c) A non-bioabsorbable barrier membrane has been placed to cover the defect. (d) After membrane removal, newly formed tissue appears to fill the furcation completely. (e) The regenerated tissue is covered with the flap. (f) Clinical appearance and surgery entry (g) after 1 year shows that the degree II furcation is almost completely resolved.
**Fig. 43-33** (a) Left mandibular first molar presenting with a deep degree II furcation involvement. (b) Horizontal loss of tooth support of 7 mm was probed. (c) An e-PTFE barrier membrane has been trimmed and sutured to cover the furcation. (d) At membrane removal after 5 weeks, newly formed tissue fills the furcation completely. (e) At 1 year, a 3-mm gain of tooth support was measured, but a residual 4-mm degree II furcation involvement was still present.
A subset analysis of the studies reported in Table 43-4 indicated that furcations treated with non-bioabsorbable barrier membranes (287) showed a gain in horizontal clinical attachment of 1.8 ± 1.4 mm (95% CI 1.5–2.1 mm) as compared with 2.3 ± 1.2 mm H-CAL gain (95% CI 2–2.6 mm) in 174 defects treated with bioabsorbable barrier membranes. Five controlled clinical trials compared treatment with non-resorbable e-PTFE membranes and treatment with different types of bioabsorbable membranes (Table 43-5). In particular, one investigation reported significantly greater H-CAL gain in the non-bioabsorbable group (Bouchard _et al_. 1993), while another one (Hugoson _et al_. 1995) showed a significantly greater H-CAL gain in the bioabsorbable group. The remaining three investigations failed to detect any significant differences between the outcomes of treatment with bioabsorbable or non-bioabsorbable membranes. Generally the results indicate that the predictability of GTR in the treatment of mandibular degree II furcations is questionable, if the treatment objective is the complete resolution of the furcation involvement.
**Table 43-4** Clinical outcomes and weighted mean of GTR treatment of mandibular degree II furcations
**Table 43-5** Controlled clinical trials comparing clinical outcomes of GTR procedures with e-PTFE non-bioabsorbable barrier membranes with different types of bioabsorbable barrier membranes in mandibular degree II furcations
Significant gain in vertical attachment level (VCAL) and reduction in pocket depth (PPD) was also reported by several investigators following treatment of mandibular degree II furcation defects (Pontoriero _et al_. 1988; Lekovic _et al_. 1989, 1990; Blumenthal 1993; Machtei _et al_. 1993, 1994; Black _et al_. 1994; Laurell _et al_. 1994; Mellonig _et al_. 1994; Wang _et al_. 1994; Hugoson _et al_. 1995; Polson _et al_. 1995b). The reported mean values ranged from 0.1 mm to 3.5 mm for V-CAL gain and from 1 mm to 4 mm for PPD reduction.
**Table 43-6** Controlled clinical trials comparing clinical outcomes of GTR procedures with access flap procedures in mandibular degree II furcations
The effect of using barrier membranes for the treatment of mandibular degree II furcations was investigated in six controlled randomized clinical trials in which GTR procedures were directly compared to flap surgery (Table 43-6). Sixty-six furcations treated with flap surgery and 87 treated with GTR were included. Three of the four studies reporting H-CAL gains concluded that GTR resulted in statistically significantly greater horizontal attachment level gains than flap surgery (Pontoriero _et al_. 1988; Van Swol _et al_. 1993; Wang _et al_. 1994). The weighted mean of the results reported in Table 43-6 indicated that the H-CAL in furcations treated with GTR was 2.5 ± 1 mm (95% CI 2.1–2.9 mm) while the flap surgery resulted in a mean H-CAL gain of 1.3 ± 1 mm (95% CI 0.8–1.8 mm). These results indicate an added benefit from GTR in the treatment of mandibular degree II furcations.
### Maxillary degree II furcations
Results reported in three controlled studies (Metzeler _et al_. 1991; Mellonig _et al_. 1994; Pontoriero & Lindhe 1995a) comparing GTR treatment of maxillary degree II furcations with non-bioabsorbable e-PTFE membranes and with open-flap debridement, indicate that GTR treatment of such defects is generally unpredictable. In a study including 17 pairs of degree II furcations Metzeler _et al_. (1991) measured CAL gains of 1.0 ± 0.9 mm in the GTR-treated sites versus 0.2 ± 0.6 mm in the control sites. Following re-entry, horizontal probing attachment gains (H-OPAL) of 0.9 ± 0.4 mm and 0.3 ± 0.6 mm were detected in the GTR- and flap-treated furcations, respectively. No differences were found and none of the furcations of the two groups were completely resolved. Similarly, Mellonig _et al_. (1994) treated eight pairs of maxillary degree II furcations which resulted in H-OPAL gains of 1.0 mm (GTR sites) and 0.3 mm (flap-treated sites). No differences were found and none of the treated furcations were completely closed. On the other hand, in a study on 28 maxillary degree II furcations Pontoriero and Lindhe (1995a) found a significant gain in CAL (1.5 mm) and horizontal bone (1.1 mm) in buccal degree II furcations.
Although these three investigations show a slight clinical improvement following treatment of degree II maxillary furcations with GTR, the results are generally inconsistent.
### Degree III furcations
Four investigations on the treatment of mandibular degree III furcations (Becker _et al_. 1988; Pontoriero _et al_. 1989; Cortellini _et al_. 1990; Pontoriero & Lindhe 1995b) indicate that the treatment of such defects with GTR is unpredictable. A controlled study of Pontoriero _et al_. (1989) showed that only eight out of 21 "through-and-through" mandibular furcations treated with non-bioabsorbable barrier membranes healed with complete closure of the defect. Another ten defects were partially filled, and three remained open. In the control group, treated with open flap debridement, 10 were partially filled and 11 remained open. Similar results were reported by Cortellini _et al_. (1990) who, in a case cohort of 15 degree III mandibular furcations, found that 33% of the defects had healed completely, 33% were partially closed, and 33% were still through-and-through following treatment. Becker _et al_. (1988) did not observe complete closure of any of 11 treated degree III mandibular furcations. Similarly, in a controlled clinical trial by Pontoriero and Lindhe (1995b) on 11 pairs of maxillary degree III furcations randomly assigned to GTR or flap surgery, none of the furcation defects were closed.
**Fig. 43-34** Following marginal incisions and vertical releasing incisions on the buccal aspect of the jaw, buccal and lingual full-thickness flaps are elevated.
Based on present evidence, it seems that mandibular degree II furcations in the first or second molars, either buccal or lingual, with deep pockets at baseline and a gingival thickness of >1 mm, may benefit from GTR treatment.
## Surgical issues with barrier membranes
Surgery is initiated by sulcular incisions at both the buccal and lingual aspect of the jaw, followed by buccal and vertical releasing incisions, if necessary. For intrabony defects, the releasing incisions must be placed a minimum of one tooth anterior and/or posterior to the tooth that is being treated (Fig. 43-34). Care should be taken during this procedure to preserve the interdental papillae. All pocket epithelium is excised so that fresh connective tissue is left on the full-thickness flaps following reflection. After elevation of the tissue flaps, all granulation tissue is removed and thorough debridement of the accessed root surfaces is carried out using curettes, burs, etc.
Various types of bioabsorbable and non-bioabsorbable barrier materials are available in a variety of configurations designed for specific applications. The configuration most suitable for covering the defect is selected and additional adaptation of the material to the shape and extent of the defect is performed. The shaping of the material is carried out in such a way that it adapts closely to the tooth and completely covers the defect, extending at least 3 mm on the bone beyond the defect margins after placement (Fig. 43-35). This assures good stability of the material and protects the underlying blood clot during healing. At placement it is essential to ensure good adaptation of the barrier material to the alveolar bone surrounding the defect and to avoid overlaps or folds of the material.
Although exceptions exist, the barrier materials available are fixed to the tooth with a suture using a sling technique. For optimal performance, the barrier should be placed with its margin 2–3 mm apical to the flap margin. To maximize coverage of the barrier, a horizontal releasing incision in the periosteum may assist in the coronal displacement of the flap at the suturing of the wound. However, care should be taken not to compromise the blood supply to the flap. The interdental space near the barrier should be closed first. In order to achieve good closure, an internal vertical mattress suturing technique is advocated (Fig. 43-36).
**Fig. 43-35** The barrier material is placed in such a way that it completely covers the defect and extends at least 3 mm on the bone beyond the defect margin.
**Fig. 43-36** The elevated tissue flaps are coronally displaced and sutured in such a way that the border of the barrier material is at least 2 mm below the flap margin.
To reduce the risk of infection and to assure optimal healing, the patient should be instructed to brush the area gently post-operatively with a soft bristle toothbrush and to rinse with chlorhexidine (0.2%) for a period of 4–6 weeks. In addition, systemic antibiotics are frequently administered immediately prior to surgery and for 1–2 weeks after surgery. When a non-bioabsorbable barrier is used, it should be removed after 4–6 weeks. However, if complications develop it may be necessary to remove it earlier.
Removal of the material requires a minor surgical procedure (Fig. 43-37). To obtain access to the barrier material, a small incision is made extending one tooth mesial and distal to the border of the barrier. The soft tissue flap is gently reflected and the barrier material dissected free from the flap using a sharp blade. During this procedure it is essential not to compromise the newly regenerated tissue. At removal of the barrier material there will usually be some pocket formation on the outer surface of the material. It is important that this epithelium is removed so that fresh connective tissue is in contact with the newly regenerated tissue after wound closure. It is essential that the newly regenerated tissue is completely covered after suturing. The patient is instructed to rinse with chlorhexidine for 2–3 weeks during which period frequent visits for professional tooth cleaning are recommended. After this period, brushing and interdental cleaning can be resumed, chlorhexidine rinsing discontinued, and the patient enrolled in a regular periodontal maintenance program.
**Fig. 43-37** In order to remove the barrier material an incision is made extending one tooth mesially and distally to the border of the barrier. After reflecting the covering tissue flaps, the barrier can be removed without compromising the newly regenerated tissue.
If the flap is excessively traumatized during surgery either part or all of it may slough during healing. Perforations may also occur, particularly in sites with sharp bony ledges. A minor osteoplasty during placement may help to allow the barrier to better follow the contours of the ridge. Abscess formation may also occur in the wound, probably due to severe bacterial contamination of the barrier. Dependent on the severity of such complications, early removal of the barrier may be indicated.
# Bone replacement grafts
Bone replacement grafts (BRG) comprise a heterogeneous group of materials of human (autologous or allogeneic), animal or synthetic origin. Some consist of bone or exoskeletal mineral; others contain mainly bone matrix. Only few materials present evidence of periodontal regeneration. A randomized controlled clinical trial provided histologic support that the healing outcome following application of demineralized freeze-dried bone allograft (DFDBA) in intrabony defects has a regenerative component in the apical to middle portion of the depth of the defect (Bowers _et al_. 1989a,b,c). Isolated evidence also supports the fact that allograft and bovine bone mineral may yield a regenerative outcome when used alone (i.e. without other regenerative materials such as barrier membranes or biologically active regenerative materials (BARG) – see also Chapter 25) (Nevins _et al_. 2000).
Bone replacement grafts were the first periodontal regenerative materials to be applied clinically. Today they are widely used in North America as demineralized freeze-dried allografts and are frequently used in combination with other regenerative materials (GTR and/or BARG).
The clinical efficacy of allografts in terms of bone fill and clinical attachment level gains is supported by a meta-analysis indicating that an additional bone fill of 1 mm and additional clinical attachment level gains of 0.4 mm were observed (Reynolds _et al_. 2003). The total number of defects contributing to this meta-analysis however is relatively small (136 for clinical attachment level gain and 154 for bone fill). Furthermore no large-scale multi-center trial has ever been performed and hence the applicability of these results to clinical practice settings remains to be established.
As to their use, BRG can be applied alone following elevation of a papilla preservation flap for the treatment of intrabony defects. The graft is applied to overfill the defect to compensate for a degree of shedding of the graft expected in cases of imperfect containment of the graft by the closed flap. A study has suggested using BRG in combination with an antibiotic powder to enhance control of the bacterial contamination of the surgical wound (Yukna & Sepe 1982). This study reported improved outcomes from mixing the graft with tetracycline powder.
# Biologically active regenerative materials
Preclinical and clinical evidence for the use of biologically active regenerative materials has been reviewed (see also Chapter 25). Currently, two preparations consisting of growth and/or differentiation factors are available for use in periodontal regeneration: enamel matrix derivative (EMD) in a gel form and platelet-derived growth factor (PDGF) mixed in a beta tricalcium phosphate bone replacement graft.
Significant preclinical evidence supports the positive effect of PDGF on periodontal wound healing and regeneration (Howell _et al_. 1997). Clinically, support for use of PDGF comes from a single multi-center trial performed in North America (Nevins _et al_. 2005). In that study 180 defects comprising both intrabony and furcation defects were treated with one of two concentrations of PDGF (0.3 mg/ml and 1.0 mg/ml) combined with the beta tricalcium phosphate delivery device or tricalcium phosphate alone. Results were assessed at 3 and 6 months and included both clinical and radiographic assessments. Clinical attachment level gains at 6 months failed to demonstrate a significant benefit of either concentration of PDGF compared to the bone replacement graft alone. With regards to radiographic assessments, however, the lower tested concentration of PDGF resulted in significantly higher percentages of radiographic bone fill of the defect (57% vs. 18%) and linear radiographic bone growth (2.6 mm vs. 0.9 mm). The results of this study led to the approval by the US Food and Drug Administration of this material. The authors interpreted the dichotomy represented by the significance of the added benefit in terms of radiographic parameters without the presence of significant changes in CAL as the result of biologic action of the growth factor formulation in shortening the healing time of the hard tissues. As of today, however, the results of this study have not been independently confirmed.
**Fig. 43-38** Clinical case illustrating the use of enamel matrix derivative to regenerate defects located on two adjacent teeth. At re-evaluation, deep pockets associated with deep intrabony defects are evident on the distal aspect of the first and second molars (a,b). Defects were accessed with the modified papilla preservation technique on the distal aspect of the first molar and with the use of a crestal incision in the retromolar area (c,d). Deep defects were exposed following debridement and root instrumentation (c,d). Following application of enamel matrix derivative in gel form, primary closure was obtained with multilayered sutures. At 1-year follow-up, shallow probing depths associated with the elimination of the defects were observed (e,f).
The benefit of use of EMD gel in the treatment of intrabony defects is supported by human histologic evidence, case report studies, meta-analysis of randomized controlled clinical trials, and a large multi-center trial (Heijl _et al_. 1997; Heden _et al_. 1999; Sculean _et al_. 1999b; Silvestri _et al_. 2000; Heden 2000; Tonetti _et al_. 2002; Giannobile & Somerman 2003; Heden & Wennstrom 2006) (Fig. 43-38).
Given their hydrophobic nature, enamel matrix proteins are mixed in a gel carrier at low pH for clinical use. Following an increase in pH in the periodontal wound and rapid elimination of the gel, EMD proteins (consisting mainly of amelogenins) are deposited in the wound environment and the root surface. While the mechanism(s) of action of EMD are not fully understood, significant evidence suggests that periodontal ligament cells exposed to EMD switch their phenotype by increasing expression of a host of growth and differentiation factor related genes (Brett _et al_. 2002; Parkar & Tonetti 2004), including transforming growth factor beta (Lyngstadaas _et al_. 2001).
A secondary analysis of a multi-center trial has shown that, in intrabony defects, the added benefit of EMD was greater in three-wall defects than in one-wall defects (Tonetti _et al_. 2002). Furthermore, another secondary analysis of the same material assessing the effect of the radiographic defect angle on the outcome (Tsitoura _et al_. 2004) has uncovered a negative association between the ragiographic angle of the defect and the clinical attachment level gains observed at 1 year. These data have questioned the suitability of the gel formulation of the EMD for the treatment of defects with a non-supporting anatomy (wide defects with missing bony walls).
These observations have spurred considerable research interest in the incorporation of EMD in a variety of bone replacement grafts in order to enhance wound stability and space maintenance. At this stage, however, no systematic evidence is available to support the use of such combinations.
Clinically, the rate of wound healing following application of EMD seems to be enhanced. A study looking at soft tissue density in the surgical site by using underexposed radiographs (Tonetti _et al_. 2004b) has found that the rate of increase in soft tissue density following application of EMD may be faster than in the access flap control. Such modulation has been interpreted as the outcome of the local release of growth and differentiation factors by the cells involved in local wound healing.
# Membranes combined with other regenerative procedures
Compromised results after GTR may be obtained in cases where the membrane collapses/falls (partially or totally) into the defect and/or towards the root surface, thereby reducing the space available for invasion of new tissue capable of forming periodontal ligament and bone in particular. Reduced amounts of regenerated bone due to membrane collapse were noticed in early studies of GTR. In the study of Gottlow _et al_. (1984), it was observed that collapse of the membrane towards the root surface resulted in new cementum formation on the entire exposed root surfaces, whereas bone regeneration was minimal. Although the authors reported that the degree of coronal regrowth of bone was unrelated to the amount of new cementum formation, they did not comment on what effect membrane collapse might have had. Experimental studies, however, recognized the negative effect of membrane collapse on periodontal regeneration generally and on bone formation in particular (Caton _et al_. 1992; Haney _et al_. 1993; Sigurdsson _et al_. 1994; Sallum _et al_. 1998). Haney _et al_. (1993) observed a highly significant correlation between the space provided by the membrane and the amount of regenerated alveolar bone using a supra-alveolar defect model in dogs. This finding corroborates that of Cortellini _et al_. (1995c) who reported that clinical application of self-supporting (reinforced with titanium) e-PTFE membranes, which could be positioned more coronally than ordinary e-PTFE membranes, yielded a statistically significant increase in PAL gain in intrabony defects. A particular risk for membrane collapse exists in cases where the configuration of the defect is incapable of supporting/preserving the membrane at the position where it was originally placed.
As already discussed, membrane materials must possess certain characteristics in order to be efficient. Among those it is important that the membrane is capable of keeping its shape and integral features, thereby maintaining the space created adjacent to the root surface. The e-PTFE membranes reinforced with titanium are the closest in meeting these requirements but they have the disadvantage that they are non-resorbable. At present there are no resorbable membranes available that fulfill this requirement sufficiently, which means that the placement of a resorbable membrane on, for instance, a wide one-wall defect involves the risk of membrane collapse. The collapse may be prevented by means of implantation of a biomaterial into the defect to support the membrane so that it maintains its original position (Fig. 43-39). However, the biomaterial to be used for this purpose must not interfere with the process of periodontal regeneration and ideally it may also promote bone regeneration.
As previously described, periodontal regeneration has been attempted with a variety of grafting materials, among which demineralized freeze-dried bone allografts (DFDBA) apparently facilitated regeneration in humans (Ouhayoun 1996). Schallhorn and McClain (1988) reported on improved clinical results in intrabony defects and degree II furcations, following a combination therapy including barrier membranes plus DFDBA and citric acid root conditioning.
In three controlled clinical trials, the treatment of a total of 45 pairs of intrabony defects with DFDBA grafting and GTR were compared to GTR alone (Table 43-7). The weighted mean of the results of the reported investigations showed similar gain in CAL in the GTR group (2.1 ± 1.1 mm, 95% CI 1.6–2.6 mm) and in the GTR plus DFDBA group (2.3 ± 1.4 mm, 95% CI 1.7–2.9 mm). The differences between the two treatments did not reach statistical significance, thus indicating no added effect of combining DFDBA with barrier materials in the treatment of intrabony defects. Guillemin _et al_. (1993) compared the effect of DFDBA alone with a combination of barrier materials and DFDBA in 15 pairs of intrabony defects. Both treatments resulted in significant amounts of CAL gains and bone fill at 6 months, but no difference was found between the treatments.
**Fig. 43-39** Clinical case illustrating the application of bone replacement graft to support a bioresorbable membrane in a defect with poor space maintaining anatomy. Following control of periodontitis and risk factors, the upper right contral incisor presented with a 12-mm deep pocket associated with a defect extending close to the apex of the tooth (a–c). The defect was accessed with the modified papilla preservation flap to reveal an 8-mm intrabony component (d). A bone replacement graft was placed under a bioresorbable collagen membrane (e). Primary closure was achieved with a multilayered suture technique (f). Excellent early healing was observed already at the 2-week follow-up (g). At 1 year, periodontal regeneration resulted in shallow probing depths and good resolution of the intrabony defect (h,i). Radio-opaque bone replacement graft particles are visible within the newly formed mineralized tissue.
**Table 43-7** Summary of controlled clinical trials evaluating the combined effects of decalcified freeze-dried bone allografts (DFDBA) and barrier membranes in deep intrabony defects
**Table 43-8** Controlled clinical trials comparing clinical outcomes of GTR procedures with e-PTFE non-bioabsorbable barrier membranes with or without the adjunctive use of grafts in mandibular degree II furcations
In three studies on mandibular degree II furcations, GTR treatment alone was compared with GTR treatment combined with hydroxyapatite or DFDBA (Table 43-8). In one of these investigations, a statistically significant improvement was found in terms of horizontal open probing attachment levels (H-OPAL) in the group of furcations treated with the combination therapy (Anderegg _et al_. 1991). In another of these three studies the difference between the two treatments was not statistically significant, but the combination therapy resulted in a greater extent of furcation fill (Lekovic _et al_. 1990). In the third investigation (Wallace _et al_. 1994), the two treatments were equivalent in terms of H-OPAL gains. The weighted mean of the cited studies showed greater H-OPAL gains in the cases treated with the combination therapy (2.1 ± 0.9 mm, 95% CI 1.6–2.6 mm) when compared to GTR treatment alone (0.9 ± 0.5 mm, 95% CI 0.6–1.1 mm), indicating a possible added benefit from the use of grafting materials in combination with non-bioabsorbable barrier membranes for the treatment of mandibular degree II furcations.
Promising clinical results with a PAL-gain of 1.0– 5.5 mm were obtained in human case reports, in which the GTR technique was combined with grafting of Bio-Oss® for the treatment of intrabony periodontal defects (Lundgren & Slotte 1999; Mellonig 2000; Paolantonio _et al_. 2001). The combined Bio-Oss® and GTR treatment resulted in greater PPD reduction, PAL gain and defect fill than the mere implantation of Bio-Oss® in case series (Camelo _et al_. 1998) and than flap surgery alone in a split-mouth study (Camargo _et al_. 2000).
In a recent randomized controlled clinical study including 60 patients (Stavropoulos _et al_. 2003), Bio-Oss® alone or impregnated with gentamicin was used as an adjunct to GTR in the treatment of one-wall or two-wall intrabony defects, and the outcomes were compared to those obtained following GTR alone or flap surgery. Treatment with a membrane alone (Fig. 43-40) resulted in a mean PAL gain of 2.9 mm, while it was 3.8 and 2.5 mm, respectively, when Bio-Oss® grafts with or without gentamicin were placed in the defects prior to membrane coverage (Fig. 43-41). The control defects treated with flap surgery demonstrated a gain of PAL of only 1.5 mm. The clinical improvements in defects treated with GTR alone or in combination with Bio-Oss® grafting were significantly better than those obtained with flap surgery, whereas the differences between the groups treated with membranes were not statistically significant.
In a controlled study (Pietruska 2001), similar clinical improvements were obtained when Bio-Oss® combined with GTR was compared with biomodification of the root surface with enamel matrix protein (Emdogain®).
Camelo _et al_. (1998) and Mellonig (2000) presented histologic data indicating that the use of Bio-Oss® under a membrane may result in partial regeneration of the periodontal apparatus, but in all the cases, most of the defect was still occupied by deproteinized bone particles. Bone was not observed near the root, and the connective tissue fibers of the "new" periodontal ligament were mostly oriented parallel to the root surface. These results corroborate findings reported by Paolantonio _et al_. (2001), who observed only limited bone formation in the vicinity of the pre-existing bone in a biopsy, taken from a site treated 8 months earlier with Bio-Oss® and a collagen membrane. Most of the space in the defect was occupied by Bio-Oss® particles embedded in connective tissue. However, in a case report where intrabony defects were treated with Bio-Oss® combined with intraoral autogenous bone and GTR, new attachment formation had occurred consistently, but a major portion of the regenerated osseous tissue consisted of deproteinized bone particles (Camelo _et al_. 2001). The effect of combining citric acid root biomodification with GTR treatment was evaluated in two randomized controlled clinical trials in intrabony defects. The first investigation (Handelsman _et al_. 1991) demonstrated significant amounts of CAL gains in both the test (e-PTFE membranes and citric acid; CAL gain 3.5 ± 1.6 mm) and control sites (e-PTFE membranes alone; CAL gain 4.0 ± 1.4 mm). Less favorable results following these two treatment modalities were reported by Kersten _et al_. (1992) who found CAL gains of 1.0 ± 1.1 mm in the test group, and CAL gains of 0.7 ± 1.5 mm in the control group. Both studies, however, failed to demonstrate any added effect of the use of citric acid in combination with non-bioabsorbable barrier membranes.
**Fig. 43-40** Right lateral maxillary incisor with an 8-mm deep pocket associated with an intrabony defect on the distal aspect (a), as seen on the radiograph (b). Full-thickness buccal and palatal flaps have been raised and the defect has been debrided (c). A bioabsorbable membrane has been adopted over the defect (d). The level of the interdental gingiva is maintained after 1 year (e) and the intrabony defect (f) is resolved.
Root surface biomodification with tetracycline alone and in combination with GTR was evaluated in two controlled studies on degree II furcations (Machtei _et al_. 1993; Parashis & Mitsis 1993). Both investigations failed to show significant differences between sites treated with non-bioabsorbable barrier membranes alone or in combination with tetracycline root surface biomodification. Similarly, the use of other surface active chemicals like EDTA also failed to provide a significant added effect to GTR treatment in humans (Lindhe & Cortellini 1996).
# Root surface biomodification
The suggested role of root surface biomodification for improving periodontal regeneration has been recently assessed in a systematic review (Mariotti _et al_. 2003). The results of that exhaustive review of the evidence indicated that there was no evidence of a measurable improvement following root conditioning with agents like citric acid, tetracycline HCl, phosphoric acid, fibronectin or EDTA.
**Fig. 43-41** Left mandibular canine with an 8-mm deep pocket (a) associated with an intrabony defect on its mesial aspect (b). The defect is debrided after flap elevation (c) and Bio-Oss® particles are placed in the defect (d) prior to placement of a bioabsorbable membrane. After 1 year (e), no gingival recession has occurred and the intrabony defect is almost resolved (f).
# Clinical strategies
Periodontal regeneration in intrabony defects has been successfully attempted with a variety of different approaches. As discussed, meta-analyses of randomized controlled clinical trials as well as human and animal histologic findings support the potential of barrier membranes (Nyman _et al_. 1982; Gottlow _et al_. 1986), demineralized freeze dried bone allograft (DFDBA) (Bowers _et al_. 1989a,b,c), combination of barrier membranes and grafts (Camelo _et al_. 1998; Mellonig 2000), and the use of enamel matrix derivative (Mellonig 1999; Yukna & Mellonig 2000) to induce periodontal regeneration. Controlled clinical trials report that the above-mentioned approaches provide added benefits in terms of clinical attachment level (CAL) gain as compared to open-flap debridement alone (Needleman _et al_. 2002; Murphy _et al_. 2003; Trombelli _et al_. 2002; Giannobile & Somerman 2003; Tonetti _et al_. 2004a). Comparisons among some of the cited regenerative approaches failed to demonstrate a clear superiority of one of the tested materials (Murphy _et al_. 2003; Giannobile & Somerman 2003; Reynolds _et al_. 2003).
The existing evidence, therefore, does not support the choice of a single approach among the different regenerative possibilities. In addition, all the cited studies have shown a substantial degree of variability, in terms of CAL gains, reporting failures or unsatisfactory outcomes in part of the treated population.
Research conducted mostly in the past decade has clearly established that the variability observed in outcomes of periodontal regenerative procedures is dependent on a variety of patient, defect, and surgical associated factors.
While relevant patient factors include cigarette smoking, residual periodontal infection, and oral hygiene, factors associated with the morphology of the defect are consistently found to be of relevance for the final outcome (Tonetti _et al_. 1998; Cortellini _et al_. 2001). Interestingly, however, the number of residual bony walls defining the defect seems to impact the outcomes of different periodontal regenerative materials in a divergent way. Non-resorbable (e-PTFE and titanium-reinforced e-PTFE) barrier membranes, and bioresorbable barriers supported by a graft do not seem to be affected by the number of residual bony walls of the defect (Tonetti _et al_. 1993a, 1996a, 2004b), while EMD results in better outcomes in three-wall defects (Tonetti _et al_. 2002). Furthermore, healing following application of bioresorbable barriers and non-resorbable e-PTFE barriers as well as EMD is associated with the radiographic width of the intrabony defect (Tonetti _et al_. 1993a; Falk _et al_. 1997; Tsitoura _et al_. 2004). No such association has been found for the use of a xenogenic bone replacement graft and resorbable barrier graft combination (Tonetti _et al_. 2004b).
Among the technical/surgical factors, membrane exposure and contamination have been associated with reduced outcomes (Selvig _et al_. 1992; Nowzari & Slots 1994; Nowzari _et al_. 1995; De Sanctis _et al_. 1996a,b). Similar problems were also encountered with bone grafting (Sanders _et al_. 1983). Reduced outcomes were also observed when the regenerated tissue was not properly protected with the flap at removal of non-resorbable barrier membranes (Tonetti _et al_. 1993a; Cortellini _et al_. 1995c).
A controlled clinical trial demonstrated that the combination of a papilla preservation flap and titanium-reinforced e-PTFE membrane resulted in greater amounts of clinical attachment level gains as compared to a conventional flap approach associated with an e-PTFE membrane (Cortellini _et al_. 1995c). This evidence, also partly supported by a systematic review (Murphy _et al_. 2003), strongly suggests that optimization of the surgical approach and control of surgical variables, particularly in relation to flap design and management and selection of the regenerative material, could improve outcomes. In the context of GTR, several specific flap designs aimed at the full preservation of the soft tissues during access to the defect have been described (Cortellini _et al_. 1995c,d, 1996c, 1999; Murphy 1996). Experimental testing of these regenerative flaps reported great improvements in achieving primary closure during the surgical session with optimal interdental closure being obtained in virtually all cases (Tonetti _et al_. 2004b; Cortellini _et al_. 1995c,d, 1999, 2001). During the subsequent healing, however, dehiscence of the interdental tissue and membrane exposure was observed in up to a third of the cases. The ability to accomplish and maintain primary closure of the tissues over a GTR membrane was further improved by the use of a microsurgical approach that resulted in maintenance of primary wound closure in 92.3% of the treated sites for the whole healing period (Cortellini & Tonetti 2001, 2007a,b).
This body of evidence can be utilized together with a degree of clinical experience to develop an "evidence-based regenerative strategy" to guide clinicians through a decision-making process aimed at the optimization of the clinical outcomes of periodontal regeneration in intrabony defects (Cortellini & Tonetti 2000a, 2005). Key steps of this process are the careful evaluation of the patient and of the defect, the access of the defect with a papilla preservation flap, the possibility of choosing the most appropriate regenerative technology/material, and the ability to seal the regenerating wound from the contaminated oral environment with optimal suturing techniques.
Two to three months after completion of periodontal therapy, baseline clinical measurements are recorded. The regenerative strategy is selected according to a decision-making process. Surgical procedures, according to the principles of periodontal regeneration, are performed. Patients are then enrolled in a stringent periodontal supportive care program for 1 year followed by regular supportive periodontal care.
The appropriate regenerative strategy for the individual case is selected according to a recently modified, evidence-based operative decision tree (Cortellini & Tonetti 2000a, 2005) (Figs. 43-42, 43-43, 43-44).
The surgical access to the intrabony defects is selected from among three different surgical approaches: the simplified papilla preservation flap (SPPF) (Cortellini _et al_. 1999), the modified papilla preservation technique (MPPT) (Cortellini _et al_. 1995d), and the crestal incision (Cortellini & Tonetti 2000a). The SPPF is chosen whenever the width of the interdental space is 2 mm or less, as measured at the level of the papilla; the MPPT is used at sites with an interdental width greater than 2 mm (Fig. 43-42); the crestal incision is applied next to an edentulous area.
Selection of the regenerative material is based on the defect anatomy (Figs. 43-43, 43-44). A non-resorbable titanium-reinforced e-PTFE membrane is used when the defect anatomy is not "supportive", such as in wide and one- or two-wall defects. Alternatively, a bioresorbable membrane supported with a bone replacement graft material can be used in these instances. The latter is preferred to titanium-reinforced e-PTFE when the non-supportive defects are associated with narrow interdental spaces. A bioresorbable membrane is applied alone in "supportive" defects, like the narrow and the two-to-three-wall ones. EMD is preferred in defects with a prevalent three-wall morphology or in well supported two-wall defects.
The suturing approach is chosen according to the defect anatomy and to the type of regenerative strategy used in each case. It consists of the combination of two sutures applied in the defect-associated interdental area to reach primary closure of the papilla in the absence of any tension. The first interdental suture is positioned between the apical part of the buccal gingiva, near the mucogingival junction, and an apical area of the lingual/ palatal flap. In supportive defects (three-wall defects) or in the presence of a supportive membrane (titanium e-PTFE membrane), or a supported membrane (bioresorbable and bone replacement graft), an internal horizontal crossed mattress suture is used. In non-supportive defects and in the presence of bioresorbable membranes or EMD, an offset internal mattress suture is preferred. When a crestal incision is performed, internal horizontal mattress sutures can be conveniently applied. The aims of this first suture are to relieve the residual tension of the flaps in the defect-associated area and to displace the buccal flap coronally. A second, more coronal internal mattress suture is placed to close the interdental papilla passively over the regenerative material.
**Fig. 43-42** Decision-making algorithm illustrating the parameters to take into account when deciding how to access an interdental intrabony defect: the simplified papilla preservation flap (SPPF) is used for narrow interdental spaces (2 mm or narrower), while the modified papilla preservation technique (MPPT) is used to access defect associated with wider interdental spaces (3 mm or wider).
**Fig. 43-43** Decision-making algorithm discussing the choice of currently available technologies for application in the treatment of intrabony defects with wide, non-space supporting anatomy. Either titanium-reinforced membranes or bioresorbable membranes are used to obtain a stable regenerative environment, provide space, and support the soft tissues.
**Fig. 43-44** Decision-making algorithm discussing the choice of currently available technologies for application in the treatment of intrabony defects with narrow, space-supporting anatomy. Enamel matrix derivative in gel form is preferred for three-wall defects, while bioresorbable membranes are used for the other narrow type of defects.
The surgical procedures can be performed with the aid of magnification such as loupes or an operating microscope. Microsurgical instruments can be utilized to complement the normal periodontal set of instruments.
An empirical protocol for the control of bacterial contamination consisting of doxycycline (100 mg bid for 1 week), 0.12% chlorhexidine mouth rinsing three times per day, and weekly prophylaxis is prescribed. Patients are requested to avoid brushing, flossing, and chewing in the treated area for 6–10 weeks. Nonresorbable membranes are removed after 6 weeks. Patients can resume full oral hygiene and chewing function in the treated area 2–4 weeks after membrane removal or when bioresorbable membranes are fully resorbed. Patients treated with EMD resume full oral hygiene after a period of 4–5 weeks. At the end of the "early healing phase", patients are placed on monthly recall for 1 year.
The performance of this clinical strategy has been recently assessed in a 40-patient consecutive case series (Cortellini & Tonetti 2005). Following completion of initial, cause-related periodontal therapy, subjects presented full-mouth plaque scores of 10.2 ± 2.7% and full-mouth bleeding scores at baseline of 7.9 ± 2.8%. At the intrabony defects, clinical attachment levels (CAL) were 10.2 ± 2.4 mm and probing depths (PD) amounted to 8.9 ± 1.8 mm. The radiographic defect angle was 29º ± 5.9º. Distance from the cemento-enamel junction to the bottom of the defect (CEJ-BD) was 11.2 ± 2.7 mm and the intrabony component of the defects (INFRA) was 6.6 ± 1.7 mm.
In this population the simplified papilla preservation flap could be used in 37.5% of sites, while the modified papilla preservation technique was selected in 45% of cases. The remaining sites, presenting with defects adjacent to edentulous areas, were accessed with a crestal incision.
Based on defect anatomy, non-resorbable titanium-reinforced e-PTFE barrier membranes were used in 30% of cases. In these cases defect angles ranged from 27–42º (average 32.4º ± 4.3º), and two out of three of the selected defects had a one-wall intrabony sub-component of 1–3 mm (average one-wall component of the 12 sites was 1.4 ± 1.2 mm).
Ten of the 11 defects treated with bioresorbable membranes supported with a bone replacement graft, presented a one-wall sub-component of 1–5 mm (average one-wall component of the 11 sites 1.8 ± 1.3 mm); defect angles in this group ranged from 21–45º (average 31.4º ± 7º).
Bioresorbable barriers alone were used in seven sites presenting with a prevalent two- and three-wall morphology and narrow defect angles, ranging from 20–28º (average 24.1º ± 3.7º). EMD was applied to ten defects with a prevalent three-wall component. The defect angle in this group ranged from 19–31º (average 26.5º ± 4.3º).
In all treated sites primary closure was obtained at completion of the surgical procedure. At the 1-week follow-up, when sutures were removed, two sites, both accessed with a SPPF, presented with a small interdental wound dehiscence: one had been treated with a bioresorbable membrane and bone replacement graft, the other with EMD. At week 2, two additional small wound dehiscences were detected: one accessed with MPPT and treated with a bioresorbable membrane and bone replacement graft, the other accessed with SPPF and treated with a bioresorbable barrier alone. All the other sites (90%) remained closed during the whole early healing phase.
The 40 patients presented at the 1-year follow-up visit with excellent levels of plaque control and low levels of bleeding on probing. The 1-year CAL clinical attachment gain was 6 ± 1.8 mm (range 4–11 mm). No sites gained less then 4 mm of CAL; 77.5% gained 5 mm or more and 40% more then 6 mm. Residual probing depths were 2.7 ± 0.6 mm, with an average pocket depth reduction of 6.1 ± 1.9 mm. Only four sites showed a residual probing depth of 4 mm; all the other sites resulted with a 1-year PPD of 3 mm or less. A minimal increase of 0.1 ± 0.7 mm in gingival recession between baseline and 1 year was recorded.
The performance of each of the four treatments was described in the study and it indicated that, whenever the choices were made according to the protocol (i.e. based on: width of the interdental space to chose the papilla preservation surgery; morphology of the defect to choose the regenerative material; and choice of the material and local anatomy to select the suturing approach) all four approaches gave excellent results with clinical attachment level gains equal to 88–95% resolution of the original depth of the intrabony component of the defect (Cortellini & Tonetti 2005).
The use of this decision-making protocol in the reported case series resulted in 6 ± 1.8 mm of CAL gain at 1 year. These results were obtained in defects with an intrabony component of 6.6 ± 1.7 mm. The percentage clinical attachment gain therefore was 92.1 ± 12%. This indicates that a large part of the intrabony component of the defects was resolved. Using the Ellegaard criteria (Ellegaard _et al_. 1971), resolution of the intrabony component of the defect was either satisfactory or complete in all treated cases. In particular 40.5% of defects had attachment level gains equal to or greater then the baseline depth of the intrabony component, while the defect with the worst response showed a 71.4% CAL gain. Historical comparison with clinical experiments using bone grafting or GTR clearly indicates that the results of this trial approach were in the top percentiles in terms of clinical attachment level gains and defect resolution (Cortellini & Tonetti 2000a; Rosen _et al_. 2000).
### Conclusions
GTR represents the best documented regenerative procedure for obtaining periodontal regeneration in intrabony defects and in degree II furcations. GTR has demonstrated significant clinical improvement beyond that achieved with only debridement in such defects. Regarding degree II maxillary furcations, the results following GTR treatment are inconsistent, and the treatment of degree III furcation defects is unpredictable. An added benefit may be obtained by the use of grafting materials in combination with GTR in some situations: in particular in furcation defects or to support bioresorbable membranes.
DFDBA alone gives documented improvements in some type of intrabony defects, in particular three-wall and two-wall defects.
EMD in gel formulation gives significant benefits in the treatment of intrabony defects, particularly those with a supportive anatomy (three-wall defects and narrow two-wall defects).
Differences between individuals and studies regarding the results of treating intrabony defects and class II furcations are related to patient compliance, maintenance procedures, selection of defects, surgical management, etc.
Periodontal regeneration obtained following GTR is stable on a long-term basis, provided good oral hygiene is maintained and a proper recall program is established. Current data indicate that, in patients participating in a supportive periodontal care program, 96% of teeth with severe intrabony defects and treated with a periodontal regenerative procedure could be retained for a period up to 15 years.
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# Chapter 44
# Mucogingival Therapy – Periodontal Plastic Surgery
Jan L. Wennström, Giovanni Zucchelli, and Giovan P. Pini Prato
* * *
Introduction
Gingival augmentation
Gingival dimensions and periodontal health
Marginal tissue recession
Marginal tissue recession and orthodontic treatment
Gingival dimensions and restorative therapy
Indications for gingival augmentation
Gingival augmentation procedures
Healing following gingival augmentation procedures
Root coverage
Root coverage procedures
Clinical outcome of root coverage procedures
Soft tissue healing against the covered root surface
Interdental papilla reconstruction
Surgical techniques
Crown-lengthening procedures
Excessive gingival display
Exposure of sound tooth structure
Ectopic tooth eruption
The deformed edentulous ridge
Prevention of soft tissue collapse following tooth extraction
Correction of ridge defects by the use of soft tissue grafts
Surgical procedures for ridge augmentation
* * *
# Introduction
_Mucogingival therapy_ is a general term used to describe periodontal treatment involving procedures for correction of defects in morphology, position, and/or amount of soft tissue and underlying bone support at teeth and implants ( _Glossary of Terms in Periodontol-ogy_ 2001).
A more specific term, _mucogingival surgery_ , was introduced in the 1950s by Friedman (1957) and was defined as "surgical procedures designed to preserve gingiva, remove aberrant frenulum or muscle attachments, and increase the depth of the vestibule". Frequently, however, the term "mucogingival surgery" was used to describe all surgical procedures that involved both the gingiva and the alveolar mucosa. Consequently, not only were techniques designed (1) to enhance the width of the gingiva and (2) to correct particular soft tissue defects regarded as mucogingival procedures but (3) certain pocket elimination approaches were also included in this group of periodontal treatment modalities. In 1993 Miller proposed the term _periodontal plastic surgery_ , considering that mucogingival surgery had moved beyond the traditional treatment of problems associated with the amount of gingivae and recession type defects to also include correction of ridge form and soft tissue esthetics. Periodontal plastic surgery would accordingly be defined as "surgical procedures performed to prevent or correct anatomic, developmental, traumatic or disease-induced defects of the gingiva, alveolar mucosa or bone" (Proceedings of the World Workshop in Periodontics 1996). Among treatment procedures that may fall within this definition are various soft and hard tissue procedures aimed at:
* Gingival augmentation
* Root coverage
* Correction of mucosal defects at implants
* Crown lengthening
* Gingival preservation at ectopic tooth eruption
* Removal of aberrant frenulum
* Prevention of ridge collapse associated with tooth extraction
* Augmentation of the edentulous ridge.
The focus of this chapter is mainly on treatment procedures for corrections of soft tissue defects in relation to the tooth and the edentulous ridge, while bone augmentation procedures are covered in Chapter 49.
# Gingival augmentation
A review of the literature on gingival augmentation reveals that the rationale for increasing the width of gingiva as a means of promoting gingival health and improving attachment levels is poorly supported by scientific evidence. Usually clinical impressions, case reports, and anecdotal information have been used as the main reference to justify surgical intervention. In this perspective a discussion of the scientific evidence forming the basis for our current understanding of the role played by the gingiva in the protection of the periodontium proper seems appropriate.
## Gingival dimensions and periodontal health
For many years the presence of an "adequate" zone of gingiva was considered critical for the maintenance of marginal tissue health and for the prevention of continuous loss of connective tissue attachment (Nabers 1954; Ochsenbein 1960; Friedman & Levine 1964; Hall 1981; Matter 1982). Clinicians had the "impression" that sites with a narrow zone of gingiva (Fig. 44-1) were often inflamed while the wide zone of gingiva found at neighboring teeth remained healthy. The prevailing concept was thus that a narrow zone of gingiva was insufficient (1) to protect the periodontium from injury caused by friction forces encountered during mastication and (2) to dissipate the pull on the gingival margin created by the muscles of the adjacent alveolar mucosa (Friedman 1957; Ochsenbein 1960). Moreover it was believed that an "inadequate" zone of gingiva would (1) facilitate subgingival plaque formation because of improper pocket closure resulting from the movability of the marginal tissue (Friedman 1962) and (2) favor attachment loss and soft tissue recession because of less tissue resistance to apical spread of plaque-associated gingival lesions (Stern 1976; Ruben 1979). It was also considered that a narrow gingiva in combination with a shallow vestibular fornix might (1) favor the accumulation of food particles during mastication, and (2) impede proper oral hygiene measures (Gottsegen 1954; Rosenberg 1960; Corn 1962; Carranza & Carraro 1970).
**Fig. 44-1** A clinical photograph of a mandibular front tooth region. The gingiva on the buccal aspect of tooth 41 has a narrow width and shows more pronounced signs of inflammation than adjacent gingival units with a wider zone of gingiva.
The opinions expressed concerning what could be regarded as being an "adequate" or "sufficient" dimension of the gingiva varied. While some authors suggested that less than 1 mm of gingiva may be sufficient (Bowers 1963), others claimed that the apicocoronal height of keratinized tissue ought to exceed 3 mm (Corn 1962). A third category of authors had a more biologic approach to the question and stated that an adequate amount of gingiva is any dimension of gingiva which (1) is compatible with gingival health or (2) prevents retraction of the gingival margin during movements of the alveolar mucosa (Friedman 1962; De Trey & Bernimoulin 1980).
One of the first studies in which attempts were made to evaluate the significance of the gingival zone for the maintenance of periodontal health was carried out by Lang and Löe (1972) on dental students who had their teeth professionally cleaned once a day for 6 weeks. All buccal and lingual sites were examined for plaque, gingival conditions, and apico-coronal height of gingiva. The results showed that despite the fact that the tooth surfaces were free from plaque, all sites with less than 2 mm of gingiva exhibited persisting clinical signs of inflammation. Based on this observation the authors suggested that 2 mm of gingiva is an adequate width for maintaining gingival health. Subsequent clinical trials (Miyasato _et al_. 1977; Grevers 1977), however, failed to substantiate this concept of a required minimum dimension of gingiva. In fact, these clinical trials demonstrated that it is possible to maintain clinically healthy marginal tissues even in areas with less than 1 mm of gingiva.
The question whether a firmly attached portion of gingiva is critical for the protection of the periodontium proper was addressed by Wennström and Lindhe (1983a,b) utilizing the beagle dog model. In these studies dentogingival units with different clinical characteristics were experimentally established; (1) units with only a narrow and mobile zone of keratinized tissue and (2) units with a wide, firmly attached gingiva (Fig. 44-2). With daily performed mechanical plaque-control measures, the gingival units could be maintained free from clinical as well as histologic signs of inflammation irrespective of the presence or absence of an attached portion of gingiva. When bacterial plaque was allowed to accumulate (for 40 days), clinical signs of inflammation (redness and swelling) developed that were more pronounced in tooth regions with mobile gingiva (Fig. 44-3a) than in areas with presence of a wide and firmly attached gingival zone (Fig. 44-3b). However, histologic analysis revealed that the size of the inflammatory cell infiltrate and its extension in an apical direction (an assessment which indirectly may be used as an estimate of the apical migration of the bacterial plaque) were similar in the two categories of dentogingival units. The finding that the clinical signs of gingival inflammation did not correspond with the size of the inflammatory cell infiltrate illustrates the difficulties inherent in the interpretation of data from clinical examinations made in areas with varying width of gingiva. This should be kept in mind when interpreting the data by Lang and Löe (1972) showing that clinically visible signs of inflammation, such as redness and swelling, were more frequent in areas with less than 2 mm of gingiva than in areas with a wider zone of gingiva.
**Fig. 44-2** Two teeth in a dog with varying dimensions of the marginal gingiva. (a) A buccal tooth site with a wide zone of attached gingiva. (b) A site with an unattached, narrow band of gingiva.
**Fig. 44-3** The same teeth as in Fig. 44-2 after 40 days of plaque accumulation. The clinical signs of inflammation are more pronounced at the site with the narrow band of gingiva (b) than at the site with the wide zone of attached gingiva (a).
The necessity for and effectiveness of gingival augmentation in maintaining periodontal attachment was examined by Dorfman _et al_. (1980). Ninety-two patients with bilateral facial tooth surfaces exhibiting minimal keratinized tissue (i.e. less than 2 mm) had a free gingival graft placed on one side, while the contralateral side served as the untreated control. Prior to and after surgery the patients were subjected to scaling and root planing and instruction in oral hygiene measures. Not surprisingly, the investigators found a significant increase (approximately 4 mm) in the width of keratinized tissue at the grafted sites. This increased width of gingiva, as well as the clinical attachment level, was maintained throughout the 2 years of follow-up. In the control sites the width of gingiva was less than 2 mm and did not vary significantly during the observation period. However, the attachment level was also maintained unchanged in the non-grafted areas. Thus, the resistance to continuous attachment loss was not linked to the height (width) of gingiva, a conclusion that was further substantiated by subsequent 4- and 6-year follow-up reports of this patient material (Dorfman _et al_. 1982; Kennedy _et al_. 1985).
Further support for the conclusion that a minimal zone of gingiva may not compromise periodontal health is available in a number of other longitudinal clinical studies (e.g. Hangorsky & Bissada 1980; De Trey & Bernimoulin 1980; Lindhe & Nyman 1980; Schoo & van der Velden 1985; Kisch _et al_. 1986; Wennström 1987; Freedman _et al_. 1999). Hence, Hangorsky and Bissada (1980), who evaluated the long-term clinical effect of free soft tissue grafts, concluded that while the free gingival graft is an effective means to widen the zone of the gingiva, there is no indication that this increase has direct influence upon periodontal health.
### Conclusion
Gingival health can be maintained independent of its dimensions. Furthermore, there is evidence from both experimental and clinical studies that, in the presence of plaque, areas with a narrow zone of gingiva possess the same "resistance" to continuous attachment loss as teeth with a wide zone of gingiva. Hence, the traditional dogma of the need of an "adequate" width (in millimeters) of gingiva, or attached portion of gingiva, for prevention of attachment loss is not scientifically supported.
**Fig. 44-4** Recessions associated with toothbrushing trauma. The marginal gingiva is clinically healthy and abrasion defects of various extension can be noted in the exposed roots.
## Marginal tissue recession
Marginal tissue recession, i.e. displacement of the soft tissue margin apical to the cemento-enamel junction (CEJ) with exposure of the root surface, is a common feature in populations with high standards of oral hygiene (e.g. Sangnes & Gjermo 1976; Murtomaa _et al_. 1987; Löe _et al_. 1992; Serino _et al_. 1994), as well as in populations with poor oral hygiene (e.g. Baelum _et al_. 1986; Yoneyama _et al_. 1988; Löe _et al_. 1992; Susin _et al_. 2004). In populations maintaining high standards of oral hygiene, loss of attachment and marginal tissue recession are predominantly found at buccal surfaces (Löe _et al_. 1992; Serino _et al_. 1994), and are frequently associated with the presence of a "wedge-shaped defect in the crevicular area of one or several teeth" (Sangnes & Gjermo 1976). In contrast, all tooth surfaces are usually affected with soft tissue recession in periodontally untreated populations, although the prevalence and severity is more pronounced at single-rooted teeth than at molars (Löe _et al_. 1978; 1992; Miller _et al_. 1987; Yoneyama _et al_. 1988).
Tissue trauma caused by vigorous toothbrushing is considered to be a predominant causative factor for the development of recessions, particularly in young individuals. Traumatizing toothbrushing and tooth malposition are the factors most frequently found to be associated with marginal tissue recession (Sangnes 1976; Vekalahti 1989; Checchi _et al_. 1999). In addition, Khocht _et al_. (1993) showed that recessions are related to the use of hard toothbrushes. Other local factors that have been associated with marginal tissue recession are (1) alveolar bone dehiscences (Bernimoulin & Curilivic 1977; Löst 1984), (2) high muscle attachment and frenal pull (Trott & Love 1966), (3) plaque and calculus (van Palenstein Helderman _et al_. 1998; Susin _et al_. 2004), and (4) iatrogenic factors related to restorative and periodontal treatment procedures (Lindhe & Nyman 1980; Valderhaug 1980).
**Fig. 44-5** A recession associated with localized plaqueinduced inflammatory lesion.
At least three different types of marginal tissue recessions may exist:
* _Recessions associated with mechanical factors, predomi-nately toothbrushing trauma_ (Fig. 44-4). Recessions resulting from improper toothbrushing techniques are often found at sites with clinically healthy gingiva and where the exposed root has a wedge-shaped defect, the surface of which is clean, smooth and polished.
* _Recessions associated with localized plaque-induced inflammatory lesions_ (Fig. 44-5). Such recessions may be found at teeth that are prominently positioned, i.e. the alveolar bone is thin or absent (bone dehiscence), and where in addition the gingival tissue is thin (delicate). An inflammatory lesion that develops in response to subgingival plaque occupies the connective tissue adjacent to the dentogingival epithelium. Measurements made by Waerhaug (1952) suggest that the distance between the periphery of microbial plaque on the tooth surface and the lateral and apical extension of the inflammatory cell infiltrate seldom exceeds 1– 2 mm. Thus, if the free gingiva is voluminous the infiltrate will occupy only a small portion of the connective tissue. In a thin and delicate gingiva, on the other hand, the entire connective tissue portion may be engaged. Proliferation of epithelial cells from the oral as well as the dentogingival epithelium into the thin and degraded connective tissue may bring about a subsidence of the epithelial surface which clinically becomes manifest as recession of the tissue margin (Baker & Seymour 1976) (Fig. 44-6).
* _Recessions associated with generalized forms of destruc-tive periodontal disease_ (Fig. 44-7). The loss of periodontal support at proximal sites may result in compensatory remodeling of the support at the buccal/lingual aspect of the teeth leading to an apical shift of the soft tissue margin (Serino _et al_. 1994).
**Fig. 44-6** Clinical photographs illustrating the development of a soft tissue recession as a result of plaque-induced inflammation in a beagle dog. (a) Note the thin but healthy gingiva (arrow) at the start of the plaque accumulation period. (b) Pronounced clinical signs of inflammation are seen after 20 days. (c) After 40 days of no tooth cleaning, the gingival margin has receded.
Cross-sectional studies showing that a correlation exists between the presence of recession defects and the height (width) of the gingiva (e.g. Stoner & Mazdyasna 1980; Tenenbaum 1982) have often been interpreted as an evidence that a narrow zone of gingiva is a contributing factor in the development of soft tissue recessions (Fig. 44-8). It should be realized, however, that data derived from cross-sectional studies can neither prove nor disprove a cause–effect relationship. Consequently, the data reported from such studies may equally well be interpreted to demonstrate that the formation of a recession defect results in a reduced height of the gingiva. Fig. 44-1 illustrates a lower incisor tooth region with a localized gingival recession at the buccal aspect of tooth 41. The gingiva apical to the recession defect is narrow ("insufficient") while at neighboring teeth the gingival height may be considered "adequate". It is reasonable to assume that the gingiva at tooth 41, _before the recession defect developed_ , had a height that was similar to that found at tooth 31 and tooth 42. In other words, the narrow zone of gingiva found at tooth 41 may be the result of _loss of gingival tissue during the period of recession development_ , rather than being the cause of the formation of the defect. If this interpretation is valid, the rationale for increasing the height of the gingiva in an area _apical to the existing defect_ as a means of preventing further recession may appear somewhat obscure. In fact, data obtained from prospective, longitudinal studies of patients showing areas with only a minimal zone of gingiva favor the conclusion that a certain quantity of gingiva is not essential for the preclusion of soft tissue recessions.
**Fig. 44-7** Recessions associated with generalized forms of destructive periodontal disease. Recession of the soft tissue is found not only at the facial aspect of the teeth but also at proximal sites.
**Fig. 44-8** A mandibular tooth segment with multiple buccal recessions illustrating the association proposed between recession depth and height of gingiva.
Lindhe and Nyman (1980) examined the alterations of the position of the gingival margin following periodontal surgery in 43 patients with advanced periodontal breakdown. Following active treatment, all patients were recalled once every 3–6 months for maintenance care. The position of the soft tissue margin in relation to the CEJ was assessed on the facial aspect of all teeth after initial healing and after 10–11 years of maintenance. The presence or absence of keratinized tissue after surgical treatment was also determined. The results showed that both in areas with and without visible keratinized tissue after healing, a small coronal regrowth (≈1 mm) of the soft tissue margin had occurred during the period of maintenance. In other words, no recession was observed in this group of patients maintained on a careful prophylaxis program.
Dorfman _et al_. (1982) reported a 4-year follow-up study including 22 patients with bilateral tooth areas exhibiting gingival recession and lack of firmly attached marginal soft tissue. In conjunction with scaling and root planing a free gingival graft was placed on one side, while the contralateral control side was treated by scaling and root planing only. All patients were recalled for prophylaxis once every 3–6 months during a 4-year period. The data obtained from the examinations of the non-grafted control areas revealed that no further recession of the soft tissue margin or loss of probing attachment had occurred despite the lack of attached marginal tissue. In fact, there was a slight gain of probing attachment. The authors concluded that recession sites without attached gingiva might not experience further attachment loss and recession if the inflammation is controlled. In a subsequent report (Kennedy _et al_. 1985), the authors reported data on 10 patients who had not participated in the maintenance program for a period of 5 years. In these patients plaque and clinical signs of inflammation as well as some further recession were noted at the 5-year examination as compared with the data obtained after termination of active treatment. However, except for the clinical signs of inflammation, which were more pronounced in non-grafted sites, no differences were observed between control sites with <1 mm or complete lack of attached gingiva and grafted sites.
**Fig. 44-9** (a) Clinical photographs of a canine and a first premolar in the mandibular jaw with <1 mm of attached portion of gingiva 6 months after surgical treatment. (b) Note the increase of the width of the gingiva at the facial aspect of the teeth and the more coronally positioned gingival margin 5 years later.
The lack of relationship between the height of gingiva and the development of soft tissue recession is further validated by results from longitudinal clinical studies (Schoo & van der Velden 1985; Kisch _et al_. 1986; Wennström 1987; Freedman _et al_. 1999). The study by Wennström (1987) reports observations made at 26 buccal sites surgically deprived of all keratinized tissue. A baseline examination carried out 6 months after treatment revealed that these sites had regained a zone of gingiva which was, however, not attached or had only a minimal (<1 mm) portion attached to the underlying hard tissues (Figs. 44-9a and 44-10a). Adjacent teeth with a broad zone of attached gingiva were also included in the examinations. In most sites the position of the soft tissue margin had been maintained unchanged over 5 years (Figs. 44-9b and 44-10b). A further apical displacement of the soft tissue margin had occurred at two out of 26 sites with no/minimal attached portion of gingiva and at three out of 12 adjacent control sites with a wide attached zone of gingiva. Since four of these five sites were found in one patient (Fig. 44-11), and all sites were free from clinical signs of inflammation, excessive toothbrushing was considered to be the causative factor, and following correction of the brushing technique no further progression was observed. Furthermore, the development of soft tissue recession at the control sites resulted in a decreased width of the gingiva, an observation that supports the concept that a narrow zone of gingiva apical to a localized recession is a consequence rather than a cause of the recession.
### Conclusion
Marginal soft tissue recession is a common feature in populations with good as well as poor standards of oral hygiene. There is evidence to suggest that the predominant cause for localized recessions in young individuals is toothbrushing trauma, while periodontal disease may be the primary cause in older adults. Evidence from prospective longitudinal studies shows that the gingival height is not a critical factor for the prevention of marginal tissue recession, but that the development of a recession will result in loss of gingival height.
**Fig. 44-10** (a) A mandibular canine and first premolar tooth region showing a very narrow zone of gingiva 6 months after surgical therapy. (b) No major change in the position of the soft tissue margin has occurred during a 5-year period despite the lack of attached gingiva.
## Marginal tissue recession and orthodontic treatment
Results from clinical and experimental research have documented that most forms of orthodontic therapy are innocuous to the periodontium (see Chapter 57). The clinician may experience, however, that some patients respond to frontal movements of incisors and lateral movements of posterior teeth by gingival recession and loss of attachment (Maynard & Ochsenbein 1975; Coatoam _et al_. 1981; Foushee _et al_. 1985) (Fig. 44-12). Based on the clinical observation that recession may occur during orthodontic therapy involving sites that have an "insufficient" zone of gingiva, it was suggested that a grafting procedure to increase the gingival dimensions should precede the initiation of orthodontic therapy in such areas (Boyd 1978; Hall 1981; Maynard 1987).
As discussed previously, the presence of an alveolar bone dehiscence is considered to be a prerequisite for the development of a marginal tissue recession, i.e. a root dehiscence may establish an environment that is conducive for loss of gingival tissue. With respect to orthodontic therapy, this would imply that as long as a tooth is moved exclusively within the alveolar bone, soft tissue recession will not develop (Wennström _et al_. 1987). On the other hand, predisposing alveolar bone dehiscences may be induced by uncontrolled facial expansion of a tooth through the cortical plate, thereby rendering the tooth liable to development of soft tissue recession. In this context it is interesting to note that experimental studies have shown that labial bone will reform in the area of a dehiscence when the tooth is retracted towards a proper positioning of the root within the alveolar process (Engelking & Zachrisson 1982; Karring _et al_. 1982) (Fig. 44-13). It is therefore likely that the reduction in recession seen at a previously prominently positioned tooth that has been moved into a more proper position within the alveolar process (Fig. 44-14) is also accompanied by bone formation.
**Fig. 44-11** Clinical photographs of the mandibular right canine–premolar tooth region in a patient showing several sites with apical displacement of the soft tissue margin during the 5 years of observation. (a) At the initial examination the two premolars had <1 mm and the canine >1 mm of attached portion of gingiva. (b) After 5 years, recession and loss of keratinized tissue can be seen on the buccal aspect of the canine, which initially had a broad zone of gingiva (black arrow). The second premolar also showed further apical displacement of the soft tissue margin (white arrow).
Alterations occurring in gingival dimensions and marginal tissue position in conjunction with orthodontic therapy are related to the _direction of tooth movement_. Facial movement results in reduced facial gingival dimensions, while an increase is observed following lingual movement (Coatoam _et al_. 1981; Andlin-Sobocki & Bodin 1993). Recession of the labial gingival margin and loss of attachment was demonstrated in experimental studies in the monkey following either tipping and extrusion movements or bodily movements of incisors (Batenhorst _et al_. 1974; Steiner _et al_. 1981). However, similarly designed studies carried out in dogs (Karring _et al_. 1982; Nyman _et al_. 1982) and humans (Rateitschak _et al_. 1968) failed to demonstrate that labial tooth movement is accompanied by marginal tissue recession and attachment loss. The conflicting results may be related to differences with respect to e.g. (1) the amount of labial tooth displacement, (2) the presence/absence of plaque and gingival inflammation in the regions subjected to tooth movement, and/or (3) differences in gingival dimensions. Steiner _et al_. (1981) speculated on mechanisms by which gingival tissue could be lost as a result of labial tooth movement and suggested that tension in the marginal tissue created by the forces applied to the teeth could be an important factor. If this hypothesis were valid, obviously the volume (thickness) of the gingival tissue at the pressure side, rather than its apico-coronal height, would determine whether or not marginal tissue recession develops during orthodontic therapy.
**Fig. 44-12** Soft tissue recession at tooth 11 observed during the course of active orthodontic treatment.
**Fig. 44-13** (a) Schematic drawing illustrating alterations occurring in the marginal periodontal tissues following lingual movement of a tooth prominently positioned in the arch and having a bone dehiscence. (b) An increase in bone height and gingival height will be seen as well as a coronal migration of the soft tissue margin following lingual positioning of the tooth.
**Fig. 44-14** (a) A prominently positioned 13 showing soft tissue recession. (b) The same tooth following the completion of the orthodontic tooth movement. Note the reduction of the recession that has taken place as a consequence of the changed position of the tooth.
Support for the hypothesis is obtained from an experimental study in monkeys (Wennström _et al_. 1987) in which teeth were orthodontically moved into areas with varying thickness and quality of the marginal soft tissue. Following extensive bodily movement of incisors in a labial direction through the alveolar bone (Fig. 44-15), most teeth showed a small apical displacement of the soft tissue margin but no loss of connective tissue attachment (Fig. 44-16). In other words, the apical displacement of the gingival margin was the result of a reduced height of the free gingiva (Fig. 44-17), which in turn may be related to tension ("stretching") in the soft tissues during the facial tooth movement and reduced bucco-lingual tissue thickness. Similar to results presented by Foushee _et al_. (1985) from a study in humans, no relationship was found between the initial apicocoronal width (height) of the gingiva and the degree of apical displacement of the soft tissue margin during orthodontic therapy. Thus, the findings do not lend support to the concept of a certain zone of gingiva as essential for the prevention of recession during orthodontic therapy, but rather collaborate observations reported by Coatoam _et al_. (1981) that the integrity of the periodontium can also be maintained during orthodontic therapy in areas which have only a minimal zone of gingiva.
**Fig. 44-15** Occlusal view of the maxillary jaw in a monkey showing the position of the central incisors before (a) and after (b) bodily movement in labial direction. The canines and lateral incisors were joined in an individual fabricated silver splint and used as anchorage teeth.
In the experimental studies by Steiner _et al_. (1981) and Wennström _et al_. (1987) it was observed that teeth, which experienced loss of connective tissue attachment when orthodontically moved facially, showed obvious clinical signs of inflammation throughout the experimental period. Since it has been demonstrated that, in presence of plaque-induced suprabony lesions, orthodontic forces generating bodily tooth movement are not capable of causing accelerated destruction of the connective tissue attachment (Ericsson _et al_. 1978), a decreased bucco-lingual dimension of the border tissue due to "stretching" of the facial gingiva may have favored the destructive effect of the plaque-associated inflammatory lesion. This assumption is validated by the observations that, in the presence of plaque-induced gingivitis, a thin marginal soft tissue is more susceptible to complete breakdown than a thick one (Baker & Seymour 1976). Furthermore, no difference in attachment loss was observed at plaque-infected teeth that were bodily moved _within the alveolar bone_ , irrespective of the type of bordering soft tissue (gingiva or lining mucosa) (Wennström _et al_. 1987). Hence, the _thickness rather than the quality_ of the marginal soft tissue on the pressure side of the tooth may be the determining factor for the development of the recession. The interpretation is supported by findings of recent clinical studies in humans analyzing factors of importance for the development of recessions during labial movement of mandibular incisors. Melsen and Allais (2005) found that gingival inflammation and a "thin gingival biotype" were significant predictors for gingival recession, and Yared _et al_. (2006) reported that 93% of the teeth that developed recession had a gingival thickness less than 0.5 mm. Hence, the observations made in the studies discussed strongly emphasize the importance of adequate infection control during orthodontic treatment.
**Fig. 44-16** The buccal aspect of the central incisors shown in Fig. 44-15, before (a) and after (b) the labial tooth movement. No obvious change in the location of the gingival margin has occurred despite the pronounced labial displacement of the incisors.
**Fig. 44-17** Histologic specimens showing (a) reduced alveolar bone height at an incisor bodily moved in labial direction and (b) normal alveolar bone height at a non-moved control tooth. Note the maintained level of connective tissue attachment and the reduced height of the free gingiva at the labially displaced incisor (a). Large arrows indicate the position of the cemento-enamel junction and small arrows the position of the alveolar bone crest.
### Conclusion
The clinical implication of the results from the studies discussed is that labial tooth movement should be preceded by careful examination of the dimensions of the tissues covering the facial aspect of the teeth to be moved. As long as the tooth can be moved within the envelope of the alveolar process, the risk of harmful side effects in the marginal tissue is minimal, irrespective of the dimensions and quality of the soft tissue surrounding the tooth. If, however, the tooth movement is expected to result in the establishment of an alveolar bone dehiscence, the volume (thickness) of the covering soft tissue should be considered as a factor that may influence the development of soft tissue recession during, as well as after, the phase of active orthodontic therapy. A thin gingiva may serve as a _locus minorus resistentia_ to developing soft tissue defects in the presence of plaque-induced inflammation or toothbrushing trauma.
## Gingival dimensions and restorative therapy
The placement of restoration margins subgingivally may not only create a direct operative trauma to the tissues (Donaldson 1974), but may also facilitate subgingival plaque accumulation, with resultant inflammatory alterations in the adjacent gingiva and recession of the soft tissue margin (Parma-Benfenati _et al_. 1985; Lang 1995; Günay _et al_. 2000). Over a 10 year period, Valderhaug (1980) evaluated longitudinally the soft tissue alterations taking place at facial sites of 286 teeth with subgingivally or supragingivally placed crown margins in 82 patients. The reexamination performed 1 year after insertion of the restorations revealed that the gingivae at teeth with subgingival restoration margins were more inflamed than at those with supragingivally placed borders. Of the 150 teeth which had the facial crown margin located subgingivally at the time of cementation, 40% already showed supragingival exposure of the crown margin after 1 year, and at the 10-year examination as many as 71% had become supragingivally positioned due to recession of the soft tissue margin. Compared to teeth with supragingivally placed crown margins the amount of recession and clinical attachment loss was greater at sites with subgingivally placed restoration margins.
Stetler and Bissada (1987) evaluated the periodontal conditions at teeth with subgingivally placed restoration margins on teeth with varying apico-coronal height of gingiva and found that teeth having a narrow (<2 mm) band of gingiva showed more pronounced clinical signs of inflammation than restored teeth with a wide gingival zone, but that there was no difference in loss of probing attachment. However, if subgingivally placed restorations favor plaque accumulation and the adjacent gingiva is thin, there may be a potential risk for the development of soft tissue recession. In fact, an experimental study in the beagle dog (Ericsson & Lindhe 1984), in which metallic strips were inserted subgingivally in areas with varying width of gingiva, showed that in sites with a thin gingival margin, recession was a more likely consequence of the combined tissue trauma caused by the insertion of the strip and subsequent plaque accumulation during a 6-month period than in sites with a broad gingival zone. The authors suggested that the placement of restorations in a subgingival position might favor plaque retention and at sites with a thin gingiva this will lead to loss of tissue height, i.e. an apical displacement of the soft tissue margin. Accordingly, if such an apical displacement as a consequence of plaque-induced inflammation is to be prevented, either the plaque-control standard has to be improved or the _thickness_ of the gingival margin has to be increased. However, an increased gingival dimension will not prevent the apical propagation of the plaque-associated lesion and the associated loss of periodontal attachment.
### Conclusion
Subgingival placement of the margin of a restoration is likely to result in soft tissue recession over time. Experimental and clinical data suggest that the thickness of the marginal gingiva, but not the apicocoronal width of the gingiva, may influence the magnitude of recession taking place as a result of direct mechanical trauma during tooth preparation and bacterial plaque retention.
**Fig. 44-18** The use of vestibular extension operations for increasing the width of the gingiva involves the production of a wound extending from the gingival margin to a level some millimeters apical to the mucogingival junction. With the "denudation" technique all soft tissue is removed leaving the alveolar bone exposed. With the "split flap" procedure only the superficial portion of the oral mucosa is removed leaving the bone covered with connective tissue.
## Indications for gingival augmentation
Scientific data obtained from well controlled clinical and experimental studies have unequivocally demonstrated that the apico-coronal width of gingiva and the presence of an attached portion of gingiva are not of decisive importance for the maintenance of gingival health and the height of the periodontal tissues. Consequently, the presence of a narrow zone of gingiva _per se_ cannot justify surgical intervention (Proceedings of the 1st European Workshop on Periodontology 1994; Proceedings of the World Workshop in Periodontics 1996). However, gingival augmentation should be considered in situations where, for example, the patient experiences discomfort during toothbrushing and/or chewing due to an interfering lining mucosa. Furthermore, when orthodontic tooth movement is planned and the final positioning of the tooth can be expected to result in an alveolar bone dehiscence, an increase of the _thick-ness_ of the covering soft tissue may reduce the risk for development of soft tissue recession. An increase of the _thickness_ of the gingival margin may also be considered in certain situations when subgingival restorations are placed in areas with a thin marginal tissue.
## Gingival augmentation procedures
Gingival augmentation operations comprise a number of surgical techniques, the majority of which have been developed mainly on an empiric basis and without sufficient knowledge about the biology of the involved tissues. The earliest of these techniques are the "vestibular extension operations" which were designed mainly with the objective of extending the depth of the vestibular sulcus (Bohannan 1962a,b). In recent years, however, the use of pedicle or free soft tissue grafts have become the most commonly used techniques in the management of "insufficient" gingival dimensions, because of higher predictability of the healing result.
### Vestibular/gingival extension procedures
The "denudation techniques" included the removal of all soft tissue within an area extending from the gingival margin to a level apical to the mucogingival junction leaving the alveolar bone completely exposed (Ochsenbein 1960; Corn 1962; Wilderman 1964) (Fig. 44-18). Healing following this type of treatment resulted often in an increased height of the gingival zone, although in some cases only a very limited effect was observed. However, the exposure of alveolar bone produced severe bone resorption with permanent loss of bone height (Wilderman _et al_. 1961; Costich & Ramfjord 1968). In addition, the recession of marginal gingiva in the surgical area often exceeded the gain of gingiva obtained in the apical portion of the wound (Carranza & Carraro 1963; Carraro _et al_. 1964). Due to these complications and severe postoperative pain for the patient, the use of the "denudation technique" can hardly be justified.
With the "periosteal retention" procedure or "split flap" procedure (Fig. 44-18) only the superficial portion of the oral mucosa within the wound area was removed leaving the bone covered by periosteum (Staffileno _et al_. 1962, 1966; Wilderman 1963; Pfeifer 1965). Although the preservation of the periosteum implies that less severe bone resorption will occur than following the "denudation technique", loss of crestal bone height was also observed following this type of operation unless a relatively thick layer of connective tissue was retained on the bone surface (Costich & Ramfjord 1968). If a thick layer was not secured, the periosteal connective tissue tended to undergo necrosis and the subsequent healing closely resembled that following the "denudation technique" described above.
Other described gingival extension procedures may be considered as modifications of the "denudation" and "split flap" techniques or combinations of these procedures. The apically repositioned flap procedure (Friedman 1962), for instance, involved the elevation of soft tissue flaps and their displacement during suturing in an apical position, often leaving 3–5 mm of alveolar bone denuded in the coronal part of the surgical area. This resulted in the same risk for extensive bone resorption as other "denudation techniques". It was proposed by Friedman (1962) that a post-surgical increase of the width of the gingiva can be predicted with the "apically repositioned flap", but several studies indicated that the presurgical width most often was retained or became only slightly increased (Donnenfeld _et al_. 1964; Carranza & Carraro 1970).
The vestibular/gingival extension procedures referred to were based on the assumption that it is the frictional forces encountered during mastication that determines the presence of a keratinized tissue adjacent to the teeth (Orban 1957; Pfeifer 1963). Therefore, it was believed that by the displacement of muscle attachments and the extension of vestibular depth, the regenerating tissue in the surgical area would be subjected to physical impacts and adapt to the same functional requirements as those met by "normal" gingiva (Ivancie 1957; Bradley _et al_. 1959; Pfeifer 1963). Later studies, however, showed that the characteristic features of the gingiva are determined by some inherent factors in the tissue rather than being the result of functional adaptation and that the differentiation (keratinization) of the gingival epithelium is controlled by morphogenetic stimuli from the underlying connective tissue (see Chapter 1).
### Grafting procedures
The gingival and palatal soft tissues will maintain their original characteristics after transplantation to areas of the alveolar mucosa (see Chapter 1). Hence, the use of transplants offers the potential to predict the post-surgical result. The type of transplants used can be divided into (1) pedicle grafts, which maintain their connection with the donor site after placement at the recipient site (Fig. 44-19), and (2) free grafts that are completely deprived of their connection with the donor area (Fig. 44-20). For gingival augmentation free grafts have been used most commonly (Haggerty 1966; Nabers 1966; Sullivan & Atkins 1968a; Hawley & Staffileno 1970; Edel 1974). Acellular freeze-dried dermal matrix (ADM) allografts may be utilized as an alternative to the use of an autogenous mucosal graft from the palate (Wei _et al_. 2000; Harris 2001), but the increase in the width of keratinized tissue following the use of these grafts may not be as predictable as with the use of autogenous grafts.
**Fig. 44-19** Pedicle graft procedure for gingival augmentation. (a) A lower central incisor with facial soft tissue recession associated with high attachment of a frenulum. (b) The frenulum is released and a split flap of keratinized tissue is dissected from the area of the neighboring tooth. (c) The mobilized soft tissue flap is laterally moved and secured in position at the recipient site. (d) The healing result 1 year post-treatment shows the establishment of a broad zone of keratinized tissue without interfering frenulum.
**Fig. 44-20** Grafting procedure for gingival augmentation. (a) A lower molar at which the patient experiences discomfort during toothbrushing due to interfering lining mucosa and high attachment of a frenulum. Decision was made to displace the attachment of the frenulum apically and augment the gingival zone through the placement of a free graft. (b) A partial-thickness flap is dissected to prepare a recipient bed. The flap is displaced apically and sutured. (c,d) A graft with a thickness of 1.5–2 mm and of sufficient size and contour (a foil template of the recipient site may be used) is dissected from the palatal mucosa in the region of the premolars. (e) The graft is immediately transferred to the prepared recipient bed and anchored by sutures to secure a close adaptation of the graft to the recipient bed. (f) A periodontal dressing is applied to protect the graft. Following healing a broad zone of keratinized tissue has been established.
#### _Technique_
* The surgical procedure is initiated with the preparation of the recipient site (Fig. 44-20a-b). A periosteal bed free from muscle attachment and of sufficient size is prepared by sharp dissection. The partial-thickness flap is displaced apically and sutured.
* In order to ensure that a graft of sufficient size and proper contour is removed from the donor area, usually the palatal mucosa in the region of the premolars, it is recommended to produce a foil template over the recipient site. The template is transferred to the donor site where it is outlined by a shallow incision (Fig. 44-20c). A graft with a thickness of approximately 1.5–2 mm is then dissected from the donor area (Fig. 44-20d). It is advocated to place the sutures in the graft before it is cut completely free from the donor area since this may facilitate its transfer to the recipient site.
* The graft is immediately transferred to the prepared recipient bed and sutured (Fig. 44-20e). In order to immobilize the graft at the recipient site the sutures must be placed in the periosteum or the adjacent attached gingiva. After suturing, pressure is exerted against the graft for 5 minutes in order to eliminate blood and exudate from between the graft and the recipient bed. The graft and the palatal wound are protected with a periodontal dressing. To retain the dressing in the palatal site, a stent usually has to be used.
* The sutures and periodontal dressing are removed after 1–2 weeks.
For description of the pedicle graft procedure, see "Root coverage procedures".
**Fig. 44-21** Schematic drawing illustrating different stages of healing following the "split-flap" (a) and "denudation" (b) techniques. Cells from the oral mucosa, bone, and periodontal ligament (arrows) participate in granulation tissue formation. Due to the difference in the degree of bone resorption (a-2, b-2), a larger area of the coronal portion of the wound is filled with granulation tissue from the periodontal ligament following "denudation" than following the "split-flap" technique. Since granulation tissue from the periodontal ligament possesses the ability to induce a keratinized epithelium, "denudation" usually results in a wider zone of keratinized tissue than is the case following the "split-flap" technique (a-3, b-3).
## Healing following gingival augmentation procedures
### Vestibular/gingival extension procedures
Since the specificity of the gingiva is determined by some inherent factor in the tissues, the post-operative results of vestibular extension procedures depend on the degree to which the various tissues contribute to the formation of granulation tissue in the wound area (Karring _et al_. 1975). Following the "denudation" or "split flap technique", the wound area is filled with granulation tissue derived from the periodontal ligament, the tissue of the bone marrow spaces, the retained periosteal connective tissue, and the surrounding gingiva and lining mucosa (Fig. 44-21). The degree of bone resorption induced by the surgical trauma influences the relative amount of granulation tissue that grows into the wound from these various tissue sources. The resorption of crestal bone exposes varying amounts of the periodontal ligament tissue in the marginal area allowing granulation tissue from the periodontal ligament to fill out the coronal portion of the wound. The greater the bone loss, the greater is the portion of the wound that becomes filled with granulation tissue from the periodontal ligament. This particular tissue possesses the capability to induce keratinization of the covering epithelium. This means that the widening of the keratinized tissue following "denudation" and "split flap" operations is achieved at the expense of a reduced bone height. The "denudation technique" usually results in more bone loss than the "split flap technique". Therefore, a greater amount of granulation tissue with the capability of inducing a keratinized epithelium develops in the marginal area following the "denudation technique" than following the "split flap technique". This is in accordance with the clinical observation that the "denudation technique" usually is superior to the "split flap technique" in increasing the width of keratinized tissue (Bohannan 1962a,b).
**Fig. 44-22** (a) Clinical photograph of the buccal aspect of a canine and a premolar following the removal of the entire zone of gingiva by a gingivectomy procedure. (b) The healing result 9 months after surgery shows the regain of keratinized tissue.
**Fig. 44-23** Clinical photographs of a tooth region subjected to excision of the entire zone of gingiva by a flap procedure. (a) The alveolar mucosa has been displaced coronally to achieve complete coverage of the surgically exposed alveolar bone. (b) Healing has resulted in the reformation of a narrow zone of gingiva on the buccal aspect of the teeth, 9 months post surgery.
In a clinical study by Wennström (1983) periodontal pockets were eliminated by the use of a "gingivectomy" or a "flap" procedure which both involved the complete removal of the keratinized tissue. In the "gingivectomy" procedure the wounded area was left to heal by second intention, while in the "flap" procedure the alveolar mucosa was repositioned to achieve complete coverage of the surgically exposed alveolar bone (Figs. 44-22a and 44-23a). Irrespective of the surgical technique used, healing resulted in the reformation of keratinized tissue, the width of which, however, was greater following the "gingivectomy" procedure than following the "flap" procedure (Figs. 44-22b and 44-23b). The gingiva was formed because granulation tissue from the periodontal ligament, with the capacity of inducing a keratinized epithelium, had proliferated coronally along the root surface. This granulation tissue formation was obviously favored by a more pronounced bone resorption during the healing following the "gingivectomy" procedure.
It can be concluded that the success or failure in extending the width of keratinized tissue by the "denudation" or "split flap" techniques rests with the origin of granulation tissue, which is related to the extent of bone loss induced by the surgical trauma. This in turn means that the result with respect to increasing the gingival width by methods involving periosteal exposure or denudation of the alveolar bone is unpredictable. The use of such methods is therefore not justified in periodontal therapy. The procedures discussed merely represent examples on how lack of knowledge about basic biologic principles may lead to the development of inappropriate therapeutic methods.
### Grafting procedures
Healing of free soft tissue grafts placed entirely on a connective tissue recipient bed were studied in monkeys by Oliver _et al_. (1968) and Nobuto _et al_. (1988). According to these authors healing can be divided into three phases (Fig. 44-24):
1. _The initial phase (from 0–3 days)_. During these first days of healing a thin layer of exudate is present between the graft and the recipient bed. During this period the grafted tissue survives with an avascular "plasmatic circulation" from the recipient bed. Therefore, it is essential for the survival of the graft that a close contact is established to the underlying recipient bed at the time of operation. A thick layer of exudate or a blood clot may hamper the "plasmatic circulation" and result in rejection of the graft. The epithelium of the free graft degenerates early in the initial healing phase, and subsequently it becomes desquamated. In placing a graft over a recession, part of the recipient bed will be the avascular root surface. Since the graft is dependent on the nature of its bed for diffusion of plasma and subsequent revascularization, the utilization of free grafts in the treatment of gingival recessions involves a great risk of failure. The area of the graft over the avascular root surface must receive nutrients from the connective tissue bed that surrounds the recession. Thus, the amount of tissue that can be maintained over the root surface is limited by the size of the avascular area.
2. _Revascularization phase (from 2–11 days)_. After 4–5 days of healing, anastomoses are established between the blood vessels of the recipient bed and those in the grafted tissue. Thus, the circulation of blood is re-established in the pre-existing blood vessels of the graft. The subsequent time period is characterized by capillary proliferation, which gradually results in a dense network of blood vessels in the graft. At the same time a fibrous union is established between the graft and the underlying connective tissue bed. The re-epithelialization of the graft occurs mainly by proliferation of epithelium from the adjacent tissues. If a free graft is placed over the denuded root surface, apical migration of epithelium along the tooth-facing surface of the graft may take place at this stage of healing.
3. _Tissue maturation phase (from 11–42 days)_. During this period the number of blood vessels in the transplant becomes gradually reduced, and after approximately 14 days the vascular system of the graft appears normal. Also, the epithelium gradually matures with the formation of a keratin layer during this stage of healing.
**Fig. 44-24** Schematic drawings illustrating healing of a free gingival graft placed entirely on a connective tissue recipient bed (a). A cross-section through the area is shown in (b). The framed areas (c) illustrate the three phases into which the healing process can be divided.
The establishment and maintenance of a "plasmatic circulation" between the recipient bed and the graft during the initial phase of healing is critical for the result of this kind of therapy. Therefore, in order to ensure ideal conditions for healing, blood between the graft and the recipient site must be removed by exerting pressure against the graft following suturing.
# Root coverage
The main indications for root coverage procedures are esthetic/cosmetic demands (Fig. 44-25) and root sensitivity. Changing the topography of the marginal soft tissue in order to facilitate plaque control is also a common indication for root coverage procedures (Fig. 44-26).
It should be recalled that the two major causative factors in the development of marginal tissue recession are trauma caused by toothbrushing and plaque-induced periodontal inflammation. The control of these factors will prevent further progression of the recession in most cases. This means that in tooth regions with a thin covering soft tissue, with or without an incipient recession, the patient should be encouraged to carry out effective but at the same time non-traumatic plaque-control measures. With respect to toothbrushing, the Bass method (Chapter 35) should be avoided and the patient should be instructed to use a technique creating as little apically directed pressure on the soft tissue margin as possible. A soft toothbrush should, of course, be used.
**Fig. 44-25** (a) A 25-year-old woman with esthetic concerns due to multiple soft tissue recessions in the maxilla and a high lip line. The gingiva is healthy and several of the exposed root surfaces show abrasion defects, indicating toothbrushing trauma as the causative factor for the development of the recessions. The brushing technique was altered and root coverage was achieved surgically. (b) The 2-year post-treatment view.
**Fig. 44-26** (a) A mandibular canine with a deep recession, which offers problems with respect to self-performed plaque control. (b) To facilitate plaque control the position of the soft tissue margin was altered surgically.
Miller (1985a) described a useful classification of recession defects taking into consideration the anticipated root coverage that is possible to obtain (Fig. 44-27):
* Class I: marginal tissue recession not extending to the mucogingival junction. No loss of interdental bone or soft tissue.
* Class II: marginal tissue recession extends to or beyond the mucogingival junction. No loss of interdental bone or soft tissue.
* Class III: marginal tissue recession extends to or beyond the mucogingival junction. Loss of interdental bone or soft tissue is apical to the CEJ, but coronal to the apical extent of the marginal tissue recession.
* Class IV: marginal tissue recession extends beyond the mucogingival junction. Loss of interdental bone extends to a level apical to the extent of the marginal tissue recession.
While complete root coverage can be achieved in class I and II defects, only partial coverage may be expected in class III. Class IV recession defects are not amenable to root coverage. Consequently, the critical clinical variable to assess in order to determine the possible outcome of a root coverage procedure is the level of periodontal tissue support at the proximal surfaces of the tooth.
Recession defects in the child need particular attention. In the growing child recession defects may be eliminated spontaneously, provided adequate plaque control is established and maintained (Fig. 44-28). Andlin-Sobocki _et al_. (1991) reported from a 3-year prospective study that 25 out of 35 recession defects with an initial depth of 0.5–3.0 mm healed spontaneously following improvement of the oral hygiene standard. Furthermore, all but three remaining recessions showed a decrease and no site demonstrated an increase in depth. Hence, reparative surgical treatment of soft tissue recessions in the developing dentition may not be necessary and should preferably be postponed until the growth is completed.
In an orthodontic case showing a recession defect and a thin (delicate) gingiva associated with a prominent, facially positioned tooth (Fig. 44-29a), surgical treatment for root coverage should be postponed until the orthodontic therapy is completed. The recession, as well as the dehiscence, will decrease as a consequence of the lingual movement of the tooth into a more proper position within the alveolar bone (Fig. 44-29b), and, if still indicated, the root coverage procedure will show higher predictability if performed after rather than before the tooth movement.
## Root coverage procedures
Surgical procedures used in the treatment of recession defects may basically be classified as (1) _pedicle soft tissue graft procedures_ and (2) _free soft tissue graft procedures_.
**Fig. 44-27** The Miller classification of recession defects (see text).
**Fig. 44-28** A 9-year-old boy showing recession at tooth 41. (a) The tooth is rotated and buccally positioned. The minimal amount of gingiva found apical to the recession shows pronounced signs of inflammation. The plaque control in the region was improved but surgical intervention was postponed. (b) The same tooth area at the age of 14 years. Note the spontaneous soft tissue repair that has taken place at tooth 41 as a consequence of the improved plaque control and the growth in the alveolar process.
The pedicle graft procedures are, depending on the direction of transfer, grouped as (1) _rotational flap procedures_ (e.g. laterally sliding flap, double papilla flap, oblique rotated flap) or (2) _advanced flap procedures_ (e.g. coronally repositioned flap, semilunar coronally repositioned flap). The latter procedures do not include rotation or lateral movement of the pedicle graft. Regenerative procedures are also included within the group of pedicle graft procedures, i.e. rotational and advanced flap procedures involving the placement of a barrier membrane between the graft and the root or the application of enamel matrix proteins.
The autogenous free soft tissue graft procedure may be performed as (1) an epithelialized graft or as (2) a subepithelial connective tissue graft (nonepithelialized graft), both usually taken from the area of the masticatory mucosa in the palate.
Factors, such as depth and width of recession, availability of donor tissue, presence of muscle attachments, and esthetics, have to be taken into consideration in the selection of treatment procedure.
**Fig. 44-29** Spontaneous repair of soft tissue recessions following orthodontic tooth movement. (a) A 22-year-old woman showing recessions and thin marginal tissues at prominently positioned teeth, particularly 23, 33, 41, and 43. (b) Following proper alignment of the teeth, the recessions have spontaneously been resolved and an increased gingival height can be noted.
**Fig. 44-30** (a) A canine showing pronounced recession and a composite resin restoration in the exposed root. Following removal of the restoration the exposed root was surgically covered with soft tissue (pedicle graft). (b) 2-year post-operative healing result.
### Treatment of the exposed root surface
Before root coverage is attempted the exposed portion of the root should be rendered free from bacterial plaque. Preferably, this is achieved by the use of a rubber cup and a polishing paste. Controlled clinical trials have shown no differences in terms of root coverage or residual probing depth between teeth that had been instrumented (root planed) or polished only (Oles _et al_. 1988; Pini Prato _et al_. 1999). Extensive root planing may therefore only be performed in situations where a reduced root prominence would be considered beneficial for graft survival or tissue regeneration, or if a shallow root caries lesion is diagnosed. The presence of a filling in the root does not preclude the possibility for root coverage (Fig. 44-30), but the filling should be removed before the root is covered with soft tissue.
The use of root surface demineralization agents has been advocated as important not only for the removal of the smear layer, but also to facilitate the formation of a new fibrous attachment through exposure of collagen fibrils of the dentine matrix and to allow subsequent interdigitation of these fibrils with those in the covering connective tissue. However, controlled clinical trials comparing the clinical outcome of root coverage procedures with and without root conditioning (Ibbott _et al_. 1985; Oles _et al_. 1985; Bertrand & Dunlap 1988; Laney _et al_. 1992; Bouchard _et al_. 1997; Caffesse _et al_. 2000) failed to demonstrate a beneficial effect from the use of acid root biomodification. Gottlow _et al_. (1986) evaluated the healing following treatment of localized gingival recessions with coronally positioned flaps and citric acid root biomodification in a controlled study in dogs. Histologic analysis after 3 months of healing disclosed no differences in the amount of root coverage or new connective tissue attachment between citric acid-treated sites and saline-treated control sites. Although root resorption was a common finding among the citric acid-treated teeth in this dog model, such a finding has not been reported to be common in humans. In conclusion, the literature clearly indicates that the inclusion of root conditioning does not improve the healing outcome of root coverage procedures.
### Pedicle soft tissue graft procedures
#### _Rotational flap procedures_
The use of a laterally repositioned flap to cover areas with localized recession was introduced by Grupe and Warren (1956). This technique, which was called _the laterally sliding flap_ operation, involved the reflection of a full-thickness flap in a donor area adjacent to the defect and the subsequent lateral displacement of this flap to cover the exposed root surface (Fig. 44-19). In order to reduce the risk for recession on the donor tooth, Grupe (1966) suggested that the marginal soft tissue should not be included in the flap. Staffileno (1964) and Pfeifer and Heller (1971) advocated the use of a split-thickness flap to minimize the potential risk for development of dehiscence at the donor tooth. Other modifications of the procedure presented are _the double papilla flap_ (Fig. 44-31) (Cohen & Ross 1968), _the oblique rotational flap_ (Pennel _et al_. 1965), _the rotation flap_ (Patur 1977), and _the transpositioned flap_ (Bahat _et al_. 1990).
The technique is as follows:
* The rotational flap procedure (Fig. 44-32) is initiated with the preparation of the recipient site. A reverse bevel incision is made all along the soft tissue margin of the defect (Fig. 44-32a). After removal of the dissected pocket epithelium, the exposed root surface is thoroughly curetted.
* At a distance of approximately 3 mm from the wound edge, which delineates the defect at the side opposite the donor area, a superficial incision is performed extending from the gingival margin to a level approximately 3 mm apical to the defect (Fig. 44-32b). Another superficial incision is placed horizontally from this incision to the opposite wound edge. The epithelium together with the outer portion of the connective tissue within the area delineated by these incisions and the wound edges is removed by sharp dissection (Fig. 44-32c). In this way a 3 mm wide recipient bed is created at the one side of the defect, as well as apical to the defect.
* A tissue flap to cover the recession is then dissected in the adjacent donor area. The preparation of this flap is initiated by a vertical superficial incision placed parallel to the wound edge of the recession and at a distance that exceeds the width of the recipient bed and the exposed root surface by approximately 3 mm (Fig. 44-32c). This incision is extended beyond the apical level of the recipient bed and is terminated within the lining mucosa with an oblique releasing incision directed towards the recession site. An incision connecting the vertical incision and the incision previously made around the recession is placed approximately 3 mm apical to the gingival margin of the donor site.
* A split-thickness flap is then prepared by sharp dissection within the area delineated by these incisions so that a layer of connective tissue is left covering the bone in the donor area when the flap is displaced laterally over the denuded root surface (Fig. 44-32d). It is important that the oblique releasing incision is made so far apically that the tissue flap can be placed on the recipient bed without being subjected to tearing forces when adjacent soft tissues are moved. The prepared tissue flap is rotated about 45º when sutured at the recipient bed (Fig. 44-32e).
* The suturing of the flap should secure a close adaptation of the pedicle graft to the underlying recipient bed. Pressure is applied against the flap for 2–3 minutes in order to further secure a good adaptation. To protect the surgical area during the initial phase of healing, a periodontal dressing may be applied. A light-cured dressing material, e.g. BarricaidTM (Dentsply International Inc., Milford, DE, USA), is preferably used since this can be applied without dislocating the flap and has, in addition, a favorable esthetic appearance.
* Following removal of the dressing and the sutures, usually after 10–14 days, the patient is instructed to avoid mechanical tooth cleaning for further 2 weeks, but to use twice daily rinsing with a chlorhexidine solution as a means of infection control.
**Fig. 44-31** Double papilla flap procedure. (a) Pre-treatment view of a maxillary canine with facial soft tissue recession. Using split incisions, soft tissue flaps are mobilized from both sides of the recession (b) and sutured together for coverage of the exposed root (c). The healing result 6-month post-operatively shows complete root coverage (d).
**Fig. 44-32** Rotational flap procedure. Schematic drawings illustrating the surgical technique in utilizing rotational pedicle grafts to cover localized recession defects (see the text for explanation).
#### _Advanced flaps_
Since the lining mucosa is elastic, a mucosal flap raised beyond the mucogingival junction can be stretched in coronal direction to cover exposed root surfaces (Harvey 1965; Sumner 1969; Brustein 1979; Allen & Miller 1989; Wennström & Zucchelli 1996; De Sanctis & Zucchelli 2007). The coronally advanced flap can be used for root coverage of a single tooth as well as multiple teeth, provided suitable donor tissue is available. In situations with only shallow recession defects and minimal probing pocket depth labially, the _semilunar coronally repositioned flap_ may offer an alternative approach (Harlan 1907; Tarnow 1986). For the treatment of an isolated deep gingival recession affecting a lower incisor, or the mesial root of the first maxillary molar, Zucchelli _et al_. (2004) suggested the use of a _laterally moved and coronally advanced flap_.
**Fig. 44-33** Coronally advanced flap procedure. Schematic drawings illustrating the surgical technique in utilizing coronally advanced pedicle grafts to cover localized recession defects (see the text for explanation).
The technique for a _coronally advanced flap procedure_ is as follows (Fig. 44-33):
* The coronally advanced flap procedure is initiated with the placement of two apically divergent vertical releasing incisions, extending from a point coronal to the CEJ at the mesial and distal line axis of the tooth and apically into the lining mucosa (Fig. 44-33a).
* A split-thickness flap is prepared by sharp dissection mesial and distal to the recession and connected with an intracrevicular incision. Apical to the receded soft tissue margin on the facial aspect of the tooth, a full-thickness flap is elevated to maintain maximal thickness of the tissue flap to be used for root coverage (Fig. 44-33b). Approximately 3 mm apical to the bone dehiscence, a horizontal incision is made through the periosteum, followed by blunt dissection into the vestibular lining mucosa to release muscle tension. The blunt dissection is extended buccally and laterally to such an extent that the mucosal graft is tension-free when positioned coronally at the level of the CEJ. The facial portion of the interdental papillae may be de-epithelialized to allow for a final placement of the flap margin coronal to the CEJ.
* The tissue flap is coronally advanced, adjusted for optimal fit to the prepared recipient bed, and secured at the level of the CEJ by suturing the flap to the connective tissue bed in the papilla regions (Fig. 44-33c). Additional lateral sutures are placed to carefully close the wound of the releasing incisions. Mechanical tooth cleaning is avoided during the first 3–4 weeks of healing (rinsing with a chlorhexidine solution is prescribed), and when re-instituted, instructions in the use of a toothbrushing technique creating minimal apically directed trauma to the soft tissue margin is given.
Figure 44-34 illustrates the treatment of a recession defect with the use of the coronally advanced flap procedure. To allow the positioning of the flap margin coronal to the CEJ at the buccal surface the interdental papillae have to be de-epithelialized before suturing (Fig. 44-35).
The technique for a _laterally moved, coronally advanced flap_ is as follows (Fig. 44-36):
* A vertical incision is made approximately 3 mm from the lateral edge of the recession defect at the side opposite the donor area, and parallel to the lateral border of the recession defect. The incision is extended from the level of the CEJ to a point approximately 3 mm apical to the defect. At the marginal end of the vertical incision (at the level of the CEJ), a horizontal incision is made towards the recession defect. A third incision is made parallel to the lateral soft tissue margin of the recession defect on the donor side, from the bottom of the defect to the apical termination of the vertical incision on the recipient side. The area delineated by these incisions is de-epithelialized. In this way a 3 mm wide recipient bed is created lateral as well as apical to the defect.
* A pedicle graft is harvested from the adjacent tooth site by the use of three incisions: (1) a beveled intrasulcular incision along the lateral edge of the recession defect, (2) a horizontal submarginal incision with a 6 mm greater length than the width of the recession defect, and (3) a beveled oblique vertical incision extending into the alveolar mucosa and parallel to the first incision. The outline of the submarginal incision should preserve 3 mm of marginal soft tissue at the donor tooth, and preferably provide at least 2 mm of keratinized tissue along the entire mesial–distal extension of the flap.
* The flap is mobilized as a split-thickness flap in its lateral parts, while the center part, which will be placed over the exposed root, is elevated as a full-thickness flap. Apical to the mucogingival line, the elevation is continued as split-thickness until it is possible to passively move the mucosal graft laterally to the recipient site.
* Blunt dissection is performed into the vestibular mucosa to release muscle tension to permit coronal advancement and passive adaptation of the flap to a level coronal to the CEJ.
* The facial surface of the interdental papillae is de-epithelized to create connective tissue beds to which the laterally moved, coronally advanced flap can be sutured.
* The suturing of the flap starts with the placement of two interrupted periosteal sutures in the most apical end of the vertical releasing incisions, and continues with a series of interrupted sutures, directed in a apical–coronal direction from the flap to the adjacent wound edge. A horizontal double mattress periosteal suture is placed apical to the vertical incisions to reduce lip tension on the root coverage portion of the flap. The coronal suture is a sling suture, which permits a precise adaptation of the flap against the root surface and the interdental connective tissue beds.
**Fig. 44-34** Coronally advanced flap procedure. (a) A deep and wide recession defect on a canine with a composite resin restoration in the exposed root portion. Before preparation of the pedicle graft, the root is polished with pumice and a rubber cup. (b) A split flap has been dissected mesial and distal to the root, and a full-thickness flap apical to the recession. Approximately 4 mm apical to the bone dehiscence the periosteum has been cut and a blunt dissection performed to facilitate the coronal positioning of the pedicle graft. (c) The composite resin restoration is removed. (d) Close suturing of the pedicle graft to cover the exposed root surface. (e) Healing outcome 1 year post-operatively.
**Fig. 44-35** Coronally advanced flap procedure. (a) A recession defect affecting a first premolar. (b) Schematic outline of the flap preparation. Blue line = amount (in mm) of intended coronal advancement of the flap; dotted red area = de-epithelialized papillae; Split = split-thickness elevation; Full = full-thickness elevation. (c) Flap elevated. The papilla areas are then deepithelialized to allow anchorage of the flap coronal to the cemento-enamel junction (CEJ). (d) The flap is advanced and anchored at a level coronal to the CEJ with a sling suture. (e) Clinical healing at 1 year.
Figure 44-37 illustrates the treatment of a recession defect at a maxillary molar with the use of the _laterally moved, coronally advanced flap_ procedure.
Zucchelli and De Sanctis (2000) described a flap design for the treatment of multiple recessions, which allows for optimal adaptation of the flap following its coronal advancement without placement of vertical releasing incisions. The technique for this _coronally advanced flap procedure for multiple recessions_ is as follows (Fig. 44-38):
**Fig. 44-36** The laterally moved, coronally advanced flap (see text for explanation). (a) A cenral insicor with recession defect. (b) Schematic outline of the preparation of the recipient site and the pedicle graft. Dotted pink area = receiving area for lateral flap; dotted red area = deepithelialized papillae; x = recession width at the level of the cemento-enamel junction; Split = split-thickness elevation; Full = full-thickness elevation. (c,d) The flap is transpositioned laterally and coronally, and secured in position by sutures. A horizontal double mattress suture is performed to reduce lip tension on the marginal portion of the flap. (e) Clinical healing at 1 year.
* Oblique submarginal incisions are made in the interdental areas and connected with intracrevicular incisions at the recession defects. The incisions are extended to include one tooth on each side of the teeth to be treated to facilitate coronal repositioning of the flap. The oblique incisions over the interdental areas are placed in such a manner that the "surgically created papillae" mesial to the midline of the surgical field are dislocated apically and distally, while the papillae of the flap distal to the midline are shifted in a more apical and mesial position (Fig. 44-37a).
* Starting at the oblique interdental incisions, a splitthickness flap is dissected (Fig. 44-38c). Apical to the level of the root exposures, a full-thickness flap is raised to provide maximum soft tissue thickness of the flap to be positioned coronally over the roots (Fig. 44-38d).
* At the most apical portion of the flap, the periosteum is incised and followed by dissection into the vestibular lining mucosa to eliminate all muscle tension. The mobilized flap should be able to passively reach a level coronal to the CEJ at each single tooth in the surgical field.
* The remaining facial portion of the interdental papillae is de-epithelialized to create connective tissue beds to which the flap can be sutured.
* Sutures are placed to accomplish a precise adaptation of the coronally advanced flap against the teeth and to the interdental connective tissue beds (Fig. 44-38e). In addition, a horizontal double mattress suture is placed to reduce lip tension on the marginal portion of the flap.
The technique for a semilunar coronally repositioned flap procedure is as follows (Fig. 44-39):
**Fig. 44-37** The laterally moved, coronally advanced flap. (a–c) A recession defect at a first maxillary molar treated because of root sensitivity (see text for explanation). (d) Clinical healing at 1 year.
* A semilunar incision is placed apical to the recession and at a distance from the soft tissue margin, which should be approximately 3 mm greater than the depth of the recession. The outline of the incision should be parallel to the curvature of the gingival margin (Fig. 44-39a). The incision is extended into the papilla region on each side of the tooth, but care should be taken to maintain a broad base of anchorage to secure a collateral blood supply to the pedicle graft.
* A split-thickness dissection of the facially located tissue is then made by an intracrevicular incision extending apically to the level of the semilunar incision (Fig. 44-39b). The mid-facial soft tissue graft is coronally repositioned to the level of the CEJ (Fig. 44-39c) and stabilized by light pressure for 5 minutes.
* No suturing is needed but a light-cured dressing may be applied for wound protection.
#### _Pedicle soft tissue graft procedures combined with a barrier membrane_
The use of a barrier membrane, according to the principles of guided tissue regeneration (GTR, see Chapter 25), in conjunction with pedicle soft tissue graft procedures was introduced as a treatment modality for root coverage by Pini Prato _et al_. (1992). In order create space for tissue formation between the facial root surface and the membrane Pini Prato _et al_. (1992) suggested that extensive root planing should be carried out to produce concave root morphology. Specially designed membranes for the treatment of recession type defects are available, such as non-absorbable titanium-reinforced expanded polytetrafluoroethylene (e-PTFE) membranes (Fig. 44-40c). In addition, a variety of bioabsorbable membranes are commercially available, but many of these may not be rigid enough for maintaining required space during healing.
The pedicle graft used in the GTR procedure is generated through the preparation of a coronally advanced flap (Fig. 44-40):
* Apically divergent vertical releasing incisions are made at the mesial and distal line axis of the tooth, extending from a point coronal to the CEJ and apically into the lining mucosa. A trapezium-shaped full-thickness flap is raised beyond the bone dehiscence (Fig. 44-40b). The periosteum at the base of the raised mucoperiosteal flap is incised, followed by a blunt supraperiosteal dissection to such a depth that the trapezoidal flap easily can be advanced coronally to the desired position. Depending on the degree of coronal repositioning, the facial portion of the interdental papillae may need to be de-epithelialized to prepare proper recipient beds for the pedicle graft.
* The root is extensively planed or ground to obtain a concave profile of the root surface, thereby providing space for tissue formation. If a titanium-reinforced membrane is used, the root profile may not need to be changed to establish the required space between the root and the membrane.
* The membrane barrier to be used is trimmed to cover the exposed root and approximately 3 mm of the bone lateral and apical to the dehiscence (Fig. 44-40c) and anchored to the tooth by a sling suture placed at the level of the CEJ.
* The mobilized flap is positioned coronally and secured by interdentally placed interrupted sutures (Fig. 44-40d). The membrane should be completely covered by the flap to reduce the risk for bacterial contamination during healing. Additional sutures are placed to close the lateral wound of the releasing incisions.
* The patient is advised to use a chlorhexidine mouth rinse for infection control and not to use any mechanical cleaning devices for at least 6 weeks in the tooth region subjected to surgery.
* The use of non-biodegradable membrane barriers requires a second surgery for membrane removal, usually after 5–6 weeks (Fig. 44-40e,f). A partial-thickness trapezoidal flap is raised to expose the membrane. Following its removal, the flap is repositioned at the level of the CEJ to completely cover the newly formed tissue. Mechanical plaque control is reinstituted 4 weeks after membrane removal.
**Fig. 44-38** Coronally advanced flap procedure for multiple recessions (see text for explanation). (a–e) The oblique incisions over the interdental areas are placed in such a manner that the "surgically created papillae" mesial to the midline of the surgical field are dislocated apically and distally, while the papillae of the flap distal to the midline are shifted in a more apical and mesial position. (f) The 1-year post-treatment view.
#### _Pedicle soft tissue graft procedures combined with enamel matrix proteins_
Abbas _et al_. (2003) described a surgical procedure for periodontal regenerative therapy of recession defects utilizing enamel matrix derivative bioactive material (Emdogain®):
* The surgical technique utilized is the coronally advanced flap as described above (Fig. 44-33). The interdental papillae should be de-epithelialized to allow for maximum coronal positioning of the tissue flap over the exposed root surface at suturing.
* Following preparation of the coronally advanced flap, the exposed root surface is conditioned with PrefGelTM (24% EDTA-gel, pH 6.7; Straumann Biologics, Switzerland) for 2 minutes to remove the smear layer.
* After thorough rinsing with sterile saline, the enamel matrix protein gel (Emdogain®, Straumann Biologics, Switzerland) is applied to the exposed root surface. The pedicle graft is advanced coronally and secured at a level slightly coronal to the CEJ by suturing the flap to the de-epithelialized papilla regions using non-irritating sutures. The vertical incisions are then closed with two to three sutures. Mechanical tooth cleaning is avoided during the first 3–4 weeks of healing (rinsing with a chlorhexidine solution is prescribed), and when re-instituted, a toothbrushing technique creating minimal apically directed trauma to the soft tissue margin is used.
**Fig. 44-39** Semilunar coronally repositioned flap procedure. Schematic drawings illustrating the surgical technique in utilizing coronally displaced pedicle grafts to cover shallow localized recession defects (see text for explanation).
### Free soft tissue graft procedures
A free soft tissue graft of masticatory mucosa is usually selected when there is no acceptable donor tissue present in the area adjacent to the recession defect or when a thicker marginal tissue is desirable. The procedure can be used for the treatment of a single tooth as well as for groups of teeth. The graft used may either be (1) an _epithelialized graft_ or (2) a _subepithelial connective tissue graft_ of palatal masticatory mucosa.
#### _Epithelialized soft tissue graft_
The epithelialized free soft tissue graft procedure can be performed either as a two-step surgical technique, where an epithelialized free soft tissue graft is placed apical to the recession and following healing is positioned coronally over the denuded root (Fig. 44-41) (Bernimoulin _et al_. 1975; Guinard & Caffesse 1978), or as a one-step technique by which the graft is placed directly over the root surface (Sullivan & Atkins 1968a,b; Miller 1982) (Fig. 44-42). The latter of the two techniques has been most commonly used.
The principles of utilizing free mucosal grafts were outlined by Sullivan and Atkins (1968a,b) and later modified by Miller (1982):
* Before any incisions the exposed root surface is carefully scaled and root planed (Fig. 44-42a). The convexity of the root may be reduced to minimize the mesio-distal avascular recipient bed.
* As in the treatment with pedicle grafts, the preparation of _the recipient bed_ is crucial for the success of free graft procedure. A 3–4 mm wide recipient connective tissue bed should be prepared apical and lateral to the recession defect (Fig. 44-42b). The area is demarcated by first placing a horizontal incision, at the level of the CEJ, in the interdental tissue on each side of the tooth to be treated. Subsequently, two vertical incisions, extending from the incision line placed in the interdental tissue to a level approximately 4–5 mm apical to the recession, are placed. A horizontal incision is then made connecting the two vertical incisions at their apical termination. Starting from an intracrevicular incision, a split incision is made to sharply dissect the epithelium and the outer portion of the connective tissue within the demarcated area.
* To ensure that a graft of sufficient size and proper contour is removed from the donor area, a foil template of the recipient site is prepared. This template is transferred to the donor site, the palatal mucosa in the region of the premolars, and the required size of the graft is outlined by a shallow incision. A graft with a thickness of 2–3 mm is then dissected from the donor area (Fig. 44-20c–d). It is advocated to place sutures in the graft before it is cut completely free from the donor area since this may facilitate its transfer to the recipient site. Following the removal of the graft, pressure is applied to the wound area for control of bleeding.
* The graft is immediately placed on the prepared recipient bed. In order to immobilize the graft at the recipient site, sutures must be anchored in the periosteum or in the adjacent attached gingiva. Adequate numbers of sutures are placed to secure close adaptation of the graft to the underlying connective tissue bed and root surface (Fig. 44-42c). Before the placement of a periodontal dressing, pressure is exerted against the graft for some minutes in order to eliminate blood from between the graft and the recipient bed. Following the control of bleeding, the wound in the donor area in the palate is covered by a periodontal dressing. An acrylic plate may be required to maintain the dressing in place during healing phase.
* The sutures and periodontal dressing are usually maintained for 2 weeks. The appearance of a grafted area after 3 months of healing is shown in Fig. 44-42d. A gingivoplasty may be indicated to achieve a satisfactory esthetic appearance of the grafted area (Fig. 44-42e,f).
**Fig. 44-40** Coronally advanced flap procedure combined with a titanium-reinforced non-biodegradable membrane barrier. (a–f) A recession defect at tooth 23 requiring treatment due to the patient's esthetic demands (see the text for explanation). (g) The 1-year post-operative result.
**Fig. 44-41** Two-stage epithelialized free soft tissue graft procedure. (a–c) An epithelialized soft tissue graft is placed apical to the recession and allowed to heal. At a second stage surgery, a coronally advanced flap procedure is performed to achieve coverage of the denuded root. (d) The 1-year post-operative result.
**Fig. 44-42** Epithelialized free soft tissue graft procedure. A recession defect at a mandibular central incisor treated with the free graft procedure (see the text for explanation).
#### _Connective tissue graft_
The techniques utilizing a subepithelial soft tissue graft, i.e. the connective tissue, involve the placement of the graft directly over the exposed root and the mobilization of a mucosal flap coronally (Fig. 44-43) or laterally (Fig. 44-44) for coverage of the graft (Langer & Langer 1985; Nelson 1987; Harris 1992; Bruno 1994; Zucchelli _et al_. 2003). An alternative technique is to place the base of the connective tissue graft within an "envelope" prepared by an undermining partial-thickness incision from the soft tissue margin, i.e. part of the graft will rest on the root surface coronal to the soft tissue margin (Fig. 44-45) (Raetzke 1985; Allen 1994). For the treatment of multiple adjacent recessions, a multi-envelope recipient bed ("tunnel") may be prepared (Zabalegui _et al_. 1999). The subepithelial connective tissue graft is harvested from the palate or the retromolar pad by the use of a "trap door" approach (Fig. 44-46). Compared to the epithelialized graft, the connective tissue graft is preferable due to a less invasive palatal wound and an improved esthetic result.
**Fig. 44-43** Free connective tissue graft combined with a coronally advanced flap procedure – single recession (see the text for explanation). (a) Deep gingival recession at a cuspid with minimal height of keratinized tissue apical to the root exposure. (b) The graft has been sutured to leave an area between the cemento-enamel junction and the graft available for the marginal keratinized tissue of the flap. (c) The flap has been advanced coronally and sutured. (d) Clinical healing at 1 year.
**Fig. 44-44** (a–e) Free connective tissue graft combined with a double papilla flap procedure. (f) The 1-year post-treatment result.
The technique for the _connective tissue graft combined with a coronally advanced flap_ is as follows (Fig. 44-43):
* The surgical technique utilized is the coronally advanced flap as described above, but with the difference that the flap is elevated entirely as a split-thickness flap. The interdental papillae should be de-epithelialized to allow for maximum coronal positioning of the tissue flap over the exposed root surface at suturing (Fig. 44-43b).
* A subepithelial connective tissue graft of masticatory mucosa is harvested on the palatal aspect of the maxillary premolars/first molar (or from the retromolar pad) by the use of a "trap door" approach (Fig. 44-46). Before incisions are placed, the available thickness of the mucosa is estimated by the use of the tip of the syringe. A horizontal incision, perpendicular to the underlying bone surface, is made approximately 3 mm apical to the soft tissue margin (Fig. 44-46a). The mesio-distal extension of the incision is determined by the graft size required, which is 6 mm longer than the width of the dehiscence measured at the level of the CEJ. To facilitate the removal of the graft, a vertical releasing incision may be made at the mesial termination of the primary incision. An incision is then placed from the line of the first incision and directed apically to perform a split incision of the palatal mucosa (Fig. 44-46b–f). A small periosteal elevator or scalpel is used to release the connective tissue graft from the bone.
* The graft is immediately transferred to the recipient site and positioned at a distance from the CEJ equal to the height of keratinized tissue originally present apical to the recession defect. The graft is secured in position with two double vertical mattress sutures to adjacent soft tissue lateral to the dehiscence (Fig. 44-43c). A sling suture is placed in the papilla regions to position the margin of the covering advanced flap about 1 mm coronal to the CEJ. Interrupted sutures are used to close the wound along the vertical incisions (Fig. 44-43d).
**Fig. 44-45** (a–c) Free connective tissue graft procedure – the "envelope technique" (see text for explanation). (d) The 1-year post-treatment result. (Courtesy of Dr. P. Cortellini, Italy.)
Figure 44-47 illustrates the procedure applied to a case with multiple recession sites.
_The "envelope" technique_ (Fig. 44-48) is as follows:
* With the use of the "envelope" technique the recipient site is prepared by first eliminating the sulcular epithelium by an internal beveled incision (Fig. 44-48a). Secondly, an "envelope" is prepared apically and laterally to the recession by split incisions (Fig. 44-48b). The depth of the preparation should be 3–5 mm in all directions. In an apical direction, the preparation of the site should extend beyond the mucogingival junction to facilitate the placement of the connective tissue graft and to allow for coronal advancement of the mucosal flap at time of suturing.
* A foil template may be used for the harvest of an appropriately sized connective tissue graft. The graft, which is obtained by the "trap door" approach described above (Fig. 44-46), is inserted into the prepared "envelope" and positioned to cover the exposed root surface (Fig. 44-48c–d).
* Sutures are placed to secure graft in position (Fig. 44-48d). A crossed sling suture may be placed to advance the mucosal flap coronally. Pressure is applied for 5 minutes to adapt the graft closely to the root surface and covering soft tissue.
Figure 44-45 shows the treatment of a recession defect with the "envelope" technique.
_The "tunnel" technique_ (Fig. 44-49) is as follows:
* In case multiple adjacent recessions are to be treated, "envelopes" are prepared for each tooth as described above. However, the lateral split incisions are extended so that the multi-envelopes are connected mesially and distally to form a mucosal tunnel. Care should be taken to avoid detachment of the papillae.
* The graft is gently positioned inside the tunnel and its mesial and distal extremities are fixed with two interrupted sutures. Sling sutures may be placed to advance the mucosal flap coronally over the exposed portions of the connective tissue graft. Pressure is applied for 5 minutes to closely adapt the graft to the root surface and covering soft tissue. Application of a periodontal dressing is often not required.
**Fig. 44-46** "Trap-door" technique for harvest of a free connective tissue graft (see text for explanation).
**Fig. 44-47** (a–d) Free connective tissue graft combined with a coronally advanced flap procedure – multiple recessions (see the text for explanation). (e) The 1-year post-treatment result.
**Fig. 44-48** Free connective tissue graft procedure – the "envelope technique". Schematic drawings illustrating the surgical technique (see the text for explanation).
**Fig. 44-49** Free connective tissue graft procedure – the "tunnel technique". Schematic drawings illustrating the surgical technique (see the text for explanation).
**Table 44-1** Summary of the data available in the literature on the amount of root coverage obtainable with various procedures (Miller class I–II defects)
## Clinical outcome of root coverage procedures
Independent of the modality of surgical procedure used to obtain soft tissue root coverage, shallow residual probing depths, gain in clinical attachment, and an increase in gingival height are the common characteristics of treatment outcome. Although the major indication for performing root coverage procedures is esthetic/cosmetic demands by the patient, few studies have included assessments of esthetics as an end-point of success. Instead, the common outcome variables used are the amount of root coverage achieved, expressed in percentage of the initial depth of the recession defect, and the proportion of treated sites showing complete root coverage.
### Root coverage
An overall comparison of the treatment outcome of various root coverage procedures is hampered by the fact that comparatively few studies have presented well documented clinical data and that there is substantial heterogeneity between studies (Roccuzzo _et al_. 2002; Oates _et al_. 2003). A summary with regard to the average amount of initial Miller class I–II recession defects that was successfully covered following treatment, based on the data published in a systematic review by Pagliaro _et al_. (2003) and relevant data from studies published between 2003 and 2006 (Table 44-1), shows that an average of 63–86% root coverage may be expected. However, the variability in the treatment outcome for the various procedures, both within and between studies, is large. This indicates that the procedures are operator sensitive and/or that various factors influencing the treatment outcome have not been adequately considered.
Complete coverage of the recession defect is the ultimate goal of the therapy. Table 44-2 summarizes data on the predictability of this event with the use of the various surgical procedures. The average percentage of complete root coverage following pedicle or free graft procedures varies between 28 and 72%, with large variability between studies irrespective of surgical procedure used. According to the systematic reviews by Roccuzzo _et al_. (2002) and Oates _et al_. (2003), coronally advanced flaps with connective tissue grafts result in significantly greater root coverage compared to guided tissue regeneration. The lower mean predictability of complete root coverage achieved with the GTR procedure has been associated with the problem of membrane exposure during healing (Trombelli _et al_. 1995), but whether a bioabsorbable or a non-biodegradable barrier membrane is used does not seem to affect the treatment outcome (Roccuzzo _et al_. 1996).
**Table 44-2** Summary of the data available in the literature on the predictability of complete root coverage following the use of various procedures (Miller class I–II defects)
#### _Factors influencing the degree of root coverage_
_Patient-related factors_. As with other surgical periodontal treatment procedures, poor oral hygiene is a factor that will negatively influence the success of root coverage procedures (Caffesse _et al_. 1987). Further, the predominant causative factor in the development of gingival recession is toothbrushing trauma, and hence this factor has to be corrected to secure an optimal outcome of any root coverage procedure. Treatment outcome in terms of root coverage is usually less favorable in smokers than in non-smokers (Trombelli & Scabbia 1997; Zucchelli _et al_. 1998; Martins _et al_. 2004; Erley _et al_. 2006; Silva _et al_. 2006), although some studies showed no differences (Tolmie _et al_. 1991; Harris 1994).
_Site related factors_. Among site-specific factors, the level of interdental periodontal support may be of greatest significance for the outcome of root coverage procedures. From a biological point of view complete root coverage is achievable in class I–II recession defects (Fig. 44-50), while when loss of connective tissue attachment also involves proximal tooth sites (class III–IV recession defects), only partial facial root coverage is obtainable (Miller 1985b) (Fig. 44-51).
An additional factor shown to influence the degree of attainable root coverage is the dimensions of the recession defect. Less favorable treatment outcome has been reported at sites with wide (>3 mm) and deep (≥5 mm) recessions (Holbrook & Ochsenbein 1983; Pini Prato _et al_. 1992; Trombelli _et al_. 1995). In a study comparing the treatment effect of coronally advanced flap and free connective tissue graft procedures, Wennström and Zucchelli (1996) reported that complete root coverage was observed in only 50% of the defects with an initial depth of ≥5 mm compared to 96% in shallower defects. Pini Prato _et al_. (1992) suggested, based on clinical observations in a controlled clinical trial, that a more favorable result with respect to root coverage might be obtained with the GTR procedure in sites with deep (≥5 mm) recession defects as compared to the coronally advanced flap. At the 18-month examination the average coverage was 77% with and 66% without the inclusion of a membrane barrier. However, data presented from recent systematic reviews and meta-analyses (Roccuzzo _et al_. 2002; Oates _et al_. 2003) showing that the predictability of root coverage is significantly reduced with the use of barrier membranes, limit the justification of using the GTR procedure in the treatment of recession defects. The pre-treatment gingival height apical to the recession defect is not correlated to the amount of root coverage obtained (Romanos _et al_. 1993; Harris 1994).
**Fig. 44-50** (a) Buccal recession defects but no loss of periodontal support at proximal surfaces. Complete root coverage can be achieved. (b) 3-year follow-up.
**Fig. 44-51** (a) A deep buccal recession at tooth 11. The tooth has loss of support at proximal sites (Miller class III) and complete root coverage is not achievable. Also neighboring teeth show recessions at all tooth surfaces. (b) 2-year healing result following attempted root coverage at the facial aspect of tooth 11. The coronal position of the soft tissue margin is defined by the extension of proximal loss of periodontal support.
_Technique-related factors_. Several technique-related factors may influence the treatment outcome of a pedicle graft procedure. In a systematic review including data from 15 studies (Hwang & Wang 2006) a positive correlation was demonstrated between the thickness of the tissue flap and recession reduction. For complete root coverage the critical threshold thickness was found to be about 1 mm. However, whether a full- or split-thickness pedicle graft is used for root coverage may not influence the treatment outcome (Espinel & Caffesse 1981).
Elimination of flap tension is considered an important factor for the outcome of the coronally advanced flap procedure. Pini Prato _et al_. (2000a) measured the tension in coronally advanced flaps to compare the amount of root coverage in sites with and without residual flap tension. At sites that had residual tension (mean 6.5 g) the root coverage amounted to 78% 3 months post-surgically and 18% of the treated sites showed complete root coverage. Sites without tension demonstrated mean root coverage of 87% and complete root coverage in 45% of the cases. Furthermore, a statistically significant negative association was shown between the magnitude of residual tension in the flap and the amount of recession reduction.
Although the connective tissue areas lateral to the recession defect are considered important for the retention of the advanced flap when positioned over the root surface, the dimension of the interdental papilla is not a prognostic factor for the clinical outcome of the root coverage procedure (Saletta _et al_. 2001). As can be expected, the position of the gingival margin relative to the CEJ after suturing affects the probability of complete root coverage following healing. Pini Prato _et al_. (2005) demonstrated that for 100% predictability of complete root coverage in the treatment of Miller class I recessions with a coronally advanced flap procedure the flap margin has to be positioned at least 2 mm coronal to the CEJ.
With regard to free graft procedures, the thickness of the graft is a factor influencing the success of treatment procedure (Borghetti & Gardella 1990). A thickness of the free graft of about 2 mm is recommended.
**Fig. 44-52** Increased dimension of keratinized tissue 1 year following root coverage with a coronally advanced flap procedure. Before (a) and 1-year post-operatively (b). Arrows indicate the position of the mucogingival line.
### Increased gingival height
An increased apico-coronal height of the gingiva is found following all procedures in which pedicle grafts of adjacent gingiva or free grafts from the palate have been placed over the recession defect. It is interesting to note, however, that an increased gingival height is also a common finding following a coronally advanced flap procedure only involving the existing gingiva apical to the recession (Fig. 44-52). This finding may be explained by several events taking place during the healing and maturation of the marginal tissue. Granulation tissue formation derived from the periodontal ligament tissue will form a connective tissue similar to the one of gingiva and with the potential to induce keratinization of the covering epithelium (Karring _et al_. 1971). A second factor to consider is the tendency of the mucogingival line to regain its "genetically" defined position following its coronal "dislocation" with the coronally advanced flap procedure used to achieve root coverage. Support for the concept that the mucogingival line will regain its original position over time is generated from a study by Ainamo _et al_. (1992). The authors performed an apically repositioned flap procedure in the lower anterior tooth region, which resulted in a 3 mm apical displacement of the mucogingival line. Re-examination after 18 years showed no differences in position of the mucogingival line between sites treated with the apically repositioned flap and contralateral control sites treated with a procedure not interfering with the mucogingival line, indicating that the mucogingival line had regained its original position.
## Soft tissue healing against the covered root surface
Treatment of gingival recessions by pedicle grafts or free grafts may be clinically successful, but does the treatment result in a healing characterized by the formation of a connective tissue attachment or an epithelial attachment? Independent of the quality of attachment formed, however, root coverage procedures evidently rarely result in the formation of a deep periodontal pocket.
### Healing of pedicle soft tissue grafts
In the areas surrounding the recession defect, i.e. where the recipient bed consists of bone covered by connective tissue, the pattern of healing is similar to that observed following a traditional flap operation. Cells and blood vessels from the recipient bed as well as from the tissue graft invade the fibrin layer, which gradually becomes replaced by connective tissue. After 1 week a fibrous reunion is already established between the graft and the underlying tissue.
Healing in the area where the pedicle graft is in contact with the denuded root surface was studied by Wilderman and Wentz (1965) in dogs. According to these authors the healing process can be divided into four different stages (Fig. 44-53):
1. _The adaptation stage (from 0–4 days)._ The laterally repositioned flap is separated from the exposed root surface by a thin fibrin layer. The epithelium covering the transplanted tissue flap starts to proliferate and reaches contact with the tooth surface at the coronal edge of the flap after a few days.
2. _The proliferation stage (from 4–21 days)._ In the early phase of this stage the fibrin layer between the root surface and the flap is invaded by connective tissue proliferating from the subsurface of the flap. In contrast to areas where healing occurs between two connective tissue surfaces, growth of connective tissue into the fibrin layer can only take place from one surface. After 6–10 days a layer of fibroblasts is seen in apposition to the root surface. These cells are believed to differentiate into cementoblasts at a later stage of healing. At the end of the proliferation stage, thin collagen fibers are formed adjacent to the root surface, but a fibrous union between the connective tissue and the root has not been observed. From the coronal edge of the wound, epithelium proliferates apically along the root surface. According to Wilder-man and Wentz (1965), the apical proliferation of epithelium may stop within the coronal half of the defect although further downgrowth of epithelium was also frequently observed.
3. _The attachment stage (from 27–28 days)._ During this stage of healing thin collagen fibers become inserted in a layer of new cementum formed at the root surface in the apical portion of the recession.
4. _The maturation stage._ This last stage of healing is characterized by continuous formation of collagen fibers. After 2–3 months bundles of collagen fibers insert into the cementum layer on the curetted root surface in the apical portion of the recession.
**Fig. 44-53** (a) Schematic drawing illustrating healing following treatment of a localized soft tissue recession with a pedicle graft. (b) Cross section through the area immediately after operation. The framed areas (1–4) illustrate the four stages into which the healing process can be divided. (c) Area after healing. Approximately 50% of the successfully covered defect may show new connective tissue attachment.
Results of experimental studies in monkeys and dogs on the healing characteristics of the periodontal wound have been interpreted to indicate that gingival connective tissue lacks the ability to form a new connective tissue attachment to the root, but may induce root resorption (see Chapter 25). This finding is of particular interest when considering the rationale for the treatment of recession defects by free or pedicle soft tissue grafts. Since, in these surgical procedures, gingival connective tissue is placed in contact with a denuded root surface, root resorption should be expected to occur. The reason why it is not a common complication following this type of treatment can be explained by two possible events. Either cells from the periodontal ligament form a fibrous attachment to the root surface or epithelial cells proliferate apically, forming a root-protective barrier (long junctional epithelium) towards the gingival connective tissue.
Histologic studies on whether it is the one or the other type of attachment that results following treatment of recessions with pedicle grafts indicate that new connective tissue attachment may be formed in part of the defect. In the study by Wilderman and Wentz (1965) a connective tissue attachment of around 2 mm and an epithelial attachment of the same height had formed in the soft tissue covered portion of the defect, i.e. about 50% of the successfully covered defect showed new connective tissue attachment. Gottlow _et al_. (1986) examined the result of healing following treatment of experimentally produced recession type defects with a coronally advanced flap in dogs (Fig. 44-54). The histologic analysis after 3 months of healing disclosed that, on average, 20% of the apico-coronal length of the original defect had been exposed due to recession during healing (i.e. about 80% root coverage was achieved), 40% was covered by epithelium and 40% demonstrated connective tissue attachment with cementum formation (Fig. 44-55). Determining factors for the type of healing result were the size and the shape of the defect. The possibility of achieving a new connective tissue attachment in the apical portion of the defect seemed to be considerably better in narrow recession defects than in wider ones, most likely because the periodontal ligament at the lateral parts of the defect will serve as a source of granulation tissue from which a new connective tissue attachment can develop.
**Fig. 44-54** Clinical photographs illustrating the treatment of an experimentally induced localized recession defect in a dog with a coronally displaced flap. (a) Presurgical appearance of the localized recession defect. (b) The site following flap closure of the defect and (c) following 3 months of healing.
**Fig. 44-55** Microphotograph of the healing following a coronally displaced flap in the dog as illustrated in Fig. 44-54. A new connective tissue attachment is formed and extends coronally from the apical border of the notch prepared at the bottom of the bone dehiscence (N1) to the apical termination of the epithelium (aJE) located within the notch indicating the presurgical level of the soft tissue margin (N2). B = alveolar bone crest.
Healing following pedicle graft procedures has also been histologically studied in monkeys (Caffesse _et al_. 1984; Gottlow _et al_. 1990), and in these studies 38–44% of the successfully covered recession defects demonstrated formation of new connective tissue attachment. The study by Gottlow _et al_. (1990) also showed that the use of a GTR membrane between the root surface and the pedicle graft generated significantly more new connective tissue attachment (79% of the covered part of the recession defect). A significantly increased amount of cementum formation with inserting collagen fibers was also demonstrated following the utilization of enamel matrix proteins in combination with a coronally advanced flap for treatment of experimentally produced recession defects in dogs (Sallum _et al_. 2004).
Some case reports with human block sections provide further evidence that new connective tissue attachment may be formed following pedicle graft procedures. Histologic evaluation of two teeth treated with a laterally positioned flap revealed that connective tissue attachment was re-established in the apical quarter of the successfully covered portion of the root (Sugarman 1969). Cortellini _et al_. (1993) examined histologically a tooth treated with the GTR procedure and showed that connective tissue faced 74% of the length of the recession defect. New cementum with inserting collagen fibers, i.e. new connective tissue attachment, covered 48% of the distance between the apical border of the root instrumentation and the soft tissue margin. In addition, histomorphometric assessments of a tooth treated with enamel matrix proteins revealed that new cementum covered 73% of the original defect (Heijl 1997).
### Healing of free soft tissue grafts
Survival of a free soft tissue graft placed over a denuded root surface depends on diffusion of plasma and subsequent revascularization from those parts of the graft that are resting on the connective tissue bed surrounding the dehiscence. The establishment of collateral circulation from adjacent vascular borders of the bed allows the healing phenomenon of "bridging" (Sullivan & Atkins 1968a). Hence, the amount of tissue that can be maintained over the root surface is limited by the size of the avascular area (Oliver _et al_. 1968; Sullivan & Atkins 1968). Other factors considered critical for the survival of the tissue graft placed over the root surface are that a sufficient vascular bed is prepared around the dehiscence and that a thick graft is used (Miller 1985b).
Another healing phenomenon frequently observed following free graft procedures is "creeping attachment", i.e. coronal migration of the soft tissue margin. This occurs as consequence of tissue maturation during a period of about 1 year post treatment.
There are few histologic evaluations of the nature of the attachment established to the root surface following the use of free grafts for root coverage. Sugarman (1969) reported from a histologic evaluation of a human tooth treated with a free soft tissue graft that new connective tissue attachment was found in the apical quarter of the successfully covered recession defect. Harris (1999) and Majzoub _et al_. (2001), each reporting the histologic outcome of free connective tissue grafts in two cases, found only minimal amounts of new cementum formation in the most apical part of the recession defect and that healing resulted in a long junctional epithelium occupying the interface between the covering soft tissue and the root. Carnio _et al_. (2002) performed histologic evaluation of four cases of root coverage with a connective tissue graft combined with application of enamel matrix proteins (Emdogain®). They reported that the healing resulted in connective tissue adhesion to the root surface and that the formation of new cementum was observed only in the most apical end of the grafted area.
Thus, the limited histologic information available from humans on the healing of free soft tissue grafts indicates that a healing pattern similar to the one discussed above following pedicle graft procedures may result, namely that connective tissue attachment may be established in the most apical and lateral parts of the recession defect, but that an epithelial attachment is formed along the major portion of the root. Further, the application of enamel matrix proteins may prevent the apical migration of the epithelium but may not favor the formation of a true connective tissue attachment between the free graft and the root surface.
# Interdental papilla reconstruction
There may be several reasons for loss of papilla height and the establishment of "black triangles" between teeth. The most common reason in the adult individual is loss of periodontal support due to plaque-associated lesions. However, abnormal tooth shape, improper contours of prosthetic restorations, and traumatic oral hygiene procedures may also negatively influence the outline of the interdental soft tissues.
Nordland and Tarnow (1998) proposed a classification system regarding the papillary height adjacent to natural teeth, based on three anatomic landmarks: the interdental contact point, the apical extent of the facial CEJ, and the coronal extent of the proximal CEJ (Fig. 44-56):
* _Normal_ : the interdental papilla occupies the entire embrasure space apical to the interdental contact point/area.
* _Class I_ : the tip of the interdental papilla is located between the interdental contact point and the level of the CEJ on the proximal surface of the tooth.
* _Class II_ : the tip of the interdental papilla is located at or apical to the level of the CEJ on the proximal surface of the tooth but coronal to the level of the CEJ mid-buccally.
* _Class III_ : the tip of the interdental papilla is located at or apical to the level of the CEJ mid-buccally.
In an observational study in humans, Tarnow _et al_. (1992) analyzed the correlation between the presence of interproximal papillae and the vertical distance between the contact point and the interproximal bone crest. When the vertical distance from the contact point to the crest of bone was 5 mm or less, the papilla was present almost 100% of the time, whereas if the distance was 6 mm or more only partial papilla fill of the embrasure between the teeth was most commonly found. Considering that a supracrestal connective tissue attachment zone of approximately 1 mm is normally found (Gargiulo 1961), the observation indicates that the biologic height of the interdental papilla may be limited to about 4 mm. This interpretation is supported by the observation that in interdental areas denuded following an apically repositioned flap procedure, an up-growth of around 4 mm of soft tissue had taken place 3 years after surgery (Van der Velden 1982). Hence, before attempts are made to surgically reconstruct an interdental papilla, it is important to carefully assess both (1) the vertical distance between the bone crest and the apical point of the contact area between the crowns and (2) the soft tissue height in the interdental area. If the distance bone crest–contact point is ≤5 mm and the papilla height is less than 4 mm, surgical intervention for increasing the volume of the papilla could be justified in order to solve the problem of an interdental "black triangle". However, if the contact point is located >5 mm from the bone crest, because of loss of periodontal support and/or an inappropriate interdental contact relationship between the crowns, means to lengthen the contact area apically between the teeth should be selected rather than a surgical attempt to improve the topography of the papilla.
**Fig. 44-56** Schematic drawing illustrating the classification system for papilla height (Nordland & Tarnow 1998).
**Fig. 44-57** Papilla reconstruction – pedicle graft technique. Schematic drawings illustrating the surgical technique (see the text for explanation).
If loss of papilla height is only caused by soft tissue damage from oral hygiene devices, interproximal hygiene procedures must be initially discontinued to allow soft tissue recovery and then successively modified in order to eliminate/minimize traumatic injury to the papillae.
## Surgical techniques
Several case reports have been published regarding surgical techniques for reconstruction of deficient papillae (e.g. Beagle 1992; Han & Takei 1996; Azzi _et al_. 1999). However, the predictability of the various procedures has not been documented and no data are available in the literature providing information on the long-term stability of surgically regained interdental papillae.
Beagle (1992) described a pedicle graft procedure utilizing the soft tissues palatal to the interdental area (Fig. 44-57). A split-thickness flap is dissected on the palatal aspect of the interdental area. The flap is elevated labially, folded, and sutured to create the new papilla at the facial part of the interdental area. A periodontal dressing is applied on the palatal aspect only, in order to support the papilla.
Han and Takei (1996) proposed an approach for papilla reconstruction ("semilunar coronally repositioned papilla") based on the use of a free connective tissue graft (Fig. 44-58). A semilunar incision is placed in the alveolar mucosa facial to the interdental area and a pouch-like preparation is performed into the interdental area. Intrasulcular incisions are made around the mesial and distal half of the two adjacent teeth to free the connective tissue from the root surfaces to allow coronal displacement of the gingival–papillary unit. A connective tissue graft, taken from the palate, is placed into the pouch to support the coronally positioned interdental tissue.
Azzi _et al_. (1999) described a technique in which an envelope-type flap is prepared for coverage of a connective tissue graft (Fig. 44-59). An intrasulcular incision is made at the tooth surfaces facing the interdental area to be reconstructed. Subsequently, an incision is placed across the facial aspect of the interdental area and an envelope-type split-thickness flap is elevated into the proximal site as well as apically to a level beyond the mucogingival line. A connective tissue graft is harvested from the tuberosity area, trimmed to adequate size and shape, and placed under the flaps in the interdental papilla area. The flaps are brought together and sutured with the connective tissue graft underneath.
# Crown-lengthening procedures
## Excessive gingival display
In most patients, the lower edge of the upper lip assumes a "gum-wing" profile which limits the amount of gingiva that is exposed when a person smiles. Patients who have a high lip line expose a broad zone of gingival tissue and may often express concern about their "gummy smile" (Fig. 44-60a). The form of the lips and the position of the lips during speech and smiling cannot be easily changed, but the dentist may, if necessary, modify/control the form of the teeth and interdental papillae as well as the position of the gingival margins and the incisal edges of the teeth. In other words, it is possible by a combination of periodontal and prosthetic treatment measures to improve dentofacial esthetics in this category of patient.
As a base for treatment decisions, a careful analysis of the dentofacial structures and how they may affect esthetics should be performed. It should include the following features:
* Facial symmetry
* Interpupillary line; even or uneven
* Smile line: low, median or high
* Dental midline in relation to facial midline
* Gingival display during speech and during broad, relaxed smile
* Harmony of gingival margins
* Location of gingival margins in relation to the CEJs
* Tooth size and proportions/harmony
* Incisal plane/occlusal plane.
**Fig. 44-58** Papilla reconstruction – the "semilunar coronally repositioned papilla" technique. (a–c) Schematic drawings illustrating the surgical technique (see the text for explanation). (d–f) Reconstruction of papillae distal to the central incisors with the use of the semilunar coronally repositioned papilla technique in a patient with a fixed bridge reconstruction.
**Fig. 44-59** Papilla reconstruction – "envelope" technique. Schematic drawings illustrating the surgical technique (see the text for explanation).
**Fig. 44-60** Crown-lengthening procedure. (a,b) Pretreatment views. The clinical crowns are considerably shorter than the anatomic crowns. The lateral incisors were congentially missing and orthodontic treatment had been carried out to move the posterior teeth anteriorly. The canine teeth in the position of the lateral incisors added to the esthetic disharmony. (c) A gingivectomy was performed to expose the anatomic crowns of the teeth. (d) One month post surgery. At this appointment, the canine and first premolar teeth were reshaped and bonded. (e) Tooth form and proportional balance were improved by bonding. (f) At 3 years post-treatment, the gingival tissues exhibited no rebound and retained the architectural form sculpted into the tissue at the time of the surgical procedure.
If excessive gingival exposure is due to insufficient length of the clinical crowns, a crown-lengthening procedure is indicated to reduce the amount of gingiva exposed, which in turn will favorably alter the shape and form of the anterior teeth. To select the proper treatment approach for crown lengthening, an analysis of the individual case with regard to crown–root–alveolar bone relationships should also be included.
In the young adult with an intact periodontium the gingival margin normally resides about 1 mm coronal to the CEJ. However, some patients may have a height of free gingiva that is greater than 1 mm, resulting in an disproportional appearance of the clinical crown. If such a patient complains about their "small front teeth" and the periodontium is of a thin biotype, full exposure of the anatomic crown can be accomplished by a gingivectomy/gingivoplasty procedure (Fig. 44-60).
**Fig. 44-61** (a) Pretreatment view. The patient disliked her "small front teeth" and diastema. Radiographs and probing indicated the gingival tissues were covering the cervical one third of the crowns. Crestal bone was thin and in normal relationship to the cemento-enamel junctions. The patient preferred "pink gums" if she could possibly have them. (b) A long externally beveled path of incision was used to accomplish the gingivectomy. (c) This view shows the color changes and pleasing architecture produced in the anterior gingiva at 2 months post surgery. The diastema was partially closed by direct bonding at this time. (d) Post-treatment view showing the enhancement of esthetic values for the patient.
An assessment should also be made regarding the amount and pattern of pigmentation existing within the gingival tissues, and the patient's desire to maintain or lessen the pigmentation contained within the tissues. The externally beveled path of incision that is usually employed in a gingivectomy procedure will remove the pigmentation and produce pink gingival tissue upon initial healing (Fig. 44-61). The surgically induced color change in the tissues comes about rapidly and markedly affects esthetic values. For this reason, an externally beveled gingivectomy procedure should not be terminated at the midline in patients that have pigmented gingival tissues. It should be extended across the midline to the premolar area to avoid a color mismatch in the esthetic zone of the anterior teeth. The color change may be permanent or the pigmentation may slowly return over a period of a year or more. Patients should be informed of the changes in tissue color that will occur and be allowed to make a choice as to the color of the tissue they will have post-surgically. If they wish to maintain their pigmentation, an internally beveled path of incision (internal gingivectomy) should be employed (Fig. 44-62).
If the periodontium is of the thick biotype and there is a bony ledge at the osseous crest, an apically positioned flap procedure (see Chapter 38) should be performed. This will allow for osseous recontouring (Fig. 44-63).
More extensive bone recontouring is required to solve esthetic problems found in patients who do indeed have short anatomic crowns in the anterior section of the dentition. In this category of patients, prosthetic measures must be used after resective periodontal therapy to increase the apico-coronal dimension of the crowns (Fig. 44-64). Patients who are candidates for this kind of resective therapy can be divided into two categories:
1. Subjects who have normal occlusal relationships and incisal guidance. In this category the incisal line of the front teeth must remain unaltered but the clinical crowns can be made longer by surgically exposing root structure and by locating the cervical margins of the restorations apical to the CEJ (Fig. 44-64).
2. Subjects who have abnormal occlusal relationships with excessive interocclusal space in the posterior dentition when the anterior teeth are in edge-to-edge contact. In this category of patients the length of the maxillary front teeth can be reduced without inducing posterior occlusal interferences. In addition, the marginal gingiva can be resected or relocated to an apical position before crown restorations are made.
**Fig. 44-62** (a) Pretreatment view. This patient disliked the looks of her "small front teeth"; she sought consultation to have her teeth made longer by crowning them. Probing and radiographs revealed normal osseous morphology and a wide zone of attached gingiva that covered the cervical one third of the incisors. It was explained to the patient that a surgical solution was preferred to restorative procedures to make her teeth longer. The patient made a request that the color of her gingival tissues remain unchanged. (b) An internally beveled path of incision was use to effect an "internal gingivectomy" to maintain the pigmentation in the tissues. This created mini flaps in the areas of the papillae. (c) 5-0 gut sutures were used to stabilize the papillae. (d). The crown lengthening that was achieved with maintenance of color harmony can be seen in this view at 3 months post surgery. (Courtesy of Dr. E. Saacks, Pennsylvania, USA.)
**Fig. 44-63** (a) Pretreatment view. The patient, a dentist, requested crown lengthening to lessen his "gummy smile" and give him a more masculine appearance. The patient had a wide zone of attached gingiva and thick crestal bone. Palpation indicated bony exostoses. (b) An apically positioned flap and osseous resective surgery, from second premolar to second premolar, were used to lengthen the teeth. The surgery was confined to the labial surfaces. This view shows one half of the surgery completed. (c) Vertical mattress sutures were utilized to hold the flap apically. (d) Three years post-treatment. Note that the gingival tissues retain the morphology created at the time of surgery.
**Fig. 44-64** Crown lengthening by surgical and prosthetic procedures. (a) Pretreatment view. The patient displayed "short front teeth" and a broad exposure of gum tissue. The full anatomic crown is exposed in this case and the surgically induced recession will expose root structure. (b) The patient had an unusually wide zone of attached gingiva. The gingival margins were positioned apically by making an internally beveled flap with a submarginal entrance incision as outlined in red ink. The crest of the bone was reduced in height. (c) After the tissues had matured following surgery, individual crowns were prepared for each of the anterior teeth. Crown lengthening was achieved and the patient no longer exposed a broad expanse of gum tissue. (Courtesy of Dr. D. Garber, Atlanta, GA, USA.)
In some individuals with an excessive display of gingiva, the size and shape of the teeth and the location of the gingival margins may be perfectly normal. The excessive display of gingiva in these cases is often caused by vertical maxillary excess and a long mid-face (Fig. 44-65). Periodontal crown lengthening procedures will not suffice to solve their problems, but rather the maxilla must be altered by a major maxillofacial surgical procedure. The risk–benefit and cost–benefit ratios must be thoroughly evaluated before recommending this type of surgical therapy to correct esthetic problems.
## Exposure of sound tooth structure
Crown-lengthening procedures may be required to solve problems such as (1) inadequate amount of tooth structure for proper restorative therapy, (2) subgingival location of fracture lines, and (3) subgingival location of carious lesions. The techniques used to accomplish crown lengthening include (1) apically positioned flap procedure including bone resection and (2) forced tooth eruption with or without fiberotomy.
**Fig. 44-65** This patient displays a large expanse of gingival tissue when smiling or speaking. The patient has a long midface and vertical maxillary excess. The gingival margins reside 1 mm coronal to the cemento-enamel junction and the anatomic and clinical crowns are approximately equal.
**Fig. 44-66** Surgical resective therapy for crown lengthening cannot be confined to the tooth in need of treatment. The principles of osseous resection require that bone be removed from the adjacent teeth to create a gradual rise and fall in the profile of the osseous crest. This causes a loss of attachment apparatus and recession of the adjacent teeth as well.
### Apically positioned flap with bone recontouring
The apically positioned flap technique with bone recontouring (resection) may be used to expose sound tooth structure. As a general rule, at least 4 mm of sound tooth structure must be exposed at the time of surgery. During healing the supracrestal soft tissues will proliferate coronally to cover 2–3 mm of the root (Herrero _et al_. 1995; Pontoriero & Carnevale 2001; Lanning _et al_. 2003), thereby leaving only 1–2 mm of supragingivally located sound tooth structure. When this technique is used for crown lengthening it must also be realized that gingival tissues have an inherent tendency to bridge abrupt changes in the contour of the bone crest. Thus, in order to retain the gingival margin at its new and more apical position, bone recontouring must be performed not only at the problem tooth but also at the adjacent teeth to gradually reduce the osseous profile (Fig. 44-66). Consequently, substantial amounts of attachment may have to be sacrificed when crown lengthening is accomplished with an apically positioned flap technique. It is also important to remember that, for esthetic reasons, symmetry of tooth length must be maintained between the right and left sides of the dental arch. This may, in some situations, call for the inclusion of even more teeth in the surgical procedure.
* _Indication:_ crown lengthening of multiple teeth in a quadrant or sextant of the dentition.
* _Contraindication:_ surgical crown lengthening of single teeth in the esthetic zone (Fig. 44-67).
* _Technique:_ The apically positioned flap technique and methods used for bone recontouring are discussed in Chapter 38.
### Forced tooth eruption
Orthodontic tooth movement can be used to erupt teeth in adults (Reitan 1967; Ingber 1974, 1976; Potashnick _et al_. 1982). If moderate eruptive forces are used, the entire attachment apparatus will move in unison with the tooth. The tooth must be extruded a distance equal to or slightly longer than the portion of sound tooth structure that will be exposed in the subsequent surgical treatment. After the tooth has reached the intended position and has been stabilized, a full-thickness flap is elevated and bone recontouring is performed to expose sound root structure. For esthetic reasons it is important that the bone and soft tissue levels at adjacent teeth remain unchanged.
**Fig. 44-67** A deformity which interfered with dentofacial esthetics was created at the right central incisor by using a surgical crown lengthening procedure at one single tooth to expose sound tooth structure. The soft tissues cannot follow the abrupt and steep changes in the osseous profile. The crown preparation invaded the zone of normal supracrestal connective tissue. This created a chronic periodontal pocket and adversely affected esthetics. (Courtesy of Dr. A. Winnick, Toronto, Canada.)
Forced tooth eruption can also be used to level and align gingival margins and the crowns of teeth to obtain esthetic harmony. Instead of using surgical procedures to position the gingival margins of unaffected normal teeth apically to the level of a tooth with recession or orthodontic malalignment, the tooth that is malpositioned or has sustained recession is erupted to the level of the normally positioned teeth. The entire attachment apparatus and dentogingival junction will follow the root of the tooth as it is moved coronally (Fig. 44-68).
**Fig. 44-68** Forced tooth eruption (show method) used to level gingival margins, treat recession on a single tooth and create esthetic harmony. (a,b) Recession on the left central incisor exposed the root surface darkened from root canal treatment. The uneven gingival margins and dark root surface detracted from an otherwise attractive smile. (c) A nitol wire with an offset bracket was used to slowly extrude the incisor. (d) Occlusal adjustment was done on the lingual side of the crown to create room for the tooth to erupt. This view, at 1 month in tooth movement, shows the gingival tissues moving with the root of the tooth. (e) Sufficient eruption had occurred by 3 months to level the gingival margins. The orthodontic brackets were used for temporary stabilization and a new crown was prepared. (f) The new crown masked the show-through of the dark root. The even gingival margins and beautiful crown created esthetic harmony. (Courtesy of Dr. J. Ingber, Philadelphia, PA, USA.)
* _Indication:_ crown lengthening at sites where removal of attachment and bone from adjacent teeth must be avoided. The forced eruption technique can also be used as a means of reducing pocket depth at sites with angular bony defects (Brown 1973; Ingber 1974, 1976). The angular bony defect at the problem tooth can be reduced while the attachment level at the adjacent tooth surface remains unchanged (Fig. 44-69).
* _Contraindication:_ the forced eruption technique requires the use of fixed orthodontic appliances. Thus, in patients who only have a few teeth remaining, an alternative approach for crown lengthening has to be selected.
* _Technique:_ orthodontic brackets are bonded to the problem tooth and to adjacent teeth and are combined with an arch wire. Another type of mechanical system can be utilized by placing a heavy gauge bar or wire in grooves prepared in the adjacent teeth and over the problem tooth. A power elastic is tied from the bracket to the arch wire (or the bar), which pulls the tooth coronally. If most of the crown structure is lost, root canal therapy is required. A post placed in the root canal is fitted with a power elastic, which is also joined with the arch wire. The direction of the tooth movement must be carefully checked to ensure that the problem tooth is not tilted or moved toward the adjacent tooth surfaces.
**Fig. 44-69** Slow tooth eruption procedure used to level cemento-enamel junctions and angular bone crests. (a) Pretreatment radiograph. (b) A nitol wire was used to erupt the molar. (c) The crown was shortened over a period of 4 months by selective grinding. (d) Radiograph taken 8 months after the start of treatment. The angular bone defects were leveled.
### Forced tooth eruption with fiberotomy
If fiberotomy is performed during the forced tooth eruption procedure the crestal bone and the gingival margin are retained at their pre-treatment locations, and the tooth–gingiva interface at adjacent teeth is unaltered. Fiberotomy is performed by the use of a scalpel at 7–10-day intervals during the forced eruption to sever the supracrestal connective tissue fibers, thereby preventing the crestal bone from following the root in coronal direction. In the case presented in Fig. 44-70, fiberotomy was performed only at the mesial half of the root. Radiographs obtained after 9 weeks demonstrate that crestal bone migration has occurred at the distal but not at the mesial surface of the erupted tooth (Pontoriero _et al_. 1987).
* _Indication:_ crown lengthening at sites where it is important to maintain the location of the gingival margin at adjacent teeth unchanged.
* _Contraindication:_ fiberotomy should not be used at teeth associated with angular bone defects.
* _Technique:_ similar to the technique described for the forced tooth eruption procedure. Fiberotomy is performed once every 7–10 days during the phase of forced tooth eruption.
## Ectopic tooth eruption
Surgical intervention is often indicated for teeth erupting ectopically, i.e. with an eruption position facial to the alveolar ridge (Fig. 44-71). To create a satisfactory width of the gingiva for the permanent tooth, the tissue entrapped between the erupting tooth and the deciduous tooth is usually utilized as donor tissue (Agudio _et al_. 1985; Pini Prato _et al_. 2000b).
Three different techniques have been described for the interceptive mucogingival treatment of buccally erupting teeth, depending on the distance from the donor site (entrapped gingiva) to the recipient site (area located facially–apically to the erupting permanent tooth) (Agudio _et al_. 1985; Pini Prato _et al_. 2000b):
* _Double pedicle graft_ (Fig. 44-72). This flap procedure is indicated when the permanent tooth erupts within the zone of keratinized tissue but close to the mucogingival junction. An intrasulcular incision is performed at the deciduous tooth and extended laterally to the gingival crevice of the adjacent teeth and apically to the erupting permanent tooth. By mobilization of the flap apical to the mucogingival line, the entrapped gingiva can be elevated and transposed for positioning apically to the erupting tooth. Sutures may be placed to secure the position of the gingival tissue facial to the erupting tooth.
* _Apically positioned flap_ (Fig. 44-73). When the permanent tooth is erupting apical to the mucogingival junction, vertical releasing incisions have to be placed to allow for apical positioning of the keratinized tissue. Two lateral releasing incisions are made and extended apically beyond the mucogingival junction. An intrasulcular incision is performed at the deciduous tooth and a partial-thickness flap is elevated beyond the ectopically erupting tooth. The mobilized gingival flap is moved apical to the erupting tooth and secured in position by sutures.
* _Free gingival graft_ (Fig. 44-74). If the tooth is erupting within the alveolar mucosa distant to the mucogingival junction, a free gingival graft procedure may be selected. The entrapped gingiva is removed by a split incision and used as an epithelialized connective tissue graft. The free gingival graft is placed at a prepared recipient site facial/apical of the erupting tooth. Careful suturing is performed to secure close adaptation of the graft to the underlying connective tissue bed.
**Fig. 44-70** Rapid tooth eruption procedure in conjunction with fiberotomy procedure. (a) Buccal view, the fracture on the first premolar extended subgingivally. (b) Soft tooth structure was excavated and a twisted wire with an occlusal hook was temporarily cemented in the root canal. A bar was placed into the amalgam restoration on the premolar and bonded to the lingual surface of the canine. (c,d) Sulcular fiber resection was performed at the mesial half of the tooth to the level of the bone crest. The distal half remained as a control surface. The fiber resection was repeated once a week during the 3-week eruption phase. (e) The tooth was stabilized for 6 weeks, and at that time a full-thickness flap was raised. The bone crest had a "positive" angulation at the distal surface and remained unchanged at the "test" mesial surface. Osseous resection was used to level the bony septum on the distal surface. (f) Ample crown lengthening was obtained and the gingival margins healed to their former shape and location. (g) Pretreatment radiograph enlarged to show the normal shape of the crests of the interdental septae. (h) Enlargement of the post-eruption radiograph (3 weeks of rapid eruption and 6 weeks of stabilization) to show the "positive" angular crest on the "control" distal side and the unchanged crest on the mesial "test" side. (Courtesy of Dr. R. Pontoriero, Milan, Italy.)
**Fig. 44-71** Ectopic tooth eruption. The permanent tooth is erupting close to the mucogingival junction.
**Fig. 44-72** Ectopically erupting tooth – double pedicle graft. Schematic drawings illustrating the surgical technique (see text for explanation).
**Fig. 44-73** Ectopically erupting tooth – apically positioned flap. Schematic drawings illustrating the surgical technique (see text for explanation).
All the described procedures have been proven to be effective in establishing a facial zone of gingival following the alignment of teeth erupting in an ectopic position (Pino Prato _et al_. 2000b,c).
**Fig. 44-74** Ectopically erupting tooth – free gingival graft. Schematic drawings illustrating the surgical technique (see text for explanation).
# The deformed edentulous ridge
A partially edentulous ridge may retain the general shape of the alveolar process. Such a ridge is traditionally referred to as a normal ridge. Even though this normal ridge has retained the bucco-lingual and apico-coronal dimensions of the alveolar process, it is not normal in many other respects; the eminences that existed in the bone over the roots are no longer present, and the interdental papillae are missing.
The smooth contours of the normal ridge create problems for the restorative dentist. In a fixed bridge the pontics (1) frequently give the impression that they rest on the top of the ridge rather than emerge from within the alveolar process, (2) lack a root eminence, and (3) lack marginal gingivae and interdental papillae. Dark triangles, which almost always interfere with dentofacial esthetics, are present in the embrasure area between the pontics and between the abutments and the pontics. In other words, in the presence of a normal ridge it may be difficult or impossible to produce a fixed prosthesis which truly restores the esthetics and function of the natural dentition.
## Prevention of soft tissue collapse following tooth extraction
Following extraction of a tooth, the topography of the surrounding soft and hard tissues will be altered. The soft tissue margin will collapse and the height of the adjacent papillae will be reduced. This soft tissue collapse may be prevented by immediate post-extraction placement of an ovate pontic to support the soft tissues. Figure 44-75 illustrates such a situation where a central incisor had to be extracted due to root fracture. With the immediate placement of the pontic the facial soft tissue margin and the papillae were maintained almost unchanged following the healing of the extraction site. Also, in situations where several adjacent teeth have to be extracted, insertion of ovate pontics may facilitate the preservation of the outline of the soft tissue ridge (Fig. 44-76).
Prevention of ridge collapse due to alveolar bone resorption following tooth extractions must also be considered. Borghetti and Laborde (1996) recommended means for prevention of bone ridge collapse after tooth extraction in any case of:
1. Fracture of the vestibular osseous plate during tooth extraction or due to trauma
2. Resorption of the vestibular osseous plate
3. Presence of a thin vestibular bone plate.
**Fig. 44-75** (a) A central incisor that cannot be maintained because of root fracture which also caused pronounced periodontal destruction. (b) Immediately following tooth extraction, an ovate pontic was inserted to support the facial and proximal soft tissues. (c,d) Radiographic and clinical view of the area 6 weeks after tooth extraction. (e) Follow-up 1 year after the placement of permanent prosthetic reconstruction (single implant).
**Fig. 44-76** (a) A 26-year-old female patient who had a trauma against the maxillary central incisors. Due to root fracture and endodontic complications both central incisors had to be extracted. (b) A Rochette bridge with ovate pontics was fabricated as a temporary replacement for the incisors. (c) Clinical view if the front tooth region 8 weeks after tooth extraction and placement of the resin bonded temporary bridge.
Among procedures proposed for prevention of ridge collapse in conjunction with tooth extractions are (1) flap elevation for complete soft tissue closure of the extraction sites (Borghetti & Glise 2000), (2) placement of connective tissue grafts over the extraction sites (Nevins & Mellonig 1998), (3) placement of bone grafts (Becker _et al_. 1994), and (4) utilization of barrier membranes (Lekovic _et al_. 1997). Procedures for preservation of the bone dimensions following tooth extraction are discussed in Chapter 49.
## Correction of ridge defects by the use of soft tissue grafts
A deformed ridge may result from tooth extractions, advanced periodontal disease, abscess formations, etc. The deformity that exists in the ridge is directly related to the volume of root structure and associated bone that is missing or has been destroyed. According to Siebert (1983) ridge defects can be divided into three classes:
* Class I: loss of bucco-lingual width but normal apico-coronal height
* Class II: loss of apico-coronal height but normal bucco-lingual width
* Class III: a combination of loss of both height and width of the ridge.
Ridge augmentation procedures should be preceded by careful surgical–prosthetic treatment planning with joint consultations involving the surgeon and the restorative dentist in order to attain an optimal esthetic result. The following factors should be determined prior to the initiation of therapy:
* Volume of tissue required to eliminate the ridge deformity
* Type of graft procedure to be used
* Timing of various treatment procedures
* Design of the provisional restoration
* Potential problems with tissue discolorations and matching tissue color.
Ideally, a provisional restoration should be made prior to surgery. The shape of the teeth in the provisional restoration, the axial inclination and emergence profile of the teeth, and embrasure form should be an exact prototype of the final prosthesis that is to be constructed. It is the task of clinician performing the surgery to augment the tissues to meet the provisional prosthesis in the most exact manner possible. If a gingival flange of pink-colored acrylic is used around single or multiple pontics on a temporary removable partial denture, the flange must be cut away in order to avoid pressure on the graft and give the tissues room to swell during the immediate post-surgical phase of healing. The soft tissue at the surgically treated recipient site for a graft will undergo considerable swelling during the early phase of healing and the tissues will conform to the tissue-facing surfaces of the bridge or partial denture. The prosthesis is thus used to help in shaping the outline of the augmented ridge to the desired form. The location and shape of interproximal embrasure areas in the provisional bridge will determine where the "papillae" created in the ridge will be located.
## Surgical procedures for ridge augmentation
Numerous surgical graft and implant procedures attempting to reconstruct a partially edentulous ridge or ridge defect have been described in the literature over the years. The procedures may be grouped according to the means used for ridge augmentation as (1) soft tissue augmentation procedures and (2) hard tissue augmentation procedures. In this chapter only soft tissue augmentation procedures will be addressed, while hard tissue augmentation procedures are covered in Chapter 49. To illustrate various approaches for utilization of soft tissues for ridge augmentation, the following procedures will be discussed:
* Pedicle graft procedure:
* Roll flap procedure
* Free graft procedures:
* Pouch graft procedure
* Interpositional graft procedure
* Onlay graft procedure.
Studer _et al_. (1997) proposed the use of the pedicle graft procedure for correction of a single-tooth ridge defect with minor horizontal and vertical loss, whereas submerged free connective tissue graft procedures should be selected for larger defects. The onlay full-thickness graft procedure is indicated primarily for ridge augmentation in the presence of additional mucogingival problems such as insufficient gingival width, high frenum, gingival scarring, or tattoo. These recommendations were based on short-term evaluation of the obtained volumetric increase of the edentulous ridge following various augmentation procedures, which demonstrated superior results with the use of submerged connective tissue grafts compared to the use of full-thickness grafts (Studer _et al_. 2000).
### The "roll flap procedure"
#### _Surgical concept_
The "roll flap procedure" (Abrams 1980) involves the preparation of a de-epithelialized connective tissue pedicle graft, which is subsequently placed in a subepithelial pouch (Fig. 44-77). This procedure is used in the treatment of small to moderate class I ridge defects, primarily in cases with a single-tooth space. The technique enables the surgeon to augment tissue apically and labially to the cervical area of a pontic and to give the recipient site the appearance of a normal tooth–gingiva interface. Hence, a buccolingual ridge concavity can be converted into a ridge convexity resembling the eminence produced by the roots of the adjacent teeth (Fig. 44-78).
#### _Technique_
A rectangular pedicle of connective tissue is prepared on the palatal side of the defect (Fig. 44-77). The length of the pedicle must match the amount of apico-coronal augmentation that is planned. This, in turn, is related to the amount of root eminence that exists on either side of the defect. If a two- or three-tooth pontic space is treated with the roll technique, two or three separate pedicles are raised. Each of these pedicles will form a new "root–cervical margin".
**Fig. 44-77** Sequence of steps in the "roll flap procedure". (a) Cross section of the residual edentulous ridge prior to treatment. (b) The removal of the epithelium. (c) The elevation of the pedicle. (d) The pouch is created. (e) Sutures are placed at the mucogingival junction to catch the tip of the pedicle flap and pull it into place in the pouch. (f) The flap is secured. A convexity in the ridge was created.
**Fig. 44-78** "Roll flap procedure". (a) Pretreatment view of a class I ridge defect in the area of the right lateral incisor. Note the marked concavity in the ridge. (b) This view shows the surgical site 1 week after surgery and prior to the removal of the sutures. (c) The tissue surface of the pontic was relined with autopolymerizing resin. (d) Final prosthesis in place. Note the illusion of a root eminence and a free gingival margin apical to the lateral incisor pontic tooth. (Courtesy of Dr. L. Abrams, Philadelphia, PA, USA.)
The epithelium on the palatal surface of the donor site is first removed. A maximum amount of supraperiosteal connective tissue is raised from the palate using sharp dissection. The void that is produced at the donor site will gradually fill in with granulation tissue. Caution must be exercised in dissection of the pedicle flap so that tissue perforation is avoided when the plane of dissection approaches the facial (labial) surface. A pouch is made in the supraperiosteal connective tissue at the facial (labial) surface of the ridge. In order to preserve as much connective tissue and blood supply as possible at the recipient site, the dissection must be made as close as possible to the periosteum of the facial bone.
The pedicle is tucked into the pouch as a try-in procedure. Adjustment of pedicle size should now be made. Once the pedicle fits as desired, it is made ready for the stabilizing suture. The suturing scheme is illustrated in Fig. 44-77. The suture must be positioned close to the mucobuccal fold. This enables the surgeon to pull the pedicle to the apical portion of the pouch. The suture should not be tied tightly, since it only serves as a positioning and stabilizing device. The use of a resorbable suture material is recommended.
#### _Adjustment of pontic contours_
Measures used to adapt the tissue surface of the pontic to the contour of the surgically treated ridge are common to all soft tissue ridge augmentation procedures in patients with fixed bridgework. A light contact is maintained between the pedicle graft and the tissue surface of the pontics. The post-operative swelling will cause the tissue to conform to the shape of the pontic. This enables the clinician to shape the soft tissue into a form that is intended for the augmented site. Autopolymerizing resin is added to the tissue surface of the pontics and is allowed to cure until the resin reaches a dough-like state. The bridge is then seated and pressed into the grafted site. When the resin has set to a firm consistency, the bridge is removed and placed in hot water to complete the process of polymerization (Fig. 44-78). The tissue surface of the pontics and the embrasure areas are then carved to the shape that is intended for the final bridge. The surface of the pontic is polished and the bridge put in place using appropriate temporary cement.
#### _Post-operative care_
A periodontal dressing is placed over the donor site. No dressing should be placed over the facial (labial) surface of the grafted area where swelling will occur. The dressing at the donor site should be changed at weekly intervals and maintained until wound healing has progressed to a point where the tissue is no longer tender to touch.
### Pouch graft procedures
#### _Surgical concept_
A subepithelial pouch is prepared in the area of the ridge deformity, into which a free graft of connective tissue is placed and molded to create the desired contour of the ridge. The entrance incision and the plane of dissection may be made in different ways (Kaldahl _et al_. 1982; Seibert 1983; Allen _et al_. 1985; Miller 1986; Cohen 1994):
* Coronal–apically: the horizontal incision is made on the palatal or lingual side of the defect and the plane of dissection carried in an apical direction (Fig. 44-79).
* Apical–coronally: the horizontal incision is made high in the vestibule near the mucobuccal fold and the plane of dissection is carried coronally to the crest of the ridge.
* Laterally: one or two vertical entrance incisions are started from either side of the defect (Fig. 44-80). The plane of dissection is made laterally across the span of the deformity.
#### _Indication_
The technique is used to correct class I defects. Patients with large-volume defects may have thin palatal tissues, which are insufficient to provide the volume of the donor tissue necessary to fill the deformity. In such cases, various procedures for hard tissue augmentation may be selected (see Chapter 49).
#### _Technique_
The pouch is prepared as described above. The mesio-distal entrance incision for the edge of the pouch should be made with a long bevel and must be started well to the palatal (lingual) side of the defect (Fig 44-79). After the pouch has been filled with graft, the facial tissue will be stretched. The long bevel of the entrance incision permits the palatal edge of the flap to slide toward the facial surface without opening a gap at the incision line. Sometimes vertical releasing incisions have to be made lateral to the border of the defect.
**Fig. 44-79** Sequence of steps in the "pouch graft procedure" utilizing a free graft of connective tissue (CT) to expand the ridge. (a) Cross section of the residual edentulous ridge prior to treatment. (b) The horizontal incision to create the pouch is made well to the palatal side of the defect. The incision is started partial-thickness to leave CT to suture to when the flap is closed. The dissection is made supraperiosteal on the labial side of the ridge to (1) ensure an adequate blood supply within the pedicle and (2) permit the flap to expand labially or labially and coronally free of tension. (c,d) The CT graft can be placed as shown for maximal bucco-lingual augmentation. (e,f) If vertical augmentation is desired, the CT implant can be placed closer to the crest of the ridge. As is shown in (d) and (f), the more the flap is stretched or extended to gain augmentation, the more difficult it is to gain primary flap closure.
**Fig. 44-80** Pouch graft procedure. (a) Pretreatment view of a class I ridge deformity. (b) Placement of the free connective tissue graft in a tunnel prepared by split incision between the two vertical incisions. The graft is brought into position by the use of a suture placed in one end of the free graft. (c) Four months post treatment showing restored facial dimension of the edentulous ridge.
A suitable donor site is selected in the palate, the tuberosity area, or in an edentulous area and a free graft of connective tissue is excised by the use of a "trap-door" approach. The graft is immediately transferred to the recipient site and properly positioned. The palatal entrance incision and the releasing incisions are closed with sutures.
### Interpositional graft procedure
#### _Surgical concept_
Interpositional grafts are not completely submerged and covered in the manner that a subepithelial connective tissue graft is placed (Fig. 44-81) (Seibert 1991, 1993a,b). Therefore, there is no need to remove the epithelium from the surface of the donor tissue. If augmentation is required not only in the buccolingual but also in the apico-coronal direction, a portion of the graft must be positioned above the surface of the tissue surrounding the recipient site (Fig. 44-82). A certain amount of the grafted connective tissue will thus be exposed in the oral cavity.
#### _Indications_
Interpositional graft procedures are used to correct class I as well as small and moderate class II defects.
#### _Technique_
An envelope flap, or a split-thickness flap with releasing incisions, is prepared at the facial surface of the defect area. The provisional bridge is placed in position to serve as a reference when estimates are made regarding the amount of tissue that has to be grafted to fill the defect. A periodontal probe may be used to measure the length, width and depth of the void of the pouch. A suitable donor site is selected in the palate or the tuberosity area, and a free graft of epithelium–connective tissue is excised (Fig. 44-81).
The donor tissue is transferred to the recipient site and placed in position. If gain in ridge height is not intended, the epithelial surface for the graft is placed flush with the surrounding epithelium. The graft is sutured along its entire circumference to the tissues of the recipient site. The provisional bridge is placed in position and the pontics are trimmed and adjusted as discussed above. No dressing is used to cover the recipient site.
If gain also in ridge height is intended, a certain portion of the graft has to be kept above the surface of the surrounding tissue (Fig. 44-82d). Granulation tissue formed during healing will eventually make the border between the graft and the adjacent tissue smooth and properly epithelialized. The swelling, which occurs post-operatively, will assist in sculpting the contour of the ridge.
**Fig. 44-81** Schematic illustrations of the interpositional graft procedure. (a) Cross section of class I ridge defect. (b) A labial flap (partial-thickness dissection preferred) is used to create the pouch. (c) A wedge-shaped graft is removed from the palate. (d) The epithelial surface of the graft is placed flush with the surface of the tissue surrounding the pouch and sutured around its circumference.
### Onlay graft procedures
#### _Surgical concept_
The onlay procedure was designed to augment ridge defects in the apico-coronal plane, i.e. to gain ridge height (Meltzer 1979; Seibert 1983). Onlay grafts are epithelialized free grafts which, following placement, receive their nutrition from the de-epithelialized connective tissue of the recipient site. The amount of apico-coronal augmentation that can be obtained is related to the initial thickness of the graft, the events of the wound healing process, and the amount of graft tissue that survives (Figs. 44-82, 44-83, 44-84). If necessary, the grafting procedure can be repeated at 2-month intervals to gradually increase the ridge height.
#### _Indications_
Onlay graft procedures are used in the treatment of large class II and III defects. They are not suitable in areas where the blood supply at the recipient site has been compromised by scar tissue formation from previous wound healing.
#### _Technique_
An attempt must be made to retain as much of the lamina propria of the recipient site as possible. The anesthetic solution should be placed high in the vestibular fornix and in the palate, thus keeping vasoconstriction in the recipient site to a minimum. A scalpel blade is used to remove the epithelium. The scalpel is moved with short, saw-like strokes across the recipient site at a level approximately 1 mm below the outer surface of the epithelium. The least amount of connective tissue possible should be excised. The margins of the recipient site can be prepared with either a butt joint or a beveled margin. The prepared recipient site should be covered with a surgical gauze moistened with isotonic saline while the donor tissue is dissected (Fig. 44-82g–i).
#### _Selection of donor site_
Onlay graft procedures, as well as interpositional graft procedures, require large amounts of donor tissue. As a general rule, the palatal vault region of premolars and first molars, midway between the gingival margin and the midline raphae, is the only area in the maxilla that contains the necessary volume of tissue required to augment large ridge defects. During the presurgical planning phase, the tissue of the palate should be probed with a 30-gauge syringe needle to ensure that an acceptable volume of tissue can be obtained at the time of surgery.
The major palatine artery emerges from the posterior palatine foramen located adjacent to the distal surface of the maxillary second molar, midway between the gingival margin and the midline raphae (Fig. 44-85). The artery passes in an anterior direction close to the surface of the palatal bone. It is important therefore that the second and third molar regions are not used as donor sites for large volume grafts.
#### _Planning in graft preparation_
As a rule the graft should be made a few millimeters wider and longer than the dimensions required at the recipient site. The dimensions of the graft are outlined on the palate with the use of a scalpel and light bleeding is provoked to define the surface borders. In order to avoid interference with the palatine artery, the borders of the graft must be planned in such a way that its thinner portions are located high in the palatal vault or in the first molar area. The thicker portions should be harvested from the premolar areas.
**Fig. 44-82** (a) Pretreatment view, class III ridge defect. A two-stage procedure will be used to augment the ridge. (b) A pouch was prepared to receive an interpositional graft. Epithelium was removed from the borders of the recipient site to permit some of the graft to be placed above the level of the surrounding tissue in order to gain apico-coronal augmentation. (c) The wedgeshaped graft was 10 mm thick at its center. (d) The interpositional graft is both displacing the labial surface of the pouch in the labial direction as well as adding height to the ridge. (e) Two months post-treatment. Additional augmentation is needed apicocoronally. (f) A second-stage onlay graft will be used to create a papilla and fill the dark triangle between the pontics. (g) Two months after the first surgical procedure, the ridge was de-epithelialized and cuts were made into the connective tissue prior to placing the second-stage onlay graft into position. (h) The onlay graft was sutured into position. (i) The pontics were adjusted and brought into light contact with the graft. (j) Marked swelling occurred within the graft at 14 days post surgery. (k) Two months following the second surgical procedure, a gingivoplasty was performed to deepen the pontic receptacle sites for the ovate pontics. (l) Post-treatment view 1 year after the final surgical procedure. (Courtesy of Dr. J. Seibert & Dr. P. Malpeso, USA.)
#### _Dissection of donor tissue_
The base of the graft should be V- or U-shaped to match the shape of the defect in the ridge. The different planes of incision prepared in the palate must therefore converge towards an area under the center or toward one edge of the donor site. It is comparatively easy, with the use of a scalpel, to dissect in an antero-posterior or, from an area high in the palate, in a lateral direction towards the teeth. It is, however, difficult to dissect in an anterior direction from the distal edge of the donor site. There is a variety of blade holders available which permit the scalpel blade to be positioned at different angles to the holder and which enable the surgeon to cut with a back-action. When the donor tissue has been removed, it must be stored in pieces of surgical gauze moistened in isotonic saline at all times.
#### _Treatment of the donor site_
Since it is difficult to anchor and maintain a periodontal dressing at the donor site in the palatal vault, an acrylic stent should be fabricated prior to surgery. The stent should be made with wrought wire clasps on each side to add retention and to aid the patient in removing and inserting the device.
The donor site must be inspected carefully for signs of arterial bleeding. If any small vessel bleeding is observed, a circumferential suture must be placed around the vessel distal to the bleeding point. Immediately thereafter, the void at the donor site should be packed with a suitable hemostatic agent and the edges of the wound be brought closer together with sutures. The stent is then put into position.
#### _Try-in and stabilization of graft_
The graft is transferred with tissue forceps to the recipient site for a try-in. The graft is trimmed to the proper shape and adjusted to fit the connective tissue surface of the prepared ridge. A series of parallel cuts may be made deep into the exposed lamina propria of the recipient site to sever large blood vessels (Fig. 44-82g) immediately before suturing. A series of interrupted sutures is placed along the borders of the graft. The dental assistant should stabilize the onlay graft against the surface of the recipient site, while the surgeon completes the placement of sutures.
**Fig. 44-83** Onlay graft procedure. (a) Pretreatment view. The gingival tissues were distorted from previous attempts at esthetic reconstruction. The patient wished to have a papilla between the right maxillary lateral and central incisor and a natural looking bridge. (b) The pontic area, including the papilla on the mesial of the right lateral incisor, was de-epithelialized and a thick (5 mm) onlay graft was sutured into position. (c) The pontic was shortened at the time of surgery to accommodate the thick graft. At 3 months post surgery the graft had undergone maximum shrinkage and gingivoplasty could now be done. (d) Incisal view at 3 months post surgery. Note the "papilla" that has been created. The indentation in the ridge was naturally created by the tissue swelling against the pontic tooth. (e) Rotary diamond point gingivoplasty was done to reshape the bulky graft to normal contours, deepen the receptacle site for the ovate pontic and level the gingival margins. (f) This view shows the esthetic harmony that was obtained in the soft tissues and tooth form at 2 years post treatment. (Courtesy of Dr. J. Seibert & Dr. C. Williams, USA.)
**Fig. 44-84** Onlay graft procedures utilized to augment ridge and create papillae. (a) Pretreatment view. The left lateral incisor was extracted after a traumatic injury. The patient detested the dark triangle on the mesial of the pontic, the poor tooth form in the bridge and the irregular contours in her gingival tissue. (b,c) An onlay graft was used to gain apico-coronal and buccolingual ridge augmentation as well as to develop papillae. Note how the graft was extended to the palatal side of the ridge to gain greater blood supply from a larger connective tissue base. (d,e) At 2 months post surgery, a second-stage veneer graft was used to eliminate the surface irregularities on the surface of the gingiva and gain greater bucco-lingual augmentation. (f) At 4 months post second-stage surgery, gingivoplasty was done to prepare the area for an ovate form pontic. (g–h) 1 year post treatment, esthetics have been restored for this patient. (Courtesy of Dr. J. Seibert & Dr. D. Garber, USA.)
**Fig. 44-85** Basic anatomic–histologic zones of the palate. Note the normal location of the greater palatine foramen.
#### _Wound healing in the recipient site_
Considerable post-operative swelling often occurs during the first week after pouch and onlay augmentation procedures. The epithelium of the graft will slough to form a white film on the surface of the graft. Patients should rinse two to four times per day with an antimicrobial mouthwash during the first week after surgery and refrain from mechanical cleaning measures in the area until a new epithelial covering has formed over the graft, which will not occur until a functional capillary circulation has been re-established in the graft (4–7 days after the surgery). The grafted tissue will assume a normal color as the epithelium thickens via stratification. Tissue form is usually stable after 3 months, but further shrinkage may occur over a period of several months. Final restorative measures should therefore not be initiated until after 6 months.
#### _Wound healing in the donor site_
Granulation tissue will gradually fill the donor site. Initial healing is usually complete within 3–4 weeks after the removal of a 4–5 mm thick graft. Patients should wear the surgical stent for about 2 weeks to protect the healing wound. The palate returns to its presurgical contour after about 3 months.
### Combined onlay–interpositional graft procedures
Class III ridge defects pose a major challenge to the clinician since the ridge has to be augmented in both vertical and horizontal dimensions. The combined onlay–interpositional graft procedure (Fig. 44-86 and 44-87) may successfully be used in such a situation (Seibert & Louis 1996). The combined graft procedure may offer the following advantages:
* The submerged connective tissue section of the interpositional graft aids in the revascularization of the onlay section of the graft, thereby gaining a greater percentage of take of the overall graft.
* A smaller post-operative open wound in the palate donor site.
* Faster healing in the palate donor site with less patient discomfort.
* Greater latitude or ability to control the degree of bucco-lingual and apico-coronal augmentation within a single procedure.
* Vestibular depth is not decreased and the mucogingival junction is not moved coronally, thereby eliminating the need for follow-up corrective procedures.
### Refinement of pontic contours and gingivoplasty soft tissue sculpting procedures
It is desirable, when reconstructing defects within a partially edentulous ridge, to moderately overcorrect the ridge in the area of the deformity. This will compensate for wound contraction and provide the necessary bulk of tissue within the ridge to sculpt the ridge to its final form. Gingivoplasty techniques using rotary coarse diamond stones in an ultraspeed handpiece with copious water spray are used to smooth out incision lines and perfect the fit and shape of the pontic teeth to the crest of the ridge (Figs. 44-83, 44-87). Adjustments are made to shape the cervical contour and emergence profile of the pontic teeth to match that of the contralateral teeth. The tissue-contacting surfaces of the pontic teeth are immediately rebased with autopolymerizing resin and polished. This final tissue sculpting procedure and reshaping of the provisional prosthesis is minor in nature but aids greatly in defining the shape of the papillae and creating the illusion of the presence of a cuff of free gingiva at the pontic–ridge interface.
**Fig. 44-86** Diagram of the combination onlay-interpositional graft procedure. (a) Cross section of a class III ridge defect. (b) Epithelium is removed on the labial–crestal side of the ridge to prepare the recipient bed for the onlay segment of the graft. (c) Partial-thickness dissection was then used to create a pouch for the interpositional section of the graft. (d) The dissection for the graft is started at right angles to the surface of the palate. The scalpel blade is then angled to remove a long connective tissue segment for the graft. (e) Three-dimensional view of the onlay section of the graft (including epithelium) and the connective tissue segment for buccolingual augmentation. (f) Graft sutured into position. (Reprinted with permission from _The International Journal of Periodontics and Restorative Dentistry_.)
**Fig. 44-87** (a,b) The right maxillary lateral and central incisors were lost due to trauma. These views show the horizontal and vertical loss of ridge tissue 10 months after the extractions. (c) A partial-thickness path of incision was extended labially and apically to create a pouch. The amount of space created within the pouch and the degree of relaxation of the flap was then tested with a periosteal elevator. (d) The epithelialized section of the graft can be seen in this view. (e) The premolar area, maxillary right side, was used as a donor area. The area of exposed connective tissue corresponds to the onlay section of the graft. The incisions were extended another 5–7 mm towards the midline on a long bevel to obtain the interpositional segment of the graft. (f) The graft was tucked into the labial pouch and sutured first along its palatal border. The labial flap was then sutured along the epithelial connective border of the graft. The residual labial socket defect in the flap created a soft tissue discontinuity defect along the labial margin of the flap. (g) At 6 weeks post surgery, it can be seen that further augmentation would be required to gain additional soft tissue in both the vertical and horizontal planes. A second-stage procedure was done at this time. (h) An incision 1.5 mm in depth was utilized to de-epithelialize the crestal surface of the ridge. Note that the papillae were not included within the surgical field. The mesial and distal borders of the onlay section of the recipient site were then extended apically to create vertical releasing incisions. The overall recipient site was to be trapezoidal in shape. A labial flap to create the pouch section of the recipient site was made using partial-thickness dissection. (i) The left maxillary premolar area was used as the donor site for the second-stage surgery. (j) This side view clearly shows the epithelialized onlay section of the graft and the de-epithelialized connective tissue section of the graft, as well as tissue thickness. (k) The graft was sutured first along the fixed palatal border to gain initial stabilization. Then the connective tissue interpositional section was sutured along the lateral borders. The flap was then sutured over the interpositional section of the graft at the epithelialized edge of the onlay section of the graft and along the vertical incisions. (l) At 6 weeks post surgery, the provisional prosthesis was modified to bring the tissue surface of the pontics into contact with the healing ridge. (m) At 2 months post surgery, tooth form was further modified on the provisional prosthesis and gingivoplasty was done to sculpt the tissues to final form and smooth out surface irregularities. (n) The final ceramo-metal prosthesis was inserted 4 months later. The life-like reconstruction of the soft tissues and dentition restored dentofacial esthetics for the patient. (Courtesy of Dr. J. Seibert, Dr. J. Louis & Dr. D. Hazzouri, USA. Reprinted with permission from _The International Journal of Periodontics and Restorative Dentistry_.)
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# Chapter 45
# Periodontal Plastic Microsurgery
Rino Burkhardt and Niklaus P. Lang
* * *
Microsurgical techniques in dentistry (development of concepts)
Concepts in microsurgery
Magnification
Instruments
Suture materials
Training concepts (surgeons and assistants)
Clinical indications and limitations
Comparison to conventional mucogingival interventions
* * *
# Microsurgical techniques in dentistry (development of concepts)
In general, the main aim of a surgical intervention is no longer only the survival of the patient or one of his organs, but the effort to preserve a maximum amount of function and to improve patient comfort. In many surgical specialties, these demands are met owing to a minimally invasive surgical approach.
Microsurgery in general is not an independent discipline, but is a technique that can be applied to different surgical disciplines. It is based on the fact that the human hand, by appropriate training, is capable of performing finer movements than the naked eye is able to control. First reports on microsurgery go back to the nineteenth century when a microscope was developed for use in ophthalmology (Tamai 1993). Later, the first surgical operation with a microscope was performed in Sweden to correct otosclerotic deafness (Nylén 1924). Microsurgical technique, however, did not attract the interest of surgeons until the 1950s, when the first surgical microscope, OPMI 1, with a coaxial lighting system and the option for stereoscopic view, was invented and commercialized by the Carl Zeiss company.
The micro vessel surgery that later revolutionized plastic and transplantation surgery was mainly developed by neurosurgeons (Jacobsen & Suarez 1960; Donaghy & Yasargil 1967). Applying microsurgically modified techniques, small vessels of a diameter of less than 1 mm could be successfully anastomosed on a routine basis (Smith 1964). As a consequence, a completely amputated thumb was successfully replanted for the first time in 1965 (Komatsu & Tamai 1968). Between 1966 and 1973, a total of 351 fingers were replanted at the Sixth People's Hospital in Shanghai without magnification, resulting in a healing rate of 51% (Zhong-Wei _et al_. 1981). From 1973, the interventions mentioned were solely performed with surgical microscopes and the corresponding success rates of replanted fingers increased to 91.5%. These results documented the importance of a fast and successful restoration of the blood circulation in replanted extremities and free tissue grafts. Further achievements of the microsurgical technique in plastic reconstructive surgery included transplantation of toes to replace missing thumbs (Cobbett 1969), interfascicular nerve transplantation (Millesi 1979), microvascular transplantation of toe joints (Buncke & Rose 1979), micro neurovascular transplantation of the pulp of a toe to restore the sensitivity of the finger tips (Morrison _et al_. 1980), and microvascular transplantation of the nail complex (Foucher 1991). Positive results of microsurgically modified interventions have led to today's clinical routine applications in orthopedics, gynecology, urology, plastic–reconstructive and pediatric surgery.
After a few early single reports (Baumann 1977; Apotheker & Jako 1981), the surgical microscope was introduced in dentistry in the 1990s. Case reports and the applications of the microscope were described in the prosthetic (Leknius & Geissberger 1995; Friedman & Landesman 1997, 1998; Mora 1998), endodontic (Carr 1992; Pecora & Andreana 1993; Ruddle 1994; Mounce 1995; Rubinstein 1997), and periodontal literature (Shanelec 1991; Shanelec & Tibbetts 1994, 1996; Tibbetts & Shanelec 1994; Burkhardt & Hürzeler 2000).
Treatment outcomes have been statistically analyzed in prospective studies in endodontics, since the introduction of microendodontic techniques (Rubinstein & Kim 1999, 2002). Within 1 year after apical microsurgery, 96.8% of the cases were considered to be healed. At reevaluation, 5–7 years after the first post-operative year, a success rate of 91.5% measured by clinical and radiographic parameters was still evident (Rubinstein & Kim 2002). The corresponding percentage of healed cases, treated without a surgical microscope, yielded only 44.1%, 6 months to 8 years after conventional apical surgery (Friedman _et al_. 1991).
Despite the positive results in prospective studies (Rubinstein & Kim 2002; Cortellini & Tonetti 2001; Burkhardt & Lang 2005), the surgical microscope experiences a slow acceptance in prosthodontics, endodontics (Seldon 2002), and periodontal surgery. Possible reasons are the long learning curve, the impaired maneuverability of the devices and the high cost of purchasing the instrument.
# Concepts in microsurgery
The continuous development of operating microscopes, refinement of surgical instruments, production of improved suture materials and suitable training laboratories have played a decisive role for the worldwide establishment of the microsurgical technique in many specialties. The three elements, i.e. _magnification_ , _illumination_ , and _instruments_ are called the _microsurgical triad_ (Kim _et al_. 2001), the improvement of which is a prerequisite for improved accuracy in surgical interventions. Without any one of these, microsurgery is not possible.
## Magnification
An optimal vision is a stringent necessity in periodontal practice. More than 90% of the sensations of the human body are perceived by visual impressions. Vision is a complex process that involves the cooperation of multiple links between the eye, the retina, the optic nerve, and the brain. An important element to assess in human eyesight is visual acuity, measured in angular degrees. If necessary, it may be improved by corrective lenses. It is defined by the ability to perceive two objects separately. Visual acuity is influenced by anatomic and physiologic factors, such as the density of cells packed on the retina and the electrophysiologic process of the image on the retina.
Another important factor influencing visual acuity is the lighting. The relation between visual acuity and light density is well established: a low light density decreases visual acuity. The best eyesight can be achieved at a light density of 1000 cd/m2. At higher densities, visual acuity decreases. This, in turn, means that claims for optimal lighting conditions have to be implemented.
Visualization of fine details is enhanced by increasing the image size of the object. Image size can be increased in two ways: (1) by getting closer to the objects and (2) by magnification. Using the former method, the ability of the lens of the eye to accommodate becomes important and has a relevant influence on the visual capacity. By changing the form of the lens, the refraction of the optical apparatus increases, allowing it to focus on nearer objects. During ageing, the ability to focus at closer distances is compromised because the lens of the eye loses its flexibility (Burton & Bridgeman 1990). This phenomenon is called presbyopia. Presbyopia affects all people in middle age, and becomes especially notice-able when the nearest point at which the eye can focus accurately exceeds ideal working distances (Burton & Bridgeman 1991). To see small objects accurately, the focal length must be increased. As an example, an older individual reading without glasses must hold the reading matter farther from the eyes to see the print. Increasing the distance enables the person to see the words, but the longer working distance results in a smaller size of the written text. This decrease in image size, resulting from the increased working distance, needs to accommodate the limitations of presbyopia and is especially hindering in clinical practice. In periodontal practice, the tissues to manipulate are usually very fine resulting in a situation in which the natural visual capacity reaches its limits. Therefore, the clinical procedure may only be performed successfully with the use of magnification improving precision and, hence, the quality of work.
### Optical principles of loupes
In dentistry, two basic types of magnification systems are commonly used: the surgical microscope and loupes. The latter can further be classified as (1) single-lens magnifiers (clip-on, flip-up, jeweller's glasses) and (2) multilens telescopic loupes. Singlelens magnifiers produce the described diopter magnification that simply adjust the working distance to a set length. As diopters increase, the working distances decrease. With a set working distance, there is no range and no opportunity for movement; this can create difficulty in maintaining focus and, therefore, may cause neck and back strain from poor posture (Basset 1983; Diakkow 1984; Shugars _et al_. 1987). Additionally, diopter magnifiers also give poor image quality, which restricts the quality of the work (Kanca & Jordan 1995). These types of glasses cannot be considered to be a true means of magnification.
Telescopic loupes (compound or prism loupes), however, offer improved ergonomic posture as well as significant advancements in optical performance (Shanelec 1992). Instead of increasing the thickness of a single lens to increase magnification, compound loupes use multiple lenses with intervening air spaces (Fig. 45-1). These allow an adjustment of magnification, working distance, and depth of the field without excessive increase in size or weight. Prism loupes are the most optically advanced type of loupe magnification available (Fig. 45-2). While compound loupes use multiple refracting surfaces with intervening air spaces to adjust optical properties, prism loupes are actually low-power telescopes. They contain Pechan or Schmidt prisms that lengthen the light path through a series of mirror reflections within the loupes (Fig. 45-3). Prism loupes produce better magnification, larger fields of view, wider depths of field, and longer working distances than do other loupes. To guarantee proper adjustment of loupes, the knowledge of some basic definitions and key optical features of loupes is necessary (Fig. 45-4).
**Fig. 45-1** Fixed compound loupe, adjustable only in the interpupilary distance (Galilean principle).
**Fig. 45-2** Prism loupe, sealed to avoid leakage of moisture, front frame mounted and fully adjustable (Prism principle).
**Fig. 45-3** Light path through prism loupe. Even though the distance the light travels has increased, there is no decrease in brightness or image contrast, even at 4× or 5×. This is because the light does not travel through air but instead through the glass of the prism.
**Fig. 45-4** Diagram indicating the principal optical features of loupes.
#### _Working distance_
The working distance is the distance measured from the eye lense location to the object in vision. There is no set rule for how much the working distance may be increased. Depending on the height and the resulting length of the arms, the working distance with slightly bended arms usually ranges from 30 to 45 cm. At this distance, postural ergonomics are greatly improved and eye strain reduced due to lessened eye convergence. The multitude of back, neck, shoulder, and eye problems that dentists suffer, working without using loupes, frequently originate from the need to assume a short working distance to increase visual acuity (Coburn 1984; Strassler 1989). By wearing surgical loupes, the head is placed in the centre of its balance over the spine and stabilized against gravity.
#### _Working range_
The working range (depth of field) (Fig. 45-4) is the range within which the object remains in focus. The depth of field of normal vision ranges from working distance to infinity. Moving back from a close working distance, the eyes naturally accommodate and refocus to the new distance. Normally, eye position and body posture are not frozen in one place for an extended period, but vary constantly. Wearing loupes changes this geometry. Body posture and position of the extraocular muscles are confined to a range determined by the loupe's characteristics. It is important to understand that each individual's vision is limited to his/her own internal working range, which means that one may only be able to maintain focus on an object within a 15 cm range, even though the loupes have a 23 cm depth of field. With any brand of loupe, the depth of field decreases as the magnification increases.
#### _Convergence angle_
The convergence angle (Fig. 45-4) is the pivotal angle aligning the two oculars, such that they are pointing at the identical distance and angle. At a defined working distance, the convergence angle varies with interpupillary distance. Wider-set eyes will have more eye convergence at short working distances. Therefore, the convergence angle defines the position of the extraocular muscles that may result in tension of the internal and external rectus muscles; this may be an important source of eye fatigue.
#### _Field of view_
The field of view (Fig. 45-4) is the linear size or angular extent of an object when viewed through the telescopic system. It also varies depending on the design of the optic lens system, the working distance, and the magnification. As with depth of field, when magnification increases, the field of view decreases.
#### _Interpupillary distance_
The interpupillary distance (Fig. 45-4) depends on the position of the eyes of each individual and is a key adjustment that allows long-term, routine use of loupes. The ideal setting, as with binoculars, is to create a single image with a slightly oval-shaped viewing area. If the viewing area is adjusted to a full circle, excess eye muscle strain would limit the ability to use loupes for long periods.
#### _Viewing angle_
The viewing angle (Fig. 45-4) is the angular position of the optics allowing for comfortable working. The shallower the angle, the greater the need to tilt the neck to view the object being worked at. Therefore, loupes for dental clinicians should have a greater angulation than loupes designed for industrial workers. A slight or no angulation, which results when magnifiers are embedded in the lenses of the eyeglasses, may cause the operator to unduly tilt his or her head to view a particular object. This, again, may lead not only to neck discomfort, but also to pain in the shoulder muscles and possibly to a headache. As the working posture is likely to change over time, the loupes should be adjustable to any posture change.
#### _Illumination_
Most of the manufacturers offer collateral lighting systems or suitable fixing options. These systems may be helpful, particularly for higher magnification in the range of 4× and more. Loupes with a large field of view will have better illumination and brighter images than those with narrower fields of view. Important considerations in the selection of an acces-sory lighting source are total weight, quality, and the brightness of the light, ease of focusing and directing the light within the field of view of the magnifiers, and ease of transport between surgeries (Strassler _et al_. 1998).
It should be realized that each surface refraction in a lens will result in a 4% loss in transmitted light due to reflection. In telescopic loupes, this could amount to as much as 50% reduction in brightness. Anti-reflective coatings have been developed to counteract this effect by allowing lenses to transmit light more efficiently. The quality of lens coatings also varies and should be evaluated when selecting loupes (Shanelec 1992).
#### _Choice of loupes_
Before choosing a magnification system, different loupes and appropriate time for a proper adjustment have to be considered. Ill fitting or improperly adjusted loupes and the quality of the optics will influence the performance. For the use in periodontal surgery, an adjustable, sealed prism loupe with high-quality, coated lenses offering a magnification between 4× and 4.5×, either headband- or front frame-mounted, with a suitable working distance and a large field of view, seems to be the instrument of choice. The information in Table 45-1 serves as a basic guide to making an adequate selection.
### Optical principles and components of a surgical microscope
The surgical microscope is a complicated system of lenses that allows stereoscopic vision at a magnification of approximately 4–40× with an excellent illumination of the working area. In contrast to loupes, the light beams fall parallel onto the retinas of the observer so that no eye convergence is necessary and the demand on the lateral rectus muscles is minimal (Fig. 45-5). The microscope consists of the optical components, the lighting unit, and a mounting system. To avoid an unfavorable vibration of the microscope during use, the latter should be firmly attached to the wall, the ceiling or a floor stand. Mounted on the floor, the position of the microscope in the room must provide quick and easy access.
**Fig. 45-5** Diagram illustrating the comparison of vision enhancement with loupes and a microscope. The loupes necessitate eye convergence while vision is paralleled through the microscope.
Table 45-1 Features to consider in the selection of a magnifying loupe system
**Compound loupes** | • Magnification range 2–3.5×
---|---
(Galilean) | • Lighter in weight
| • Shorter working distance
| • Shorter loupe barrel
**Prism loupes** | • Magnification range 3–5×
(Keplerian) | • Heavier in weight
| • Longer working distance
| • Longer loupe barrel
**Front-frame mounted** | • Allow up to 90% of peripheral vision
| • No prescription glasses
| • Require soft and cushioned nose piece
| • Better weight distribution
**Head-band mounted** | • Restricted peripheral vision
| • Allow to use prescription glasses
| • Better weight distribution
| • Require adjustment more often
**Fixed-lens magnifiers** | • No adjustment options when changing posture
| • Minimum weight
**Flip-up capability** | • Require removable, sterilizable handle
| • Allow switch from magnified to regular vision
**Quality of the lenses** | • Corrected for chromatic and spherical aberration
| • No drop-off in clarity when approaching the edges
| • Sealed system to avoid leakage of moisture
| • Option for disinfection
**Adjustment options** | • Interpupillary distance
| • Viewing angle
| • Vertical adjustment
| • Lock in adjusted position
| • Convergence angle (preset angle may be more user-friendly)
**Lens coating** | • Brighter image
| • More light
**Accessories** | • Transportation box
| • Side and front shields for protection
| • Mounted light source
| • Removable cushions
The optical unit includes the following components (Fig. 45-6) : (1) magnification changer, (2) objective lenses, (3) binocular tubes, (4) eyepieces, and (5) lighting unit (Burkhardt & Hürzeler 2000).
#### _Magnification changer_
The magnification changer or "Galilean" changer consists of one cylinder, into which two Galilean telescope systems (consisting of a convex and concave lens) with various magnification factors are built. These systems can be used in either direction depending on the position of the magnification changer. A total of four different magnification levels are available. Straight transfer without any optics yields no magnification. The combination of the magnification changer with varying objective lenses and eyepieces yields an increasing magnification line when the control is adjusted.
The stepless motor-driven magnification changer must achieve a magnification of 0.5–2.5× with one optical system, which is operated by either a foot pedal or an electric rotating control, mounted on the microscope. The operator should decide whether to use the manual or motorized magnification changer. If the magnification must be changed frequently, it can be accomplished more quickly with the manual than with the motorized changer, the former not having in-between levels. While the motorized system improves the focus and comfort compared to the manual system, the former is more expensive.
#### _Objective lenses_
As processed by a magnification changer, the image is only projected by a single objective. This simultaneously projects light from its source twice for deflection by the prisms into the operation area (i.e. coaxial lighting). The most frequently used objective is 200 mm (f = 200 mm). The focal length of the objective generally corresponds to the working distance of the object.
#### _Binocular tubes_
Depending on the area of use, two different binocular tubes are attached (i.e. straight and inclined tubes). With straight tubes, the view direction is parallel to the microscope axis. Using inclined tubes, an angulation to the microscope axis of 45º is achieved. In dentistry, only inclined, swivelling tubes, that permit continuously adjustable viewing, are feasible for ergonomic reasons (Fig. 45-7). The precise adjustment of the interpupillary distance is the basic prerequisite for the stereoscopic view of the operation area.
#### _Eyepieces_
The eyepieces magnify the interim image generated in the binocular tubes. Varying magnifications can be achieved (10×, 12.5×, 16×, 20×) using different eyepieces. Eyepiece selection not only determines the magnification, but also the size of the field of view. Corresponding to the loupe spectacles, an indirect relationship exists between the magnification and the field of view. The 10× eyepiece generally provides a sufficient compromise between magnification and field of view. Modern eyepieces allow a correction facility within −8 to +8 diopters that is a purely spherical correction.
**Fig. 45-6** System components of a surgical microscope.
**Fig. 45-7** Tiltable viewing tube which provides an ergonomic posture during clinical work, a prerequisite for optimal performance using microsurgical technique.
The majority of surgical microscopes consist of modules and can be equipped with attachments that include integrated video systems, photographic adapters for cameras, units for image storage, colour printers, and powerful lighting sources. Prior to purchasing accessories, inexperienced clinicians should gather information about the needed equipment. The use of magnifying loupes is recommended prior to purchasing a microscope to accustom oneself to working under magnification.
#### _Lighting unit_
Optimal illumination is necessary with high magnifications. In recent years, the use of halogen lamps became popular. These lamps provide a whiter light than do lamps using conventional bulbs due to their higher colour temperature. As halogen lamps emit a considerable portion of their radiation within the infrared part of the spectrum, microscopes are equipped with cold-light mirrors to keep this radiation from the operation area. An alternative to the halogen light is the xenon lamp that functions up to ten times longer than the halogen lamp. The light has daylight characteristics with even a whiter colour and delivers a brighter, more authentic image with more contrast.
### Advantages and disadvantages of loupes and surgical microscopes
A substantial number of periodontists have already adopted the use of low magnification in their practices and recognize its great benefits. Most of the present results are based on subjective statements of patients or observations of the attending surgeons. At present, it can only be speculated how significantly the selection of magnification influences the result of the operation. The magnification recommended for surgical interventions ranges from 2.5–20× (Apotheker & Jako 1981; Shanelec 1992). In periodontal surgery, magnifications of 4–5× for loupe spectacles and 10–20× for surgical microscopes appear to be ideal depending on the kind of intervention. As the depth of field decreases with increasing magnification, the maximum magnification for a surgical intervention is limited to about 12–15×, when dealing with a localized problem such as the coverage of a single soft tissue recession or interdental wound closure after guided tissue regeneration of an infrabony defect. A magnification range of 6–8× seems appropriate for clinical inspections or surgical interventions when the entire quadrant is under operation. Higher magnifications such as 15–25× are more likely limited to the visual examination of clinical details only, such as in endodontic interventions.
Loupes have the advantage over the microscope in that they reduce technique sensitivity, expense, and learning phase. The lighting of the operation field is often insufficient, however, and that may limit magnifications more than 4.5×. The surgical microscope guarantees a more ergonomic working posture (Zaugg _et al_. 2004), optimal lighting of the operation area, and freely selectable magnification levels. These advantages are countered by increased expenses of the equipment and an extended learning phase for the surgeon and his assistant. In order to visualize lingual or palatal sites that are difficult to access, the microscope must have sufficient maneuverability. Recent developments have enabled direct viewing of oral operation aspects. By means of these optical devices, it will be possible to perform all periodontal interventions with the surgical microscope.
## Instruments
Proper instrumentation is fundamental for microsurgical intervention. While various manufacturers have sets of microsurgical instruments, they are generally conceived for vascular and nerve surgery and, there-fore, inappropriate for the use in plastic periodontal surgery. As the instruments are primarily manipulated by the thumb, index and middle finger, their handles should be round, yet provide traction so that finely controlled rotating movements can be executed. The rotating movement of the hand from two o'clock to seven o'clock (for right-handed persons) is the most precise movement the human body is able to perform. The instruments should be approximately 18 cm long and lie on the saddle between the operator's thumb and the index finger; they should be slightly top-heavy to facilitate accurate handling (Fig. 45-8). In order to avoid an unfavorable metallic glare under the light of the microscope, the instruments often have a coloured coating surface. The weight of each instrument should not exceed 15–20 g (0.15–0.20 N) in order to avoid hand and arm muscle fatigue. The needle holder should be equipped with a precise working lock that should not exceed a locking force of 50 g (0.5–N). High locking forces generate tremor, and low locking forces reduce the feeling for movement.
**Fig. 45-8** Illustration demonstrating proper hand position for utilization of microsurgical instruments. Fine rotary movements which you get gripping the instrument like a pencil are needed for precise movements.
Appropriate sets of steel or titanium instruments for periodontal surgery are available from different manufacturers. A basic set comprises a needle holder, micro scissors, micro scalpel holder, anatomic and surgical forceps, and a set of various elevators. In order to avoid sliding of the thread when tying the knot, the tips of the forceps have flat surfaces or can be finely coated with a diamond grain that improves the security by which the needle holder holds a surgical needle (Abidin _et al_. 1990). The configuration of the needle holder jaw has considerable influence on needle holding security. The presence of teeth in the tungsten carbide inserts provides the greatest deterrent to either twisting or rotating of the needle between the needle holder jaws. This benefit must be weighed against the potential damaging effects of the teeth on suture material. Smooth jaws without teeth cause no demonstrable damage to 6-0 monofilament nylon sutures, whereas needle holder jaws with teeth (7000/in2) markedly reduce the suture breaking strength (Abidin _et al_. 1990). Additionally, the sharp outer edges of the needle holder jaws must be rounded to avoid breakage of fine suture materials (Abidin _et al_. 1989). When the needle holder jaws are closed, no light must pass through the tips. Locks aid in the execution of controlled rotation movements on the instrument handles without pressure. The tips of the forceps should be approximately 1–2 mm apart, when the instrument lies in the hand idly.
Various shapes and sizes of micro scalpels can be acquired from the discipline of ophthalmology or plastic surgery instrument sets and supplemented with fine instruments (fine chisels, raspatories, elevators, hooks, and suction) from conventional surgery.
In order to prevent damage, micro instruments are stored in a sterile container or tray. The tips of the instruments must not touch each other during sterilization procedures or transportation. The practice staff should be thoroughly instructed about the cleaning and maintenance of such instruments, as cleansing in a thermo disinfector without instrument fixation can irreparably damage the tip of these very expensive micro instruments.
## Suture materials
Suture material and technique are essential factors to consider in microsurgery (Mackensen 1968). Wound closure is a key prerequisite for healing following surgical interventions and most important to avoid complications (Schreiber _et al_. 1975; Kamann _et al_. 1997). The most popular technique for wound closure is the use of sutures that stabilize the wound margins sufficiently and ensure proper closure over a defined period of time. However, the penetration of a needle through the soft tissue in itself causes a trauma, and the presence of foreign materials in a wound may significantly enhance the susceptibility to infection (Blomstedt _et al_. 1977; Österberg & Blomstedt 1979). Hence, it is obvious that needle and thread characteristics influence wound healing and surgical outcome.
### Characteristics of the needle
The needle consists of a swage, body, and tip and differs concerning material, length, size, tip configuration, body diameter, and the nature of connection between needle and thread. In _atraumatic_ sutures, the thread is firmly connected to the needle through a press-fit swage or stuck in a laser-drilled hole. There is no difference concerning stability between the two attachment modalities (Von Fraunhofer & Johnson 1992). The body of the needle should be flattened to prevent twisting or rotating in the needle holder. The needle tips differ widely depending on the specialty in which they are used. Tips of cutting needles are appropriate for coarse tissues or atraumatic penetration. In order to minimize tissue trauma in periodontal microsurgery, the sharpest needles, reverse cutting needles with precision tips or spatula needle with micro tips (Fig. 45-9), are preferred (Thacker _et al_. 1989).
The shape of the needle can be straight or bent to various degrees. For periodontal microsurgery, the 3/8" circular needle generally ensures optimum results. There is a wide range of lengths, as measured along the needle curvature from the tip to the proximal end of the needle lock. For papillary sutures in the posterior area, needle lengths of 13–15 mm are appropriate. The same task in the front aspect requires needle lengths of 10–12 mm, and for closing a buccal releasing incision, needle lengths of 5–8 mm are adequate. To guarantee a perpendicular penetration through the soft tissues without tearing, an asymptotic curved needle is advantageous in areas where narrow penetrations are required (e.g. margins of gingivae, bases of papillae). To fulfil these prerequisites for ideal wound closure, at least two different sutures are used in most surgical interventions. Table 45-2 serves as a basic guide to select the appropriate suture material.
### Characteristics of the suture material
The suture material may be either _resorbable_ or _non-resorbable_ material. Within these two categories, the materials can be further divided into _monofilament_ and _polyfilament_ threads. The bacterial load of the oral cavity demands attention in the choice of the suture material. Generally, in the oral cavity the wound healing process is uneventful, hereby reducing the risk of infection caused by contamination of the thread. As polyfilament threads are characterized by a high capillarity, monofilament materials are to be preferred (Mouzas & Yeadon 1975). _Pseudomonofilaments_ are coated polyfilament threads with the aim of reducing mechanical tissue trauma. During suturing the coating will break and the properties of the pseudomonofilament thread then corresponds to that of the polyfilament threads (Macht & Krizek 1978). Additionally, fragments of the coating may invade the surrounding tissues and elicit a foreign body reaction (Chu & Williams 1984).
#### _Resorbable sutures_
Resorbable threads may be categorized as _natural_ or _synthetic_. Natural threads (i.e. surgical gut) are produced from intestinal mucosa of sheep or cattle. The twisted and polished thread loses its stability within 6–14 days by enzymatic breakdown (Meyer & Antonini 1989). Histologic examinations confirmed the inflammatory tissue reactions with a distinct infiltrate. For that reason, natural resorbable threads are generally obsolete (Bergenholtz & Isaksson 1967; Helpap _et al_. 1973; Levin 1980; Salthouse 1980).
Synthetic materials are advantageous due to their constant physical and biologic properties (Hansen 1986). The materials used belong to the polyamides, the polyolefines or the polyesters and disintegrate by hydration into alcohol and acid. Polyester threads are mechanically stable and, based on their different hydrolytic properties, lose their firmness in different, but constant times. A 50% reduction of breaking resistance can be expected after 2–3 weeks for polyglycolic acid and polyglactin threads, 4 weeks for polyglyconate, and 5 weeks for polydioxanone threads. The threads are available in twisted, polyfilament forms, and monofilament forms for finer suture materials. The capillary effect is limited and hardly exists for polyglactin sutures (Blomstedt & Österberg 1982).
**Fig. 45-9** (a) Intact sharp spatula needle. (b) Damaged needle tip after sticking into the enamel surface.
Table 45-2 Ideal needle–thread combinations (non-resorbable) for use in periodontal microsurgery
#### _Non-resorbable sutures_
Polyamide is a commonly used material for fine monofilament threads (0.1–0.01 mm) that show adequate tissue properties. Tissue reactions seldom occur except after errors in the polymerization process (Nockemann 1981). Polyolefines, as a variation of choice, are inert materials that remain in the tissues without hydrolytic degradation (Salthouse 1980; Yu & Cavaliere 1983). Polypropylene and its newest development, polyhexafluoropropylene, are materials with excellent tissue properties. After suturing, the thread will be encapsulated in connective tissues and keep its stability for a longer period. In 5-0 and thicker gauges, the monofilament threads are relatively stiff and, for that reason, may impair patient comfort.
A substance with similar biologic, but improved handling properties, is polytetrafluoroethylene. Due to its porous surface structure, the monofilament threads should only be used with restriction in the bacterially loaded oral cavity.
### Intraoral tissue reactions around suture materials
The initial tissue reaction after suturing is a result of the penetration trauma, and reaches its culmination at the third post-operative day (Selvig _et al_. 1998). It is quite similar for resorbable and non-resorbable suture threads (Postlethwait & Smith 1975). Histologically, this early response is characterized by three zones of tissue alteration (Selvig _et al_. 1998) : (1) an intensive cellular exudation in the immediate vicinity of the entry to the stitch canal, followed by (2) a concentric area, harboring damaged cells as well as intact tissue fragments, and (3) a wide zone of inflammatory cells in the surrounding connective tissues.
If a resorbable suture is left _in situ_ for more than 2 weeks after wound closure, an acute inflammatory reaction still exists. This phenomenon is caused by bacteria entering the stitch canal and penetrating along the thread (Chu & Williams 1984; Selvig _et al_. 1998). The bacteriostatic effect of glycolic acid during the resorption process of polyglactin threads (Lilly _et al_. 1972) cannot be established (Thiede _et al_. 1980), and the resorption process of the polyglycolic thread is additionally inhibited by the acid environment caused by the infection (Postlethwait & Smith 1975). Such studies confirm the increased risk for bacterial migration along the thread in the moist and bacterially loaded oral cavity. Experimental and clinical data indicate that most wound infections begin around suture material left within the wound (Edlich _et al_. 1974; Varma _et al_. 1974). Polyfilament threads additionally facilitate bacterial migration; bacteria can also penetrate into the inner compartment of the thread and evade the immunologic response of the host (Blomstedt _et al_. 1977; Haaf & Breuninger 1988). This is only one reason why monofilament, non-resorbable sutures should be preferred and removed at the earliest biologically acceptable time (Gutmann & Harrison 1991). The infectious potential can be further reduced by using an anti-infective therapy based on a daily rinsing or topical application of chlorhexidine (Leknes _et al_. 2005).
Another promising option to reduce bacterial migration along the suture is coating it with a bacteriostatic substance. Vicryl® Plus (Ethicon®, Norderstedt, Germany) is a resorbable suture material, coated with triclosan that inhibits bacterial growth for up to 6 days by damaging the membrane of the cells (Rothenburger _et al_. 2002; Storch _et al_. 2002).
## Training concepts (surgeons and assistants)
The benefits of the operating microscope in periodontal surgery seem to be obvious. What then can be the reasons for the delay in taking advantage of periodontal surgery under the microscope? The main reason is that most surgeons do not adjust to the surgical microscope and those who have been using microscopes successfully, have not made adequate indepth practical recommendations to help other periodontal surgeons overcome their initial problems. Working with magnification changes the clinical settings as the visual direction during the surgical intervention does not meet the working ends of the instruments and the field of view has a smaller diameter. Additionally, the minimal size of tissue structures and suture threads requires a guidance of movement by visual rather than tactile control. This altered clinical situation requires an adjustment of the surgeon.
The three most common errors in the use of the surgical microscope are: (1) using magnification that is too high, (2) inadequate task sharing between surgeon and assistant, and (3) lack of practice.
### High magnification
There is a tendency to use magnification which is too high. As described above, this is one of the fundamental optical principles: the higher the magnification, the narrower the field of vision and the smaller its depth. This concept is important because high magnification causes surgery to become more difficult, especially when it involves considerable movement. In these circumstances low magnification of 4–7× should be used. On the other hand, higher magnification of 10–15× may be useful when dissecting within a small area requiring less movement, e.g. in papilla pre servation techniques. In general, the magnification should be that which allows the surgeons to operate with ease, and without increasing their usual operating time for a particular surgical procedure. Surgical time does not have to be increased once the surgeon has adapted fully to the microscope. The more experienced and skilled surgeons are with the microscope, the higher the magnification they can use with ease.
It may take 6 months or more for surgeons to be familiar with magnification of 10×, which usually is the maximum used in plastic periodontal surgery. A point of diminishing returns will eventually be reached where the advantages of increased magnification are outweighed by the disadvantages of a narrower field of vision.
### Task sharing between surgeon and assistant (teamwork)
In microendodontics, during root canal treatment, the whole procedure is performed with a minimum amount of position changes of the operating persons. Focusing can easily be achieved by moving the mirror towards or away from the objective lenses. In periodontal surgery both hands are used to hold the instruments and position changes are more frequently required which increase the demands on the operating team and require for an ideal cooperation between surgeon and assistant.
In all surgeries at least two operating persons are involved: a surgeon and an assistant, who assists the surgeon in the most rudimentary tasks in the operation. However, the tasks that the assistant constantly repeats in almost all operations with varying levels of skill will be taken into consideration. These tasks include: flap retraction, suction, rinsing, and cutting the sutures. To guarantee a continuous work flow during the surgical intervention, a second assistant who organizes the instruments is frequently desirable.
In periodontal microsurgery, where there is inherently very little access enjoyed by the surgeon, retraction is absolutely vital. Retraction should be done in different positions and must be devoid of all tremor or movement. This is an exceptionally strenuous task as the human assistant is expected to maintain the same posture for up to 1 hour. This is extremely energy consuming and the fatigue experienced by the assistant increases the chances of tremor as time goes by.
For an optimal work flow, magnification is also required for the assistant. An assistant wearing loupes has the advantage of an open peripheral vision to arrange the instruments and to check the patient's facial expression during the operation. On the other hand, co-observer tubes allow the same view for surgeon and assistant, enabling the assistant to point the suction tube to the right place and keep the view clear. This also becomes an issue during suturing when the air intake of the suction tube can easily suck the fine threads.
### Lack of practice
When working with high magnification, the surgeon has to adjust to being a prisoner within a narrow field of view. A new coordination has to be sought between the surgeon's eyes and hands – an adjustment which can come only after much regular practice with simple surgical procedures. The practice unit consists of a microscope, micro instruments, and different suitable models. To start training, a two-dimensional model, such as rubber dam, is appropriate to learn how to manipulate the instruments, how to pick up the needles, and tying knots. After the initial training, working with three-dimensional models (fruits, eggs, chicken) helps the surgeon to get used to the restricted depth of the field.
Another aim of training is the reduction of tremor. Its physiologic basis is uncertain, but it is important to be aware of the causes in order to prevent it. An important factor is the body posture, which must be natural, with the spinal column straight and the forearms and hands fully supported. An adjustable chair, preferably with wheels, is recommended for the surgeon who should place himself in the most comfortable position. Tremor varies with individuals and even in the same individual it varies under different conditions. In some people, intake of coffee, tea or alcohol may increase tremor; in others, emotions, physical exercise, or the carrying of heavy weights can cause it.
After the completion of appropriate training when instrument handling has become automatic, the surgeon has adjusted to the new conditions and can now fully concentrate on the surgical procedure in clinical practice without taking additional time.
# Clinical indications and limitations
The clinical benefits of a microsurgical approach in periodontal practice are mainly evaluated by case reports (Shanelec & Tibbetts 1994, 1996; Michaelides 1996; de Campos _et al_. 2006) and case–cohort studies (Cortellini & Tonetti 2001; Wachtel _et al_. 2003; Francetti _et al_. 2004). The different procedures described apply to the surgical coverage of buccal root recessions and flap closure after regenerative interventions. In both interventions, delicate soft tissue structures have to be manipulated during the surgery, which could be refined by selecting a less traumatic surgical approach. All of the studies confirmed the beneficial effects of the microsurgical approach. When covering a root recession, the vascularization of the injured tissues becomes critical as there is no blood supply from the underlying root surface. Frequently, coverage is performed by a connective tissue graft from the palate, which has different vascular characteristics compared to the supracrestal gingiva; supracrestal gingiva is the only tissue, naturally created and specifically designed, to survive and function over avascular root surfaces. As graft survival depends upon early plasmatic diffusion (Oliver _et al_. 1968; Nobutu _et al_. 1988), firm and stable flap or graft adaptation is of crucial importance to minimize the coagulum and facilitate the ingrowth of new vessels. A minimally traumatic approach allows more precise flap preparation and suturing with a reduction in tissue and vessel injuries, resulting in more rapid and more complete anastomosis of new capillary buds from the recipient bed with the existing, but severed, vessels of the graft or the flap.
The interdental gingiva is also a delicate tissue with a limited vascular network. As the gingival plexus does not extend interproximally, the central part of the interdental soft tissue is only supplied by vessels from the periodontal ligament space and arterioles that emerge from the crest of the interdental septa (Folke & Stallard 1967; Nuki & Hock 1974). These anatomic factors influence the wound-healing capacity of the tissues after surgical dissection and the small size of the structures (i.e. papilla or col) complicates a precise adaptation of the flap margins. Wound dehiscences, resulting in healing by secondary intention, are therefore a common finding after suturing the papilla in papilla-preservation techniques (Tonetti _et al_. 2004). Using microsurgery for a modified or simplified papilla preservation flap, primary wound closure could be noted in 92.3% of all treated sites 6 weeks after the intervention (Cortellini & Tonetti 2001).
Historic comparisons with studies performed by the same authors without the use of an operating microscope showed a clear advantage in the use of a microsurgical approach. Complete primary wound closure was observed in only 67% of the cases treated with a simplified (Cortellini _et al_. 1999), and in 73% of the cases treated with a modified papilla preservation flap (Cortellini _et al_. 1995). These results clearly demonstrated the improvement in tissue preservation and handling using a minimally invasive approach in order to achieve primary closure of the interdental space (Fig. 45-10).
A recently published case–cohort study, evaluating a new flap design for regeneration with enamel matrix derivates (MIST, _minimally invasive surgical technique_ ) combined with microsurgical techniques, confirmed the previous positive results, yielding a primary wound closure of the interdental tissues in all of the treated sites, 6 weeks post-operatively (Cortellini & Tonetti 2007) (Fig. 45-11).
Subjective observations of clinicians have found there is a less traumatic approach in periodontal surgery when magnification aids and fine suture materials are used. This ensures passive wound closure in most surgical interventions. This speculation was recently substantiated by an _in vitro_ experiment, which evaluated the tearing characteristics of mucosal tissue samples for various suture sizes and needle characteristics in relation to the applied tension forces (Burkhardt _et al_. 2006). The pig jaw mucosal tissue samples were attached in a test-tearing apparatus of a Swiss textile company and the tension tearing diagrams were traced for 3-0, 5-0, 6-0, and 7-0 sutures with forces up to 20 N. While the 3-0 sutures almost exclusively led to tissue breakage at an average of 13.4 N, the 7-0 sutures broke before tissues were torn in every instance, at an applied mean force of 3.6 N. With 5-0 and 6-0 sutures both events occured at random, at a mean force of 10 N. This means that a clinician can influence the amount of damage to the tissue by selecting thicker or thinner suture material. Considering this fact, it may be speculated that wound dehiscence can be prevented and passive flap adaptation can be improved by the choice of thinner sutures; this inevitably requires magnification if its benefits are to be fully appreciated.
The opponents of periodontal microsurgery often mention the adverse effect of a prolonged duration of the intervention while working with microscopes. It has been shown that the incidence and severity of complications and pain following periodontal surgery are correlated well with the duration of the surgical procedure (Curtis _et al_. 1985). It may be speculated that an extended operation time may compensate for the beneficial treatment effect of minimally invasive techniques. However, studies comparing micro- and macrosurgical approaches did not support such a hypothesis (Burkhardt & Lang 2005).
**Fig. 45-10** Primary closure of the buccal papillae after a crown-lengthening procedure. Modified mattress sutures (vertically everting) with 7-0 polyamide thread (black) and two single-knot closures with 8-0 polypropylene threads (blue) in each interdental area.
Considering all these facts there are no clinical contraindications for the use of magnification in periodontal surgery. From a user's point of view, only few areas in the oral cavity are difficult to access by an operating microscope which may limit its application. In these circumstances and in surgical interventions which require a frequent change of position, the use of loupes may be preferable.
# Comparison to conventional mucogingival interventions
Today's _plastic periodontal surgery_ , evolving from _mucogingival surgery_ , includes all surgical procedures performed to prevent or correct anatomic, developmental, traumatic or disease-induced defects of the gingiva, alveolar mucosa or bone (Proceedings of the World Workshop in Periodontics 1996). To verify the beneficial effects of a microsurgical approach, the results after using a conventional technique in all the different indications have to be evaluated first. The variables to be used as descriptors of the therapeutic end-point of success may vary, depending on the specific goal of the mucogingival therapy. Some results, such as volume changes after ridge augmentation procedures, are clinically difficult to assess due to a lack of a defined end-point and are therefore documented in the literature by qualitative measurements only. Plastic surgical interventions with clearly defined landmarks for measurement, and thus well investigated in the literature, are the guided tissue regeneration procedures (Needleman _et al_. 2006) and the coverage of buccal root recessions (Roccuzzo _et al_. 2002; Oates _et al_. 2003). While the former results in a reduction in probing measures, an improved attachment gain, and less increase in gingival recession compared to open flap debridement, the latter yields a significant reduction in recession depth and also an improvement in clinical attachment level measures. However there is a marked variability between the studies, indicating the influence of case selection, the materials used, the techniques applied, and the surgeons' dexterity. As a result, it is difficult to draw general conclusions because the factors affecting the outcomes are unclear from the literature and these might include study conduct issues such as bias. Among these factors, the dexterity of the surgeon ranks high and seems to influence the results strongly. It is a complicated, proprioceptive reflex involving eye, hand, and brain, and is therefore difficult to assess in clinical settings. To eliminate its influence and to estimate the magnitude of the real benefits of a microsurgical approach, micro- and macrosurgical techniques should be compared in controlled studies.
**Fig. 45-11** Minimally invasive surgical technique (MIST) (Cortellini & Tonetti 2007). (a) Releasing incision, ending right-angled at the gingival margin. (b) Primary closure of the buccal papilla by a mattress suture (according to Laurell) with 7-0 polyamide thread (black) and two single-knot closures with 8-0 polypropylene threads (blue). (c) Clinical appearance of the releasing incision 4 days post-operatively.
**Fig. 45-12** Recession coverage: Macro- and microsurgery in comparison (Burkhardt & Lang 2005). (a) Macrosurgical recession coverage: (a1) pre-operative clinical situation; (a2) immediately after the surgical intervention; (a3) corresponding angiographic evaluation after the intervention; (a4) healing after 7 days; (a5) angiographic evaluation after 7 days; (a6) clinical situation after 3 months (visible contours of incision lines). (b) Microsurgical recession coverage: (b1) pre-operative clinical situation; (b2) immediately after the surgical intervention; (b3) corresponding angiographic evaluation after the intervention; (b4) healing after 7 days; (b5) angiographic evaluation after 7 days; (b6) clinical situation after 3 months (no traces of the intervention visible).
Concerning the coverage of mucosal recessions, a comparison between the two approaches (micro- and macrosurgery) has been performed in a randomized controlled clinical trial (Burkhardt & Lang 2005). The study population consisted of ten patients with bilateral class I and class II recessions at maxillary canines. In split-mouth design, the defects were randomly selected for recession coverage either by a microsurgical (test) or macrosurgical (control) approach. Immediately after the surgical procedures and after 3 and 7 days of healing, fluorescent angiograms were performed to evaluate graft vascularization. The results at test sites revealed a vascularization of 8.9 ±1.9% immediately after the procedure. After 3 days and after 7 days, the vascularization rose to 53.3 ±10.5% and 84.8 ± 13.5%, respectively. The corresponding vascularization at control sites were 7.95 ± 1.8%, 44. 5 ± 5.7%, and 64.0 ± 12.3%, respectively (Fig. 45-12). All the differences between test and control sites were statistically significant.
In addition, the clinical parameters were assessed before the surgical intervention, and 1, 3, 6, and 12 months post-operatively. The clinical measurement revealed a mean recession coverage of 99.4 ± 1.7% for the test and 90.8 ± 12.1% for the control sites after the first month of healing. Again, this difference was statistically significant. The percentage of root coverage in both test and control sites remained stable during the first year, at 98% and 90%, respectively.
The present clinical experiment has clearly demonstrated that mucogingival surgical procedures designed for the coverage of exposed root surfaces, performed using a microsurgical approach, improved the treatment outcomes substantially and to a clinically relevant level when compared with the clinical performance under routine macroscopic conditions. However, the choice of micro- and macrosurgical approaches must be seen in different lights, including treatment outcomes, logistics, cost, and patient-centered parameters. Future comparative studies will produce the evidence whether the use of the surgical microscope will further increase surgical effectiveness and thus become an indispensable part of periodontal surgical practice.
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# Chapter 46
# Re-osseointegration
Tord Berglundh and Jan Lindhe
* * *
Introduction
Is it possible to resolve a marginal hard tissue defect adjacent to an oral implant?
Non-contaminated, pristine implants at sites with a wide marginal gap (crater)
Contaminated implants and crater-shaped bone defects
Re-osseointegration
Is re-osseointegration a feasible outcome of regenerative therapy?
Regeneration of bone from the walls of the defect
"Rejuvenate" the contaminated implant surface
Is the quality of the implant surface important in a healing process that may lead to re-osseointegration?
The surface of the metal device in the compromised implant site
* * *
# Introduction
In Chapter 24 (Peri-implant Mucositis and Peri-implantitis) important features of inflammatory lesions in the peri-implant tissues were described. Peri-implantitis is defined as a progressive inflammatory process that involves the mucosa and the bone tissue at an osseointegrated implant in function, and that this process results in loss of osseointegration and supporting bone (Fig. 46-1).
In Chapter 41 (Treatment of Peri-implant Lesions) it is emphasized that peri-implantitis is associated with the presence of submarginal deposits of plaque and calculus and that the successful treatment of the condition must include (1) comprehensive debridement of the implant surface and (2) subsequent interceptive supportive therapy including professional and self-performed plaque removal measures.
An obvious, additional goal in the treatment of peri-implantitis is the regeneration and _de novo_ bone formation, i.e. "re-osseointegration", at the portion of the implant that lost its "osseointegration" in the inflammatory process. Furthermore, since the level of the peri-implant mucosa is dependent on the level of the marginal bone, an increase of the height of the osseous tissue will result in a marginal shift of the mucosa. Soft tissue esthetics may also be enhanced, therefore, through re-osseointegration.
# Is it possible to resolve a marginal hard tissue defect adjacent to an oral implant?
## Non-contaminated, pristine implants at sites with a wide marginal gap (crater)
Peri-implantitis lesions are per definition associated with bone loss and loss of osseointegration. The pattern of bone loss is angular and the ensuing defect often has the shape of a marginally open crater.
Findings from animal experiments and fracture healing suggested that hard tissue bridging, through woven bone formation, may occur in a bone defect provided that the distance between the fracture lines was ≤1 mm (Schenk & Willenegger 1977). This concept was translated to implant dentistry. Thus, it was implied that if a large (>1 mm) marginal defect were present between a newly installed oral implant and the host bone of the alveolar process, osseointegration would become compromised (Wilson _et al_. 1998, 2003).
Results presented by Botticelli _et al_. (2004) challenged this hypothesis. In a human study that included implant placement in fresh extraction sockets, they were able to demonstrate that a large void (gap) between the newly installed implant and the socket walls could become completely resolved within a 4-month period. Furthermore, in animal experiments Botticelli _et al_. (2003a,b, 2005, 2006) produced – by mechanical means – large hard tissue defects in the marginal portion of edentulous sites prior to implant installation. The authors reported that (1) the presence of the wide marginal defect _per se_ was not an impediment for osseointegration, (2) depending on the surface characteristics of the implant, complete resolution of the defect occurred within a 4-month period, and (3) bone fill in the defect was always the result of appositional osteogenesis.
**Fig. 46-1** Schematic drawing illustrating characteristics of peri-implantitis including the inflammatory lesion and the associated bone defect.
## Contaminated implants and crater-shaped bone defects
### Experimental model
In order to study the ability of the tissues in the periimplant defect to regenerate and to establish _de novo_ bone tissue deposition on the contaminated implant surface, a research model was developed. The model was used to induce well defined peri-implantitis lesions in the dog (Lindhe _et al_. 1992) or in the monkey (Lang _et al_. 1993; Schou _et al_. 1993) and is described in detail in Chapter 24.
## Re-osseointegration
"Re-osseointegration" can be defined as the establishment of _de novo_ bone formation and _de novo_ osseointegration to a portion of an implant that during the development of peri-implantitis suffered loss of bone-to-implant contact and became exposed to microbial colonization (alt. the oral environment) (Fig. 46-2). A treatment procedure that aims at reosseointgration must (1) ensure that substantial regeneration of bone from the walls of the defect can occur and (2) "re-juvenate" the contaminated (exposed) implant surface.
**Fig. 46-2** Clinical photograph from a peri-implantitis site following flap elevation. Granulation tissue was removed and the implant surface was cleaned. The decision on whether a regenerative procedure may be considered is based on the morphology of the crater-like bone defect.
# Is re-osseointegration a feasible outcome of regenerative therapy?
## Regeneration of bone from the walls of the defect
Persson _et al_. (1999) induced peri-implant tissue breakdown in beagle dogs according to the Lindhe model referred to above (Lindhe _et al_. 1992). Mandibular premolars were extracted, socket healing allowed, and fixtures (Brånemark System®) with a turned surface were placed and submerged. Abutment connection was performed after 3 months. When the mucosa surrounding all implants had attained a clinically normal appearance, plaque accumulation was allowed and ligatures (cotton floss) were placed around the neck of the implants and retained in a position close to the abutment/fixture junction. After 3 months when the soft tissue exhibited signs of severe inflammation and deep craterlike defects had formed in the peri-implant bone compartments, the ligatures were removed (Fig. 46-3a). Treatment was performed and included (1) systemic administration of antibiotics (amoxicillin and metronidazole for 3 weeks), (2) elevation of fullthickness flaps at the experimental sites and curettage of the hard tissue defect, (3) mechanical debridement of the exposed portion of the implants, (4) removal of the abutment portions of the implants and placement of pristine cover screws, and finally (5) flap management and closure of the soft tissue wound. Radiographs and biopsies were obtained after 7 months of submerged healing. The analysis of the radiographs indicated a complete bone fill in the hard tissue defects (Fig. 46-3b). The histologic analysis of the biopsy sections revealed that treatment had resulted in (1) a complete resolution of the soft tissue inflammation and (2) the formation of substantial amounts of new bone (appositional osteogenesis) in the previous hard tissue defects (Fig. 46-4). However, only small amounts of "re-osseointegration" to the decontaminated titanium surface could be observed and consistently only at the apical base of the defects. In most sites a thin connective tissue capsule separated the "exposed" implant surface from the newly formed bone (Fig. 46-5). Similar findings were reported by Wetzel _et al_. (1999) from another study in the beagle dog and the use of implants with various surface characteristics (turned, plasma sprayed, and sandblasted–etched surfaces).
**Fig. 46-3** (a) Radiographs obtained from two sites exposed to experimental peri-implantitis. (b) The sites in (a) at 7 months of submerged healing after treatment of peri-implantitis. Note the bone fill in the previous osseous defects.
**Fig. 46-4** Ground section representing 7 months of submerged healing after treatment of peri-implantitis. Note the newly formed bone in the hard tissue defects.
**Fig. 46-5** The ground section in Fig. 46-4 in polarized light. Note the connective tissue capsule located between the newly formed bone and the implant surface.
_Conclusion:_ Based on the outcome of the above studies it was concluded (1) that the inflammatory lesions in experimentally induced peri-implantitis can be resolved, (2) that _de novo_ bone formation (appositional growth) predictably will occur from the hard tissue walls of the defect, and (3) that often the large defects may become more or less completely filled with new bone following a treatment that is based on antimicrobial measures. Hence, the problem inherent in re-osseointegration appears to be the implant surface rather than the host tissues at the site.
## "Rejuvenate" the contaminated implant surface
Different techniques have been proposed for a local therapy aimed at "rejuvenating" the once contaminated implant surface. Such techniques have included mechanical brushing of the surface, the use of air–powder abrasives, and the application of chemicals such as citric acid, hydrogen peroxide, chlorhexidine, and delmopinol (Persson _et al_. 1999; Wetzel _et al_. 1999; Kolonidis _et al_. 2003). These local therapies were effective in cleaning the titanium surface and allowing soft tissue healing and bone fill in the bone craters, but only limited amounts of re-osseointegration occurred.
# Is the quality of the implant surface important in a healing process that may lead to re-osseointegration?
## The surface of the metal device in the compromised implant site
It is well known that pristine implants made of commercially pure titanium are covered with a thin layer of titanium dioxide (Kasemo & Lausmaa 1985, 1986). This dioxide layer gives the implant a high surface energy that facilitates the interaction between the implant and the cells of the host tissues. Contamination of a titanium surface, however, alters its quality and an implant with a low surface energy results. Such a surface may not allow tissue integration to occur but may instead provoke a foreign body reaction (Baier & Meyer 1988; Sennerby & Lekholm 1993).
The problem regarding the implant surface was addressed a dog study (Persson _et al_. 2001a) in which pristine implant parts were placed in crater-like bone defects that had developed during "experimental periimplantitis" (a.m. Lindhe _et al_. 1992). The test implants used were comprised of two separate parts, one 6 mm long apical and one 4 mm long marginal part, that were joined together via a connector. During surgical therapy following experimental periimplantitis, the marginal portions of the implants were removed and replaced with pristine analogues. In biopsies obtained after 4 months of healing it was observed that new bone had formed in the crater-like defects and that "re-osseointegration" had occurred to a large area of the pristine implant components.
In an experiment in the dog, Persson _et al_. (2001b) evaluated the potential for "re-osseointegration" to implants designed with either smooth (polished) or roughened (SLA; sandblasted, large grit acid etched) surfaces. Custom-made solid screw implants were placed in the edentulous mandible; in the right side implants with a rough, SLA surface (Fig. 46-6) and in the left side implants with a smooth surface (Fig. 46-7). "Experimental peri-implantitis" was induced and then blocked when about 50% of the peri-implant bone support was lost (Fig. 46-8a). Treatment included (1) systemic antibiotics (amoxicillin and metronidazole for 17 days), (2) flap elevation and curettage of the bone defect, and (3) mechanical debridement of the implant surface (cotton pellets soaked in saline). The implants were submerged and biopsies obtained after 6 months of healing. In all implant sites most of the crater-like defects had been filled with newly formed bone (Fig. 46-9b). However, at sites with smooth surface implants only small amounts of "re-osseointegration" (Fig. 46-10) had occurred. Examination of the histologic sections from sites with rough surface implants, however, revealed that >80% of the previously exposed rough surface exhibited "re-osseointegration" (Fig. 46-11).
**Fig. 46-6** Custom-made implant with a roughened (SLA) surface.
**Fig. 46-7** Custom-made implant with a smooth (polished) surface.
**Fig. 46-8** Radiographs illustrating crater-like bone defects following experimental peri-implantitis at implants with a rough (a) and smooth (b) surface.
**Fig. 46-9** Radiographs illustrating substantial bone-fill in bone defects at 6 months of healing after treatment of experimental peri-implantitis at implants with a rough (a) and smooth (b) surface.
**Fig. 46-10** (a) Ground section representing 6 months of healing after treatment of peri-implantitis at sites with smooth surface implants. The red line indicates the outline of the previous hard tissue defect. (b) Note the connective tissue capsule between the newly formed bone and the implant surface.
**Fig. 46-11** (a) Ground section representing 6 months of healing after treatment of peri-implantitis at sites with rough surface implants. The red line indicates the outline of the previous hard tissue defect. (b) Note the high degree of re-osseointegration to the previously exposed rough implant surface.
_Conclusion:_ Based on the above documentation it is proposed that the rough implant surface may have contributed to a better stability of the blood clot in the bone crater. In addition, during the phase of contraction of the coagulum and formation of granulation tissue, the rough surface may have ensured a continued contact between the newly formed immature tissue and the implant. This upheld contact relationship may, in turn, have facilitated the subsequent formation of a provisional matrix, an osteoid, and eventually woven bone (see Chapter 4). The maintained contact may thus have made possible the bridging of the gap between the walls of the hard tissue crater and the previously exposed implant surface.
In this context it is important to point out that the surface characteristics (smooth vs. rough) of the implant may also influence the risk for a rapid progression of peri-implantitis once initiated (see Chapter 24). Thus, in an experimental study in dogs Berglundh _et al_. (2007) demonstrated that progression of peri-implantitis was more pronounced at implants with a rough (SLA) than with a smooth (polished) surface.
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# Part 14: Surgery for Implant Installation
47 Timing of Implant Placement
_Christoph H.F. Hämmerle, Maurício Araújo, and Jan Lindhe_
48 The Surgical Site
_Marc Quirynen and Ulf Lekholm_
# Chapter 47
# Timing of Implant Placement
Christoph H.F. Hämmerle, Maurício Araújo, and Jan Lindhe
* * *
Introduction
Type 1: placement of an implant as part of the same surgical procedure and immediately following tooth extraction
Ridge corrections in conjunction with implant placement
Stability of implant
Type 2: completed soft tissue coverage of the tooth socket
Type 3: substantial bone fill has occurred in the extraction socket
Type 4: the alveolar ridge is healed following tooth loss
Clinical concepts
Aim of therapy
Success of treatment and long-term outcomes
* * *
# Introduction
Restorative therapy performed on implant(s) placed in a fully healed and non-compromized alveolar ridge, has high clinical success and survival rates (Pjetursson _et al_. 2004). Currently, however, implants are also being placed in (1) sites with ridge defects of various dimensions, (2) fresh extraction sockets, (3) the area of the maxillary sinus, etc. Although some of these clinical procedures were first described many years ago, their application has only recently become common. Accordingly one issue of primary interest in current clinical and animal research in implant dentistry includes the study of tissue alterations that occur following tooth loss and the proper timing thereafter for implant placement.
In the optimal case, the clinician will have time to plan for the restorative therapy (including the use of implants) prior to the extraction of one or several teeth. In this planning, a decision must be made whether the implant(s) should be placed immediately after the tooth extraction(s) or if a certain number of weeks (or months) of healing of the soft and hard tissues of the alveolar ridge should be allowed prior to implant installation. The decision regarding the timing for implant placement, in relation to tooth extraction, must be based on a proper understanding of the structural changes that occur in the alveolar process following the loss of the tooth (teeth). Such adaptive processes were described in Chapter 2.
The removal of single or multiple teeth will result in a series of alterations within the edentulous segment of the alveolar ridge. Hence during socket healing the hard tissue walls of the alveolus will resorb, the center of the socket will become filled with cancellous bone and the overall volume of the site will become markedly reduced. In particular, the buccal wall of the edentulous site will be diminished not only in the bucco-lingual/palatal direction but also with respect to its apico-coronal dimension (Pietrokovski & Massler 1967; Schropp _et al_. 2003). In addition to hard tissue alterations, the soft tissue in the extraction site will undergo marked adaptive changes. Immediately following tooth extraction, there is a lack of mucosa and the socket entrance is thus open. During the first weeks following the removal of a tooth, cell proliferation within the mucosa will result in an increase of its connective tissue volume. Eventually the soft tissue wound will become epithelialized and a keratinized mucosa will cover the extraction site. The contour of the mucosa will subsequently adapt to follow the changes that occur in the external profile of the hard tissue of the alveolar process. Thus, the contraction of the ridge is the net result of bone loss as well as loss of connective tissue. Figure 47-1 presents a schematic drawing illustrating the tissue alterations described above. It is obvious that no ideal time point exists following the removal of a tooth, at which the extraction site presents with (1) maximum bone fill in the socket and (2) voluminous mature covering mucosa.
A consensus report was published in 2004, describing issues related to the timing of implant placement in extraction (Hammerle _et al_. 2004). Attempts had previously been made to identify advantages and disadvantages with early, delayed, and late implant placements. Hämmerle and coworkers considered it necessary, however, to develop a new concept (classification) that incorporated the growing knowledge in this field of implant dentistry. This new classifica-tion took into consideration data describing structural alterations that occur following tooth extraction as well as knowledge derived from clinical observations.
The classification presented in Table 47-1 was introduced in the consensus report. Important aspects of this new classification included the following:
**Fig. 47-1** Schematic drawing depicting the changes in the soft and hard tissues following tooth extraction over time. T1–4 represent the four different time points regarding timing for implant placement.
* In clinical practice the decision to place an implant following tooth extraction is usually determined by some soft and hard tissue characteristics of the healing socket. Healing does not necessarily follow rigid time frames, and may vary according to site and patient factors.
* To avoid temporal-based descriptions, this new classification used numerical descriptors – types 1, 2, 3, and 4 – that reflect the conditions of the hard and soft tissues:
* Type 1 placement: the implant is placed immediately following the extraction of a tooth
* Type 2 placement: the implant is placed in a site where the soft tissues have healed and a mucosa is covering the socket entrance
* Type 3 placement: the implant is placed in an extraction site at which substantial amounts of new bone have formed in the socket
* Type 4 placement: the implant is placed in a fully healed ridge
* It was further recognized that there is a clear separation between hard tissue healing and soft tissue healing within and around the extraction socket.
Advantages and disadvantages with the various timings are presented in Table 47-1.
Two methods for flap closure have been described at implant sites. One approach requires primary would closure, whereas the other one allows for a transmucosal position of the implant or the healing cap. No differences regarding survival rates and interproximal bone levels were found when these two methods were compared in a split-mouth design (Ericsson _et al_. 1997; Astrand _et al_. 2002; Cecchinato _et al_. 2004). These studies did, however, not analyze in detail the differences between submerged or transmucosal healing in sites of high esthetic importance. Hence, not only the width of the gap but also the width of the alveolar ridge are parameters to be con-sidered during treatment planning.
Table 47-1 Classification types 1–4, descriptive definition as well as advantages and disadvantages of each type
# Type 1: placement of an implant as part of the same surgical procedure and immediately following tooth extraction
## Ridge corrections in conjunction with implant placement
It has become common to insert implants immediately after the removal of teeth that were scheduled for extraction for various reasons. Over the years, many claims have been made regarding advantages of immediate implant placement (Chen _et al_. 2004). These advantages include easier definition of the implant position, reduced number of visits in the dental office, reduced overall treatment time and costs, preservation of bone at the site of implantation, optimal soft tissue esthetics, and enhanced patient acceptance (Werbitt & Goldberg 1992; Barzilay 1993; Schwartz-Arad & Chaushu 1997a; Mayfield 1999; Hammerle _et al_. 2004).
It was proposed that placement of an implant in a fresh extraction socket may stimulate bone tissue formation and osseointegration and hence counteract the adaptive alterations that occur following tooth extraction. In other words, type 1 implant installation may allow the preservation of bone tissue of the socket and the surrounding jaw. It was in fact recommended (e.g. Denissen _et al_. 1993; Watzek _et al_. 1995; for review see Chen _et al_. 2004) that implant installation should be performed directly following tooth extraction as a means to avoid bone atrophy.
Clinical studies in man (Botticelli _et al_. 2004; Covani _et al_. 2004) and experiments in dogs (Araujo & Lindhe 2005; Araujo _et al_. 2006a,b) have examined the influence of implant installation in the fresh extraction socket on bone modeling and remodeling in the surgical site.
Botticelli _et al_. (2004) examined hard tissue alterations that occurred in the alveolar ridge during a 4-month period of healing following implant placement in fresh extraction sockets. Eighteen subjects (21 extraction sites) with moderate chronic periodontitis were studied. The treatment planning of all 18 subjects called for extraction of single teeth, and restoration by means of implants in the incisor, canine, and premolar regions of the dentition.
Following sulcus incisions, full-thickness mucosal flaps were raised and the tooth was carefully mobilized and removed with forceps. The site was prepared for implant installation with the use of pilot and twist drills. The apical portion of the socket was pre-tapped. A non-cutting solid screw implant (Straumann®; Basel, Switzerland) with a rough surface topography was installed. The implant was positioned in such a way that the marginal level of its rough surface portion was located apical of the marginal level of the buccal and lingual/palatal walls of the socket (Fig. 47-2a). After implant installation (1) the distance between the implant and the inner and outer surface of the buccal and/or lingual bone plates, and (2) the width of the marginal gap that was present between the implant and the buccal, lingual, mesial, and distal bone walls were determined with the use of sliding calipers.
The soft tissue flaps were replaced and the implants were "semi-submerged" during healing (Fig. 47-2b). After 4 months of healing a surgical re-entry procedure was performed (Fig. 47-2c). The clinical measurements were repeated so that alterations that had occurred during healing regarding (1) the thickness and height of the buccal and lingual/palatal socket walls and (2) the width of the marginal gap could be calculated.
Figure 47-3a presents a photograph of an extraction socket immediately after the removal of a maxillary canine tooth. At re-entry it was realized that the marginal gap had completely resolved. Furthermore, the thickness of the buccal as well as the palatal bone walls had become markedly reduced (Fig. 47-3c,d). In Fig. 47-3d the implant surface can be seen through the very thin remaining buccal bone wall.
**Fig. 47-2** (a) Clinical view of the implant position in the fresh extraction socket. (b) Clinical view of the flaps replaced and sutured. (c) Clinical buccal view of the implant site after 4 months of healing.
**Fig. 47-3** (a) Clinical view of the alveolar socket of a maxillary canine. (b) Clinical view of the implant position in the fresh extraction socket. (c) Clinical occlusal view of the implant site after 4 months of healing. (d) Clinical buccal view of the implant site after 4 months of healing. Note the very thin bone covering the buccal aspect.
Another site from this clinical study is presented in Fig. 47-4. The first maxillary premolar (tooth 14) was removed (Fig. 47-4a) and one implant was placed in the palatal socket of the fresh extraction site. A second implant was placed in the healed edentulous ridge and in position 25 (Fig. 47-4b). At re-entry, it was observed that (1) the marginal gap had been entirely resolved and (2) the distance between the implant and the outer surface of the buccal bone plate had become markedly reduced (Fig. 47-4c).
Botticelli _et al_. (2004) reported that during the 4 months of healing following tooth extraction and implant installation practically all marginal gaps had become resolved. At the time of implant placement, the mean distance (18 subjects, 21 sites) between the implant and the outer surface of the buccal bone wall was 3.4 mm while the matching dimension on the lingual/palatal aspect was 3.0 mm. At re-entry after 4 months, the corresponding dimensions were 1.5 mm (buccal) and 2.2 mm (lingual). In other words, the reduction of the buccal dimension was 1.9 mm (or 56%) while the equivalent reduction of the lingual dimension was 0.8 mm (or 27%).
The findings by Botticelli _et al_. (2004) strongly indicate that implant placement in a fresh extraction socket may, in fact, not prevent the physiologic modeling/remodeling that occurs in the ridge following tooth removal.
In order to study bone modeling/remodeling that occurs in the fresh extraction site following implant placement in more detail, Araújo and Lindhe (2005) performed an experiment in the dog. In this study the authors used histologic means to determine the magnitude of the dimensional alterations that occurred in the alveolar ridge following the placement of implants in fresh extraction sockets. Buccal and lingual full-thickness flaps were elevated in both quadrants of the mandible of beagle dogs. The distal roots of the 3rd and 4th premolars were removed (Fig. 47-5a). In the right jaw quadrants, implants (solid screw, Straumann®, Basel) with a rough surface were placed in the sockets so that the marginal border of the rough surface was below the buccal and lingual bone margin (Fig. 47-5b). The flaps were replaced to allow a "semi-submerged" healing (Fig. 47-5c). In the left jaws the corresponding sockets were left without implantation and the extraction sockets were fully submerged under the mobilized flaps (Fig. 47-5d). After 3 months, the mucosa at the experimental sites in the right and left jaw quadrants appeared properly healed (Fig. 47-6). The animals were sacrificed and tissue blocks containing the implant sites and the edentulous socket sites were dissected and prepared for histologic examination.
**Fig. 47-4** (a) Clinical occlusal view of the alveolar socket of a maxillary first premolar. (b) Clinical view of the implants placed in the previously healed edentulous ridge and in the alveolar socket. (c) Clinical view of the implant sites after 4 months of healing. Note that the distance between the implant and the outer surface of the buccal bone plate had become markedly reduced.
**Fig. 47-5** (a) Photograph illustrating a mandibular premolar site (from a dog experiment) from which the distal root of the 4th premolar was removed. (b) In the test side of the mandible, the implant was placed in the socket in such way that the rough surface marginal limit was flush with the bone crest. (c) The mucosal, full-thickness flaps were replaced and sutured to allow a "semi-submerged" healing. (d) In the contralateral side of the mandible, the sockets were left without implantation.
**Fig. 47-6** Photograph illustrating the implant (a) and edentulous (b) sites after 6 months of healing.
**Fig. 47-7** Buccal–lingual section of the edentulous site. Note that the remaining buccal crest (continuous line) is located far below the lingual counterpart (dotted line). B = buccal aspect; L = lingual aspect.
**Fig. 47-8** Buccal–lingual section of the implant site. Note that the remaining buccal crest (continuous line) is located far below the lingual counterpart (dotted line). B = buccal aspect; L = lingual aspect.
Figure 47-7 presents a buccal–lingual section of one edentulous site after 3 months of healing. Newly formed bone is covering the entrance of the socket. The lamellar bone of the buccal, cortical plate is located about 2.2 mm apical of its lingual counter-part. Figure 47-8a presents a similar section from an implant site in the same dog. The marginal termination of the buccal bone plate is located about 2.4 mm apical to the lingual crest. In other words, the placement of an implant in the fresh extraction socket failed to influence the process of modeling that occurred in the hard tissue walls of the socket following tooth removal. Thus, after 3 months of healing the amount of reduction of the height of the buccal bone wall (in comparison to lingual bone alteration) was similar at the implant sites and the edentulous sites. At 3 months, the vertical discrepancy between the buccal and lingual bone margins was >2 mm in both categories of sites; edentulous sites = 2.2 mm and implant sites = 2.4 mm.
In a follow-up experiment in the dog, Araújo _et al_. (2006a,b) studied whether osseointegration, once established following implant placement in a fresh extraction socket, could be lost as a result of continued tissue modeling of the bone walls during healing. As was the case in their previous study the distal roots of the 3rd and 4th premolars in both quadrants of the mandible were removed following flap elevation. Implants were installed in the fresh extraction sockets, and initial stability of all implants was secured. The flaps were replaced and "semi-sub-merged" healing of the implant sites was allowed. Immediately following flap closure, biopsies were obtained from two dogs, while in five dogs healing periods of 1 month and 3 months were permitted prior to biopsy.
**Fig. 47-9** (a) Buccal–lingual section of an extraction site immediately after implant installation. (b) Contact was established between the pitch on the surface of the implant body and the walls of the socket. B = buccal aspect; L = lingual aspect.
**Fig. 47-10** (a) Buccal–lingual section 4 weeks after implant installation. The void between the implant surface and the bone wall was completely filled with newly formed bone in both lingual (b) and buccal (c) aspects. B = buccal aspect; L = lingual aspect.
Figure 47-9a presents a buccal–lingual aspect of an extraction site immediately after implant installation. Contact was established between the pitch on the surface of the implant body and the walls of the socket. A coagulum resided in the void between the contact regions (Fig. 47-9b) and also in the marginal gap. In sections representing 4 weeks of healing, it was observed that this void had become filled with woven bone that made contact with the rough surface part of the implant (Figs. Fig 47-10). In this 4-week interval, (1) the buccal and lingual bone walls had undergone marked surface resorption, and (2) the height of the thin buccal hard tissue wall had been reduced.
In the interval between 4 weeks and 12 weeks of healing the buccal bone crest shifted further in an apical direction (Fig. 47-11). The woven bone at the buccal aspect that in the 4-week sample made contact with the implant in the marginal gap region had modeled and only fragments of this bone remained (Fig. 47-11c). At the end of the study, the buccal bone crest was located >2 mm apical to the marginal border of the rough implant surface.
These findings demonstrate that the bone (woven bone)-to-implant contact that was established during the early phase of socket healing following implant installation, was in part lost when the buccal bone wall underwent continued atrophy.
It is obvious, therefore, that the alveolar process following tooth extraction (loss) will adapt to the altered functional demands by atrophy and that an implant, in this respect is unable to substitute for the tooth. The clinical problem with type 1 placement is that the bone loss will frequently cause the buccal portion of the implant to gradually lose its hard tissue coverage, and that the metal surface may become visible through a thin peri-implant mucosa and cause esthetic concerns (Fig. 47-12).
The question now arises whether it is possible to overcome this problem. This issue was studied in a beagle dog experiment by Araújo _et al_. (2006b). The distal root of the 3rd mandibular premolar and the distal root of the 1st mandibular molar were removed and implants placed in the fresh extraction sockets. The 3rd premolar socket in this dog model is comparatively small, and hence the implant inserted (Straumann® Standard Implant, diameter 4.1 mm) occupied most of the hard tissue wound (Fig. 47-13). During healing resorption of the buccal bone wall occurred (Fig. 47-14) and >2 mm of the marginal portion of the implant became exposed to periimplant mucosa.
**Fig. 47-11** (a) Buccal–lingual section 12 weeks after implant installation. Note that buccal bone crest shifted in an apical direction and fragments of it could be seen on the denuded implant surface (c). The lingual bone crest, however, remained stable (b). B = buccal aspect; L = lingual aspect.
**Fig. 47-12** Clincal view of an implant lacking the buccal bone. Note that the metal surface had become visible through the thin mucosa.
**Fig. 47-13** Photograph illustrating implant installation in the narrow, 3rd premolar alveolar socket.
The molar socket, on the other hand is very large (Fig. 47-15) and hence after implant (Straumann® Standard Implant, diameter 4.1 mm) placement a >1 mm wide marginal gap occurred between the metal body and the bone walls (Fig. 47-16b). Primary stability of the implant was achieved through contacts between the metal body and the bone in the apical (periapical) portions of the socket. During the early phase of healing this gap in the molar site became filled with woven bone. In the interval when the buccal bone wall underwent programmed atrophy, the newly formed bone in the gap region maintained osseointegration and continued to cover all surfaces of the implant (Fig. 47-16a,b).
_Conclusion:_ The data reported illustrate an important biologic principle. Atrophy of the edentulous ridge will occur following tooth loss. This contraction of the ridge cannot be prevented by placing an implant in the fresh extraction socket. The atrophy includes a marked reduction of the width and the height of both the buccal and lingual bone plates; in particular the buccal bone plate will undergo marked change. To some extent the problem with buccal bone resorption can be overcome by placing the implant deeper into the fresh socket and in the lingual/palatal portion of the socket.
**Fig. 47-14** Buccal–lingual section of the healed premolars sites representing (a) 4 and (b) 12 weeks after implant installation. B = buccal aspect; L = lingual aspect.
**Fig. 47-15** Photograph illustrating implant installation in the wide, 1st molar alveolar socket.
As a consequence of the above described healing, bone regeneration procedures may be required to improve or retain bone volume and the buccal contour at a fresh extraction site. Such bone augmentation is sometimes mandatory in the esthetic area.
## Stability of implant
Another issue with type 1 (and also type 2) placement is the anchorage of the implant to obtain primary stability in a position in the jaw that will enable the subsequent restoration to meet high demands regarding esthetics and function. In most cases of type 1 placement, the implants are fixed in native bone apical to the alveolus (Fig. 47-17). Additional retention may be achieved by anchoring the implant in the bony structures of the alveolar walls or inter-radicular septa.
In a recently presented controlled clinical trial (Siegenthaler _et al_. 2007) it was observed that primary stability for some implants in a type 1 procedure could not always be achieved. In this study implants were inserted to replace teeth either exhibiting periapical pathology (test) or presenting healthy periapical conditions (control). In four implant sites in the test group and one in the control group no implants could be placed due to an unfavorable bone morphology, which precluded primary implant stability.
# Type 2: completed soft tissue coverage of the tooth socket
There are several reasons why the type 2 approach is often recommended. At this stage of healing the socket entrance is covered with a mucosa. The soft tissue is (1) comparatively mature, (2) has proper volume, and (3) can be easily managed during flap elevation and replacement procedures. Furthermore, the type 2 timing permits an assessment of the resolution of periapical lesions that may have been associated with the extracted tooth. The disadvantages inherent in the type 2 approach include (1) resorption of the socket walls and (2) an extended treatment time (Table 47-1).
Following tooth extraction, the socket becomes filled with a coagulum that is replaced with granulation tissue within a few weeks. In the normal case it takes about 4–8 weeks before the soft tissue (granulation tissue, provisional connective tissue; see Chapter 2) fills the socket and its surface becomes covered with epithelium (Amler 1969; Zitzmann _et al_. 1999; Hämmerle & Lang 2001; Nemcovsky & Artzi 2002). The maturation of the soft tissue (further deposition and orientation of collagen fibers) that may facilitate flap management may require an even longer healing time.
The larger amount of soft tissue that is present at the site of implant placement when the type 2 approach is used will allow for precise management of the mucosal flap and hence optimal soft tissue healing (Fig. 47-18). This advantage with the type 2 timing must be matched against the hard tissue reduction and the change of the ridge contour that results from the resorption of the socket walls and of the buccal bone plate. It must be observed that at some extraction sites the mucosa may remain adherent via scar tissue to the underlying bone or to the provisional connective tissue of the socket. In such cases it may be difficult to separate the soft tissue from the bone and to mobilize the flap. In such a situation, the trauma caused in conjunction with flap elevation may rupture the soft tissue and compromise healing. This in turn may result in soft tissue dehiscence, local infection, and inflammation (Zitzmann _et al_. 1997).
**Fig. 47-16** Buccal–lingual section of the healed molars sites representing (a) 4 and (b) 12 weeks after implant installation. B = buccal aspect; L = lingual aspect.
**Fig. 47-17** Type 1 implant placement provides optimal availability of existing bone contours. Note the presence of a thin buccal bone plate. Anchorage of an implant can be achieved by engaging the bone apical to the apex of the extracted tooth and the palatal wall of the socket.
**Fig. 47-18** The soft tissues have completely healed over the extraction socket 8 weeks after tooth removal (type 2).
As described in the schematic drawing in Fig. 47-1 the initial gain in mucosa (area and volume) is later followed by an overall loss of soft tissue volume. This is evidenced by the fact that the volume of alveolar ridge – including the bone as well as the mucosal compartments – markedly decreased during the first 12 months following tooth extraction (Schropp _et al_. 2003).
During the 4–8 weeks between tooth extraction and type 2 implant placement only small amounts of new bone (woven bone) will form in the socket. This means that the risk of not achieving primary implant stability is similar in type 1 and type 2 approaches. Thus, in sites where the available bone height apical to the tip of the root is less than 3 mm, it is frequently impossible to obtain primary implant stability in the bone beyond the apex of the extracted tooth. When, in addition, a wide alveolus is precluding the engagement of its bony walls, the type 3 approach may be favored.
# Type 3: substantial bone fill has occurred in the extraction socket
The type 3 time frame is chosen for implant installation at sites where, for various reasons, bone fill is required within the extraction socket. Newly formed woven bone will occupy the socket area after healing periods extending from 10–16 weeks (Evian _et al_. 1982). In this period, however, the walls of the socket extraction socket 8 weeks after tooth removal (type 2).are frequently completely resorbed and replaced with woven bone. The entrance to the socket is closed with a cap of woven bone that is in the process of remodeling. The mucosa that covers the extraction site is (1) residing on a mineralized ridge, and (2) mature and more easy to manage during surgical flap elevation and replacement procedures.
The type 3 approach often allows the clinician to place the implant in a position that facilitates the prosthetic phase of the treatment. The disadvantages with the type 3 approach encompass (1) a prolonged treatment time, (2) additional resorption and diminuton of the ridge including a substantial change of its contour, and (3) a concomitant loss of soft tissue volume.
# Type 4: the alveolar ridge is healed following tooth loss
In the type 4 approach the implant is placed in a fully healed ridge. Such a ridge can be found after 4 but more likely after 6–12 months of healing following tooth extraction (loss). After 6–12 months of healing following tooth extraction, the clinician will find a ridge that is lined by a mature, often well keratinized mucosa that resides on dense cortical bone. Beneath the cortical bone plate, cancellous bone occupies a varying portion of the alveolar process (for detail see Chapter 2).
In a study including human volunteers it was observed that the rate of formation of new bone within the extraction site started to decrease after 3–4 months of healing. At this stage the newly formed bone and the remaining bone of the socket walls entered into a phase of remodeling (Evian _et al_. 1982). Concomitant with the remodeling of this centrally located bone tissue, extra-alveolar resorptive processes leading to a further contraction of the ridge and change of its contour continued for at least 12 months (Schropp _et al_. 2003).
The advantage of type 4 installation is that healing is more or less complete and that only minor additional change of the ridge may occur. The disadvantages include (1) increased treatment time and (2) further reduction of the overall volume of the ridge and change of its external contour. This pronounced additional loss of ridge volume may at times require complicated bone augmentation procedures (Fig. 47-19). As a consequence type 4 placement is avoided in most cases when the tooth (teeth) to be replaced is (are) present at the time of examination and treatment planning.
# Clinical concepts
When implants are to be placed in the edentulous portion of the ridge, factors other than the tissue changes over time must be considered. Thus, in the treatment planning phase aspects, such as (1) the overall objective of the treatment, (2) the location of the tooth within the oral cavity – in the esthetic or non-esthetic zone – and (3) the anatomy of the bone and the soft tissue at the site(s) to be treated, must be evaluated.
**Fig. 47-19** A buccal dehiscence defect is present at an implant placed into a ridge, which has undergone substantial buccal bone resorption since tooth extraction several months ago (type 4).
## Aim of therapy
Dental implants are most often used to restore health and function. During the surgical phase of therapy, therefore, ideal conditions must be established for successful bone and soft tissue integration to the implant. In a growing number of cases, however, treatment must also satisfy demands regarding the esthetic outcome. In such cases, the overall surgical and prosthetic treatment protocol may become more demanding, since factors other than osseointegration and soft tissue integration may play an important role.
### Restoration of health and function
In cases where the restoration of health and function constitutes the primary goal of the treatment, the location and volume of available hard and soft tissues are the important factors to consider. In such cases the type 1 approach is usually selected (Wichmann 1990).
The replacement of a single-rooted tooth with an implant in a fully healed ridge will, in most cases, ensure proper primary stability with the implant in a correct position (Fig. 47-20). In addition, the soft tissues are sufficient in volume and area. The mucosal flap can be adapted to the neck (or the healing cap) of the implant (one-stage protocol). When primary wound closure is intended (two-stage protocol), mobilization of the soft tissue will allow tension-free adaptation and connection of the flap margins.
When an implant is placed in the fully healed site of a multi-rooted tooth, the surgical procedure becomes more demanding. Often the ideal position for the implant is in the area of the inter-radicular septum. If the septa are delicate, anchorage for primary implant stability may become difficult to achieve. In addition, in molar sites there is often only a small amount of soft tissue present. This may create a problem with respect to wound closure with a mobilized, tension-free flap. In some molar sites, primary wound closure may not be possible at times following implant installation.
**Fig. 47-20** (a) Immediate implant placement (type 1) in a mandibular premolar extraction socket. Note the buccal bone deficiency, where bone will be augmented by guided bone regeneration (GBR). (b) The same site as in (a) following adaptation of the flap around the neck of the implant obtaining a transmucosal mode of healing.
The presence of marginal defects (gaps) between the implant and the fully healed ridge following type 4 placement was regarded in the past as a significant problem that could compromise osseointegration. Recent studies in man and animals have demon-strated, however, that in such a horizontal marginal defect (gap) of ≤2 mm, new bone formation as well as defect resolution and osseointegration of the implant (with a rough titanium surface) will occur (Wilson _et al_. 1998; Botticelli _et al_. 2004; Cornelini _et al_. 2005).
### Esthetic importance and tissue biotype
The replacement of missing teeth with implants in the esthetic zone is a demanding procedure. Deficiencies in the bone architecture and in the soft tissue volume and architecture may compromise the esthetic outcome of treatment (Grunder 2000). Hence, when an implant is to be placed in the esthetic zone, not only the anatomy of the hard tissues but also the texture and the appearance of the soft tissues must be considered.
Type 2 installation is often to be preferred when implants are placed in the esthetic zone (Fig. 47-21). The key advantage in type 2 (as opposed to type 1) is the increased amount of soft tissue that has formed during the first weeks of healing following tooth extraction. It must be emphasized, however, that comparative studies analyzing the treatment outcomes in randomly selecting type 1 or type 2 placements have so far not been reported.
In a recent clinical study, implants were placed in fresh extraction sockets (Botticelli _et al_. 2004). During healing, the implants became clinically osseointegrated within the borders of the previous extraction socket. Significant loss of buccal bone height (contour) however also occurred. In esthetically critical situations this loss of contour may lead to a compromised outcome. Hence not infrequently, tissue augmentation procedures must be performed in the esthetic zone.
In this context it is important to realize that when a two-stage implant placement protocol is used, the labial mucosa will recede following abutment connection surgery. Mean values of recession between 0.5 mm and 1.5 mm with large variations have been reported in several clinical studies (Grunder 2000; Oates _et al_. 2002; Ekfeldt _et al_. 2003). These findings additionally stress the necessity for a careful treatment approach when implants are placed in the esthetic zone.
The biotype (see Chapter 3) of the soft and hard tissue tissues may play a role regarding the esthetic outcome of implant therapy. Characteristics of soft and hard tissues at teeth were described and classified into two biotypes: the flat thick or the pronounced scalloped thin biotype (Weisgold _et al_. 1997; Olsson & Lindhe 1991; Olsson _et al_. 1993). The thin tissues in the pronounced scalloped biotype include a thin free gingiva, a narrow zone of attached mucosa, and a pronounced "scalloped" contour of the gingival margin. In addition, the scalloped thin biotype is associated with a delicate bone housing. In a recent study it was found that buccal tissue recession at singletooth implants was more pronounced in patients exhibiting a thin biotype compared to patients with a thick biotype (Evans & Chen 2007). Based on these findings and on clinical experience it was proposed that patients exhibiting a pronounced scalloped biotype should be treated with a type 2, 3, or 4 rather than with a type 1 implant installation approach (Fig. 47-22). Data collected from properly designed clinical studies regarding this issue are presently lacking.
**Fig. 47-21** (a) A single tooth gap 8 weeks following tooth extraction. The soft tissues have completely healed over the extraction socket. (b) The same site as in (a). An implant has been placed in the edentulous gap. The resulting buccal dehiscence defect will be augmented with bone by applying GBR.
**Fig. 47-22** A patient exhibiting a thin tissue biotype as characterized by a thin free gingiva, a narrow zone of keratinized and of attached mucosa, shallow probing depths, and a pronounced "scalloped" contour of the gingival margin including recessions at some maxillary anterior teeth. Tooth 11 is scheduled for extraction and replacement by an implant using a type 2 or 3 approach.
## Success of treatment and long-term outcomes
Numerous clinical studies have demonstrated that type 1 implant placement is a successful and predictable clinical method (Lang _et al_. 1994; Schwartz-Arad & Chaushu 1997b; Hämmerle _et al_. 1998; Covani _et al_. 2004). In addition, success and survival rates for type 1 implants have been reported to be of the same magnitude as implants placed in healed ridges (Gelb 1993; Grunder 2000; Gomez-Roman _et al_. 2001; Gotfredsen 2004; Schwartz-Arad _et al_. 2004). Histologic studies in animals confirmed the viability of type 1 placement. Unloaded titanium implants placed in extraction sockets showed a high degree of osseointegration (Anneroth _et al_. 1985), i.e. similar to the one at implants placed in healed sites. Furthermore, a few studies analyzing survival rates of type 2 and 3 placements have shown similar survival rates as the ones reported for types 1 and 4 (Watzek _et al_. 1995; Nir-Hadar _et al_. 1998; Polizzi _et al_. 2000).
### Conclusions
In situations where teeth are to be replaced with implants, various factors govern the decision regarding the optimal time point for implantation following tooth extraction. Of special importance are the overall objective of the treatment, the location of the tooth within the oral cavity, the anatomy of the bone and the soft tissue at the site, and the adaptive changes of the alveolar ridge following tooth extraction. The decision regarding the timing for implant placement needs to be based on a thorough understanding of the structural changes that occur in the alveolar process following tooth extraction, with and without implant placement as presented in this chapter.
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# Chapter 48
# The Surgical Site
Marc Quirynen and Ulf Lekholm
* * *
Bone: shape and quality
Clinical examination
Radiographic examination
Planning for implant placement
Implant placement
Guiding concept
Flap elevation
Flapless implant insertion
Model-based guided surgery
Bone preparation
Anatomic landmarks with potential risk
Implant position
Number of implants
Implant direction
Healing time
* * *
# Bone: shape and quality
It is imperative that the conditions of the soft and hard tissues as well as of the shape of the bone in the recipient sites intended for implants are carefully examined. Both clinical and radiographic parameters must be used in this examination.
## Clinical examination
The clinical examination should include assessment of (1) colour and texture alterations of the mucosa (indicative of a lesion) and (2) the thickness of the soft tissues. The recipient site should also be palpated in order to estimate the volume of the tissues available in the edentulous region of the jaw. It must be realized, however, that both the mucosa and the bone of the edentulous region are included in this clinical measure. Hence, the clinician must realize that palpation may overestimate the volume of hard tissue present at the site.
The clinical examination must also determine the inter-arch gap and the dimensions of the edentulous area to ascertain that enough space is present (1) to allow optimal maneuvering (access of the hand piece together with the preparation drills) during surgical procedures, (2) to avoid damage of the periodontium of teeth adjacent to the edentulous area during implant insertion, and (3) to allow placement of the prosthetic device. As a rule of thumb, the inter-arch distance should be ≥5 mm, and the distance between a tooth and an implant should be ≥3 mm. If the size of the edentulous region is diminutive, implants with a small diameter must be selected, and eventually a surgical guide (stent) used to assist the surgeon during implant installation. This might help to avoid contact with the neighboring teeth.
The jaw relation (angle class) must also be determined, as this will have an influence on the direction of insertion of the implants (further discussed below). In the final step of the clinical examination impressions of the jaws (dentition) are obtained and stone cast models prepared. Such models can later be used during treatment planning and for the preparation of surgical position and direction stents.
## Radiographic examination
The radiographic examination (see Chapter 28) will provide more detailed information on the amount and quality of the bone available at the recipient site. Lekholm and Zarb (1985) proposed that the edentulous jaw (segment of the jaw) should be classified regarding its shape and quality. Thus a grading into five groups was used to describe the shape of the jaw (Fig. 48-1a) while four groups were used to describe the quality of the bone tissue (Fig. 48-1b).
Panoramic and intraoral apical radiographic images give a first impression of the bone, as well as of important anatomic landmarks such as: the floor of sinusal and nasal cavities; the incisive nerve; the inferior alveolar nerve; the roots and apices of neigh-boring teeth; and the crest of the alveolar ridge. From the two-dimensional images it is also possible to obtain some information about the available height of the bone at the recipient site, while three-dimensional radiographs are essential to determine the width of the alveolar crest. It is important to realize that the definitive evaluation of the dimension of the recipient site should not be based on observations made in intraoral radiographs or in orthopan-tomograms. This is especially true in cases where intraoral palpation indicated the presence of a narrow ridge (jaw). Indeed, the precise location of the inferior alveolar nerve must be identified via measurements made in images from conventional or computer-assisted tomography (CT). Correct identi-fication of the mandibular canal may assist the clinician to avoid damaging the nerve during surgery and thereby preventing the occurrence of complications such as impaired sensory function and paresthesia of the lower lip and neighbouring soft tissues (Abarca _et al_. 2006).
**Fig. 48-1** Schematic drawings showing (a) residual jaw shape classification, and (b) jaw bone quality classification, according to Lekholm and Zarb (1985).
The cylinder-shaped cavity prepared in the recipient site to house the endosseous part of the implant is, as a rule, 1–2 mm longer than the titanium device _per se_. Thus, for a 7-mm long implant, the required minimum height of the bone of the recipient site is 8–9 mm (Fig. 48-2). In cases where implants are to be installed in positions above the inferior alveolar nerve, a minimum height of 9–10 mm of bone is required for a 7-mm long implant.
## Planning for implant placement
Radiographs are used to make preliminary decisions regarding the position (s) as well as the number and dimensions of implants to be used. The location of the most distal implant is determined first (Fig. 48-3). The number and the position of more mesially located implants are identified thereafter. In this treatment planning process it must be recognized that the interimplant distance must be ≥3 mm.
**Fig. 48-2** Schematic drawings showing minimum bone volume needed for standard implants of the Brånemark System.
**Fig. 48-3** Schematic drawings indicating location of minimum bone volume areas in distal directions, and giving distances needed for various numbers of implants. Arrows indicate prominence and apex of the nearest tooth.
The final decision regarding the number and dimension of implants to be inserted, however, is most often made during surgery, i.e. after the soft tissue flaps have been elevated and the bone of the recipient sites has been exposed.
**Fig. 48-4** An example (for this illustration without soft tissues) of part of a jawbone in which a progressively larger defect has been created, initially within the spongious bone (a–c), later (d,e) also perforating the cortex. The images (f–j) represent the corresponding radiographs.
### Defects in the jaw bone
Intraoral (conventional or digital) as well as extraoral radiographic images (conventional tomography, spiral CT) may not necessarily reveal all lesions and defects in the jawbone. In a recent _ex vivo_ study (Van Assche _et al_. 2007), intraoral radiographs were taken of progressively larger, artificially created, defects in both the mandible and the maxilla. As illustrated in Fig. 48-4, a defect first became visible in the radio-graph when the area (junction) including the cortical plate and cancellous bone was involved. This indicates that the clinician may overlook such intra-ridge lesions (Quirynen _et al_. 2005).
During implant installation surgery, minor fenestrations or marginal dehiscences sometimes occur. Hence some threads of the implants may be exposed (not covered by bone). In most cases such uncovered threads may be left unattended since no adverse reactions have been observed in the mucosa at such locations (Lekholm _et al_. 1996). On the other hand, if the jaws contain defects of such a magnitude that the implants cannot be placed in proper positions without having major parts of their surfaces exposed, ridge augmentation is often recommended. This may include guided bone regeneration (Molly _et al_. 2006) and/or bone grafting (Buser _et al_. 1994; Deporter 2001). A recent systematic review on augmentation techniques (Chiapasco _et al_. 2006) indicated that several different procedures may enhance the bone volume in a predictable manner and establish better conditions for implant insertion. For further details regarding ridge augmentation see Chapter 49.
_Summary:_ the local condition of edentulous areas considered for implants must be properly evaluated, and no pathology in the soft and/or hard tissues of the jaws should be accepted at the time of implant placement. Radiographic evaluations are necessary in order to identify important landmarks in the jaws as well as to study the shape and the quality of the bone tissue in areas considered for implants. Tomography is used when implants are to be placed above the inferior alveolar nerve, and/or when the clinical examination indicates that the recipient site harbors minute amounts of bone. The minimum amount of bone required for implant surgery is related to the size and surface of the implants to be used.
# Implant placement
## Guiding concept
The main purpose for the use of implants in dentistry is to establish a stable anchorage for a fixed or removable prosthesis (Brånemark _et al_. 1985). In order to allow osseointegration to occur and be maintained, the handling of the bone tissue during surgery must be diligent. It is important to recognize that bone is a living tissue that must not be exposed to undue trauma. The surgical procedure must be performed according to carefully established guidelines (e.g. Adell _et al_. 1985; Lekholm & Jemt 1989). Furthermore, the surgeon must pay maximum attention to basic rules of sterility and asepsis. It is often noticed that sterile drapes are used while the nose, the most infected site of the entire facial area, is left uncovered. The use of a sterile nose cap that allows the patient to breath freely but prevents the contamination of the sterile gloves and instruments (van Steenberghe _et al_. 1997) is recommended.
## Flap elevation
The mucosa of the ridge can be incised using either a crestal or a vestibular approach. At present there is no information available to indicate that one of the two approaches is more advantageous than the other. Consequently, the clinician can select the method best suited for the individual situation. Crestal incisions may be preferred at sites where the crest of the ridge is wide. If the crest is high but narrow, a buccal approach might be preferred. Moreover, when ridge augmentation is to become part of the surgical procedure, incisions on top of the area to be augmented should be avoided (to prevent early exposure of bone substitute or membrane). In cases of so-called one-stage installation surgery, a crestal incision is, of course, mandatory.
Implants are often placed in edentulous sites that are bordered by teeth. Whenever possible, and in particular in the "esthetic zones", the gingiva (papillae) of the neighboring teeth should not be included in the flap. Shrinkage of the papillae during healing is therefore avoided and the occurrence of black triangles in the "tooth–implant" region prevented.
At narrow edentulous sites where implants must be placed close to teeth, it is often necessary to include the gingiva in the flap. In such cases, the crestal incision made in the edentulous area is continued mesially and/or distally into the pocket of the adjacent teeth and is sometimes combined with vertical releasing incisions in the gingiva. The flap is hereby increased in dimension, will receive a more adequate vascular support, and may be managed to allow full soft tissue coverage of the bone and the implant (s).
It is important to make sure that, during the soft tissue elevation procedure, the entire periosteum is properly released from the walls of the jaw and included in the flap (full-thickness flap). This is particularly important when a flap is released from the lingual side of the mandible. The exposure of the lingual hard tissue wall of the mandible allows the surgeon to detect an accidental perforation of the lingual cortex during drilling and implant installation. It is also important to release a full-thickness flap on the buccal side of both the maxilla and the mandible. This will make it possible to observe the presence of cavities and/or protrusions of the jaws, contours of tooth roots, and nerve entrances, i.e. structures that may influence the positioning of the implants. Finally flap elevation and exposure of the osseous tissue will facilitate irrigation (cooling) of the site during drilling.
## Flapless implant insertion
Implant installation without flap elevation and exposure of the bone tissue was recently introduced. This approach is obviously supported by commercial pressure. Flapless surgery no doubt may offer some advantages including (1) reduction in complications for the patient (less pain and swelling), (2) reduced surgical time and no suturing, and (3) good fit between implant and soft tissues that facilitates the restorative phase of treatment. The success of this implant installation approach depends to a large extent on the quality of the surgical template (stent) that must be used.
The scientific data on flapless implant surgery is sparse (Becker _et al_. 2005; van Steenberghe _et al_. 2005; Fortin _et al_. 2006). Hence, the use of flapless implant insertion as "routine" procedure in daily practice is questioned, due to the absence of long-term data.
## Model-based guided surgery
With the use of a plaster model that presents the edentulous area and with additional information on the thickness of the soft tissues, the dental technician can replicate the underlying jaw bone. The implant insertion can be planned and performed on the plaster model and the most convenient position for the permanent restoration can also be determined. In a next step, the model can be used to prepare a surgical template. The template can be fitted with sleeves (canals) to guide the drilling procedure. Since the model also reproduces the soft tissues of the recipient site, fabrication of a provisional restoration can be made even before the implants are actually inserted in the jaw of the patient.
## Bone preparation
Bone tissue must not be exposed to adverse heat. Drilling in bone tissue may increase the temperature at the recipient site (Brånemark _et al_. 1985). The threshold level for osteocyte damage lies around 47ºC, only about 10ºC above body temperature (Eriksson & Adell 1986). Consequently, all mechanical preparation of the jaw must be performed with a minimum rise in temperature. This can be achieved via the use of an intermittent drilling technique, together with the use of sharp burs. The preparation of the implant bed should be performed in a sequence of steps, and consistently with profuse saline irrigation (Adell _et al_. 1985). In the presence of particularly dense bone, e.g. in the symphysis region of the mandible, it is also recommended to use an extra wide twist drill, prior to the pretapping procedure and/or insertion the implants (Friberg 1994). When implants are to be placed in soft bone, drilling must be performed with the greatest care, as there is a risk that the entrance of the implant site may be widened too much, and the inserted implant may become unstable. To minimize the risk of initial implant instability, an adjusted surgical technique using either thinner drills or wider diameter implants was recommended (Bahat 1993; Friberg 1994; Watzek & Ulm 2001).
**Fig. 48-5** Schematic drawing showing maximum drilling depth (x) without reaching the nerve, as measured from the top of the crest, and implant site length (y), as measured from the lowest bone level in the canal entrance.
The only structure that can clearly be identified both in radiographs and clinically is the top of the alveolar crest. Consequently, this configuration has to be used as reference for all measurements, both in radiographs and during surgery. During the preparation of the site it is also of particular importance to keep an eye on the depth indicators of the drills and how they relate to the top of the crest. It must be pointed out that during the preparation of the site, the reference point on the crest for the depth measurements may move in an apical direction, particularly if a narrow and drop-shaped alveolar crest is present in the recipient site (Fig. 48-5).
# Anatomic landmarks with potential risk
Implant surgery is often regarded/promoted, especially by implant companies, as a safe and minimally invasive procedure. This is not the case, however, especially when implants are placed in the lower jaw (Mraiwa _et al_. 2003a,b). Mechanical compression and/or direct injury during implant insertion may (1) disturb the nerve and initiate a neural degenerative process, or (2) disturb the microcirculation and cause edema and/or a local hematoma.
Neurosensory disorders of the inferior alveolar, mental, or incisive nerves have been reported to occur after implant surgery. Usually the resulting anesthesia, paresthesia, or even dysesthesia are transient phenomena, but certain long-lasting/permanent neuropathies have been reported. An optimal radiographic analysis of the lower jaw is mandatory when planning for implant placement in the neigh-borhood of the mental foramen or above the inferior alveolar nerve. It still remains a matter of discussion whether injury to the incisive canal in the lower jaw can cause neuropathy.
Several cases of severe hemorrhage in the floor of the mouth, with subsequent life-threatening upper airway obstruction, have been recorded in association with implant placement in both the anterior and posterior portions of the mandible (for review see Kalpidis & Setayesh 2004). Two arteries are responsible for the vascular supply to the mandible (Fig. 48-6a). At the anterior border of the hypoglossus muscle, the lingual artery gives rise to the sublingual artery. This important artery (2 mm in diameter) traverses the floor of the mouth in a frontal direction, near the medial and superior surface of the mylohyoid muscle, medially to the sublingual gland, and inferio-medially to the submandibular duct and the lingual nerve. The sublingual artery gives off several alveolar branches for complementary blood supply to the lingual anterior cortical plate of the mandible. A second small artery, the submental artery (2 mm in diameter), a branch of the facial artery, runs along the inferior plane of the mylohyoid muscle lateral to the anterior belly of the digastric muscle. As illustrated in Fig. 48–6b, the submental artery runs close to the lingual lower border of the mandible. The largest branches of this artery may be seen on a cone-beam or dental CT as they extend into the bone (Fig. 48-6c–e).
The intimate proximity of these arteries, or their vascular plexa, to the lingual cortical plate explains why a lingual perforation in the lower third of the mandible can result in a massive hematoma in the floor of the mouth. Due to the presence of the strong cervical fasciae in the neck region (the _superficial layer_ , the _fasciae of the infra-hyoid muscles_ , the _pretracheal layer_ ), the hematoma will displace the tongue and floor of the mouth superiorly and posteriorly, posing a potentially serious threat of obstruction of the upper airway (for review see Kalpidis & Setayesh 2004). Several reports have appeared in the literature describing massive hematoma in the floor of the mouth, where unfortunately a tracheostomy or intubation was the only option to save the life of the patient.
The shape of the lower jaw exhibits large individual variation. A small proportion of jaws (3%) (Quirynen _et al_. 2003) has a distinct lingual depression between lateral incisor and second premolar, superior to the mylohyoid muscle, to house the lingual gland (called the sublingual fovea). Perforation of the bone with a drill in this region must be avoided. As stated previously, deep dissection of the mucoperiosteal flap lingually is strongly recommended in implant installation surgery to expose the cortical plate of the mandible.
**Fig. 48-6** (a) Schematic representation of the arterial anatomy in the floor of the mouth. The mandible is depicted in a midsagittal cross section. The sublingual and submental arteries follow almost parallel pathways, respectively superior and inferior to the mylohyoid muscle. The intimate proximity of these arteries (or their branches) to the lingual cortical plate of the mandible explains the risks for a hematoma after perforation of the latter. (b) Dissection, _ex vivo_ , of submental artery illustrating its proximity with the lower lingual cortex of the mandible. (c) Axial slice with clear appearance of artery running into the bone at the canine position. (d) Reformatted cross section at canine position, fortunately the implant remained far away from the artery as well as from the lingual cortical plate. (e) Dissection of branches from sublingual artery running into the bone to make anastomosis with incisive artery.
# Implant position
If possible an implant should be placed in tooth position (Fig. 48-7), both in a mesio-distal and in a bucco-lingual direction. To achieve this, the starting point for the insertion in the bone must, in most instances, be located towards the buccal side of the crest in the mandible, and towards the palate in the maxilla. This is due to the presence of concavities that often exist in the jaws. Depending on the size of such concavities, the starting point (for the instertion) will be located either close to the top of the crest, as in the case of a wide alveolar process, or deeper down palatally or buccally (Fig. 48-7), if the jaw is thin in its coronal portion.
**Fig. 48-7** Schematic drawings showing implant positions in mesial–distal and buccal–lingual dimensions. Indicated starting points for drilling are marked with black arrows.
In cases of partial edentulism, the recipient site closest to a tooth must first be identified. The cylindrical canal in the recipient site is prepared approximately 3.5–4 mm away from the prominence of the tooth. The subsequent implant positions, in a distal direction, are then identified. The minimum amount of bone that must be present in a recipient site is dependent on the dimension of the implants used; as a rule of thumb: the bone tissue of the site should be about 4(5) mm (in a horizontal direction) and about 7(9) mm (in a vertical direction) (Figs. 48-2, 48-3).
In a fully edentulous jaw, it might be preferable to start by placing the most distal implants, so that the position of other implants can be selected accordingly. The longest distance that can be accepted between two implants has not yet been properly defined. As an alternative to a reduced interimplant distance, and an increased number of implants, it is sometimes possible to use wider diameter implants, as discussed below.
**Fig. 48-8** Schematic drawing indicating a tripod placement of the implants in order to minimize individual load distribution onto each implant by creating several rotational axes.
## Number of implants
In partially edentulous jaws preferably three implants should be inserted in order to avoid overloading of the anchorage units (Rangert _et al_. 1989). The failure rate has been reported to be higher for reconstorations placed on two than for those on three or more implants (Jemt & Lekholm 1993). Furthermore, the implants should be placed in a tripod position (Fig. 48-8) instead of being inserted in a straight line, thereby minimizing the transmission of bending forces on to each individual implant (Rangert _et al_. 1989). If only one implant can be inserted, then in most cases this anchorage should be used to support a single crown restoration. Implants should never be placed in the midline of the maxilla, not only because they might eventually expand the suture between the two maxillae, but such implants may eventually compromise the esthetics and phonetics after the prosthetic device has been inserted.
# Implant direction
After the position of the implant has been identified, the direction/inclination of the implant in the jaw (bucco-lingual and mesiodistal) must be determined. If possible the implants should be placed in tooth position. This means that in the normal case the long axis of the implant should be directed through the occlusal surface of the final restoration. Regarding the bucco-lingual dimension (Fig. 48-9), the long axis of mandibular implants will mainly be directed towards the limbus part of the incisors or the palatal cusps of the teeth in the maxilla. For implants placed in the maxilla, the corresponding inclination should be towards the incisal edges of the frontal teeth or the buccal cusps of the premolars or molars of the mandible. If the starting point of the implant sites in the maxilla is located close to the top of the crest, and if a concavity on the buccal side of the ridge is present, there is a risk that the surgeon leans the long axis of the implants too far buccally. The equivalent for the mandible is an implant directed too far lingually owing to the presence of lingual concavities. Such adverse directions can impair the esthetics and function of the future restoration (Fig. 48-7), even though angulated abutments may to some extent compensate for such a surgical shortcoming.
**Fig. 48-9** Schematic drawings showing the most favorable starting points and implant directions in a buccal–lingual dimension within (a) the mandible and (b) the maxilla. A = closest distance of a site to a tooth.
In addition, the inclination of the implants to be inserted will depend on the existing jaw relation. In the case of angle class I jaw relation, the implants should be placed rather vertically in both jaws. In angle class II, the implants should often be placed vertically in the maxilla and slightly buccally in the mandible. In angle class III relations, the implants are inclined buccally in the maxilla and more lingually in the mandible. If the relation between the jaws is markedly adverse, orthognatic surgery may be considered (Clokie 2001) to correct the abnormal jaw relation. Another treatment option in such cases is an overdenture, retained by a bar construction on two implants in the mandible and/or on four implants in the maxilla. The overdenture often offers a favorable outcome to the patient with respect to esthetics, speech, lip and facial support, and function (Naert _et al_. 1998; van Steenberghe _et al_. 2001; Mericske-Stern _et al_. 2002; Eckert & Carr 2004; Kronstrom _et al_. 2006), even though the success rates of the supporting implants might be slightly lower than for implants that support fixed full bridges (Schwartz-Arad _et al_. 2005).
For the mesio-distal orientation of the implant (Fig. 48-10), the rule is that the implant closest to the last tooth is placed parallel with the long axis of the root of this tooth. The further distally the site is located into the molar region, on the other hand, the more inclined are the positions of the implants. In the mandible, for example, it is recommended that the most distal implants be placed in a slightly mesial direction to facilitate the connection of the abutments with the fixed bridge restoration.
**Fig. 48-10** Drawings showing implant directions in the mesial–distal dimension of posterior parts of the jaws. In the maxilla, the most distal implant is directed distally due to the orientation of the sinus wall to engage more bone. In the mandible, the implant is tilted mesially to provide better access for instruments during abutment and prosthetic procedures.
In extremely resorbed mandibles, the most distal implant that is placed immediately in front of the mental foramen, can be tilted distally in order to achieve optimal spreading of the supporting units (Maló _et al_. 2005). Correspondingly, in the resorbed maxilla, the canal prepared for the most distal implant (lateral to the canine) can be directed slightly distally and follow the mesial wall of the maxillary sinus, thereby allowing a longer implant to be placed (Maló _et al_. 2005). An alternative to this procedure would be to use of sinus elevation and grafting techniques (Hochwald & Davis 1992; Neukam & Kloss 2001).
# Healing time
According to early protocols the healing time following installation of implants with a turned surface was 3–4 months (Lekholm & Zarb 1985). For the maxilla and occasionally in the posterior areas of the mandible the healing time was 5–6 months, as the bone is normally more cancellous in these portions of the jaws (Adell _et al_. 1985; Watzek & Ulm 2001). Furthermore, for implants placed in quality 4 bone (Lekholm & Zarb 1985), it was recommended that the healing time in the mandible was also extended another 1 or 2 months (Friberg 1994). As variations may exist between different regions of the same jaw, e.g. between frontal and distal segments or even between different sites within the same region (Watzek & Ulm 2001), it is also important to individualize the healing time and to allow the softest bone site to decide the timing.
For implants with a (mechanically or chemically) modified surface, reduced healing times (6 weeks) have been advocated. Such implants have also been recommended for early or even immediate loading protocols (see also Chapter 47). Immediate loading of implants, both with the use of provisional (Balshi & Wolfinger 1997; Schnitman _et al_. 1997) and/or definite reconstructions has been proposed (Brånemark _et al_. 1999; Randow _et al_. 1995; Ericsson _et al_. 2000a; van Steenberghe _et al_. 2005). The current experience with immediate occlusal loading of oral implants was summarized in several consensus reports and systematic reviews (Aparicio _et al_. 2003; Cochran _et al_. 2004; Misch _et al_. 2004a,b; Nkenke & Fenner 2006). Thus, the outcomes of short-term randomized controlled trials have shown that survival and success rates of immediately loaded implants in fully edentulous jaws may be similar to those of conventionally loaded implants (Chiapasco _et al_. 2001; Romeo _et al_. 2002).
The survival rate of immediately restored single-tooth implants was similar to or slightly lower than that of conventionally loaded single-tooth implants (Ericsson _et al_. 2000b; Cannizzaro & Leone 2003). Ericsson _et al_. (2000b) had a restoration placed immediately on the implant, but occlusal contacts were avoided. Some clinicians try to protect "immediately loaded" implants from forces exerted by the tongue or during chewing by using occlusal splints (Lorenzoni _et al_. 2003). To date, there are no controlled studies that enable evidence-based decisions to be made as to whether single-tooth implants can be loaded immediately or should only be restored without occlusal contacts (Nkenke & Fenner 2006).
Currently, it is not possible to draw conclusions concerning exclusion and inclusion criteria for immediate loading, threshold values for implant stability that allow immediate loading, bone quality needed for immediate loading, and the relevance of immediate functional loading and immediate non-functional loading (Nkenke & Fenner 2006). In most of the studies on immediate loading, good bone quality has been mentioned as an important prognostic factor for the success of the procedure (Chiapasco _et al_. 2001; Romeo _et al_. 2002). Although this conclusion seems reasonable, the level of evidence that supports the assumption is low (Nkenke & Fenner 2006). There are, in fact, no controlled studies that have been especially designed to compare immediate loading of oral implants placed in bone of varying density (soft/hard). The same is true for the lengths and diameters of implants that should be used for immediate loading. In one controlled study, moderately rough implant surfaces appeared to improve the survival rate of immediately loaded implants (Rocci _et al_. 2003a,b). In this study, however, the difference between the moderately rough as opposed to the machined-surface implants was not significant.
Review papers on immediate loading have also addressed additional biomechanical aspects of this procedure (Szmukler-Moncler _et al_. 2000; Gapski _et al_. 2003; Chiapasco 2004; Nkenke & Fenner 2006). Based on different experimental studies, it was stated that a micromotion threshold should not be exceeded; otherwise, osseointegration would be hindered. The critical threshold seems to be 50–150 μm (Pilliar _et al_. 1986; Szmukler-Moncler _et al_. 1998). Therefore, it has been claimed that a high initial stability is necessary for immediate loading of dental implants (Chaushu _et al_. 2001; Calandriello & Tomatis 2005). For this purpose, these authors used modified drilling protocols combined with bone compaction with osteotomes to achieve increased primary stability. Some authors have chosen insertion torque as a measure of implant stability, and arbitrarily selected torque values of ≥32–40 Ncm as thresholds to allow immediate loading (Wöhrle 1998; Hui _et al_. 2001; Lorenzoni _et al_. 2003). With resonance frequency analysis (Meredith _et al_. 1996) it has become possible to measure initial implant stability, i.e. the density of the bone surrounding the implant. The bone quality can thereby be analyzed repeatedly over time and the healing period individualized without using any invasive technique for the tests. An implant stability quotient (ISQ) value of >60 was recommended (Sennerby & Meredith 2002) to allow oral implants to be loaded directly after their insertion. Until now, controlled studies that have compared the relationship between different levels of implant stability and implant survival rate have been lacking. Consequently, there is currently no proven threshold value that indicates that immediate loading will be successful. Besides high initial stability, it has been stressed that immediately loaded implants in multi-unit situations should be rigidly splinted by the use of superstructures (Nikellis _et al_. 2004; van Steenberghe _et al_. 2004). In order to optimize splinting, the use of metalreinforced superstructures was advocated. High success rates have also been reported for immediate loading of implants connected with superstructures that were not reinforced with metal (Nikellis _et al_. 2004).
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# Part 15: Reconstructive Ridge Therapy
49 Ridge Augmentation Procedures
_Christoph H.F. Hämmerle and Ronald E. Jung_
50 Elevation of the Maxillary Sinus Floor
_Bjarni E. Pjetursson and Niklaus P. Lang_
# Chapter 49
# Ridge Augmentation Procedures
Christoph H.F. Hämmerle and Ronald E. Jung
* * *
Introduction
Patient situation
Bone morphology
Horizontal bone defects
Vertical bone defects
Soft tissue morphology
Augmentation materials
Membranes
Bone grafts and bone graft substitutes
Long-term results
Clinical concepts
Ridge preservation
Extraction sockets (class I)
Dehiscence defects (classes II and III)
Horizontal defects (class IV)
Vertical defects (class V)
Future developments
Growth and differentiation factors
Delivery systems for growth and differentiation factors
Membrane developments
Future outlook
* * *
# Introduction
Successful implant therapy is dependent upon an adequate volume of bone at the site of implant placement, since the long-term prognosis of dental implants is adversely affected by inadequate bone volume (Lekholm _et al_. 1986).
In principle, four methods have been described to increase the rate of bone formation and to augment bone volume: osteoinduction by the use of appropriate growth factors (Reddi 1981; Urist 1965); osteoconduction, where a grafting material serves as a scaffold for new bone growth (Buch _et al_. 1986; Reddi _et al_. 1987); distraction osteogenesis, by which a fracture is surgically induced and the two fragments are then slowly pulled apart (e.g. Ilizarov 1989a,b); and finally, guided tissue regeneration (GTR), which allows spaces maintained by barrier membranes to be filled with new bone (Dahlin _et al_. 1988, 1991a; Kostopoulos & Karring 1994; Nyman & Lang 1994).
Among these methods, guided bone regeneration (GBR) is the best documented for the treatment of localized bone defects in the jaws. GBR has allowed the use of endosseous implants in areas of the jaw with insufficient bone volume. Lack of bone volume may be due to congenital, post-traumatic, or post-surgical defects or result from disease processes. The predictability and success which can now be achieved with GBR procedures enable the clinician to obtain similar rates of treatment success at sites with bone defects compared to sites without defects (Hammerle _et al_. 2002).
Although bone augmentation procedures are an important part of contemporary implant therapy, other factors are also critical in order to obtain treatment success. In this respect a systematic approach to a given patient situation is key to achieving the desired aim. In complex cases with a multitude of problems, several aspects have to be taken into consideration. These include the patient's general health status, behavior of the patient, environmental factors, the presence of any oral diseases, and the situation at the site planned for implantation as well as the regions of the dentition adjacent to and opposing this site.
GBR is frequently part of complex treatments, but this chapter will focus only on the aspects of bone augmentation at localized defects in the alveolar process.
More than two decades have passed since the introduction of GBR into clinical practice. Today, general understanding of the mechanisms leading to regeneration of desired tissues still agrees with the initially published statements (Karring _et al_. 1980; Nyman _et al_. 1980, 1989). In brief, when a space is formed, cells from the adjacent tissues will grow into this space to form their parent tissue, i.e. the tissue they migrated in from. In order to give preference to cells from desired tissues, membranes are placed to prevent cells from undesired tissues having access to the space.
# Patient situation
It is generally agreed that certain general health conditions represent a risk for successful GBR procedures. In a recent consensus conference one group examined the effect of systemic diseases on implant success (Mombelli & Cionca 2006). It was found that the scientific literature is inconclusive on these issues due to a lack of well performed clinical studies. Hence, it was concluded that neither the same rate of success nor an increased rate of failures have been documented in the presence of the specific systemic conditions under investigation. Furthermore, no conclusive data are available with respect to bone augmentation procedures in patients suffering from systemic diseases which cause impaired tissue healing. The same was found for patients who show behaviors (e.g. smoking, poor compliance) which lead to impaired tissue healing or to a higher susceptibility for disease development. Risk–benefit analysis should be performed with these uncertainties in mind, when planning implant therapy in the presence of bone defects.
It has been demonstrated that implant therapy in patients who have lost their teeth due to periodontal disease will be subject to more implant failures and complications regarding the supporting tissues than in patients who have lost their teeth due to other reasons (Mengel _et al_. 2001; Hardt _et al_. 2002; Karoussis _et al_. 2003; Wennstrom _et al_. 2004). Although, there are few well controlled studies available, it may be expected that these problems also exist when implants are supported by regenerated bone.
# Bone morphology
Bone defects may be classified into intra-alveolar, horizontal, and vertical defects. Intra-alveolar defects are dealt with in Chapter 43.
When examining a clinical situation regarding bone morphology, the following aspects are of therapeutic importance: the presence of a bone defect; the size of the edentulous gap (single-tooth, double-tooth or multiple-tooth); and the bone level at the teeth adjacent to the defect.
## Horizontal bone defects
Horizontal bone defects are the ones most frequently encountered. They include dehiscences and fenestrations.
The treatment of these types of defects has been shown to be highly successful in numerous studies (Balshi _et al_. 1991; Jung _et al_. 2003; Lundgren _et al_. 1994b; Mayfield _et al_. 1997; Simion _et al_. 1997). In addition, both bioresorbable and non-resorbable membranes have been successfully employed (Sandberg _et al_. 1993; Sevor _et al_. 1993; Schliephake _et al_. 1994; Crump _et al_. 1996; Chung _et al_. 1997; Hammerle _et al_. 1997, 1998; Lundgren _et al_. 1997). In a controlled clinical trial 18 implants with exposed surfaces were treated in nine patients (Simion _et al_. 1997). In the test sites bioresorbable membranes of polylactic and polyglycolic acid (PLA/PGA) were used, whereas non-resorbable membranes of expanded polytetrafluoroethylene (e-PTFE) were applied in the control sites. Autogenic bone was additionally placed to cover the exposed implant threads prior to membrane adaptation. The results at re-entry, 6–7 months later, revealed favorable healing and bone regeneration in both test and control sites, with the control sites demonstrating slightly higher amounts of bone regeneration.
In situations with a bone defect at a site where primary stability of an implant cannot be achieved, or when implant placement is not possible in the ideal location for subsequent prosthetic therapy, GBR prior to implantation represents the method of choice.
Experimental research on ridge augmentation using GBR was presented in the early 1990s (Seibert & Nyman 1990). In a dog model, large defects of the alveolar ridge were surgically prepared both in the mandible and in the maxilla. Morphologic and histologic analysis revealed that, in sites treated with membranes, with or without the addition of grafts, the entire space between the membrane and the jawbone was filled with bone. In the absence of membranes, bone formation was lacking.
The conclusions drawn from these and other pioneering experiments were that the method of GBR can indeed be successfully employed in the regeneration of alveolar ridge defects (Seibert & Nyman 1990; Schenk _et al_. 1994; Smukler _et al_. 1995).
Ridge augmentation in a lateral direction has been shown to be a method with predictable success (Nyman _et al_. 1990; Dahlin _et al_. 1991b; Becker _et al_. 1994b; Nevins & Mellonig 1994; Buser _et al_. 1996; von Arx _et al_. 1996). Successful methods regarding augmentation of the alveolar ridge in a vertical direction, however, are not well established.
## Vertical bone defects
Data from animal experiments have clearly demonstrated that gain of bone above the external borders of the skeleton were possible using GBR (Lundgren _et al_. 1995; Hämmerle _et al_. 1996, 1997; Schliephake & Kracht 1997; Schmid _et al_. 1997; Lorenzoni _et al_. 1998).
Vertical ridge augmentation represents the most demanding indication in GBR therapy. Established techniques involve the placement of autogenous, particulated or block bone grafts, or bone substitute materials in combination with e-PTFE membranes of various configurations (Simion _et al_. 1994b, 1998; Tinti _et al_. 1996; Tinti & Parma-Benfenati 1998; Chiapasco _et al_. 2004). The membranes were either supported by the graft alone or additionally supported by the implant protruding vertically from the host bone for various lengths. The results after submerged healing consistently showed bone formation reaching above the previous border of the alveolar crest. In some situations vertical bone formation reached up to 4 mm above the previous border of the alveolar crest. Within the area of the newly formed bone, osseointegration of the implants had occurred as demonstrated by histologic analysis of experimentally retrieved test implants. The amount of vertical bone formation, however, was not predictable and bone growth to the top of the membrane was not consistently reached when several millimeters of new bone formation were attempted. The remainder of the space between the newly formed bone and the membrane was occupied by non-mineralized tissue (Simion _et al_. 1994a).
# Soft tissue morphology
The morphology of the soft tissues at the site of bone regeneration has a significant impact on the result of treatment. On the one hand, soft tissue coverage is a prerequisite for successful bone augmentation. On the other hand, in situations with high esthetic importance the soft tissues and the reconstruction determine whether or not a result is esthetically pleasing.
In many situations the availability of the soft tissues will limit the amount of bone formation possible. In other words a lack of soft tissues may prevent large amounts of bone volume gain because it is impossible to cover the area intended for regeneration. In such situations it may be advisable first to augment the volume of the soft tissues and then perform the bone augmentation procedure as a second step.
Critical aspects regarding the soft tissues include: vertical or horizontal soft tissue defects; level of the soft tissues at the teeth neighboring the gap; gingival biotype; and scars, pathologies or discolorations in the soft tissues lining the area of the bone defect.
# Augmentation materials
## Membranes
A wide range of membrane materials has been used in experimental and clinical studies to achieve GBR, including polytetrafluoroethylene (PTFE), expanded PTFE (e-PTFE), collagen, freeze-dried fascia lata, freeze-dried dura mater allografts, polyglactin 910, polylactic acid, polyglycolic acid, polyorthoester, polyurethane, polyhydroxybutyrate, calcium sulfate, micro titanium mesh, and titanium foils. Devices used for GBR in conjunction with endosseous implants should be safe and effective. Since no life-threatening diseases or deficiencies are treated, possible adverse effects emerging from the implanted devices should be kept to a minimum. At the same time, documentation of the effectiveness of the procedures and materials should be available. Certain critical criteria regarding membranes used for GTR have been formulated (Hardwick _et al_. 1994): biocompatibility, cell occlusiveness, integration by the host tissues, clinical manageability, and the space making function. For bioresorbable and biodegradable membranes additional criteria need to be fulfilled. Tissue reactions resulting from the resorption of the membrane should be minimal, these reactions should be reversible, and they should not negatively influence regeneration of the desired tissues (Gottlow 1993).
Although GBR is quite a successful procedure, a better understanding of the factors critical for success or failure is mandatory. This understanding will lead to more refined clinical protocols and will allow for the manufacturing of membrane materials with improved performance for a given indication. Some of these factors include membrane stability, duration of barrier function, enhanced access of bone and bone marrow-derived cells to the area for regeneration, ample blood fill of the space, prevention of soft tissue dehiscence, _in situ_ forming, and delivery of factors influencing tissue formation beneficially.
### Non-resorbable membranes
With the presentation of the first successful GBR procedures and the subsequent wide and successful application of e-PTFE membranes, this material soon became a standard for bone regeneration. Expanded PTFE is characterized as a polymer with high stability in biologic systems. It resists breakdown by host tissues and by microbes and does not elicit immunologic reactions.
A frequent complication with membrane application in conjunction with implants is membrane exposure and infection. Wound dehiscence and membrane exposure have been reported to impair the amount of bone regenerated in a number of experimental animal (Gotfredsen _et al_. 1993; Kohal _et al_. 1999a) and clinical investigations (Gher _et al_. 1994; Simion _et al_. 1994a; Hämmerle _et al_. 1998).
In situations where bone formation is desired in large defects or in supracrestal areas, conventional e-PTFE membranes do not adequately maintain space unless supported by grafting materials. The alternative approach involves the use of membranes with a stable form, such as titanium-reinforced membranes. Recent research has demonstrated the successful use of these membranes in vertical ridge augmentation and in the treatment of large defects in the alveolar process (Jovanovic & Nevins 1995; Tinti _et al_. 1996; Simion _et al_. 1998).
Many of the factors critical for successful bone formation were identified in experimental studies applying e-PTFE membranes. Furthermore, clinical protocols regarding surgical procedures, postoperative care, and healing times required were established using non-resorbable membranes. Today, as evidence of the effectiveness of bioresorbable membranes increases, non-resorbable membranes are losing importance in clinical practice and their use is increasingly limited to specific indications. Since e-PTFE membranes have been documented to allow successful GBR therapy, results obtained using new materials should always be compared with results of e-PTFE membranes.
### Bioresorbable membranes
Non-resorbable membranes have to be removed during a second surgical intervention. The removal surgery will impose morbidity and psychologic stress on the patient and represents a risk for tissue damage. Since these disadvantages do not occur when working with bioresorbable membranes, they are increasingly applied in the clinic.
Apart from the fact that there is no need for surgical intervention for removal of the membrane, bioresorbable membranes offer some additional advantages. These include improved soft tissue healing (Lekovic _et al_. 1997, 1998; Zitzmann _et al_. 1997), the incorporation of the membranes by the host tissues (depending on material properties), and quick resorption in case of exposure, thus eliminating open microstructures prone to bacterial contamination (Zitzmann _et al_. 1997; Lorenzoni _et al_. 1998).
Bioresorbable materials that may be used for the fabrication of membranes all belong to the groups of natural or synthetic polymers. The best known groups of polymers used for medical purposes are collagen and aliphatic polyesters. Currently tested and used membranes are made of collagen, or of polyglycolide and/or polylactide or copolymers thereof (Hutmacher & Hürzeler 1995).
A wide range of bioresorbable membranes made of either collagen or polyglycolide and/or polylactic acid has been investigated in experimental and clinical studies (Lundgren _et al_. 1994a; Mayfield _et al_. 1997; Simion _et al_. 1997; Zitzmann _et al_. 1997). Results have generally been good, partly because of the low rate of complications, so bioresorbable membranes have become the standard for most clinical situations and have, thus, largely replaced the non-resorbable e-PTFE membranes.
It should be realized, however, that in a recent systematic review a reasonable comparison between bioresorbable and non-resorbable membranes could not be drawn due to a lack of well designed studies (Chiapasco _et al_. 2006). Only a few studies could be identified which compared the results of bioresorbable and non-resorbable membranes (Zitzmann _et al_. 1997, 2001b; Christensen _et al_. 2003). These studies did not find any difference between the two treatment modalities.
Obviously, choice of material is critical when it comes to bioresorbable membranes for GBR. Inflammatory reactions have been documented in the tissues adjacent to some bioresorbable membranes, ranging from mild (Sandberg _et al_. 1993; Piatelli _et al_. 1995; Aaboe _et al_. 1998; Kohal _et al_. 1999a,b) to severe (Gotfredsen _et al_. 1994). Another study reported on therapeutic failures using polylactic membranes for bone regeneration at periimplant defects in dogs (Schliephake _et al_. 1997). Soft tissue complications were frequent, and the results did not reveal any improvement over control sites without the use of membranes.
Convincing results of bone regeneration in animal experiments have been reported for collagen membranes (Hürzeler _et al_. 1998; Zahedi _et al_. 1998). Furthermore, reports of human cases or case series (Hämmerle & Lang 2001) as well as controlled clinical studies (Zitzmann _et al_. 1997) have been presented describing the successful use of collagen membranes for GBR at exposed implant surfaces.
Bioresorbable membranes that are commercially available at present are not capable of maintaining adequate space unless the defect morphology is very favorable (Oh _et al_. 2003; Lundgren _et al_. 1994b). Even if the membranes seem able to maintain space initially, they generally lose their mechanical strength soon after implantation into the tissues. Favorable results have been reported only in situations where the bony borders of the defects adequately support the membrane. When defects do not maintain the space by themselves, failure of bone regeneration results (Zellin _et al_. 1995; Mellonig _et al_. 1998). Therefore, they need to be supported in some way.
In summary, animal experiments, human case reports, and initial controlled clinical studies demonstrate that bioresorbable and non-resorbable membranes can successfully be used for bone regeneration at implants with exposed surface areas. It appears, however, that bioresorbable membranes generally show better clinical performance compared with non-resorbable membranes. Hence, unless the defect morphology or other factors prevent the application of bioresorbable membranes their use is to be preferred. The choice of the best material has to be based on the individual patient situation.
## Bone grafts and bone graft substitutes
Bone grafts have long been used in reconstructive surgery with the aim of increasing the bone volume in the previous defect area. Bone grafts and bone substitute materials may be classified into two main groups: autogenic and xenogenic materials. The term autogenic graft refers to tissues that are transplanted within one and the same organism. Xenogenic grafts encompass all materials of an origin other than the recipient organism and may further be divided into materials from the same species but different individuals, materials from other species, and finally products of non-organic origin.
Bone grafts or bone graft substitutes in conjunction with GBR need to fulfill a number of requirements. They should adequately support the membrane to provide a predefined volume of the regenerated bone. In addition, they should serve as a guiding structure into which the bone can grow or is even encouraged to grow. As a result capillaries and perivascular cells can easily form and migrate, respectively, within the voids provided by the supporting material. Later bone-forming cells can populate the spaces and produce new bone. Finally, the supporting material should be resorbed and replaced by the patient's own bone (Jensen _et al_. 1996; Fugazzotto 2003a,b).
The successful combination of autogenic cortico-cancellous bone grafts and GBR has been shown in a clinical study (Buser _et al_. 1990). A group of 40 patients, who had been treated with this method, demonstrated very low frequency of soft tissue complications and successful ridge augmentation in 66 sites. A mean gain in crest width of 3.5 mm was measured allowing implant placement in a proper position in all 66 sites. More recently, studies in humans and animals have lead to further development and refinement of this method with very good clinical success (Buser _et al_. 1996).
The necessity for membranes in conjunction with block grafts was tested in a prospective randomized clinical study involving 13 patients (Antoun _et al_. 2001). Patients were either treated with onlay bone grafts alone or additionally covered by e-PTFE membranes. The width of the ridges was evaluated clinically immediately following graft placement and at the time of membrane removal 6 months later. In the group with membranes significantly less resorption had occurred. This controlled clinical study confirms animal experimental data and is in accordance with case series reporting the occurrence of pronounced resorption of bone grafts (Jensen _et al_. 1995; Widmark _et al_. 1997; von Arx _et al_. 2001; Cochran _et al_. 2002).
Xenogenic bone substitutes have been developed and applied to GBR. Experimental studies have dealt with materials manufactured synthetically, derived from corals or algae, or originated from natural bone mineral (for review see Hammerle & Jung 2003). These materials are regarded to be biocompatible and osteoconductive. Nevertheless, considerable differences have been reported in their behavior based on material properties.
In a recent systematic review it was concluded that the paucity of available scientific data precludes clear recommendations regarding the choice of a specific supporting material for GBR procedures (Chiapasco _et al_. 2006). Comparative data were rarely found (Christensen _et al_. 2003) and no randomized controlled clinical trials were available as a basis for decision making.
The studies evaluating clinical outcomes of lateral ridge augmentation with GBR procedures in staged implantation commonly used autogenous bone as filler materials in combination with non-resorbable membranes (Nevins & Mellonig 1994; Buser _et al_. 1996). Limited data are available reporting on the application of bone substitutes in combination with bioresorbable membranes for ridge augmentation prior to implant placement (Zitzmann _et al_. 2001a; Friedmann _et al_. 2002; Hammerle _et al_. 2008).
In one of these studies 12 patients with 15 sites exhibiting lateral bone defects were treated using blocks of deproteinized bovine bone mineral and bioresorbable collagen membranes (Hammerle _et al_. 2008). The size of the defects precluded implant placement without prior bone augmentation. Initially the average ridge width amounted to 3.2 mm. At the re-entry operation 9–10 months later, the mean crestal bone width had increased to 6.9 mm. In all of the cases but one, the resulting bone volume was adequate to place the implant in a prosthetically optimal position. In one case, no gain of bone volume had occurred during the phase of regeneration for unknown reasons. While in previous clinical studies, small bone defects at implant sites had been augmented by use of DBBM (Hämmerle & Lang 2001; Zitzmann _et al_. 2001a; Friedmann _et al_. 2002; Hellem _et al_. 2003), larger bone defects were predictably augmented in this case series (Hammerle _et al_. 2008).
The technique of applying biomaterials to support bioresorbable membranes avoids the risks associated with harvesting autogenic bone (Nkenke _et al_. 2001; von Arx _et al_. 2005). This is a significant benefit to the patient and represents an important step in the development of GBR procedures. Future research should be focused on such patient-centered outcomes. The development of biomaterials, ideally coupled with the incorporation of bone growth factors and bioactive peptides, represents an important line of research in this direction (Jung _et al_. 2003).
# Long-term results
Recent systematic reviews have compiled the literature regarding survival and success rates of implants partly or fully placed into regenerated bone (Hammerle _et al_. 2002; Fiorellini & Nevins 2003; Chiapasco _et al_. 2006). The survival rate of implants placed into sites with regenerated/augmented bone using barrier membranes varied between 79% and 100% with the majority of studies indicating more than 90% after at least 1 year of function. The survival rates obtained in the studies identified by these systematic reviews were similar to those generally reported for implants placed conventionally into sites without the need for bone augmentation. Two studies were identified that provided internal control data (Mayfield _et al_. 1998; Zitzmann _et al_. 2001b). In particular, the data from these two studies provided survival and success rates with no significant differences for implants in regenerated compared to non-regenerated bone. In addition, the loss of crestal bone was not different between test and control implants in one of these studies (Mayfield _et al_. 1998).
The long-term stability of vertically augmented bone was assessed in a multi-center study involving 123 patients (Simion _et al_. 2001). The results demonstrated marginal bone level changes to be within the range of variations reported for implants placed into intact bony beds.
Long-term analysis of the stability of the regenerated bone is almost exclusively focused on radiographic assessments of the interproximal bone and on implant survival. There is a need for studies to evaluate the fate of the buccal bone plate, regenerated or not, over time. As has been suggested in previous studies, the stability of the regenerated bone may be assessed using various clinical or radiographic measures (Chiapasco _et al_. 1999).
# Clinical concepts
Analysis of the bony defect morphology is the basis for deciding which treatment strategy to follow and which materials to apply for GBR. Basically there are two procedures: a one-step (combined approach) and a two-step (staged approach) procedure. Whenever the bone morphology allows anchorage of the implant with primary stability in prosthetically correct position the one-step approach is preferred. In situations where the defect morphology precludes primary implant stability, the two-step procedure is performed, i.e. the bone volume is first augmented to a degree allowing implant placement in a second intervention. The classification of bone defects is intended as a guideline for choosing the best techniques and materials for GBR at implant sites (Fig. 49-1).
## Ridge preservation
In situations where there is a substantial lack of soft and/or hard tissues it may be advisable to apply methods for improving hard tissue as well as soft tissue healing. Attempts have been made to maintain the contour of the ridge by placing non-resorbable materials into the fresh extraction socket. Cones of hydroxyapatite were placed into the socket (Denissen & de Groot 1979; Quinn & Kent 1984). Whereas the resorption of the ridge could be somewhat reduced the overall result was not satisfactory. A large number of soft tissue dehiscences occurred and in some situations the cones had to be removed (Kwon _et al_. 1986).
GBR has been used to preserve or augment the alveolar ridge at the time of tooth removal. Supporting materials were placed into fresh extraction sockets and subsequently covered by non-resorbable membranes (Nemcovsky & Serfaty 1996; Lekovic _et al_. 1997; Fowler _et al_. 2000). One of the problems encountered, as described above, is the lack of soft tissue to cover the GBR site completely. In order to solve this problem coronal and lateral sliding flaps or soft tissue grafts were employed. In some studies no attempt was made to contain the filler material with membranes nor was the soft tissue manipulated to allow for primary closure. In these situations and when necrosis of the covering soft tissues occurred, loss of grafting particles was a common finding (Nemcovsky & Serfaty 1996).
Histomorphometric analysis of biopsies revealed that more vital bone had formed at sites treated with GBR compared to sites that were left to spontaneous healing. The investigators attributed this positive finding to the characteristics of the filler materials. Both osteoconductivity and resorbability of the materials apparently influenced new bone formation in a positive manner (Smukler _et al_. 1999; Artzi _et al_. 2000; Bolouri _et al_. 2001; Froum _et al_. 2002).
**Fig. 49-1** Schematic drawing depicting the defect classification with classes 0–V.
When applying GBR procedures it was clinically observed that the rate of resorption of the alveolar process could be reduced compared to untreated control sites (Lekovic _et al_. 1997, 1998; Yilmaz _et al_. 1998; Camargo _et al_. 2000). Complications with soft tissue dehiscences, however, frequently occurred in GBR-treated sites (Fowler _et al_. 2000; Yang _et al_. 2000). Although, the method of using GBR to reduce the loss of ridge volume has been well documented, it is not practical in many clinical situations due to the following shortcomings: it requires a long healing period before the implant therapy can be continued; the method is invasive and technique sensitive; soft tissue coverage is difficult to achieve and may lead a compromized esthetic result; and it is costly.
A different approach to provide optimal conditions for implant therapy regarding the profile of the alveolar ridge has led to the development of techniques aimed at improving the soft tissue conditions. Previous case reports described the use of autogenous soft tissue grafts to seal extraction sites before (Landsberg & Bichacho 1994) or at the time of implant placement (Evian & Cutler 1994; Landsberg 1997; Chen & Dahlin 1996; Tal 1999). Several problems exist with these procedures, including necrosis of the transplanted mucosa and poor color integration at the recipient site. In order to address this issue in a systematic way 20 patients in need of tooth extraction received soft tissue grafts to seal the entrance to the alveolus of the freshly extracted tooth (Jung _et al_. 2004) (Fig. 49-2a). First a grafting material was placed into the socket with the aim of maintaining the contour of the ridge. Subsequently, a soft tissue graft harvested from the palate was carefully sutured to cover the grafting material and thus seal off the alveolus from the oral cavity (Fig. 49-2b). Six weeks later, the vitality of the graft and the color match with respect to the surrounding mucosa were assessed. More than 99% of the grafted tissue area appeared vital. Digital measurement of the color difference between the grafted and the neighboring host tissues generated values below thresholds for normally detectable values in such situations (Fig. 49-2c). This technique, therefore, beneficially influenced the conditions at extraction sites for subsequent implant placement and soft tissue management in comparison to spontaneous healing (Fig. 49-3). Due to the effort and expense necessary to perform this treatment approach, it is primarily recommended for situations with high esthetic priority.
At times the implant is completely inserted into native bone but the buccal contour of the hard and soft tissues is insufficient for an optimal treatment outcome. This may be the case in esthetically highly demanding situations. In order to improve the esthetic result an augmentation procedure is conducted (class 0). A membrane-supporting material and a membrane are placed to promote labial bone formation in order to obtain the desired tissue contours.
**Fig. 49-2** (a) Occlusal view of an extraction site 11 immediately following removal of the tooth. Note the normal appearance of the external ridge contour and the soft tissue deficit over the extraction socket. (b) A soft tissue graft taken from the palate has been placed and sutured to seal the entrance of the alveolus. (c) After 6 weeks of healing, the soft tissue graft is completely integrated at the recipient site and a healthy soft tissue cover of the former entrance of the alveolus is present.
## Extraction sockets (class I)
Currently implants are often placed in fresh extraction sockets. Although some of these clinical procedures were first described many years ago, their application has become more common in recent years.
**Fig. 49-3** An extraction site after 6 weeks of spontaneous healing. Note the incomplete healing rendering soft tissue management difficult.
In situations where teeth are to be replaced with implants, a decision must be taken during treatment planning whether the implant should be placed immediately after tooth extraction or if a certain number of weeks of healing of the soft and hard tissues of the alveolar ridge should be allowed prior to implant placement. For details regarding timing of implant placement into extraction sockets see Chapter 47.
If bone augmentation is required at implants immediately placed into extraction sockets, the following procedure is recommended. A flap is raised to allow easy access to the site and the implant is inserted. A membrane-supporting material is adapted to support the membrane. Depending on the defect morphology (for details see Chapter 47) this material is placed into the space between the walls of the socket and the implant surface. In addition, in some situations, especially in the esthetic zone, it may be necessary to augment the bone beyond the labial wall of the socket. Thus, the membrane-supporting material is also applied in order to correct the ridge profile to obtain a more prominent labial tissue contour. Subsequently, the membrane is adapted to cover the supporting material and a narrow zone of the adjacent bone and the flap is adapted and sutured. Whenever a partial or complete loss of the buccal wall of the socket is encountered the procedure described for dehiscence defects is applied.
## Dehiscence defects (classes II and III)
Dehiscence defects may range from a very small lack of marginal bone to large areas of denuded implant surfaces. As long as the implant can be securely anchored in the existing bone, concomitant implantation and bone regeneration may be performed. When the defect is quite small, it may be questionable whether or not a regeneration procedure will improve the treatment outcome and its long-term stability (Hämmerle 1999). Often the esthetic result, as well as aspects of health and function, is important. In esthetically demanding situations it is generally recommended to perform an augmentation procedure, whereas in other areas of the mouth recommendations are not as strict. It needs to be understood, however, that the presently available scientific data do not allow an evidence-based statement to be made regarding the borderline between a situation requiring bone augmentation and a situation without this requirement (Chiapasco _et al_. 2006).
In situations where it is decided to carry out a GBR procedure, the material of choice should fulfill the following requirements: it should have proven efficacy; be thoroughly researched and scientifically documented; and be re-evaluated at regular intervals. In recent clinical studies, it has been demon-strated that the application of bone substitutes in conjunction with the placement of implants lead to successful coverage of the previously exposed implant surfaces (Zitzmann _et al_. 1997; Hämmerle _et al_. 1998; Moses _et al_. 2005). Hence, harvesting of autogenous bone for the treatment of dehiscence defects may not always be necessary for a successful treatment outcome.
The grafting material should reliably support the area intended for bone augmentation, allow or preferably promote in-growth of bone forming cells, and support bone–implant contact formation. Among other materials deproteinized bovine bone mineral is very well researched and has consistently demon-strated excellent clinical results (Esposito _et al_. 2006).
When choosing an appropriate membrane the same basic documentation as required for the supporting materials needs to be available: i.e. it should have proven efficacy; be thoroughly researched and scientifically documented; and be re-evaluated at regular intervals. Additional parameters regarding selection of a suitable membrane include the mechanical properties, the risk for soft tissue dehiscence, and the ease of clinical handling. In most situations with dehiscence defects a bioresorbable collagen membrane will be optimal regarding the scientifically and clinically required characteristics. In contrast, in situations, where the defect morphology requires improved stability of the area to be regenerated, e-PTFE membranes are most suitable. Apart from the substantial risk for soft tissue dehiscence and subsequent infection of the area, the need for membrane-removal surgery represents the major disadvantage of non-resorbable membranes. As a consequence, bioresorbable membranes are preferred whenever possible for the treatment of small and larger dehiscence defects.
The clinical protocol to promote bone formation for successful coverage of exposed implant surfaces includes the following steps. After a flap is raised, the implant is inserted (Fig. 49-4a). A membrane-supporting material is placed in the area of the buccal dehiscence defect with the aim of promoting bone formation for bone integration of the implant and obtaining a natural appearance of the bone and soft tissue contours of the alveolar ridge. Subsequently a membrane is adapted and placed to cover the supporting material and the defect. A decision has to be taken on how the membrane is fixed in place to provide the stability necessary for bone to form. This fixation may be obtained by simply adapting the membrane to the intact walls of the bone defect, by tacking it with pins, by suturing it to the soft tissues, or by adapting it to the implant. Thereafter, the flap is adapted and sutured to allow for submerged or transmucosal healing of the implant site. Following 4–6 months of healing the former defect is filled with new bone (Fig. 49-4b). The same clinical protocol is applied for the treatment of larger dehiscence defects (Fig. 49-5).
**Fig. 49-4** (a) A small labial dehiscence defect at an implant in position of tooth 44. The defect is treated by GBR applying a bioresorbable membrane and a deproteinized bovine bone mineral for membrane support. (b) The same case as in (a) at re-entry surgery. New bone has formed within the previous defect area. A thin layer of non-mineralized tissue covers the regenerated bone.
**Fig. 49-5** (a) A large labial dehiscence defect at an implant in position of tooth 43. The defect is also treated by GBR applying a bioresorbable membrane and a deproteinized bovine bone mineral for membrane support. (b) The same case as in (a) at re-entry surgery. The dehiscence defect has been augmented with bone, which is covered by a thin layer of non-mineralized tissue.
## Horizontal defects (class IV)
The autogenous block transplant represents the gold standard for treatment of horizontal ridge defects (Becker _et al_. 1994a; Buser _et al_. 1996; von Arx _et al_. 2001). Both intraoral and extraoral harvesting procedures have been described. Intraoral sites have been preferred, especially for the treatment of localized bone defects in partially edentulous jaws (Joshi & Kostakis 2004). Intraorally, common donor sites include the chin and the area of the retromolar region in the mandible. Intraoral harvesting procedures also have disadvantages, such as limited availability of bone graft volume, complications including altered sensation of teeth, neurosensory disturbances, wound dehiscence, and infection (Nkenke _et al_. 2001; von Arx _et al_. 2005).
The advantages of autogenic block grafts include the large scientific and clinical documentation, handling properties, stabilization of the area intended for regeneration due to the possibility of securing the grafts in place by metal screws, and the optimal biologic properties. The disadvantages include donor site morbidity, technically difficult harvesting procedures, and the impossibility of using the graft as a carrier for growth factors.
Clinical procedures require harvesting of the graft, adaptation to the defect area, fixation by screws, coverage with a membrane, and primary closure with the soft tissue flap. During a second surgical intervention after 4–9 months of healing, the result of the augmentation procedure can be seen and implants can be placed (Fig. 49-6).
**Fig. 49-6** (a) An extensive bone defect in the anterior maxilla. A bone graft harvested from the chin is adapted and secured in place by titanium screws. In the periphery bone chips and deproteinized bovine bone mineral are added to improve contouring of the area. Subsequently, a bioresorbable collagen membrane is placed to cover the area intended for bone augmentation and the flap is closed. (b) The same case as in (a) at the time of implant placement. Note the large volume of bone available for implant placement and as a basis for achieving an optimal esthetic result.
**Fig. 49-7** (a) A lateral bone defect at a single tooth gap. A block of deproteinized bovine bone mineral and chips generated from this block are placed to support a bioresorbable collagen membrane before the flap is closed. (b) The same case as in (a) at the time of implant placement. Note the substantial volume of bone available for implant placement as a basis for achieving an optimal result.
As described above recent case reports and case series have described the use of deproteinized bovine bone mineral in conjunction with bioresorbable collagen membranes and found successful bone augmentation at lateral ridge defects (Zitzmann _et al_. 2001a; Friedmann _et al_. 2002; Hammerle _et al_. 2008). During the second surgical intervention implants could be placed in a prosthetically optimal position in most situations (Fig. 49-7).
These newer studies indicate that, provided the appropriate protocols are developed, ridge augmentation without the use of autogenous block grafts could become a standard procedure.
## Vertical defects (class V)
The indications for vertical ridge augmentation include situations where the remaining bone height is too small for proper anchorage of oral implants, where unfavorable crown:implant ratios will result, and where unfavorable esthetic outcomes are expected from the lack of remaining hard and soft tissues.
The same procedures are recommended for patient treatment as described for the class IV defects with the exception that the bone block is partially or fully placed on to the ridge in order to gain bone in a vertical direction. Other than that the materials and the techniques applied are identical to the ones for lateral bone augmentation using bone grafts. Obviously, flap adaptation is more difficult due to the increased volume intended for regeneration, which needs to be covered by the flap.
It appears that varying amounts of bone height may be gained, depending on the clinical treatment protocol. The factors critical for success or failure have not been elucidated. In addition, no data is presently available indicating whether there is a biologically limited maximum of bone gain, and if so, what parameters influence this maximum.
# Future developments
Progress in every medical discipline is largely based on better understanding of the physiologic and pathologic mechanisms governing health, disease, and healing. This understanding is a key step to the development of new strategies and materials in medicine. The aim is to develop more effective techniques that predictably promote the body's natural ability to regenerate lost tissue instead of using external materials to repair lost tissue. The most intriguing method currently being investigated is the application of polypeptide or natural proteins that regulate wound and tissue regeneration.
## Growth and differentiation factors
In the past decade a number of basic science experiments and clinical studies have clarified biologic mechanisms of several growth and differentiation factors on the regeneration of oral soft and hard tissue (Howell _et al_. 1997a). Growth and differentiation factors currently believed to contribute to periodontal and alveolar ridge augmentation include platelet-derived growth factor (PDGF), insulin-like growth factor (IGF-I and IGF-II), transforming growth factor beta (TGF-β), fibroblast growth factor (a-FGF and b-FGF), and bone morphogenetic proteins (BMPs 1–15). Among these bone morphogenetic protein is the most widely studied in the dental literature. BMP, by chemotaxis, triggers proliferation and differentiation of mesenchymal progenitor cells (Wozney _et al_. 1988). Recombinant biotechnology has enabled characterization of at least 15 BMPs and production of quantities of purified recombinant protein for therapeutic application (Groeneveld & Burger 2000). Recombinant human BMP-2 (rhBMP-2) has been found to exhibit very high osteogenic activity in experimental (Sigurdsson _et al_. 1996; Hanisch _et al_. 1997; Cochran _et al_. 1999; Higuchi _et al_. 1999; Jung _et al_. 2005) and in clinical studies (Boyne _et al_. 1997; Howell _et al_. 1997a; Jung _et al_. 2003, 2005).
## Delivery systems for growth and differentiation factors
The regenerative potential of growth and differentiation factors depends upon the carrier material (Sigurdsson _et al_. 1996; Hunt _et al_. 2001). The effect of such proteins is dependent upon a carrier material, which serves as a delivery system and as a scaffold for cellular in-growth (Ripamonti & Reddi 1994).
Collagen has extensively been studied as a carrier material for growth factors applied to promote bone formation in different kinds of indications (Nevins _et al_. 1996; Boyne _et al_. 1997; Howell _et al_. 1997b). Different studies (Barboza _et al_. 2000) using rhBMP-2 in an absorbable collagen sponge (ACS) for alveolar ridge augmentation gained only small amounts of bone. The investigators concluded that the compromised results were due to the failure of the ACS to adequately support the supra-alveolar wound space. In order to overcome this lack of structural strength rh-BMP-2/ACS has been combined with hydroxyapatite (HA) in an experiment attempting lateral ridge augmentation (Barboza _et al_. 2000). In contrast to rhBMP-2/ACS alone, a significant clinical improvement in ridge width was observed with the addition of HA to rhBMP-2/ACS. However, the HA particles were largely encapsulated by fibrous tissue and they appeared partially to obstruct bone formation. The investigators concluded that space maintenance in BMP-induced bone formation is an important factor (Barboza _et al_. 2000). A recent study demonstrated that the results of GBR procedures in humans could be improved by the addition of rhBMP-2 to a xenogenic bone substitute mineral. This improvement was documented by a higher degree of bone maturation and an increased graft–bone contact fraction at the BMP-treated sites (Jung _et al_. 2003). Synthetic polymers, on the other hand, can reproducibly be fabricated and the growth factors can be incorporated under controlled manufacturing conditions (Weber _et al_. 2002).
In a recent study in dogs implants were placed in the mandible and peri-implant infraosseous defects were prepared (Jung _et al_. 2007). The defects were grafted with a synthetic polyethylene glycol (PEG) matrix, which was either empty or contained a 35 amino acid peptide of parathyroid hormone (cys-PTH1–34). Control defects were grafted with autogenous bone or left empty. One and three months later, the sites with PEG and PTH showed similar amounts of bone formation compared with the sites grafted with autogenous bone. In the two other groups less bone formation was observed. It was concluded that the synthetic PEG hydrogel containing PTH1–34 was a suitable matrix-differentiation factor system to obtain bone regeneration.
However, the ideal carrier material, which is easy to apply, able to provide space for regeneration, bioresorbable, and allows controlled release of the bioactive molecules, has not yet been discovered. Further research is needed to determine the ideal combination of factors for regeneration, the best delivery system, and the optimum doses.
## Membrane developments
The benefit of using both barrier membranes and BMP for bone augmentation remains controversial (Linde & Hedner 1995; Howell _et al_. 1997b; Cochran _et al_. 1999; Jung _et al_. 2003). It was found that the presence of a non-resorbable e-PTFE membrane initially (4 weeks) inhibited bone formation with rhBMP-2 but did no longer do so at later time points (12 weeks) (Cochran _et al_. 1999). It has been shown that bone induction by rhBMP-2 occurs at early time points and that rhBMP-2 undergoes rapid clearance. Hence, the use of a membrane may potentially reduce the bone-forming effect of rhBMP-2 due to limited availability of inducible cells. Another animal study in rats reported no difference in bone healing with the combination of rhBMP-2 and an e-PTFE membrane compared to rhBMP-2 alone (Linde & Hedner 1995). From a clinical point of view, the use of a membrane simplifies the handling and stabilization of the bone substitute mineral at the time of bone augmentation, but from a biologic point of view the use of a membrane may block the recruitment of cells from the environment.
The question whether or not bioactive molecules are best used in conjunction with membranes or in the absence of membranes has not yet been answered conclusively. On the one hand, it is reasonable to apply them as adjunctive agents to GBR therapy in order to accelerate membrane-guided bone regeneration. On the other hand, it may be hypothesized that their mode of action is best taken advantage of when membranes are not applied simultaneously, thus allowing all inducible cells from the wound environment access to the area to be regenerated.
Common to all presently used membranes is the fact that their fabrication is completed before they are delivered for patient use. Consequently, they are made available in standard sizes and forms and need to be adapted to the patient's individual situation. Alternatively, a membrane could be custom made directly for an individual defect intra-operatively, using a material different from the ones mentioned above.
Hydrogels made of PEG fulfill a number of criteria required to serve as synthetic membranes which form _in situ_. Polyethylene glycol has been shown to be highly biocompatible (Pang 1993; Working _et al_. 1997). It is presently approved for several pharmaceutical applications (Zalipsky & Harris 1997) and as medical devices, e.g. a sprayable adhesion barrier.
In a recent study in rabbits, four evenly distributed craniotomy defects, 6 mm in diameter, were prepared in the area of the right and left parietal and frontal bones (Jung _et al_. 2006). All sites were grafted with highly porous hydroxyapatite (HA)/tricalciumphosphate (TCP) granules. The sites were covered towards both the internal and external soft tissue either with e-PTFE or PEG membranes or left uncovered as control sites. A similar amount of newly formed bone was observed within the former defect space at e-PTFE- and PEG-treated sites. These findings demonstrated that the PEG membrane formed _in situ_ could be successfully applied for bone regeneration.
## Future outlook
Further developments in bone augmentation procedures can be related to either the simplification of clinical handling or influencing of biologic processes. In order to simplify clinical handling new materials should be comprised of a matrix with optimal cell in-growth capacities and with good mechanical properties providing space for tissue regeneration. No membrane and no specific procedures for mechanical fixation should be necessary. This would reduce the technique sensitivity and therefore increase the predictability of bone augmentation.
From a biologic point of view the growth and differentiation factors may induce earlier bone growth into the area to be regenerated. Thus, the area of regeneration would be stabilized earlier. Furthermore, the use of such materials would allow treatment of extensive bone defects. At present, large bone defects are regularly augmented with autogenous block grafts and membranes. The use of synthetic materials would result in lower surgical risks and lower morbidity in the augmentation procedure and would represent an important step forward in simplifying bone regeneration techniques.
### Acknowledgments
The authors express their special thanks to Dr. Gianandrea Hälg and to Samantha Merki for valuable support in the preparation of this chapter.
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# Chapter 50
# Elevation of the Maxillary Sinus Floor
Bjarni E. Pjetursson and Niklaus P. Lang
* * *
Introduction
Treatment options in the posterior maxilla
Sinus floor elevation with a lateral approach
Anatomy of the maxillary sinus
Pre-surgical examination
Indications and contraindications
Surgical techniques
Post-surgical care
Complications
Grafting materials
Success and implant survival
Sinus floor elevation with the crestal approach (osteotome technique)
Indications and contraindications
Surgical technique
Post-surgical care
Grafting material
Success and implant survival
Short implants
Conclusions and clinical suggestions
* * *
# Introduction
Elevation of the maxillary sinus floor was first reported by Boyne in the 1960s. Fifteen years later, Boyne and James (1980) reported on elevation of the maxillary sinus floor in patients with large, pneumatized sinus cavities as a preparation for the placement of blade implants. The authors described a two-stage procedure, where the maxillary sinus was grafted using autogenous particulate iliac bone at the first stage of surgery. In the second stage of surgery after approximately 3 months, the blade implants were placed and later used to support fixed or removable reconstructions (Boyne & James 1980).
As implant dentistry developed, it became more evident that the posterior maxillary region was often limited for standard implant placement, since the residual vertical bone height was reduced (Fig. 50-1). An elevation of the maxillary sinus floor was an option in solving this problem. Several surgical techniques have been presented for entering the sinus cavity, elevating the sinus membrane, and placing bone grafts.
A crestal approach for sinus floor elevation with subsequent placement of implants was first suggested (Tatum 1986). Utilizing this crestal approach, a "socket former" for the selected implant size was used to prepare the implant site. A "green-stick fracture" of the sinus floor was accomplished by hand tapping the "socket former" in a vertical direction. After preparation of the implant site, a root- formed implant was placed and allowed to heal in a submerged way.
Summers (1994) later described another crestal approach, using tapered osteotomes with increasing diameters (Fig. 50-2). Bone was conserved by this osteotome technique because drilling was not performed. Adjacent bone was compressed by pushing and tapping as the sinus membrane was elevated. Then, autogenous, allogenic or xenogenic bone grafts were added to increase the volume below the elevated sinus membrane. A follow-up of 173 press-fit submerged implants, placed using this technique, reported a success rate of 96% at 18 months after loading (Rosen _et al_. 1999).
Today, two main procedures of sinus floor elevation for dental implant placement are in use: a two-stage technique using the lateral window approach, and a one-stage technique using a lateral or a crestal approach. The decision to use the one- or the two-stage technique is based on the amount of residual bone available and the possibility of achieving primary stability for the inserted implants.
# Treatment options in the posterior maxilla
Implant placement in the posterior maxilla remains a challenge. Reduced bone volume due to alveolar bone resorption and pneumatization of the sinus cavity makes it more difficult to place implants to support a dental prosthesis.
**Fig. 50-1** Radiograph of a posterior maxilla, showing reduced residual bone height which will not allow standard implant placement.
**Fig. 50-2** In 1994, Summers introduced a set of tapered osteotomes with different diameters to compress and push the residual bone from the implant preparation into the sinus cavity and to elevate the sinus membrane.
Several treatment options have been used in the posterior maxilla to overcome the problem of inadequate bone quantity. The most conservative treatment option would be to place short implants to avoid entering the sinus cavity. For placement of short implants, there is still a need for at least 6 mm of residual bone height, however. Another way of avoiding grafting the maxillary sinus would be to place tilted implants in a position mesial or distal to the sinus cavity if these areas have adequate bone ( **Fig. 50-3**). Furthermore, extra-long zygomatic implants can be placed in the lateral part of the zygomatic bone.
However, in patients with appropriate residual bone height, minor augmentation of the sinus floor can be accomplished via the crestal approach using the osteotome technique (Summers 1994; Rosen _et al_. 1999; Ferrigno _et al_. 2006). The problem of inadequate bone height may be overcome by elevating the maxillary sinus floor via the closed technique to provide sufficient quantity of bone for dental implant placement.
**Fig. 50-3** Radiograph showing a tilted implant placed in the position of 25 to avoid entering the sinus cavity. After remodeling, the bone level on the distal aspect of the implant is more apical than at the time of implant placement. This may lead to increased probing pockets depths around tilted implants. (The dotted lines represent the outlines of the residual bone.)
**Fig. 50-4** Patient with a shortened dental arch. Three implants were placed in the positions of 15, 14, and 25 without elevating the maxillary sinus floor and, consequently, the patient was restored to the second premolar.
The most invasive treatment option in the posterior maxilla is the one- or two-stage sinus floor elevation with a lateral approach. By mastering these different methods, most edentulous areas in the maxilla can by restored with implant-supported reconstructions. The concept of a shortened dental arch must also be kept in mind. The work of Käyser (1981) has shown that patients maintained adequate (50–80%) chewing capacity with a premolar occlusion ( **Fig. 50-4**).
# Sinus floor elevation with a lateral approach
## Anatomy of the maxillary sinus
The maxilla consists of a variety of anatomic structures, including the maxillary sinus, the lateral nasal walls, the pterygoid plates, associated vasculature structures, and teeth.
The maxillary sinus is pyramidal in shape. The base of the pyramid is the medial wall of the sinus that is also the lateral wall of the nasal cavity, and its apex is pointed towards the zygomatic bone. The roof of the sinus is also the floor of the orbit. The sinus has a non-physiologic drainage port high on the medial wall (maxillary ostium) that opens into the nasal cavity between the middle and lower nasal conchae.
The maxillary sinus maintains its overall size while the posterior teeth remain in function. It is, however, well known, that the sinus expands with age, and especially when posterior teeth are lost. The average volume of a fully developed sinus is about 15 ml but may range between 4.5 and 35.2 ml. The sinus cavity expands both inferiorly and laterally, potentially invading the canine region. This phenomenon is possibly the result of atrophy caused by reduced strain from occlusal function. One or more septa termed "Underwood's septa" may divide the maxillary sinus into several recesses.
The overall prevalence of one or more sinus septa is between 26.5% and 31% (Ulm _et al_. 1995; Kim _et al_. 2006) and is most common in the area between the second premolar and first molar. Edentulous segments have a higher prevalence of sinus septa than dentate maxillary segments.
The sinus is lined with respiratory epithelium (pseudo-stratified ciliated columnar epithelium) that covers a loose, highly vascular connective tissue (Fig. 50-5). Underneath the connective tissue, immediately next to the bony walls of the sinus, is the periosteum. These structures (epithelium, connective tissue, and periosteum) are collectively referred to as the Schneiderian membrane.
The blood supply to the maxillary sinus is derived primarily from the maxillary artery and, to a lesser degree, from the anterior ethmoidal and superior labial arteries. The sinus floor receives blood supply from the greater/lesser palatine and sphenopalatine arteries. These vessels penetrate the bony palate and ramify within the medial, lateral, and inferior walls of the sinus. The posterior superior alveolar artery has tributaries that perfuse the posterior and lateral walls. The posterior superior alveolar and infraorbital arteries anastomose in the bony lateral wall, on average 19 mm from the alveolar bone crest (Solar _et al_. 1999). The dense vascular network of the maxilla reduces after tooth loss and with increased age. The vast majority of the blood vessels in the maxilla (70–100%) come from the periosteum (Chanavaz 1990, 1995). Venous drainage is into the sphenopalatine vein and pterygomaxillary plexus. Neural supply comes from branches of the maxillary nerve.
**Fig. 50-5** Pseudostratified, ciliated columnar epithelium.
Non-hemolytic and alpha-hemolytic streptococci and _Neisseria_ spp. are the normal commensal microbiota of the maxillary sinus. Staphylococci, diphtheroids, _Hemophilus_ spp., pneumococci, _Mycoplasma_ spp., and _Bacteroides_ spp. are also found in varying amounts (Timmenga _et al_. 2003).
The healthy maxillary sinus is self-maintaining by postural drainage and actions of the ciliated epithelial lining, which propels bacteria toward the ostium. The maxillary sinus also produces mucus containing lysozymes and immunoglobulins. The significant vascularity of the Schneiderian membrane helps maintain its healthy state by allowing lymphocytic and immunoglobulin access to both the membrane and the sinus cavity.
The fact that the maxillary sinus opening to the nasal cavity is not in the lower part of the sinus (where a graft may be placed) is important and provides an anatomic rationale to sinus floor elevation, as the grafting procedure does not interfere with normal sinus function. In fact, a maxillary sinus floor elevation may improve symptoms of sinusitis/ congestion by bringing the floor of the sinus closer to the drainage port.
## Pre-surgical examination
Prior to planning complicated surgical procedures like elevation of the maxillary sinus floor, a thorough examination, including medical and dental history, should be obtained (see Chapters 27, 30, and 33).
The dental and periodontal status are evaluated using clinical and radiologic examination methods. The vitality of the neighbouring teeth has to be tested. The infraorbital, lateral nasal, and superior labial areas of the face must be examined regarding tenderness to palpation, swelling or asymmetry. The patient's history along with findings made during the clinical examination should provide sufficient information for diagnosing acute, allergic, and chronic sinusitis.
Pre-operative screening to assess a potential pathologic condition in the maxillary sinus should include radiographic examination, such as e.g. orthopantomography (OPT), tomography, computerized tomography (CT) scans or aquitomo-scans (see Chapter 28).
Before performing the sinus floor elevation surgery, all dentate patients should receive cause-related therapy (see Chapters 34–37).
Medical or surgical therapy of sinusitis, and removal of polyps and tumors must be completed prior to sinus floor elevation.
## Indications and contraindications
The main indication for maxillary sinus floor elevation utilizing a lateral approach is reduced residual bone height, which does not allow standard implant placement or placement of implants in combination with minor sinus floor elevation using the osteotome technique. In cases of reduced bone height due to alveolar bone resorption and pneumatization of the sinus cavity the so-called lateral approach, with or without horizontal bone augmentation, is indicated.
Contraindications for sinus floor elevation can by divided into three groups: intraoral contraindications, medical conditions, and local contraindications.
The _medical_ contraindications include: chemotherapy or radiotherapy of the head and neck area at the time of sinus floor elevation or in the preceding 6 months depending on the field of radiation; immunocompromised patients; medical conditions affecting bone metabolism; uncontrolled diabetes; drug or alcohol abuse; patient non-compliance; and psychiatric conditions.
Whether or not smoking is an absolute contraindication for maxillary sinus floor elevation remains controversial. In a case series, Mayfield and coworkers (2001) evaluated survival of implants placed in combination with bone augmentations (horizontal, vertical, and sinus elevations). The survival rate of these implants was 100% for non-smokers compared to only 43% for smokers after 4–6.5 years of functional loading (Mayfield _et al_. 2001). This reduced survival rate has been corroborated by several other authors (Bain & Moy 1993; Jensen _et al_. 1996; Gruica _et al_. 2004). However, a large study evaluating 2132 implants after sinus floor elevation with simultaneous implant placement found conflicting results (Peleg _et al_. 2006). Two hundred and twenty-six sinus floor elevations (627 implants) were performed on smokers, and 505 sinus floor elevations (1505 implants) on non-smokers. After a follow-up time of up to 9 years, the survival rate of the implants was 97.9%, and there were no statistically significant differences between survival rates in smokers and in non-smokers.
Alteration of the nasal–maxillary complex that interferes with normal ventilation as well as the mucociliary clearance of the maxillary sinus, may be a contraindication for sinus floor elevation. However, such abnormal conditions may be clinically asymptomatic or only present with mild clinical symptoms. These conditions include viral, bacterial, and mycotic rhinosinusitis, allergic sinusitis, sinusitis caused by intra-sinus foreign bodies, and odontogenic sinusitis resulting from necrotic pulp tissue. All odontogenic, periapical, and radicular cysts of the maxillary sinus should be treated prior to sinus floor elevation.
A sinus floor elevation under any of the above conditions may disturb the fine mucociliary balance, resulting in mucus stasis, suprainfection or a subacute sinusitis.
Absolute local contraindications for sinus floor elevation are: acute sinusitis; allergic rhinitis and chronic recurrent sinusitis; scarred and hypofunctional mucosae; local aggressive benign tumors; and malignant tumors.
## Surgical techniques
The original Caldwell-Luc technique, commonly referred to as the lateral window or lateral approach, describes an osteotomy prepared in a superior position just anterior to the zygomatic buttress. Two other positions have also been described: a mid-maxillary position between the alveolar crest and zygomatic buttress area, and a low anterior position near the level of the existing alveolar ridge (Lazzara 1996; Zitzmann & Scharer 1998). The technique described in this chapter is a modification of these techniques:
* A presurgical rinse with chlorhexidine 0.1% is performed for a period of 1 minute.
* Local anesthesia is delivered buccal and palatal to the surgical area.
* The initial incision is midcrestal extending well beyond the planned extension of the osteotomy. The incision is carried on forward beyond the anterior border of the maxillary sinus. Releasing incisions are made anteriorly extending into the buccal vestibulum to facilitate reflection of a fullthickness mucoperiosteal flap.
* A mucoperiosteal flap is raised slightly superior to the anticipated height of the lateral window.
* After the lateral sinus wall has been exposed, a round carbide bur in a straight hand piece is used to mark the outline of the osteotomy (Fig. 50-6). When the bone has been trimmed down to a thin bony plate, the preparation is continued with a round diamond bur (Fig. 50-7) in a straight hand piece until a bluish hue of the sinus membrane is observed (Fig. 50-8). Three methods for handling the buccal cortical bone plate have been proposed. The most common one is the thinning of the buccal bone to a paper-thin bone lamella using a round bur, and removing it prior to the elevation of the sinus membrane (Fig. 50-9). The second method is to fracture the cortical bony plate like a trap-door and use it as the superior border to the sinus compartment, leaving it attached to the underlying mucosa. Since the cortical bony plate is resistant to bone resorption this may protect the graft. The third method proposed is to remove the cortical bony plate during sinus floor elevation and replace it on the lateral aspect of the graft at the end of the grafting procedure. The rationale for this method was the notion that the lateral window would not completely heal without replacement of its cortical plate. However, healing of the lateral window by bone apposition has been demonstrated to occur without replacing the cortical bony plate (Boyne 1993).
* The next step will be chosen according to the technique used. If the buccal wall is eliminated, the sinus membrane is elevated directly with blunt instruments (Fig. 50-10). On the other hand, gentle tapping is continued until movement of the bony plate is observed if the "trap-door" technique is used. Then, in combination with the elevation of the sinus membrane in the inferior part of the sinus, the bony plate is rotated inwards and upwards to provide adequate space for grafting material (Fig. 50-11). Care should be taken not to perforate the sinus membrane.
**Fig. 50-6** The outline of the lateral window has been marked with a round bur.
**Fig. 50-7** The buccal bony plate is trimmed to a paper-thin lamella with a fine grit round diamond bur, avoiding the perforation of the sinus membrane.
**Fig. 50-8** After removing the buccal bony plate, the bluish hue of the sinus membrane becomes clearly visible.
**Fig. 50-9** Before elevating the sinus membrane the entire buccal bone is removed to gain access to the membrane.
**Fig. 50-10** The sinus membrane is carefully elevated using a blunt instrument. To avoid penetration, it is essential to keep contact with the underlying bone at all time during this procedure.
**Fig. 50-11** The buccal cortical bony plate was fractured and moved upwards and inwards like a "trap-door". The cortical bony plate is delineating the superior border of the maxillary sinus compartment.
**Fig. 50-12** The sinus compartment has been filled with a loosely packed 1 : 1 mixture of particulate autogenous bone and a xenograft.
**Fig. 50-13** The lateral window has been covered with single or double layer of resorbable barrier membrane.
Depending on the clinical condition and the surgeon's preference, a delayed (two-stage) or a one-stage sinus floor elevation simultaneously with the implant installation is chosen.
* Two-stage sinus elevation (delayed installation of the implant):
* Grafting material is placed in the compartment made by the elevation of the sinus membrane. The grafting material should not be densely packed, because this reduces the space needed for ingrowth of newly forming bone. In addition, pressurizing the thin sinus membrane may result in a late perforation.
* After the compartment has been filled with grafting material (Fig. 50-12), the lateral window is closed by covering it with a resorbable or a non-resorbable barrier membrane (Fig. 50-13). Subsequently, the flap is closed free of tension. In most conditions, there is a need for deep periosteal incisions to achieve tension-free closure.
* One-stage sinus floor elevation with simultaneous implant placement:
* After the sinus membrane has been elevated, the implant sites are prepared. If rotary instruments are used, the sinus membrane has to be protected using a periosteal elevator (Fig. 50-14). Osteotomes of different diameters may be used to prepare the implant site, and then the membrane can be protected by inserting sterile gauze into the sinus compartment (Fig. 50-15).
* The appropriate implant length is measured with a blunt depth gauge (Fig. 50-16). Before placing the implant, the grafting material is inserted into the medial part of the sinus compartment (Fig. 50-17). After implant placement (Fig. 50-18), the lateral part of the compartment is filled with grafting material (Fig. 50-19).
* The subsequent steps coincide with those described for the two-stage procedure.
**Fig. 50-14** If rotary instruments are used to prepare the implant site, the sinus membrane has to be protected with a periosteal elevator that is placed into the sinus compartment.
**Fig. 50-15** If osteotomes are utilized to prepare the implant site, the sinus membrane can be protected by inserting sterile gauze into the sinus compartment.
**Fig. 50-16** If sinus floor elevation and simultaneous implant placement are performed, the height of the sinus compartment and implant length may be determined by inserting a blunt depth gauge into the implant site. Care must be taken not to apply too much pressure on the sinus membrane.
**Fig. 50-17** Before placing the implants, grafting material has to be inserted into the medial part of the sinus compartment, because access to the medial part of the sinus compartment is restricted after implant installation.
The main differences between the methods used presently are the position and technique used to prepare the lateral window, the amount of sinus membrane elevation, the type of graft utilized, and the choice of one-stage or two-stage approaches.
Histomorphometric evidence of enhanced bone formation following membrane placement over the lateral window is available. In a randomized controlled clinical trial (Tarnow _et al_. 2000), a split mouth design with bilateral sinus grafts was performed for 12 patients with or without covering the lateral window using a membrane. After 12 months, histologic samples were taken through the lateral window. The mean percentage of vital bone formation was 25.5% with and 11.9% without a covering barrier. Similar results were obtained in a controlled clinical trial (Froum _et al_. 1998) measuring bone formation in 113 sinuses grafted either with xenograft alone or a composite of xenograft and autograft. The mean vital bone formation was 27.6% when a membrane was used compared to 16% without.
**Fig. 50-18** Two implants have been installed after filling the medial part of the sinus compartment.
**Fig. 50-19** After implant installation the lateral part of the sinus compartment is filled up with loosely packed grafting material.
## Post-surgical care
In order to minimize post-operative pain and discomfort for the patient, surgical handling should be as atraumatic as possible. Precautions must be taken to avoid perforation of the flap and the sinus membrane. The bone should be kept moist during the surgery, and a tension-free primary flap closure is essential. The pain experienced by patients is mostly limited to the first days after surgery. Swelling and bruising of the area are usually the chief post-operative sequelae. Often, swelling and bruising extend from the inferior border of the orbit to the lower border of the mandible or even to the neck. In order to reduce swelling, it is important to cool the area with cooling pads at least for the first post-operative hours. Occasionally, minor bleeding may arise from the nose. It is important to inform the patients that some irritation in the nasal area may be expected. In the event of the need for sneezing, the nose should not be covered so that air pressure is allowed to escape. After the surgery, patients are placed on antibiotic therapy. Furthermore, antiseptic rinses with 0.1–0.2% chlorhexidine twice daily are indicated for the first 3 weeks after surgery.
**Fig. 50-20** The most frequent complication during maxillary sinus floor elevation is perforation of the sinus membrane. A medium-sized perforation can be detected after elevation of the membrane.
## Complications
When performing sinus floor elevation, the risk of complications must be considered and the appropriate treatment foreseen. The most common intra-operative complication is perforation of the sinus membrane (Fig. 50-20). Presence of maxillary sinus septa and root apices penetrating into the sinus may increase the risk of membrane perforation. The risk of perforation has been reported to be between 10 and 40% during surgery (Block & Kent 1997; Timmenga _et al_. 1997; Pikos 1999). In the event of a membrane perforation, it is recommended to elevate the membrane in the opposite direction to prevent further enlargement of the perforation. Smaller perforations (<5 mm) may be closed by using tissue fibrin glue, suturing or by covering them with a resorbable barrier membrane (Fig. 50-21). In cases of larger perforations, larger barrier membranes, lamellar bone plates or suturing may be used either alone or in combination with tissue fibrin glue to provide a superior border for the grafting material. In instances of larger perforations, where a stable superior border cannot be achieved the grafting of the maxillary sinus must by aborted and a second attempt at sinus floor elevation may be performed 6–9 months later (Tatum _et al_. 1993; van den Bergh _et al_. 2000).
Other complications that were reported during surgery included excessive bleeding from the bony window or the sinus membrane, and wound dehiscences. Iatrogenic complications include injury of the infraorbital neurovascular bundle from deep dissection to free the flap from tension or blunt trauma due to the compression of the neurovascular bundle during retraction. Implant migration, hematoma, and adjacent tooth sensitivity have also been reported.
**Fig. 50-21** Small- to mediumsized sinus membrane perforations may be closed by applying a resorbable barrier membrane.
Infection of the grafted sinuses is a rare complication. However, the risk for infection increases with a membrane perforation. Hence, it is recommended to avoid sinus grafting and simultaneous implant placement in situations of membrane perforation (Jensen _et al_. 1996). Infection of the grafted sinuses is usually seen 3–7 days post surgically and may lead to a failure of the graft. Possible complication secondary to infection may involve a parasinusitis with the spread of the infection to the orbita or even to the brain. For these reasons, infected sinus grafts must be treated immediately and aggressively. Surgical removal of the entire graft from the sinus cavity and administration of high doses of antibiotics are essential.
Sinusitis is another complication that may occur after sinus grafting. In a study (Timmenga _et al_. 1997) evaluating the function of the maxillary sinus after sinus floor elevation, 45 patients who had received 85 sinus grafts underwent endoscopic examination. Of these, five were diagnosed with sinusitis. In these five patients, the endoscopic examination revealed oversized turbinates and septal deviation. Hence, the result of this study showed that the incidence of sinusitis was low and mainly found in patients with an anatomic or functional disorder prior to the sinus grafting.
Late failure reports include chronic infection, graft exposure, loss of the entire bone graft, oro-antral fistula, ingrowth of soft tissue through the lateral window, granulation tissue replacing the graft, and sinus cysts.
## Grafting materials
There are differences in opinion on the necessity of grafting material when elevating the maxillary sinus floor.
### Sinus floor elevation without grafting material
Studies in monkeys (Boyne 1993) showed that implants protruding into the maxillary sinus following elevation of the sinus membrane without grafting material, exhibited spontaneous bone formation over more than half of the implant's height. Hence, protrusion of an implant into the maxillary sinus does not appear to be an indication for bone grafting. In the same study, it was also seen that the design of the implant influenced the amount of spontaneous bone formation. Implants with open apices or deepthreaded configurations did not reveal substantial amounts of new bone formation. On the other hand, implants with rounded apices tended to show spontaneous bone formation extending all around the implants if they only penetrated 2–3 mm into the maxillary sinus. However, when the same implants penetrated 5 mm into the maxillary sinus, only a partial (50%) growth of new bone was seen towards the apex of the implant.
In a clinical study (Ellegaard _et al_. 2006), 131 implants were placed using the lateral approach. The sinus membrane was elevated, implants were inserted and left to protrude into the sinus cavity. The sinus membrane was allowed to settle on to the apex of the implants, thus creating a space to be filled with a blood coagulum. After a mean follow-up time of 5 years, the survival rate of these implants was 90%. It must be kept in mind, however, that the residual bone height in this study was at least 3 mm.
### Autogenous bone
Autogenous bone grafts are considered the gold standard for grafting due to their maintenance of cellular viability and presumptive osteogenic capacity. The use of autogenous grafts in sinus floor elevation was first reported by Boyne and James (1980) and Tatum (1986).
Grafts may be harvested intraorally or extraorally. Common intraoral donor sites are the maxillary tuberosity, the zygomatico-maxillary buttress, the zygoma, the mandibular symphysis and the mandibular body and ramus (Fig. 50-22). Bone may be harvested in block section or in particulate form. The extraoral donor sites that have been utilized are the anterior and posterior iliac crest, the tibial plateau, the rib, and the calvaria.
Autologous bone grafts contain bone morphogenic proteins (BMPs) that are capable of inducing osteogenic cells in the surrounding tissues. They also contain other growth factors essential for the process of graft incorporation. Processing of autograft, with grinding or morselizing, does not seem to disturb the viability of the osteogenic cells (Springer _et al_. 2004). The main source of osteogenic cells during graft consolidation is the periosteum that includes mesenchymal progenitor cells and provides a rich source of blood vessels. Osteoclasts are then required for remodeling of the graft–woven bone complex. The consolidation of the graft depends on the properties of the graft material and the osteogenic potential of the recipient bed. Initially, cortical bone grafts act as weight-bearing space fillers and remain a mixture of necrotic and viable bone for a prolonged period of time. The ideal graft material has to allow ingrowth of blood vessels and formation of bone on its surfaces for integration into the recipient bed (osteoconductivity).
**Fig. 50-22** The most suitable sites used to harvest block or particulate bone grafts intraorally are the mandibular body and the mandibular ramus.
In situations of sinus floor elevations that do not eventually receive dental implants, the bone grafts may resorb due to the lack of functional load and strain.
### Bone substitutes
Loss of autografts during healing occurs when resorption of the autograft exceeds new bone formation during the consolidation phase. Thus, to overcome excessive resorption of autografts, bone substitutes that are known for their slow resorption process, are added to autografts to increase the stability of grafts during the consolidation phase.
Tricalcium phosphate was the first bone substitute to be applied successfully for sinus floor elevation (Tatum 1986). Over the years, allografts, alloplasts, and xenografts of various types have been used alone or in combination with autografts. Studies in animal models showed that the use of bone substitutes, such as bovine bone mineral, either alone or in combination with autografts, preserved the vertical height of the graft over time (Fig. 50-23). In a human study, sinus grafts consisting of autografts and demineralized allografts, were observed over a period of time. A graft resorption of up to 25% was seen. Furthermore, a more recent human study (Hatano _et al_. 2004) showed also significant reduction in graft volume, when either autogenous bone alone or a mixture of autogenous bone and xenografts were used. There is a definitive need for good long-term studies that address the stability of the different types of grafting materials in the maxillary sinuses over time.
**Fig. 50-23** A 1 : 1 mixture of particulate autologous bone and bone substitute. The autologous bone particles include viable osteogenic cells, bone morphogenic proteins, and other growth factors. The bone substitute is supposed to decrease the resorption of the grafting material.
**Fig. 50-24** The bovine bone mineral particles (xenograft) are mostly surrounded by new mature compact bone. No gaps can be seen at the interface between the xenograft particles and the newly formed bone. (Courtesy of Dr. Dieter D. Bosshardt, Berne.)
Histologic analysis of human biopsy specimens from sinuses augmented with xenografts revealed that xenograft particles were mostly surrounded by mature compact bone (Fig. 50-24). In some Haversian canals, it was possible to observe small capillaries, mesenchymal cells, and osteoblasts in conjunction with new bone. No gaps were noted at the interface between the xenograft particles and the newly formed bone (Piattelli _et al_. 1999).
A human study (Froum _et al_. 1998) evaluating bone formation after sinus floor elevation using xenografts alone or in combination with autogenous bone and/or demineralized freeze-dried bone allografts reported statistically significant increase in vital bone formation, when as little as 20% of autologous bone was added to the bone substitutes. The mean vital bone formation was 27.1% after a healing period of 6–9 months. However, comparative studies (Hising _et al_. 2001; Hallman _et al_. 2002a,b; Valentini & Abensur 2003) reported higher survival rates for implants placed into sinuses grafted with 100% xeno-graft as compared to those placed in sinuses grafted with 100% autogenous bone or composite graft of xenograft and autogenous bone.
Another indication for using bone substitutes is to reduce the volume of bone that must be harvested. When a large sinus cavity is grafted with autologous bone alone, 5–6 ml of bone may be necessary. Using bone substitutes alone or in combination with auto-grafts, the amount of autogenous bone to be harvested is greatly reduced.
## Success and implant survival
Jensen and co-workers (1996) published the findings from the Consensus Conference of the Academy of Osseointegration. Retrospective data was collected from 38 clinicians who collectively performed 1007 sinus floor elevations and placed 2997 implants over a 10-year period. The majority of the implants had been followed for 3 years or more. Two hundred and twenty-nine implants were lost resulting in a overall survival rate of 90.0%. However, the database was so variable that no definitive conclusions regarding the grafting material, the type of implants, and the timing for implant placement could be drawn.
Survival of implants cannot be the sole criterion for success of maxillary sinus floor elevation. Factors, such as the pre-operative residual bone height, the long-term stability of the bone graft, and the incidence of failing two-stage sinus grafting due to graft resorption must also be considered.
Of the 900 patient records that were screened for the Consensus Conference in 1996, only 100 had radiographs of adequate quality for analysis of the residual bone height. In total, only 145 sinus grafts in 100 patients, with 349 implants, were analyzed. After a mean follow-up period of 3.2 years, 20 implants were lost. Of the implants lost, 13 were initially placed in residual bone with a height ≤4 mm, seven were placed in residual bone with a height of 5–8 mm. None of the implants placed in residual bone height of more than 8 mm was lost. There was a statistically significant difference in implant loss when residual bone height was 4 mm or less as compared to 5 mm or greater (Jensen _et al_. 1996).
A critical appraisal of the dental literature on maxillary sinus floor elevation shows that the two-stage approach (delayed implant installation) is more likely to be used in situations with less residual bone height compared to the one-stage approach (simultaneous implant placement).
**Fig. 50-25** One-stage sinus floor elevation. (a) A panoramic radiograph showing oblique inferior sinus borders and a residual bone height between 2 and 6 mm in the position of 25. (b) Two implants were placed, a standard implant placement in the position of 24 and an implant installed in combination with sinus floor elevation in the position of 25. A 1 : 1 mixture of particulate autologous bone harvested from the maxillary tuberosities and the zygomatic bone combined with bovine bone mineral was used as the grafting material. (c) OPT taken 1 year after functional loading. A new inferior border of the maxillary sinus and a stable graft volume was evident. (d) The clinical situation at the 1-year follow-up visit.
The efficacy of performing a one-stage sinus floor elevation in patients whose residual alveolar bone height in the posterior maxilla was between 3 and 5 mm was assessed (Peleg _et al_. 1999). Using the modified Caldwell-Luc technique, the maxillary sinus was elevated with composite grafts of symphysal autograft and demineralized freeze-dried bone allograft in a 1 : 1 ratio. One hundred and sixty implants were placed in 63 elevated sinuses. A 100% survival rate of the implants was reported after 4 years. In a second study (Peleg _et al_. 1998) using a similar protocol on 55 implants placed into 20 elevated sinuses, the residual alveolar bone height was only 1–2 mm. All implants osseointegrated successfully, and no implants were lost after 2 years of functional loading.
Only one randomized controlled clinical trial (Wannfors _et al_. 2000) compared one- and two-stage sinus floor elevation, in 40 patients divided into groups. The residual bone height ranged from 2 to 7 mm. The one-stage protocol (Fig. 50-25) with 75 implants placed reported a survival rate of 85.5% as compared to the two-stage protocol (Fig. 50-26) with 90.5% survival rate for 74 implants placed after 1 year in function. Apparently, the risk of implant failure in grafted areas for the one-stage procedure was greater than for two-stage procedure, although the results did not reach statistical significance.
The stability of the sinus graft height was evaluated on panoramic radiographs for 349 implants. After a mean follow-up period of 3.2 years, the reduction of the graft height varied between 0.8 mm (autograft and alloplast) and 2.1 mm (autograft). This indicated that all of the graft materials appeared to be stable, with only 1–2 mm of the graft height being lost over the 3-year period (Jensen _et al_. 1996). Further studies evaluating the long-term stability of sinus grafts (Block _et al_. 1998; Hatano _et al_. 2004) yielded similar results.
**Fig. 50-26** Two-stage sinus floor elevation. (a) An OPT showing a large pneumatized maxillary sinus in the 1st quadrant and a residual bone height of only 1–2 mm. (b) The maxillary sinus floor was elevated with a 1 : 1 mixture of particulate autologous bone harvested from the mandibular ramus and bovine bone mineral. (c) Three 12 mm implants were inserted in a second-stage surgery 6 months after the elevation of the sinus floor. (d) OPT taken after 1 year of functional loading, indicating a stable situation. No changes in graft volume are visible. (e) The clinical situation at the 1-year follow-up visit.
In 2003, Wallace and Froum published a systematic review on the effect of maxillary sinus floor elevation on the survival of dental implants. The inclusion criteria were human studies with a minimum of 20 interventions, a follow-up time of 1 year of functional loading and with an outcome varied of implant survival. The main results indicated:
1. A survival rate of implants placed in conjunction with sinus floor elevation with the lateral approach varied between 61.7 and 100%, with an average of 91.8%.
2. Implant survival rates compared favorably to reported survival rates for implants placed in the non-grafted maxilla.
3. Rough-surfaced implants yielded higher survival rate than machined-surface implants when placed in grafted sinuses.
4. Implants placed into sinuses augmented with particulate autografts showed higher survival rates than those placed in sinuses that had been augmented with block grafts.
5. Implant survival rates were higher when barrier membranes were placed over the lateral window.
6. The utilization of grafts consisting of 100% autogenous bone or the inclusion of autogenous bone as a component of composite grafts did not affect implant survival.
# Sinus floor elevation with the crestal approach (osteotome technique)
The osteotome technique was first developed to compress soft, type III and IV maxillary bone. The concept is intended to increase the density of bone in the maxilla leading to better primary stability of inserted dental implants.
In the maxilla, the bone crest in edentulous ridges is often narrow in the bucco-palatal dimension. This limits the possibility of standard drilling in preparing an implant site. Thus, to address this difficult situation, tapered round osteotomes of increasing diameters have been used to expand the compactible cancellous maxillary bone and gently move it in a lateral direction to increase crestal width. This procedure is known as "ridge expansion osteotome technique" and will not be addressed further in this chapter.
**Fig. 50-27** Set of straight and tapered osteotomes used to prepare the implant site and to elevate the maxillary sinus floor.
Tatum (1986) described the crestal approach to elevate the sinus floor. The osteotome technique for sinus floor elevation, using a set of osteotomes of varying diameters (Fig. 50-27) to prepare the implant site, was first presented by Summers (1994). The bone-added osteotome sinus floor elevation (BAOSFE), today referred to as the _Summers technique_ , may be considered to be a more conservative and less invasive approach than the conventional lateral approach of sinus floor elevation. A small osteotomy is made through the crest of the edentulous ridge, at the inferior region of the maxillary sinus. This intrusion osteotomy procedure elevates the sinus membrane, thus creating a "tent". This creates space for bone graft placement. It should be noted that the bone grafts are placed blindly into the space below the sinus membrane. Hence, the main disadvantage of this technique is the uncertainty of possible perforation of the sinus membrane. However, an endoscopic study has shown that the sinus floor can be elevated up to 5 mm without perforating the membrane (Engelke & Deckwer 1997).
## Indications and contraindications
Indications for the transalveolar osteotome technique (crestal approach) include a flat sinus floor with a residual bone height of at least 5 mm and adequate crestal bone width for implant installation.
The contraindications for the osteotome technique are similar to those previously described for the lateral approach. In addition, however, patients with a history of inner ear complications and positional vertigo are not suitable for the osteotome technique. As for the local contraindications, an oblique sinus floor (>45º inclination) is not suitable for the osteotome technique either (Fig. 50-28). The reason is the fact that the osteotomes first enter the sinus cavity at the lower level of an oblique sinus floor, while still having bone resistance on the higher level. In this situation, there is a high risk of perforating the sinus membrane with the sharp margin of the osteotome (Fig. 50-29).
**Fig. 50-28** Edentulous space in position 15. The oblique inferior border of the maxillary sinus lies at approximately 60º to the inferior border of the alveolar crest (the dotted lines represent the outlines of the residual bone). In a clinical situation like this, it is difficult to elevate the maxillary sinus floor with osteotomes. The osteotomes will first enter the sinus cavity distally at the lowest level of oblique sinus floor while still having bone resistance on the cranial level of the sinus floor. Hence, the risk of the sharp margin perforating the sinus membrane is high.
## Surgical technique
Apart from the original technique (Summers 1994), only minor modifications have been presented (Rosen _et al_. 1999; Fugazotto 2001; Chen & Cha 2005). The technique described in this chapter represents a modification of the original technique:
* Pre-surgical patient preparation includes oral rinsing with 0.1% chlorhexidine for a period of 1 minute.
* Local anesthesia is administered into the buccal and palatal regions of the surgical area.
* A mid-crestal incision with or without releasing incision is made and a full-thickness mucoperiosteal flap is raised.
* With a surgical stent or a distance indicator, the implant positions are marked on the alveolar crest with a small round bur (#1). After exactly locating the implant positions, the opening of the preparations are widened with two sizes of round burs (#2 and #3) to a diameter about half a millimeter smaller than the implant diameter that is chosen (Fig. 50-30).
* The distance from the crestal floor of the ridge to the floor of the maxillary sinus, measured prior to implant site preparation on the pre-operative radiograph, can in most cases, be confirmed at surgery by penetrating the opening of the preparation with a blunt periodontal probe through the soft trabecular bone (type III or IV bone) to the floor of the maxillary sinus.
* After confirming the distance to the sinus floor, pilot drills with small diameters (1–1.5 mm smaller than the implant diameter) are used to prepare the implant site to a distance of approximately 2 mm below from the sinus floor (Fig. 50-31a). In conditions of soft type IV bone and a residual bone height of 5–6 mm, there is usually no necessity to use the pilot drills. It is sufficient to perforate the cortical bone at the alveolar crest with the round burs.
* The first osteotome used in the implant site is a small diameter tapered osteotome (Fig. 50-32). With light malleting, the osteotome is pushed towards the compact bone of the sinus floor (Fig. 50-31b). After reaching the sinus floor, the osteotome is pushed about 1 mm further with light malleting in order to create a "greenstick" fracture on the compact bone of the sinus floor. A tapered osteotome with small diameter is chosen to minimize the force needed to fracture the compact bone.
* The second tapered osteotome, with a diameter slightly larger then the first one, is used to increase the fracture area of the sinus floor (Fig. 50-33). The second osteotome is applied to the same length as the first one.
* The third osteotome used is a straight osteotome with a diameter about 1–1.5 mm smaller than the implant to be placed (Fig. 50-34).
**Fig. 50-29** (a) A sinus floor elevation was performed with the osteotome technique in a situation of an oblique sinus floor. The cortical bone of the sinus floor was infractured and rolled-up causing a perforation of the sinus membrane. Due to the membrane perforation no grafting material was utilized. (b) The same patient at the 5-year follow-up visit. The implant was stable, but only minor new bone formation is visible at the distal aspect of the implant.
**Fig. 50-30** The exact position of the implant site is first marked with a small round bur (#1) and then extended with two sizes of round burs (#2 and #3) to a diameter about 0.5–1 mm smaller than that of the implant to be installed.
From this point onwards, the technique utilized in the surgical procedure depends on whether or not bone grafts or bone substitutes will be placed.
### Implant placement without grafting material
* Without applying grafting material, the straight osteotome with a diameter about 1–1.5 mm smaller than that of the implant will be pushed further until it penetrates the sinus floor.
* The last osteotome to be used must have a form and diameter suitable for the implant to be placed. For example, for a cylindrical implant with a diameter of 4.1 mm, the last osteotome should be a straight osteotome with a diameter about 0.5 mm smaller than the implant diameter (3.5 mm). It is important that last osteotome only enters the preparation site once (Fig. 50-35). If several attempts have to be made in sites with soft bone (type III or IV), there is a risk of increasing the diameter of the preparation that might jeopardize achieving good primary stability. On the other hand, if the last osteotome diameter is too small compared to the implant diameter, too much force must be used to insert the implant. By squeezing the bone, more bone trauma and, hence, greater bone resorption will occur, delaying the osseointegration process (Abrahamsson _et al_. 2004). It is thus important, especially when placing implants in sites with reduced bone volume, that the fine balance between good primary stability and traumatizing the bone is respected.
* During the entire preparation, it is crucial to maintain precise control of the penetration length. Regular osteotomes have sharp cutting edges, thus entry into the sinus cavity increases the risk of membrane perforation. The final step before placing the implant is to check that the preparation is patent to the planned insertion depth. An osteotome with a rounded tip or a depth gauge, for the relevant implant diameter, is pushed to the decided length (Fig. 50-36).
**Fig. 50-31** (a) The implant site is prepared to a distance of approximately 2 mm below the sinus floor with a small diameter pilot drill. (b) After reaching the sinus floor, the osteotome is pushed approximately 1 mm further with light malleting in order to create a "greenstick" fracture on the compact bone of the sinus floor. (c) Grafting material is slowly pushed into the sinus cavity with a straight osteotome. This procedure is repeated several times. (d) The tip of the osteotome is only supposed to enter the sinus cavity after some grafting material has been pushed through the preparation site to elevate the sinus membrane. (e) The inserted implant and the grafting material maintain space below the sinus membrane.
**Fig. 50-32** The first osteotome used in the implant site is a small-diameter tapered osteotome. Such an osteotome is chosen to minimize the force needed to fracture the compact bone.
**Fig. 50-33** A second osteotome, which is also tapered, but with a diameter slightly larger then the first one, is used to increase the fractured area of the sinus floor.
**Fig. 50-34** The third osteotome utilized is a straight osteotome with a diameter about 1–1.5 mm smaller than that of the implant to be placed.
**Fig. 50-35** The last osteotome to be used must have a form and diameter suitable for the implant to be placed. For example, for a cylindrical implant with a diameter of 4.1 mm, the last osteotome should be straight with a diameter approximately 0.5 mm smaller than that of the implant (3.5 mm). It is important that the last osteotome is allowed to enter the preparation site only once.
### Implant placement with grafting materials
* When performing the osteotome technique with grafting materials, the osteotomes are not supposed to enter the sinus cavity _per se_. Repositioned bone particles, grafting materials, and the trapped fluid will create a hydraulic effect moving the fractured sinus floor and the sinus membrane upwards. The sinus membrane is less likely to tear under this kind of pressure that has a fluid consistency.
* After pushing the third osteotome up to the sinus floor and before placement of any grafting material, the sinus membrane must by tested for any perforations. This is tested with the Valsalva maneuver (nose blowing). The nostrils of the patients are compressed (Fig. 50-37), and the patient blows against the resistance. If air leaks out of the implant site, the sinus membrane is perforated, and no grafting material should be placed into the sinus cavity.
* If the sinus membrane is judged to be intact, the preparation is filled with grafting material (Fig. 50-38). The grafting material is then slowly pushed into the sinus cavity with the same straight third osteotome (Fig. 50-39). This procedure is repeated four to five times (Fig. 50-31c) until about 0.2–0.3 g of grafting material has been pushed into the sinus cavity below the sinus membrane (Fig. 50-40). In the fourth and fifth time of applying grafting material, the tip of the osteotome may enter about 1 mm into the maxillary sinus cavity to test if there is resistance in the preparation site (Fig. 50-31d).
* Finally, before implant placement (Fig. 50-41), the preparation is checked for patency, as mentioned before, and the Valsalva maneuver is repeated.
**Fig. 50-36** The final step before placing the implant is to check that the preparation is patent to the planned insertion depth. An osteotome with a rounded tip or a depth gauge, for the relevant implant diameter, is pushed to the decided length.
**Fig. 50-37** To test the sinus membrane, the nostrils of the patients are compressed and the patient is asked to blow against the resistance. If air leaks out of the implant site, the sinus membrane is perforated, and no grafting material should be placed into the sinus cavity.
**Fig. 50-38** If the sinus membrane is intact, the preparation site is filled four to five times with grafting material.
**Fig. 50-39** The grafting material is then slowly pushed into the sinus cavity with a straight osteotome with a diameter about 1–1.5 mm smaller than that of the intended implant.
## Post-surgical care
The post-surgical care after placing implants with the osteotome technique is similar to that after standard implant placement. In addition to the standard oral home care, antiseptic rinsing with 0.1–0.2% chlorhexidine twice daily for the first 3 weeks after surgery is highly recommended. However, if bone substitutes were used, the patients are placed on antibiotic prophylaxis for a period of 1 week.
## Grafting material
There is still controversy with regards to the necessity of a grafting material to maintain the space for new bone formation after elevating the sinus membrane utilizing the osteotome technique. Shortly after Summers introduced the BAOSFE, a multi-center retrospective study of eight centers was performed. Evaluation was carried out with 174 implants placed in 101 patients. The use of grafting material was decided by the individual clinician. Autografts, allografts, and xenografts were used, alone or in combinations. The authors concluded that the type of grafting material did not influence implant survival (Rosen _et al_. 1999).
**Fig. 50-40** A radiograph, taken after implant placement, showing a dome-shape configuration of the graft. In this instance, 0.25 g of grafting material (xenograft) was used to elevate the sinus membrane (the dotted lines represent the outlines of the residual bone).
**Fig. 50-41** A rough-textured implant was installed after preparing the implant site with the osteotome technique. Good primary stability was achieved.
When no grafting material is used, some dense structure is often visible apical to the implant, immediately after implant placement. However, after at least 1 year of remodeling, this structure may no longer be detectable and only a moderate amount of bone gain mesially and distally may persist (Pjetursson _et al_. 2008a,b). When grafting material is used, a cloudy dome-shaped structure with a hazy demarcation may be visible after implant placement. The size of this dome is usually reduced after remodeling but still gives a definite increase in bone volume compared to the pre-operative situation (Pjetursson _et al_. 2008a,b) (Fig. 50-42).
**Fig. 50-42** (a) A radiograph, taken at the 5-year follow-up visit, of an implant placed in the 1st quadrant utilizing the osteotome technique without grafting material. A new cortical bony plate at the inferior border of the maxillary sinus is clearly visible, but no bony structure can be detected apical to the implant. (b) A radiograph (same patient) of an implant placed in the 2nd quadrant utilizing the osteotome technique with xenograft grafting material, taken after 5 years in function. A dome-shaped structure is clearly visible documenting a definite increase in bone volume compared to the initial situation. The "dome" is surrounded with a new cortical bony plate.
**Fig. 50-43** Grafted area apical to the implants undergoes shrinkage and remodeling and the original border of the sinus is eventually consolidated and replaced by a new cortical plate (Brägger _et al_. 2004).
Brägger and co-workers (2004) investigated the patterns of tissue remodeling after placement of 25 implants in 19 patients using the osteotome technique with composite xenografts and autografts. Intraoral radiographs were obtained pre-surgically and post-surgically at 3 and 12 months. The mean height of the new bone reaching apical and mesial to the implants was 1.52 mm at surgery, but was reduced significantly to 1.24 mm at 3 months and 0.29 mm after 12 months (Fig. 50-43). It was concluded that the grafted area apical to the implants underwent shrinkage and remodeling (Fig. 50-44) and the original outline of the sinus was eventually consolidated and replaced by a new cortical plate.
Implants installed into the sinuses of 40 patients using an osteotome technique with no graft or cushion materials were recently evaluated (Leblebicioglu _et al_. 2005). The authors reported a mean gain of alveolar bone height in scanned panoramic radiographs of 3.9 ± 1.9 mm.
## Success and implant survival
In a multi-center retrospective study (Rosen _et al_. 1999) evaluating the Summers technique applied to the placement of 174 implants in 101 patients, the survival rate was 96%, when residual bone height was 5 mm or more, but dropped down to 85.7% when residual bone height was 4 mm or less (Fig. 50-45).
Survival and success rates of 588 implants placed in 323 consecutive patients with a residual bone height ranging from 6–9 mm after a mean observation period of 5 years were 94.8% and 90.8%, respectively (Ferrigno _et al_. 2006). During the study period, only 13 perforations of the sinus membrane were detected, giving a perforation rate of only 2.2%. The authors also concluded that the installation of short implants in conjunction with osteotome sinus floor elevation is predictable and may reduce the indications for more invasive and complex procedures, such as the sinus floor elevation by the lateral approach.
Moreover, a systematic review (Emmerich _et al_. 2005) evaluated the effectiveness of sinus floor elevation using osteotomes. The inclusion criteria considered studies that had more than ten patients and at least 6 months of functional loading. Eight studies met these inclusion criteria. Within the limits of the small amount of long-term data, the reviewers concluded that the short-term success rates were similar to success rates of implants conventionally placed in partially edentulous patients (96.0% after 36 months). Long-term outcomes (>5 years) of implants placed with the osteotome technique are still scarse. The database was heterogenous regarding different surgical techniques, implant types, and grafting materials. Hence, no statistical analysis was performed on these parameters.
**Fig. 50-44** (a) Radiograph taken immediately after implant insertion with the osteotome technique and grafting material, showing a cloudy dome-shaped structure extending 2–3 mm apical to the implant. (b) Radiograph of the same implant taken 1 year later showing significant reduction of the size of the "dome", but the new bony structure is clearly visible apical to the implant (the dotted lines represent the outlines of the grafting material and the residual bone).
**Fig. 50-45** Radiograph of a 6 mm implant that was inserted utilizing the osteotome technique without grafting material. The residual bone height was only 3 mm. After 6 months of functional loading, the implant became loose and had to be removed. After a healing time of 2 months, the maxillary sinus floor was elevated with the lateral approach and two new implants were placed simultaneously (the dotted lines represent the outlines of the residual bone).
# Short implants
In the light of sinus floor elevation techniques being indicated to facilitate the installation of dental implants in the maxillary posterior region without adequate bone volume, treatment alternatives have to be discussed (see Chapter 31). Since patient-centered outcomes and morbidity associated with these procedures have not been addressed so far, it has to be anticipated that a great number of patients may not choose sinus floor elevation for their treatment. Hence, shortened dental arches (Käyser 1981) may have to be considered in treatment planning.
Another variation to conventional implant installation in the posterior maxilla is the choice of short implants to avoid penetration into the sinus cavity. Jemt and Lekholm (1995) reported that implant failure in edentulous maxilla correlated significantly with bone quality especially for short (7 mm) implants. Other studies (Friberg _et al_. 1991; Jaffin & Berman 1991) had also reported low survival rates of short implants. However, it must be kept in mind that all these studies reported on implants with machined surface geometries. Based on these studies and others, the clinical "dogma" has been followed, that generally only long implants should be inserted in type IV "poor-quality" bone in the posterior maxilla.
A targeted review (Hagi _et al_. 2004) of study outcomes with short (≤7 mm) implants placed in partially edentulous patients, concluded that machined-surface implants experienced greater failure rates than rough-textured implants. The implant surface geometry appeared to be a major determinant in the performance of these short implants.
In a multi-center study (ten Bruggenkate _et al_. 1998) evaluating 6-mm non-submerged roughsurface dental implants, only one of 208 short implants placed in the mandible was lost compared to six of 45 implants placed in the maxilla. Four of these implants were lost during the healing phase with three remaining in function. The survival rates were 99.5% and 86.7% respectively, after a follow-up time up to 7 years.
In contrast, recent clinical studies (Fugazotto _et al_. 2004; Renouard & Nisand 2005) on short implants with rough surfaces, designed for high initial stability, reported survival rates of about 95% which correlates with the survival rate reported for implants after 5 years in a systematic review (Berglundh _et al_. 2002). Two multi-center studies on rough-surface implants (Buser _et al_. 1997; Brocard _et al_. 2000) analyzed the survival and success rates of implants of different lengths. No significant difference was found between 8, 10, and 12 mm implants with roughsurface geometry after up to 8 years follow-up time.
The most recent review prepared for the Consensus Meeting of the European Association of Osseointegration (EAO) (Renouard & Nisand 2006) concluded on the basis of 12 studies on machined-surface implants meeting the inclusion criteria and 22 studies on rough-textured implants that the survival and success rates of short (<10 mm) implants was comparable to those obtained with longer implants, provided that surgical preparation was related to bone density, rough-textured implants were employed and operators' surgical skills were developed.
The use of short implants may be considered in sites thought unfavorable for implant placement, such as those associated with bone resorption or previous injury and trauma. While in these situations implant failure rates may be increased, outcomes should be compared with those associated with advanced surgical procedures such as bone grafting and sinus floor elevation.
# Conclusions and clinical suggestions
In the posterior maxilla, implants with morphometry designed to achieve high initial stability and with rough surface geometry giving high percentage of bone-to-implant contact during initial healing phase (Abrahamsson _et al_. 2004), are to be preferred. Implants with slightly conical morphometry or implants with wider implant neck tend to give better primary stability in cases of reduced residual bone height and soft bone geometry.
The clinical decision on which method (short implants, osteotome technique or lateral approach) should be chosen, depends on the residual bone height of the alveolar crest and surgeons' preferences. The following recommendations are suggested:
1. Residual bone height of 8 mm or more and flat sinus floor: standard implant placement (Fig. 50-46).
2. Residual bone height of 8 mm or more and oblique sinus floor: standard implant placement using short implant or elevation of the maxillary sinus floor using the osteotome technique without grafting material (Fig. 50-47).
3. Residual bone height of 5–7 mm and flat sinus floor: elevation of the maxillary sinus floor using the osteotome technique with grafting material that is resistant to resorption (Fig. 50-48).
4. Residual bone height of 5–7 mm and oblique sinus floor: elevation of the maxillary sinus floor using lateral approach with grafting material, and simultaneous implant placement (one-stage) (Fig. 50-49).
5. Residual bone height of 3–4 mm and flat or oblique sinus floor: elevation of the maxillary sinus floor using lateral approach with grafting material, and simultaneous implant placement (one-stage) (Fig. 50-50).
6. Residual bone height of 1–2 mm and flat or oblique sinus floor: elevation of the maxillary sinus floor using lateral approach with grafting material and delayed implant placement 4–8 months later (twostage) (Fig. 50-51).
**Fig. 50-46** Radiograph of a short (8 mm) implant in the posterior maxilla (the dotted lines represent the outlines of the residual bone).
**Fig. 50-47** Radiograph of an implant inserted in the posterior maxilla with an oblique sinus floor and a residual bone height of 8–10 mm. The osteotome technique without grafting material was used. The distal aspect of the apex of the implant extends into the sinus cavity, but the mesial aspect is covered with residual bone.
**Fig. 50-48** Radiograph of an implant inserted in the posterior maxilla with a flat sinus floor and a residual bone height of 5–6 mm. The osteotome technique with grafting material was used. The radiograph shows a dome-shaped formation covering the entire apex of the implant (the dotted lines represent the outlines of the residual bone).
**Fig. 50-49** Radiograph of an implant inserted in the posterior maxilla with a oblique sinus floor and a residual bone height between 2 and 8 mm. The maxillary sinus floor was elevated using the lateral approach, and one implant was inserted simultaneously (the dotted lines represent the outlines of the residual bone).
**Fig. 50-50** Radiograph of an implant inserted in the posterior maxilla with a flat sinus floor and a residual bone height between 2 and 3 mm. The maxillary sinus floor was elevated using the lateral approach, and one implant was inserted simultaneously (the dotted lines represent the outlines of the residual bone).
**Fig. 50-51** Radiograph showing a large pneumatized maxillary sinus, where a two-stage sinus floor elevation with a delayed implant insertion has to be used.
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# Part 16: Occlusal and Prosthetic Therapy
51 Tooth-Supported Fixed Partial Dentures
_Jan Lindhe and Sture Nyman_
52 Implants in Restorative Dentistry
_Niklaus P. Lang and Giovanni E. Salvi_
53 Implants in the Esthetic Zone
_Urs C. Belser, Jean-Pierre Bernard, and Daniel Buser_
54 Implants in the Posterior Dentition
_Urs C. Belser, Daniel Buser, and Jean-Pierre Bernard_
55 Implant–Implant and Tooth–Implant Supported Fixed Partial Dentures
_Clark M. Stanford and Lyndon F. Cooper_
56 Complications Related to Implant-Supported Restorations
_Y. Joon Ko, Clark M. Stanford, and Lyndon F. Cooper_
# Chapter 51
# Tooth-Supported Fixed Partial Dentures
Jan Lindhe and Sture Nyman
* * *
Clinical symptoms of trauma from occlusion
Angular bony defects
Increased tooth mobility
Progressive (increasing) tooth mobility
Tooth mobility crown excursion/root displacement
Initial and secondary tooth mobility
Clinical assessment of tooth mobility (physiologic and pathologic tooth mobility)
Treatment of increased tooth mobility
Situation I
Situation II
Situation III
Situation IV
Situation V
* * *
# Clinical symptoms of trauma from occlusion
## Angular bony defects
It has been claimed that _angular bony defects_ and _increased tooth mobility_ are important symptoms of trauma from occlusion (Glickman 1965, 1967). The validity of this suggestion has, however, been questioned (see Chapter 14). Thus, angular bony defects have been found at teeth affected by _trauma from occlusion_ as well as at teeth with normal occlusal function (Waerhaug 1979). _This means that the presence of angular bony defects cannot_ per se _be regarded as an exclusive symptom of trauma from occlusion_.
## Increased tooth mobility
_Increased tooth mobility_ , determined clinically, is expressed in terms of amplitude of displacement of the crown of the tooth. Increased tooth mobility can, indeed, be observed in conjunction with _trauma from occlusion_. It may, however, also be the result of a reduction of the height of the alveolar bone with or without an accompanying angular bony defect caused by plaque-associated periodontal disease (see Chapter 14). Increased tooth mobility resulting from occlusal interferences may further indicate that the periodontal structures have become adapted to an altered functional demand, i.e. a widened periodontal ligament with a normal tissue composition has become the end result of a previous phase of progressive tooth mobility (see Chapter 14) associated with trauma from occlusion.
## Progressive (increasing) tooth mobility
In Chapter 14, it was concluded that the diagnosis trauma from occlusion should be used solely in situations where a progressive mobility could be observed. Progressive tooth mobility can be identified only through a series of repeated tooth mobility measurements carried out over a period of several days or weeks.
# Tooth mobility crown excursion/root displacement
## Initial and secondary tooth mobility
A tooth which is surrounded by a normal periodontium may be moved (displaced) in horizontal and vertical directions and may also be forced to perform limited rotational movements. Clinically, tooth mobility is usually assessed by exposing the crown of the tooth to a certain force and determining the distance the crown can be displaced in buccal and/or lingual direction. The mobility (= movability) of a tooth in a horizontal direction is closely dependent on the height of the surrounding supporting bone, the width of the periodontal ligament, and the shape and number of roots present (Fig. 51-1).
The mechanism of tooth mobility was studied in detail by Mühlemann (1954, 1960) who described a standardized method for measuring even minor tooth displacements. By means of the "Periodontometer" a small force (∼45 kg (100 pounds)) is applied to the crown of a tooth (Fig. 51-2). The crown starts to tip in the direction of the force. The resistance of the tooth-supporting structures against displacement of the root is low in the initial phase of force application and the crown is moved only 5/100–10/100 mm. This movement of the tooth was called _"initial tooth mobility"_ (ITM) by Mühlemann (1954) and is the result of an _intra-alveolar_ displacement of the root (Fig. 51-3). In the pressure zone (see Chapter 14) there is a 10% reduction in the width of the periodontal ligament and in the tension zone there is a corresponding increase. Mühlemann and Zander (1954) stated that "there are good reasons to assume that the initial displacement of the root (ITM) corresponds to a reorientation of the periodontal membrane fibers into a position of functional readiness towards tensile strength". The magnitude of the ITM varies from individual to individual, from tooth to tooth, and is mainly dependent on the structure and organization of the periodontal ligament. The ITM value of ankylosed teeth is therefore zero.
**Fig. 51-1** The mobility of a tooth in horizontal direction is dependent on the height of the alveolar bone (H), the width of the periodontal ligament (encircled arrows), and the shape and number of roots.
**Fig. 51-2** Tooth mobility measurements by means of the Periodontometer. d = dial indicator; p = pointer; L = labial excursion of the crown; P = palatal excursion of the crown; T = L + P = total excursion of the crown.
**Fig. 51-3** Initial tooth mobility (ITM) means the excursion of the crown of a tooth when a force of 100 pounds is applied to the crown. Secondary tooth mobility (STM) means the excursion of the crown of the tooth when a force of 500 pounds is applied.
When a larger force (∼225 kg (500 pounds)) is applied to the crown, the fiber bundles on the tension side cannot offer sufficient resistance to further root displacement. The additional displacement of the crown that is observed in _"secondary tooth mobility"_ (STM) (Fig. 51-3) is allowed by distortion and compression of the periodontium in the pressure side. According to Mühlemann (1960) the magnitude of STM, i.e. the excursion of the crown of the tooth when a force of 500 pounds is applied, (1) varies between different types of teeth (e.g. incisors 10–12/100 mm, canines 5–9/100 mm, premolars 8– 10/100 mm and molars 4–8/100 mm), (2) is larger in children than in adults, and (3) is larger in females than males and increases during, for example, pregnancy. Furthermore, tooth mobility seems to vary during the course of the day; the lowest value is found in the evening and the largest in the morning.
A new method for determining tooth mobility was presented by Schulte and co-workers (Schulte 1987; Schulte _et al_. 1992) when the Periotest® (SiemensAG, Bensheim, Germany) system was introduced. The Periotest device measures the reaction of the periodontium to a defined percussion force which is applied to the tooth and delivered by a tapping instrument. A metal rod is accelerated to a speed of 0.2 m/s with the device and maintained at a constant velocity. Upon impact the tooth is deflected and the rod decelerated. The contact time between the tapping head and the tooth varies between 0.3 and 2 milliseconds and is shorter for stable than mobile teeth. The Periotest scale (the Periotest values) ranges from −8 to +50 and the following ranges should be considered:
* −8 to +9: clinically firm teeth
* 10–19: first distinguishable sign of movement
* 20–29: crown deviates within 1 mm of its normal position
* 30–50: mobility is readily observed.
The Periotest values correlate well with (1) tooth mobility assessed with a metric system, and (2) degree of periodontal disease and alveolar bone loss. The simple Periotest device is likely to be used in both the clinic and research settings in the future.
## Clinical assessment of tooth mobility (physiologic and pathologic tooth mobility)
If, in the traditional clinical measurement of tooth mobility, a comparatively large force is exerted on the crown of a tooth which is surrounded by a normal periodontium, the tooth will tip within its alveolus until a closer contact has been established between the root and the marginal (or apical) bone tissue. The magnitude of this tipping movement, which is normally assessed using the tip of the crown as a reference point, is referred to as the _"physiologic"_ tooth mobility. The term _"physiologic"_ implies that _"pathologic"_ tooth mobility may also occur.
What, then, is "pathologic" tooth mobility?
1. If a similar force is applied to a tooth which is surrounded by a periodontal ligament with an increased width, the excursion of the crown in horizontal direction will become increased; the clinical measurement consequently demonstrates that the tooth has an increased mobility. Should this increased mobility be regarded as _pathologic_?
2. An increased tooth mobility, i.e. an increased displacement of the crown of the tooth after force application, can also be found in situations where the height of the alveolar bone has been reduced but the remaining periodontal ligament has a normal width. At sites where this type of bone loss is extensive, the degree of tooth mobility (i.e. excursion of the crown) may be pronounced. Should this increased tooth mobility be regarded as "pathologic"?
Figure 51-4b illustrates a tooth which is surrounded by alveolar bone of reduced height. The width of the remaining periodontal ligament, however, is within normal limits. A horizontally directed force applied to the crown of the tooth in this case will result in a larger excursion of the crown than if a similar force is applied to a tooth with normal height of the alveolar bone and normal width of the periodontal ligament (Fig. 51-4a). There are reasons to suggest that the _so-called increased mobility_ measured in the case of Fig. 51-4b is, indeed, _physiologic_. The validity of this statement can easily be demonstrated if the displacement of the two teeth is assessed not from the crown but from a point on the root at the level of the bone crest. If a horizontal force is directed to the teeth as indicated in Fig. 51-4 the reference points (*) on the root surfaces will be displaced a similar distance in both instances. _Obviously, it is not the length of the excursive movement of the crown that is important from a biologic point of view, but the displacement of the root within its remaining periodontal ligament_.
In plaque-associated periodontal disease, bone loss is a prominent feature. Another so-called classical symptom of periodontitis is "increased tooth mobility". It is important to realize, however, that in many situations with even or "horizontal" bone loss patterns, the increased crown displacement (tooth mobility) assessed in clinical measurements should, according to the above discussion, also be regarded as physiologic; the movement of the root within the space of its remaining "normal" periodontal ligament is normal.
3. Increased crown displacement (tooth mobility) may also be detected in a clinical measurement where a "horizontal" force is applied to teeth with angular bony defects and/or increased width of the periodontal ligament. If this mobility does not increase gradually – from one observation interval to the next – the root is surrounded by a periodontal ligament of increased width but normal composition. This mobility should also be considered _physiologic_ since the movement is a function of the height of the alveolar bone and the width of the periodontal ligament.
4. Only _progressively increasing tooth mobility_ , which may occur in conjunction with trauma from occlusion, is characterized by active bone resorption (see Chapter 14) and which indicates the presence of inflammatory alterations within the periodontal ligament tissue, may be considered _pathologic_.
**Fig. 51-4** (a) The normal "physiologic" mobility of a tooth with normal height of the alveolar bone and normal width of the periodontal ligament. (b) The mobility of a tooth with reduced height of the alveolar bone. The distance of the horizontal displacement of the reference point (*) on the root is the same in the two situations (a,b).
# Treatment of increased tooth mobility
A number of situations will be described below which may call for treatment aimed at reducing an increased tooth mobility.
## Situation I
**Increased mobility of a tooth with increased width of the periodontal ligament but normal height of the alveolar bone**
If a tooth (for instance a maxillary premolar) is fitted with an improper filling or crown restoration, occlusal interferences develop and the surrounding periodontal tissues become the seat of inflammatory reactions, i.e. trauma from occlusion (Fig. 51-5). If the restoration is so designed that the crown of the tooth in occlusion is subjected to undue forces directed in a buccal direction, bone resorption phenomena develop in the buccal–marginal and lingual–apical pressure zones with a resulting increase of the width of the periodontal ligament in these zones. The tooth becomes hypermobile or moves away from the "traumatizing" position. Since such traumatizing forces in teeth with normal periodontium or overt gingivitis cannot result in pocket formation or loss of connective tissue attachment, the resulting increased mobility of the tooth should be regarded as a physiologic adaptation of the periodontal tissues to the altered functional demands. A proper correction of the anatomy of the occlusal surface of such a tooth, i.e. occlusal adjustment, will normalize the relationship between the antagonizing teeth in occlusion, thereby eliminating the excessive forces. As a result, apposition of bone will occur in the zones previously exposed to resorption, the width of the periodontal ligament will become normalized and the tooth stabilized, i.e. it reassumes its normal mobility (Fig. 51-5). In other words, resorption of alveolar bone which is caused by trauma from occlusion is a reversible process which can be treated by the elimination of occlusal interferences.
The capacity for bone regeneration after resorption following trauma from occlusion has been documented in a number of animal experiments (Waerhaug & Randers-Hansen 1966; Polson _et al_. 1976a; Karring _et al_. 1982; Nyman _et al_. 1982). In such experiments, the induced bone resorption not only involved the bone within the alveolus but also the alveolar bone crest. When the traumatizing forces were removed, bone tissue was deposited not only in the walls of the alveolus, thereby normalizing the width of the periodontal ligament, but also on the bone crest area, whereby the height of the alveolar bone was normalized (Fig. 51-6) (Polson _et al_. 1976a). In the presence of an untreated, plaque-associated lesion in the soft tissue, however, substantial bone regrowth did not always occur (Fig. 51-7) (Polson _et al_. 1976b).
**Fig. 51-5** (a) Contact relationship between a mandibular and a maxillary premolar in occlusion. The maxillary premolar is fitted with an artificial restoration with an improperly designed occlusal surface. Occlusion results in horizontally directed forces (arrows) which may produce an undue stress concentration within the "brown" areas of the periodontium of the maxillary tooth. Resorption of the alveolar bone occurs in these areas. A widening of the periodontal ligament can be detected as well as increased mobility of the tooth. (b) Following adjustment of the occlusion, the horizontal forces are reduced. This results in bone apposition ("red areas") and a normalization of the tooth mobility.
**Fig. 51-6** Photomicrographs illustrating the interdental area between two mandibular premolars in the monkey. In (a) the two premolars are exposed to jiggling forces. Note the reduction of alveolar bone in the area and the location of the bone crest. Ten weeks after the elimination of the jiggling forces (b) a considerable regeneration of bone has occurred. Note the increase of the height of the interdental bone and the normalization of the width of the periodontal ligaments. The apical end of the junctional epithelium is located at the cemento-enamel junction. (Courtesy of Dr. A.M. Polson; from Polson _et al_. (1976a).)
## Situation II
**Increased mobility of a tooth with increased width of the periodontal ligament and reduced height of the alveolar bone**
When a dentition has been properly treated for moderate to advanced periodontal disease, gingival health is established in areas of the dentition where teeth are surrounded by periodontal structures of reduced height. If a tooth with a reduced periodontal tissue support is exposed to excessive horizontal forces (trauma from occlusion), inflammatory reactions develop in the pressure zones of the periodontal ligament with accompanying bone resorption. These alterations are similar to those which occur around a tooth with supporting structures of a normal height; the alveolar bone is resorbed, the width of the periodontal ligament is increased in the pressure/tension zones and the tooth becomes hypermobile (Fig. 51-8a). If the excessive forces are reduced or eliminated by occlusal adjustment, bone apposition to the "pretrauma" level will occur, the periodontal ligament will regain its normal width and the tooth will become stabilized (Fig. 51-8b).
### Conclusion: situations I and II
Occlusal adjustment is an effective therapy against increased tooth mobility when such mobility is caused by an _increased width_ of the periodontal ligament.
## Situation III
**Increased mobility of a tooth with reduced height of the alveolar bone and normal width of the periodontal ligament**
The increased tooth mobility which is the result of a reduction in height of the alveolar bone without a concomitant increase in width of the periodontal membrane cannot be reduced or eliminated by occlusal adjustment. In teeth with normal width of the periodontal ligament, no further bone apposition on the walls of the alveoli can occur. If such an increased tooth mobility does not interfere with the patient's chewing function or comfort, no treatment is required. If the patient experiences the tooth mobility as disturbing, however, the mobility can only be reduced in this situation by splinting, i.e. by joining the mobile tooth/teeth together with other teeth in the jaw into a fixed unit – a splint.
**Fig. 51-7** In the presence of an existing marginal inflammation, alveolar bone, lost by jiggling trauma (a), will not always regenerate following elimination of the traumatic forces (b). ICT =infiltrated connective tissue; CEJ =cemento-enamel junction; JE = apical end of junctional epithelium; BC =alveolar bone crest; BBD = bottom of angular bony defect. From Polson _et al_. (1976b).
**Fig. 51-8** If a tooth with reduced periodontal tissue support (a) has been exposed to excessive horizontal forces, a widened periodontal ligament space ("brown" areas) and increased mobility (arrow) result. (b) Following reduction or elimination of such forces, bone apposition will occur and the tooth will become stabilized.
A splint, according to the Glossary of Periodontic Terms (1986) is "an appliance designed to stabilize mobile teeth". A splint can be fabricated in the form of joined composite fillings, fixed bridges, removable partial prostheses, etc.
## Example: Case A, 64-year-old male
The periodontal condition of this patient is illustrated by the probing depth, furcation involvement and tooth mobility data as well as the radiographs from the initial examination in Fig. 51-9. Periodontal disease has progressed to a level where, around the maxillary teeth, only the apical third or less of the roots is invested in supporting alveolar bone. The following discussion is related to the treatment of the maxillary dentition.
In the treatment planning of this case it was decided that the first premolars (teeth 14 and 24) had to be extracted due to advanced periodontal disease and furcation involvement of degree III. For the same reasons, teeth 17 and 27 were scheduled for extraction. Teeth 16 and 26 were also found to have advanced loss of periodontal tissue support in combination with deep furcation involvements. The most likely _definitive_ treatment should include periodontal and adjunctive therapy in the following parts of the dentition: 15 and 25, and 13, 12, 11, 21, 22, 23. For functional and esthetic reasons, 14 and 24 obviously had to be replaced. The question now arose as to whether these two premolars should be replaced by two separate unilateral bridges, using 13, 15 and 23, 25 as abutment teeth, or if the increased mobility of these teeth and also of the anterior teeth (12, 11, 21, 22) (Fig. 51-9) called for a bridge of cross-arch design, with the extension 15–25, to obtain a splinting effect. If 14 and 24 are replaced by two unilateral bridges, each one of these three-unit bridges will exhibit the same degree of mobility in a bucco-lingual direction as the individual abutment teeth (degree 2) (Fig. 51-9), since a unilateral straight bridge will not have a stabilizing effect on the abutment teeth in this force direction.
**Fig. 51-9** Case A, 64-year-old male. Periodontal status (a) and radiographs (b) prior to therapy.
From the radiographs it can be seen that the increased mobility observed in the maxillary teeth of this patient is associated mainly with reduced height of the alveolar bone and not with increased width of the periodontal ligaments. This means that the mobility of the individual teeth should be regarded as normal or "physiologic" for teeth with such a reduced height of the supporting tissues. This in turn implies that the increased tooth mobility in the present case does not call for treatment unless it interferes with the chewing comfort or jeopardizes the position of the front teeth. This particular patient had not recognized any functional problems related to the increased mobility of his maxillary teeth. Consequently, there was no reason to install a cross-arch bridge in order to splint the teeth, i.e. to reduce tooth mobility.
Following proper treatment of the plaque-associated periodontal lesions, two separate provisional bridges of unilateral design were produced (15, 14, 13; 23, 24, 25, 26 palatal root). The provisional acrylic bridges were used for 6 months during which the occlusion, the mobility of the two bridges and the position of the front teeth were all carefully monitored. When, after 6 months, no change of position of the lateral and central incisors had occurred and no increase of the mobility of the two provisional bridges had been noted, the definitive restorative therapy was performed.
Figure 51-10 presents radiographs obtained 10 years after initial therapy. The position of the front teeth and the mobility of the incisors and the two bridges have not changed during the course of the maintenance period. There has been no further loss of periodontal tissue support during the 10 years of observation, no further spread of the front teeth and no widening of the periodontal ligaments around the individual teeth, including the abutment teeth for the bridgework.
### Conclusion: situation III
Increased tooth mobility (or bridge mobility) as a result of reduced height of the alveolar bone can be accepted and splinting avoided, provided the occlusion is stable (no further migration or further increasing mobility of individual teeth), and provided the degree of existing mobility does not disturb the patient's chewing ability or comfort. Consequently, splinting is indicated when the mobility of a tooth or a group of teeth is so increased that chewing ability and/or comfort are disturbed.
## Situation IV
**Progressive (increasing) mobility of a tooth (teeth) as a result of gradually increasing width of the reduced periodontal ligament**
Often in cases of advanced periodontal disease the tissue destruction may have reached a level where extraction of one or several teeth cannot be avoided. In such a dentition, teeth which are still available for periodontal treatment may, after therapy, exhibit such a high degree of mobility, or even signs of progressively increasing mobility, that there is an obvious risk that the forces elicited during function may mechanically disrupt the remaining periodontal ligament components and cause extraction of the teeth.
It will only be possible to maintain such teeth by means of a splint. In such cases a fixed splint has two objectives: (1) to stabilize hypermobile teeth and (2) to replace missing teeth.
### Example: Case B, 26-year-old male
Figure 51-11 presents radiographs taken prior to therapy and Fig. 51-12 those obtained after periodontal treatment and preparation of the remaining teeth as abutments for two fixed splints. All teeth except 13, 12, and 33 have lost around 75% or more of the alveolar bone and widened periodontal ligaments are a frequent finding. The four distal abutments for the two splints are root-separated molars, the maintained roots being the following: the palatal root of 17, the mesio-buccal root of 26, and the mesial roots of 36 and 47. It should be observed that tooth 24 is root-separated and the palatal root maintained with only minute amounts of periodontium left. Immediately prior to insertion of the two splints, all teeth except 13, 12, and 33 displayed a mobility varying between degrees 1 and 3. From the radiographs in Fig. 51-12 it can be noted that there is an obvious risk of extraction of a number of teeth such as 24, 26, 47, 45, 44, 43, and 36 if the patient is allowed to bite with a normal chewing force without the splints in position.
**Fig. 51-10** Case A. Radiographs obtained 10 years after periodontal therapy and installation of two unilateral bridges in the maxilla.
**Fig. 51-11** Case B, 26-year-old male. Radiographs illustrating the periodontal conditions prior to therapy.
**Fig. 51-12** Case B. Radiographs obtained after periodontal treatment and preparation of the abutment teeth for two fixed splints.
Despite the high degree of mobility of the individual teeth, the splints were entirely stable after insertion, and have maintained their stability during a maintenance period of more than 12 years. Figure 51-13 describes the clinical status and Fig. 51-14 presents the radiographs obtained 10 years after therapy. From these radiographs it can be observed (compare with Fig. 51-12) that during the maintenance period there has been no further loss of alveolar bone or widening of the various periodontal ligament spaces.
### Conclusion: situation IV
Splinting is indicated when the periodontal support is so reduced that the mobility of the teeth is progressively increasing, i.e. when a tooth or a group of teeth are exposed to extraction forces during function.
**Fig. 51-13** Case B. Clinical status 9 years after therapy.
**Fig. 51-14** Case B. Radiographs obtained 10 years after therapy.
## Situation V
**Increased bridge mobility despite splinting**
In patients with advanced periodontal disease it can often be observed that the destruction of the periodontium has progressed to varying levels around different teeth and tooth surfaces in the dentition. Proper treatment of the plaque-associated lesions often includes multiple extractions. The remaining teeth may display an extreme reduction of the supporting tissues concomitant with increased or progressive tooth mobility. They may also be distributed in the jaw in such a way as to make it difficult, or impossible, to obtain a proper splinting effect even by means of a cross-arch bridge. The entire bridge/ splint may exhibit mobility in frontal and/or lateral directions.
It was stated above (situation III) that a certain mobility of a tooth or a bridge of unilateral design can be accepted provided this mobility does not interfere with the patient's chewing ability or comfort. This is also valid for a cross-arch bridge/splint. From a biologic point of view there is no difference between increased tooth mobility on the one hand and increased bridge mobility on the other. However, neither progressive tooth mobility nor progressive bridge mobility are acceptable. In cases of extremely advanced periodontal disease, a cross-arch splint with an increased mobility may be regarded as an acceptable result of rehabilitation. The maintenance of status quo of the bridge/splint mobility and the prevention of tipping or orthodontic displacement of the total splint, however, requires particular attention regarding the design of the occlusion. Below, a case is reported which may serve as an interesting illustration of this particular clinical problem.
### Example: Case C, 52-year-old female
Figure 51-15 shows radiographs obtained at the initial examination. A 12-unit maxillary bridge was installed 10–15 years prior to the present examination using 18, 15, 14, 13, 12, 11, 21, 22, 23, and 24 as abutments. After a detailed clinical examination it was obvious that 15, 14, 22, and 24 could not be maintained because of severe symptoms of caries and periodontal disease. The remaining teeth were subjected to periodontal therapy and maintained as abutments for a new bridge/splint in the maxilla extending from tooth 18 to the region of 26, i.e. a cross-arch splint was installed which carried three cantilever units, namely 24, 25, and 26. The mobility of the individual abutment teeth immediately prior to insertion of the splint was the following: degree 1 (tooth 18), degree 0 (tooth 13), degree 2 (teeth 12 and 11), degree 3 (tooth 21), and degree 2 (tooth 23).
Radiographs obtained 5 years after therapy are shown in Fig. 51-16. The bridge/splint had a mobility of degree 1 immediately after its insertion and this mobility was unchanged 5 years later. The radiographs demonstrate that no further widening of the periodontal ligament occurred around the individual teeth during the maintenance period.
When a cross-arch bridge/splint exhibits increased mobility, the center (fulcrum) of the movement must be identified. In order to prevent further increase in the mobility and/or to prevent displacement of the bridge, it is essential to design the occlusion in such a way that when the bridge/splint is in contact with the teeth of the opposing jaw, it is subjected to a balanced load, i.e. equal force on each side of the fulcrum. If this can be achieved, the force to which the bridge is exposed in occlusion can be used to retain the fixed prosthesis in proper balance (a further increase of mobility being thereby prevented).
Balanced loading of a mobile bridge/splint has to be established not only in the intercuspal position (IP) and centric occlusion (CP) but also in frontal and lateral excursive movements of the mandible if the bridge shows mobility or a tendency for tipping in the direction of such movements. In other words, a force which tends to displace the bridge in a certain direction has to be counteracted by the introduction of a balancing force on the opposite side of the fulcrum of the movement. If, for instance, a cross-arch splint in the maxilla exhibits mobility in frontal direction in conjunction with protrusive movements of the mandible, the load applied to the bridge in the frontal region has to be counterbalanced by a load in the distal portions of the splint; this means that there must be a simultaneous and equal contact relationship between the occluding teeth in both the frontal and the posterior regions of the splint. If the splint is mobile in a lateral direction, the force acting on the working side of the jaw must be counteracted by a force established by the introduction of balancing contacts in the non-working side of the jaw. The principle for establishing stability of a _mobile_ cross-arch splint is consequently the same as that used to obtain stability in a complete denture. In situations where distal abutment teeth are missing in a cross-arch bridge/splint with increased mobility, balance and functional stability may be obtained by means of cantilever units. It is important in this context to point out that balancing contacts on the non-working side should not be introduced in a bridge/splint in which no increased mobility can be observed.
**Fig. 51-15** Case C, 52-year-old female. Radiographs obtained at the initial examination.
**Fig. 51-16** Case C. Radiographs obtained 5 years after therapy.
The maxillary splint in the patient described in Figs. 51-15 and 51-16 exhibited increased mobility in a frontal direction. Considering the small amount of periodontal support left around the anterior teeth, it is obvious that there would have been a risk of frontal displacement of the total bridge had the bridge terminated at the last abutment tooth (23) on the left side of the jaw. The installation of cantilever units in the 24 and 25 region prevented such a displacement of the bridge/splint by the introduction of a force counteracting frontally directed forces during protrusive movements of the mandible (Fig. 51-17). In addition, the cantilever units provide bilateral contact relationship towards the mandibular teeth in the intercuspal position, i.e. bilateral stability of the bridge.
In cases similar to the one described above, cantilever units can thus be used to prevent increasing mobility or displacement of a bridge/splint. It should, however, be pointed out that the insertion of cantilever units increases the risk of failures of a technical and biophysical character (fracture of the metal frame, fracture of abutment teeth, loss of retention, etc.).
In cases of severely advanced periodontal disease it is often impossible to anticipate in the planning phase whether a bridge/splint will show signs of instability and increasing (progressive) mobility after insertion. In such cases, a provisional splint should always be inserted. Any alterations of the mobility of the bridge/splint can be observed over a prolonged period of time and the occlusion continuously adjusted until, after 4–6 months, it is known whether stability (i.e. no further increase of the mobility) can be achieved. The design of the occlusion of the provisional acrylic bridge is then reproduced in the permanent bridge construction. If, on the other hand, stability cannot be obtained, the rehabilitation of the case cannot be achieved with a fixed splint. The alternative treatment then is a complete denture or an implant-supported restoration.
**Fig. 51-17** Case C. The cantilever section including teeth 24, 25, and 26.
### Conclusion: situation V
An increased mobility of a cross-arch bridge/splint can be accepted provided the mobility does not disturb chewing ability or comfort and the mobility of the splint is not progressively increasing.
References
Glickman, I. (1965). Clinical significance of trauma from occlusion. _Journal of the American Dental Association_ 70, 607–618.
Glickman, I. (1967). Occlusion and periodontium. _Journal of Dental Research_ 46 (Suppl), 53.
Glossary of Periodontic Terms (1986). _Journal of Periodontology_. Supplement.
Karring, T., Nyman, S., Thilander, B. & Magnusson, I. (1982). Bone-regeneration in orthodontically produced alveolar bone dehiscences. _Journal of Periodontal Research_ 17, 309– 315.
Mühlemann, H.R. (1954). Tooth mobility. The measuring method. Initial and secondary tooth mobility. _Journal of Periodontology_ 25, 22–29.
Mühlemann, H.R. (1960). Ten years of tooth mobility measurements. _Journal of Periodontology_ 31, 110–122.
Mühlemann, H.R. & Zander, H.A. (1954). Tooth mobility, III. The mechanism of tooth mobility. _Journal of Periodontology_ 25, 128.
Nyman, S., Karring, T. & Bergenholtz, G. (1982). Bone regeneration in alveolar bone dehiscences produced by jiggling forces. _Journal of Periodontal Research_ 17, 316–322.
Polson, A.M., Meitner, S.W. & Zander, H.A. (1976a). Trauma and progression of marginal periodontitis in squirrel monkeys. III. Adaptation of interproximal alveolar bone to repetitive injury. _Journal of Periodontal Research_ 11, 279–289.
Polson, A.M., Meitner, S.W. & Zander, H.A. (1976b). Trauma and progression of marginal periodontitis in squirrel monkeys. IV. Reversibility of bone loss due to trauma alone and trauma superimposed upon periodontitis. _Journal of Periodontal Research_ 11, 290–298.
Schulte, W. (1987). Der Periotest-Parodontalstatus. _Zahnärtzliche Mitteilung_ 76, 1409–1414.
Schulte, W., Hoedt, B., Lukas, D., Maunz, M. & Steppeler, M. (1992). Periotest for measuring periodontal characteristics – correlation with periodontal bone loss. _Journal of Periodontal Research_ 27, 184–190.
Waerhaug, J. (1979). The infrabony pocket and its relationship to trauma from occlusion and subgingival plaque. _Journal of Periodontology_ 50, 355–365.
Waerhaug, J. & Randers-Hansen, E. (1966). Periodontal changes incident to prolonged occlusal overload in monkeys. _Acta Odontologica Scandinavica_ 24, 91–105.
# Chapter 52
# Implants in Restorative Dentistry
Niklaus P. Lang and Giovanni E. Salvi
* * *
Introduction
Treatment concepts
Limited treatment goals
Shortened dental arch concept
Indications for implants
Increase the subjective chewing comfort
Preservation of natural tooth substance and existing functional, satisfactory reconstructions
Replacement of strategically important missing teeth
* * *
# Introduction
Ever since oral titanium implants were shown to yield high predicability (97–98%) for incorporation (Berglundh _et al_. 2002; Pjetursson _et al_. 2007) and satisfactory longevity (survival rates of approximately 89% after 10 years of service) (Pjetursson _et al_. 2007), the choice of oral implants as abutments for reconstructing the dentition has revolutionized restorative dentistry. Without adequate evidence, some clinicians trust an implant abutment even more than a natural tooth, and there is an erroneous belief that oral implants now solve most prosthetic problems with a lot more ease and less risk than traditional reconstructive dentistry did.
Even though there is an increasing body of evidence documenting that implant-supported reconstructions have a three-times higher incidence of technical complications than tooth-supported reconstructions (Lang _et al_. 2004; Pjetursson _et al_. 2004a,b; Tan _et al_. 2004) and that the incidence of biologic complications remains approximately the same for the two alternatives, the trend in dentistry, unfortunately, is to prefer the implant over the tooth abutment.
It has to be clearly stated that the decision to maintain and treat or to extract a compromised tooth has to precede the decision regarding the need for and the modalities of tooth replacement. In this sense, " _implants are here to replace missing teeth, they are not supposed to replace teeth_ ".
If properly evaluated, the indication for oral implants as abutments in restorative dentistry is complementary to traditional approaches and helps to facilitate treatment planning in many instances.
# Treatment concepts
When reconstructing a mutilated dentition, it has to be realized that teeth were usually lost due to the two most frequently encountered oral diseases, caries and periodontitis. Only a small proportion of teeth are lost due to trauma or are not present due to agenesis. Hence, the vast majority of patients in need of reconstructions present with an oral biofilm infection of variable severity and extent. It is evident that such patients need to be treated with a cause-related approach, i.e. systematic periodontal therapy has to precede any type of reconstructive therapy. It is of utmost importance that oral biofilm infections be under control prior to the placement of oral implants, since residual periodontal pockets or untreated ecologic niches within the oral cavity may serve as a source of infection and jeopardize the health of the peri-implant region (Mombelli _et al_. 1995). Hence, implant installation and prosthetic reconstruction is generally not a treatment in itself, but belongs to a systematic approach of comprehensively establishing esthetic and functional demands under healthy conditions (see Chapter 31).
It is obvious that chewing function is affected both by tooth loss and the type of prosthetic reconstruction chosen to replace missing teeth. A quantitative comparison by measuring bite force and chewing efficiency with identical methods in subjects with overdentures, complete full dentures, and natural dentitions was performed (Fontijn-Tekamp _et al_. 2000). In the latter group, chewing efficiency was significantly greater than that of patients with full dentures irrespective of the nature of their mandibular ridge. By installing implants, bite force and chewing efficiency could be significantly improved, although it did not reach that of the dentate patients. Shortened dental arch patients exerted bite forces similar to those of patients with a complete natural dentition, but their chewing efficiency was slightly limited due to the reduced occlusal area. This, in turn, meant that patients with a shortened dental arch would have to perform approximately twice as many chewing strokes to reach the same efficiency as the fully dentate patient (Fig. 52-1).
**Fig. 52-1** Masticatory chewing efficiency. Number of chewing strokes needed to reach respective particle sizes of the same test food. From Fontijn-Tekamp _et al_. (2000).
## Limited treatment goals
Generally, efforts are made to completely reconstruct a partially edentulous dentition. The question arises whether or not missing teeth have to be replaced at all and to the full extent. Usually, single teeth are replaced because of predominantly esthetic demands, while multiple missing teeth may also affect functionality and chewing capacity and, hence, are replaced to improve these aspects. However, it is evident from a number of cross-sectional and longitudinal studies (Käyser 1981; Battistuzzi _et al_. 1987; Witter _et al_. 1988, 1990a,b, 1991, 1994) that not all teeth lost are to be replaced. The loss of one or more molars has been thoroughly studied by the Nijmegen group of clinical researchers. No clinically significant differences were found in these studies between subjects with a complete dentition and those with reduced dental arches regarding masticatory capacity, signs and symptoms of temporomandibular disorders, migration of remaining teeth, periodontal support, and oral comfort.
## Shortened dental arch concept
Studies on shortened dental arches (SDA) have shown that dentitions comprising anterior and premolar teeth generally fulfil the requirements of a functional dentition, including patient-assessed oral comfort and chewing ability. A review of the literature on SDA concluded that the concept deserves serious consideration in treatment planning for partially edentulous patients. However, with ongoing changes, e.g. in dental health and economy, the concept requires continuing research, evaluation, and discussion (Kanno & Carlsson 2006).
**Fig. 52-2** Increasing subjective chewing comfort for completely edentulous patients. Two implants in the canine region united with a bar device (or solely with a retention element without the bar) can dramatically improve masticatory ability and efficacy.
Special attention has to be given to the patient's own needs and desires for increased chewing capacity when considering the SDA as a limited treatment goal. Clinical observation, as well as research findings, indicate that elderly patients can function at an acceptable level with a reduced dentition consisting of ten or even fewer occluding pairs of teeth (Käyser 1990). The WHO goal for the year 2020, namely to maintain a natural dentition of no less than 20 teeth throughout life, is also substantiated by a recent literature review as this proposed dentition will assure oral function (Gotfredsen & Walls 2007).
The choice of implants as abutments to fulfil individual needs may, therefore, become a welcome treatment option within the concept of a shortened dental arch.
# Indications for implants
Three major indications can be defined for the use of oral implants:
* To increase subjective chewing comfort
* To preserve natural tooth substance and adequate, existing reconstructions
* To replace strategically important missing teeth.
**Fig. 52-3** Increasing subjective chewing comfort by replacing missing teeth in a free-end edentulous situation. (a) Installation of two standard size (4.1 mm diameter) Straumann® implants (10 mm), 5 and 11 mm distal to the distal aspect of tooth 45. (b) Chewing units are replaced as a premolar on implant in position 46 and a molar in position 46/47. (c) Radiographic view 5 years after the reconstruction.
**Fig. 52-4** Increasing subjective chewing comfort by replacing missing molars in a mandibular free-end situation. (a) Installation of two standard (4.1 mm diameter) Straumann® implants (8 mm), 6 and 14 mm distal to the distal aspect of tooth 35. (b) Radiographic view at the time of implant installation. (c) Two molar crowns on implants in position 36 and 37, 8 years after installation. (d) Radiographic view, 8 years after loading of the implants.
# Increase the subjective chewing comfort
Studies have demonstrated that the installation of a small number of mandibular implants (two to four) may dramatically improve chewing function, especially if the edentulous mandibular ridge showed severe resorption (Fontijn-Tekamp _et al_. 2000, 2004a,b). Hence, it is evident that the completely edentulous patient will benefit from as few as two oral implants installed in the mandibular canine region (Fig. 52-2).
Likewise, subjective chewing comfort may be improved by supplementing single premolar chewing units in the posterior region in order to fulfill individual demands for more chewing capacity under a shortened dental arch concept (Fig. 52-3). It is imperative that the implants be placed in the prosthetically correct location leaving enough space for an interdental (inter-implant) space and observing the dimensions of a premolar width (7 mm).
Instead of adding chewing comfort in premolar units, implant systems with wider necks or platforms may be installed in order to truly mimic the replacement of the missing molars. In these instances, an inter-implant distance of 8 mm has to be observed in order to create enough space for the molars and the inter-implant space (Fig. 52-4).
**Fig. 52-5** Increasing subjective chewing comfort by closing a mandibular gap. (a) Installation of two standard (4.1 mm diameter) Straumann® implants (10 mm), 5 mm distal to the distal aspect of tooth 34 and 12 mm distal to tooth 34 (=6 mm mesial to tooth 37). Total extension of the gap: 18 mm. (b) Reconstruction of the implants in premolar units to fit the size of the gap. (c) Radiographic documentation, 6 years after loading. The filling on tooth 37 was satisfactory and did not need replacement.
**Fig. 52-6** Increasing subjective chewing comfort by filling a large mandibular gap. (a) Edentulous ridge between teeth 34 and 38 is 28 mm. (b) Installation of a standard (4.1 mm diameter) Straumann® implant, 5 mm distal to the distal aspect of tooth 34 and a wide-body (4.8 mm diameter), wide-neck Straumann® implant, 20 mm distal to the distal aspect of tooth 34 and 8 mm mesial to the mesial aspect of tooth 38. (c) Three-unit implant-supported fixed prosthesis filling the gap.
**Fig. 52-7** Preservation of natural tooth substance. (a) Deciduous molar 75 has to be replaced owing to the advanced root resorption. (b) Following extraction of tooth 75, the site would be ideal for replacing the missing tooth with a three-unit bridge or a single implant. (c) The single implant is chosen to avoid jeopardizing the integrity and vitality of the two adjacent teeth, 34 and 36. Cutting preparations for full coverage of crowns will result in 10% of the prepared teeth loosing vitality after 10 years. (d) Single tooth replacement of 75, 5 years after reconstruction. (e) Occlusal view of the single implant-supported crown to replace a deciduous molar, 5 years after reconstruction. The adjacent teeth remain unsevered.
**Fig. 52-8** Preservation of intact tooth substance. Single tooth replacement of a missing central incisor 21. (a) The teeth 11 and 22 adjacent to the edentulous space 21 are intact teeth with no fillings and with periodontally healthy conditions. Both mesial and distal papillae are intact and reach coronally to the contact area in this juvenile patient. (b) Following the installation of a Standard Plus (4.1 mm diameter) Straumann® implant with a length of 12 mm, the mucosal tissue is conditioned to achieve a perfect emergence profile. (c) Radiographic documentation 2 years after the prosthetic reconstruction of the implant. (d) Tissue conditioning due to a more apical insertion of the implant for esthetic sites. (e) Implant-supported single tooth replacement 21, 2 years after reconstruction.
Considering the dimensions of premolars (7 mm) and molars (8 mm) and adequate space for the interdental/inter-implant space (4–5 mm), edentulous ridges between existing teeth may be reconstructed and chewing comfort increased without involving adjacent teeth (Fig. 52-5). Obviously, risks can be minimized by reducing the length of bridge spans.
In combinations of molar and premolar reconstructions (Fig. 52-6), the surgical positioning of the implants has to be calculated in detail and restoration-driven stents may have to be used in order to create adequate conditions for prosthetic reconstruction.
# Preservation of natural tooth substance and existing functional, satisfactory reconstructions
Oral implants are ideal abutments if natural tooth substance can be preserved. The preparation of a tooth to serve as an abutment for a crown or a bridge anchor opens about 40 000 to 70 000 dentinal tubules per mm2. This, in turn, means that the integrity of a vital tooth is severely compromized. Even though a small proportion of abutment teeth will lose their vitality immediately as a sequelae of the preparation procedure, it has been documented that approximately 10% of all vital abutments will have lost vitality after 10 years (Bergenholtz & Nyman 1984; Pjetursson _et al_. 2004b; Tan _et al_. 2004). Hence, it is obvious that an implant installation avoiding tooth preparation represents the most biologically sound way of replacing a missing tooth (Fig. 52-7).
**Fig. 52-9** Mandibular edentulous area after the extraction of teeth 35, 36 and 37. (a) Orthopantomogram revealing the neighboring anatomic structures (inferior mandibular nerve) and intact reconstructions on the teeth adjacent to the edentulous ridge. (b) Installation of two standard (4.1 mm diameter) and one wide-body (4.8 mm diameter) Straumann® implants at a distance of 5 mm, 11 mm and 20 mm distal to the distal aspect of tooth 34. (c) Transmucosal implant installation for two premolar and one molar unit. Implants covered with healing caps. The intact crown on tooth 38 is visible. (d) Radiographic documentation after 5 years. Implant crowns are splinted because of the short (6 mm) implants (in the neighborhood of the inferior mandibular nerve).
**Fig. 52-10** Replacing strategically important teeth. (a) A fixed dental prosthesis is seated on two abutment teeth, 17 and 15. Tooth 15 was root canal treated and suffered from a root fracture jeopardizing the integrity of the entire reconstruction. (b) The bridge is separated between 17 and pontic 16. (c) A new fixed dental prosthesis was seated on the implant 15 and soldered to the existing, still satisfactory crown 17. In this manner, the implant helped to avoid a costly and extensive reconstruction.
In areas of esthetic priority, the replacement of a missing tooth with a single implant may, beyond any doubt, provide the best and most esthetic treatment option (Fig. 52-8). This is especially true in a periodontally healthy dentition and in situations where the papillae towards the adjacent teeth are still present. By placing the implant in a slightly (1–2 mm) submucosal location, an optimal emergence profile can be achieved.
Instead of preserving natural tooth substance, the clinician may choose to save existing, still satisfactory reconstructions, thereby simplifying the restoration of a mutilated dentition (Fig. 52-9). Occasionally, the reconstruction may have a smaller extent and, hence, have a reduced chance of encountering technical complications during the years of service.
# Replacement of strategically important missing teeth
The loss of a strategically important tooth often creates a whole chain reaction of therapeutic measures to be taken. Treatment planning may become highly involved and extensive reconstructions may result from the loss of such a tooth. Especially in dentitions that have received multiple reconstructions, the loss of one strategic abutment may lead to time-consuming and costly therapy (Fig. 52-10). Oral implants provide valuable and indispensable treatment alternatives to redoing existing reconstructions. By the installation of oral implants in strategically correct locations, partial reconstruction of a dentition may be possible. Obviously, such implants have to be installed at locations that are restoration driven, at the proper location for prosthetic reconstruction. In cases with bone dehiscence or lack of adequate bone volume, bone augmentation procedures may have to be performed (Fig. 52-11).
**Fig. 52-11** Replacing strategically important abutments. (a) Only the two periodontally healthy maxillary canines 13 and 23 remain. To reconstruct this maxilla with a fixed dental prosthesis requires the installation of oral implants in strategically correct locations. An implant-supported maxillary front reconstruction and two mixed tooth–implant-supported reconstructions in the posterior segments are planned. (b) Eight years following implant installation. The maxillary front reconstruction is cemented on solid abutments that have been installed in the positions of 12 and 22, i.e. 5 mm mesial to the mesial aspects of the canines. The posterior segment reconstructions are cemented on the canines and screw-retained on two implants in the positions of 15 and 25, i.e. the implants are placed 11 mm distal to the distal aspects of the canines allowing the placement of three-unit reconstructions with minimal risks. A shortened dental arch as a limited treatment goal provides satisfactory chewing function.
### Conclusions
Oral implants are best used as abutments in restorative dentistry if subjective chewing comfort has to be increased, natural tooth substance or existing satisfactory reconstructions have to be preserved or strategically important missing teeth have to be replaced.
Hence, oral implants have become valuable, indispensable, and welcome treatment alternatives to traditional dental reconstructions. Obviously, oral implants should only be incorporated in oral cavities with healthy conditions, i.e. a thorough periodontal treatment has to precede restorative therapy.
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# Chapter 53
# Implants in the Esthetic Zone
Urs C. Belser, Jean-Pierre Bernard, and Daniel Buser
* * *
Basic concepts
General esthetic principles and related guidelines
Esthetic considerations related to maxillary anterior implant restorations
Anterior single-tooth replacement
Sites without significant tissue deficiencies
Sites with localized horizontal deficiencies
Sites with extended horizontal deficiencies
Sites with major vertical tissue loss
Multiple-unit anterior fixed implant restorations
Sites without significant tissue deficiencies
Sites with extended horizontal deficiencies
Sites with major vertical tissue loss
Conclusions and perspectives
Scalloped implant design
Segmented fixed implant restorations in the edentulous maxilla
* * *
# Basic concepts
The clinical replacement of lost natural teeth by osseointegrated implants has represented one of the most significant advances in restorative dentistry. Numerous studies on various clinical indications have documented high implant survival and success rates with respect to specific application criteria (Ekfeldt _et al_. 1994; Laney _et al_. 1994; Andersson _et al_. 1995, 1998; Brånemark _et al_. 1995; Lewis 1995; Jemt _et al_. 1996; Lindqvist _et al_. 1996; Buser _et al_. 1997, 2002; Ellegaard _et al_. 1997a;b; Levine _et al_. 1997; Bryant & Zarb 1998; Eckert & Wollan 1998; Ellen 1998; Lindh _et al_. 1998; Mericske-Stern 1998; ten Bruggenkate _et al_. 1998; Wyatt & Zarb 1998; Gunne _et al_. 1999; Lekholm _et al_. 1999; Van Steenberghe _et al_. 1999; Wismeijer _et al_. 1999; Behneke _et al_. 2000; Hosny _et al_. 2000; Hultin _et al_. 2000; Weber _et al_. 2000; Boioli _et al_. 2001; Gomez-Roman _et al_. 2001; Kiener _et al_. 2001; Mengel _et al_. 2001; Oetterli _et al_. 2001; Zitzmann _et al_. 2001; Bernard & Belser 2002; Haas _et al_. 2002; Leonhardt _et al_. 2002; Romeo _et al_. 2002). Several recently published studies have focused on treatment outcome of implant therapy in partially edentulous patients in general, and related to maxillary anterior implant restorations in particular. Belser (1999) reviewed selected publications which appear to have impact when it comes to the discussion of esthetic aspects which will be addressed in this chapter. In a prospective longitudinal study involving a total of 94 implants (50 in the anterior maxilla) restored with fixed partial dentures (FPDs), Zarb and Schmitt (1993) published an average success rate of 91.5% for an observation period up to 8 years. The respective data concerning the maxillary implants demonstrated a success rate of 94% (100% for the prosthesis success). It was concluded that implant therapy in anterior partial edentulism can replicate the data established in the literature for fully edentulous patients. The same authors (Schmitt & Zarb 1993) published an 8-year implant survival rate of 97.9% for single-tooth replacement in partially edentulous patients. These results were confirmed by Avivi-Arber and Zarb in 1996.
Andersson _et al_. (1998) published similarly favorable prospective 5-year data on single-tooth restorations, performed either in a specialist clinic or in general practices, while Eckert and Wollan (1998) presented a retrospective evaluation up to 11 years on a total of 1170 implants inserted in partially edentulous patients, and found no differences in survival rates with respect to the anatomic location of the implants. A meta-analysis concerning implants placed for the treatment of partial edentulism was carried out by Lindh _et al_. (1998). The 6–7-year survival rate for single implant crowns corresponded to 97.5%, while the survival rate of implant-supported FPDs was 93.6%. The influence of implant design and surface texture was investigated by Norton (1998) by means of a radiographic follow-up of 33 implants loaded for up to 4 years. A most favorable maintenance of marginal bone around the conical collar was revealed, with a mean marginal bone loss of 0.32 mm mesially and 0.34 mm distally for the whole group.
Soft tissue stability around implant restorations and adjacent teeth is of paramount importance within the appearance zone (Bengazi _et al_. 1996; Chang _et al_. 1999; Ericsson _et al_. 2000; Grunder 2000; Choquet _et al_. 2001; Cooper _et al_. 2001; Mericske-Stern _et al_. 2001; Bernard & Belser 2002; Engquist _et al_. 2002; Haas _et al_. 2002; Krenmair _et al_. 2002). Scheller _et al_. (1998) specifically addressed this parameter in their 5-year prospective multicenter study on 99 implant-supported single-crown restorations. The authors reported overall cumulative success rates of 95.9% for implants and 91.1% for implant crowns. Soft tissue levels around implant restorations and adjacent teeth remained stable over the entire evaluation period. Wyatt and Zarb (1998) published a longitudinal study on 77 partially edentulous patients, involving a total of 230 implants and 97 fixed partial dentures, with an observation period of up to 12 years (mean 5.41 years) after loading. The average implant success rate was 94%, while the continuous stability of the prostheses (fixed partial dentures) corresponded to 97%. This study comprised 70 anterior and 31 posterior maxillary implants. No significant differences with respect to longevity could be detected either between anterior and posterior locations or between maxillary and mandibular implant restorations.
Along with osseointegration and restoration of function, the patient's subjective satisfaction is a key element of the success of implant therapy. Especially when the implant is located in the anterior part of the oral cavity, an essential part of the therapy aims at creating appropriate conditions, so that the implant prosthesis cannot be distinguished from the adjacent natural teeth at the end of treatment. In this context, a variety of specific procedures have been developed, including novel bone augmentation protocols, connective tissue grafting and reconstruction of lost papillary tissue (Bahat _et al_. 1993; Salama & Salama 1993; Bahat & Daftary 1995; Salama _et al_. 1995; Price & Price 1999; Choquet _et al_. 2001).
Being part of a comprehensive textbook about clinical periodontology, this chapter will focus primarily on fixed implant restorations located in the esthetic zone.
## General esthetic principles and related guidelines
The basic parameters related to dental and gingival esthetics in general and to the maxillary anterior segment in particular are well established in the dental literature (Goldstein 1976; Belser 1982; Schärer _et al_. 1982; Seibert & Lindhe 1989; Goodacre 1990; Rüfenacht 1990; Nathanson 1991; Magne _et al_. 1993a,b, 1994, 1996; Chiche & Pinault 1994; Kois 1996; Kokich 1996; Kokich & Spear 1997; Jensen _et al_. 1999) and have been recently summarized in the form of an updated integral check-list by Magne and Belser (2002). When it comes to the characteristics of the natural maxillary anterior dentition, a number of fundamental objective criteria, including gingival health and its normal morphology as well as dimension, form, specific structural composition, color, opalescence, translucency, transparency, and surface texture of incisors and canines, have been identified (Table 53-1, Fig. 53-1). This list is completed by an addition of subjective criteria associated with esthetic integration, such as variations in the arrangement and positioning of front teeth, relative crown length and negative space.
**Table 53-1** Fundamental objective esthetic criteria (Magne & Belser 2002, copyright © Quintessence Publishing Co, Inc)
1 Gingival health
---
2 Interdental closure
3 Tooth axis
4 Zenith of the gingival contour
5 Balance of the gingival levels
6 Level of the interdental contact
7 Relative tooth dimensions
8 Basic features of tooth form
9 Tooth characterization
10 Surface texture
11 Color
12 Incisal edge configuration
13 Lower lip line
14 Smile symmetry
**Subjective criteria (esthetic integration)**
Variations in tooth form
Tooth arrangement and positioning
Relative crown length
Negative space
**Fig. 53-1** The esthetic checklist, describing a number of respective fundamental objective criteria as they relate to the maxillary anterior segment (detailed description presented in Table 53-1). (Reprinted from Magne & Belser 2002, with permission, copyright © Quintessence Publishing Co, Inc.)
Depending on the type of a given initial clinical situation requiring the replacement of one or several teeth, the patient's expectations may vary from the achievement of an almost perfect illusion, i.e. that the untrained eye cannot easily distinguish the restoration from the surrounding natural dentition, to the acceptance of various degrees of compromise from a purely esthetic point of view. The latter case is not infrequent after multiple anterior tooth loss in combination with significant hard and soft tissue deficiencies. In relation to maxillary anterior edentulous segments, patients generally expect a long-lasting functional and esthetic result with a high level of predictability (Table 53-2). To this primary objective are normally added a number of secondary goals which include parameters such as minimal invasiveness, low risk associated with eventual surgery, overall simplicity, and cost effectiveness.
**Table 53-2** Patient expectations related to maxillary anterior edentulous segments
• Long-lasting esthetic and functional result with a high degree of predictability
---
• Minimal invasiveness (preservation of tooth structure)
• Maximum subjective comfort
• Minimum risk for complications associated with surgery and healing phase
• Avoidance of removable prostheses
• Optimum cost effectiveness
**Table 53-3** Therapeutic modalities for tooth replacement in the esthetic zone
• Conventional fixed partial dentures (FPDs), comprising cantilever units
---
• Resinbonded ("adhesive") bridges
• Conventional removable partial dentures (RPDs)
• Tooth-supported overdentures
• Orthodontic therapy (closure of edentulous spaces)
• Implant-supported prostheses (fixed, retrievable or removable suprastructures)
• Combinations of the above
Prior to selecting an implant-based solution, one should comprehensively review all of the possible treatment modalities available (Table 53-3) which have the potential to solve a given clinical problem, and carefully ponder their respective advantages and eventual shortcomings, and only then take the decision together with the adequately informed patient. Currently, the restorative spectrum in the case of missing maxillary anterior teeth comprises conventional FPDs, resin-bonded bridges, removable partial dentures (RPDs), tooth-supported overdentures and implant-supported fixed or removable prostheses. Furthermore, one should not forget that occasionally orthodontic therapy, e.g. closure of limited edentulous spaces, can represent an effective and elegant alternative or adjunct to a prosthetic treatment. However, the availability of scientific evidence – when possible at its highest level – for the planned treatment modality, should be the key parameter for the final choice.
**Table 53-4** Criteria favoring implantborne restorations
• Normal wound healing capacity
---
• Intact neighboring teeth
• Unfavorable ("compromised") potential abutment teeth
• Extended edentulous segments
• Missing strategic abutment teeth
• Presence of diastemas
In this clinical decision-making process certain criteria, for example the compromised structural, periodontal and/or endodontic status of potential natural abutments, or the extended dimension of the edentulous segment, are among the factors favoring an implant-borne restoration rather than a tooth-supported fixed prosthesis (Table 53-4).
## Esthetic considerations related to maxillary anterior implant restorations
In the context of the natural dentition, long clinical crowns, the irregular contour of the gingival margin, i.e. any abrupt change in vertical tissue height between neighboring teeth, and the loss of papillary tissue often have an adverse influence on dental–facial esthetics (Seibert & Lindhe 1989). Furthermore, the same authors have underlined that in the case of a _high scalloped gingival morphotype_ (in contrast to a rather _low scalloped gingival morphotype_ ) there is mostly an unpredictable relationship between the underlying bone and the gingival contour, often leading to so called "black hole cases" and presenting a high risk for losing soft tissue (e.g. gingival or mucosal recession at the labial aspect of teeth or implants), particularly in relation to restorative procedures, as for example insertion of retraction cords and impression taking.
Another esthetically relevant concern lies in the fact that under normal conditions a maxillary front tooth extraction leads on average to approximately 2 mm loss in vertical tissue height. The mean length of the clinical crown of a maxillary central incisor is 10.2 mm, the one of a lateral incisor 8.2 mm and that of a canine 10.4 mm. Consequently, any kind of maxillary anterior restoration should aim at staying within reasonable limits of these average morphologic dimensions, if a harmonious and esthetically pleasing result is to be achieved. Ultimately, an anterior implant restoration should correspond closely to an ovate pontic of a conventional FPD with respect to the relevant soft tissue parameters (Kois 1996).
Numerous publications, mostly in the form of textbooks, book chapters, reviews, case reports and descriptions of clinical and laboratory procedures and techniques, have addressed various aspects specifically related to esthetics and osseointegration (Parel & Sullivan 1989; Gelb & Lazzara 1993; Jaggers _et al_. 1993; Vlassis _et al_. 1993; Bichacho & Landsberg 1994; Ghalili 1994; Landsberg & Bichacho 1994; Neale & Chee 1994; Studer _et al_. 1994; Carrick 1995; Corrente _et al_. 1995; De Lange 1995; Garber 1995; Garber & Belser 1995; Jansen & Weisgold 1995; Khayat _et al_. 1995; Touati 1995; Brugnolo _et al_. 1996; Davidoff 1996; Grunder _et al_. 1996; Hess _et al_. 1996; Marchack 1996; Mecall & Rosenfeld 1996; Bain & Weisgold 1997; Bichacho & Landsberg 1997; Chee _et al_. 1997; Garg _et al_. 1997; Spear _et al_. 1997; Salinas & Sadan 1998; Jemt 1999; Price & Price 1999; Belser _et al_. 2000; Tarnow _et al_. 2000).
**Table 53-5** Evaluation of anterior tooth-bound edentulous sites prior to implant therapy
• Mesio-distal dimension of the edentulous segment, including its comparison with existing contralateral control teeth
---
• Three-dimensional analysis of the edentulous segment regarding soft tissue configuration and underlying alveolar bone crest (ref. "bone-mapping")
• Neighboring teeth:
• volume (relative tooth dimensions), basic features of tooth form and three-dimensional position and orientation of the clinical crowns
• structural integrity and condition
• surrounding gingival tissues (course/scalloping of the gingival line)
• periodontal and endodontic status/conditions
• crown-to-root ratio
• length of roots and respective inclinations in the frontal plane
• eventual presence of diastemata
• Interarch relationships:
• vertical dimension of occlusion
• anterior guidance
• interocclusal space
• Esthetic parameters:
• height of upper smile line ("high lip" versus "low lip")
• lower lip line
• course of the gingival-mucosa line
• orientation of the occlusal plane
• dental versus facial symmetry
• lip support
In view of maxillary anterior implant restorations, the systematic and comprehensive evaluation of edentulous sites, including the surrounding natural dentition, is of paramount importance (Table 53-5). Key parameters comprise the mesio-distal dimension of the edentulous segment, the three-dimensional analysis of the underlying alveolar bone crest, the status of the neighboring teeth, and interarch relationships as well as specific esthetic parameters.
As one should consider the implant as the apical extension of the ideal future restoration and not the opposite, a respective optimal three-dimensional ("restoration-driven") implant position is mandatory (Table 53-6). Consequently, parameters addressing vertical (sink-depth) and oro-facial implant shoulder location, have been defined, as well as guidelines related to the long axis of the implant, as the latter has a significant impact on the subsequent technical procedures during suprastructure conception and fabrication.
**Table 53-6** Optimal three-dimensional implant positioning ("restoration-driven implant placement") in anterior maxillary sites
• Correct vertical position of implant shoulder (sink depth) using the cemento-enamel junction of adjacent teeth as reference:
---
• no visible metal
• gradually developed, flat axial profile
• Correct orofacial position of point of emergence for future suprastructure from the mucosa:
• similar to adjacent teeth
• flat emergence profile
• Implant axis compatible with available prosthetic treatment options (ideally: implant axis identical with "prosthetic axis")
Implant = apical extension of the ideal future restoration.
Recently, the ITI Consensus Conference has approved the distinctly submucosal implant shoulder location in the maxillary anterior segment in order to respond to natural esthetic demands (Buser & von Arx 2000). As the current implant design – in contrast to the scalloped cemento-enamel junction – features a straight horizontal, "rotation–symmetrical" restorative interface, interproximal implant crown margins are often located several millimeters submucosally, and are thus difficult to reach by the patient's routine oral hygiene efforts (Belser _et al_. 1998). Mainly for this reason a screw-retained implant suprastructure (Sutter _et al_. 1993; Hebel & Gajjar 1997; Keller _et al_. 1998) is preferred to a cemented one, as it benefits from the surface quality and marginal fidelity of prefabricated, machined components, and avoids potential problems associated with cement excess that may be difficult to reach and thoroughly eliminate.
# Anterior single-tooth replacement
Favorable 5-year multicenter results for 71 single-tooth replacements in the anterior maxilla (implant success rate of 96.6%) were reported by Henry _et al_. (1996) ; however, this group mentioned an associated 10% esthetic failure rate. In a retrospective study on 236 patients treated with single-tooth implant restorations in the anterior maxilla (Walther _et al_. 1996), a Kaplan–Meier survival rate of 89% was found for an observation period of 10 years. The failure rate for lateral incisor replacement was lower than that for central incisors. Furthermore, 5% of the related prosthetic suprastructures had to be replaced during the 10 years of observation. Kemppainen _et al_. (1997) prospectively documented 102 implants (ASTRA/ITI) for single-tooth replacement in the anterior maxilla of 82 patients and found survival rates of 97.8% and 100%, respectively, after 1 year. Still related to single-tooth maxillary anterior implants, a prospective study on 15 patients revealed a 100% implant survival rate after 2 years of function (Palmer _et al_. 1997). At crown insertion (6 months after implant placement) the mean bone level was located 0.47 mm apically to the top of the implants. No significant additional changes in crestal bone level occurred during the remainder of the study.
Today, it is generally accepted that the final implant shoulder sink depth for esthetic fixed single-tooth restorations can be determined primarily by the location of the cemento-enamel junction (CEJ) of the neighboring teeth and by the level of the free gingival margin at the vestibular aspect of these same teeth. This means that the implant shoulder is positioned 1–2 mm more apically to the labial CEJ of the adjacent teeth (Belser _et al_. 1998, 2000). However, the noticeable esthetic progress made in this kind of implant restoration is the result of recent developments in the absence of extensive long-term documentation. Because the exclusive use of clinical signs for establishing peri-implant health or disease may not be sufficient, the evaluation of additional objective parameters is needed. A number of diagnostic tests have been utilized by clinicians to supplement clinical signs with objective methods. These tests include microbiologic monitoring, proteolytic bacterial enzyme markers, markers of tissue destruction, and finally, markers of tissue repair and regeneration. In this context peri-implant crevicular fluid (PICF) analysis has become the focus of intense investigation. It has been observed that the volume of crevicular fluid did not differ between implant sites and natural teeth and that the features of inflammation seem to be the same around teeth and implants. In addition, the histologic arrangement of peri-implant soft tissues resembles basically that observed around natural teeth, although there are also some aspects of scar tissue (Abrahamson _et al_. 1996, 1997; Berglundh & Lindhe 1996; Lindhe & Berglundh 1998).
Giannopoulou _et al_. (2003) investigated the effect of intracrevicular restoration margins on peri-implant health of 61 maxillary anterior implants – mainly single-tooth replacements – in 45 patients for up to 9 years. Results revealed that the only statistically significant differences between baseline and follow-up examination concerned pocket probing depth (PPD) and the distance between the implant shoulder and the mucosal margin (DIM measurements), which increased slightly over time. The remainder of the clinical measurements and almost all of the microbiologic and biochemical parameters analyzed did not change significantly. Probably the most critical parameter from a purely esthetic point of view is the DIM value, particularly on the labial aspect of the maxillary anterior implants investigated in this study. A mean value of −1.5 ± 1.1 mm was found at baseline examination, and a slight increase (−1.7 ± 1.1 mm) at the follow-up. This indicates that the risk for exposure of the implant-to-crown interface or margin can be considered low. These findings corroborate recently published data addressing similar parameters (Grunder 2000). The consistently negative Periotest scores confirmed the stability and osseointegrated status of the implants examined. Furthermore, no associations were observed between the above results and the number of years that the implants had been in function. Based on these clinical, microbiologic, and biochemical data, and on an observation period of 4–9 years (mean 6.8 years), it was concluded that in patients with appropriate oral hygiene, implant-supported maxillary anterior crowns with distinctly intracrevicular margins did not predispose to unfavorable peri-implant host and microbial responses. In particular, overall healthy and stable peri-implant tissue conditions – a paramount criterion when it comes to esthetic implant crowns – were consistently encountered and maintained longitudinally. One of the patients participating in this study and who recently passed the 10-year clinical and radiographic follow-up control, is presented in Figs. 53-2 to 53-6. An adequate esthetic integration of the two single-tooth restorations, replacing the congenitally missing lateral incisors, could be achieved and maintained over time.
**Fig. 53-2** Ten-year follow-up of a 28-year-old female patient. Both congenitally missing lateral incisors were replaced by implants, restored with screw-retained porcelain-fused-to-metal crowns.
**Fig. 53-3** The frontal view in centric occlusal position documents the harmonious integration of the two implant restorations after 10 years of clinical service.
**Fig. 53-4** Ten-year post operative radiograph of the maxillary right lateral single-tooth implant restoration.
**Fig. 53-5** Ten-year post-operative radiograph of the maxillary left lateral single-tooth implant restoration.
**Fig. 53-6** During unforced smiling an adequate balance between implant-crowns and natural dentition can be noticed.
**Fig. 53-7** Schematic representation of an intact maxillary right anterior segment. The alveolar bone follows the scalloped course of the cemento-enamel junction for a distance of approximately 2 mm (white dotted line), whereas, accordingly, the gingival tissue occupies the interdental area completely.
**Fig. 53-8** Schematic representation of the same segment after loss of the lateral incisor. While the interproximal bone height has basically been maintained, the corresponding gingival tissue is flattened due to a lack of support originally provided by the now missing tooth.
In a simplistic way, the morphologic and esthetic consequences in the frontal plane of the loss of a single maxillary incisor, when compared to the original intact situation, can be summarized as follows: maintenance of the tooth-sided interproximal bone height at the neighboring teeth, and vertical loss ("flattening") of the corresponding gingival tissue due to a lack of support originally provided by the now missing tooth (Figs. 53-7, 53-8). In case of an anterior single-tooth replacement, the related implant restoration should aim at replicating the clinical crown of the contralateral control tooth from the line of soft tissue emergence to the incisal border. Additionally, a gradually developed, flat emergence profile from the implant shoulder to the peri-implant mucosal margin is mandatory (Figs. 53-9, 53-10).
The basic considerations related to maxillary anterior single-tooth replacement, including the respective general achievements and limitations, and addressing edentulous segments with different types of labial bone deficiencies, are presented in Table 53-7.
**Fig. 53-9** The treatment objective in the case of an anterior single-tooth replacement is an implant restoration with a gradually developed, flat emergence profile from the implant shoulder to the peri-implant mucosal surface. Ideally, the clinical crown of the implant restoration should aim at replicating the clinical crown of the corresponding contralateral tooth.
**Fig. 53-10** Schematic comparison in the sagittal plane between a natural maxillary incisor and a respective implant borne single-tooth restoration. The decrease of alveolar bone height on the labial and palatal aspect following tooth loss leads to a more palatal implant position when compared to the original root position, which in turn influences the axial profile of the restoration.
## Sites without significant tissue deficiencies
An increasing body of evidence indicates that the most determinant parameter for achieving an esthetic single-tooth restoration is the interproximal bone height at the level of the teeth confining the edentulous gap. The related bone should be within a physiologic distance, i.e. approximately 2 mm, of the CEJ and thus provide the essential support for the overlaying soft tissue compartments. Consequently, preoperative diagnosis will include interproximal radiographic bone height assessment and periodontal probing of the soft tissue attachment level.
**Fig. 53-11** Pre-operative close-up view of the upper right anterior region of a 22-year-old female patient with a missing right central incisor. The scalloped course of the gingiva is maintained, featuring interproximal soft tissue at the level of the cemento-enamel junction.
Table 53-7 Basic considerations related to anterior single-tooth replacement
**Achievements**| Predictable and reproducible results regarding both esthetic parameters and longevity in sites without significant vertical tissue deficiencies
---|---
| Well defined and well established surgical protocols:
| • _restoration-driven_ implant placement Adequate and versatile restorative protocols and prosthetic components:
| • occlusal/transverse screw-retention
| • angulated abutments
| • high-strength ceramic components
**Sites with buccal bone deficienies**| Lateral bone augmentation using _autografts_ and _barrier membranes_ :
| • technique offers efficacy and predictability
| • _simultaneous_ or _staged approach_ depending on defect extension and defect morphology
| Lateral bone augmentation by means of _alveolar bone crest splitting_ and/or various _osteotome techniques_ :
| • limited clinical long-term documentation
**Limitations**| Combined vertical bone and soft tissue deficiencies:
| • following removal of ankylosed teeth or failing implants
| • advanced loss of periodontal tissues, including gingival recession, on neighboring teeth
| • limited scientific documentation related to _vertical bone augmentation_ and _distraction osteogenesis_
If the comprehensive presurgical analysis of a given maxillary anterior single-tooth gap has confirmed a favorable vertical level of both soft tissue and underlying alveolar bone at the interproximal aspect of the two adjacent teeth on the one hand (Figs. 53-11 to 53-13), and no major vestibular bone deficiencies on the other hand, the site can be considered compatible with a straightforward implant surgical protocol. In order to ensure the best probability of a successful and long-lasting esthetic treatment outcome, the actual implant placement has to be carried out meticulously according to the surgical guidelines defined in Table 53-6. These guidelines include key parameters such as low-trauma surgical principles in general and precise three-dimensional ("restoration-driven") implant positioning in particular. In the case of standard single-tooth sites, most surgeons do not advocate the use of a surgical guide or stent, as the adjacent teeth and associated anatomic structures normally offer sufficient morphologic landmarks to reach the therapeutic objective safely. As far as the detailed surgical protocol is concerned, readers are referred to Chapter 48. Buser and von Arx (2000) have published the surgical step-by-step procedure related to maxillary anterior single-tooth implants, and insisted on a slightly palatal incision technique to preserve a maximum of keratinized mucosa on the labial aspect of the future implant restoration. Another crucial parameter is the maintenance of at least 1 mm of bone plate on the vestibular aspect of the implant in order to minimize the risk for peri-implant soft tissue recessions, a factor parameter when it comes to esthetics. Under such conditions one may consistently achieve post-surgical treatment outcomes featuring unaltered vertical soft tissue and underlying bone levels at the interproximal aspect of the adjacent natural teeth (Figs. 53-14 to 53-16).
**Fig. 53-12** The corresponding radiograph displays favorable bony conditions in view of implant therapy. Note in particular the interproximal bone height, following the cemento-enamel junction for a distance of less than 2 mm.
**Fig. 53-13** The oblique close-up view confirms optimal conditions for the insertion of an implant, namely interproximal soft tissue height and no significant loss of the buccal bone plate.
**Fig. 53-14** Clinical view of the maxillary anterior implant site 8 weeks after insertion of a solid screw implant according to a one-stage transmucosal surgical protocol. A harmonious peri-implant soft tissue profile has been established by means of a titanium healing cap featuring a respective emergence profile and thus offering adequate interproximal soft tissue support.
**Fig. 53-15** The corresponding radiograph displays a continuous close contact between bone and implant and confirms that the vertical interproximal bone level has been maintained.
**Fig. 53-16** The occlusal view reveals an implant position in the orofacial plane that is in accordance with the adjacent natural roots and thus permits development of a flat emergence profile.
**Fig. 53-17** On a stone model derived from the clinical situation, the laboratory technician defines the treatment objective in wax. At this stage priority is given to esthetic principles and maintenance of symmetry rather than to the actual position of the underlying implant.
**Fig. 53-18** The configuration of the peri-implant soft tissue is subsequently adapted on the stone model according to the diagnostic wax-up. Ultimately, it will be the restoration itself that completes the last phase of soft tissue conditioning by subtle respective physical displacement.
**Fig. 53-19** An appropriate secondary titanium component (abutment) is selected as support for the planned screw-retained implant restoration.
Once osseointegration is confirmed radiologically and clinically, the clinical situation is transferred to the master model by means of an impression, normally assisted by auxiliary components in the form of prefabricated impression copings. On the master model, which in turn contains a replica (analogue) of the implant, the laboratory technician defines the final configuration of the single-tooth implant restoration by means of a diagnostic wax-up (Fig. 53-17). Under normal circumstances, i.e. when the natural contralateral control tooth corresponds mostly to the esthetic and functional requirements of an appropriate "target model", the technician basically copies the clinical crown of this control tooth in wax, regardless of the actual underlying implant position. At this stage a close-to-ideal restoration is planned, while its connection to the underlying implant will be addressed later. This approach comprises the minute shaping of the peri-implant soft tissue configuration (on the master model in the form of stone), in view of an identical emergence from the labial and interproximal soft tissue margin, to the one observed on the natural tooth site (Fig. 53-18). Only after having completed this preparatory step, will the ceramist select the most adequate secondary component (i.e. abutment), depending on the three following cardinal criteria (Fig. 53-19):
1. Implant shoulder depth in relation to the labial mucosal margin
2. Oro-facial implant shoulder position with respect to the future line of emergence of the suprastructure
3. Long axis of the implant.
In most instances, preference will be given to a screw-retained implant suprastructure, unless a combination of mesiostructure and cemented restoration is chosen. Screw-retention is primarily preferred due to a marked submucosally located implant shoulder, in particular at the interproximal aspect, which may render the removal of excess cement difficult, and which is mostly not within reach of the patient's routine oral hygiene measures. In addition, screw-retained suprastructures benefit from the close-to-perfect surface quality characteristics and the marginal precision of machined, prefabricated components. Nowadays several of the leading implant systems also offer high-strength ceramic ter tiary components which may positively contribute to the esthetic treatment outcome, particularly in the case of a rather thin labial peri-implant mucosa (Fig. 53-20). Another parameter which is of primary importance when it comes to esthetic considerations relates to maxillary anterior implant restorations and is associated with the suprastructure design itself at the interproximal aspect. In order to provide optimal conditions for the related soft tissue, a long interdental contact line is established, located slightly more towards the palatal aspect of the restoration (Figs. 53-21, 53-22). This design offers optimal support for the interproximal soft tissue and thereby reduces the potential hazard of a so-called "black triangle" (Figs. 53-23 to 53-25). In this context some studies have indicated that there exists a predictable relationship between the location of the interdental contact point and the associated alveolar bone crest when it comes to presence or absence of interdental papillae fully occupying the interdental space of maxillary anterior teeth (Tarnow _et al_. 1992; Tarnow & Eskow 1995).
**Fig. 53-20** Using a silicon template as guide, a prefabricated ceramic blank is inserted and subsequently reduced to provide adequate space for the external layers of cosmetic porcelain.
**Fig. 53-21** Labial view of the completed ceramo-ceramic restoration on the master cast.
**Fig. 53-22** In particular, the completed screw-retained allceramic restoration displays a high degree of translucency on its incisal third.
**Fig. 53-23** A titanium abutment will serve as infrastructure for the transocclusally screw-retained high-strength allceramic restoration.
**Fig. 53-24** The 1-year post-operative radiograph confirms favorable conditions at the bone-to-implant interface. Note a high degree of radio-opacity of the all-ceramic substrate, permitting the evaluation of the fidelity of the marginal adaptation.
**Fig. 53-25** An acceptable overall integration of the metal-free implant-borne restoration on site 11 can be noted.
## Sites with localized horizontal deficiencies
In a case of a localized (minor) horizontal deficiency, i.e. a confined vestibular alveolar bone crest defect at the vestibular aspect of a maxillary anterior single-tooth gap, one prefers to place the implant and simultaneously undertake a lateral bone augmentation procedure, on condition that several well defined prerequisites are fulfilled. These include an implant placement in accordance with the guidelines presented in Table 53-6 ("restoration-driven" implant placement), the achievement of an adequate primary stability and a resulting cervical dehiscence-type bony defect which is compatible with a predictable bone augmentation procedure. More specifically, the dehiscence should have the form of a two-wall bony defect, and the labial aspect of the inserted implant should not exceed the surrounding bone contours. Under such conditions, the treatment of choice consists of the application of autogenous bone chips, harvested at the site of the implant surgical intervention. The bone chips, which can be combined with one of the numerous available bone substitutes (e.g. BioOss®) if necessary, will provide adequate support for a subsequently adapted barrier membrane. The described grafting material is finally complemented with "bone slurry", constantly collected during the entire procedure. Subsequently, a bioabsorbable membrane is applied prior to repositioning and tension-free suturing of the mucoperiosteal flap. This implicates a rather extended flap design, comprising vertical releasing incisions.
In conclusion, a simultaneous lateral augmentation procedure is recommended if the three following conditions are present:
1. Ideal three-dimensional ("restoration-driven") implant position
2. Adequate primary implant stability
3. Localized two-wall bony defect, exceeding the labial contour of the implant and hereby assuring an appropriate bone regeneration potential and providing the necessary stability to the applied bone graft.
**Fig. 53-26** Schematic representation of a horizontal section at the cemento-enamel junction level of the maxillary right anterior segment.
Under these specific conditions, the implant can be functionally loaded after 2–4 months, depending on size and configuration of the respective bone defect.
It is not infrequent in the anterior maxilla, due to its specific alveolar bone crest morphology, that "restoration-driven" rather than "bone-driven" implant positioning leads to a fenestration-type defect in the apical area of the implant. If adequate primary implant stability can be obtained, a similar simultaneous lateral bone augmentation procedure, as described for localized dehiscence-type defects, appears feasible. Under such circumstances the healing time prior to functional implant loading remains the same as advocated for standard implant protocols (i.e. 2 months for SLA-coated screw-type titanium implants).
## Sites with extended horizontal deficiencies
In the case of more extended horizontal alveolar bone crest deficiencies, a simultaneous implant placement and lateral bone augmentation procedure becomes technically more difficult and less predictable, as the ultimate goal remains an optimal "restoration-driven" implant positioning (Figs. 53-26, 53-27). The described extended horizontal bone deficiency, on the one hand, may often not permit acceptable primary implant stability to be achieved, and, on the other hand, may lead to a vestibular bone dehiscence that does not have a distinct two-wall morphology. Furthermore, the labial implant contour would be more prominent than the respective surrounding bone (Fig. 53-28). Under these specific circumstances the principal prerequisites for a simultaneous approach are clearly not present, thus leading to the recommendation to proceed according to a staged surgical protocol, which will address the lateral bone augmentation first and the actual implant placement in a second stage.
This may represent a major problem for some patients, as two surgical interventions, normally separated by approximately 6 months, are necessary, leading to a total treatment time of 8 months or more. It is therefore indispensable to inform the patient thoroughly about both the reasons for the staged approach associated to implant therapy, and the possible conventional prosthodontic alternatives (e.g. a traditional tooth-borne FPD, eventually in combination with a connective tissue grafting procedure to optimize the deficient edentulous ridge in view of an optimal and esthetic pontic). The patient will then be in a position to give his or her informed consent to either of the two therapeutic modalities, according to individual preference.
**Fig. 53-27** "Restoration-driven" implant placement in the horizontal plane at the site of the maxillary right lateral incisor. In order to maintain at least 1 mm of alveolar bone also on the labial aspect, the implant has to be inserted approximately 1–2 mm more towards the palate when compared to the adjacent roots.
**Fig. 53-28** In the case of an extended lateral bone deficiency, where an adequately placed implant would largely exceed the vestibular border of the alveolar bone crest, a lateral bone augmentation procedure (staged approach) is indicated.
**Fig. 53-29** After elevation of a mucoperiosteal flap a severe extended resorption on the vestibular aspect of the edentulous alveolar ridge becomes apparent. Such a morphology is hardly compatible with "restoration-driven" implant placement.
**Fig. 53-30** An autogenous bone graft, harvested from the patient's chin region, has been secured with a fixation screw and its periphery filled in with additional bone chips prior to membrane placement.
In the case of implant therapy, the first step consists of the elevation of a rather extended mucoperiosteal flap featuring vertical releasing incisions, as the added site volume (due to the block graft and barrier membrane) will require subsequent splitting of the periosteum prior to flap repositioning and suturing (Fig. 53-29). Numerous studies reporting results of various bone augmentation techniques and related materials have been published (Hürzeler _et al_. 1994; Buser _et al_. 1996; Ellegaard _et al_. 1997b; Chiapasco _et al_. 1999, 2001; von Arx _et al_. 2001a; Zitzmann _et al_. 2001). To date, autogenous bone block grafts, mostly harvested from the chin or the retromolar area, in combination with e-PTFE barrier membranes, still have the best clinical long-term documentation (Buser _et al_. 2002). These authors presented prospectively documented 5-year data of 40 consecutively treated patients, according to a staged protocol. Implants could subsequently be inserted on all laterally augmented sites. It was concluded that the clinical results of implants placed in regenerated bone were comparable to those reported for implants in non-regenerated bone. A clinical example of the described approach is presented in Figs. 53-29 to 53-37.
## Sites with major vertical tissue loss
When it comes to maxillary anterior single-tooth gaps with significant vertical tissue loss, the predictable achievement of an esthetically pleasing treatment outcome, ideally providing a so-called perfect illusion with respect to its integration in the surrounding natural dentition, gets difficult. As pointed out earlier in this chapter, a close relationship exists between the interproximal bone height and the associated soft tissue level (Figs. 53-7, 53-8). If the coronal border of the alveolar bone is no longer within the physiologic distance of approximately 2 mm from the interproximal CEJ of the teeth confining the edentulous space, there is an increased risk of an altered respective soft tissue course (due to a lack of underlying bony support) and its adverse impact on the appearance. Such situations can be encountered following the removal of ankylosed teeth or failing implants, or in case of advanced periodontal tissue loss – including gingival recession – on neighboring teeth. Under these specific circumstances, the final decision whether or not to use implants will ultimately depend on (1) the careful and comprehensive evaluation of all of the therapeutic modalities available for anterior tooth replacement (Table 53-3), and (2) the patient's individual smile line and expectations. This process includes an objective analysis of the advantages and eventual shortcomings associated with each modality.
**Fig. 53-31** Six months after the lateral ridge augmentation procedure the clinical occlusal view documents that uneventful healing has occurred and that the orofacial ridge profile has been improved.
**Fig. 53-32** During implant surgery. All key parameters characterizing an optimal implant position (shoulder sink depth, orofacial point of emergence, implant axis) could be satisfied.
**Fig. 53-33** After 3 months of healing the labial view documents a slight excess of keratinized peri-implant mucosa in a coronal direction, which is a prerequisite for the development of the final esthetic soft tissue contours. The first step of the subsequent procedure will consist of the insertion of a longer titanium healing cap, following a minor mucosaplasty.
**Fig. 53-34** Two weeks after mucosaplasty and exchange of healing caps the initiation of a harmoniously scalloped labial soft tissue course is apparent. Furthermore, the access from the surface to the underlying implant shoulder has been established.
**Fig. 53-35** The two ceramo-metal crown restorations – one tooth-borne (site 21) and one implant-borne (site 11) – display little difference in appearance since symmetry has been respected from the line of mucosal emergence to the incisal edge.
**Fig. 53-36** The 1-year follow-up radiograph confirms the stability of the osseointegrated 10 mm titanium screw implant.
**Fig. 53-37** An esthetically pleasing overall integration of the two maxillary anterior restorations is underlined by a closeup view of the patient's unforced smile.
To illustrate these clinically relevant aspects, the initial situation and the subsequent implant treatment of a 35-year-old female patient consulting with an ankylosed maxillary deciduous left canine, are presented in Figs. 53-38 to 53-46. The preoperative analysis had led to the conclusion that the fabrication of a conventional tooth-borne three-unit FPD, using the intact lateral incisor and first premolar as abutments and featuring a canine pontic, was not opportune from several points of view. Among these should be particularly mentioned aspects related to the questionable mechanical resistance of the resulting conventional prosthesis, specific occlusal considerations (e.g. canine guidance in a pontic area), lack of esthetic superiority when compared to a virtual implant-borne fixed restoration, and, last but not least, the conflict with the general principle of minimal invasiveness (maximum preservation of intact tooth structure).
**Fig. 53-38** Pre-operative view of a 35-year-old female patient consulting with a persistant primary tooth in the position of the maxillary left canine. Note the irregular course of the adjacent gingiva in general and the loss in vertical tissue height in particular.
**Fig. 53-39** One month after removal of the deciduous canine, the root of which was severely resorbed, a mucoperiosteal flap with vertical releasing incisions is elevated and the preparation of a calibrated implant bed performed. One can note an increased distance between the cemento-enamel junction and the coronal border of the alveolar bone and the left lateral incisor.
**Fig. 53-40** Buccal view after insertion of the implant.
**Fig. 53-41** In a case of rather thin mucosa, the utilization of a connective tissue graft, harvested from the palate, may be indicated to create a sufficient thickness of soft tissue at the implant site.
**Fig. 53-42** Prior to flap closure, the connective tissue graft is secured to the flap with bioabsorbable sutures.
**Fig. 53-43** Coverage of most of the healing cap during suturing is recommended, leading to a submerged or at least to a "semi-submerged" healing mode.
**Fig. 53-44** The clinical aspect after insertion of the ceramometal implant crown reveals stable and esthetic peri-implant soft tissue contours.
**Fig. 53-45** The 2-year follow-up radiograph confirms the stability of the osseointegrated 10 mm solid screw titanium implant.
**Fig. 53-46** On a left lateral view, during the patient's forced smiling, one can note that the lack of vertical soft tissue in the interproximal area has been compensated for with an apically extended interdental contact line.
**Fig. 53-47** Labial close-up view of the maxillary right anterior region of a 19-year-old female patient. The interdental soft tissue height distal to the central incisor and the corresponding underlying alveolar bone height are markedly reduced, leading to exposure of the cemento-enamel junction.
**Fig. 53-48** The contralateral side of the dental arch shows perfectly intact and harmonious conditions with respect to the course of the gingiva.
**Fig. 53-49** On the occlusal view of the edentulous site a significant lateral crest deficiency becomes apparent, which calls for both a bone and soft tissue augmentation procedure, particularly if an implant solution is planned.
**Fig. 53-50** Six months after combined lateral bone and soft tissue augmentation, the site appears to be compatible with "restoration-driven" implant placement.
Once the decision was made, both the implant surgical and the restorative strategies focused on improving or at least optimally exploiting the pre-existing limited esthetic potential of the site. From the surgical side, this comprised a deeper than normal implant shoulder sink depth (Fig. 53-40), the use of a connective tissue graft on the vestibular aspect (Fig. 53-41), a localized lateral bone augmentation (simultaneous approach) procedure (Fig. 53-42) and a coronally repositioned flap (Fig. 53-43). The metal–ceramic implant restoration featured a trans-verse screw-retention to provide maximum space for esthetic porcelain stratification and a long contact line on the mesial aspect to compensate for the missing interdental soft tissue height (Figs. 53-44 to 53-46).
A more severe preoperative situation of vertical tissue deficiency, combined with a marked horizonstal bone defect, is presented in Figs. 53-47 to 53-49. This 19-year-old female patient lost her maxillary right lateral incisor due to a localized periodontal problem. Again, the comprehensive site analysis concluded that a single-tooth implant restoration was the best compromise in view of major disadvantages associated with all of the conventional prosthodontic options. From a purely esthetic point of view, none of the therapeutic modalities had the potential to pre-dictably lead to a perfect re-establishment of a symmetrical, harmoniously scalloped soft tissue course at its original physiologic level. However, a rather low lip-line during the patient's normal communication and unforced smiling permitted the least invasive approach to be chosen. Following a lateral connective tissue and bone augmentation procedure (Fig. 53-50), an implant could be inserted in an acceptable position and subsequently restored with a screw-retained crown. The final frontal view, allowing a direct comparison between the intact (Fig. 53-51) and the restored side, clearly demonstrates the current esthetic limitations associated with implant therapy in sites with a marked vertical tissue deficiency (Fig. 53-52).
# Multiple-unit anterior fixed implant restorations
The normal consequence following loss of two or more adjacent upper anterior teeth comprises a flattening of the edentulous segment. In particular one can observe the disappearance, in an apical direction, of the crestal bone originally located between the incisor teeth. This phenomenon is not, or only minimally, present at the interproximal aspect of the remaining anterior teeth and thus explains the fundamental difference between a maxillary anterior single-tooth gap and a multi-unit edentulous segment.
**Fig. 53-51** The buccal view in centric occlusion position before therapy summarizes the problems associated with localized vertical tissue deficiencies: lack of a harmoniously scalloped soft tissue course in general and missing interdental papillae in particular.
**Fig. 53-52** The corresponding view after lateral bone and soft tissue augmentation and insertion of an implant-borne single-tooth restoration on the site of the right lateral incisor, underlines the resulting shortcomings with respect to esthetic parameters. Vertical tissue deficiencies – which at present cannot be predictably compensated for – clearly compromise the overall integration of an otherwise successful treatment.
If two standard screw-type titanium implants are inserted to replace two missing maxillary central incisors (Figs. 53-53, 53-54), an additional peri-implant bone remodeling process will take place. In the frontal plane, two different characteristic processes, one between the natural tooth and the implant and the other between the two implants, can be distinguished. At the site between tooth and implant, the tooth-sided interproximal bone height should theoretically remain at its original location, i.e. within 2 mm from the CEJ, from where the implant-sided interproximal bone height drops in an oblique manner towards the first implant-to-bone contact, normally located approximately 2 mm apically of the junction ("microgap") between the implant shoulder and the abutment or suprastructure. This phenomenon has been referred to in the literature as "saucerization" or establishment of a "biologic width" (Hermann _et al_. 1997, 2000, 2001a,b). In contrast, the inter-implant bone height normally decreases further in an apical direction, once the respective abutments or suprastructures are connected to the implant shoulder. This process is mostly accompanied by a loss of interimplant soft tissue height and hence may lead to unsightly, so-called "black interdental triangles". The schematic close-up views comparing the original dentate situation with the status after integration of two adjacent implant restorations, clearly demonstrate the negative consequences on the course of the marginal soft tissue line in a case of multiple adjacent maxillary anterior implants (Figs. 53-55, 53-56).
**Fig. 53-53** Schematic representation of the six maxillary anterior teeth, including their bony support and the course of the marginal soft tissue, corresponding ideally approximately to the cemento-enamel junction (dotted line).
**Fig. 53-54** Loss of the two central incisors and their subsequent replacement by implant restorations normally leads to well defined bone loss ("micro-gap", establishment of a "biologic width") around the implant sites. The main consequence from an esthetic point of view consists of vertical soft tissue deficiencies, namely between adjacent implants (dotted lines).
The basic considerations related to the current state of achievements and limitations of maxillary anterior fixed multiple-unit implant restorations in sites with and without horizontal and/or vertical soft and hard tissue deficiencies are summarized in Table 53-8.
**Fig. 53-55** Schematic close-up view of the relationship between cemento-enamel junction, alveolar bone, and course of the gingiva in the maxillary incisor area.
**Fig. 53-56** Same area after implant therapy. The red arrow represents the distance between the inter-implant bone crest and the interdental contact point. The lack of bony support for the interdental soft tissue often causes the appearance of black triangles, compromising the esthetic treatment outcome.
## Sites without significant tissue deficiencies
Due to the previously described shortcomings inherent in multiple adjacent implant restorations, the clinical decision-making process will thus address both the height of the patient's smile line (low, medium, high) and the individual gingival phenotype (thick and low scalloped or thin and high scalloped). In the presence of a favorable gingival morphotype, some restorative "tricks", including peri-implant soft tissue conditioning and particular interproximal crown design, need to be implemented to predictably achieve an acceptable esthetic compromise (Figs. 53-57 to 53-62). Peri-implant soft tissue conditioning is primarily achieved by using either healing caps featuring an appropriately shaped, continuously increasing (in a coronal direction) axial emergence profile, or by means of plastic components permitting the customization of the best suited axial contour in the region from the implant shoulder or abutment to the mucosal margin (Fig. 53-58). The particular suprastructure design concerns the interimplant aspect, where, instead of an interdental contact point, a long and slightly palatal contact line is developed in the form of two adjacent "wings", which are more color-saturated in order to create a discrete shade transition ("blending-in") at the mucosal margin. If the mesial oblique triangular ridges of the two adjacent implant restorations are located at their normal location, the ceramic crowns will not – despite their increased vestibular diameter – optically appear larger (Fig. 53-61). This design reduced the inter-implant cervical triangle to a minimum at the moment of the crown insertion (Fig. 53-59), and favored a coronal soft tissue increase, clearly visible at the 6-year clinical follow-up (Fig. 53-60).
Table 53-8 Basic considerations related to anterior fixed multiple-unit implant restorations in sites with horizontal and/or vertical soft and hard tissue deficiencies
**Achievements**| Predictable and reproducible results regarding lateral bone augmentation using barrier membranes supported by autografts:
---|---
| • allows implant placement in patients with a low lip line
**Limitations**| Vertical bone augmentation is difficult to achieve and related surgical techniques lack prospective clinical long-term documentation
| Inter-implant papillae cannot predictably be reestablished as of yet
**Fig. 53-57** Clinical close-up view of the maxillary anterior segment of a 32-year-old female patient following placement of two 12-mm solid screw implants according to a one-stage transmucosal surgical protocol.
**Fig. 53-58** Conditioning of the peri-implant mucosa, in view of the future restorations, has been performed by means of auxiliary plastic components with the possibility of individualizing the emergence profile.
**Fig. 53-59** The corresponding clinical close-up view, taken shortly after insertion of the two screw-retained ceramo-metal restorations, documents the effect of a long interdental contact line, the presence of pronounced mesial ridges, and a slight increase of color saturation in the cervico-interdental area. Such technical measures contribute to the compensation of a flat and more apically located labial mucosa line.
**Fig. 53-60** Clinically, a slight fill-in of interimplant mucosa and an overall stable soft tissue situation can be noted after 6 years of clinical service.
## Sites with extended horizontal deficiencies
If the absence of multiple adjacent teeth in the anterior maxilla is accompanied by a marked, but primarily horizontal, resorption of the edentulous alveolar bone crest towards the palate, one can adopt two different strategies. One consists of a so-called "bone-driven" implant placement which will lead to a distinct palatal implant position. In most instances this strategy calls for an implant assisted overdenture-type prosthesis which can more easily compensate for the discrepancy between the required position of the teeth to be replaced and the actual implant location, when compared to a fixed implant prosthesis. Furthermore, the denture flange can quite efficiently solve shortcomings related to esthetics, phonetics, and/or insufficient labial and facial tissue support. Normally, denture stability and subjective comfort are excellent and – owing to its removable nature – access for oral hygiene is easy (Mericske-Stern 1998; Kiener _et al_. 2001). One should be aware, however, that this approach also has its inherent limits and has to take into account crucial parameters such as phonetics and minimal room required for the tongue. As this chapter focuses primarily on fixed maxillary anterior implant restorations, we refer to the relevant respective literature.
**Fig. 53-61** In order to compensate for the reduced height of the interimplant soft tissue, the ceramist has used an apically prolonged interdental contact line in the form of so-called "mini-wings". These interdental ceramic extensions are made of a more saturated root-like porcelain and are slightly displaced to the palatal aspects of the crowns. This approach results in restorations that integrate successfully, although they are physically larger than the original anatomic crowns.
**Fig. 53-62** Six years after placement of the 12 mm solid screw titanium implants, the respective radiographs reveal stable conditions at the osseointegrated interface and adequate marginal adaptation.
Another approach consists of one of the various lateral bone augmentation procedures reported in the literature (Buser _et al_. 1996, 1999, 2002; Chiapasco _et al_. 1999; von Arx _et al_. 2001a,b; Zitzmann _et al_. 2001), which ultimately should lead to a more "restoration-driven" implant placement, ideally compatible with a straightforward fixed implant prosthesis featuring a continuous, flat axial emergence profile. To date a scalloped course of the peri-implant mucosa cannot be predictably achieved around multiple adjacent maxillary anterior fixed implant restorations, and as an increased clinical crown length is normally inherent in this approach as well, the pre-operative assessment of the patient's lip line or smile line (Jensen _et al_. 1999) is of primary importance during the related decision-making process.
## Sites with major vertical tissue loss
The replacement of multiple missing adjacent maxillary anterior teeth with a fixed implant prosthesis still represents a major therapeutic challenge in the presence of combined major horizontal and vertical alveolar ridge deficiencies. Vertical bone augmentation techniques, for example the distraction osteogenesis procedure (Chiapasco _et al_. 2001), hold promise for the future but lack clinical long-term documentation at present.
As a consequence, the treatment of choice consists in most instances of an implant-assisted (e.g. spherical attachments, bar devices) removable overdenture.
# Conclusions and perspectives
When implants are to be inserted within the esthetic zone in view of a fixed restoration, deep placement – close to or at the alveolar bone crest level – of the shoulder of implants, often specifically designed for this indication, permits the suprastructure margin to be hidden below the mucosa, and the development of a gradual harmonious emergence profile from the implant shoulder to the surface. The resulting clinical crown replicates the profile of the natural control tooth despite a slightly more palatal implant position. This in turn leads to a secondary peri-implant bone loss or bone remodeling – particularly in a case of multiple adjacent implants – due to the reorganization of a biologic width (Hermann _et al_. 1997, 2000, 2001a,b). Under these particular circum-stances, screw-retained restorations, based on pre-fabricated, machined components, will assure a maximum marginal adaptation, favoring the mainte-nance of the long-term stability of the esthetic result (Belser 1999; Belser _et al_. 1998, 2000). The currently flat, "rotation–symmetrical" design of standard screw-type titanium implants, leading to a marked submucosal implant shoulder position at the interproximal aspect, may not, however, represent the optimal design, in particular in the context of multi-ple adjacent implants.
## Scalloped implant design
As pointed out earlier in this chapter, the traditional implant design may lead to esthetic shortcomings in a case of multiple adjacent maxillary anterior fixed implant restorations. One could hypothesize in this context whether a modified design at the coronal end of the implant, in the sense of a scalloped, more "CEJ-like" configuration, might lead to an improved preservation of peri-implant bone at the interproximal aspect in general, and between adjacent implants in particular. One of the possible design solutions and its anticipated theoretical impact on bone and esthetic parameters are presented in Figs. 53-63, 53-64, and 53-68. More specifically, this approach ultimately aims at creating an inter-implant bone height and resulting soft tissue level situation compatible with generally accepted esthetic criteria. Among these one should primarily mention the establishment and/or maintenance of a harmoniously scalloped course of the marginal peri-implant mucosa. At present, the combination of the following three elements appears important:
**Fig. 53-63** Instead of the traditional implant design, featuring a flat rotation–symmetrical coronal aspect, a scalloped connection, inspired by the natural cemento-enamel junction, may lead to a more superficial implant insertion and by this to the preservation of more bone in the interproximal area.
**Fig. 53-64** Comparison in the sagittal plane of a natural maxillary central incisor and a titanium implant featuring a scalloped design at its coronal end. The radius corresponds to the amount of bone which might theoretically be preserved.
**Fig. 53-65** Vestibular view in centric occlusion position of a 24-year-old male patient. The two maxillary central incisors have been lost due to a traumatic injury.
**Fig. 53-66** After 1 year of clinical service, there is a harmoniously scalloped marginal soft tissue course, including the most critical inter-implant area.
1. Screw-type titanium implant body, featuring optimal surface characteristics
2. Tooth-colored transmucosal portion with adequate axial emergence profile and scalloped coronal end
3. Mechanically sound suprastructure connection, permitting both screw retention and cementation.
The clinical potential of such a novel, scalloped implant design is documented in Figs. 53-65 to 53-67, presenting a 24-year-old male patient who had lost his two maxillary central incisors in the course of an accident. The 1-year clinical and radiographic follow-up appears to support – at least short-term – the hypothesis that such an approach may preserve interimplant crestal bone and overlying soft tissue to a certain extent.
## Segmented fixed implant restorations in the edentulous maxilla
Another particular challenge from both a surgical and a prosthodontic point of view represents the implant-supported fixed prosthetic rehabilitation of the edentulous maxilla. Undoubtedly esthetic considerations and certain aspects associated with the patient's subjective comfort – both during the actual treatment phase and once the prosthesis is completed – also play a major role in this context. We will limit our reflections to (1) specific aspects of pre-implant diagnosis, (2) the importance of implant number, alignment and spatial distribution, and (3) conception of the suprastructure.
**Fig. 53-67** The 1-year follow-up radiograph shows prototype of titanium implants featuring a scalloped design at their coronal end. This design permits a more superficial implantinsertion, aiming at a better preservation of interimplant alveolar bone.
**Fig. 53-68** Schematic representation of the theoretical advantages of a scalloped implant design: more superficial implant placement, increased bone and soft tissue preservation particularly in the interimplant area, and improved esthetics (in combination with interdental "mini-wings").
These elements are addressed in the form of a respective clinical case presentation, involving a 67-year-old female patient, edentulous in the maxilla (Figs. 53-69 to 53-89). Besides the traditional clinical and radiologic investigation, an in-mouth try-in of the envisioned treatment objective in the form of a set-up of teeth without vestibular denture-type flange is of primary importance (Fig. 53-73). Among other aspects, this approach will allow the visualization of the length of the clinical crowns of the future fixed implant prosthesis, and the evaluation of whether a fixed prosthesis will provide sufficient lip and facial support (Fig. 53-74). A surgical guide, derived from the described tooth set-up, will guarantee that the future implant positions are in accordance with the determined tooth positions. Whenever possible, par-allelism of implants is recommended, as it permits an eventual early or immediate loading approach (Szmukler-Moncler _et al_. 2000; Cooper _et al_. 2001; Andersen _et al_. 2002; Cochran _et al_. 2002), and facili-tates the subsequent clinical and laboratory procedures. Although little scientific evidence exists to indicate how many implants of which dimension and in what position are required for a predictable and long-lasting fixed implant rehabilitation of an edentulous maxilla, some clinical trends – mostly derived from traditional prosthodontic experience – do exist. If one plans to extend the prosthesis to the first molar area, and if the anatomic conditions allow the use of standard-size (length and diameter) implants, between six and eight implants seem reasonable. However, in order to increase the overall prosthetic versatility and to be able to apply the principle of segmenting, which includes the ease of eventual re-interventions in a case of localized complications (Priest 1996; Goodacre _et al_. 1999; Lang _et al_. 2000; Johnson & Persson 2001), eight implants may be con-sidered adequate. The recommended respective positions are on both sides of the jaw: the sites of the central incisors, the canines, the first premolars, and the first molars (Fig. 53-76). This approach will ulti-mately allow the fabrication of four independent three-unit FPDs, with all the related technical and clinical advantages (Figs. 53-78 to 53-89). Some of the scientific data available to date and supporting the concept of smaller segments rather than full-arch splinting will be presented and discussed in Chapter 54.
**Fig. 53-69** Vestibular view of a 67-year-old female patient, edentulous in the maxilla for 18 months. The pre-existing fixed prosthetic rehabilitation had to be removed due to periodontal disease and was replaced by an immediate complete upper denture to which she never adapted. In the mandible a natural dentition is present to the premolar area.
**Fig. 53-70** The corresponding panoramic radiograph reveals – at least as far as the vertical bone volume is concerned – favorable conditions in view of implant therapy in both the upper and the lower posterior jaw.
**Fig. 53-71** The oblique view confirms the presence of an appropriate intermaxillary relationship which is essential for a fixed implant-supported prosthesis.
**Fig. 53-72** On the occlusal view of the edentulous maxilla, one can note overall favorable conditions for implant therapy and the clinical signs of the recently performed tooth extractions.
**Fig. 53-73** During an unforced smile, the height of the smile line and the eventual need for additional lip support, are evaluated. Both parameters are decisive for the selection between a fixed implant prosthesis or an implant overdenture.
**Fig. 53-74** In order to evaluate the feasibility of a fixed implant prosthesis, the clinical try-in of a diagnostic tooth setup is of paramount importance. One should perform this tooth set-up without vestibular denture flange, so that the patient can realize how long the clinical crowns will be.
**Fig. 53-75** A duplicate of the diagnostic tooth set-up in transparent acrylic will serve as a surgical guide. For optimal stability during surgery, the guide is extended to the posterior palate, an area which will not be concerned by the flap elevation.
**Fig. 53-76** Intrasurgical view of the edentulous maxilla, prepared for the insertion of eight implants to support a fixed prosthesis. Particular attention has been paid to achieving optimal parallelism of the implants by means of a respective surgical guide.
**Fig. 53-77** Insertion of a titanium solid screw implant, featuring an SLA surface, in the area of the maxillary left canine.
**Fig. 53-78** Eight weeks after implant surgery, osseointegration is confirmed radiologically and clinically. Screw-retained impression copings are inserted to perform an implant-level impression.
**Fig. 53-79** Prior to the master cast fabrication, color-coded implant replicas (analogues) are secured to the respective impression copings.
**Fig. 53-80** The maxillary master cast features a removable silicon representation of the peri-implant soft tissues.
**Fig. 53-81** After mounting the master cast in a second-generation, semi-adjustable articulator, the most suitable secondary components (abutments) in view of a cementable fixed implant prosthesis are selected.
**Fig. 53-82** Using a silicon key, derived from the diagnostic wax-up, as a guide, the laboratory technician has fabricated the cast metal framework in the form of four independent three-unit segments. Each segment will be supported by two implants.
**Fig. 53-83** The completed ceramo-metal implant prosthesis on the master cast, ready to be inserted in the patient's mouth.
**Fig. 53-84** Prior to cementation of the described ceramometal suprastructure, the secondary implant components (abutments) are tightened to 35 Ncm with a calibrated torque wrench.
**Fig. 53-85** The corresponding clinical view documents that a design similar to that applied in the natural dentition has been used.
**Fig. 53-86** In the mandible the bilaterally shortened arch has been prolonged to the first molar area by means of two fixed cemented ceramo-metal implant prostheses.
**Fig. 53-87** The oblique clinical close-up view of the final implant restoration reveals an acceptable integration both from a functional and an esthetic point of view.
**Fig. 53-88** Finally, an esthetically pleasing result could be achieved by means of a fixed implant-supported prosthesis.
**Fig. 53-89** The 1-year post-operative panoramic radiograph confirms osseointegration and documents that the maxillary prosthesis has been completed in four independent segments.
In conclusion, the concepts and therapeutic modalities do exist nowadays to solve – by means of implants – elegantly as well as predictably a majority of clinical situations requiring the replacement of missing teeth in the esthetic zone, and the most promising novel approaches and perspectives can already be identified on a not too distant horizon.
## Acknowledgments
The authors wish to acknowledge and thank Drs Jean-Paul Martinet, Nicholas Roehrich, and Dimitri Thiébaud (all of them clinicians at the School of Dental Medicine, University of Geneva, and involved in the treatment of some of the patients presented in this chapter) for their contributions. We would also like to thank the laboratory technicians and ceramists Michel Bertossa, Michel Magne, and Alwin Schönenberger, for their expertise and meticulous execution of the implant suprastructures presented in this chapter. Furthermore, our gratitude is extended to Dr. Pascal Magne (Senior Lecturer, University of Geneva) for his competent assistance in development of the schematic illustrations.
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# Chapter 54
# Implants in the Posterior Dentition
Urs C. Belser, Daniel Buser, and Jean-Pierre Bernard
* * *
Basic concepts
General considerations
Indications for implant restorations in the load carrying part of the dentition
Controversial issues
Restoration of the distally shortened arch with fixed implant-supported prostheses
Number, size, and distribution of implants
Implant restorations with cantilever units
Combination of implant and natural tooth support
Sites with extended horizontal bone volume deficiencies and/or anterior sinus floor proximity
Multiple-unit tooth-bound posterior implant restorations
Number, size, and distribution of implants
Splinted versus single-unit restorations of multiple adjacent posterior implants
Posterior single-tooth replacement
Premolar-size single-tooth restorations
Molar-size single-tooth restorations
Sites with limited vertical bone volume
Clinical applications
Screw-retained implant restorations
Abutment-level impression versus implant shoulder-level impression
Cemented multiple-unit posterior implant prostheses
Angulated abutments
High-strength all-ceramic implant restorations
Orthodontic and occlusal considerations related to posterior implant therapy
Concluding remarks and perspectives
Early and immediate fixed implant restorations
* * *
# Basic concepts
## General considerations
The overall favorable long-term survival and success rates reported in the recent literature for osseointegrated implants in the treatment of various types of edentulism (Brånemark _et al_. 1995; Jemt _et al_. 1996; Lindqvist _et al_. 1996; Buser _et al_. 1997, 1998b, 2002; Andersson _et al_. 1998; Eckert & Wollan 1998; Lindh _et al_. 1998; Mericske-Stern 1998; ten Bruggenkate _et al_. 1998; Wyatt & Zarb 1998; Gunne _et al_. 1999; Lekholm _et al_. 1999; Van Steenberghe _et al_. 1999; Wismeijer _et al_. 1999; Behneke _et al_. 2000; Hosny _et al_. 2000; Hultin _et al_. 2000; Weber _et al_. 2000; Boioli _et al_. 2001; Gomez-Roman _et al_. 2001; Kiener _et al_. 2001; Mengel _et al_. 2001; Oetterli _et al_. 2001; Zitzmann _et al_. 2001; Bernard & Belser 2002; Haas _et al_. 2002; Leonhardt _et al_. 2002; Romeo _et al_. 2002) permit consideration of dental implants as one of the reliable therapeutic modalities during the establishment of any prosthetic treatment plan. In numerous clinical situations implants can clearly contribute to a notable simplification of therapy, frequently enabling removable prostheses to be avoided, keeping it less invasive with respect to remaining tooth structure or rendering the treatment both more elegant and versatile as well as more predictable (Belser _et al_. 2000).
As part of a textbook focusing essentially on clinical periodontics, this chapter will address primarily implant therapy performed in the posterior segments of partially edentulous patients. In this context, the use of implants may often significantly reduce the inherent risk of a "borderline" conventional tooth-borne fixed prosthesis (e.g. compromised or missing "strategic" abutment teeth, long-span fixed partial dentures, cantilevers) by implementing the principle of segmentation. It is currently widely accepted that – in comparison with extended splinted prosthetic segments – small ones are preferable as they are easier to fabricate, generally provide improved "passive fit" and marginal fidelity, offer better access for the patient's oral hygiene, and ultimately are less complicated to handle where there is need for re-intervention. When it comes to treatment planning in general, and to the choice _implant versus tooth-borne fixed partial denture (FPD) versus tooth_ in particular, the related decision-making criteria should be essentially derived from scientific evidence and objective prosthetically oriented risk assessment in the broad sense, including additional parameters such as simplicity, cost effectiveness, and quality of life. Beyond any doubt, the advent of osseointegration has had a fundamental impact on the therapeutic approach and strategies implemented today in the field of prosthetic rehabilitation of the compromised posterior dentition. The implant statistics of the University of Geneva School of Dental Medicine, for example, reveal that from April 1989 until May 2002 more than 3600 implants of 6–12 mm length were inserted in about 1400 patients presenting with different types of edentulism (Figs. 54-1, 54-2). This treatment method is increasingly applied worldwide and has had a tremendous influence on traditional prosthodontic attitudes (Beumer _et al_. 1993; Zarb & Schmitt 1995; Tarnow _et al_. 1997; Zitzmann & Marinello 1999; Belser _et al_. 2000; Schwarz-Arad & Dolev 2000; Brägger _et al_. 2001; Deporter _et al_. 2001; Zitzmann & Marinello 2002). Since most of the established dental implant systems today comprise a wide range of mostly screw-type implants with different diameters and dimensions to replace missing premolars and molars (Fig. 54-3), the versatility of implant therapy in the load-carrying part of the dentition of partially edentulous patients has been significantly enhanced.
**Fig. 54-1** University of Geneva implant statistics, 1989–2002. Indications.
**Fig. 54-2** University of Geneva implant statistics, 1989–2002. Implant length distribution.
**Fig. 54-3** Different implant diameters are available for the replacement of posterior teeth.
Numerous other indications have been added to the so-called classical indications for the use of implants, i.e. severely atrophied edentulous jaws, missing teeth in otherwise intact dentitions (congenitally missing teeth; tooth loss due to trauma or due to a localized endodontic/restorative/periodontal complication or failure), and the distally shortened dental arch (particularly when premolars are missing). Among these other indications one should mention all the strategies aiming at either reducing the prosthodontic risk in general or rendering the treatment simpler and more cost effective. Virtually no limits for the placement of implants seem to exist any more owing, for example, to advanced bone augmentation techniques, comprising anterior sinus floor elevation and distraction osteogenesis (Buser _et al_. 1993, 1995, 1996, 1998a, 2002; Chiapasco _et al_. 1999, 2001a; Buser & von Arx 2000; Simion _et al_. 2001; von Arx _et al_. 2001a,b).
When it comes to the technique of placing implants in the posterior segments of the jaws, a one-step non-submerged surgical protocol can be associated with notable advantages. On the one hand, healing of the peri-implant soft tissues occurs simultaneously with osseointegration, and on the other hand the location of the junction between the implant shoulder and the secondary components is normally positioned close to the mucosal surface. It is ultimately the position of this junction which determines the apical migration of the peri-implant epithelium and the crestal bone level, once the so-called biologic width has been established (Abrahamson _et al_. 1997; Hermann _et al_. 1997, 2000, 2001a,b; Lindhe & Berglundh 1998; Engquist _et al_. 2002; Wyatt & Zarb 2002). Positioning of the transition between implant shoulder and secondary components at the level of the mucosa rather than at the crestal bone also represents a biomechanical advantage, as it contributes to the reduction of the lever effect and resulting bending moments acting on the junction between implant and suprastructure. This is clinically relevant, as one should be aware of the existence of an increasing body of evidence reporting technical complications, such as loosening/fracture of screws or fracture of components/veneers, related to implant-supported prosthetic suprastructures (Lundgren & Laurell 1994; Wie 1995; Hebel & Gajjar 1997; Rangert _et al_. 1997; Bosse & Taylor 1998; Glantz & Nilner 1998; Taylor 1998; Brägger 1999; Goodacre _et al_. 1999; Isidor 1999; Keith 1999; Schwarz 2000; Johnson & Persson 2001). Besides mechanical types of complications, a number of other conditions that are rather biologic in nature, for example peri-implantitis, are reported in the recent literature (Ellegaard _et al_. 1997a,b; Ellen 1998; Lang _et al_. 2000; Brägger _et al_. 2001; Quirynen _et al_. 2001, 2002). As these are addressed in detail in another chapter, we will only focus on aspects related to fixed posterior implant restoration design and maintenance.
It is the aim of this chapter to present clinically oriented guidelines and procedures for implant therapy of various types of edentulism located in the load-carrying part of the dentition, addressing primarily the partially dentate patient and mainly focusing on fixed implant-supported prostheses.
## Indications for implant restorations in the load carrying part of the dentition
When it comes to partial edentulism in the posterior segments of the jaws, implants are increasingly used either to preserve sound mineralized tooth structure or to avoid removable partial dentures (RPDs) and high-risk conventional fixed partial dentures (FPDs). This includes situations with missing teeth in otherwise intact dentitions (Figs. 54-4, 54-5), the distally shortened dental arch (Figs. 54-6 to 54-8), extended edentulous segments, missing "strategic" tooth abutments, and structurally, endodontically or periodontally compromised potential abutment teeth (Table 54-1).
**Fig. 54-4** Occlusal view of the mandible of a 22-year-old male patient. All premolars are congenitally missing, the remainder of the dentition is intact.
**Fig. 54-5** Final view after insertion of four implants, restored with cemented metal–ceramic suprastructures.
**Fig. 54-6** Bilaterally distally shortened dental arch in the mandible of a 66-year-old female patient.
**Fig. 54-7** Four implants have been inserted to lengthen the arch bilaterally to the region of the first molars.
**Fig. 54-8** Five premolar-sized metal–ceramic elements were used to restore the four implants.
The rapid advance in terms of the broad utilization of dental implants is not exclusively based on the associated favorable long-term reports for this treatment modality. Other parameters such as purely "mechanical" advantages and the availability of prefabricated components and auxiliary parts, which in turn contribute notably to the simplification of the treatment, had a significant impact on current con-cepts and strategies as well (Table 54-2). Furthermore, clinical decision making based on prosthetically oriented risk assessment (Table 54-3), frequently leads to the need for an increased number of abutments. The objective is to reduce the overall risk associated with a given prosthetic solution on the one hand, and to implement the principle of segmenting on the other.
A representative clinical example is given in Figs. 54-9 and 54-10. Instead of a conventional five-unit FPD, replacing the missing maxillary left first and second premolars as well as the absent first molar, three implants have been inserted. This approach allowed the avoidance of a long-span bridge, a full coverage preparation of the second molar, and an associated surgical crown-lengthening procedure. The additional cost related to the three implants was justified by an overall reduced prosthodontic risk. The question about adequate number, size, and distribution of implants will be addressed later in this chapter. Prosthetically oriented risk assessment comprises the comprehensive evaluation of potential natural abutment teeth, including their structural, restorative, periodontal, and endodontic status. Several well documented treatment modalities are often possible to replace missing posterior teeth, so this objective evaluation is of primary importance and represents an ever increasing challenge to the clinician. This is illustrated by a maxillary posterior segment where both the first premolar and the first molar were missing (Figs. 54-11 to 54-14). The insertion of a five-unit tooth-borne FPD was discarded because of its too invasive nature related to the intact canine, and owing to a slightly questionable status of the endodontically treated second premolar in view of its eventual use as so-called "peer-abutment". Finally, an implant has been placed at the site of the missing first premolar and subsequently restored with a single-unit restoration. As the proximity of the maxillary sinus at the location of the missing first molar would have required a grafting procedure to make an implant installation possible, a three-unit tooth-supported FPD was ultimately chosen, after having duly discussed the respective advantages and shortcomings with the patient. Having attributed a "strategic value" to the moderately compromised second premolar by using it as abutment of a short-span bridge, there was still a difficulty in consistently establishing clinical treatment plans that were fully based on scientific evidence.
**Fig. 54-9** Maxillary occlusal view displaying natural and implant abutments prior to the insertion of an extended porcelain-fused-to-metal restoration. In order to avoid a highrisk long-span FPD, three implants have been added in the left posterior segment.
**Fig. 54-10** A similar restorative design has been chosen for both natural and implant-supported metal–ceramic suprastructures.
**Table 54-1** Indications for posterior implants
• Replacement of missing teeth in intact dentitions (e.g. congenitally missing premolars), i.e. preservation of tooth structure
---
• Avoidance of removable partial dentures (RPDs)
• Increase of the number of abutments:
• Reduction of the prosthetic risk
• Application of the principle of segmenting
• Ease of eventual reinterventions
• Maintenance of pre-existing crowns and FPDs
• Following prosthetic complications and failures
**Table 54-2** Impact of dental implants related to the treatment of posterior partial edentulism
• Favorable overall long-term results
---
• Preservation of mineralized tooth structure
• Mechanical" advantages:
• Commercially pure (c.p.) titanium (biocompatibility, mechanical properties, no risk for caries)
• Reproducible, prefabricated ("machined") primary, secondary and tertiary components and auxiliary parts
• Simplified clinical and laboratory protocols
**Table 54-3** "High risk" conventional fixed partial dentures (FPDs)
• Long-span fixed partial bridges
---
• Cantilever units (mainly distal extensions)
• Missing "strategic" tooth abutments
• Structurally/periodontally/endodontically compromised tooth abutments
• Reduced interarch distance
• Presence of occlusal parafunctions/bruxism
**Fig. 54-11** Pre-operative radiograph of the left maxilla, revealing two missing dental elements. One should note in particular an intact canine, a structurally reduced second premolar, and an extended recessus of the sinus in the area of the missing first molar.
**Fig. 54-12** Vestibular view of the prosthetic rehabilitation of the maxillary left quadrant: an implant-supported singletooth restoration on the site of the first premolar, and a threeunit tooth-borne FPD to replace the missing first molar.
**Fig. 54-13** The post-operative radiograph documents that an endodontic revision has been performed on the second premolar prior to its restoration with an adhesive carbonfibre-post based build-up and a metal–ceramic crown (bridge retainer).
**Fig. 54-14** An identical prosthetic design has been applied for both the implant-supported and the tooth-supported restoration.
**Fig. 54-15** Ad hoc radiograph of the upper right posterior sextant. One notes the presence of a structurally compromised second premolar. The treatment of that particular root would require build-up and crown lengthening (margin exposure, creation of an adequate ferrule) which in turn would negatively affect the adjacent teeth.
Still under the influence of the high level of predictability and longevity reported for implant therapy, the clinician is currently not only pondering implant-borne restorations versus conventional FPDs, but increasingly implant versus maintaining a compromised tooth (Figs. 54-15, 54-16). In this particular clinical case, the evaluation focused on whether or not it was objectively opportune to restore the structurally compromised root of a maxillary second premolar. This would have required – after elimination of the decayed dentin – a surgical crown-lengthening procedure to create access to the margin, which in turn would have included the risk for an adverse effect (furcation proximity of the adjacent first molar) on the neighboring teeth. Furthermore, a three-unit FPD was out of the question for obvious reasons. Based on this rationale and in the context of a more comprehensive analysis of the situation, it was finally decided to extract a _per se_ treatable root and to replace it by an implant. One should never forget, however, that this trend to consider, under certain circumstances, an implant as a better solution than "acrobatically" treating a severely compromised tooth, calls for well defined evidence-based respective criteria and represents a non-negligible ethical responsibility for the clinician.
**Fig. 54-16** The post-operative radiograph documents that the root of the second premolar has been replaced by a singletooth implant restoration. In particular, the pre-existing metal–ceramic crown on the first molar could be maintained by this approach.
## Controversial issues
Despite the ever-growing body of scientific evidence indicating that implant therapy in the partially edentulous patient is an overall highly predictable treatment modality, several conceptional issues remain controversial to date (Table 54-4). These controversial issues include open questions addressing adequate number, size, and distribution of implants for optimal therapy of a given type and configuration of partial edentulism, as well as parameters related to occlusion and occlusal materials, to implant axis, to the minimal acceptable ratio between suprastructure height and implant length, and – last but not least – related to questions focusing more specifically on the mechanical aspects and requirements of posterior implant prosthodontics. Among these, the kinds of connection between implant and abutment have to be mentioned in particular. Most of these questions will be discussed in the remainder of this chapter, at length where possible and appropriate, or more superficially when solid information is missing or when the topic is more adequately covered by other authors in this book.
**Table 54-4** Controversial issues related to posterior implant restorations
• Adequate number, size (length/diameter), configuration and distribution of implants
---
• Cemented versus screw-retained (transocclusal/transverse screw retention)
• Single units versus splinted adjacent implant restorations
• Longest possible versus shorter implants
• Impact of implant axis
• Optimal implant shoulder sink depth
• Minimal ratio between implant length and suprastructure height
• Combination of natural teeth and implants in the same restoration
• Design of the optimal abutment-to-implant connection
• Implant-specific occlusal concepts, including occluding restorative materials, non-axial loading, type of guidance during mandibular excursions
• Healing times prior to functional loading (immediate/early/delayed)
• Significance of offset/staggered implant positioning
# Restoration of the distally shortened arch with fixed implant-supported prostheses
As pointed out earlier in this chapter, from 1989–2002 the distally shortened arch represented the most frequent indication for the use of implants at the University of Geneva School of Dental Medicine. In fact, out of a total of 3638 implants, almost 1500 were placed in distally shortened arches, with close to 1000 implants inserted in the mandible and about 500 in the posterior maxilla (Fig. 54-1). Implants were primarily used when premolars were also missing. Whenever possible, the adopted treatment strategy consisted of restoring the shortened dental arch to the region of the first molars. Occasionally, implant therapy was restricted to the premolar area, according to the principles of the well established premolar occlusion concept, or extended to the second molar area if an antagonistic contact had to be established for an opposing natural second molar.
## Number, size, and distribution of implants
It is still unclear to date how many implants of which dimension at which location are required to optimally rehabilitate a given edentulous segment in the load-carrying part of the dentition. Several different respective recommendations and related strategies are currently in use, mostly derived from traditional prosthodontic experience and attitudes, and based on so-called clinical experience and common sense rather than on solid scientific evidence. In defense of the situation one should be aware, however, that it is often difficult to design and carry out randomized clinical trials evaluating exclusively and without interference one specific parameter of conceptual relevance.
In a situation where the canine is the most distal remaining tooth of a dental arch, at least five different options can be taken into consideration if one plans to replace the missing teeth up to the first molar area (Figs. 54-17 to 54-21). These include the replacement of each missing occlusal unit by one implant (Fig. 54-17), a mesial and a distal implant to support a three-unit FPD with a central pontic (Fig. 54-18), two distal implants to permit the insertion of a three-unit FPD with a mesial cantilever (Fig. 54-19), two mesial implants to sustain a three-unit FPD with a distal cantilever (Fig. 54-20) and, finally, only one distally inserted implant in view of a four-unit FPD combining implant and natural tooth support (Fig. 54-21).
**Fig. 54-17** Schematic representation of the distally shortened dental arch. One therapeutic option consists of replacing each missing occlusal unit up to the first molar area with an implant.
**Fig. 54-18** An alternative option would be the replacement of the three missing occlusal units by two implants to support a three-unit suprastructure with a central pontic.
**Fig. 54-19** In a case of an inadequate bone volume in the area of the missing first premolar, the placement of two distal implants may be considered, leading to a three-unit suprastructure with a mesial cantilever.
**Fig. 54-20** In a case of an inadequate bone volume in the area of the missing first molar, the placement of two mesial implants may be considered, leading to a three-unit suprastructure with a distal cantilever.
**Fig. 54-21** In a case of inadequate bone volume in the area of the two missing premolars, the placement of a distal implant may be considered, leading to a four-unit suprastructure with a mixed (tooth and implant) support.
As far as the recommendation to use premolar-sized units for implant-borne posterior FPDs is concerned, it has proven its practical validity in more than 10 years of clinical experience (Buser _et al_. 1997; Bernard & Belser 2002). In fact, a crown featuring a mesio-distal diameter of 7–8 mm at its occlusal surface allows the optimal generation of a harmonious axial profile, gradually emerging from the standard implant shoulder (diameter 4–5 mm on average) to the maximum circumference. In addition, the width of the occlusal table is confined, thereby limiting the risk for unfavorable bending moments to the implant–abutment–suprastructure complex (Belser _et al_. 2000).
Based on an increasing body of scientific evidence, most clinicians' first choice represents the mesial and distal implant and the respective FPD with the central pontic (Fig. 54-22). Prospective long-term multicenter data (Buser _et al_. 1997; Bernard & Belser 2002) have confirmed the efficacy and predictability of this specific modality. In fact, it permits the defined treatment objective with a minimal number of implants and associated costs. Although presently still lacking formal evidence at the level of prospectively documented, randomized clinical trials, it appears from clinical experience that the use of two implants to support a four-unit FPD with two central pontics (Figs. 54-23, 54-24) may be adequate in certain clinical situations. Clinicians tend to use this approach in the presence of favorable bone conditions, permitting standard-size or wide-diameter implants with appropriate length (i.e. 8 mm or more).
**Fig. 54-22** (a) Occlusal view of a cemented three-unit metal–ceramic FPD, supported by a mesial and a distal implant. (b) The corresponding 3-year follow-up radiograph confirms stable conditions at the implant to bone interface of the two 12 mm solid screw implants.
**Fig. 54-23** Occlusal view of a cemented four-unit metal–ceramic FPD supported by a mesial and a distal implant.
**Fig. 54-24** The related 2-year follow-up radiograph documents that at the distal site a 10 mm solid screw implant with an increased diameter ("wide-body implant") has been used.
If the alveolar bone crest dimension is also sufficient in an oro-facial direction, the utilization of wide-diameter/wide-platform implants is preferred. Due to their increased dimensions a more adapted suprastructure volume and improved axial emergence profile of the implant restoration – when compared to a so-called premolar unit – can be achieved in the molar area (Figs. 54-25 to 54-28). By this token the intercuspation with an opposing natural molar is also facilitated.
## Implant restorations with cantilever units
There is strong evidence in the relevant dental literature that cantilever units – in particular distal extensions – of conventional tooth-borne FPDs are associated with a significantly higher complication rate when compared to FPDs featuring a mesial and a distal abutment and a central pontic. Respective failure rates could be attributed to decisive factors such as non-vital abutment teeth as well as specific occlusal conditions such as a reduced interarch distance and/or occlusal parafunctions (Glantz & Nilner 1998). These authors concluded in their review of the current relevant literature that risks were lower for mechanical failures with cantilevered implant-borne reconstructions than with comparable conventional fixed situations. Risks, however, do exist. As loss of retention, which was one of the frequent complications encountered on conventional cantilevered prostheses, can easily be prevented when it comes to implant-supported restorations of this type, the latter seem to be a viable alternative in cases where the local alveolar bone crest conditions do not allow the insertion of an implant at the most favorable location. In such situations the clinician has to ponder whether a bone augmentation procedure can be objectively justified or if the risk for complications of a more simple, straightforward approach can be considered low.
**Fig. 54-25** Occlusal view of a bilaterally distally shortened mandibular arch. Two implants have been placed on either side to restore the arch to the area of the first molars. The two distal implants feature an increased diameter, better suited for the replacement of a missing molar.
**Fig. 54-26** The master model comprises color-coded aluminum laboratory analogues at the implant sites, facilitating the technician's work in view of the suprastructure fabrication. This is in contrast to the site of the prepared natural abutment.
**Fig. 54-27** Once the metal–ceramic restorations are completed, no noticeable design difference between implant-supported and tooth-supported suprastructures is apparent.
**Fig. 54-28** The respective clinical view confirms an acceptable integration of the four implant restorations in the existing natural dentition.
The 6-year clinical and radiographic follow-up of a three-unit FPD featuring a mesial cantilever is presented in Figs. 54-29 and 54-30.
## Combination of implant and natural tooth support
There is general agreement that, from a purely scientific point of view, the combination of implants and natural teeth to support a common FPD is feasible. Clinical studies reporting prospectively documented long-term data did not show adverse effects of splinting teeth to implants (Olsson _et al_. 1995; Gunne _et al_. 1997, 1999; Hosny _et al_. 2000; Lindh _et al_. 2001; Naert _et al_. 2001a,b; Tangerud _et al_. 2002). The issue of connecting implants and teeth by means of rigid or nonrigid connectors, however, remains controversial to date, but intrusion of natural roots has been reported in the literature as a potential hazard of non-rigid connection (Sheets & Earthman 1993). Most of the recently published respective literature reviews conclude with the general clinical recommendation that one should avoid, whenever possible, the direct combination of implants and teeth as it may frequently lead to a more complicated type of prosthesis. If there is no viable alternative available, a rigid type of connection is preferred to prevent an eventual intrusion of the involved abutment teeth (Lundgren & Laurell 1994; Gross & Laufer 1997).
Furthermore, it has been demonstrated that despite the fundamental difference between an osseointegrated implant and a tooth surrounded by a periodontal ligament, the assumption that when these two structures are combined, the entire occlusal load will ultimately go to the implant and hence create an unfavorable "cantilever-type" situation, is not valid from a scientific point of view (Richter, Isidor, Brägger). In fact, under normal function, such as during mastication, the tooth abutment is similarly load-bearing. This may change, however, during severe occlusal parafunctions, like nocturnal bruxism.
**Fig. 54-29** Six-year clinical follow-up view of a mandibular three-unit FPD supported by two distal implants.
**Fig. 54-30** The 6-year radiograph displays stable bony conditions around the two implants supporting a cemented suprastructure with a premolar-sized mesial cantilever unit.
## Sites with extended horizontal bone volume deficiencies and/or anterior sinus floor proximity
It is not infrequent that distally shortened dental arches do not feature an adequate local bone volume at the prospective implant sites. This may refer to bone height, bone width, alveolar bone crest axis or to the vicinity of noble structures such as the mandibular alveolar nerve canal or the anterior part of the maxillary sinus. Often a combination of several of the mentioned limitations is encountered. As implant insertion is clearly a three-dimensional surgical and restorative procedure on the one hand, and as "restoration-driven" rather than "bone-driven" implant placement is widely recommended on the other hand, a meticulous presurgical site analysis – based on the envisioned treatment objective – is of primary importance. In order to keep the treatment as easy and finally also as cost-effective as possible, one should comprehensively evaluate whether a minor deviation from the ideal implant position could be considered acceptable, i.e. not leading to a compromise which might adversely affect predictability, longevity, and/or subjective comfort. This approach may still permit a professionally defendable result in some cases, but without a complexity of treatment that would be difficult to bear by some patients.
Advanced invasive procedures like lateral bone augmentation, anterior sinus floor elevation, alveolar ridge splitting or distraction osteogenesis, require a high level of skills and respective experience and hence should only be deployed if the relation between benefit and risk/cost is soundly balanced (Buser _et al_. 1993, 1995, 1996, 1999, 2002; Chiapasco _et al_. 1999, 2001a; Simion _et al_. 2001; von Arx _et al_. 2001a,b; Zitzmann _et al_. 2001).
In this specific context, a complex implant treatment of a 67-year-old male patient whose most distal remaining tooth in the left maxilla was an endodontically treated canine, is shown in Figs. 54-31 to 54-44. Pre-operative diagnosis revealed the necessity to perform – according to a staged approach – first a combined lateral bone augmentation procedure and anterior sinus floor elevation and, after a 6 month healing period, the insertion of implants. For the sinus floor elevation the so-called "trap-door" technique was used and the created space grafted with autogenous bone chips and BioOss®. The lateral bone augmentation comprised the fixation of a large block graft in the area of the first premolar. After application of an e-PTFE barrier membrane, primary wound closure was achieved by sectioning of the periosteum of the respective mucoperiosteal flap. This often leads to a lack of attached keratinized mucosa on the vestibular aspect of the surgical site, which has to be subsequently corrected, most conveniently at the moment of implant placement. When it comes to sites that have been previously grafted, the majority of surgeons advocate inserting one implant per missing occlusal unit. This attitude appears to be based more on the reflection that the overall heaviness of the approach would largely justify this additional security and/or on the hypothesis that augmented bone may not have exactly the same "load-bearing" capacity as the pre-existing bone, than on irrefutable scientific evidence. Accordingly, three adjacent screw-type implants – the most distal one an increased-diameter titanium screw – had been placed and subsequently restored by a three-unit splinted metal-ceramic FPD (Figs. 54-38 to 54-44).
**Fig. 54-31** Initial radiograph of the maxillary left posterior segment of a 67-year-old male patient. The canine represents the most distal remaining tooth element. Note the marked extension of the anterior recessus of the sinus.
**Fig. 54-32** After elevation of a mucoperiosteal flap, an insufficient horizontal bone volume in the region of the premolars becomes apparent.
**Fig. 54-33** In view of an anterior sinus floor elevation procedure, the first step for a respective osteotomy is performed. Attention is given not to perforate the Schneiderian membrane.
**Fig. 54-34** After the so-called "trap-door" procedure in the region of the maxillary sinus, an autogenous bone block graft, harvested from the patient's retromolar area, is positioned and then immobilized by a fixation screw at the location of the missing first premolar.
**Fig. 54-35** The lateral bone augmentation procedure is completed by adding a combination of autogenous bone chips, bone slurry, and BioOss®.
**Fig. 54-36** Prior to flap repositioning and suturing, a barrier membrane is applied.
**Fig. 54-37** One month after primary wound closure and uneventful healing, the involved soft tissues have recovered their normal appearance.
**Fig. 54-38** Eight months following the combined anterior sinus floor elevation and lateral bone augmentation procedure, the site is reopened and three implants are inserted.
**Fig. 54-39** In order to increase the amount of keratinized mucosa on the vestibular aspect of the implants, the flap is repositioned accordingly. The resulting deficiency on the palatal aspect is compensated for by means of a connective tissue being part of the partial-thickness flap.
**Fig. 54-40** Three months after implant placement, favorable peri-implant soft tissue conditions have been re-established.
**Fig. 54-41** The corresponding radiograph confirms successful osseointegration of the three implants that are mostly located in augmented bone.
**Fig. 54-42** In a case of implant shoulder location compatible with cementation, respective solid abutments are selected and tightened to 35 Ncm with a calibrated torque wrench.
**Fig. 54-43** Clinical view of the final three-unit metal–ceramic implant suprastructure, featuring a flat and continuous emergence profile and adequate access for interimplant oral hygiene.
**Fig. 54-44** The 4-year follow-up radiograph confirms stable conditions at the osseointegrated interface.
Results from a recently published longitudinal clinical study (Buser _et al_. 2002) on 40 consecutively enrolled patients, who were first treated with a lateral bone augmentation procedure and subsequently, in a second stage, received implants inserted in the previously augmented area. Implants could finally be placed as planned in all the treated sites, and a 97% success rate was revealed at the 5-year clinical and radiographic follow-up examination. It was thus concluded that lateral bone augmentation is indeed a predictable procedure and that implants subsequently inserted in augmented sites do have similar success rates to implants placed in comparable non-augmented sites.
# Multiple-unit tooth-bound posterior implant restorations
## Number, size, and distribution of implants
When it comes to implant therapy in extended posterior edentulous segments confined mesially and distally by remaining teeth, the question about optimal number, size, and distribution of implants has to be raised again. Among the key parameters to be addressed during the decision-making process are the mesio-distal dimension of the edentulous segment, the precise alveolar bone crest volume (including bone height and crest width in an orofacial direction), the opposing dentition (premolars or molars), interarch distance and specific occlusal parameters, as well as the periodontal, endodontic, and structural conditions of the neighboring teeth.
One feasible approach consists of segmenting the edentulous space in premolar-size units of approximately 7 mm of mesio-distal diameter at the level of the occlusal plane, and of approximately 5 mm at the prospective implant shoulder. On posterior locations, clinicians increasingly prefer a rather superficial implant shoulder location or in many instances even a supramucosal one, so the respective measurements can be carried out at the crest level of study casts. It is important during this process to anticipate a minimal distance between implant shoulders of approximately 2 mm, and between a natural tooth and an implant of about 1.5 mm (to be measured at the interproximal soft tissue level). Again, the treatment objective, i.e. a long-lasting implant-supported FPD, should be predictably reached (1) with optimal efficacy and (2) with a minimum of invasiveness and cost. The still existing controversy of whether each missing occlusal unit should be replaced by one implant or whether a minimal number of implants should be used, has already been addressed earlier in this chapter.
**Fig. 54-45** Schematic representation of a tooth-bound posterior edentulous segment, restored by two implants and a three-unit FPD with a central pontic.
**Fig. 54-46** In the case of three missing occlusal units, an implant-supported FPD with a central pontic (approximately 7 mm in width) may be considered as a viable solution.
In the case of three missing occlusal units and in the absence of other particular restrictive conditions such as limited local bone volume, the authors recommend the insertion of a mesial and a distal implant to support a three-unit FPD with a central pontic (Fig. 54-45). This approach permits the fabrication of three metal–ceramic elements featuring a mesio-distal diameter of about 7 mm each. Based on an average implant shoulder dimension of approximately 5 mm, one can anticipate a gradually increasing, harmonious emergence profile from the implant shoulder to the occlusal surface. In order to satisfy the remaining important dimensional conditions, i.e. respecting the minimal distance between adjacent implants and in between teeth and implants, one needs to dispose of a minimal total mesio-distal gap distance of 21–22 mm (Fig. 54-46).
In the case of two missing occlusal units, one should try as a general rule to select the largest possible implant diameters with respect to the total mesio-distal distance of the given tooth-bound edentulous segment. Decisive parameters are again interimplant distance and space between implants and adjacent teeth, as well as oro-facial crest width at the two prospective implant sites. For a total gap diameter of about 14–15 mm, two standard-size implants are most suitable (Fig. 54-47), while for one of 17 to 18 mm the combination of one standard and one wide-diameter/wide-platform implant is considered adequate (Fig. 54-48). It goes without saying that the latter choice also requires the respective oro-facial bone volume.
**Fig. 54-47** If a given tooth-bound edentulous space only permits the insertion of two adjacent implants, a minimal interimplant distance of 2 mm and a minimal implant-totooth distance of 1.5 mm (at the interproximal soft tissue level) should be respected.
**Fig. 54-48** In the presence of a mesio-distal gap width of approximately 17 mm, one may consider the combination of a standard and an increased-diameter ("wide-neck") implant. The same minimal interimplant and implant-to-tooth distances have to be respected.
These are just frequently encountered clinical examples, but in the function of other morphology and dimensions of edentulous tooth-bound segments, additional approaches and implant combinations may be envisioned. Two such clinical situations are presented in Figs. 54-49 to 54-52 and Figs. 54-53 to 54-55. In the first case, the gap diameter required the two adjacent implants to be spaced wider than the normally advocated interproximal 2 mm. The laboratory technician compensated for this excess of space with a root-imitation pontic which in turn provided an excellent guide facilitating the use of an interdental brush (Fig. 54-49). In the second case, only the placement of three standard-size implants was possible due to a restricted bone volume in orofacial direction. Again, the technician could optimally distribute the different restoration volumes but still comply with basic prerequisites such as a flat axial emergence profile and optimal access for the patient's oral hygiene (Figs. 54-53, 54-54).
**Fig. 54-49** Vestibular aspect of a metal–ceramic restoration supported by two screw-type implants. Due to an excess of mesio-distal space, the implants have been separated by approximately 4 mm. Instead of a traditional pontic, a root imitation has been performed close to the distal implant, providing an adequate guide for an interdental brush in view of an efficient plaque control at the marginal area of the implant restoration.
**Fig. 54-50** With respect to cleanability, the respective prosthesis design is clearly visible on the post-operative radiograph.
**Fig. 54-51** The corresponding master model visualizes the different dimensions and distances involved in this individual case.
**Fig. 54-52** On an oblique view the vestibular axial profile of the implant restoration becomes visible. Soft tissue (cheek and tongue) support and harmony with adjacent teeth are of paramount importance.
**Fig. 54-53** Buccal view of an extended edentulous right mandibular tooth-bound gap treated with an implant restoration. In the pontic area a design favoring the efficacy of an interdental brush close to the implant margins has been applied.
**Fig. 54-54** The related radiograph illustrates the chosen design in the pontic area in terms of access to and efficacy of interproximal plaque control.
**Fig. 54-55** Occlusal view of the completed 4-unit implant-borne fixed porcelain-fused-to-metal prosthesis.
**Table 54-5** Splinting of multiple adjacent posterior implants
Parameters to consider:
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• Access for oral hygiene
• Marginal adaptation/"passive fit"
• Technical simplicity/ease of eventual reinterventions
• "Overload" of the osseointegrated interface
• "Rotational forces" on implant components
• Screw-loosening/fatigue fractures
## Splinted versus single-unit restorations of multiple adjacent posterior implants
Another persisting controversial issue relates to the question whether multiple adjacent implants in the load-carrying part of the dentition should support splinted or segmented single-unit restorations (Table 54-5). There still appears to be a confrontation between rather "biological" considerations versus more "mechanical" thinking.
Generally speaking, the biologically oriented considerations, insisting on easy access for oral hygiene and optimal marginal adaptation, represent probably the more scientifically-based point of view. Clinicians advocating splinting of multiple adjacent implants do so primarily for mechanical reasons. They hypothesize that this approach decreases forces and force moments at the level of the suprastructures and the various underlying implant components, and that relatively frequent mechanical complications such as screw-loosening and fractures may be significantly reduced or prevented by this measure. The related literature does not at present provide a clear answer, as randomized long-term clinical trials addressing this particular parameter are still scarce. Some more general reports do exist, however, addressing mainly type and frequency of mechanical complications (Goodacre _et al_. 1999).
Among the frequently forwarded arguments to plead the case of splinting are reduced-diameter (Figs. 54-56 to 54-59) or short (i.e. less than 8 mm) implants, implants inserted in low-density bone, implants placed in augmented or grafted (e.g. after anterior sinus floor elevation) bone, or implant restorations in the posterior segments of patients with verified notable occlusal parafunctions or bruxism. One should be aware, however, that the majority of these arguments are primarily based on clinical opinions and eventually common sense, and that to date they lack formal scientific evidence. In fact, there is increased indication, derived from prospective multicenter studies (although not addressing this parameter in particular), that splinting does not appear to be a prerequisite for preventing excessive crestal bone resorption or even loss of osseointegration. Nowadays, the authors would seriously reconsider their respective choice related to the suprastructure design presented in Figs. 54-60 and 54-61. In the presence of standard-size (i.e. addressing both diameter and length) implants, which are placed in normal density, original (non-augmented or grafted) bone, single-unit restorations are definitely recommended as they comply better with the various parameters that are important from a more biologic point of view, as demonstrated by the clinical example presented in Figs. 54-62 and 54-63.
**Fig. 54-56** The implant shoulder-abutment complex of the three left maxillary posterior implants has been prepared with fine-grain diamond burrs under abundant water cooling in order to facilitate the configuration of the related suprastructure. Particular emphasis was given to margins following closely the scalloped course of the soft tissue.
**Fig. 54-57** In a case of reduced-diameter implants, splinting of adjacent units may reduce the risk for technical complications. A metal framework try-in prior to the application of the ceramic veneering may help to detect and eliminate an eventual non-passive fit at an early stage.
**Fig. 54-58** The vestibular view of the final metal–ceramic restoration illustrates the impact on esthetics of a metal margin. This aspect should be discussed with the patient before treatment. In case of a high smile line, one may consider an increased sink depth during implant surgery.
**Fig. 54-59** On the 1-year follow-up radiograph an acceptable marginal fidelity can be assessed.
**Fig. 54-60** Occlusal view of a right maxillary posterior threeunit implant restoration featuring premolar-sized segments.
**Fig. 54-61** The corresponding follow-up radiograph confirms acceptable peri-implant conditions.
**Fig. 54-62** Occlusal view of three independent, implantsupported fixed metal–ceramic restorations in the right posterior mandible.
**Fig. 54-63** As confirmed by the follow-up radiograph, an increased (more molar-like) dimension has been given to the most distal restoration, despite the fact that a standard-sized implant had to be used for restricted bone volume reasons.
# Posterior single-tooth replacement
At the time when most implant systems had basically only one "standard" dimension at disposition, this corresponded to approximately 4–5 mm at the implant shoulder and thus was optimally suited for premolar-size restorations, featuring a continuously increasing (towards coronally) flat axial emergence profile and a mesio-distal diameter of about 7–8 mm at the occlusal surface. Clinicians were not infrequently faced with posterior single-tooth sites, however, that did not comply with these dimensions, for example in the case of missing first molars or after the loss of persisting deciduous (primary) second molars. As a consequence, the resulting implant restorations featured either unfavorable excessive interproximal overcontour or wide open embrasures. The first situation was difficult to clean, while the second led to undesired food retention (impaction). Nowadays most of the leading implant manufacturers offer wide-body/wide-platform implants designed for the replacement of multi-rooted teeth (Fig. 54-3).
**Fig. 54-64** Occlusal view of a single-tooth implant restoration replacing a missing mandibular right second premolar.
## Premolar-size single-tooth restorations
When it comes to posterior single-tooth gaps that correspond dimensionally to an average premolar, standard-size screw-form implants are well suited. The respective implant dimensions which include both the intrabony part and the implant shoulder, offer the additional advantage of being mostly compatible with a limited bone volume in an oro-facial direction. Whenever feasible, a straightforward low-maintenance restorative design is advocated, which normally consists of a cementable porcelain-fused-tometal crown with vestibular and oral axial contours that are in harmony with the adjacent teeth and thus provide adequate guidance for cheek and tongue (Figs. 54-64 to 54-66).
## Molar-size single-tooth restorations
If a given posterior single-tooth gap corresponds rather to the mesio-distal dimension of a molar, it is recommended, for the reasons quoted in the previous paragraph, that the insertion of a wide-neck implant is planned (Bahat & Handelsman 1996). This approach, however, also requires the respective bone volume in an oro-facial direction. If this is not the case, presurgical site analysis, eventually in the form of a bone-mapping, should identify whether it is possible to have an implant placement in combination with a lateral bone augmentation procedure using a simultaneous approach. If the local bone anatomy requires a bone augmentation according to a staged protocol, one has to carefully ponder and discuss with the patient if this additional effort, risk, and ultimately also cost can be justified by an anticipated implant restoration featuring close-to-ideal axial contours and embrasures.
**Fig. 54-65** The 5-year radiographic follow-up displays favorable bony conditions around this 12 mm solid screw implant.
**Fig. 54-66** On the oblique view one can notice that an axial contour similar to that present on the adjacent natural teeth has been applied to facilitate oral hygiene and to assure adequate soft tissue (cheek and tongue) guidance and support.
A clinical example demonstrating the potential of increased-diameter implants for the optimal replacement of a single missing mandibular molar is given in Figs. 54-67 and 54-68.
## Sites with limited vertical bone volume
The clinician is quite frequently confronted with posterior single-tooth gaps that present all of the major prerequisites for successful implant therapy listed earlier in this chapter, with the exception of sufficient vertical bone height for the insertion of an implant featuring what is broadly accepted as an adequate length of the implant itself and in relation to the prospective length of the suprastructure. The question that arises is whether there is a minimal implant length required in the context of posterior single-tooth restorations and whether the ratio between implant length and suprastructure length has an influence on crestal bone resorption and ultimately on the longevity of the entire implant–suprastructure complex. The analysis of the respective implant data collected at the University of Geneva School of Dental Medicine in the frame of a prospective multicenter study from 1989 to 2002, permitted the conclusion that shorter implants (6–8 mm) did not show more average crestal bone resorption than longer implants (10–12 mm), and that a so-called unfavorable ratio between implant length and suprastructure height did not lead to more pronounced crestal bone resorption (Bernard _et al_. 1995a; Bernard & Belser 2002). This data is corroborated by other recently published reports (ten Bruggenkate _et al_. 1998; Bischof _et al_. 2001; Deporter _et al_. 2001).
**Fig. 54-67** In a case of the replacement of a single missing molar, ideally the use of an implant with corresponding dimensions is recommended to permit a restoration featuring optimal subjective comfort and cleansibility.
**Fig. 54-68** On the 1-year radiographic follow-up a diameter-increased ("wide-neck") implant can be noted which is essential for a suprastructure design without extremely open interdental embrasures, which would be prone to food retention and oral parafunctions.
Two examples of respective clinical anecdotal-type evidence, one premolar-size and one molar-size single-tooth restoration, are presented in Figs. 54-69 and 54-70, and Figs. 54-71 and 54-72, respectively.
**Fig. 54-69** Clinical aspect of a single-tooth implant restoration in the mandibular right premolar area.
**Fig. 54-70** The related 2-year follow-up radiograph shows a so-called unfavorable relationship between the height of the suprastructure and the length of the supporting implant. The placement of a longer implant was not possible due to the limited local bone conditions.
**Fig. 54-71** Oblique view of a molar single-tooth implant restoration in the left mandible.
# Clinical applications
## Screw-retained implant restorations
For many years there was a strong tendency to design most of the fixed implant restorations as screw-retained suprastructures. Retrievability, and by this maintaining the possibility for modification, extension or eventually repair of the prosthesis, was the main rationale for this strategy. One should be aware, however, that this approach also encompasses notable specific inconveniences: colonization of the inner compartments of the implant–abutment–suprastructure complex with mostly anaerobic microorganisms, risk for loosening or fracture of screws, increased technical complexity and related costs, possible interference with structural parameters (weakening of the metal-ceramic design) and esthetics, as well as a "higher maintenance profile" (Sutter _et al_. 1993; Wie 1995; Hebel & Gajjar 1997; Keller _et al_. 1998). As far as the microbial colonization is concerned, it remains unknown to date whether and under which conditions this may have an adverse effect on the longevity of osseointegrated implants.
**Fig. 54-72** A short diameter-increased screw implant supporting a long molar-sized suprastructure is displayed on the 1-year follow-up radiograph. Note that a normal level of the first bone-to-implant contact has been maintained.
**Table 54-6** Indications for screw-retained posterior fixed implant restorations
Parameters to consider:
---
• Implant shoulder location incompatible with a cemented suprastructure, i.e. inaccessible for meticulous excess cement removal (>2 mm submucosally)
• Reduced intermaxillary distance (<5 mm)
• Foreseeable need for reintervention at the respective implant site
• Extended implant-supported rehabilitations, involving numerous implants
• High overall level of complexity (e.g. non-parallel implants)
For these reasons there is currently a distinct trend towards cementable fixed implant restorations in the load-carrying part of the dentition.
The main indications for screw-retention are listed in Table 54-6.
## Transocclusal screw retention
If for one of the aforementioned reasons a transocclusally screw-retained suprastructure is adopted, several parameters should be taken into consideration. First, the screw-access channel should be centered on the occlusal surface in order not to interfere too much with the area to be occupied by the cuspids.
**Fig. 54-73** Left lateral view showing the intermaxillary relationship of a young patient in centric occlusion. The missing maxillary second premolar has been replaced by a single-tooth, screw-retained implant restoration. Screw retention was chosen for two reasons: limited interocclusal distance and implant shoulder location incompatible with cementation.
**Fig. 54-74** One-year follow-up radiograph of the described 8 mm solid screw implant.
**Fig. 54-75** Ideally, the screw-access channel should be located in the center of the occlusal surface. This reduces both the risk for interference with an appropriate metal–ceramic design in general, and the risk for porcelain fractures in particular.
A typical clinical example documenting an indication for a screw-retained posterior single-tooth restoration is given in Figs. 54-73 to 54-75. A reduced interarch distance has led to a deeper than usual implant shoulder location which in turn is neither accessible for well controlled excess cement removal nor in reach for the patient's routine oral hygiene. In order to benefit from their superior surface quality characteristics and marginal precision, prefabricated machined cast-on components have been used for the respective suprastructure fabrication. Ideally, the screw-access channel occupies a restricted area in the centre of the occlusal table, and the distance from the head of the screw to the occlusal surface should be sufficient for a subsequent composite cover-restoration (Fig. 54-75).
Furthermore, the principles of the metal–ceramic technology require a well defined space for develop-ing an adequate metal support for a uniform thickness of the overlaying stratification of porcelain. Even in a case of a well centered occlusal perforation, the latter occupies close to half of the mesio-distal and oro-facial diameter of the occlusal table, and thereby significantly weakens the overall mechanical resistance of the structure. If the screw-access channel is not centered, however, additional problems are created in the sense of both weakening the restoration and interfering with esthetic criteria. Under such circumstances one should consider, for example, the use of angled abutments as currently offered by most of the leading implant systems.
Another key parameter represents the interarch distance, or more specifically, the distance between the implant shoulder and the plane of occlusion. According to our experience this distance should be at least equal to 5 mm. This is minimal and does not permit – for esthetic reasons – the occlusal screw to be subsequently covered with a composite resin restoration. In this context 6–7 mm are clearly more adequate.
A combination of several well known problems, which are frequently encountered after implant placement in the posterior mandible, are shown in Figs. 54-76 to 54-78. Two implants have been inserted to restore a distally shortened arch with a three-unit FPD. Owing to the local bone anatomy, the implants were placed in a more lingual position than the original teeth (Fig. 54-76). The implant shoulder location was too superficial for these particular circumstances and did not provide sufficient distance to gradually correct the discrepancy between the actual implant shoulder position and the ideal occlusal location. Furthermore, the necessity of keeping the screw access in the center of the occlusal table, and the insufficient room for composite screw-head coverage, ultimately led to a considerable compromise (Fig. 54-77). The final radiograph (Fig. 54-78) clearly shows that the presurgical bone volume would have permitted a vertical reduction of the edentulous bone crest to be performed prior to implant insertion. By this token the suboptimal implant position could have been partially corrected by the implant restoration, and the occlusal screw covered by composite resin, or a screw-retained restoration eventually avoided as there would be adequate conditions for a cemented suprastructure.
**Fig. 54-76** Occlusal view of a mandibular master model comprising two posterior implant analogues and a prepared natural second premolar abutment. Note the proximity of the mesial implant and the second premolar on the one hand, and the distinct lingual position of the two implants on the other.
**Fig. 54-77** The clinical view of the completed transocclusally screw-retained three-unit implant-supported FPD demonstrates that the lingual implant position did not allow for a suprastructure that is in line with the adjacent teeth. Furthermore, the screws are reaching the occlusal surface, leaving no space for an esthetic coverage with composite resin.
**Fig. 54-78** The related 3-year follow-up radiograph documents an only minimal distance between implant shoulder and occlusal surface. Under such conditions, a slight reduction of the alveolar ridge prior to implant placement would have provided more vertical leeway for compensating the lingual implant position and ultimately for covering the occlusal screw.
**Fig. 54-79** Occlusal configuration of a three-unit metal–ceramic implant restoration designed for transverse screw retention. Note the absence of any interference due to screws on the occlusal aspect of the restoration.
**Fig. 54-80** The oral aspect of that same prosthesis features the decisive elements related to the transverse screw retention: improved esthetics, no weakening of the ceramo-metal design. The screw-access channels are completely protected by the metal framework.
## Transverse screw retention
When it comes to screw-retained posterior implant restorations one should not forget the option of transverse screw retention (Figs. 54-79 to 54-84). This specific technical approach leaves the occlusal surface of the restoration free from any screw and permits the design of a screw-access channel on the oral aspect, featuring a metal protection on the entire circumference of the perforation (Fig. 54-80). These two factors significantly improve both the overall mechanical resistance and the esthetic appearance. Furthermore, the metal protects the surrounding porcelain during removal and tightening of the transverse screw and thereby prevents the induction of fissures prone to subsequent propagation and ultimately leading to ceramic fractures. One has to be aware, however, that from a purely technical and economic point of view, transverse screw-retained restorations require additional, more complex components and advanced technical skills, and are more expensive. In the long-term, on the other hand, the distinct advantages should clearly outweigh these inconveniences in numerous clinical situations.
**Fig. 54-81** Clinical 5-year follow-up of this three-unit implant restoration. No significant changes can be noticed on the occlusal surface.
**Fig. 54-82** Palatal view of the transverse screw-retained implant prosthesis after 5 years of clinical service. The screwaccess channels are blocked by a temporary material.
**Fig. 54-83** Pre-operative radiograph of the patient's maxillary right posterior segment, revealing a tooth-borne long-span FPD which had failed after 4 years of function due to loss of retention and subsequent damage on the mesial abutment.
**Fig. 54-84** Five-year follow-up radiograph of the same quadrant, now restored with a three-unit transverse screwretained metal–ceramic implant suprastructure. Note that the distal retainer of the original tooth-borne FPD could be maintained.
**Fig. 54-85** Example of a typical mandibular master model, derived from an impression at the abutment level, comprising four colour-coded implant–abutment analogues.
## Abutment-level impression versus implant shoulder-level impression
Most of the leading implant systems currently offer the possibility of taking impressions either at the level of a previously inserted abutment or at the level of the implant shoulder itself (Figs. 54-85 and 54-86). The former approach is mostly indicated if the patient does not wear a removable temporary prosthesis and in the case of optimally placed, "restoration-driven" implants, comprising accessibility of the implant shoulder, point of emergence from the soft tissue, implant axis, interarch distance, and overall easy access for use of simple "pop-on" plastic transfer copings. As shown later, a clear preference is given to cemented suprastructures under such simple, straightforward conditions. In fact, the clinician is only required to keep a limited stock of components, i.e. cementable titanium abutments of various heights and injection-molded impression copings, in his office. Whenever the clinical situation deviates notably from the previously described conditions, one may consider taking an impression directly at the level of the implant shoulder. For that approach, only transfer copings have to be available in the dental practice. In fact, the patient is leaving the office after the impression session exactly as he came in, i.e. with the same cover screw and with the same unaltered temporary prosthesis. After master model fabrication and articulator mounting, the technician will then select the most appropriate secondary components in the laboratory and ultimately deliver the finished restoration together with the respective supporting abutments.
**Fig. 54-86** Example of a typical mandibular master model, derived from an impression at the implant shoulder level, comprizing three colour-coded implant analogues.
## Cemented multiple-unit posterior implant prostheses
In recent years, an increasing trend towards cemented posterior implant restorations, using either temporary or permanent luting agents, could be observed. The associated original paradigm, indicating that maintaining "retrievability" was one of the fundamental advantages of implant-borne suprastructures, permitting re-intervention, modification, and/or extension at any time, has been lately challenged by parameters such as increased clinical and technical simplicity, low-maintenance design of the restorations, and superior cost effectiveness. As more implants are utilized in clinical situations where conventional FPDs would also be easily possible, but where the latter have become second choice, the sites are more favorable for this type of therapy and these implants come closer to the characteristics currently termed as "restoration-driven". Parallel to this improved mastering of three-dimensional implant positioning, secondary components such as abutments that are optimally designed for subsequent cemented restorations have been developed, in combination with auxiliary parts such as simplified impression copings, laboratory analogues, and burn-out patterns. A typical clinical example of the treatment of an extended tooth-bound posterior segment by means of implants and a subsequently cemented suprastructure is presented in Figs. 54-87 to 54-94. Three screw-type implants have been inserted according to a single-step transmucosal (non-submerged) surgical protocol, leading 8 weeks after implant installation to a clinical situation which is well suited for a restorative procedure similar to the one traditionally used in the context of natural tooth abutments. More particularly, all of the involved implant shoulders are easily accessible (Figs. 54-87 to 54-90) for restorative procedures and later for maintenance, and the surrounding peri-implant mucosa healing and tissue maturation has occurred simultaneously with implant osseointegration, both being key factors in facilitating prosthetic procedures. Furthermore, the superficially located interface between implant shoulder and suprastructure or abutment will reduce the length of suprastructure leverage and by this the resulting bending moments. Under the assumption that presurgical site analysis and, derived from that, prosthetic treatment planning has predictably led to optimal implant positioning, the resulting implant prosthesis should almost by definition feature a gradually increasing, flat axial emergence profile, adequate embrasures and overall design, and occlusal characteristics similar to those advocated for tooth-borne FPDs (Figs. 54-92 to 54-94).
**Fig. 54-87** Occlusal view of the mandibular right posterior quadrant with three implants that had been placed according to a single-step transmucosal surgical protocol.
**Fig. 54-88** In accordance with the available interocclusal space, adequately dimensioned solid abutments are selected, inserted and subsequently tightened to 35 Ncm in view of a cemented suprastructure.
**Fig. 54-89** With the solid abutments in place, the interimplant parallelism is confirmed. Note the easily accessible implant shoulders which will facilitate the following impression and restorative procedures.
**Fig. 54-90** Prefabricated injection-molded, self-centering impression copings and related color-coded positioning cylinders are inserted prior to impression taking with a stock tray.
**Fig. 54-91** The completed master model comprises colorcoded aluminum implant analogues.
**Fig. 54-92** Based on prefabricated burn-out patterns, the final metal–ceramic restoration has been completed. Note the continuous flat axial emergence profile of the individual elements.
**Fig. 54-93** The clinical occlusal view of the cemented fourunit implant prosthesis composed of premolar-sized segments.
**Fig. 54-94** The radiographic control confirms both successful osseointegration of the involved implants and accurate marginal adaptation of the suprastructure.
## Angulated abutments
It is not infrequent that all of the parameters defining an optimal three-dimensional implant position cannot be readily reached. Under such conditions the clinician basically has three options. Either a bone augmentation procedure is undertaken, or a conventional tooth-borne prosthesis is chosen, or one evaluates carefully whether a minor positional compromise can be considered acceptable. The related parameters have to be objectively pondered prior to taking the respective decision together with the duly informed patient. The heaviness of a so-called "site-development" procedure (e.g. lateral or vertical bone augmentation or anterior sinus floor elevation) should definitely be put in direct relation with the expected benefit. In some instances this approach allows significantly invasive procedures to be avoided. Particularly in situations where only the implant axis interferes with an otherwise optimal implant positioning, the subsequent use of angled abutments may still lead to a largely acceptable treatment outcome (Figs. 54-95 to 54-98). In other word, there appears to exist limited room for sometimes considering a slightly "bone-driven" instead of a purely "restoration-driven" implant placement in order to render implant therapy bearable for a given individual patient.
**Fig. 54-95** Lateral view of a master model comprising implant level analogues in the right mandibular posterior sextant. Angulated abutments have been selected to correct a too distal implant axis.
**Fig. 54-96** The corresponding occlusal aspect visualizes the amount of axis correction achieved.
Angled abutments, encompassing various inclinations and dimensions, are currently part of the armamentarium of most of the leading implant systems. They are frequently used and compatible with both a cementable or a screw-retained suprastructure design.
**Fig. 54-97** Using an appropriate index, the two angulated abutments are transferred intraorally and subsequently tightened to 35 Ncm with a torque wrench.
**Fig. 54-98** Clinical occlusal view of the cemented two-unit metal–ceramic implant restoration.
## High-strength all-ceramic implant restorations
Additional options, such as milled titanium frameworks as infrastructures for metal–ceramic prostheses or high-strength all-ceramic restorations, have also become recently available in the context of posterior implant restorations. Some of these approaches are based on computer-assisted design and computer-assisted machining (CAD/CAM) technology. As implants and their secondary components are mostly industrially produced or machined, and as their related dimensions and tolerances are well defined, they appear particularly well suited to this kind of technology. In this context, and in order to explain the particular interest associated with this type of technology, it has to be underlined that using either the same metal (i.e. c.p. titanium) or no metal at all for the suprastructure fabrication, would be highly preferable. Porcelain-fused-to-metal alloys with high gold content are primarily utilized due to their superior casting ability.
**Fig. 54-99** Mandibular right posterior segment, featuring a full-coverage preparation on the non-vital second premolar and two implants equipped with solid abutments in the area of the missing first molar.
**Fig. 54-100** Master model including the stone die of the prepared premolar and the two implant analogues.
**Fig. 54-101** Three respective aluminous oxide copings have been fabricated according to the PROCERA® technique.
It would go beyond the scope of this textbook to describe in detail the current evolution in the field of CAD/CAM systems in general and to their impact on implant dentistry in particular. A representative clinical example, however, is given in Figs. 54-99 to 54-105.
All-ceramic implant suprastructures are still preferred as single-unit restorations, primarily for purely technical reasons.
**Fig. 54-102** Clinical try-in of the high-strength porcelain infrastructures.
**Fig. 54-103** Vestibular view of the cemented final all-ceramic restorations.
**Fig. 54-104** The 1-year radiographic follow-up displays sufficient radio-opacity of the all-ceramic substrate to evaluate the marginal adaptation of the three single-unit restorations.
## Orthodontic and occlusal considerations related to posterior implant therapy
As one increasingly strives for the best possible biologic, functional and esthetic integration of a given implant restoration in the pre-existing dentition, three-dimensional pre-operative site analysis is of paramount importance. It is not infrequent that this subsequently calls for a pluridisciplinary approach termed "site development", which may also include presurgical orthodontic therapy (Figs. 54-106 to 54-119). The objective is clearly to create local conditions that are best suited for the type of therapy chosen. If implants are to be involved, the local bone and soft tissue anatomy, as well as the mesio-distal and orofacial distances of a given edentulous segment, have to comply optimally with the respective most appropriate implant dimensions. Quite often mesio-distal gap dimensions have to be optimized orthodontically and neighboring roots aligned, so that they will not interfere with "restoration-driven" implant positioning. Site development in the broad sense of the term also comprises parameters associated with intermaxillary relationships such as occlusal plane, interarch space, and occlusal guidance during mandibular excursions. As osseointegrated implants do provide excellent anchorage for orthodontic appliances (Melsen & Lang 2001), and thus can significantly contribute to the efficacy and simplicity of such a treatment, one may also consider implant insertion prior to orthodontic therapy. This, however, requires meticulous pre-operative analysis and precise three-dimensional implant positioning, anticipating perfectly the ideal location with respect to the final treatment objective.
**Fig. 54-105** Occlusal view of the two posterior implant-borne premolar-sized suprastructures and the tooth-supported ceramic restoration on the second premolar.
**Fig. 54-106** Right lateral view of a 19-year-old female patient, congenitally missing all four permanent maxillary premolars. One can note both an inadequate mesio-distal gap width and a reduced interarch distance.
**Fig. 54-107** A similar situation regarding interarch distance is present on the patient's left side.
**Fig. 54-108** The corresponding radiograph underlines the need for additional orthodontic therapy prior to the insertion of an implant in order to optimize the gap width and the interradicular distance.
**Fig. 54-109** Although to a lesser degree, presurgical orthodontic therapy is also indicated on the maxillary left posterior segment.
**Fig. 54-110** The clinical occlusal view displays the bilateral edentulous spaces in the premolar area. Despite previously performed orthodontic therapy, aiming at reducing the edentulous spaces to the size of one premolar, the mesiodistal gap width on the right side is insufficient for the insertion of an implant.
**Fig. 54-111** After six months of additional orthodontic treatment using an upper fixed full-arch appliance, the dimensions of the two prospective implant sites appear compatible with this kind of therapy.
**Fig. 54-112** The respective radiograph confirms adequate space in the upper right premolar region for the placement of a standard single-tooth implant.
**Fig. 54-113** A similar presurgical situation is radiographically confirmed for the upper left premolar site.
**Fig. 54-114** The right oblique occlusal view of the implant restoration clearly demonstrates the advantage of the transverse screw-retention design: no occlusal screw access channel interfering with the functional occclusal morphology and esthetics or with structural requirements inherent to the metal–ceramic technology.
**Fig. 54-115** As described for the patient's right side, the left maxillary fixed single-tooth implant restoration integrates appropriately the existing natural dentition.
**Fig. 54-116** The follow-up radiograph taken 1 year after the insertion of the 12 mm solid screw implant, shows adequate marginal fidelity and stable conditions at the bone-to-implant interface.
**Fig. 54-117** Similar findings are present in the corresponding left-sided follow-up radiograph.
**Fig. 54-118** The final right lateral view in centric occlusion features acceptable general interarch conditions and related intercuspation.
**Fig. 54-119** During the right lateral excursion of the mandible (working-side movement), a canine guidance could be established.
**Table 54-7** Hypothetical implant-specific occlusal concept
• "Light infraocclusion" in centric occlusion position (CO) on posterior implant restorations
---
• "Narrow" occlusal table
• Only "axial" loading on implant restorations
• No or only "minimal contacts" on implant restorations during "mandibular excursions"
• No canine guidance on implants
• Eventually "minimal" group function on the working side
When it comes to occlusal considerations related to posterior implant restorations, one should note that most of the relevant literature available to date addresses eventual effects of occlusal loading on the various components of the implant–abutment–suprastructure complex (Brägger 1999, 2001; Bassit _et al_. 2002; Wiskott _et al_. 2002). In fact, various recommendations are derived from such studies, including various occlusal restorative materials, type and mechanical characteristics of different abutment to implant connections, as well as general guidelines for optimal suprastructure design.
Little information is presently available regarding an eventual direct relationship between occlusal loading and maintenance of osseointegration in general and occurrence of peri-implant crestal bone resorption in particular (Wiskott & Belser 1999; Duyck _et al_. 2001; Engel _et al_. 2001; Gotfredsen _et al_. 2001a,b,c; O'Mahony _et al_. 2001; Engquist _et al_. 2002; Wright _et al_. 2002). Attempts have been made to take into account the fundamental differences between a tooth surrounded by a periodontal ligament and an "ankylosed" osseointegrated implant, the latter disposing neither of local mechanoreceptors nor of a so-called "damping" capacity. This led to a hypothetical implant-specific occlusal concept (Table 54-7), featuring parameters such as lighter contacts in centric occlusion when compared with the surrounding natural dentition, and no or only minimal contacts on implant restorations during mandibular excursions. One should clearly note, however, that these guidelines are primarily derived from clinical experience, subjective opinions and eventually common sense, and that there is little or no solid scientific evidence available to date which would support such a concept (Taylor _et al_. 2000).
# Concluding remarks and perspectives
## Early and immediate fixed implant restorations
Currently, one can observe a strong tendency towards shortened healing delays and ultimately towards immediate loading or at least "immediate restoration" protocols in association with dental implants (Tarnow _et al_. 1997; Ericsson _et al_. 2000; Gatti _et al_. 2000; Szmuk-ler-Moncler _et al_. 2000; Bernard _et al_. 2001; Chiapasco _et al_. 2001b; Ganeles _et al_. 2001; Gomez-Roman _et al_. 2001; Roccuzzo _et al_. 2001; Romanos _et al_. 2002). Improved implant surface characteristics have contributed to this evolution (Buser _et al_. 1998a; Deporter _et al_. 2001; Gotfredsen _et al_. 2001b; Roccuzzo _et al_. 2001; Cochran _et al_. 2002). Numerous studies have reported that such an approach can be considered predictable under certain well defined conditions. These conditions include four to six implants inserted in the interforaminal part of the edentulous mandible and which are subsequently splinted with a bar device (Gatti _et al_. 2000), as well as multiple implants evenly distributed around an edentulous arch and then immediately restored – according to the principle of "cross-arch stabilization" – with a splinted full-arch FPD (Tarnow _et al_. 1997). Achieving adequate primary stability at the moment of implant installation, and confining, during the crucial first healing period, an eventual mobility below the threshold of approximately 50 microns, appear to be among the decisive parameters for predictably achieving osseointegration (Szmukler _et al_. 2000). With regard to the routine application of immediate loading protocols for posterior single-tooth restorations, it appears advisable to wait for scientific confirmation of its respective potential in the form of randomized controlled clinical trials.
In conclusion, the possibility of performing highly predictable treatments which are more simple, require less time and which can be conducted in a standard dental practice set-up, as well as the associated quality of treatment outcomes, have nowadays made implant therapy in the load-carrying part of the dentition an integral part of the restorative spectrum for any kind of edentulism. This evolution is most dynamic and holds promise for further significant developments.
## Acknowledgments
The authors wish to acknowledge and thank Drs Viviana Coto-Hunziker, Stephan Dieth, Thierry Doumas, German Gallucci, Robin Jaquet, Nikolaos Perakis, and Valérie Wouters (all of them clinicians at the School of Dental Medicine, University of Geneva, and involved in the treatment of some of the patients presented in this chapter) for their contributions. We would also like to thank the laboratory technicians and ceramists, Michel Bertossa, Cédric Bertsch, Pierre Martini, Roger Renevey, Alwin Schönenberger, and Gérard Verdel, for their expertise and meticulous execution of the implant supra-structures presented in this chapter. Furthermore, our gratitude is extended to Dr. Pascal Magne (Senior Lecturer, University of Geneva) for his competent assistance in development of the schematic illustrations.
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# Chapter 55
# Implant–Implant and Tooth–Implant Supported Fixed Partial Dentures
Clark M. Stanford and Lyndon F. Cooper
* * *
Introduction
Initial patient assessment
Implant treatment planning for the edentulous arch
Prosthesis design and full-arch tooth replacement therapy
Complete-arch fixed complete dentures
Prosthesis design and partially edentulous tooth replacement therapy
Implant per tooth versus an implant-to-implant FPD?
Cantilever pontics
Immediate provisionalization
Disadvantages of implant–implant fixed partial dentures
Tooth–implant fixed partial dentures
* * *
# Introduction
The restoration of the fully and partially edentulous situation involves a combination of systematic diagnosis, treatment planning, and careful assessment of the therapy choices and the outcomes. The replacement of a continuous span of teeth creates challenges involving assessment of anatomic, physiologic, cost, time, impact on quality of life (QOL), and patient desires. The clinician is faced with balancing each of these aspects when developing a treatment plan for the patient. Modern dental care assures that tooth replacement therapy is provided in an economical and expedient manner. To this end, dental implants offer advantages for many clinical situations. In certain situations, the restoration of missing teeth using individual free-standing implant-supported crowns is a logical and satisfactory treatment option. At other times use of an implant-supported fixed partial denture (FPD) is a satisfactory approach (Fig. 55-1). Because of functional and esthetic priorities, anterior and posterior multi-tooth implant restorations can present different clinical challenges. This chapter will consider implant-toimplant supported FPD (bridges) separately from tooth-to-implant supported prosthesis since there are unique issues with each type of prosthesis. The use of a fixed complete denture to replace all of the teeth in an arch will be considered as a form of a fixed partial denture.
# Initial patient assessment
The predictable esthetic and functional outcomes of implant treatment require comprehensive diagnostic and treatment planning (Stanford 2005a). As a member of the implant team, the prosthodontist needs to collaborate with the surgical specialist, laboratory technician, and allied team members such as radiologists, and dental and surgical assistants. The initial assessment of the patient's medical and dental history assists in the determination of the implant system and devices that will meet the patient's therapeutic needs. The initial patient interview should establish the patient's individual esthetic requirements. This assessment should determine a patient's history of bruxism, periodontal disease, tobacco use, uncontrolled diabetes mellitus, and metabolic bone diseases (Moy _et al._ 2005). Recent literature suggests implant therapy in patients with advanced chronic periodontitis may have an altered prognosis, although stabilized with maintenance therapy (Nevins & Langer 1995; Ellegaard _et al._ 1997; Brocard _et al._ 2000; Pjetursson _et al._ 2004; Wennstrom _et al._ 2004a). Maintenance therapy is vital since longitudinal implant bone loss occurs and can be observed after many years of asymptomatic clinical service (Hardt _et al._ 2002; Fransson _et al._ 2005). In addition, the assessment should educate patients about the etiology of tooth loss, reveal their attitudes about treatment as well as the ability to tolerate it, and inform them of estimated treatment costs (Pjetursson _et al._ 2005; Stanford 2005a). Throughout the surgical and prosthetic phases of the implant reconstruction, the dental practitioner should obtain comprehensive written and verbal informed consent for patient treatment. The consent form should document the risks, benefits, and alternatives discussed with the patient. The option for and consequences of no treatment should be included. This initial assessment phase should provide the clinical team with sufficient information to characterize the patient-related risk factors that will influence treatment.
**Fig. 55-1** Implant-supported fixed partial denture (FPD). (a) Patient restored with two implants (44 and 46) and three-unit FPD. (b) Five-year recall radiograph demonstrates stability of osseous tissues around the implants.
To assure the implant location, number, and implant dimension are congruent with the anticipated prosthesis, it is essential the dentist design and compose the proposed prosthesis during the diagnostic phase. Pre-operative planning gives insights into both technical aspects (number, implant dimension, position, and angulation) as well as potential surgical site development needed prior to or at the time of implant placement. The complete treatment plan then assimilates clinical, radiographic, and psychologic information gathered using the patient interview, clinical examination, and radiographic survey. During the clinical examination, the dentist carefully evaluates the residual ridge for shape and contour, and evaluates alternative intraoral sites for mucosal recession. A careful evaluation of patient's risk factors for soft and hard tissue changes, whatever final restoration is planned, should be made to comply with the informed consent process and encourage realistic patient expectations. However, to move beyond assessing the feasibility of implant treatment, it is essential to utilize articulated diagnostic study casts to fully assess the tissue architecture and relationship of teeth and mucosa with existing edentulous areas.
**Fig. 55-2** Diagnostic wax-up for implant therapy demonstrating desired contours for the planned definative restorations.
Thus, the initial clinical examination should conclude only when sufficient materials are available to accurately mount diagnostic casts and interpret the study casts and screening radiographs using recorded clinical information. Based on this diagnostic information, a surgical guide or denture is fabricated using a process of diagnostic waxing of the planned prostheses, evaluation of the desired implant position, angulation, probable abutment dimension and angulation, and, finally, the need for hard or soft tissue augmentation as supportive therapy to implant placement (Fig. 55-2). The diagnostic waxing process is a key step in the assessment of local risk factors affecting fixed partial dentures supported by dental implants and is critical to the process of strategically planning implant placement to limit these risks.
# Implant treatment planning for the edentulous arch
The edentulous mandibular arch can be restored using a fixed complete denture, fixed partial dentures or an overdenture. The fixed complete denture can be a gold casting or CAD/CAM milled titanium framework, either with prosthetic acrylic resin teeth or teeth veneered with porcelain (Adell _et al._ 1990) The edentulous arch can also be restored with a series of FPDs that allows the clinic to manage multiple implants without seeking the precision fit of a full-arch prosthesis (Fig. 55-3). This approach also provides for greater flexibility in case of complications related to porcelain fracture, recession, wear, etc., and has demonstrated successful long-term outcomes (Bragger _et al._ 2001). An overdenture with attachment to the implant can be fully implant supported and retained or a combination mucosa/implant-borne prosthesis. Clinical studies indicate high patient acceptance of this form of therapy (Feine _et al._ 1994, 2002; Duyck _et al._ 2004; Naert _et al._ 2004a,b; Zitzmann _et al._ 2005).
**Fig. 55-3** Use of fixed partial dentures to restore missing hard and soft tissue. (a) Patient presented with a 40-year history of an edentulous space in the maxilla. Following placement of eight implants (b), a long-term acrylic resin provisional was fabricated simulating desired tooth and soft tissue dimensions (c). (d) Based on the long-term provisional, a ceramometal fixed prosthesis was fabricated using mucosa-colored ceramic materials on a metal framework. (e,f) Five-year recall demonstrating fixed prosthetic outcomes and anterior esthetics.
## Prosthesis design and full-arch tooth replacement therapy
If minimal bone resorption exists, restoring the edentulous maxillae with a porcelain-fused-to-metal restoration has a reasonable outcome (Stanford 2005a). The restorative dentist must perform a diagnostic work-up including impressions, jaw relationship records, and an esthetic try-in using prosthetic denture teeth on a trial denture base. The degree of lip support and smile line (i.e. anterior and posterior occlusal planes) of the diagnostic denture set-up should be evaluated intraorally. It is also useful to evaluate the patient's lip support with and without the anterior facial denture flange (Lewis _et al._ 1992; Stanford 2002). The amount of tooth exposure of the anterior smile line (relaxed and exaggerated), provides clues about the expected crown length, gingival display, and potential need to use gingival tone porcelain for appropriate tooth length and esthetics in a full-arch reconstruction. Communication and discussion with the dental laboratory technician is very helpful at this point prior to finalizing the treatment plan. A fixed maxillary prosthesis has greater incidence of esthetic, phonetic, and oral hygiene problems compared with an overdenture prosthesis, in part associated with excessively long anterior teeth, excessive facial cantilever pontics, and mesial–distal complications with embrasure forms (Lewis _et al._ 1992). Given the clinical and laboratory complexity of these prostheses, a maxillary overdenture on four to six implants may be an alternative (Phillips & Wong 2001; Anon. 2003; Naert _et al._ 2004b).
## Complete-arch fixed complete dentures
A complete-arch fixed complete denture (FCD) provides excellent function and patient acceptance (Lewis _et al._ 1992; Feine _et al._ 1994). During the diagnostic phases, the advantages and disadvantages of the FCD compared with those of an overdenture should be discussed with the patient. If using a ceramometal full-arch fixed reconstruction, consider replacing every three teeth with a three-unit fixed partial denture on two implants (e.g. #13–11) using the pontic contours to adjust for implant alignment and esthetic demands (Fig. 55-3) (Stanford 2002). A fixed maxillary reconstruction entails between six and eight implants (first molar, first premolar, canine, and central incisor) with four independent fixed partial dentures (molar to premolar, canine to central incisor, bilaterally) (Stanford 2005a). With care made to limit loading, six implants may be used with distal cantilevers on two fixed partial dentures (cantilever pontics limited to one premolar sized tooth). An overdenture should use a sufficient number of implants for long-term stability, typically four in the maxilla (canine and second premolar region) and two in the lower canine or first premolar region (Mericske-Stern _et al._ 2000). Using the denture set-up, a radiographic guide is fabricated with radio-opaque markers (e.g. gutta-percha or bur shanks) within the denture at the sites of interest. An alternative approach involves duplicating the denture set-up with teeth made using 5% medical grade barium sulfate mixed with clear autopolymerizing resin. This approach allows easy visualization of tooth size, angle, and position on conventional and/or CT-aided treatment planning. In the mandible, the trial set-up evaluates the height and position of the prosthetic teeth relative to the symphyseal cross-sectional anatomy. A conventional fixed complete denture with acrylic teeth requires a minimum of 15 mm from the alveolar crest to the planned incisal edge (Stanford 2005a). If the vertical dimension of occlusion and jaw anatomy is insufficient, one alternative is to perform an aggressive alveoectomy or to rehabilitate with ceramometal restorations (along with treatment planning for the additional cost).
Radiographic information and diagnostic set-up will help determine the type of definitive prosthesis design. Skeletal class I and II relationships with minimal resorption may allow normal contours and lip support with a fixed complete denture. Prognathic class III relationship can increase prosthetic problems, especially if implants cannot be placed distal to the mental foramens. In such cases, an over-denture approach yields a more predictable result (Naert _et al._ 1997).
# Prosthesis design and partially edentulous tooth replacement therapy
Clinician or patient preferences for the use of implants for restoration of partial edentulism using FPDs must be carefully weighed against the potential limitations associated with this therapy. Technical complications related to implant components and the suprastructure are more frequently reported than complications related to peri-implant tissues (Berglundh _et al_., 2002). Also, these complications for implant-supported fixed partial dentures are together more frequent than implant loss or implant fracture. For example, Bragger _et al_. (2001) reported for a 10-year follow-up period that the percentage of reconstructions without any biologic nor technical failure/complication was 66.5% for single-crown implant restorations, 54.4% for implant-supported FPD, and 50% for tooth–implant-supported FPD. Importantly, the authors concluded that prostheses with history of complications were at greater risk of implant failure. It may be possible to infer that complications reflect the functional features of the prosthesis or the patient and, furthermore, that some of these complications are due to limitations in implant and prosthesis planning, placement, construction or the innate limitations of implant components. Complications most frequently observed for FPDs include veneer fracture, opposing restoration fracture, bridge screw loosening or fracture, abutment screw loosening or fracture, and metal framework fractures (Goodacre _et al_. 2003a). The considerations for treatment planning of implant-supported FPDs must include features that affect not only implant success, but also abutment and bridge screw performance, and prosthesis esthetics and longevity.
Primary among clinical considerations for any implant prosthesis is some estimation of the potential forces that will be exerted during function. It is well recognized that masticatory forces increase as the point of interaction moves posterior in the arch. Additionally, damaging bending moments are increased with the acting lever arm length. Greater concern is warranted when implants are planned to support prostheses with large occluso-gingival dimension (extensive resorption) or for prostheses with extensive mesial, buccal or lingual cantilevers or any substantial distal cantilever. Additional immediate considerations typically address the esthetic potential of the prosthesis. This is clearly most relevant for anterior FPDs. Tooth-like restorations are dependent on proper dimensions and, again, greater concern is raised with increasing residual ridge resorption. However, basic features of implant placement such as avoiding encroachment of embrasures are critically important for anterior FPDs. These matters are revealed through the process of evaluating the diagnostic waxing (Fig. 55-4).
**Fig. 55-4** (a) Diagnostic wax-up demonstrating desired tooth position and wax used to demonstrate the amount of planned augmentation needed. (b) At the time of site development, the surgical guide demonstrates the difference between the desired tooth position and the residual ridge.
The current absence of discrete rules governing the number and dimension of implants (or a particular implant) needed to support a given masticatory function is acknowledged. Krekmanov _et al_. (2002) proposed that support factors can be attributed to implants and that relative risk can be assigned to various clinical scenarios. This approach of recognizing relative risk factors and modifying the clinical approach to therapy – even in a subjective way – merits consideration. At the very least, each clinical scenario should be considered in terms of prosthetic and implant risk both biologically and biomechanically and treatment should be adapted to recognize these risks if possible. Obvious examples would include the use of additional or larger implants to support molar function as opposed to premolar function and the avoidance of distal cantilevers in bruxing patients.
A simple strategy for reducing the biomechanical risks to implants and prostheses of implant-supported FPDs is to plan for implants located beneath the cervical aspect of the terminal mesial and distal FPD retainers whenever possible. This approach reduces the length of bending moments, irrespective of the imposed load, and also assures that the implant and abutment do not encroach on the embrasures to limit oral hygiene or esthetic potential of the restoration (Fig. 55-1).
When multiple implants are placed in an edentulous span, careful treatment planning will indicate mesial and distal width of desired restorative teeth. This plan will in turn indicate proposed sites where implants (e.g. every other tooth) may be placed for stability of the prosthesis. Choice of implant location may depend on available osseous tissues, soft tissue thickness, esthetics, phonetics, and need for ridge development.
## Implant per tooth versus an implant-to-implant FPD?
In having a dialog with patients about the desired tooth replacement therapy, clinicians often recommend an implant per tooth approach when replacing multiple contiguous teeth. When this approach is done with individual free-standing crowns, the approach provides potential for a natural tooth-bytooth replacement. On the other hand, it can create significant issues for the prosthetic restoration if the implants are not placed in exactly the desired location. The use of short-span FPDs therefore has certain general advantages. First, the use of two implants to replace three teeth allows the technician to judiciously use the pontic contours to alter the shape and contour of the prosthesis, compensating for implants that are not optimally positioned. For instance, implants that emerge at the interproximal area can be compensated by the use of angled abutments or custom abutments facilitating the use of the connector dimensions to create an illusion of natural teeth. Another advantage cited by some is the establishment of interproximal contacts between the prosthesis and adjacent teeth.
In order to assess the predictability of these types of restorations, clinical research studies need to be assessed. Randomized, controlled clinical trials of partially edentulous patients with a previous history of periodontal bone loss were evaluated in a 5-year trial by Wennström _et al._ (2004a). This study reported on 149 self-tapping implants (Astra Tech AB, Mölndal, Sweden) placed in the maxilla (n = 83) and mandible (n = 66) in the premolar and molar area. Each patient received two implants (machined surface versus grit blasted with Ti dioxide) that were allowed to heal for 6 months prior to loading. Screw-retained FPDs were completed and maintenance therapy provided following the CIST program (Lang _et al._ 2004). Implant loss was 5.9% at the subject level. FPDs demonstrated a total 5-year bone loss from implant placement of 0.41 ± 0.78 mm (subject level) (Wennstrom _et al._ 2004a). There was a statistical difference in the frequency of bone loss between those placed in the upper versus those in the lower jaw: 38% of the maxillary implants demonstrated >1 mm bone loss while 9% of the FPD in the lower arch had >1 mm bone loss at 5 years.
Previous studies evaluating bone loss with the implant system used in this study have reported mean marginal bone loss from implant placement to be an average of −0.46 ±0.38 mm (Olsson _et al._ 1995; Yusuf & Ratra 1996; Karlsson _et al._ 1997, 1998; Makkonen _et al._ 1997; Norton 1997, 2001; Arvidson _et al._ 1998; Astrand _et al._ 1999; Cooper _et al._ 1999, 2001; Palmer _et al._ 2000, 2005; Puchades-Roman _et al._ 2000; van Steenberghe _et al._ 2000; Gotfredsen & Karlsson 2001; Steveling _et al._ 2001; Weibrich _et al._ 2001; Engquist _et al._ 2002; Wennstrom _et al._ 2004a,b, 2005; Rasmusson _et al._ 2005). When implants were placed in the posterior maxilla with the indirect sinus lift technique and restored with FPDs at 6 weeks using a fluoride-modified implant, outcomes demonstrated bone loss −0.19 to −0.4 mm (sd = 0.73) from implant placement with a 98.3% cumulative implant survival rate (CISR) (Stanford 2006). These data support the concept that partially edentulous patients can be restored with FPDs (Gotfredsen & Karlsson 2001). However, post-insertion maintenance is critical. Hardt _et al._ (2002) observed in a population with a history of bone loss associated with periodontitis, that poor oral hygiene and compliance with maintenance therapy resulted in an elevated failure rate of 8% at 5 years; 62% of the implants in patients susceptible to periodontitis vs. 44% in non-perio groups demonstrated more than 2 mm bone loss (Hardt _et al._ 2002). This emphasizes the need for ongoing supportive care for patients undergoing tooth replacement therapy (Lang _et al._ 2004a; Schou _et al._ 2004).
## Cantilever pontics
In managing tooth replacement therapy there are times when a mesial or distal extension is needed to the FPD. The use of cantilever extensions increases the mechanical angular moment on the prosthesis and increases the potential for early fatigue and prosthetic complications (Brunski 2003). The use of cantilever extensions were first advocated as a routine prosthetic approach in the Toronto mandibular fixed complete denture designed for the edentulous arch (Zarb 1988; Zarb and Schmitt 1990a,b, 1991). Clinical studies on the use of cantilever extensions suggest greater complications with longer extensions beyond 15 mm, although there are many opinion-based recommendations that range from 10–20 mm (Shackleton _et al._ 1994). Cantilever extensions increase the angular moment on the most distal implant and abutment connection and the complications such as loosening screws, fractured components, etc. are related to a combination of factors including cantilever design, composition, occlusion, jaw relationships, and implant/abutment design (Brunski _et al._ 1986). In a survival analysis though 80 months of fixed complete dentures with an acrylic resin tooth replacement and the external hex Branemark system, Shackleton _et al._ (1994) observed a 100% survival rate for cantilever extension <15 mm but a decline to <30% survival for extension >15 mm.
In the anterior quadrant where esthetics are desired, there are often missing lateral incisors that leave only minimal mesial–distal space for implant placement. One option may be to use narrow diameter implants in such sites but control of occlusion is important (Stanford 2005b). An alternative, especially when there are missing adjacent teeth, is to use cantilever pontics of minimal dimension to replace the missing teeth (Fig. 55-5). This has the potential for more predictable esthetics without excessive site development, expense, and time. The use of cantilever pontics in the posterior quadrants is more controversial. Cantilever pontics in ceramometal FPDs create larger moment arms on the prosthesis and have the potential for increase mechanical complications with the implant–abutment stack (Stanford 1999; Brunski 2000, 2003; Brunski _et al._ 2000; Gratton _et al._ 2001). There are times where posterior cantilever pontics are useful but the clinician should consider these for areas of controlled occlusal forces and primarily for esthetics. Further, in use with ceramometal FPD, their use should be limited with no more than a premolar size pontic (∼7 mm mesial-distal dimension) with only light centric occlusal contacts on the pontic (Stanford 2005b).
There are ongoing issues regarding cemented relative to screw-retained FPDs. While the choice of prosthesis is dependent on multiple factors (clinician preference, flexibility, passivity of fit, cost, etc.) there are times when one approach is preferable. For instance, in situations where the patient has multiple clinical signs of recession (thin tissue biotype, recession, lack of keratinized mucosa, etc.) a screw-retained fixed prosthesis may be preferable (Stanford 2005a). This approach will allow the clinician to remove the prosthesis at a later point in time and make repairs which may salvage the prosthesis. Patients with a history of implant loss in the area, difficult implant placement or elevated medical risk are other indications to consider a screw-retained fixed prosthesis. Further, if the prosthesis needs to be routinely removed (e.g. in a research protocol) for accurate measurements of pocket probing depths (PPD) and bleeding on probing (BOP), the clinician may want to chose a screw-retained prosthesis. At times there are indications for fabricating a fixed prosthesis that replaces both hard and soft tissues (Garcia & Verrett 2004). In sites where there has been considerable loss of supporting structures, common following trauma or long-term chronic bone loss such as periodontal disease, it may be necessary to replace both dental and osseous supporting structures (Fig. 55-3). If this cannot be accomplished with biological site development, the clinicians may need to reconstruct this area with a combination of porcelain teeth developed with the appropriate mesial-distal and inciso-gingival dimensions to match the adjacent teeth and blend into the esthetic contours of the dentition and face. In doing so, it may become obvious that the gingival tissues need to be replicated in "mucosal" colored porcelain or acrylic. The development of tissue-matched mucosal shades takes significant laboratory skill and dexterity and often means the patient needs to be seen directly by the technician along with the restorative dentist (Malament 2000; Malament & Neeser 2004). Custom mucosal shades often need to be developed and matched chairside. While these approaches can be quite time consuming the end results can be quite satisfactory and surpass what can be accomplished by repeated soft tissue procedures (Fig. 55-6). The restorative dentist needs carefully to assess the patient early in the diagnostic process for implant therapy and determine if they are at elevated risk for unpredictable loss of soft tissue. Key factors to assess are thin tissue biotype, previous history of recession, mucosal inflammation, tooth loss due to trauma or chronic progressive osseous disease (e.g. periodontitis). All of these conditions influence the stability and position of the mucosal tissues following implant tooth replacement therapy.
**Fig. 55-5** Use of cantilever pontics to replace missing lateral incisors as a part of fixed partial denture (FPD) therapy. (a) Four implants were placed in the maxilla in the second premolar and canine region. (b) A four-unit FPD with cantilever pontics (12 and 22) was fabricated. (c) Restoration of eight missing teeth with four implants allowing establishment of an acceptable esthetic result (d).
**Fig. 55-6** Soft and hard tissue prosthetic replacement. (a) Patient presented with soft tissue loss in the area of 21 and 22. (b) Missing mucosal and hard tissue contours were replaced with a combination of gingival and tooth-colored ceramic materials. (c) A prosthetic solution to a difficult esthetic situation. Ceramic reconstruction by Henry Husemann CDT (University of Iowa).
## Immediate provisionalization
The application of implant-supported FPDs has a unique role especially in early and immediate loading procedures. While the splinting of implants for long-term osseointegration is not considered routinely necessary, the early splinting of multiple implants during the osseous healing process is considered important (Cooper _et al._ 2002, 2005, 2006; Slaets _et al._ 2005; De Kok _et al._ 2006; Duyck _et al._ 2006). Immediate provisionalization procedures have the potential to provide rapid function, esthetics, and patient satisfaction, and the use of implant-supported FPD prosthetic designs plays an intimate role in controlling micromotion and allowing successful outcomes similar to conventional loading procedures (De Kok _et al._ 2006; Duyck _et al._ 2006; Hall _et al._ 2006; Peleg _et al._ 2006).
The immediate provisionalization of implant-supported fixed dentures has a unique role in the retreatment of failing fixed prostheses. When large fixed prostheses are present with only one or two failing abutments, further tooth-supported restoration often requires extensive restoration. This is particularly true if strategic abutments such as a canine or terminal abutment tooth are not salvageable due to caries, fracture or localized periodontitis. In such cases, segmental resection of the failed tooth and supported pontic teeth can be replaced by dental implants. The advantages are obvious in terms of preventing the retreatment of a much larger FPD and providing an esthetic and functional treatment option for an anterior restoration.
## Disadvantages of implant–implant fixed partial dentures
The disadvantages of FPDs on implants are associated with increased difficulty of cleaning and maintaining the prosthesis along with the prosthesis complications associated with conventional tooth-supported FPDs. Based on patient expectations, there is the potential that the patient isn't satisfied with the inability to clean between the retainers and pontic contours. FPDs on implants can also be more difficult to fabricate in the laboratory. In this case there may be issues with the path of insertion on the abutments (necessitating customized abutment) or difficulties in obtaining draw and passive fit between multiple abutments. There is also the danger of mechanical wear and material failure with the completed prosability is critical but the screw access hole itself may weaken the strength of the veneering material. Lastly, there is the danger that if one of the supporting implants are lost or the abutment demonstrates recession exposing the transmucosal titanium surface, the entire prosthesis may have to be replaced increasing time and expense to the patient.
In assessing the clinical success of implant-supported FPDs, it is difficult to determine outcomes due to incomplete reporting of the specific types of prosthesis in a range of dental implant studies and yet the primary measure of evidence-based care is the systematic assessment of the clinical question of interest. The literature supporting the use of this type of prosthesis is often retrospective in nature with different outcome measures, end points, duration of recall, etc. This makes comparisons between studies difficult and limited. In the assessment of prosthodontic mechanical complications, the pattern of defects often will vary with a time-dependent pattern. In implant-supported FPDs, early failures (before loading) are often associated with implant loss (Goodacre _et al._ 2003b). As discussed by Pjetursson _et al._ (2004), implant loss prior to restoration can be expected on average to be 2.5% of all implants placed with an additional 2–3% lost over the first 5 years of function. In this systematic assessment of the more recent literature from the 1990s though 2004, 21 studies of 176 reviews were considered based on the inclusion and exclusion criteria. The authors summarized the current literature of five implant systems with 1123 patients, 1336 FPDs on 3578 implants followed for at least 5 years. Implant survival, FPD survival, success, and complications were reported (Table 55-1). The authors outlined that this type of assessment has limitations based on the quality of the studies, their duration, drop-outs, and reliability but in this instance, with the limited dataset, the authors outlined that the most common complication was loss of veneering material (often acrylic facings) followed by other mechanical complications inherent in screw-retained style prosthesis. Biologic complications such as peri-implantitis (probing pocket depth >5 mm) with bleeding on probing (BOP) have been reported in one study to average 10% of patients (Pjetursson _et al._ 2004). Pjetursson _et al._ (2004) used a random-effects Poisson modeling approach to determine a pooled cumulative rate of 8.6% for biologic complications (95% CI: 5.1–14.1%) based on a assessment of nine studies providing sufficient information for analysis.
**Table 55-1** Implant supported fixed partial dentures (FPDs) with an average of 5 years' follow-up (Pjetursson _et al_. 2004: in this review, 90% of the FPDs were screw-retained)
| **Average**| **95% confidence interval**
---|---|---
Implant survival| 95.6%| 93.3–97.2%
FPD prosthesis survival*| 95%| 92.2–96.8%
FPD success†| 61.3%| 55.3–66.8%
Complications| 38.7%|
Veneer fracture| 13.2%| 8.3–20.6%
Lost occlusal restorations| 8.2%|
Loose screws| 5.8%| 3.8–8.7%
Fractured abutments/ occlusal screws| 1.5%| 0.8–2.8%
Fractured implants| 0.4%| 0.1–1.2%
* Survival was defined as retained in function within the mouth. Prosthesis may have had multiple repairs.
† Success was defined as in function with no clinical complications.
Table 55-2 Local features considered in risk assessment for implant-supported fixed partial dentures (FPDs)
FPD location | Anterior locations possess higher esthetic risk Posterior locations may possess higher functional risk
---|---
Length of span | Long span increases complexity of prosthesis, mechanical loads and prosthetic complications Short span may increase abutment crowding and restrict hygiene
Occluso-gingival dimension | Increased occluso-gingival dimension results in lower bending moments at abutment and bridge screw connections Reduced occluso-gingival dimension (<6 mm) may limit prosthesis construction and integrity
Excessive vertical residual ridge resorption | Excessive vertical residual ridge resorption results in increased occluso-gingival dimensions of the restoration
Implant malposition | Buccal or lingual malposition creates unintended buccal or lingual cantilever of prosthesis Mesial or distal malposition encroaches on embrasure and hygiene access; both reduce esthetic potential Excessive deep placement increases bending moment at abutment screw, may create anaerobic environment, can lead to bone resorption and esthetic complications
Thin mucosal biotype | Risk of mucosal resorption and unesthetic display of abutment material
History of periodontitis | Elevated risk for peri-implantitis if control is absent. May need multiple staged procedures to replace hard and soft tissue contours
A FPD supported by two or more implants provides a valuable treatment option. It has a role in providing rehabilitation for patients with challenging implant positions and angulation, lost hard and soft tissues, reduced cost, and may allow avoidance of some grafting procedures (e.g. sinus grafting). The selection of a FPD supported by implants often represents the alternative to selecting a much larger FPD supported by many teeth (Table 55-2). While recent reviews suggest there may be little difference in the long-term complication rates for FPDs supported by teeth and implants, it is of practical importance that implant-supported FPDs often are smaller prostheses. On balance, the use of FPDs plays a valuable role in providing multiple tooth replacement therapy.
# Tooth–implant fixed partial dentures
The use of dental implants combined with teeth as retainers for FPDs has been advocated by a number of clinicians to restore multiple missing teeth. There are multiple case reports in the literature of prosthesis designs that have either a rigid connection between the natural tooth and implant retainers and or that utilize a non-rigid connection to ostensibly allow individual movement of the implant (s) relative to the greater mobility of the natural teeth (Stanford & Brand 1999). The difference in mobility can be of the order of about one magnitude with mobility on teeth with a healthy PDL being 50–200 μm while an integrated implant will have mobility of <10 μm (Brunski & Hipp 1984; Brunski 1988a,b, 1999, 2003; Rangert _et al._ 1997). The use of implant–tooth FPD does have the potential to reduce costs, time, and morbidity especially if the outcome provides a service to the patient that would be equivalent to implant–implant FPD or single-tooth implant restorations (Fig. 55-7). The advantages must be balanced with the potential complication of pathology associated with the dental retainers or the implant (s). The fate of both is tied together.
Lang _et al._ (2004b) performed a systematic review of the clinical studies that evaluated tooth–implant FPDs over at least 5 years and were able to identify 13 studies using the inclusion/exclusion criteria. Of these, nine were prospective and four retrospective in nature addressing outcomes with five different implant systems in 555 patients (538 FPDs on 1002 implants) ; the majority (91%) were reported as being screw-retained. The authors assessed the thirteen studies by evaluating those with follow-up from 5– 6.5 years. In this group, of the 932 implants installed, 25 were lost prior to restoration and 65 during the recall period. This resulted in a 5-year implant survival proportion of 90.1% (CI: 82.4–94.5%) (Lang _et al._ 2004b). In the second group, followed though 10 years, implant survival was estimated at 82.1% (CI: 55.8–93.6%). Following the same theme, a systematic review of biologic and technical complications (Berglundh _et al_. 2002) indicated that tooth–implantborne FPDs were at greater risk for implant loss (irrespective of complications leading to abutment tooth loss) than implant–implant FPDs. In regards to the prosthesis survival, estimates of 94.1% (CI: 90.2– 96.5%) at 5 years and 77.8% (CI: 66.4–85.7%) at 10 years were determined (Lang _et al._ 2004). Assessment of dental abutment survival indicated 3.2% were lost by 5 years due to fracture, caries, or endodontic or periodontal complications (Lang 2004) If the patient has the option to restore missing teeth with a conventional removable partial denture combined with implant-fixed prosthodontics it is interesting to assess the long-term outcomes.
**Fig. 55-7** Implant–tooth fixed partial denture. (a) Example demonstrates use of a rigid fixed partial denture (FPD) framework on a three-unit FPD (35–37). (b) A metal–ceramic prosthesis was cemented which has been monitored with frequent recall over 5 years (c). (d) Five-year recall radiograph indicates healthy peri-apical and peri-implant osseous tissues.
There has been a number of concerns raised with connecting teeth to implants with FPDs. Some of these complications are associated with technical complications of the prosthesis. For instance, the prognosis of the FPD can be shortened by veneer fractures and other esthetic issues (Kindberg _et al._ 2001). Loss of retention through fracture of the abutment/prosthetic screws or loss of cement retention are possible. Lang _et al._ (2004b) reported in a systematic review of two studies that assessed lost retention and described an average of 6.2% (CI: 3.7–10.4%) at 5 years (Hosny _et al._ 2000; Naert _et al._ 2001; Lang _et al._ 2004b). Endodontic complications on the abutment teeth can also be a significant concern with a range of 3–28% of teeth needing post-insertion root canal therapy (RCT) (average of 11%) (Goodacre _et al._ ). Naert _et al._ (2001) reported on the complications after a mean period of 6.5 (1.5–15) years in a retrospective comparison study of implant–implant to tooth–implant FPDs on 123 patients in each group with tooth-implant FPDs. The authors reported a history of chronic apical periodontitis (3.5%), tooth fracture (0.6%) along with a tooth intrusion (3.4%), and cement failure (8%) (Naert _et al._ 2001).
An interesting and unusual observation is the issue of natural tooth intrusion that has been observed (Pesun 1997). Earlier use of implants combined with teeth advocated the use of non-rigid attachments within the prosthetic design to allow differential movement between the implant and tooth. In some cases, the natural tooth appears to retract away from the prosthesis. This phenomenon has been suggested to be due to the interplay of disuse atrophy, food impaction, rebound memory of the PDL, and/or mechanical binding (Rieder & Parel 1993; Schlumberger _et al._ 1998; Cordaro _et al._ 2005; Palmer _et al._ 2005). In a multicenter study, Block _et al._ (2002) assessed posterior FPD connected either rigidly or non-rigidly with one type of attachment. Of the 30 subjects followed though 5 years, there was no difference in bone loss between the two types of connections but there was a 66% incidence of measurable intrusion in the non-rigid group versus 44% for the rigid group. The authors concluded that tooth–implant FPD had a higher level of maintenance and post-operative complications. Fugazzotto _et al._ (1999) retrospectively assessed a multi-group practice outcome of 843 patients (1206 implants, 3096 attachments) over a period of 3–14 years and observed nine instances of intrusion (0.3%) associated with fractured or lost lateral set screws (rigid-retention). In a prospective study through 3 years, Palmer _et al._ (2005) evaluated 19 subjects with rigid cemented prostheses between natural teeth and implants. These short-term outcomes at 3 years indicated no greater implant bone loss than would be expected (0.78 ±0.64 mm) with no signs of intrusion with the rigid tooth–implant FPD designs. These results have led to the clinical recommendation that if the clinician needs to join natural teeth with implants, a rigid connection is advocated with close monitoring for clinical signs of complications (Naert _et al._ 2001; Palmer _et al._ 2005; Stanford 2005a).
Fixed partial dentures joining teeth to implants is a controversial issue. There are times when an assessment of clinical needs, patient desires, costs, time, and risk provide support for the clinician to consider this treatment option. It is critical that the patient be informed of the relative risks associated with this type of prosthesis, the implant, and the abutment tooth in the process of informed consent.
### Conclusion
Fixed partial denture therapy for the restoration of multiple missing teeth has a long track record in dental implant care. Connecting two or more implants, or in selected cases, teeth with implants, can provide a stable, esthetic, and predictable outcome. All treatment options need to start with a careful assessment of anatomic, clinical, and patient needs and desires. The patient needs to be informed of the assumptions made and the relative costs and benefits that this treatment approach can provide.
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# Chapter 56
# Complications Related to Implant-Supported Restorations
Y. Joon Ko, Clark M. Stanford, and Lyndon F. Cooper
* * *
Introduction
Clinical complications in conventional fixed restorations
Clinical complications in implant-supported restorations
Biologic complications
Mechanical complications
Other issues related to prosthetic complications
Implant angulation and prosthetic complications
Screw-retained vs. cement-retained restorations
Ceramic abutments
Esthetic complications
Success/survival rate of implant-supported prostheses
* * *
# Introduction
The quality of dental implants and prosthetic outcomes has significantly improved since their introduction. This has been coupled with the steady increase in the clinical success and/or survival rate (Cochran 1996; Esposito _et al._ 1998; Lindh _et al._ , 1998; Jokstad _et al._ 2003). The biologic aspect, namely osseointegration, has been the particular target of intensive investigation and there have been conspicuous advances. As a part of these developments there have been continuous efforts to improve the characteristics, microtopographies and chemistries of the implant surface. A major change in surface topo graphy can be summarized by the evolution from machined surfaces to a production-based moderately roughened surface. Superior biologic response, or osseointegration, to roughened implant surfaces has been widely documented in the literature (Astrand _et al._ 1999; Rocci _et al._ 2003; Schneider _et al._ 2003). The cumulative effect of all these efforts is reflected in the extremely high biologic success rate of dental implants. With the enhanced predictability of the integration process of implants becoming well documented, an ongoing issue is related to restorative complications of therapy. These complications can be related to both biologic and prosthetic issues. This chapter discusses potential complications of dental implant-supported restorations, particularly focusing on complications related to the prosthetic aspects of therapy.
# Clinical complications in conventional fixed restorations
Implant dentistry shares many of the long-term mechanical complications shared with conventional dental restorative therapy. Goodacre _et al._ (2003b) presented data regarding the incidence of clinical complications associated with conventional dental fixed restorations/prostheses including single crowns (all-metal, metal ceramic, resin veneered metal) and fixed partial dentures (all-metal, metal ceramic, resinveneered metal); all-ceramic crowns; resin-bonded prostheses; and posts and cores. Regarding single crowns, the most common complication was postcementation endodontic therapy (3%), followed by porcelain fracture (3%), loss of retention (2%), periodontal disease (0.6%), and caries (0.4%). Regarding fixed partial dentures, the most common complications were: caries (18% abutments; 8% prostheses), need for endodontic treatment (11% abutments; 7% prostheses), loss of retention (7%), esthetics (6%), periodontal disease (4%), tooth fracture (3%), prosthesis fracture (2%), and porcelain veneer fracture (2%). In this narrative review, the authors concluded that complication incidence with conventional dental fixed partial dentures was significantly higher than single crowns. In addressing issues related to implant restorations, material failure and wear are common occurrences with both dental and implant-supported restorations (Fig. 56-1). It is likely that the higher biomechanical complexity of the design of the prosthesis contributes to higher complication incidence. Among these complications, pulpal complications, periodontal disease, and caries will apply to only tooth-supported restorations.
**Fig. 56-1** Prosthetic challenges related to wear and component fracture. Wear, fracture, and change in esthetics is a common occurrence with acrylic resin teeth (a) as are fractures of acrylic resin prosthetic teeth on fixed complete denture (b). While implant fractures are rare, the consequences are challenging. (c) Case example of implant that was mobile 2 years after delivery; (d) the prosthesis was removed and the head of the implant was fractured. (e) The implant was replaced with a wide diameter implant in order to increase the wall thickness and provide a greater abutment-to-implant interface. (f) Recall at 10 years.
Tan _et al._ (2004) assessed the long-term success/ survival rate of conventional fixed partial dentures (FPDs) and evaluated the failure rates of FPDs due to specific biologic and technical complications. The result of the systematic review based meta-analysis indicated a 10-year survival rate of FPDs was 89.1%. The 10-year success rate of FPDs declined to 71.1%. Success suggests no intervention was needed over the recall period, relative to survival which suggests retention with or without intervention during the recall period. In general in the literature, the mean 10-year survival rate of conventional FPDs was 90%, and success rate 80%. In this study, the most common reasons for dental FPD failure include periodontal disease and secondary caries. Regarding the complications related to caries, the 10-year risk for decay on abutments was 9.5%, but only 2.6% of FPDs were lost as a result of this disease process. In this study, it was clear that loss of vitality of abutment teeth occurred at a later date and so could not be attributed to the trauma from the preparation of the teeth. This may either indicate a slow progressive tissue degeneration induced by the procedure or reflect the increased susceptibility of pulpal infection by dentinal tubules in advanced periodontitis (Bergenholtz & Nyman 1984). The presence of cast post and dowels and non-vital abutments, especially in distal abutments, has been shown to be associated with increased loss of retention and fracture of teeth and cores. This cautions against over-dependence on non-vital teeth as strategic abutments.
The 10-year risk of loss of FPDs due to recurrent periodontitis was only 0.5%. Overall, there seemed to be no adverse changes in FPDs incorporated into periodontally well-maintained patients even if they presented with a history of advanced periodontal disease. Where the recall or maintenance is less stringent, periodontal breakdown may occur, and may be more pronounced when margins were subgingivally located (Valderhaug & Karlsen 1976). Secondary use of the bridge for removable prosthesis has a detrimental effect on the gingival tissue (Libby _et al._ 1997). The 10-year risk for technical complications, such as loss of retention, loss due to abutment fracture and the occurrence of material complications, were also calculated in this study. An issue in any of these studies is the multifactorial nature of the causes of failure. The highest 10-year risk was for loss of retention, amounting to 6.4%. Far lower was the 10-year risk for the loss of FPD due to abutment tooth fracture. Relatively low 10-year risks were obtained for material complications. These included fractures of the framework, veneers and/or cores and amounted to a 10-year risk of 3.2%. A comparison of the difference in survival between FPDs with acrylic facings and metal–ceramic FPDs showed that over an 18-year period, 38% of FPDs with acrylic facings and 4% with metal ceramic FPDs were replaced (Sundh & Odman 1997). Reasons cited for the increase in failures were the greater incidence of discoloration and fracture after extensive wear of the acrylic resin material.
# Clinical complications in implant-supported restorations
## Biologic complications
### Surgical complications
Surgical complications directly related to implant placement are generally rare. However, due to the surgical nature of implant therapy, it is impossible to avoid surgical sequelae. Recent surgical methods propose excluding tissue flap openings (so called "flapless approaches") which seek to minimize surgical trauma but carry their own risks as well. Goodacre _et al._ (2003a) provided data regarding the types of complications that have been reported in conjunction with endosseous root form implants. The most common surgical complications associated with implant surgery were hemorrhage-related complications (24%), neurosensory disturbance (7%), and mandibular fracture (0.3%).
## Implant loss
To date, there is no known single factor that contributes to an implant loss. Some of the factors that are generally accepted as the etiology include infection and/or contamination, patients' physical status, trauma from surgical procedure, excessive and/or premature occlusal loading, unfavorable axial loading, etc. Most of the surgery-related implant losses can be managed by maintaining a strict infection control protocol, meticulous patient screening prior to the surgery, and reducing the amount of time/trauma during surgery. Occlusal loading is a more challenging factor since the operator has more limited control. Premature occlusal loading can be detrimental to the osseointegration when it is combined with excessive load and/or off-axis force. This can happen during the stage of early or immediate provisionalization and illustrates that the patient should be closely monitored during this initial healing period. In the literature, it has been stated that overloading at any stage of osseointegration can lead to bone loss or even complete disintegration of the implant (Isidor 1996, 1997; Brunski _et al._ 2000; Steigenga _et al._ 2003). However, the concept of implant "overload" has recently been questioned with a series of studies indicating bone is highly responsive to dynamic loads and is resistant to bone loss even with high levels of occlusal function (Stanford & Brand 1999; Duyck _et al._ 2000, 2001; Stanford 2005b).
According to the literature, implant loss ranges from a high of 19% with maxillary overdentures to a low of 3% that occurred with both mandibular fixed complete dentures and single crowns (Goodacre _et al._ 2003a). Implant loss is greater with implants 10 mm or less in length compared with implants greater than 10 mm long (ten Bruggenkate _et al._ 1998; Lekholm _et al._ 1999; Friberg _et al._ 2000; Palmer _et al._ 2000). The implant loss is more likely to occur in the presence of type IV bone compared with more favorable typed bones (Stanford, 1999, 2005b; Stanford & Brand, 1999). Other risk factors that have been suggested include smoking and a previous history of radiation therapy (Moy _et al._ 2005). If indeed a loss of implant occurs, approximately half or more of the lost implants were lost prior to functional loading. This result is in agreement with the result from a previous systematic review (Berglundh _et al._ 2002).
## Peri-implant complications
Possible peri-implant complications include marginal bone loss, peri-implant mucosal inflammation/proliferation, soft/hard tissue fenestration/dehiscence, fistula, etc. It is widely accepted that continuous marginal bone loss around established implants over time jeopardizes the potential success and/or survival of the implant therapy. Factors that potentially induce marginal bone loss include surgical trauma during implant placement, trauma during repeated abutment insertions and removal, functional load transfer and concentration, micromotion at the implant–abutment junction, and peri-implant gingival inflammation. According to the literature, the mean bone loss occurring during the first year is, on average, around 0.9–1.5 mm, and the subsequent loss per year after the first year is around 0.1 mm (Albrektsson _et al._ 1986).
Peri-implantitis is defined as an inflammatory reaction associated with the loss of supporting bone in the tissues around a functioning implant (Albrektsson _et al._ 1994). Peri-implantitis could be asymptomatic but it often accompanies bleeding and/or suppuration. Clinically, bony defects are detected by increased probing depth. Radiographically, a saucer-shaped radiolucent lesion may be observed around the implant. From a prosthetic perspective, the onset of peri-mucositis or peri-implantitis (associated with bone loss) can lead to soft tissue recession and unesthetic show of abutment or prosthetic components.
Marginal defects on the facial aspect of the implant complex are not only esthetically compromising, but can jeopardize the stability and long-term success of the implant. These defects, dehiscence or fenestration, are typically caused by the resorption of the buccal/labial plate of the alveolar bone. In order to prevent this type of defect it is important to maintain a minimum of 1 mm thickness of buccal/labial plate (Stanford 2005a). However, in certain areas, this may be difficult to achieve. To reduce the risks of facial marginal defects one can utilize bone augmentation procedures, mainly autogenous, around the marginal alveolar bone in order to maintain the thickness around the implants. In this case, autogenous bone particles derived from the drilling of the osteotomy may be enough for the purpose. In terms of the timing of implant placement after tooth extraction, it is generally accepted that immediate placement has a greater risk of facial marginal defects compared to delayed placement (Nemcovsky _et al._ 2002).
## Malpositioned implants
The definition of a 'malpositioned implant' is an implant placed in a position that created restorative and biomechanical challenges for an optimal result. A malpositioned implant could be caused by numerous factors, the most common being deficiency of the osseous housing around the proposed implant site. Bone resorption is observed in osseous remodeling following tooth loss, osteoporosis, orthopedic revisions, craniofacial defects, or post oral cancer ablation associated with surgery/radiation. For the best biologic, biomechanical, and esthetic result of implant rehabilitations, proper implant placement is essential. The placement of an implant into a defective osseous site not only prevents adequate positioning of the final prosthetic restoration, but also results in compromised integration and subsequently a poor prognosis for the therapeutic outcome. In order to place an implant in the optimal prosthetic position for a restoration, augmentation procedures are often necessary. Current approaches in bone reconstruction use biomaterials, autografts or allografts, although restrictions on all these techniques exist. Restrictions include donor site morbidity and donor shortage for autografts (Damien & Parson 1991), as well as immunologic barriers for allografts and the risk of transmitting infectious diseases (Meyer _et al._ 2004). Numerous artificial bone substitutes containing metals, ceramics, and polymers have been introduced to maintain bone function. However, each material has specific disadvantages, and none of these can perfectly substitute for autografts in current clinical dentistry.
If the status of the existing, deficient bone were addressed prior to the surgery and the restorative dentist confirms it will be possible to fabricate the final prosthesis with the implant(s) in the proposed location, generally implant placement can be a straightforward procedure. It is a significant complication for the implant team and the patient when the implants are placed only in the available bone ignoring the optimal desired prosthetic position (Fig. 56-2). Communication between the surgical and restorative team is vital. The best way of communication between the two parties is through use of comprehensive treatment planning, diagnostic wax-up on mounted casts, and fabrication of a surgical guide. The standard protocol for placing implants will start with a treatment plan developed by the restorative dentist. The surgical guide represents the ideal position and angle of the implant determined by a series of diagnostic procedures. The surgical guide should ideally indicate the three dimensions of the proposed implant position – horizontal position, vertical position, and angle (Fig. 56-3). Horizontally, the surgical guide should clearly indicate the bucco-lingual and mesiodistal location of the proposed site. In most cases, this is determined by the morphology and location of the diagnostic wax-up of the missing tooth. Vertically, the surgical guide should indicate how deep the surgeon should place the implant relative to the planned cemento-enamel junction (CEJ). This is particularly important for implants placed in the esthetic zone. As a general rule, the restorative margin for an implant-supported restoration should be located at the vertical height slightly deeper than that of the CEJ of the adjacent teeth. Thus, when an implant system in which the head of the implant represents the restorative margin, the implant should be placed 2– 3 mm below the planned CEJ or occasionally on a line connecting the CEJ of adjacent teeth. When an implant system is used which is capable of adjusting the height of the restorative margin through a separate abutment(s), the depth of the implant may be more flexible (Fig. 56-4). Whichever system is used, the surgical guide should have a component that could notify the surgeon of the proposed depth of the implant. The angle of the implant should also be correct to prevent facial or lingual fenestration of the implant as well as penetration into the radicular portions of adjacent teeth or other structures. The angle should be correct for the prosthesis as well. Should the angle of the implant be too facial, the restorative dentist could face significant esthetic challenges, for example, screw access hole position, necessity of the use of angled abutments, expensive custom abutments, etc. (Fig. 56-5).
**Fig. 56-2** Prosthetic complications with malpositioned implants. (a) Patient had an implant placed in area of 24 with facial angulation. (b) The provisional fixed bridge demonstrated the facial position. Due to the depth and position of the implant, a fixed prosthesis was made that rested on the implant abutment (c) allowing a satisfactory esthetic and functional restoration (d).
**Fig. 56-3** Surgical guides for implant placement. Using a guide with a restrictive channel allows for evaluation in diagnostic imaging studies and during the surgical placement phase.
## Mechanical complications
### Overdenture complications
Numerous studies indicate that the use of an acrylicbased implant overdenture has the highest number of post-operative complications (complication being defined as a need for some form of intervention, the degree of which is not necessarily defined). Complications include loss of attachment retention or fracture of the attachment system, fracture of components of the denture, prosthesis-related adjustments, etc.
**Fig. 56-4** The restorative margin may be the head of the implant with certain implant designs necessitating the surgeon placing the implant to have a clear idea of where the final margin will be. Other systems use an abutment for cemented restorations that allows variation in the vertical position of the restorative margin.
**Fig. 56-5** Innovative use of abutments. (a) Patient presented with a healing abutment indicating placement within the residual ridge. (b) Soft tissue health was adequate though final impression coping (c) indicates angled position relative to remaining teeth. Patient was restored with a cement retained restoration but using a low profile abutment designed for a conventional screw-retained crown (d,e). (Courtesy of Dr. Michael Scalia DDS, and Mr. Henry Husemann CDT (University of Iowa).)
Goodacre _et al._ (2003a) suggested the most common complication in this category was the need for adjustments due to loss of retention and/or attachment system fracture. O-ring systems, Hader-bar and clip-, IMZ-, Ceka-, ERA-, ZAAG-, Locatorattachments all use various forms of plastic components within the anchorage system. Over time, the plastic component tends to wear and distort. Traditional ball attachment systems utilize metal spring matrices and these, too, tend to deform and lose retention with time. Studies that assessed the difference in frequency of maintenance requirement between bar/clip systems and individual attachment systems indicated that individual attachment systems require more frequent adjustments mainly due to loss of retention of the matrix or patrix (van Kampen _et al._ 2003; Walton 2003; MacEntee _et al._ 2005). However, the simplicity and ease of the repair procedure in some individual attachment systems may reduce frequent maintenance and have lead to increasing popularity of these abutment designs. Systems with exchangeable plastic components have especially become popular due to easy maintenance procedures. Further, the conversion of a complete denture patient who rarely returns for maintenance therapy to a routine recall patient (valuable for early caries detection, oral cancer exams, etc.) by way of their desire to have the attachment system serviced provides a valuable ethical service for the patient.
**Fig. 56-6** Fractures of veneering ceramic material. (a) Example of facial shear fracture of porcelain on posterior unit. (b) Ceramic shear fracture on facial surface of 22 all-ceramic restoration.
Because of the housing and attachment components, overdentures typically have a reduced thickness of acrylic resin base in certain areas compared to conventional dentures. It is these thin areas that have a higher risk of fracture. In addition, patients with implant-supported overdentures have a tendency to generate higher masticatory force compared to patients with conventional dentures. The incidence of acrylic base fracture may increase depending on the opposing occlusion. For example, an overdenture opposing an implant-supported fixed complete denture will be at a greater risk of fracture, accelerated wear or prosthetic tooth fracture than one opposing a conventional denture. Overdenture fracture is a relatively common problem according to some studies, and could be as high as 7% of all the mechanical complications related to implantsupported restorations (Carlson & Carlsson 1994; Goodacre _et al._ 2003a).
Prosthesis-related adjustments include reline/ rebase of the overdenture, occlusal adjustments, denture adjustment due to soft tissue complications, etc. Normally the hard and soft tissue under the overdenture will remodel with time. Additionally, overdentures only allow limited rotational movements between the abutment and the anchorage system. This means there will be positive vertical and horizontal load on the edentulous ridge, in the area away from the anchorage system. This may increase the rate of resorption and induce the need for denture relines. The change in mucosal adaptation of the prostheses will induce subsequent problems like occlusion changes and soft tissue trauma.
### Fracture of fixed restoration veneers/fixed restorations
Without the periodontal ligament (PDL) to provide shock absorption and proprioceptive reflex, dental implants are essentially ankylosed to the surrounding bone. Further, patients tend to generate higher masticatory forces on implant-supported restorations relative to the natural dentition. It has been reported that the maximum bite force generated with conventional dentures is around 50–60 N, whereas implantsupported restorations can generate above 200 N (Carr & Laney 1987; Mericske-Stern _et al._ 1996; Fontijn-Tekamp _et al._ 1998; Morneburg & Proschel 2002; Steigenga _et al._ 2003). As a result, an implantsupported prosthesis is exposed to a risk of higher restorative material failure. Of prosthetic failures, studies suggest the fracture of the restorative veneer material is the most common type of mechanical complication (Fig. 56-6). It includes fracture of the veneering porcelain or resin. Veneer fracture can happen anywhere in the mouth; restorations in the areas of heavy functional forces and higher non-axial forces, such as the occlusal surfaces of mandibular posterior restorations, facial cusps of maxillary posterior restorations, and maxillary anterior restorations, have a greater tendency to shear. To reduce or avoid material failure, especially veneer material fracture, the restoration should have sound supporting structures. The framework that supports the restorative veneer should have sufficient strength and stability to safely support the overlying veneer material. The framework should have minimal flexure even under functional loading – veneer materials usually lack tensile strength and as a result are weak under flexural stress. The framework should be carefully designed so that it will provide maximum support with no unsupported areas of the veneer material (Fig. 56-7). Another important approach to reduce the complication of veneering materials is through control of the occlusion. To reduce or eliminate excessive stress on one particular tooth or restoration, wide distribution of the occlusal force will be better than loads concentrated on a localized area. Also limiting the main occlusal force on to the restoration directly supported by implants may be beneficial: cantilevered restorations may be at higher risk of fracture than those supported by the implant/ abutment under an identical amount of occlusal load (Becker 2004; Pjetursson _et al._ 2004).
**Fig. 56-7** Fractured all-ceramic implant restoration. Patient had a three-unit fixed partial denture (FPD) (12 to 21) with glassinfused ceramic structure. (a) Restoration demonstrated catastrophic rupture 2 years after delivery. Restoration was removed (b), zirconia abutments cleaned and a new Zirconia reinforced FPD fabricated for enhanced strength (c). (d) Final esthetic appearance for the FPD.
Occlusal wear is more evident in implantsupported restorations for the same reason. When there is a mismatch of opposing restorative materials, the wear could be especially dramatic. Thus one must be prudent in not only selecting the material for the occlusal surface of the restoration but also the status of polishing to avoid serious maintenance issues. It is known that porcelain can be abrasive when opposed with enamel, metal, resin, or even porcelain, especially when it lacks a highly polished surface (Monasky & Taylor 1971). Exposed opaque layer and use of external characterizations with metal oxides all add to the abrasiveness of porcelain and should be used with care.
A rare but possible complication related to prosthesis fracture is the fracture of mandibular implantsupported fixed complete denture at the midline (Fig. 56-8). It is speculated that the flexure of the mandible during function can cause this type of complication. Repeated extreme mouth opening can accumulate fatigue in the metal framework, and once this accumulated fatigue exceeds the fatigue strength of the material, the prosthesis may facture or veneering material delaminate from the framework. Clinically, patients with this type of restoration may feel tightness of the mandible especially during function, and once the restoration fails, they express "relief" from the tightness. To avoid this problem, fabricating a two-piece fixed restoration has been advocated by some, although this has generated its own problem: because of the lack of the bracing effect and rigidity of the framework, these restorations may tend to have a higher incidence of screw-related problems.
**Fig. 56-8** Splitting full-arch ceramometal restoration at the midline to reduce impact of mandibular flexure.
### Implant screw-related complications
Numerous studies indicate that complications related to the screw components of the implant system are very common and require clinical intervention, which could range from simple retightening of the screw(s) to total replacement of the abutment and screw(s). This requires additional time and cost for both dentists and patients. Jemt and Linden (1992) observed with earlier screw abutment designs that screw loosening occurred in 49% of maxillary implantsupported restorations and 20.8% of prostheses in the mandible. They also observed that 57% of the abutment screw loosening occurred within the first year of service and only 37% remained stable over a 3-year period. Goodacre _et al._ (2003a) observed that the frequency of complications related to implant screws like screw loosening or fracture of abutment or prosthetic screws could be as high as 19% of all the potential mechanical complications in implant restorations. Ding _et al._ (2003) reported that the incidence of screw loosening for an external hex system could be as high as 38%. In their systematic review, Pjetursson _et al._ (2004) found that abutment or occlusal screw loosening/fracture was the third most common technical complication, only after restoration veneer fracture and loss of occlusal screw access hole restoration. Its cumulative incidence after 5 years of follow-up was 7.3%.
Theoretically, the lifespan of an abutment or prosthetic screw in an implant restoration needs to last greater than 108 cycles of loading or approximately 20 years under the assumption that the system is accurately constructed and the loading conditions are simulating the natural oral environment (Patterson & Johns 1992). However, there are several factors that could drastically reduce the predicted service life resulting in screw loosening and/or fracture. For example, the abutment/implant interface geometry, precision of fit and/or passivity of components, and the amount of preload may lead to reduced service life. In external hexagonal implant system studies, it has been shown that larger implant/abutment contact area provides superior stability of the system and resistance to screw complications and has been one driving force for the use of wider-diameter implant devices (Binon 2000). Additionally, precise anti-rotational features should be present for the joint components to withstand rotational movements that could potentially cause screw loosening (Khraisat 2005). Precise fit of the abutment to the implant interface is highly important. In a study on machining accuracy of several different external hex implant systems, all systems demonstrated rotational movement in excess of four degrees (Binon 1995). Systems that have such "slip-joint" figures such as external hex implant systems are naturally vulnerable to vibration and micromotion during functional loading (Schwarz 2000; Hoyer _et al._ 2001). In the absence of passivity between the implant components, it has been shown that screws accumulate internal stress and this eventually results in metal fatigue failure and screw loosening/fracture (Kano _et al._ 2006). The resulting clamping force exhibited between the abutment and implant generated by the screw is called _preload_. In an external hex system, the preload, along with the frictional force of the abutment/implant joint wall, is the major force resisting functional loads. In most implant systems, a tightening torque is applied and the preload stress in the interface is increased, where this stress should be within the elastic range of the screw material. The screw tightening should result in optimum preload level for the maximum outcome of the implant complex after dynamic loading. Literature indicates that as long as the external loading stress does not exceed the preload stress, the abutment/implant connection can be regarded as safe (Patterson & Johns 1992; Lang _et al._ 2003). Insufficient or excessive preload stress could result in compromised lifespan of the abutment/implant connection.
Chronic problems associated with the external hex or butt-joint interface implant systems have been documented. Because of these inherent problems with external hex design, investigators have presented new concepts in implant design, which aim to improve support and reduce the complications associated with external hex design, by means of additional frictional force between the internal wall of the implant and the external wall of a 1-piece abutment/ abutment screw. Sutter and colleagues proposed an 8-degree internal-taper connection between the implant and abutment (ten Bruggenkate _et al._ 1998). The original concept of Morse taper comes from engineering, particularly from the area of machine taper. When connecting exchangeable working bits into the work piece, a popular and very effective method is to use frictional forces between the two components, where the pressure of the spindle against the workpiece drives the tapered shank tightly into the tapered hole. The friction across the entire interface surface area provides a surprisingly large amount of torque transmission. The abutment/implant junction can be designed such that an internal connection is utilized with minimal taper (2–15•), while the screw base portion of the abutment will be connected into the receiving portion of the implant. There are numerous studies reporting on the higher mechanical and enhanced clinical behavior of these internal connection designed implants (Binon 2000). Norton (1997, 1999) verified that the internal conical designed systems significantly enhanced the resistance of connection system against external bending forces. Levine _et al._ (1999) found that the internal connection showed significantly lower incidence (3.6–5.3%) of screw-related complications compared to external hex designed systems. The use of the internal interference fit abutment designs has simplified the prosthetic phase of therapy and has increased the long-term stability of the screw–joint connections (Stanford & Brand 1999; Brunski 2000, 2003; Jokstad _et al._ 2003).
**Fig. 56-9** Incomplete seating of abutment in a two-piece implant system. Implant abutment was incompletely seated in implant due to contact on the adjacent osseous contours.
### Abutment-related complications
In positioning an abutment into the implant, there are potential mechanical complications that can arise. One common issue is incomplete seating of the abutment to the implant body (Fig. 56-9). Depending on the implant position and depth, it is also possible that the peri-implant bone may inhibit complete seating of the abutment (giving the dentist the impression that the abutment is fully seated when in fact it is resting on adjacent bone). This may or may not be evident on a radiograph depending on the implant abutment angulation relative to the central beam of the radiographic unit.
Since most prefabricated abutments are produced in standard size and shape, it can be challenging to customize them to individual patients. The modification procedures to a prefabricated abutment may in turn compromise the biomechanical properties of the abutment to achieve an esthetic result. Some systems provide a stock titanium abutment that can be modified by conventional laboratory reshaping or though use of CAD/CAM milling approaches. Depending on the angulation of the implant relative to the prosthesis, the presence of a central abutment screw can sometimes become a complication. This is especially true for narrow-diameter abutments which generally lack sufficient wall thickness for an ideal preparation.
When the head of the implant is placed below the adjacent bone, the architecture of the bone can develop sloped architecture extending from the PDL support of the adjacent teeth down and across to the implant. This often happens in the maxilla area where implants are generally placed deeper to avoid esthetic issues. Periodically this scalloped osseous architecture necessitates the prosthodontist to assess and then modify the abutment and occasionally the implant body in this area (Fig. 56-10). In this case, the mucosal transition zone of the abutment is modified to avoid placing pressure on the bone and soft tissues. It is also helpful to develop a flat or even concave emergence profile of the final restoration to maintain soft tissue dimensions around the restoration (Stanford 2005a).
# Other issues related to prosthetic complications
## Implant angulation and prosthetic complications
The role of angled implants on clinical outcomes is often of significant concern. Clelland _et al._ (1995) evaluated the stresses and strains generated by an abutment system capable of three angulations (0•, 15•, and 20•). In this study, they observed peak stresses were located in the cortical bone, and the magnitude of these stresses increased with an increase in the abutment angulation. The maximum stress values were generally within the physiologic parameters described for animals, but in one case, the peak compressive stress for the 20• abutment was slightly above this physiologic zone. Peak tensile strains also increased with abutment angulation, but maximum compressive strain values were the same for all three angles. This study suggested that angled abutments were safe to use relative to the bone stability around the implant body.
One approach advocated by some has been to use multiple implants and place a facial–lingual offset between them to enhance the mechanical stability of a connected FPD. Sutpideler _et al._ (2004) evaluated the effect of an offset on the force transmission to bone-supporting implants aligned in either a straightline configuration or an offset configuration. Also, they addressed the effect of different prosthesis heights and different directions of force application. They observed vertical loading of an implantsupported prosthesis produced the lowest stress to the supporting bone and increasing the angle resulted in greater stress that theoretically simulated surrounding bone. They also observed reducing the height of the prosthesis from 12 mm to 6 mm (crown to implant ratio) or establishing an offset implant location for the middle of three implants can reduce stress, but this reduction did not compensate for the increase in stress found with non-axial loading. This concept has been extended with the recent advocacy for intentionally placing implants at significant angulation relative to each other to avoid vital structures and sinus cavities, and to improve the putative biomechanical position of the implants (Krennmair _et al._ 2005).
**Fig. 56-10** Implant and abutment modification. (a) Patient presented with soft tissue dehiscence on an integrated implant, necessitating placement of an abutment and preparation of the abutment and implant body (b). A fixed partial denture was fabricated using the modified abutment (c) that achieved a reasonable esthetic and functional outcome for this compromised situation (d). Restorative work accomplished by Dr. Manuel Romo DDS (University of Iowa).
Chun _et al._ (2006) investigated the effect of three different abutment types (one-piece, internal-hex, and external-hex) on stress distribution in bone under vertical and inclined loads by finite element analysis. With one-piece implant designs, they observed that the load was transferred evenly into bone as well as within the implant system. However, the maximum stress generated in bone with the one-piece system was always higher than that generated with the internal-hex implant, regardless of load angle inclination. In the case of the internal-hex implant, the contact condition with friction between abutment and implant in the tapered joints and at abutment neck reduced the effect of bending caused by horizontal component of inclined load. The maximum stress in bone was the highest for the external-hex implants.
Erneklint _et al._ (2006) evaluated the load resistance in a conical implant system with two different screwretained abutment angled designs (20• and 45•) and three different retaining screw materials. They observed that the 20• abutment withstood non-axial forces to a greater extent than a 45• abutment, regardless of retaining screw material. The 45• abutment failed under oblique loads between 450 and 530 N while the 20• abutment failed at 1280–1570 N. Regarding the retaining screw materials, differences were more obvious in a 20• abutment, but not insignificant in the 45• abutment as well. In general, they concluded that abutment taper angles were more important than retaining screw material in determining the assembly strength.
The angulation of the implants can also influence the outcomes of implant overdenture therapy. Gulizio _et al._ (2005) evaluated the retentive capacity of gold and titanium overdenture attachments placed on implants positioned at 0•, 10•, 20•, and 30• from a vertical reference axis. They observed that significant differences in retention of gold matrices were noticed when ball abutments were positioned at 20• and 30•, but not at 0• and 10•. Also they noticed significantly higher variance in retention among the titanium matrices, despite the finding that angle was not a factor affecting retention for titanium matrices. In other words, angle of the implants had an effect on the retention of gold matrices, but not for titanium matrices. This study supports the clinical observation that implant-supported overdentures have higher maintenance needs and may have higher long-term ongoing costs relative to conventional tooth replacement therapies (Naert _et al._ 2004a,b; Krennmair _et al._ 2005; Zitzmann _et al._ 2005; Trakas _et al._ 2006; Visser _et al._ 2006).
## Screw-retained vs. cement-retained restorations
The method of attachment of the prosthesis to the implant/abutment can create prosthetic complications. The major advantages of screw-retained implant-supported restorations include their retrievability and freedom from residual cement problems. Thus this type of restoration scheme can be applied when there is a need for future removal, e.g. necessary hygiene maintenance procedures or questionable prognosis of the restoration. It could also be applied when the restorative margin is located too deep for removal of excess cement at the time of restoration delivery. The same advantage applies to provisional restorations as well. However, this type of restoration has inherent disadvantages. Because of the required screw access hole, it not only compromises the esthetics and occlusion, but also has the potential to undermine the strength of the restoration due to the lack of material. The presence of the prosthetic screw also bears the potential of screw complications. Additionally, this type of restoration is more sensitive to the passive fit of the restoration to the supporting implants.
Regarding the clinical performance of each type of restoration, the literature indicates that screwretained restorations may present more postoperative complications compared to cement-retained restorations. Duncan _et al._ (2003) reported that patients restored with screw-retained restorations had problems with prosthetic screws and screw access hole filling material while no complications were encountered with patients restored with cementretained restorations after 3 years. Karl _et al._ (2006) found that cement-retained FPDs may result in lower strain levels compared to conventional screw-retained FPDs at the time of either the cementation or screwtightening procedure. Higher strain level at the time of delivery may reduce the passivity of the fit of the restoration and increase potential future complications. This result is in accordance with other _in vitro_ studies (Guichet _et al._ 2000; Taylor _et al._ 2000). However, this study carefully suggests that regardless of the type of restoration, no true passive fit can be achieved. Skalak (1983) theorized that a nonpassive fit of the restoration can induce biologic and prosthetic complications. However, Jemt and Book (1996) reported that they could not find a direct association between implant prosthesis misfits with marginal bone loss over 5 years. Vigolo _et al._ (2004) found no evidence of different behavior of the peri-implant marginal bone and soft tissue response around screwretained or cement-retained single-tooth implant restorations.
Overall, there is no consensus of the superiority of one type over the other – it may be determined by the clinical situation and the operator's preference.
## Ceramic abutments
Ceramic implant abutments have recently gained in popularity due to superior esthetic results compared to conventional titanium abutments, especially in thin tissue biotypes (Stanford 2005a). Because of the strength concerns, the current material of choice for ceramic abutments is reinforced ceramic abutment, e.g. alumina (Al2O3) or yettria-stabilized Zirconia (ZrO2) (Fig. 56-7). These abutments were introduced during the 1990s and the first of these abutments consisted of densely sintered aluminum oxide (alumina). Andersson _et al._ (2003) conducted a 5-year multi-center prospective study evaluating the clinical outcome of alumina ceramic abutments. According to this study, the cumulative success rate for alumina ceramic abutments was 98.1% at 5 years compared to 100% for conventional titanium abutments. More recently, zirconia has become popular for ceramic implant abutments. Because ceramic materials are vulnerable to tensile stress, especially around defects or cracks, a ceramic material with higher fracture toughness will be a good material for ceramic abutments. Zirconia is generally known to have higher range of fracture toughness (KIC, ∼7–15 MPam−1) than that of alumina (KIC, ∼4–4.5 MPam−1). Its fracture toughness is comparable to that of metal alloys (KIC, ≥20 MPam−1) (Piconi & Maccauro 1999; Kelly 2004). Zirconia is known to have the relatively unique property of transformation toughening, where the metastable tetragonal phase can be converted into monoclinic phase with the associated volume expansion (Chevalier 2006). This phenomenon is induced by stress concentration at defect or crack tips, through which the crack is put into compression and its growth retarded. This is the main mechanism for its higher fracture toughness, and it could significantly extend the reliability and lifetime of the restoration. However, there is little evidence if the abutment will still retain this property after being reduced down to less than 1 mm during clinical usage. Further, the hydrolytic properties of water interacting with the material during ageing (hydrolytic ageing) is still an active area of laboratory investigation (Rekow & Thompson 2005). There are outstanding questions relative to the use of this material including long-term fatigue strength, degree of preparation/wall thickness needed, intraoral sites, clinical long-term prognosis, etc. Due to the relatively short period after its introduction, there are few studies that assess the clinical performance of these abutments (Att _et al._ 2006; Denry & Holloway 2006; Deville _et al._ 2006; Itinoche _et al._ 2006; Studart _et al._ 2006).
## Esthetic complications
The most frustrating and challenging complication is unacceptable esthetic outcome either at the time of restoration or during long-term follow up. With the growing population of esthetically concerned patients, esthetic complications are a serious matter even if the implant team has done its best throughout the procedure. This is an important issue that the implant team and the patient need to be aware of and endeavor to find solutions to prevent or overcome. Common esthetic complications include complications due to malpositioned implants, thin tissue biotypes, and unfavorable soft tissue responses.
**Fig. 56-11** Soft tissue recession on facial aspect of implant supported restoration.
The potential cause and impact of malpositioned implants was previously described. A very difficult aspect of implant rehabilitation is that sometimes a slight malpositioning can induce dramatic esthetic compromises which do not become evident until the technician is working with the case. A facially malpositioned implant can become a major challenge for the restorative team (Fig. 56-11). In this case, the restorative dentist may have to address a variety of potential problems, including excessive incisogingival dimensions of the crown, exposed head of the implant, unequal gingival margins, etc. Usually, facially malpositioned implants create greater problems than other malpositioned implants. A 1 mm lingual position to the implant in the maxillary esthetic zone can create a prosthetic challenge to have the final restoration appear even and uniform with the natural dentition. Mesially, or distally malpositioned implants can induce improper anatomy of the restoration as the technician attempts to compensate for implant components in the interproximal space (Fig. 56-12).
Unfavorable soft tissue response can also make the treatment very difficult. It is generally accepted that individuals that have relatively thin attached gingiva, or thin tissue biotype, are more vulnerable to gingival/periodontal disease and subsequent sequelae including gingival recession. Similar findings are reported for the tissue response around implant restorations (Kan _et al._ 2003). Thin biotype tissues tend to show more recessive response to trauma. Restorative procedures, like preparation, impression, repeated abutment/provisional removal, or even toothbrushing, can sometimes cause enough trauma to these thin biotype tissues to result in significant recession and compromise the treatment outcome. It is very important to identify the tissue type early at the treatment planning stage to prevent unfavorable treatment outcome.
**Fig. 56-12** Challenges in creating esthetic outcomes when implants are insufficiently placed. Example demonstrates teeth 11 and 21 with compromised contours due to close proximity of the implants.
## Success/survival rate of implant-supported prostheses
As previously described, the biologic success/survival rate is extremely high and has become more predictable even in areas that were considered of high risk (e.g. maxillary posterior region). It may be beneficial to know what the literature indicates regarding the success/survival rate of restorations fabricated on the osseointegrated implants. Pjetursson _et al._ (2004) obtained estimates of the long-term survival/success rates of implant-supported FPDs and of the incidence of technical complications in partially edentulous patients with an observation period of more than 5 years. "FPD survival" was defined as "the FPD remaining _in situ_ with or without modification for the observation period", as compared to the definition of "FPD success" being "FPD being free of all complications over the entire observation period" in this study. The cumulative FPD survival rate was 95% after 5 years and 86.7% after 10 years, respectively. In this study, the authors noted an important fact that most of the prosthetic complications occur after 5 years of clinical service. The underlying issue this illustrates is the problem associated with the rapid rate of manufacturing market changes in implant products and components. By the time the restoration needs repair or replacement, the required components may be difficult if not impossible to obtain. Regarding comparison of different implant systems, there is little evidence of superiority of one system over another in terms of mechanical failure. Implant–abutment joint geometry, design of the restoration, and patient factors like parafunctional habits or heavy occlusal forces tend to have more impact on the outcome of implant-supported restoration than implant surface material or topography (Rangert _et al._ 1995; Astrand _et al._ 1999; Naert _et al._ 2002a,b). Some studies indicate that the cumulative complication rate of prosthetic problems can be as high as 43.1% after 5 years (Jemt _et al._ 2003), compared to other studies finding it to be as low as 19.3% after 5 years (Bragger _et al._ 2001; Pjetursson _et al._ 2004). A summary of these studies indicates that one may expect one out of four implant-supported restorations will require some type of repair whether it be minor, such as screw or abutment tightening, or major, such as entire restoration replacement, after 5 years. This implies that significant chair time may be necessary for the maintenance of these restorations (Pjetursson _et al._ 2004).
Berglundh _et al._ (2002) also noticed the higher mechanical/technical complication rate compared to the lower biologic complication rate. This study observed interesting aspects: the incidence of implant loss prior to functional loading was higher by threefold when multiple implants are placed for larger restorations like overdentures or fixed complete restorations than that of single-tooth restorations; implant loss during function occurred in 2–3% of implants supporting fixed reconstructions, while twice as many implants were lost in overdenture therapy during a 5-year period. In this case, the highest frequencies of implant loss during function occurred in the maxilla.
### Conclusions
Implant therapy provides many benefits as a form of tooth replacement therapy. As with any form of prosthetic rehabilitation it has limitations including wear, material fatigue and fracture, soft tissue recession and subsequent complications, increased maintenance and costs. The benefits, though, can be enormous with the enhanced patient quality of life that comes with a definitive replacement of teeth. Patients need to be aware during the treatment planning process that the treatment provided may need to be replaced periodically as normal ageing and wear occurs. Specific patient-based risk factors such as parafunctional habits should be discussed and the patient made aware of the risks to the prosthetic reconstructions.
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# Part 17: Orthodontics and Periodontics
57 Tooth Movements in the Periodontally Compromised Patient
_Björn U. Zachrisson_
58 Implants Used for Orthodontic Anchorage
_Marc A. Schätzle and Niklaus P. Lang_
# Chapter 57
# Tooth Movements in the Periodontally Compromised Patient
Björn U. Zachrisson
* * *
Orthodontic tooth movement in adults with periodontal tissue breakdown
Orthodontic treatment considerations
Esthetic finishing of treatment results
Retention – problems and solutions; long-term follow-up
Possibilities and limitations; legal aspects
Specific factors associated with orthodontic tooth movement in adults
Tooth movement into infrabony pockets
Tooth movement into compromised bone areas
Tooth movement through cortical bone
Extrusion and intrusion of single teeth – effects on periodontium, clinical crown length, and esthetics
Regenerative procedures and orthodontic tooth movement
Traumatic occlusion (jiggling) and orthodontic treatment
Molar uprighting, furcation involvement
Tooth movement and implant esthetics
Gingival recession
Labial recession
Interdental recession
Minor surgery associated with orthodontic therapy
Fiberotomy
Frenotomy
Removal of gingival invaginations (clefts)
Gingivectomy
* * *
Orthodontic treatment may be adjunctive to periodontal therapy. The loss of periodontal support or teeth may result in elongation, spacing, and proclination of incisors, rotation, and tipping of premolars and molars with collapse of the posterior occlusion, and decreasing vertical dimension. But orthodontic tooth movement can also facilitate the management of several restorative and esthetic problems in adults. Such difficulties may be related to subgingivally fractured or lost teeth, tipped abutment teeth, excess spacing, inadequate implant or pontic space, supraerupted teeth, narrow alveolar ridges that prevent implant placement, and other conditions (Ong _et al_. 1998). The purpose of this chapter is to discuss how recent basic and clinical information may be used to improve treatment planning, clinical management, and retention for patients in whom different malocclusions are caused or complicated by moderate to advanced periodontal destruction
# Orthodontic tooth movement in adults with periodontal tissue breakdown
Poorly executed orthodontic treatment in periodontal patients can certainly contribute to further periodontal tissue breakdown. In particular, the combination of inflammation, orthodontic forces, and occlusal trauma may produce a more rapid destruction than would occur with inflammation alone (Kessler 1976). However, with properly performed treatment, extensive orthodontic tooth movement can be made in adults with a reduced but healthy periodontium without further periodontal deterioration. Figures 57-1 to 57-6 show the pretreatment and post-treatment conditions in four different adult orthodontic patients with advanced periodontitis. The findings of no significant further periodontal tissue breakdown in these patients were the result of carefully controlled treatment planning considerations
Only a few well controlled studies have been published on groups of adults with advanced periodontitis, who have received comprehensive orthodontic fixed-appliance treatment. Boyd _et al_. (1989) described ten adults with generalized periodontitis who received pre-orthodontic periodontal treatment including surgery, and then regular maintenance at 3-month intervals during a 2-year orthodontic treatment period. They were compared with ten control adults who had normal periodontal tissues, and 20 adolescent orthodontic patients. The results demonstrated that:
**Fig.57-1** Adult male patient with advanced periodontitis and marked pathologic migration of the anterior teeth before (left column) and after (right column) periodontal and orthodontic fixed-appliance treatment for 2 years. Clinical appearance of the face and dentition are dramatically improved after the combined periodontic/orthodontic treatment. The dental result is maintained by means of bonded lingual retainer wires. A maxillary two-unit and a mandibular three-unit bridge were constructed. Some interdental recession was unavoidable in the mandibular anterior region (d), but it does not show much clinically (b)
* Adults were more effective than adolescents in removing plaque, especially late in the orthodontic treatment period.
* Tooth movement in adults with reduced, but healthy, periodontium did not result in significant further loss of attachment (none of the adults had additional mean loss of attachment of more than 0.3 mm).
* Adults with teeth that did _not_ have healthy periodontal tissues may experience further breakdown and tooth loss due to abscesses during orthodontic treatment.
In another study by Årtun and Urbye (1988), 24 patients with advanced loss of marginal bone and pathologic tooth migration received active appliance therapy for an average of 7 months, following periodontal treatment. Bone level measurements on radiographs indicated that the majority of sites showed little or no additional loss of bone support. However, a few sites demonstrated pronounced additional bone loss
More recent studies on much larger groups (350– 400 patients) of consecutively treated adult patients from different practices (Nelson & Årtun 1997; Re _et al_. 2000) have confirmed that: (1) pretreatment evidence of periodontal tissue destruction is no contraindication for orthodontics, (2) orthodontic therapy improves the possibilities of saving and restoring a deteriorated dentition, and (3) the risk of recurrence of an active disease process is not increased during appliance therapy. However, these larger samples have indicated that adult orthodontic patients are at a somewhat higher risk than adolescents for tissue breakdown. The mean bone loss on radiographs of the six anterior teeth in the study of Nelson and Årtun (1997) was 0.54 mm (SD 0.62). Only 2.5% of the patients had average bone loss of 2 mm or more, but as many as 36% of these patients had one or more surfaces with bone loss exceeding 2 mm
**Fig. 57-2** Long-term radiographic follow-up of the same patient as in Fig. 57-1. Radiographs of maxillary and mandibular anterior regions 7 years after the completion of orthodontic therapy (b,d) show reduced but healthy periodontium, with no progression of periodontal tissue destruction compared with the initial situation (a,c)
## Orthodontic treatment considerations
The key element in the orthodontic management of adult patients with periodontal disease is to eliminate, or reduce, plaque accumulation and gingival inflammation. This implies much emphasis on oral hygiene instruction, appliance construction, and periodic check-ups throughout treatment (Zachrisson 1996)
**Fig. 57-3** Adult female periodontitis patient with pathologic migration of the maxillary incisors before (a,b), during (c–e), and after (f) periodontal and orthodontic treatment. An attempt had been made by the periodontist to grind and splint the overextruded right central incisor with composite resin (b) before orthodontic treatment was started. Due to extensive mesial and distal recontouring of the incisors (stripping) during the treatment (c,d), it was possible to obtain an esthetic final result with almost intact gingival papillae between the incisors in both the maxilla and in the mandible (f)
The most appropriate method for tooth movement must be determined in each particular case. Although minor or partial orthodontic treatment with sectional or removable appliances may be possible in some instances, in the majority of cases a fully controlled technique with fixed appliances in both dental arches is preferred in order to carefully control the movement of teeth in three planes
The orthodontic appliance has to be properly designed. It must provide stable anchorage without causing tissue irritation, and must be esthetically acceptable. For psychologic reasons bonded ceramic brackets are preferred in the most visible regions (Figs. 57-3 to 57-6), generally for the maxillary teeth, whereas stainless steel or gold-coated attachments are commonly used elsewhere in the mouth (Figs. 57-3, 57-5)
To counteract the tendency of orthodontic appliances to increase the accumulation of plaque on the teeth, attempts should be made to keep the appliances and mechanics simple, and avoid hooks, elastomeric rings, and excess bonding resin outside the bracket bases. The use of steel ligatures is recommended on all brackets (Figs. 57-3 to 57-6), since elastomeric rings have been shown to be signifi cantly more plaque attractive than steel ties (Forsberg _et al_. 1991). Bonds are preferable to bands (Boyd & Baumrind 1992). Bonded molars show less plaque accumulation, gingivitis, and loss of attachment interproximally than banded molars during orthodontic treatment of adults. However, bonding is more complicated in adult patients than in adolescents. Many adults have amalgam restorations and crown-and-bridge restorations made of porcelain or precious metals. Thanks to the introduction of new techniques and materials, it is feasible to bond orthodontic brackets, buccal tubes, and retainer wires to artificial surfaces. Clinical experience with bonding to different artificial tooth surfaces, except gold, is excellent (Zachrisson 2000a,b)
**Fig. 57-4** Radiographic and clinical occlusal appearance of the same patient as in Fig. 57-3. No noticeable progression of the periodontal tissue destruction has occurred (compare a and b), and although markedly reduced the periodontium is healthy after the orthodontic therapy (b,c). The treatment result is maintained by means of gold-coated lingual retainers over six maxillary and eight mandibular anterior teeth (d,e).These bonded retainers act as effective orthodontic retainers as well as neat and hygienic periodontal splints. Despite the unfavorable crown–root ratios of particularly the mandibular incisors, the situation is largely unchanged 6 years later (f,g), and the gingival papillae fill in the spaces between the lower anterior teeth nicely (h)
**Fig. 57-5** Another adult female periodontitis patient with pathologic migration of the maxillary incisors before (a–c), during (d,e), and after (f) periodontal and orthodontic treatment. Despite the advanced periodontal tissue break-down, the case was treated with extraction of two upper first premolars (d). Due to the extensive mesial and distal recontouring of the incisors (stripping) during the treatment (e), it was also possible in this case to obtain an esthetic final result with almost intact gingival papillae between the incisors (h). The clinical and radiographic situation 1.5 years after treatment is shown in g–i. Note goldcoated short labial retainer wires about the closed extraction sites to prevent space reopening (f)
**Fig. 57-6** Adult female periodontitis patient with marked loss of the interdental papilla between the maxillary central incisors (a,b). This gap is caused by the "fan-shaped" morphology of the central incisors, which places the interproximal contact too near the incisal edge. To eliminate the unesthetic soft tissue gap, the mesial surfaces of the central incisors were reshaped (c) to lengthen their connector area and move the contact point gingivally (d). After continued orthodontic space closure, a more esthetic final result was achieved (e,f)
Renewed oral hygiene instruction and motivation is made after placement of the orthodontic appliances. During the treatment period professional tooth cleaning by a dental hygienist or periodontist may be performed at 3-month intervals (Boyd _et al_. 1989; Boyd & Baumrind 1992), or after regular examination updates at 6- and 12-month intervals, depending on the situation. The re-examinations should include recordings of probing depths, mobility, bleeding on probing, suppuration, gingival recessions, bone levels, etc. Professional scaling may be indicated during _active intrusion_ of elongated maxillary incisors, since orthodontic intrusion may shift supragingival plaque to a subgingival location (Ericsson _et al_. 1977, 1978). If efforts at maintaining excellentto-good oral hygiene are unsuccessful, orthodontic treatment should be terminated (Machen 1990)
After appliance removal, reinstruction in oral hygiene measures should be given. Otherwise, subsequent labial gingival recession may be risked due to overzealous toothbrushing, since cleaning is now easier to perform
## Esthetic finishing of treatment results
Adults with a reduced periodontium represent different challenges for orthodontists than adolescents. Worn or abraded teeth, missing papillae and uneven crown lengths are common problems, and it is therefore more difficult to obtain an esthetically optimal appearance of the teeth and gingiva after bracket removal
Most incisor teeth in adults with malocclusions have more or less worn incisal edges, which represent an adaptation to functional demands. When the axial inclinations and rotations of such incisors are corrected, there is frequently a need for incisal grinding towards a more normal contour. Such grinding can be performed safely as long as the wear is limited, the overbite is adequate, and the patients display enough tooth material in conversation and on smiling. When the abrasion is more significant, however, cooperation with a restorative dentist is generally indicated
The presence of papillae between the maxillary incisors is a key esthetic factor after orthodontic treatment. Normally, when long-standing crowding with incisor overlap is corrected orthodontically in adults, it is generally not possible to have an intact papilla. This is because the contact point becomes located too far incisally on the triangular crowns that have not had a normal interdental wear pattern. Similarly, in patients with advanced periodontal disease and destruction of the crestal bone between the incisors, the papillae may be absent. This produces unesthetic gaps between the teeth after orthodontics. The best method of correcting this problem is to recontour the mesiodistal surfaces of the incisors during the orthodontic finishing stage (Tuverson 1980). When the diastemata thus created are closed, the roots of the teeth can come closer together. The contact point is lengthened and moved apically, and the papilla can fill out the interdental space more easily (Figs. 57-3, 57-5, 57-6; also see Fig. 57-28)
In patients with high or normal smile lines, the relationship of the gingival margins of the maxillary anterior teeth may be another important factor in the esthetic appearance of the crowns (Kokich 1996a,b). When adult patients have gingival margin discrepancies between adjacent teeth, the orthodontist must determine the proper solution for the problem: orthodontic movement to reposition the gingival margin (see Fig. 57-17) or surgical correction (gingivectomy) to increase the crown length of single or several teeth (see Fig. 57-29)
## Retention – problems and solutions; long-term follow-up
Due to the anatomic and biologic differences in tissue reaction between adults and children (Melsen 1991), adults undergoing extensive orthodontic treatment will generally need, at least, a longer period of retention than would an adolescent patient. Also, growth and development no longer take place and cannot aid in changing occlusal levels or in space closure by the eruption of posterior teeth with mesial drift. The space reopening tendency of closed extraction sites in adults can be mitigated by use of labially bonded retainers (Figs. 57-1, 57-5)
The migration of teeth associated with periodontal tissue breakdown around the incisors in adults is usually blamed on inflammatory swelling or the tongue thrust. However, according to Proffit (1978), two major primary factors are involved in the equilibrium which determines the final position of teeth. These are the resting pressures of lip or cheek and tongue, and forces produced by metabolic activity within the periodontal membrane. With an intact periodontium, unbalanced tongue–lip forces are normally counteracted by forces from the periodontal membrane. However, when the periodontium breaks down, its stabilizing function no longer exists and the incisors begin to move. A consequence of this concept would be that persons with advanced periodontal disease and tooth migration would need permanent retention after the orthodontic correction. For patients with minimum-to-moderate loss of periodontal tissue support, more "normal" retention periods may be sufficient
The optimal long-term retainer for adults with reduced periodontium is the flexible spiral wire (FSW) retainer bonded lingually on each tooth in a segment. The bonded retainer in the anterior region is generally used together with a maxillary removable plate. The fabrication and long-term evaluation of bonded retainers is described by Dahl and Zachrisson (1991). Figures 57-3, 57-4, 57-5 and 57-20 demonstrate different designs of FSW retainers in the maxilla and the mandible in several patients. At the same time as the FSW retainer works as a reliable, invisible orthodontic retainer, it concomitantly acts as a periodontal splint, which allows the individual teeth within the splint to exert physiologic mobility. As long as the retainer remains intact, small spaces might open up distal to, but not within, the retainer
Splinting may not be needed for most teeth with increased mobility after periodontal therapy (Ramfjord 1984). However, reduced mobility of teeth after combined periodontal and orthodontic treatment by using a bonded retainer would seem to be of considerable benefit. If a bonded retainer is not used, and instead a removable plate or spring retainer is used at night on a long-term basis, there is a risk for ongoing jiggling of the teeth because of the relapse tendency during the day. Experimental studies in animals indicate that jiggling forces may facilitate the progress of attachment loss in periodontitis, or at least result in more bone resorption. Also, more connective tissue reattachment and bone regeneration may occur around non-jiggled teeth. Monkey experiments have shown that when experimental jiggling of teeth was stopped, a significant gain of alveolar bone occurred (Nyman _et al_. 1982). Similarly, Burgett _et al_. (1992) demonstrated that healing following periodontal therapy may be more advantageous in patients who received occlusal adjustment than in non-adjusted patients
Long-term follow-up of patients who have received combined periodontal and orthodontic treatment, and have used bonded retainers for several years, demonstrates excellent stability and apparently unchanged, or even improved, periodontal condition (Figs. 57-4, 57-7, 57-8). It should be pointed out, however, that a bonded maxillary retainer must be placed out of occlusion with the mandibular incisors, because biting on a retainer wire will lead to unacceptably high bond failure rates (Årtun & Urbye 1988)
## Possibilities and limitations; legal aspects
Adult orthodontic patients with marked periodontal destruction may represent potential problems even when optimal treatment is provided. There are, however, no definite metric limits in terms of probing depths or loss of attachment when orthodontic tooth movement can no longer be performed (Diedrich 1999). Each individual treatment plan may depend on a variety of factors and can be limited by biomechanical considerations (force systems, limited anchorage), by periodontal risk factors (tooth/alveolar bone topography, sinus recesses, activity and prognosis of the periodontitis), and by limited patient motivation and poor oral hygiene cooperation
Single case reports have documented successful periodontal–orthodontic treatment with localized juvenile periodontitis (LJP) after conventional periodontal therapy (Harpenau & Boyd 2000), or with continous antiseptic and short-term systemic (Folio _et al_. 1985) or local (Hoerman _et al_. 1985) antibiotic applications, and microbiologic testing during the orthodontic treatment period to reduce the risk of recurrent disease. However, until more evidence is accumulated, it may seem wise to avoid orthodontic treatment in patients with particularly aggressive forms of periodontal disease. Similarly, multi-rooted teeth with questionable prognosis should be moved orthodontically only in exceptional situations
_"Hopeless teeth"_ : According to old concepts, the retention of teeth diagnosed as periodontally "hopeless" would accelerate the destruction of the adjacent interproximal periodontium. Such teeth were therefore frequently extracted in the past. However, the theoretic rationale for such extractions would seem unsupported, and recent follow-up studies have demonstrated that retained periodontally "hopeless" teeth do not significantly affect the interproximal periodontium of adjacent teeth following periodontal therapy (Chace & Low 1993). The clinical implication is that these teeth can be useful for orthodontic anchorage, if the periodontal inflammation can be controlled (Fig. 57-9). Occasionally, the hopeless tooth may be so improved after orthodontic treatment that it is retained (Mathews & Kokich 1997). Alternatively, a hopeless molar may be hemisectioned after the orthodontic treatment, and the best root may be used as a bridge abutment (Fig. 57-10). Most of the time, however, the hopeless tooth will be extracted, especially if other restorations are planned in the segment
For improved patient care, stress reduction, and reduction or elimination of law suits, careful exami-nation protocols, documentation and correspondence techniques, and regular progress evaluations are important. The legal implications of orthodontic risk management concepts may be that it is preferable to terminate treatment for patients who fail to improve oral hygiene care, despite the orthodontist's efforts. In the long term, this will be better for both patient and orthodontist, since termination, if properly handled, will be more easily defended than permitting the condition to worsen (Machen 1990). However, if proper procedures are followed, termination of orthodontic care for periodontal patients will very rarely be needed
**Fig. 57-7** Adult male periodontitis patient after periodontal and orthodontic therapy (a–d). The patient was treated with generalized gingivectomies according to concepts aiming at pocket elimination. The orthodontic result is maintained with a sixunit lingually bonded retainer (d). The bonded wire will act both as an orthodontic retainer and as a periodontal splint, which would appear advantageous in cases where the tissue destruction is as advanced as in this patient. (e) and (f) show the radiographic appearances 7 and 9 years, respectively, after removal of the orthodontic appliances. The left central incisor had so little bone support that if the bonded retainer had not been used, the tooth would probably had been lost over time (see also Fig. 57-8)
**Fig. 57-8** Post-treatment radiographic (a) and clinical (b) appearance of the mandibular dentition in the same patient as in Fig. 57-7 after periodontal and orthodontic treatment. The mandibular six-unit retainer bonded lingual retainer (b) concomitantly acts as a periodontal splint. Note signs of improvement of periodontal condition 7 and 9 years, respectively, after the orthodontic treatment (c,d), with marked crestal lamina dura contours
**Fig. 57-9** "Hopeless" mandibular right first molar (a) can be used as part of anchorage to move the premolars mesially and upright the second molar (b–d). The first molar may be kept, or extracted, after the orthodontic treatment period
**Fig. 57-10** "Hopeless" mandibular right first molar (a) was used as anchorage during orthodontic treatment to close spaces anteriorly, before it was hemisectioned and the distal root employed as a bridge abutment (b)
**Fig. 57-11** Schematic illustration of persisting junctional epithelium subsequent to orthodontic tooth movement (direction of arrow) into an infrabony pocket
# Specific factors associated with orthodontic tooth movement in adults
## Tooth movement into infrabony pockets
Orthodontic forces _per se_ are unlikely to convert gingivitis into destructive periodontitis. The plaqueinduced lesion in gingivitis is confined to the supra-alveolar connective tissue, whereas tissue reactions to orthodontic forces occur in the connective tissue between the root and the alveolar bone. However, infrabony pockets, i.e. angular bony defects with inflamed connective tissue and epithelium apical to the bone crest, may develop as a result of destructive periodontitis. Infrabony pockets may also be created by orthodontic tipping and/or intruding movements of teeth harboring plaque (Ericsson _et al_. 1977). The effect of bodily tooth movement into infrabony defects has been evaluated experimentally in monkeys (Polson _et al_. 1984) and in dogs (Wennström _et al_. 1993). Provided elimination of the subgingival infection was performed before the orthodontic tooth movement was started, no detrimental effects on the attachment level were observed. The angular bony defect was eliminated by the orthodontic treatment, but no coronal gain of attachment was found and a thin epithelial lining covered the root surface corresponding to its pretreatment position (Fig. 57-11). It was therefore concluded that orthodontic tooth movement into infrabony periodontal defects had no favorable effects on the level of connective tissue attachment. However, it was possible to move teeth with reduced _healthy_ periodontium without additional attachment loss. If, on the other hand, the orthodontic treatment involved movement of teeth into and through a site with inflammation and angular bone loss, an enhanced rate of periodontal destruction was noted
### Conclusion
Since orthodontic movement of teeth into inflamed infrabony pockets may create a high risk for additional periodontal destruction, and because infrabony pockets are frequently found at teeth that have been tipped and/or elongated as a result of periodontal disease, it is clinically essential that periodontal treatment with elimination of the plaque-induced lesion is performed before orthodontic therapy is begun. It is equally important that excellent oral hygiene is maintained throughout the course of the orthodontic treatment. Following these principles, clinical and radiographic observations confirm that orthodontic treatment can be successfully performed in patients with infrabony pockets resulting from periodontal disease
## Tooth movement into compromised bone areas
Orthodontic tooth movement may sometimes be performed in adults with partially edentulous dentitions (due to agenesis or previous extractions of teeth) and such patients may have a more or less compromised alveolar process. Experimental reports (Lindskog-Stokland _et al_. 1993) and clinical studies (Stepovich 1979; Hom & Turley 1984; Goldberg & Turley 1989; Thilander 1996) have shown that a reduction in vertical bone height is not a contraindication for orthodontic tooth movement towards, or into, the constricted area. Mandibular second molars can be moved mesially through remodeled edentulous first molar areas in adults (Fig. 57-12), with only a limited reduction in vertical bone height, averaging −1.3 mm (Hom & Turley 1984). Space closure is possible also in edentulous maxillary first molar areas, although vertical bone loss and some space reopening can be a complication
Histologic observations in animal experiments have confirmed that when light forces were applied to move teeth bodily into an area with reduced bone height, a thin bone plate was recreated ahead of the moving tooth (Fig. 57-13) (Lindskog-Stokland _et al_. 1993). The key to moving teeth with bone is direct resorption in the direction of tooth movement, and avoiding hyalinization. Teeth can also be moved with bone into the maxillary sinus (Melsen 1991)
### Conclusion
Although the results of clinical experiments and follow-ups are encouraging, provided light forces are used and excellent oral hygiene is maintained, it is probably wise not to stretch the indications for tooth movement into constricted bone areas too far. Marked gingival invaginations are sometimes seen in such areas (Fig. 57-12), and computer tomography analysis and human histologic findings indicate that buccal or lingual bone dehiscences may occur (Diedrich 1996). Such defects are not revealed by conventional radiography. The clinical significance of the gingival clefts and bone dehiscences with regard to relapse tendency and periodontal status is not known. For orthodontic tooth movement into markedly atrophied alveolar ridges, the possibility to acquire new bone by, for example, guided bone regeneration (GBR) procedures should be considered
## Tooth movement through cortical bone
Experimental studies in animals have demonstrated that when a tooth is moved bodily in a labial direction towards and through the cortical plate of the alveolar bone, no bone formation will take place in front of the tooth (Steiner _et al_. 1981; Karring _et al_. 1982). After initial thinning of the bone plate, a labial bone dehiscence is therefore created (Fig. 57-14). Such perforation of the cortical plate can occur during orthodontic treatment either accidentally or because it was considered unavoidable. It may happen, for example, (1) in the mandibular anterior region due to frontal expansion of incisors (Wehrbein _et al_. 1994), (2) in the maxillary posterior region during lateral expansion of cross-bites (Greenbaum & Zachrisson 1982), (3) lingually in the maxilla associated with retraction and lingual root torque of maxillary incisors in patients with large overjets (Ten Hoeve & Mulie 1976), and (4) by pronounced traumatic jiggling of teeth (Nyman _et al_. 1982). The soft tissue reactions accompanying such tooth movements are discussed later in this chapter and in Chapter 51
Interestingly, however, there is potential for repair when malpositioned teeth are moved back toward their original positions, and bone apposition may take place (Fig. 57-14). Evidently, the soft tissue facial to an orthodontically produced bone dehiscence may contain soft tissue components (vital osteogenic cells) with a capacity for forming bone following repositioning of the tooth into the alveolar process (Nyman _et al_. 1982)
### Conclusion
The clinical implication of these observations is encouraging. Bone dehiscences which may occur due to uncontrolled expansion of teeth through the cortical plate may be repaired when the teeth are brought back, or relapse, towards a proper position within the alveolar process, even if this occurs several months later. Similar repair mechanisms may be expected to occur when marked jiggling of teeth is brought under control and stabilized. In the case of buccal cross-bites, the initial discrepancy can apparently be overcorrected with both slow and rapid expansion treatment approaches without causing permanent periodontal injury to the settled occlusion
**Fig. 57-12** Orthodontic tooth movements into edentulous areas with reduced bone height in compromised mandible of adult female patient. During the orthodontic treatment (c–g), the teeth were moved to close three areas of marked alveolar bone constriction (a,b), most notably in the right first molar area. Note that the impacted third molar erupted spontaneously as the second molar was moved mesially (g). (h) Final result with bonded six-unit lingual and two-unit labial retainers
**Fig. 57-13** (a,b) Histologic specimens from experimental orthodontic tooth movement into edentulous areas in dogs. The thin bone spicule along the pressure side of the test tooth (b) indicates tooth movement with, and not through, bone. (c,d) The same patient as in Fig. 57-12. Note radiographic visualization of the thin bone spicule on the mesial side of the second molar (arrow in d). Although the molar is moved to contact the second premolar, a marked gingival invagination is present in the area (arrow in c). (a) and (b) from Lindskog-Stokland _et al_. (1993)
## Extrusion and intrusion of single teeth – effects on periodontium, clinical crown length, and esthetics
### Extrusion
Orthodontic extrusion of teeth, or so-called "forced eruption", may be indicated for (1) shallowing out intraosseous defects and (2) for increasing clinical crown length of single teeth. The forced eruption technique was originally described by Ingber (1974) for treatment of one-wall and two-wall bony pockets that were difficult to handle by conventional therapy alone. The extrusive tooth movement leads to a coronal positioning of intact connective tissue attachment, and the bony defect is shallowed out. This was confirmed in animal experiments (van Venroy & Yukna 1985) and clinical trials. Because of the orthodontic extrusion, the tooth will be in supraocclusion. Hence, the crown of the tooth will need to be shortened, in some cases followed by endodontic treatment
During the elimination of an intraosseous pocket by means of orthodontic extrusion, the relationship between the CEJ and the bone crest is maintained. This means that the bone follows the tooth during the extrusive movement. This may or may not be beneficial depending on the clinical situation. In other words, it is sometimes desirable to have the periodontium follow the tooth and in other situations it is desirable to move a tooth out of the periodontal support. This is further discussed under slow versus rapid eruption of teeth in Chapter 51
**Fig. 57-14** Techniques used by Steiner _et al_. (1981) to advance incisors bodily through the labial bone plate in monkeys (a,b) and by Engelking and Zachrisson (1982) to retract the incisors to their original position (after the teeth had remained in extreme labioversion for 8 months) in a study of periodontal regeneration to such tooth movement. (d) Tissue blocks after tooth repositioning show evident bone regeneration
#### _Extrusion with periodontium_
Orthodontic extrusion of a single tooth that needs to be extracted is an excellent method for improvement of the marginal bone level before the surgical placement of single implants (Figs. 57-15, 57-21, 57-22). Not only the bone, but also the soft supporting tissues will move vertically with the teeth during orthodontic extrusion. Using tattoo marks in monkeys to indicate the mucogingival junction and clinical sulcus bottom, Kajiyama _et al_. (1993) made a metric evaluation of the gingival movement associated with vertical extrusion of incisors. The results indicated that the free gingiva moved about 90% and the attached gingiva about 80% of the extruded distance. The width of the attached gingiva and the clinical crown length increased significantly, whereas the position of the mucogingival junction was unchanged. Orthodontic extrusion of a "hopeless" incisor is also, therefore, a useful method for esthetic improvement of the marginal gingival level associated with the placement of implants (Fig. 57-22)
#### _Extrusion out of periodontium_
In teeth with crown–root fracture, or other subgingival fractures, the goal of treatment may be to extrude the root out of the periodontium (Figs. 57-16, 57-17), and then provide it with an artificial crown. When an increased distance between the CEJ and the alveolar bone crest is aimed at, the forced eruption should be combined with gingival fiberotomy (Pontoriero _et al_. 1987; Kozlowsky _et al_. 1988). In animal experiments, Berglundh _et al_. (1991) showed that when the fiberotomy (i.e. excision of the coronal portion of the fiber attachment around the tooth) was performed frequently (every 2 weeks), the tooth was virtually moved out of the bony periodontium, without affecting the bone heights or level of the marginal gingiva of the neighboring teeth. This procedure is illustrated in Fig. 57-17
### Intrusion
Similar to the indications for extrusion, the orthodontic intrusion of teeth has been recommended (1) for teeth with horizontal bone loss or infrabony pockets, and (2) for increasing the clinical crown length of single teeth. However, the benefits of intrusion for improvement of the periodontal condition around teeth are controversial
**Fig. 57-15** (a,b) Adult female patient with evidence of local severe periodontal tissue breakdown before treatment. The bone loss is particularly pronounced on the mandibular right second premolar (g) and canine (j), whereas the bone support for the first premolar is much better (g,j). The treatment plan included slow orthodontic extrusion of the second premolar and canine to regenerate an improved vertical alveolar bone height prior to the placement of implant-supported restorations. Brackets were placed in a gingival location on the teeth to be extruded (c) and leveling was started with super-elastic rectangular arch-wires. After removal of the pulp, the crowns of the teeth to be extruded were ground with diamond instruments to avoid jiggling with the teeth in the opposing arch (c). A cantilever spring was added for the canine. After 10 months, the leveling was completed (d) and the extruded teeth were extracted with forceps (e). Note the even bone levels (e) and compare with the initial situation (b). A remarkable amount of bone build-up is seen on the radiographs at 10 months of leveling (h,k) before insertion of the implants. A comparison of the final bone heights relative to the cemento-enamel junctions of the neighboring teeth with the initial situation reveals that a significant portion of the bone support for the well integrated implants has been created by the slow vertical tooth movements. The clinical and radiographic situation at the 3-year follow-up is shown in f, i and l
**Fig. 57-16** (a) Extrusion out of the periodontium of central incisor with deep crown-root fracture. Rapid extrusion with continuous orthodontic force combined with fiberotomy every 2 weeks. The amount of extrusion can be evaluated by comparing the root ends of the incisors in a–c. (b) The situation after 1.5 months of extrusion. (c) After 4 months, the fracture line was moved from a location below the bone level (a) to a position well above it (c), and the incisor could now be properly restored
Fig. **57-17** Extrusion out of periodontium. Due to subgingival crown-root fracture on the maxillary right lateral incisor (a,d), this tooth was extruded out of the periodontium with continuous force (a,b) and fiberotomy was performed with 2-week intervals. The amount of extrusion is evident by comparison of the relationship between lateral and central incisor root ends in (e) and (f). Having moved the fracture line to a supragingival position (arrow in c), the tooth could be safely restored. (d) The clinical situation 4 years after treatment
As mentioned, the intrusion of plaque-infected teeth may lead to the formation of angular bony defects and increased loss of attachment. When oral hygiene is inadequate, tipping and intrusion of the teeth may shift supragingivally located plaque into a subgingival position, resulting in periodontal destruction (Ericsson _et al_. 1977, 1978). This explains why professional subgingival scaling is particularly important during the phase of active intrusion of elongated, tipped, and migrated maxillary incisors commonly occurring in association with advanced periodontal disease. Even in a healthy periodontal environment the question remains as to whether the orthodontic tooth movement intrudes a long epithelial attachment beneath the margin of the alveolar bone or whether the alveolar crest is continously resorbed in front of the intruding tooth
Histologic (Melsen 1986; Melsen _et al_. 1988) and clinical (Melsen _et al_. 1989) studies indicate that new attachment is possible associated with orthodontic intrusion of teeth. In monkey experiments, periodontal tissue breakdown was induced and intrusion along the axis of the incisors with light forces was initiated following flap surgery. Histologic analysis showed new cementum formation and connective tissue attachment on the intruded teeth, by an average of 1.5 mm, provided a healthy gingival environment was maintained throughout the tooth movement. The increased activity of periodontal ligament cells and the approximation of formative cells to the tooth surface was suggested to contribute to the new attachment. In the clinical study, the periodontal condition was evaluated following the intrusion of extruded and spaced incisors in patients who had advanced periodontal disease. Judging from clinical probing depths and radiography, there was a beneficial effect on clinical crown lengths and marginal bone levels in many cases, despite large individual variation
However, the reported clinical and histologic findings associated with a combined orthodontic–periodontal approach must be assessed with great caution, and these findings have not been confirmed by others. Furthermore, new techniques like guided tissue regeneration (GTR) and other regenerative procedures (see below) would appear to be more promising when it comes to creation of new attachment
Similar to the case with extrusion, metric and histologic studies have been made after experimental intrusion of teeth in monkeys. According to Murakami _et al_. (1989), the gingiva moved only about 60% of the distance when the teeth were intruded with a continuous force of 80–100 g. However, Kokich _et al_. (1984) recommended an interrupted, continuous force for levelling of gingival margins on supraerupted teeth (Fig. 57-18)
The key to understanding why intrusion can be used to increase clinical crown length is related to the subsequent restorative treatment. When orthodontic intrusion is used for levelling of the gingival margins to desired heights, such teeth must then be provided with porcelain laminate veneers or crowns (Fig. 57-18)
**Fig. 57-18** (a) Adult female patient in whom the clinical crown length of the maxillary right central incisor was shorter than that of the left central incisor. Because the sulcular depths were normal, the crown lengths were corrected by orthodontic intrusion of the right central incisor (b) and restoring the incisal edge (b) with enamel-bonded ultrathin porcelain laminate veneer (c,d). The alignment and correction of the crown length discrepancy has improved the esthetic appearance of the dentition. Restoration courtesy of Dr. S. Toreskog
## Regenerative procedures and orthodontic tooth movement
The development of barrier membranes to prevent cells of the epithelium and gingival connective tissue from colonizing the decontaminated root surface, as well as the use of Emdogain®, would appear to provide a distinct improvement in orthodontic therapy in the periodontally compromised patient. New supracrestal and periodontal ligament collagen fibers may be gained on the tension side, which can transfer the orthodontic force stimulus to the alveolar bone (Diedrich 1996). In theory, the regenerative techniques would be advantageous associated with both extrusion and intrusion of teeth with infrabony defects, and for uprighting of tipped molars with mesial angular lesions. Moreover, if the epithelium can be prevented from proliferating apically, a bodily tooth movement into or through an intraosseous defect could eliminate the bony pocket more effectively than in the past (Fig. 57-11)
So far, however, relatively little clinical information is available about the use of different regenerative procedures in connection with orthodontic treatment. Diedrich (1996) reported an experiment in dogs in which orthodontic intrusion with flap surgery and GTR were compared with flap surgery alone on periodontally affected teeth. In the presence of minimal or no round cell infiltration, the marking notch was located beneath the alveolar margin indicating that new attachment had formed. The potential of the intrusive/regenerative mechanism was most impressive within the inter-radicular area. Some clinical observations (Nemcovsky _et al_. 1996; Stelzel & Flores-de-Jacoby 1998; Rabie _et al_. 2001) confirm that different regenerative procedures may enrich the therapeutic spectrum in combined periodontal/ orthodontic approaches (Fig. 57-19). The combined regenerative and periodontal surgical treatments used together with orthodontic tooth movements create new perspectives and should be an interesting field for further experiments on adults with severe loss of periodontal tissues
However, other clinical trials have demonstrated that treatment results with barrier membranes in the GTR technique may vary between different patients and that the method is operator and technique sensitive (Leknes 1995). The patient's oral hygiene during the healing phase is critical, and inflammation around the membrane, particularly if it becomes exposed and contaminated, may lead to discouraging clinical results with marked gingival retraction
Since the membrane is covered in the GBR technique, the risk for inflammation is reduced. The possibility for orthodontic movement of teeth into alveolar processes with deficient bone volume may thus be improved (Basdra _et al_. 1995). Preorthodontic GBR of markedly constricted alveolar ridges also has the advantage that tooth movement through cancellous bone is easier, and the formation of interfering gingival invaginations can be reduced
**Fig. 57-19** (a) Pathologic tooth migration as a result of an advanced periodontal lesion in adult female patient. (b) Severe intraosseous defect between the right central and lateral incisors. (c) Three months after GTR treatment (GoreTex membrane) partial reossification is evident, possibly with new attachment. (d) Orthodontic leveling with controlled space closure and intrusion of the lateral incisor. (e) Result 6 months after orthodontic tooth movements shows no root resorption and a consolidated alveolar crest. From Diedrich (1996)
## Traumatic occlusion (jiggling) and orthodontic treatment
As discussed in Chapter 14, the role of occlusal trauma in periodontal treatment has not been determined. From an orthodontic perspective, it is of interest that several studies indicate that traumatic occlusion forces (1) do not produce gingival inflammation or loss of attachment in teeth with healthy periodontium, (2) do not aggravate and cause spread of gingivitis or cause loss of attachment in teeth with established gingivitis, (3) may aggravate an active periodontitis lesion, i.e. be a co-destructive factor in an ongoing process of periodontal tissue breakdown (in one way or another favor the apical proliferation of plaque-induced destruction), and (4) may lead to less gain of attachment after periodontal treatment – non-surgical or surgical
A major problem in this regard is the lack of established and reliable criteria to identify and quantitate different degrees of traumatic occlusion. Various clinical and radiographic indications, such as unfavorable crown/root ratio, increased tooth mobility, widened periodontal ligament space, angular bone loss, alterations in root morphology, etc. are uncertain and insufficient in diagnosis of occlusal trauma, and there have been few scientific clinical reports to evaluate these signs (Jin & Cao 1992)
The extent to which it is necessary to avoid, or reduce, occlusal trauma during orthodontic treatment is controversial and unsupported by scientific evidence. Some orthodontists use bite-planes in virtually every periodontal case with bone deformities, to reduce occlusal trauma and for the purpose of shallowing the bony defects, as teeth supra-erupt. However, independent studies have shown that surgical pocket elimination including bone sculpturing offers no advantage compared with more conservative periodontal treatment (Ramfjord 1984), and apparently there is little need to shallow or eliminate bony deformities. It would still appear sensible to avoid gross interferences, like raising the bite when a maxillary incisor in lingual inversion is moved over the mandibular teeth, and to mitigate evident occlusal interferences on single teeth with markedly increased mobility. However, it may be a futile exercise to try and eliminate all occlusal trauma during active tooth movement, and a more practical solution is to concentrate on controlling the inflammation. After appliance removal, however, occlusal adjustment by selective grinding may be required. Even though good occlusal function is part of the orthodontic treatment goal, correct cusp–fossa relationships cannot always be achieved in adults with orthodontic therapy alone. In general terms, the adjustment should be directed toward obtaining even and stable tooth contacts in centric relation, a straight forward slide from centric relation to centric occlusion without any side shifts or lateral deviation, freedom in centric, smooth gliding contacts in centric and eccentric mandibular motion, and elimination of balancing side interferences (Burgett _et al_. 1992)
The importance of reducing jiggling of teeth _after_ orthodontic treatment of patients with moderate to advanced periodontitis may be significant: (1) tooth mobility generally increases with loss of support for the teeth, (2) animal experiments have shown that bone dehiscences produced by jiggling forces will regenerate after elimination of the jiggling trauma, and (3) occlusal adjustment may be a factor in the healing of periodontal defects, especially bony defects, after periodontal treatment. Therefore, the bonded orthodontic retainers, which stabilize the teeth, may secure optimal conditions for improved periodontal healing and bone regeneration after the orthodontic treatment period (Figs. 57-5, 57-7, 57-8). In fact, long-term follow-ups of orthodontic patients with advanced periodontal tissue breakdown may demonstrate better periodontal conditions, with marked crestal lamina dura contours, many years after appliance removal than at the end of the orthodontic treatment (Figs. 57-7, 57-8). If bonded retainers had not been used in many such cases, the most affected teeth would probably have been lost with time
## Molar uprighting, furcation involvement
The problem of mesially tipped mandibular molars because of non-replacement of missing first molars has been the subject of many anecdotal reports over the past 30 years. Tipped molars have been considered a causative or at least an aggravating factor for future periodontal tissue breakdown. However, Lundgren _et al_. (1992) recently observed that 73 molars that had remained in a markedly tipped position for at least 10 years, with most molars having been tipped for as long as 20–30 years, did not constitute an increased risk for initiation or aggravation of moderate periodontal disease at their mesial surface. The study did not consider the potential risk for aggravation of already established advanced periodontitis lesions. This lack of correlation may not exclude other indications for molar uprighting, such as functionally disturbing interferences, paralleling or space problems associated with prosthetic rehabilitation, or traumatic occlusion
In this context it must be emphasized that the apparent angular bone loss along the mesial surface of tipped molars may be illusive and solely represent an anatomic variation, since lines drawn from the adjacent cemento-enamel junctions appear to parallel the alveolar crest (Ritchey & Orban 1954). While uprighting such a tooth appears to cause a shallowing-out of the angular defect, with new bone forming at the mesial alveolar crest, it may merely reflect the inclination of the molar relative to the alveolar bone, and the attachment level remains unchanged. When there is a definite osseous defect caused by periodontitis on the mesial surface of the inclined molar, uprighting the tooth and tipping it distally will widen the osseous defect. Any coronal position of bone may be due to the extrusion component of the mechanotherapy
Furcation defects generally remain the same or get worse during orthodontic treatment. For example, if tipped molars have furcation involvement before orthodontic uprighting, simultaneous extrusion may increase the severity of the furcation defects, especially in the presence of inflammation (Burch _et al_. 1992). Hence, initial periodontal therapy and maintenance is essential. The mandibular molar can be split into two roots, one or both of which may be kept and moved orthodontically into new positions. However, this is difficult treatment (Müller _et al_. 1995)
In a thorough study of periodontal conditions around tipped mandibular molars before prosthetic replacement, Lang (1977) reported that after completion of the hygiene phase, significant pocket reduction (mean 1.0 mm) was noted on all surfaces. In addition, a further significant reduction in pocket depth (mean 0.6 mm), associated with a gain of clinical attachment (mean 0.4 mm), was found on the mesial and lingual aspects of the molars as a result of the orthodontic uprighting. He concluded that uprighting of tipped molars is a simple and predictable procedure, provided excellent plaque control is maintained
Kessler (1976), on the other hand, stated that uprighting of mesially inclined molars is not a panacea, and showed some cases in which evident bone loss and furcation involvement developed during the orthodontic uprighting procedure. Because of the furcation involvement and increased mobility, these teeth were no longer considered suitable as abutments, although they were properly uprighted. Radiographic indications that furcation involvement may develop between the roots at the end of orthodontic molar uprighting is evident also in other studies, even when extrusive movement of the tipped molars has been avoided (Diedrich 1989). However, it is not unlikely that this radiolucent area reflects immature bone
### Conclusion
As risks may be involved in orthodontic uprighting of mesially tipped molars in cases with periodontal lesions along their mesial surface, or with furcation involvement, the indications for molar uprighting must be apparent. Excellent oral hygiene is required during the orthodontic treatment, with careful consideration of the force distribution, and avoiding extrusion as much as possible. The developments of regenerative techniques may make it possible in the future to obtain better outcomes in orthodontic therapy of periodontally compromised patients
## Tooth movement and implant esthetics
Osseointegrated implants may be used (1) to provide anchorage for orthodontic tooth movement and later serve as abutments for restorative treatment, and (2) to replace single missing teeth. The use of implants as anchors for orthodontic treatment is discussed in Chapter 58, and will not be dealt with here
It is difficult to achieve esthetically satisfactory results with artificial crowns on single-tooth implants, and the orthodontist may play a role in the interdisciplinary treatment planning team of specialists. There are at least three areas where orthodontics may be considered:
* Redistribution of the available space in the dental arch when tooth positions for implant placement are not optimal
* Orthodontic ridge augmentation by vertical tooth movement
* Orthodontic ridge augmentation by horizontal tooth movement.
### Redistribution of space
Orthodontic movement of neighboring teeth to optimal positions is often required in association with placement of implants substituting missing maxillary central or lateral incisors (Spear _et al_. 1997). Another common indication is a lack of adequate space for the implant. Figure 57-20 illustrates a typical case with small spaces between the teeth and not enough room to place implants in the maxillary and mandibular first premolar regions
### Ridge augmentation – vertical movement
During selective orthodontic extrusion of one single tooth, both the alveolar bone and the soft periodontal tissues will follow the extruded tooth in an incisal direction, as discussed under forced eruption earlier in this chapter. By this means, it is possible to significantly improve the periodontal tissue esthetics associated with fabrication of prosthetic crowns on single implants (Figs. 57-21, 57-22). The technique of "orthodontic extraction" of a hopeless incisor or molar (Salama & Salama 1993; Zuccati & Bocchieri 2003) may be useful to improve the results for single-tooth implants in patients in whom one or more teeth are to be extracted. Following progressive grinding of the extruded tooth to prevent it from jiggling (Figs. 57-21, 57-22), new periodontal tissues are generated that provide improved conditions for the implant, after extraction of the extruded tooth (Fig. 57-21). Upon extruding a tooth, the periodontal ligaments are pulled away from the bone and thus transfer mechanical strain to cells in the bone. A series of mechano-transduction mediators (Indian hedgehog), are expressed and lead to bone formation (Tang _et al_. 2004). The type of bone formed initially is the "emergency type of bone" with type III collagen (Chayanupatkul _et al_. 2003; Tang _et al_. 2004). This bone is somewhat weak because the cross-links between the collagen fiber matrix are weak. It takes about 6 months to mature to the more stable type I collagen (Chayanupatkul _et al_. 2003). The stable type of bone may accept an implant without showing relapse. The stability of the newly formed bone can thus be influenced by whether the clinician allows the newly formed bone to remodel to the more stable bone. It is conceivable that the time periods for the extrusion and the observation time before implant insertion should be at least 6 months for the newly formed bone to mature into more stable bone (Figs. 57-21, 57-22). To allow for rest periods in between the activations, an interrupted continuous force is recommended, by using small step bends in the arch-wires (Figs. 57-21b,c, 57-22d)
**Fig. 57-20** Typical orthodontic space reopening before insertion of two implants in the second and third quadrant in an adult female patient (a–f). Note the lingually tipped maxillary and mandibular incisors and the small spaces before treatment (a,b). Continuous force from push-coils (c) was used to open adequate space for the implants in the first premolar regions in both dental arches (d–f)
### Ridge augmentation – horizontal movement
If an implant cannot be placed because of reduced bucco-lingual ridge thickness after a previous extraction, one option is to move a premolar into the edentulous space and to place the implant in the position previously occupied by the premolar (Spear _et al_. 1997). The bucco-lingual volume of the new bone on the tension side will be markedly greater than that on the pressure side (Figs. 57-23, 57-24). This is an alternative to surgical ridge augmentation (GBR or bone graft). The situation is similar to that of when a canine is moved distally to open the space for a maxillary lateral incisor implant (Spear _et al_. 1997; Beyer _et al_. 2007). The root of the canine creates an adequate ridge through stretching of the periodontal ligament. It should be emphasized that there is much less shrinkage of the alveolar bone after horizontal tooth movements than after extractions of teeth. Spear _et al_. (1997) used cast measurements and tomograms through the edentulous ridge to measure the amount of bone loss with time in cases with orthodontic space opening for maxillary lateral incisor implants. They found less than 1% alveolar bone shrinkage from the end of treatment up to 4 years later. This contrasts with previous studies showing about 34% reduction of the alveolar ridge over 5 years when anterior teeth are extracted (Carlson 1967)
Figure 57-23 shows a case in which the distal movement of a mandibular first premolar provided new bone of adequate width for implant placement in a previously atrophied alveolar bone area. Similar generation of bone can be obtained in patients who have no molars by moving a terminal premolar distally in the dental arch. Autotransplantation of teeth also represents inherent potential for bone induction and reestablishment of a normal alveolar process after traumatic bone loss (Zachrisson et al. 2004)
**Fig. 57-21** Implant site development by "orthodontic extraction" of maxillary right central incisor with poor prognosis (a,e). The ceramic bracket was positioned in a gingival location on the incisor to be extruded (a), and initial leveling was started with continuous force from a rectangular super-elastic leveling wire. After 1 month, this arch-wire was replaced with a thin rectangular stainless steel wire, using small step-bends for the extrusion (b,e). Such step-bends create an interrupted continuous force which is active for about 2 weeks and then allows 2 weeks of rest before the re-activation at the monthly visits (b,c). The temporary crown on the implant in (d) shows the clinical status at 6 months after implant insertion. The radiographs demonstrate the extensive bone build-up at 10 months (f) and the implant in the regenerated bone at 6 months (g). Note the organization of the bony lamellae reflecting the direction of pull in (f)
**Fig. 57-22** Implant site development in young adult male patient by slow orthodontic extrusion of left central incisor with poor prognosis (a,b). Same procedure as in Fig. 57-21. The ceramic bracket was bonded in a gingival location on the tooth to be extracted. After 1 month of leveling with super-elastic wire, the remaining extrusion for 7 months was made with interrupted continuous force from stainless steel arch-wire, using small step-bends that were reinforced at monthly visits (d). The implant was inserted 4 months after the incisor was extracted. Note the improved gingival margin contour after the orthodontic extrusion (b,d), which permitted an optimal emergence profile of the implant crown (e,f)
**Fig. 57-23** Ridge augmentation by horizontal tooth movement before implant insertion in adult female patient, in whom the alveolar bone in the second premolar area was insufficient to accommodate an implant (a). The first premolar was moved distally with continuous force from a push-coil (b,c). Note wide area of bone regenerated on the tension side of the premolar (b,d) which provided optimal conditions for insertion of the implant (d)
# Gingival recession
## Labial recession
### "Normal" age changes
Gingival recession, with exposure of cementum on facial surfaces of teeth, may occur on single or multiple teeth. Many factors have been implicated in the etiology, including plaque, position of the tooth in the arch, faulty toothbrushing, traumatic occlusion, high frenum or muscle attachments, lack in dimension of gingiva, lip pressure, etc. (Baker & Seymor 1976). It is difficult to see a single cause of, or a solitary mechanism in the development of, labial gingival recession. Two basic types of recession may occur, one related to periodontal disease, or to factors associated with periodontal disease, and the other relating to mechanical factors, including toothbrushing
Labial gingival recessions are always accompanied by alveolar bone dehiscences, and there is a direct correlation between the millimetric extension of labial bone dehiscences and the corresponding gingival recessions (Bernimoulin & Curilovic 1977). It has been postulated that a root dehiscence may establish an environment which, for one reason or another, may predispose to gingival recession (Wennström 1990). The position in which a tooth erupts through the alveolar process has a profound influence on the amount of gingiva that will be established around the tooth. When a tooth erupts close to the mucogingival line, only a minimal width, or complete lack, of gingiva may be observed labially, and localized gingival recessions may occur in patients at a young age. Thus the "normal" age changes that will then take place are important. Longitudinal monitoring of labial gingival dimensions during the development of the dentition has shown that providedadequate plaque control is established and maintained, a significant increase of the gingival height will generally occur. Spontaneous improvement of localized mandibular labial recessions is the rule rather than the exception, and in some teeth the recessions were totally eliminated during a 3-year observation period (Andlin-Sobocki _et al_. 1991). Also, spontaneous changes of tooth positions in a buccolingual direction will affect the gingival dimension. These alterations in gingival dimensions are similar to, albeit less pronounced than, those observed during orthodontic treatment (see below)
**Fig. 57-24** Female patient, 41 years of age, with agenesis of both mandibular central incisors, multiple spacings, thin periodontal tissues, and prominent root topography (a–c). The alveolar bone is too thin labio-lingually to accommodate a titanium implant in the anterior regions (c). The treatment principle was, therefore, to close spaces anteriorly by moving the left first and second premolars mesially (d), and to open up space posteriorly for an implant (e). Note the wide area of alveolar bone on the tension side (d,e), providing ample bucco-lingual space for implant insertion. Permanent implant-supported crown at 3.5 years after treatment (courtesy of Dr. Roy Samuelsson, Oslo, Norway) is shown in f–h
**Fig. 57-25** Thin labial gingiva on prominent mandibular right central incisor (a,b) spontaneously became thicker when the incisor was orthodontically moved lingually and aligned (c) after premolar extractions. (d) Condition after appliance removal
### Favorable tooth movements, and tissue factors
Alterations of mucogingival dimensions may occur during orthodontic treatment. Contrary to beliefs in the past, these changes are independent of the apicocoronal width of the keratinized and attached gingiva. Wennström _et al_. (1987) found no relationship between the initial width of keratinized gingiva and the tendency for development of gingival recession during orthodontic tooth movements in monkeys. Instead, it is the bucco-lingual thickness (volume), which may be the determining factor for the development of gingival recession and attachment loss at sites with gingivitis during orthodontic treatment
A tooth that is positioned facially within the alveolar process may show an alveolar bone dehiscence with a thin covering soft tissue. When such a tooth is moved lingually during orthodontic treatment, the gingival dimensions on the labial aspects will increase in thickness (Figs. 57-25, 57-26). Furthermore, because the mucogingival junction is a stable anatomic landmark and the gingiva is anchored to the supracrestal portion of the root, it will follow the tooth during the movement lingually and will consequently get an increase in gingival height (decreased clinical crown height)
_Conclusion:_ It follows that in cases with a thin (delicate) gingiva caused by a prominent position of the teeth, there is no need for a preorthodontic gingival augmentation procedure. In the case of labial gingival recessions a mucogingival surgical procedure should not be performed before orthodontic therapy, when the position of the tooth is improved by the treatment. The recession, as well as the bone dehiscence, will decrease as a consequence of the lingual movement of the tooth into a more proper position within the alveolar bone. If still indicated at the end of orthodontic therapy, the surgical procedure will have a higher predictability of success than if it had been performed before the tooth movement (Wennström 1996)
### Unfavorable tooth movements, and tissue factors
Orthodontic movements of teeth _away_ from the genetically determined envelope of the alveolar process are risk movements for development of mucogingival problems, particularly in thin bone and gingival tissues. During frontal and lateral expansion of teeth, tension may develop in the marginal tissues due to the forces applied to the teeth. This stretching may result in thinning of the soft tissues. However, recession-type defects will not develop as long as the tooth is moved within the alveolar bone. If, however, the expansion results in the establishment of a bone dehiscence, the volume (thickness) of the covering soft tissue must be considered as a factor that may influence the development of soft tissue recessions. This may be true both during and after the active orthodontic treatment period. The labial orthodontic tooth movement _per se_ will not cause soft tissue recession. However, the thin gingiva that will be the consequence of such movement may serve as a _locus minoris resistentia_ to developing soft tissue defects in the presence of bacterial plaque and/or mechanical trauma caused by improper toothbrushing techniques, or orthodontic correction of marked rotations of the incisors
**Fig. 57-26** Marked labial gingival recession on prominent left mandibular canine in female young adult patient (a–c). (d) After extraction of two premolars and the left central incisor (sic!), the mandibular arch was leveled orthodontically. (e) and (f) show the clinical condition towards end of orthodontic therapy, and (g,h) at follow-up 1 year after appliance removal. Note spontaneous improvement of gingival recession (f–h)
For stability reasons as well, expansion in the mandibular arch should normally be avoided, if possible. If frontal expansion is still performed in association with orthodontic therapy, the bucco-lingual thickness of the hard and soft tissues should be evaluated. If surgical intervention is considered necessary in order to reduce the risk for development of soft tissue recessions, this should aim at increasing the thickness of the covering tissue (e.g. grafts), and not the apico-coronal width of the gingiva
_Conclusion_ : Before any kind of orthodontic therapy is started, it is important to check the bucco-lingual thickness of the bone and soft tissues on the pressure side of all teeth, which are to be moved. When tissues are delicate and thin, careful instructions in adequate plaque control measures should be provided, and controlled before and during treatment as well as after removal of the fixed appliances, in order to reduce the risk for development of labial gingival recession
## Interdental recession
### Esthetic considerations with regard to defect papillae
Until recently, most clinical emphasis with regard to gingival recession was given to labial defects. If left untreated, most labial gingival recessions will not progress significantly with time, at least if oral hygiene is good, and the main indication for treatment is the esthetic implication for the patient. From an esthetic point of view, however, it would appear that interdental recession, manifest as more or less pronounced empty spaces ("dark triangles") between the teeth, would be equally or more important. Compared with a labial recession, in most patients the loss of interdental papillae would be more visible, both in normal conversation and upon smiling
Since quality of life (esthetics and lack of pain) has become increasingly important in recent years in selection of periodontal therapies, disfigurement of the gingival papillae during orthodontic treatment of periodontal patients must be avoided, if possible. The development of interdental recession during orthodontic treatment in adults may be caused by one of three factors: (1) advanced periodontal disease, by the tissue destruction or due to pocket elimination by surgery, (2) triangular tooth shape due to abnormal interproximal wear of teeth in crowded positions before the orthodontic treatment, and (3) diverging roots of teeth due to improper bracket placement. To begin with, there is an obvious difference in dental esthetics between patients with advanced periodontitis who have been treated according to "old" and "new" concepts for periodontal therapy. In the past, pocket elimination by gingivectomies frequently resulted in advanced root exposure and complete loss of interdental papillae. However, even with careful non-surgical periodontal therapy in the preparation of patients with advanced periodontal disease for orthodontic treatment, the clinical outcome of the interdisciplinary treatment will normally result in marked interdental recessions, if special precautions are not taken (see below)
### Clinical options for treatment
There are only a few options available for the treatment of interdental gingival recession associated with orthodontic treatment in the periodontal patient:
1. Mucogingival surgery, using coronally positioned flaps and GTR techniques (Pini Prato _et al_. 1992)
2. The provision of a gingival prosthesis
3. Orthodontic paralleling of the roots of neighboring teeth
4. Mesio-distal enamel reduction ("stripping").
Of these techniques, the mucogingival surgery aspects are discussed in Chapter 44, and will not be commented on here. A gingival prosthesis may be useful in cases of markedly compromised dentitions, where the psychologic implications of having pronounced retractions are serious. It may be regarded as a last resort. In contrast, the mesio-distal contour-ing of teeth is a very useful technique to routinely improve the esthetic results achieved by orthodontic treatment in most adult and adolescent patients (Figs. 57-3, 57-5, 57-6, 57-27, 57-28)
### Benefits of mesio-distal enamel reduction ("stripping")
Introduced by Tuverson in 1980, mesio-distal recontouring of teeth has now become a routine procedure in orthodontics. It is generally performed on three indications: (1) treatment of slight-to-moderate crowding without arch expansion, (2) correction of width discrepancies (so-called TSD, tooth size discrepancies) between maxillary and mandibular teeth, and (3) to prevent interdental recession from developing during orthodontic treatment. The principle involved in stripping is to recontour those teeth which for one reason or another have abnormal morphology, towards an ideal anatomic shape (Figs. 57-6, 57-25). In doing so, the contact points between teeth will be relocated in an apical direction and reduce the contact-to-bone distances (Tarnow _et al_. 1992), and the connector areas (the zone in which two adjacent teeth appear to touch) can be restored towards the optimal 50-40-30 relationships (Morley & Eubank 2001). By this means, normal interdental gingival papillary contours will be achievable (Figs. 57-3, 57-6, 57-27, 57-28)
**Fig. 57-27** Adult female patient with maxillary crowding and large overjet (a,b). After premolar extractions, orthodontic distalization of canines resulted in the development of marked interdental recessions in the anterior region (c). Marked triangular incisor morphology and uneven incisal edges necessitated extensive recontouring (c,d) to allow gingival fill-in after treatment (e,f)
**Fig. 57-28** Young adult female patient with moderate periodontal tissue breakdown in the anterior region, extruded and irregular maxillary incisors with triangular crown form and incisal wear, and marked interdental gingival recession in the mandibular anterior region (a–c). After 1 month of leveling, the maxillary and mandibular incisors were recontoured by stripping to a more optimal tooth morphology (d). The "new" tooth shapes allowed space closure and leveling and aligning to an esthetic final result (e,f)
In many adult patients with malocclusion, particularly in cases with crowded and overlapping incisors, the crowns of the incisors are much wider at their incisal edges than at the cervical region. As the crowding is unraveled by orthodontic leveling in these instances, the contact point between the incisors will become located in the incisal 1 mm, and a more or less evident space develops above the interproximal contacts of the incisors. Similar, or even more pronounced, loss of the interdental papillae between the maxillary and mandibular incisors, is commonly seen after orthodontic treatment in patients with advanced periodontal destruction
Short-term (Zachrisson & Mjör 1975) and long-term (>10 years) (Thordarson _et al_. 1991; Zachrisson _et al_. 2007) follow-up studies after extensive grinding of teeth have demonstrated that no harmful side effects are observed subsequent to the procedure, provided adequate cooling is used during the grinding and the prepared surfaces are made smooth and self-cleansing. After the diastema is created, the space between the teeth is closed orthodontically. As this occurs, the roots of neighboring teeth come closer together, the contact area is lengthened, and the reduced papilla can fill out the small space between the teeth (Tarnow _et al_. 1992). In patients with advanced periodontal disease, it is not always possible to restore all papillae in the dentition. Even if it is not possible to eliminate the interdental recession completely after the orthodontic treatment, the esthetic appearance is in most patients substantially improved by stripping, even in cases with extensive periodontal tissue breakdown, such as those in Figs. 57-3 and 57-5
# Minor surgery associated with orthodontic therapy
Several forms of minor periodontal surgery may be used to improve or stabilize the results achieved by orthodontic treatment of malocclusion. More than 30 years ago, Edwards (1970) described clinical techniques to help prevent rotational relapse, reopening of closed extraction spaces (Edwards 1971), and a simple yet effective technique for frenotomy (Edwards 1977). At about the same time, a gingivectomy technique to increase clinical crown length for esthetic improvement of orthodontic results in specific situations was reported (Monefeldt & Zachrisson 1977). Removal of gingival invaginations in extraction sites following orthodontic space closure has also been a subject of considerable interest to orthodontists
## Fiberotomy
The problem of relapse of orthodontically treated teeth in general, and rotated teeth in particular, has been well recognized for years. Methods to reduce the occurrence of rotational relapse may include (1) complete correction, or overcorrection, of rotated teeth, (2) long-term retention with bonded lingual retainers, and (3) the use of fiberotomy
Two soft-tissue periodontal entities may influence the stability: the principal fibers of the periodontal ligament, and the supra-alveolar fibers. Whereas the fibers of the periodontal ligament and trans-septal groups remodel efficiently and histologically completely in only 2–3 months after orthodontic rotation of teeth, the supra-alveolar fibers are apparently more stable, with a slow turnover. Since the gingival soft tissues are composed primarily of non-elastic collagenous fibers, the exact mechanism by which the gingival soft tissues may apply a force capable of moving the teeth is as yet unknown. From a practical and clinical point of view, however, the supracrestal gingival tissues seemingly do contribute to rotational relapse, as evidenced by the effect of the circumferential supracrestal fiberotomy (CSF) technique
Basically this technique consists of inserting a scalpel into the gingival sulcus and severing the epithelial attachment surrounding the involved teeth. The blade also transects the trans-septal fibers by interdentally entering the periodontal ligament space. Various modifications of the original CSF technique have been described, in which the scalpel is inserted below the gingival margin, or the cut is reduced to interdental vertical incisions buccally and lingually. In neither case are surgical dressings indicated, and clinical healing is usually complete in 7–10 days. The fiberotomy procedure is not recommended during active tooth movement, or in the presence of gingival inflammation. When performed in healthy tissues after orthodontic therapy, there is negligible loss of attachment (Edwards 1988)
The long-term effectiveness of fiberotomy was evaluated in a prospective follow-up study over a period of 15 years by Edwards (1988). The degree of crowding was examined for CSF and control cases at 4–6 years and at 12–14 years after treatment. A significant effect of the fiberotomy was observed at both time intervals. The surgical procedure was more successful in the maxillary than in the mandibular anterior region; more effective in alleviating rotational than labiolingual relapse; and more useful in reducing relapse in cases with severe rather than mild irregularity of teeth. There was no clinically significant increase in sulcus depth, nor signs of gingival labial recession
## Frenotomy
The contribution of the maxillary labial frenum to the etiology of a persisting midline diastema, and to reopening of diastemas after orthodontic closure, is controversial. The probability for diastema closure in the long run is the same whether or not frenectomy is performed. However, very hyperplastic types of frenum, with a fan-like attachment, may obstruct diastema closure and should be relocated
In the past, the most common surgical procedure was _frenectomy_ , an excision-type operation, which was often carried over to the palatal aspects. However, a frequently observed complication may be an undesirable loss of the interdental papilla between the maxillary central incisors. For this reason, the _frenotomy_ , which represents a more gentle operation, will produce esthetically preferable results. With frenotomy, the attachment of the frenum to gingiva and periosteum is severed, and the insertion of the frenum is relocated several millimeters up on to the alveolar mucosa. If a marked sutural bone cleft is observed in the pretreatment radiographs, the cut is extended to sever the fibers within the coronal part of the midpalatal suture. Tissue healing after a frenotomy procedure is usually uneventful. To further reduce the relapse tendency and/or to increase clinical crown height of single or several teeth, the frenotomy may be combined with fiberotomy and gingivectomy
## Removal of gingival invaginations (clefts)
Incomplete adaptation of supporting structures during orthodontic closure of extraction spaces in adults may result in infolding or invagination of the gingiva. The clinical appearance of such invaginations may range from a minor one-surface crease to deep clefts that extend across the interdental papilla from the buccal to the lingual gingivae. Although gingival invaginations are quite common, the precise cause of the infolding as teeth are moved through an extraction area remains unclear. Since approximated teeth appear to displace the gingival tissue more than move through it, a "piling-up" of gingival tissue is conceivable. There is some resolution of these defects with time, but many invaginations persist for 5 years or more after completion of orthodontic therapy
Several authors have suggested that compression of trans-septal fibers and alterations of gingival tissue will contribute to extraction-space reopening, but no correlation was found between space reopening and presence and severity of invaginations by Rivera Circuns and Tulloch (1983). They still felt the damage to the gingiva was severe enough to warrant the surgical removal of these defects in selected patients. Edwards (1971) suggested that simple removal of only the excess gingiva in the buccal and lingual area of approximated teeth would be sufficient to alleviate the tendency for the teeth to separate after orthodon-tic movement. The removal of the gingival papillae in closure sites may enhance the restitution of a more normal connective tissue, although the epithelial hyperplasia, invaginations, and loss of collagen in the underlying gingiva are surprisingly long-standing
## Gingivectomy
The relationship of the gingival margins of the six maxillary anterior teeth plays an important role in the esthetic appearance of the crowns (Kokich 1996a,b). In some instances, it may be necessary to increase clinical crown length of one or several teeth during or after orthodontic treatment. If a gingival margin discrepancy is present, but the patient's lip does not move upward to expose the discrepancy upon smiling, it does not require correction. If the gingival discrepancy is apparent, however, one of four different techniques may be used:
1. Gingivectomy
2. Intrusion + incisal restoration or porcelain lami-nate veneer (Fig. 57-18)
3.Extrusion + fiberotomy + porcelain crown (Fig. 57-17)
4.Surgical crown lengthening, by flap procedure and ostectomy/ostoplasty of bone (Brägger _et al_. 1992).
Each of these techniques has its specific indications, and whenever gingival margin discrepancies are present, the clinician must determine the proper solution (see also Chapter 44). For example, gingivectomy is not indicated when there is a risk for root exposure, such as when one single incisor has supra-erupted (Fig. 57-18)
The gingivectomy technique has proven to be useful in improving orthodontic results, particularly in difficult cases with missing maxillary central or lateral incisors (Fig. 57-29) ; after premolar autotransplantation to the anterior region; and in some "gummy" smiles. Clinical and histologic examination demonstrated that it was possible to permanently increase clinical crown length after orthodontic treatment by making a labial gingivectomy to the bottom of the clinical pocket. The healing and regeneration of the gingiva was uneventful, provided excellent oral hygiene was maintained in the wound area for 2 months. The result may be explained by one or more of three factors: (1) the effect of the gingivectomy itself, (2) elimination of accumulated hyperplastic gingiva often seen associated with fixed appliance therapy (Fig. 57-29), and (3) elimination of a normally occurring deep pocket. Whatever the reason, the net gain in crown length was close to half the probing depth in all instances (Monefeldt & Zachrisson 1977). The increase in crown length of 1– 2 mm may be important to improve the clinical outcome, as shown in Fig. 57-29. Similar long-term results on the position of the marginal soft tissue following periodontal surgery have been reported by others (Lindhe & Nyman 1980). Interestingly, Wennström (1983) demonstrated that even if the gingivectomy is extended into the alveolar mucosa, the regenerated tissue will still be normal gingiva with keratinized epithelium. Thus the human periodontal membrane tissue has the capacity to form a granulation tissue which will prevent the alveolar mucosa from becoming the border tissue against the tooth. When local labial gingivectomies are made in adults, the cut is reduced mesio-distally in order to eliminate the risk for developing interdental recession. Then the incision should not follow the gingival contour all the way, but should be limited by two small verti-cal cuts towards the interdental papillae
**Fig. 57-29** Orthodontic space closure substitution after accidental loss of maxillary right central incisor in young female patient (a). The marginal gingival level on the "new" central incisor was corrected by selective intrusion bends in the arch-wire (b–d) and local gingivectomy and frenotomy (c,d). Local gingivectomies were also performed on the right first premolar in the canine position, and on the left lateral incisor (e). Enamel-bonded ultrathin porcelain veneer on lateral incisor, and vital bleaching of right canine, courtesy of Dr. S. Toreskog. By these means, it was possible to obtain an optimally esthetic result (e,f)
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# Chapter 58
# Implants Used for Orthodontic Anchorage
Marc A. Schätzle and Niklaus P. Lang
* * *
Introduction
Evolution of implants for orthodontic anchorage
Prosthetic implants for orthodontic anchorage
Bone reaction to orthodontic implant loading
Indications of prosthetic oral implants for orthodontic anchorage
Prosthetic oral implant anchorage in growing orthodontic patients
Orthodontic implants as temporary anchorage devices
Implant designs and dimensions
Insertion sites of palatal implants
Palatal implants and their possible effect in growing patients
Clinical procedures and loading time schedule for palatal implant installation
Direct or indirect orthodontic implant anchorage
Stability and success rates
Implant removal
Advantages and disadvantages
* * *
# Introduction
Anchorage is one of the limiting factors in orthodontics and its control is essential for successful orthodontic treatment. The term orthodontic anchorage was first introduced by Angle (1907) and later defined by Ottofy (1923). Orthodontic anchorage denoted the nature and degree of resistance to displacement of teeth offered by an anatomic unit when used for the purpose of tooth movement. The principle of orthodontic anchorage was implicitly explained in Newton's third law (1687) according to which an applied force can be divided into an _action_ component and an equal and opposite _reaction_ moment. In orthodontic treatment, reciprocal effects must be evaluated and controlled. The goal is to maximize desired tooth movement and minimize undesirable effects.
Basically, each tooth has its own anchorage potential as well as a tendency to move when force is applied towards the tooth. When teeth are used as anchorage, inappropriate movements of the anchoring units may result in a prolonged treatment time, and unpredictable or less-than-ideal outcomes.
Orthodontic anchorage is oriented to the quality of the biologic anchorage of the teeth. This is influenced by a number of factors such as the size of the root surfaces available for periodontal attachment, the height of the periodontal attachment, the density and structure of the alveolar bone, the turnover rate of the periodontal tissues, the muscular activity, the occlusal forces, the craniofacial morphology, and the nature of the tooth movement planned for the intended correction (Diedrich 1993). To maximize tooth-related anchorage, techniques such as differential torque (Burstone 1982), placing roots into the cortex of the bone (Ricketts 1976), and distal inclination of the molars (Tweed 1941; Begg & Kesling 1977) may be used. If the periodontal anchorage is inadequate with respect to the intended treatment goal, additional intraoral and/or extraoral anchorage may be needed to avoid negative effects. While the teeth are the most frequent anatomic units used for anchorage in orthodontic therapy, other structures, such as the palate, the lingual mandibular alveolar bone, the occiputal bone, and the neck, are also alternatives.
Additional anchorage such as extraoral and intraoral forces are visible and hence, compliance-dependent, and are associated with the risk of undesirable effects such as tipping of the occlusal plane, protrusion of mandibular incisors, and extrusion of teeth.
Implants, miniscrews and ankylosed teeth, as they are in direct contact with bone, do not possess a normal periodontal ligament. As a consequence, they do not move when orthodontic forces are applied (Melsen & Lang 2001) and hence, can be used for "absolute anchorage" that is independent of the patient's compliance.
The aim of this chapter is to present implants to be integrated into orthodontic treatment as "absolute anchorage", thereby avoiding the disadvantages listed above.
# Evolution of implants for orthodontic anchorage
The first attempt to achieve skeletal anchorage was made in 1945. Gainsforth and Higley (1945) placed vitallium screws and stainless steel wires into the ramus of dog mandibles and applied elastics that extended from the screw to the hook of a maxillary arch wire to distally tip/retract the canine by immediate orthodontic loading (Fig. 58-1). Even though the authors did not describe the development of infection, failures encountered may be attributed to infection and the lack of antibiotics at that time, as well as the early dynamic loading of the screws. Although minor tooth movement was accomplished using basal bone anchorage in two animals, an effective orthodontic force could not be maintained for more than 31 days.
A generation later, skeletal anchorage systems have evolved from two directions. One such development originated from orthognatic fixation techniques used in maxillofacial surgery. As pioneers, Creekmore and Eklund (1983) used a vitallium bone screw to treat one patient with a deep impinging overbite. The screw was inserted in the anterior nasal spine to intrude and correct the upper incisors using an elastic thread from the screw to the incisors 10 days after the screw had been placed. Subsequently, Kanomi (1997) described a miniscrew specially designed for orthodontic use.
The second development originated from applications in implant dentistry. Linkow (1969) used blade implants for rubber band anchorage to retract teeth, but never presented long-term outcomes. Later, endosseous implants for orthodontic anchorage were suggested (Ödman _et al_. 1988; Saphiro & Kokich 1988). As indicated in various animal studies, osseointegrated titanium implants remained positionally stable under orthodontic loading and thus could be used for orthodontic anchorage (Sherman 1978; Turley _et al_. 1980, 1988; Roberts _et al_. 1984, 1989; Wehrbein & Dietrich 1993; Wehrbein 1994; Wehrbein _et al_. 1998; De Pauw _et al_. 1999; Majzoub _et al_. 1999) (Figs. 58-2, 58-3). This resulted in the development of specially designed implants in the retromolar area (Roberts _et al_. 1990) and the palatal site of the maxilla (Triaca _et al_. 1992). Both applications are used for direct or indirect anchorage (see below).
**Fig. 58-1** Orthodontic appliance using vitallium screw anchorage. (Courtesy of Gainsforth, B.L. & Higley, L.B. (1945). A study of orthodontic anchorage possibilities in basal bone, _American Journal of Orthodontics and Oral Surgery_ **31** , 406–417. Reproduced with permission, copyright © Elsevier.)
**Fig 58-2** Detail of an orthodontic implant 11 months _in situ_ in the mandibular retromolar area. Tight contact between the implant shoulder and crestal bone. Signs of remodeling are visible in the peri-implant bone (zones of darker and lighter staining). Toluidine/McNeal stain. Original magnification 20×. From Wehrbein _et al_. (1998) _Clinical Oral Implants Research_.
**Fig. 58-3** Longitudinal section of an orthodontic implant after 2 years _in situ_. The implant is well osseointegrated. The shoulder, however, is not in direct contact with the bone surface. Toluidine/McNeal stain. Original magnification 6.6×. From Wehrbein _et al_. (1998) _Clinical Oral Implants Research_.
From a clinical point of view, it is of relevance whether implants are to be used only as temporary anchorage devices (TAD) (Daskalogiannakis 2000) or subsequently to be used as abutment for supporting prosthetic appliances. These aspects determine insertion sites, implant types and dimensions, as well as type of orthodontic anchorage. Moreover, the fact that these devices may have to be placed in a growing patient is of particular importance. Only TADs are suitable for such a purpose.
# Prosthetic implants for orthodontic anchorage
The insertion site of prosthetic implants for orthodontic anchorage is determined by the subsequent use of the implant as a prosthetic abutment. The dimensions in length and diameter are dependent on the later prosthetic use. The positions within the alveolar process and the number of implants, however, have to be selected with reference to prospective final tooth position and space after orthodontic treatment.
To determine the location of the prosthetic implants before orthodontic therapy may often be confusing. This is especially true if the teeth are moving towards or away from the implant during orthodontic treatment. In these situations, the presumptive outcomes must be predetermined to achieve the proper implant location and the correct size of the crowns and pontics on the implant-supported prosthesis. In order to use oral implants both for both orthodontic anchorage as well as the subsequent restorative therapy, protocols have been developed for determining the accurate placement of dental implants for prosthetic reconstruction before orthodontic therapy (Smalley 1995; Smalley & Blanco 1995). A plastic placement guide is constructed and used by the clinician to determine proper implant location. The placement guide is based on information derived from a diagnostic wax-up. Therefore, it is necessary to construct the set-up casts from an exact duplicate of the tooth and base portions of the original dental casts. The bases are used as a reference for the proposed position of the implant.
An orthodontic attachment is then either fixed to the provisional crown or to a prefabricated bonding base (Figs. 58-4, 58-5). The orthodontic force acts at the implant suprastructure. The reactive moments and forces are then directly transmitted to the implant and its adjacent bone (direct implant anchorage).
## Bone reaction to orthodontic implant loading
Dental implants should not only fulfill prosthetic stability but also withstand the stress and strain applied during orthodontic treatment. There are substantial differences between orthodontic forces and occlusal loading. Orthodontic forces are continuous and horizontal, occlusal loads, in contrast, are discontinuous and mainly in the vertical direction of the implants/teeth.
**Fig. 58-4** Schematic illustration of the assembly of an orthodontic base on a oral implant designated for prosthetic use after the orthodontic treatment.
**Fig. 58-5** Use of oral implants designated for prosthetic reconstruction as anchorage for orthodontic treatment. (a) Prefabricated orthodontic base as anchorage element. (b) Reconstruction of teeth 35 and 45 on oral implants following orthodontic treatment. (Courtesy of P. Göllner and T. Liechti, Berne, Switzerland.)
Table 58-1 Turnover characteristics of alveolar bone in relation to the magnitude of strain applied (from Melsen & Lang 2001)
The effect of orthodontic loading to the adjacent bone of the oral implant is of great interest, because the applied forces should not have a negative impact on the peri-implant bone and therefore, should not impair the long-term prognosis as a prosthetic abutment.
Specially designed oral implants were inserted in monkeys and subjected to well defined continuous loading (Melsen & Lang 2001) (Table 58-1). None of the implants had lost osseointegration after 11 weeks of loading, but loading significantly influenced the turnover of the alveolar bone in the vicinity of the implants. Bone apposition was most frequently found when the calculated strain varied between 3400 and 6600 microstrain. On the other hand, when the strain exceeded 6700 microstrain, the remodeling of the bone resulted in a net loss of bone.
These studies support the theory that apposition of bone around an oral implant is the biologic response to a mechanical stress below a certain threshold, whereas loss of marginal bone or complete loss of osseointegration may be the result of mechanical stress beyond this threshold.
Several other studies where orthodontic forces have been applied confirmed the apposition or increase in bone density rather than loss of bone surrounding an oral implant (Roberts _et al_. 1984; Wehrbein & Diedrich 1993; Asikainen _et al_. 1997; Akin-Nergiz _et al_. 1998).
## Indications of prosthetic oral implants for orthodontic anchorage
Orthodontic anchorage provided by prosthetic oral implants may be indicated in partially edentulous adult patients with intra-arch malposition of teeth to correct over-eruption, infra-eruption or tipping of teeth, to retract anteriorly displaced frontal teeth, and intra-arch protraction of teeth that are positioned distally to reduce a multi-tooth gap or improve tooth position in edentulous spaces (Fig. 58-6). Prosthetic oral implants might also be used for the correction of inter-arch malocclusion of single teeth or the whole dentition.
The most important factor of the entire process is interdisciplinary communication and planning. It is critically important for the orthodontist, periodontist, and restorative dentist to work closely as a team during the planning and treatment to achieve the best possible final result (Kokich 1996).
## Prosthetic oral implant anchorage in growing orthodontic patients
The use of prosthetic oral implants in growing individuals has been studied in both clinical (Ödman _et al_. 1988; Thilander _et al_. 1994, 1999) and animal studies (Ödman _et al_. 1991; Thilander _et al_. 1992; Sennerby _et al_. 1993). Like ankylosed teeth (Fig. 58-7), oral implants do not follow the developmental changes of the alveolar processes encountered in combination with continuous eruption of adjacent teeth (Fig. 58-8). Moreover, the osseointegrated implants will not be able to be displaced in all dimensions during growth of the jaws (Thilander _et al_. 1994; Iseri & Solow 1996) and hence, would impair the development of the surrounding bony structures and even that of adjacent teeth.
Implant therapy in young individuals with residuous growth potential has been addressed in several studies and yielded major impairment in esthetic outcomes, especially in anterior implant-borne restorations. To assess remaining facial growth potential, hand–wrist radiographs have been proposed for evaluation, but appear not to be specific enough. The best method of evaluating the completion of facial growth is based on the superimposition of sequential cephalometric radiographs. It is, therefore, advisable to await the completion of adolescent body growth in height. At that point, a cephalometric radiograph should be taken. Another radiograph should be taken at least 6 months to a year later. If these radiographs are superimposed with no changes revealed in vertical facial height (nasion to menton), the completion of the facial growth may be assumed. The installation of an oral implant at that time may no longer be associated with significant eruption of adjacent teeth (Kokich 2004).
**Fig. 58-6** (a) Occlusal view of an oral implant replacing tooth 26, 3 months after installation. Tooth 27 has tipped mesially rendering prosthetic reconstruction of tooth 26 impossible. (b) Following prosthetic abutment connection, the implant is used as anchorage for uprighting tooth 27, hereby providing adequate space for the installation of a single crown.
**Fig. 58-7** (a) Ankylosed tooth 21 after trauma and on-going composite adaptation over several years. Tooth 21 has not followed the changes associated with alveolar process growth. (b) Radiographic documentation 6 years following trauma of tooth 21 yielding the development of the alveolar process with concomitant ankylosis of tooth 21.
In most adult patients, completion of facial growth is assumed but residual growth and ageing changes affecting the alveolar process may be encountered. This was documented in a retrospective study (Bernard _et al_. 2004) supporting the assumption that mature adults may also exhibit major vertical steps after anterior restorations were inserted on osseointegrated implants.
# Orthodontic implants as temporary anchorage devices
Fundamental differences exist with respect to implant dimensions, insertion sites, type of implant anchorage, and intended duration of implant use. The most important difference is that a temporary anchorage device is to be removed after completion of intended orthodontic tooth movement (Daskalogiannakis 2000).
## Implant designs and dimensions
As regular orthodontic patients do not display edentulous alveolar bony ridges for the insertion of an implant, implants for orthodontic anchorage must be placed in areas other than the usual topographical locations foreseen for the replacement of missing teeth. Besides the installation of orthodontic anchorage implants into the retromolar area of the mandible (Roberts _et al_. 1990; Higuchi & Slack 1991), the mid-sagittal palatal region (Triaca _et al_. 1992; Block & Hoffmann 1995; Wehrbein _et al_. 1996a) was initially proposed.
**Fig. 58-8** (a) Oral implant placed prematurely (at age 9 years) in a growing patient. The implant did not follow the growth development of the alveolar process resulting in the need for multiple (three times) replacement of the prosthetic reconstruction until adolescence. Unsatisfactory esthetic outcomes persist. Radiographic documentation: (b) Following traumatic loss of tooth 11 at age 9 years. (c) Implant placement in the growing maxilla. (d) Oral implant 9 years after placement and third single tooth crown reconstruction (Courtesy of G.E. Salvi, Berne, Switzerland.)
The introduction of diameter-reduced temporary orthodontic anchorage devices such as miniscrews (<2 mm) in various lengths (Kanomi 1997; Costa _et al_. 1998) and titanium pins (Bousquet _et al_. 1996), as well as L-shaped miniplates with the long arm exposed into the oral cavity (Umemori _et al_. 1999) and the zygomatic anchors (De Clerck _et al_. 2002) both fixed by bone screws, offered new additional insertion sites: (1) the inter-radicular septum (Bousquet _et al_. 1996; Kanomi 1997); (2) the supra-apical and infrazygomatic area (Kanomi 1997; Costa _et al_. 1998; Umemori _et al_. 1999; De Clerck _et al_. 2002); and (3) the mandibular symphysis (Costa _et al_. 1998). It must be pointed out, however, that the retention of miniscrews and titanium pins constitutes only a mechanical fixation of the devices and, hence, is not based on the principle of osseointegration.
Length-reduced orthodontic anchorage devices, such as titanium flat screws (Triaca _et al_. 1992), resorbable orthodontic implant anchors (Glatzmaier _et al_. 1995), T-shaped orthodontic implants (Wehrbein _et al_. 1996) (Orthosystem®, Institut Straumann, Waldenburg, Switzerland) and the Graz implant-supported pendulum (Byloff _et al_. 2000), were subsequently introduced.
Another device, the Onplant® (Block & Hofmann 1995), placed subperiostally, is a smooth titanium disc with a hydroxyapatite-coated surface that is supposed to connect to the bone. Owing to the submerged installation, monitoring of the healing process of these Onplants® may be troublesome, and their osseointegration may be questioned (Celenza & Hochman 2000).
The most widely used orthodontic anchorage system is the Orthosytem® (Institut Straumann, Basel, Switzerland). This titanium implant consists of three distinct features (Fig. 58-9): (1) the self-tapping endosseous body, 4.2 mm long and either 4.1 mm or 4.8 mm in diameter, designed to be inserted into bone; (2) a smooth neck portion (4.8 mm in diameter and 1.8 mm long) as the transmucosal part; and (3) the trigonal head to serve as the orthodontic appliance fixation.
**Fig. 58-9** The Orthosystem® (Institut Straumann, Waldenburg, Switzerland) designed for orthodontic anchorage with an intraosseous SLA rough surface, a smooth transmucosal portion, and a trigonal orthodontic fixation base.
## Insertion sites of palatal implants
The incomplete closure of the median palatal suture during childhood and early adolescence is a limiting factor for the installation of orthodontic implants in the midsagittal region for fully grown juveniles and adults. Therefore, the paramedian regions of the hard palate (Bernhart _et al_. 2000, 2001) represent a feasible alternative. With respect to the anatomic limitations, sites chosen for palatal orthodontic anchorage device insertion should be carefully evaluated to avoid perforations into the inferior nasal turbinate (Wehrbein _et al_. 1996b). Pre-implantation examinations of the anterior palate have shown that the vertical bone volume decreases from the anterior to the posterior region.
The presence of the palatal suture and the limited bone thickness of the hard palate available may be causes of concern for the achievement of stability of palatal implants. It may be useful to perform imaging diagnosis before palatal implant insertion. Dental computed tomography and/or lateral cephalograms have been recommended for evaluating the vertical bone volume of the hard palate presurgically.
Dental computed tomography of the alveolar process is well established for the evaluation of the alveolar bone volume before implant placement (Lindh _et al_. 1995). It may also be used to assess the vertical bone volume of the hard palate and is currently the most accurate method. The greatest mean thickness was identified to be about 6–9 mm posterior to the incisal foramen in the mid-sagittal plane (Bernhart _et al_. 2000). Avoiding the midpalatal suture, the area suitable for implant placement is, therefore, located 6–9 mm posterior to the incisal foramen and 3–6 mm lateral to the mid-sagittal plane. If the necessary bone volume for an orthodontic implant installation is defined as 4 mm or more (Bernhart _et al_. 2000). In a study, 95% of the patients investigated had adequate vertical bone volume for accommodating palatal implants, 4 mm in length; this is in agreement with other clinical reports (Schiel _et al_. 1996). It must be considered, however, that the patients examined showed a great range of variation of vertical bone volume so a detailed pre-operative diagnostic process is necessary in order to avoid perforation of the lower nasal duct.
Insisting on obtaining precise information for the intended implant sites before placing palatal implants on lateral cephalograms rather than CT examination was proposed (Wehrbein _et al_. 1999). Since the former are used for orthodontic diagnosis and treatment planning, patients are spared from additional radiation exposure. Furthermore, superimposition of structures in CT scans renders this methodology complicated, imprecise, and hazardous for the presurgical assessment of bone volumes for orthodontic anchorage implants.
On wire-marked skulls, the highest bony demarcation of the palatal complex seen radiographically largely coincided with the nasal floor rather than with the mid-sagittal nasal septum, which has additional vertical bone height (Wehrbein _et al_. 1999). Hence, it was suggested that the vertical bone heights in the anterior and middle thirds of the hard palate were at least 2 mm higher vertically than identified on lateral cephalograms. A safety level of at least 2 mm is, therefore, recommended when planning treatment on the basis of lateral cephalograms (Wehrbein _et al_. 1999). It must be realized that even though some implants may project beyond the nasal floor in lateral cephalograms, they may represent false-positive results and may not be related to actual penetrations into the nasal cavity (Crismani _et al_. 2005c). If the palatal complex is perforated, intra-operative probing with a periodontal probe or a sinus probe must be performed for verification.
In addition to the palatal bony morphology, the implant's antero-posterior location and its inclination must also take into account both the pre-treatment and planned final position of the maxillary central incisor, when the implant is placed mid-sagittally (Fig. 58-10).
A distinction has to be made between the vertical bone volume in the mid-sagittal and the paramedian regions, as the indication for implant treatment in the mid-sagittal plane should be limited to adults and fully grown juveniles due to possible developmental disturbances of the palatal suture (Glatzmaier _et al_. 1995; Wehrbein _et al_. 1996b).
## Palatal implants and their possible effects in growing patients
During growth, maxillary expansion in a transverse direction is the result of two processes: appositional remodeling of the alveolar process and growth of the palatal suture (Björk & Skieller 1974). While the remodeling process leads to the expansion of the dental arches, the growth in the median suture leads to the expansion of the palate that represents the most important factor in the development of the maxillary width. An average growth in maxillary width of 3 mm was demonstrated between the ages of 10 and 18 years (Björk & Skieller 1977). Since the median or paramedian anterior palate may be chosen as insertion sites for palatal implants, the question arises whether or not the implantation of an orthodontic anchorage device may affect normal transverse palatal growth. Palatal implants affected normal transverse growth in an animal study (Asscherickx _et al_. 2005). It could be shown that implant placement resulted in less transverse sutural growth.
**Fig. 58-10** Most palatal implants are installed satisfactorily when the location of entry into the cortical bone is at the antero-posterior level of the maxillary first and second premolars – perpendicular to the palatal surface. From Männchen & Schätzle (2008).
Deficient transverse maxillary width may also cause maxillary arch length discrepancies, as demonstrated for canine impaction (McConnell _et al_. 1996). Therefore, all interventions that might cause a restriction in normal transverse maxillary growth should be avoided. Because it has been shown that the insertion of implants in the median palatal suture in adolescent beagle dogs could cause restriction in normal transverse development of the palate (McConnell _et al_. 1996), the installation of the orthodontic palatal implants is better performed in paramedian areas in growing individuals. Moreover, studies have suggested that the installation of orthodontic implants in the midpalatal suture of growing patients is contraindicated because of the questionable quality of bone to provide adequate primary stability (Bernhart _et al_. 2001; Lioubavina-Hack _et al_. 2006). The paramedian region of the anterior palate is largely stable from a growth point of view (Thilander 1995).
The most important vertical growth changes are the result of the displacement of the maxillary complex and surface remodeling processes. The sutural lowering of the maxillary complex as well as the apposition at the orbital floor and at the infrazygomatic crest will not be affected by implant installation in the palate. The resorptive lowering of the nasal floor, however, and the increase of the maxillary alveolar bone height might be influenced. The mean degree of growth from the age of 4 years to adulthood has been identified (Björk & Skieller 1977). The nasal floor appears to drift 4.6 mm caudally, and the height of the maxillary alveolar bone appears to increase 14.6 mm. Assuming that about one third of these growth changes take place from the age of 12 years to adulthood implies a residual vertical growth of about 1.5 mm in the palate and of about 5 mm in maxillary alveolar bone height (Fig. 58-11).
Fig. 58-11 Vertical growth related changes encountered from age 4 years to adulthood. From Björk & Skieller (1977), with permission from the British Orthodontic Society.
Osseointegrated implants are in direct contact with bone, do not possess a periodontal ligament and hence, behave like ankylosed teeth. Therefore, an osseointegrated palatal implant would remain 1.5 mm behind its surrounding bone, whereas an implant placed in the alveolar bone would produce an infra-occlusion of 5 mm during the same period. Consequently, palatal implants directly or indirectly attached to teeth would lead to an infra-eruption of a single tooth, several teeth or the whole upper dentition, respectively. By influencing the maxillary vertical growth dimension the horizontal displacement of the mandible will also be affected and would, therefore, cause a closing effect on the mandibular plane angle (anterior mandible rotation). It must be considered, however, that palatal implants as temporary orthodontic anchorage devices usually remain 1–2 years _in situ_. Thus, potential vertical and transversal growth impairment are likely to be limited to values of less than 1 mm.
## Clinical procedures and loading time schedule for palatal implant installation
Patient stress during implantation and/or explantation and subsequent wound healing may be minimized by applying a minimally traumatic surgical technique. Under palatal local anesthesia, the palatal mucosa is perforated to the cortical bone using a mucosal punch or a system-compatible trephine during explantation and removed with an elevator or a curette (Fig. 58-12a). After smoothing the exposed bone surface to prevent the profile drill from slipping, the centre of the implant site is marked with a round bur (Fig. 58-12b). The implant bed is then prepared to the required depth using a series of pilot and twist drills (Fig. 58-12c). The drilling axis perpendicular to the bone surface is defined based on the presurgical cephalometric analysis. While preparing the insertion site intermediate drilling and cooling of the drilling channel continuously with pre-cooled physiologic saline or Ringer's solution should be performed. The implant is then hand-installed as far as possible, and a ratchet is used to tighten the implant to its final position (Fig. 58-12d). The implant is covered with the healing cap to prevent the inner screw well of the implant from clogging up and from being covered by hyperplastic mucosal tissue (Fig. 58-12e). After insertion, the palatal Orthosystem®implant is allowed to heal _in situ_ for 12 weeks during which it should not be loaded.
In some cases, there may be a premature loss of the implant prior to orthodontic load. This loss may be caused by the lack of adequate primary stability. Such insufficient primary stability, causes inappropriate healing and the possible premature loss of the implant (Friberg _et al_. 1991; Lioubavina-Hack _et al_. 2006). Therefore, it is generally recommended to use the 4.1 mm diameter palatal Orthosystem® implant. The 4.8 mm diameter device should only be used if the prerequisite of primary stability cannot be achieved with the smaller (regular 4.1 mm) diameter implant.
Following the placement of an endosseous implant, primary mechanical stability is gradually replaced by biologic bonding. The transition from primary mechanical stability, provided by the implant design, to biologic stability, provided by the osseointegration process, occurs during the first month of wound healing (Berglundh _et al_. 2003). During this critical time, the orthodontic implant should not be used as anchorage.
The installation of implants as absolute anchorage devices facilitates and accelerates orthodontic therapy (Trisi & Rebaudi 2002), even though an inactive waiting time of at least 3 months after insertion (12 week healing time) remains (Wehrbein _et al_. 1996a, 1998; Keles _et al_. 2003; Crismani _et al_. 2005a,b). Especially in adult patients, there is a growing need to reduce this inactive waiting time and to reduce the risk for implant failure during early loading. There are several studies that have reported a successful outcome of early/immediate loaded conventional dental implants placed in the alveolar ridge (Calandriello _et al_. 2003; Rocci _et al_. 2003; Bischof _et al_. 2004; Gallucci _et al_. 2004; Glauser _et al_. 2004; Jaffin _et al_. 2004). However, as of today there is only one study evaluating early loaded palatal orthodontic implants in humans by means of resonance frequency analysis (RFA). On this basis, the possibility of loading palatal orthodontic implants earlier than recommended in the aforementioned literature was suggested with caution (Crismani _et al_. 2006).
There is still a lack of histologic documentation about adequately termed healing periods before loading orthodontic implants in the palatal region and no attempts have been made to document sequential histologic changes of the transition from primary stability to the process of osseointegration. Further studies are needed to define shorter appropriate healing periods.
After the recommended inactive healing period, an impression is taken for the construction of the transpalatal arch (TPA) connection (Fig. 58-12f,g). After integration of the TPA, the implant-related orthodontic treatment is begun. Depending on the treatment goal, schedule, and TPA design, different palatal arches may be necessary during the course of treatment in the same patient.
## Direct or indirect orthodontic implant anchorage
Reliable three-dimensional attachment of orthodontic wires to the orthodontic implant is of crucial importance. There are two principles in using implants for orthodontic anchorage:
* Orthodontic forces are applied at anchorage teeth that are not to be moved and are kept in position through a rigid connection (e.g. transpalatal arch, lingual arch) with the implant ( _indirect anchorage_ ) (Wehrbein _et al_. 1996b). The element connected directly to teeth may limit tooth movements and need adaptation or refabrication of the TPA by a dental technician (Fig. 58-12f).
* If force systems act directly between the teeth to be moved and the implant ( _direct anchorage_ ), then the TPA may be adapted more easily by adjusting the active sectional wires (Männchen 1999). It must be considered, however, that the implant should be placed paramedian on the same side in order to keep the torque moments as low as possible, if a direct unilateral sagittal force is applied to the implant (Fig. 58-12g).
The three-dimensional attachment of the orthodontic wire to the implant may be guaranteed by using a clamping cap, a welding or soldering cap or a post cap with a pre-lased wire.
**Fig. 58-12** Clinical procedures to install a palatal Orthosystem® (Straumann AG, Basel, Switzerland). (a) Perforation of the palatal mucosa using a system compatible punch or trephine. (b) Marking the center of the intended implant site with a round bur. (c) Preparation of the implant bed at the location determined presurgically and perpendicular to the bone surface. (d) Tightening of the orthodontic implant using a ratchet. (e) Covering the device with a healing cap. (f) Affixation of the transpalatal arch (TPA) for indirect loading (from Wehrbein _et al_. 1998) and (g) for direct loading (according to Männchen 1999). (h) Palatal orthodontic anchorage site after explantation.
Besides offering reliable fixation of the connecting element to the implant abutment, the connecting element must be sufficiently rigid to prevent deflection. A mean loss of anchorage of approximately 1 mm by retracting or torquing of incisors to the buccal segment has been reported (Wehrbein _et al_. 1999a). This contradiction was probably due to deformation of the TPA and/or a slight rotational play of the supraconstruction. Although this anchorage loss might be clinically irrelevant, the pre-activation of the connecting element in the opposite direction may help to avoid this side effect.
It is clear that implant-supported teeth receive continuous loading stimulation. Unfavorable jiggling forces on anchor teeth, as found in compliance-dependent anchorage aids, might be reduced or avoided. This may play a more decisive role in cases with reduced periodontal anchorage.
## Stability and success rates
Despite the small dimensions, orthodontic implant anchoring devices must maintain positional stability under orthodontic loading in order to serve as absolute anchorage. As connective tissue encapsulation would initiate implant dislocation, osseointegration is a prerequisite. Histologic examination of explanted human orthodontic implant bone specimens inserted palatally revealed that osseointegration is maintained during long-term orthodontic loading under clinical conditions (Figs. 58-2, 58-3). The percentage of implant-to-bone contact in patients varied between 34% and 93% with an average of 75% (Wehrbein _et al_. 1998), obviously an adequate anchorage to withstand orthodontic loading.
There is only one retrospective cohort study reporting the success rate of a large number of inserted palatal Orthosystem® implants (Männchen & Schätzle 2008). Only three out of 70 inserted palatal implants (4.3%) did not successfully osseointegrate. Of these, two implants were lost due to inadequate primary stability. These were replaced after a short healing period with implants of a greater dimension and osseointegrated successfully thereafter. One implant was placed penetrating the incisal canal and was lost spontaneously. Of the 67 successfully osseointegrated implants loaded actively and/or passively for approximately 19 months, only one implant (1.5%) was lost after 5 months of unilateral heavy active loading (Männchen & Schätzle 2008). This report documented success rates for palatal implants after orthodontic loading comparable to those reported for conventional oral implants (Berglundh _et al_. 2002; Pjetursson _et al_. 2007).
## Implant removal
No reports exist on "sleeping orthodontic palatal implants". As a consequence, they have to be removed after completion of the orthodontic treatment. By means of a system-compatible trephine, the peri-implant bone is separated from the device. Then, the implant may be explanted together with the surrounding bone by slow rotations with a extraction forceps. As a variation, the implant–bone contact may be broken by turning the ratchet used for seating the implant counter-clockwise, applying a torque of up to 40 N/cm, and a mechanical torque wrench The implant is then retrieved (Fig. 58-12h). After explantation, possible oro-antral communication must be verified and treated if necessary.
Full recovery at the original anchorage site may be observed 3–4 weeks after implant removal.
## Advantages and disadvantages
Even though the orthodontic treatment may be completed faster and with more predictability, patients have to undergo two minor surgical procedures. Additionally, an inactive waiting time after implant installation remains. The extra cost for placing a palatal orthodontic implant must be balanced against other treatment options. Besides cooperation and esthetic aspects to be considered, the costs of orthognathic surgery and/or prosthetic reconstruction may be avoided or reduced by installation of an implant for orthodontic anchorage. In cases in which the palatal implant is directly loaded, bonding of the whole jaw or the entire dentition may not be necessary (Fig. 58-13). The main risks encountered with the use of orthodontic implant anchorage are the development of peri-implant infection, oro-antral connection, and/or implant loss prior to completion of orthodontic treatment.
### Conclusions
Osseointegrated implants are providing absolute orthodontic anchorage and hence, are considered to be superior to any orthodontic tooth-borne anchorage device. Indications for orthodontic implant anchorage include: inadequate periodontal anchorage; non-compliant patients for extra- and/or intra-oral anchorage aids; prevention of potential side effects of conventional anchorage devices; esthetic aspects; or avoidance of orthognathic surgery after growth completion. Moreover, prosthetic reconstruction may be avoided. The simplicity in use, minimal stress during surgical implant installation and removal, as well as the reliable success rates are prerequisites for the high acceptance of this treatment by orthodontic patients. It must be kept in mind, however, that treatment objectives may be achieved by several treatment plans. Proper orthodontic anchorage should be chosen according to the preceeding diagnosis and to fit the appropriate treatment plan.
**Fig. 58-13** Absolute anchorage by means of a palatal orthodontic implant avoiding the need for bonding the entire maxillary dentition with fixed orthodontic appliances. (a) After the extraction of tooth 26, protraction of tooth 27 was initiated by direct implant loading. (b) At implant and orthodontic appliance removal, the gap between teeth 25 and 27 has been completely closed, thereby avoiding the placement of a fixed partial denture. (Courtesy of R. Männchen, Winterthur, Switzerland.)
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# Part 18: Supportive Care
59 Supportive Periodontal Therapy (SPT)
_Niklaus P. Lang, Urs Brägger, Giovanni E. Salvi, and Maurizio S. Tonetti_
_See also:_
41 Treatment of Peri-implant Lesions
_Tord Berglundh, Niklaus P. Lang, and Jan Lindhe_
# Chapter 59
# Supportive Periodontal Therapy (SPT)
**Niklaus P. Lang, Urs Brägger, Giovanni E. Salvi, and Maurizio S. Tonetti**
* * *
Definitions
Basic paradigms for the prevention of periodontal disease
Patients at risk for periodontitis without SPT
SPT for patients with gingivitis
SPT for patients with periodontitis
Continuous multi-level risk assessment
Subject risk assessment
Tooth risk assessment
Site risk assessment
Radiographic evaluation of periodontal disease progression
Clinical implementation
Objectives for SPT
SPT in daily practice
Examination, re-evaluation, and diagnosis (ERD)
Motivation, reinstruction, and instrumentation (MRI)
Treatment of reinfected sites (TRS)
Polishing, fluorides, determination of recall interval (PFD)
* * *
Clinical trials on the long-term effects of treatment of periodontitis have clearly demonstrated that post-therapeutic professional maintenance care is an integral part of the treatment. This also constitutes the only means of assuring the maintenance of long-term beneficial therapeutic effects. Reinfection could be prevented or kept to a minimum in most patients, mainly through rigid surveillance involving professional visits at regular intervals. However, the maintenance systems presented in various studies do not allow the presentation of a clear concept with general validity for the frequency of professional maintenance visits and the mode of maintenance therapy. A danger for supervised neglect of reinfection and recurrent disease in some patients coexists with a tendency for overtreatment in others.
Objective criteria for assessing the patient's individual risk for recurrent disease have been the focus of attention of recent years. However, the evaluation of the patient's individual risk still has to be based on a probability estimation based on the analysis of patient, tooth or tooth site risk assessments.
The purpose of this chapter is to discuss the basics of continuous patient monitoring following active periodontal therapy in order to prevent reinfection and the continued progression of periodontal disease following therapy. The mode and extent of interceptive therapeutic measures needed to achieve this goal will also be evaluated.
# Definitions
Periodontal treatment includes:
1. Systemic evaluation of the patient's health
2. A cause-related therapeutic phase with, in some cases
3. A corrective phase involving periodontal surgical procedures
4. Maintenance phase.
The 3rd World Workshop of the American Academy of Periodontology (1989) renamed this treatment phase "supportive periodontal therapy" (SPT). This term expresses the essential need for therapeutic measures to support the patient's own efforts to control periodontal infections and to avoid reinfection. Regular visits to the therapist should serve as a positive feedback mechanism between the patient and the therapist with the purpose of ensuring that patients have the opportunity to maintain their dentitions in a healthy status for the longest possible time. An integral part of SPT is the continuous diagnostic monitoring of the patient in order to intercept with adequate therapy and to optimize the therapeutic interventions tailored to the patient's needs.
# Basic paradigms for the prevention of periodontal disease
Periodontal maintenance care, or SPT, follows the paradigms of the etiology and pathogenesis of periodontal disease and – at present – must consider the fact that these diseases are coping with the result of the host defense on an opportunistic infection.
Almost 40 years ago, a cause–effect relationship between the accumulation of bacterial plaque on teeth and the development of gingivitis was proven (Löe _et al_. 1965). This relationship was also documented by the restoration of gingival health following plaque removal. Ten years later, a corresponding relationship between plaque accumulation and the development of periodontal disease, characterized by loss of connective tissue attachment and resorption of alveolar bone, was shown in laboratory animals (Lindhe _et al_. 1975). Since some of these animals did not develop periodontal disease despite a persistent plaque accumulation for 48 months, it must be considered that the composition of the microbiota or the host's defense mechanisms or susceptibility for disease may vary from individual to individual. Nevertheless, in the study mentioned, the initiation of periodontal disease was always preceded by obvious signs of gingivitis. Hence, it seems reasonable to predict that the elimination of gingival inflammation and the maintenance of healthy gingival tissues will result in the prevention of both the initiation and the recurrence of periodontal disease. In fact, as early as 1746, Fauchard stated that "little or no care as to the cleaning of teeth is ordinarily the cause of all diseases that destroy them" (Fauchard 1746).
From the clinical point of view, the above-mentioned results must be translated into the necessity for proper and regular personal plaque elimination, at least in patients treated for or susceptible to periodontal disease. This simple principle may be difficult to implement in all patients; however, interceptive professional supportive therapy at regular intervals may, to a certain extent, compensate for the lack of personal compliance with regard to oral hygiene standards.
These aspects have been imitated in a beagle dog model with naturally occurring periodontal disease (Morrison _et al_. 1979). Two groups of animals were used. The test group was subjected to initial scaling and root planing and, subsequently, plaque was eliminated by daily toothbrushing and biweekly polishing with rubber cups for a period of 3 years. In the control group, no initial scaling and no oral hygiene practices were performed during the same period of time. Every 6 months, however, the teeth in two diagonally opposed jaw quadrants in both test and control animals were scaled and root planed. The results showed that the reduction of probing depth and the gain of probing attachment, obtained after the initial scaling and root planing in the test animals, were maintained throughout the entire course of the study irrespective of whether or not repeated scaling and root planing had been performed. The control animals, on the other hand, continued to show increasing probing depths and loss of attachment in all quadrants irrespective of whether or not repeated scaling and root planing had been performed. However, in the jaw quadrants where the teeth were repeatedly instrumented every 6 months, the progression of periodontal destruction was significantly less pronounced (Fig. 59-1). These results indicate that professional supportive therapy, performed at regular intervals, may, at least to a certain extent, compensate for a "suboptimal" personal oral hygiene standard. In this respect, it has been demonstrated that following root instrumentation, the subgingival microbiota is significantly altered in quantity and quality (Listgarten _et al_. 1978), and that the re-establishment of a disease-associated, subgingival micro-biota may take several months (Listgarten _et al_. 1978; Slots _et al_. 1979; Mousquès _et al_. 1980; Caton _et al_. 1982; Magnusson _et al_. 1984).
In a number of longitudinal, clinical studies on the outcome of periodontal therapy, the crucial role of SPT in maintaining successful results has been documented (Ramfjord _et al_. 1968, 1975; Lindhe & Nyman 1975, 1984; Rosling _et al_. 1976; Nyman _et al_. 1977; Knowles _et al_. 1979, 1980; Badersten _et al_. 1981, 1987; Hill _et al_. 1981; Lindhe _et al_. 1982a,b; Pihlström _et al_. 1983; Westfelt _et al_. 1983a, 1985; Isidor & Karring 1986; Kaldahl _et al_. 1988). In all these studies, probing depths and clinical attachment levels were maintained as a result of a well organized professional maintenance care program (recall intervals varying between 3 and 6 months) irrespective of the initial treatment modality performed. In one of the studies (Nyman _et al_. 1977) an alarming result was that patients treated for advanced periodontal disease involving surgical techniques, but not incorporated in a supervised maintenance care program, exhibited recurrent periodontitis including loss of attachment at a rate three to five times higher than documented for natural progression of periodontal disease in population groups with high disease susceptibility (Löe _et al_. 1978, 1986). Within this area, the effect of negligence in providing adequate supportive maintenance care following periodontal treatment has been studied over a 6-year period by Axelsson and Lindhe (1981a). Following presurgical root instrumentation and instruction in oral hygiene practices, all study patients were subjected to modified Widman flap procedures. During a 2-month healing period, professional toothcleaning was performed every 2 weeks. Following this time period, baseline clinical data were obtained and one out of every three patients was dismissed from the clinic, while the other two were incorporated in a professionally conducted maintenance program with a recall once every 3 months. These patients maintained excellent oral hygiene and consequently yielded a very low frequency of bleeding sites. In addition, probing depths and probing attachment levels were maintained unchanged over the 6-year period. In contrast, the non-recalled patients demonstrated obvious signs of recurrent periodontitis at the 3-year and 6-year re-examinations. Further evidence for the likelihood of recurrent disease in patients not subjected to professional maintenance care was presented by Kerr (1981). Five years after successful treatment, 45% of the patients presented with periodontal conditions similar to their status before treatment. Supportive therapy had only been provided at intervals varying between 9 and 18 months.
**Fig. 59-1** (a) Mean probing depth reduction (+) or increase in probing depth (−) in millimeters with or without repeated scaling and root planing in experimental (oral hygiene) and control (no oral hygiene) animals relative to baseline means. (b) Mean gain (+) or loss (−) of probing attachment with or without repeated scaling and root planing in experimental (oral hygiene) and control (no oral hygiene) animals relative to baseline means. (Data from Morrison _et al_. 1979.)
Similar results have been described for private practice patients who decided not to participate in an organized maintenance care program following active periodontal therapy (Becker _et al_. 1984). Subsequent examinations revealed clear signs of recurrent periodontal disease including increased probing depths and involvements of furcations of multirooted teeth concomitant with tooth loss. Also, loss of alveolar bone observed in radiographs and tooth loss have been reported for a group of patients in whom post-therapeutic supportive maintenance care was provided less frequently than once every 12 months (De Vore _et al_. 1986). From all these studies it is evident that periodontal treatment is ineffective in maintaining periodontal health if supportive maintenance care is neglected, denied or omitted.
Even though the number of well controlled longitudinal clinical trials is rather limited for patients who, in addition to periodontal treatment, have undergone extensive reconstructive therapy, it should be realized that the concept of professional maintenance care has unrestricted validity. In a longitudinal study of combined periodontal and prosthetic treatment of patients with advanced periodontal disease, periodontal health could be maintained over a study period of 5–8 years with regular recall appointments scheduled every 3–6 months (Nyman & Lindhe 1979). Similar results have been presented by Valderhaug and Birkeland (1976) and by Valderhaug (1980) for periods of up to 15 years. Another study of 36 patients who received extensive poly-unit cantilevered bridgework following periodontal therapy, confirmed the maintenance of periodontal health over 5–12 years (Laurell _et al_. 1991). More recent studies on the long-term maintenance over 10 and 11 years of periodontal patients who, following successful treatment of chronic periodontitis, were reconstructed with extensive fixed reconstructions revealed that regularly performed SPT resulted in periodontal stability. Only 1.3% (Hämmerle _et al_. 2000) and 2.0% (Moser _et al_. 2002) of the abutments showed some minor attachment loss during these long periods of observation. In contrast, a report of insurance cases who were not regularly maintained by SPT yielded a recurrence rate for periodontitis of almost 10% after an observation of 6.5 years (Randow _et al_. 1986).
_Summary:_ The etiology of gingivitis and periodontitis is fairly well understood. However, the causative factors, i.e. the microbial challenge which induces and maintains the inflammatory response, may not be completely eliminated from the dentogingival environment for any length of time. This requires the professional removal of all microbial deposits in the supragingival and subgingival areas at regular intervals, since recolonization will occur following the debridement procedures, leading to a reinfection of the ecologic niche and, hence, giving rise to further progression of the disease process. Numerous well controlled clinical trials, however, have documented that such a development can be prevented over very long periods of time only by regular interference with the subgingival environment which aims at removal of the subgingival bacteria.
# Patients at risk for periodontitis without SPT
The effect of an omission of SPT in patients with periodontitis may best be studied either in untreated populations or patient groups with poor compliance.
One of the few studies documenting untreated periodontitis-susceptible patients reported on the continuous loss of periodontal attachment as well as teeth in Sri Lankan tea plantation workers receiving no dental therapy (Löe _et al_. 1986). In this – for the western world – rather unique model situation, an average loss of 0.3 mm per tooth surface and year was encountered. Also, the laborers lost between 0.1 and 0.3 teeth per year as a result of periodontitis. In another untreated group in the United States, 0.61 teeth had been lost per year during an observation period of 4 years (Becker _et al_. 1979). This is in dramatic contrast to reports on tooth loss in well maintained patients treated for periodontitis (e.g. Hirschfeld & Wasserman 1978; McFall 1982; Becker _et al_. 1984; Wilson _et al_. 1987). Such patients were either completely stable and lost no teeth during maintenance periods ranging up to 22 years or lost only very little periodontal attachment and only 0.03 teeth (Hirschfeld & Wasserman 1978) or 0.06 teeth (Wilson _et al_. 1987), respectively.
Non-complying, but periodontitis-susceptible patients receiving no SPT following periodontal surgical interventions continued to lose periodontal attachment at a rate of approximately 1 mm per year regardless of the type of surgery chosen (Nyman _et al_. 1977). This is almost three times more than would have to be expected as a result of the "natural" course of periodontal disease progression (Löe _et al_. 1978, 1986).
In a British study of a private practice situation (Kerr 1981) where the patients were referred back to the general dentist after periodontal therapy, 45% of the patients showed complete reinfection after 5 years.
Probably the most impressive documentation of the lack of SPT in disease-susceptible individuals arises from a clinical trial in which one third of the patients had been sent back to the referring general practitioner for maintenance, while two thirds of the patients received SPT in a well organized maintenance system (Axelsson & Lindhe 1981a). The 77 patients were examined before treatment, 2 months after the last surgical procedure and 3 and 6 years later. The 52 patients on the carefully designed SPT system visited the program every 2 months for the first 2 years and every 3 months for the remaining 4 years of the observation period. The results obtained from the second examination (2 months after the last surgery) showed that the effect of the initial treatment was good in both groups. Subsequently, the recall patients were able to maintain proper oral hygiene and unaltered attachment levels. In the non-recall group, plaque scores increased markedly from the baseline values, as did the number of inflamed gingival units (Fig. 59-2a). Concomitantly, there were obvious signs of recurrent periodontitis. The mean values for pocket depth and attachment levels at the 3-year and 6-year examinations were higher than at baseline (Fig. 59-2b). In the recall group, approximately 99% of the tooth surfaces showed either improvement, no change or less than 1 mm loss of attachment, compared to 45% in the non-recall group (Table 59-1). In the latter patients, 55% of the sites showed a further loss of attachment of 2–5 mm at the 6-year examination, and 20% of the pockets were 4 mm deep or more (Tables 59-1, 59-2).
_Summary:_ Patients susceptible to periodontal disease are at high risk for reinfection and progression of periodontal lesions without meticulously organized and performed SPT. Since all patients who were treated for periodontal diseases belong to this risk category by virtue of their past history, an adequate maintenance care program is of utmost importance for a beneficial long-term treatment outcome. SPT has to be aimed at the regular removal of the subgingival microbiota and must be supplemented by the patient's efforts for optimal supragingival plaque control.
**Table 59-1** Percentage of sites showing various changes in probing attachment level between baseline examination, 2 months after completion of active periodontal therapy, and at follow-up examination 6 years later (adapted from Axelsson & Lindhe 1981b)
**Change in attachment level** | **Percentage of surfaces showing change**
---|---
| **Recall** | **Non-recall**
Attachment level improved| 17| 1
No change| 72| 10
Attachment level worse by:
≥1 mm| 10| 34
2–5 mm| 1| 55
**Table 59-2** Percentage of various probing depths in recall and non-recall patients at the initial examination, 2 months after active periodontal treatment, and at 3- and 6-year follow-up visits (adapted from Axelsson & Lindhe 1981b)
**Fig. 59-2** Histograms showing (a) average percentages of tooth surfaces harboring visible plaque (above) and inflamed gingival units (bleeding on probing) (below), and (b) average probing depth (above) and probing attachment levels (below), at initial, baseline and follow-up examinations. (Data from Axelsson & Lindhe 1981b.)
# SPT for patients with gingivitis
Several studies, predominantly in children, have documented that periodic professional prophylactic visits in conjunction with reinforcement of personal oral hygiene are effective in controlling gingivitis (Badersten _et al_. 1975; Poulsen _et al_. 1976; Axelsson & Lindhe 1981a,b; Bellini _et al_. 1981). This, however, does not imply that maintenance visits in childhood preclude the development of more severe disease later in life. It is obvious that SPT, therefore, must be a lifelong commitment of both the patient and the profession.
Adults whose effective oral hygiene was combined with periodic professional prophylaxis were clearly healthier periodontally than patients who did not participate in such programs (Lövdal _et al_. 1961; Suomi _et al_. 1971). One particular study of historic significance was performed on 1428 adults from an industrial company in Oslo, Norway (Lövdal _et al_. 1961). Over a 5-year observation period, the subjects were recalled two to four times per year for instruction in oral hygiene and supragingival and sub-gingival scaling. Gingival conditions improved by approximately 60% and tooth loss was reduced by about 50% of what would be expected without these efforts.
In another study (Suomi _et al_. 1971) loss of periodontal tissue support in young individuals with gingivitis or only loss of small amounts of attachment was followed over 3 years. An experimental group receiving scaling and instruction in oral hygiene every 3 months yielded significantly less plaque and gingival inflammation than the control group in which no special efforts had been made. The mean loss of probing attachment was only 0.08 mm per surface in the experimental as opposed to 0.3 mm in the control group.
When adult patients with gingivitis were treated with scaling and root planing, but did not improve their oral hygiene procedures, the gingival condition did not improve compared with individuals receiving prophylaxes at 6-month intervals (Listgarten & Schifter 1982).
_Summary:_ The available information indicates that the prevention of gingival inflammation and early loss of attachment in patients with gingivitis depends primarily on the level of personal plaque control, but also on further measures to reduce the accumulation of supragingival and subgingival plaque.
# SPT for patients with periodontitis
As mentioned previously, a series of longitudinal studies on periodontal therapeutic modalities was performed over the past 25 years, first at the University of Michigan, later at the University of Gothen-burg, Sweden, and also at the Universities of Minnesota, Nebraska, and Loma Linda. These studies always incorporated the patients into a well organized maintenance care system with recall visits at regular intervals (generally 3–4 months). Although the patients performed plaque control with various degrees of efficacy, the SPT resulted in ex cellent maintenance of post-operative attachment levels in most patients (Knowles 1973; Ramfjord _et al_. 1982).
On average, excellent treatment results with maintained reduced probing depths and maintained gains of probing attachment were documented for most of the patients in the longitudinal studies irrespective of the treatment modality chosen (Ramfjord _et al_. 1975; Lindhe & Nyman 1975; Rosling _et al_. 1976; Nyman _et al_. 1977; Knowles _et al_. 1979, 1980; Badersten _et al_. 1981, 1987; Hill _et al_. 1981; Lindhe _et al_. 1982a; Pihlström _et al_. 1983; Westfelt _et al_. 1983a,b, 1985; Isidor & Karring 1986).
In a study on 75 patients with extremely advanced periodontitis, who had been successfully treated for the disease with cause-related therapy and modified Widman flap procedures (Lindhe & Nyman 1984), recurrent infection occurred in only very few sites during a 14-year period of effective SPT. However, it has to be realized that recurrent periodontitis was noticed at completely unpredictable time intervals, but was concentrated in about 25% of the patient population (15 out of 61). This suggests that, in a periodontitis-susceptible risk population, the majority of patients can be "cured" provided an optimally organized SPT is performed, while a relatively small proportion of patients (20–25%) will suffer from occasional episodes of recurrent periodontal reinfection. It is obviously a challenge for the diagnostician to identify such patients with very high disease susceptibility and to monitor the dentitions for recurrent periodontitis on a long-term basis.
As opposed to the study by Lindhe and Nyman (1984) which exclusively involved patients with advanced periodontitis, another study on 52 patients with generalized mild to moderate adult periodontitis addressed the efficacy of SPT 8 years following completion of cause-related periodontal therapy (Brägger _et al_. 1992). Full-mouth intraoral radiographs were used to assess changes in the radiographic alveolar bone height as a percentage of the total tooth length. As a result of cause-related therapy, a gain in probing attachment followed by a loss of 0.5–0.8 mm over the following 8 years was observed. The radio-graphic loss of alveolar bone height in the same time period was less than 2% and thus clinically insignificant. In this patient group initially presenting with mild to moderate periodontitis, the frequency of SPT rendered per year did not affect the rate of progression of periodontal desease. However, patients seeking SPT less than once per year over 8 years lost further periodontal attachment during the period of observation. From these studies it is evident that patients having experienced periodontitis need some kind of SPT. Obviously, the frequency of SPT visits has to be adapted to the risk of susceptibility for the disease. Patients with advanced periodontitis may need SPT at a regular and rather short time interval (3–4 months), while for mild to moderate forms of periodontitis, one annual visit may be enough to prevent further loss of attachment.
More recently, the effect of a plaque-control-based maintenance program on tooth mortality, caries, and periodontal disease progression was presented after 30 years of SPT in a private dental office (Axelsson _et al_. 2004). This prospective controlled cohort study initially included 375 test and 180 control patients that received traditional maintenance care (by the referring dentist once to twice a year). After 6 years, the control group was discontinued. The test group was subjected to prophylactic visits every second month for the first 2 years and every 3–12 months (according to their individual needs) during years 3–30. The prophylactic visits to the dental hygienist included plaque disclosure and professional mechanical tooth cleaning, including the use of a fluoride-containing dentifrice. During the 30 years of maintenance, very few teeth were lost (0.4–1.8%), and these were predominately lost because of root fractures. Within 30 years of maintenance, 1.2–2.1 new carious lesions (>80% secondary caries) were found. With the exception of buccal sites, no sites demonstrated any loss of periodontal attachment during this period. On approximal sites, there was even some gain of attachment. This unique study clearly demonstrated that SPT based on plaque control tailored to the individual needs of the patient will result in very low tooth mortality, minimal recurrent caries, and almost complete periodontal stability.
_Summary:_ SPT is an absolute prerequisite to guarantee beneficial treatment outcomes with maintained levels of clinical attachment over long periods of time. The maintenance of treatment results for the majority of patients has been documented up to 14 years, and in a private practice situation even up to 30 years, but it has to be realized that a small proportion of patients will experience recurrent infections with progression of periodontal lesions in a few sites in a completely unpredictable mode. The continuous risk assessment at subject, tooth and tooth site levels, therefore, represents a challenge for the SPT concept.
# Continuous multi-level risk assessment
As opposed to an initial periodontal diagnosis which considers the sequelae of the disease process, i.e. documents the net loss of periodontal attachment and the concomitant formation of periodontal pockets and the existence of inflammation, clinical diagnosis during SPT has to be based on the variations of the health status obtained following successful active periodontal treatment. This, in turn, means that a new baseline will have to be established once the treatment goals of active periodontal therapy (i.e. phases 1–3) are reached and periodontal health is restored (Claffey 1991). This baseline includes the level of clinical attachment achieved while the inflammatory parameters are supposed to be under control. Under optimal circumstances, supportive periodontal care would maintain clinical attachment levels obtained after active therapy for the years to come. The relevant question would, therefore, be which clinical parameters may serve as early indicators for a new onset or recurrence of the periodontal disease process, i.e. reinfection and progression of periodontal breakdown of a previously treated periodontal site.
From a clinical point of view the stability of periodontal conditions reflects a dynamic equilibrium between bacterial aggression and effective host response. As such, this homeostasis is prone to sudden changes whenever one of the two factors prevails. Hence, it is evident that the diagnostic process must be based on continuous monitoring of the multi-level risk profile. The intervals between diagnostic assessments must also be chosen based on the overall risk profile and the expected benefit. To schedule patients for supportive periodontal therapy on the basis of an individual risk evaluation for recurrence of disease has been demonstrated to be cost effective (Axelsson & Lindhe 1981a,b; Axelsson _et al_. 1991).
By virtue of their previous disease predisposition, all patients under a periodontal maintenance program represent a population with a moderate to high risk for recurrent periodontal infection. As opposed to the general population without such a history, periodontal patients need to participate in a well organized recall system which should provide both continuous risk assessment and adequate supportive care. Without this, the patients are likely to experience progressive loss of periodontal attachment (Axelsson & Lindhe 1981a; Kerr 1981; Becker _et al_. 1984; Cortellini _et al_. 1994, 1996). On the other hand, it is important to determine the level of risk for progression in each individual patient in order to be able to determine the frequency and extent of professional support necessary to maintain the attachment levels obtained following active therapy. The determination of such risk level would thus prevent undertreatment, and also excessive overtreatment, during SPT (Brägger _et al_. 1992).
## Subject risk assessment
The patient's risk assessment for recurrence of periodontitis may be evaluated on the basis of a number of clinical conditions whereby no single parameter displays a more paramount role. The entire spectrum of risk factors and risk indicators ought to be evaluated simultaneously. For this purpose, a functional diagram has been constructed (Fig. 59-3) (Lang & Tonetti 2003) including the following aspects:
**Fig. 59-3a** Functional diagram to evaluate the patient's risk for recurrence of periodontitis. Each vector represents one risk factor or indicator with an area of relatively low risk, an area of moderate risk, and an area of high risk for disease progression. All factors have to be evaluated together and hence the area of relatively low risk is found within the center circle of the polygon, while the area of high risk is found outside the periphery of the second polygon in bold. Between the two rings in bold, there is the area of moderate risk.
**Fig. 59-3b** Functional diagram of a low-risk maintenance patient. BOP is 15%, four residual pockets ≥5 mm are diagnosed, two teeth have been lost, the bone factor in relation to the age is 0.25, no systemic factor is known and the patient is a non-smoker.
1. Percentage of bleeding on probing
2. Prevalence of residual pockets greater than 4 mm
3. Loss of teeth from a total of 28 teeth
4. Loss of periodontal support in relation to the patient's age
5. Systemic and genetic conditions
6. Environmental factors such as cigarette smoking.
Each parameter has its own scale for minor, moderate, and high-risk profiles. A comprehensive evaluation, the functional diagram will provide an individualized total risk profile and determine the frequency and complexity of SPT visits. Modifications may be made to the functional diagram if additional factors become important from future evidence.
### Compliance with recall system
Several investigations have indicated that only a minority of periodontal patients comply with the prescribed supportive periodontal care (Wilson _et al_. 1984; Mendoza _et al_. 1991; Checchi _et al_. 1994; Demetriou _et al_. 1995). Since it has been clearly established that treated periodontal patients who comply with regular periodontal maintenance appointments have a better prognosis than patients who do not comply (Axelsson & Lindhe 1981a; Becker _et al_. 1984; Cortellini _et al_. 1994, 1996), non-compliant or poorly compliant patients should be considered at higher risk for periodontal disease progression. A report that investigated the personality differences of patients participating in a regular recall program as compared to patients who did not, revealed that patients who did not take part in a maintenance program following periodontal therapy had higher incidences of stressful life events and less stable personal relationships in their lives (Becker _et al_. 1988).
Fig. 59-3c Functional diagram of a medium-risk maintenance patient. BOP is 9%, six residual pockets ≥5 mm are diagnosed, four teeth have been lost, the bone factor in relation to the age is 0.75, the patient is a type I diabetic, but a non-smoker.
Fig. 59-3d Functional diagram of a high-risk maintenance patient. BOP is 32%, ten residual pockets ≥5 mm are diagnosed, ten teeth have been lost, the bone factor in relation to the age is 1.25, no systemic factor is known, and the patient is an occasional smoker.
### Oral hygiene
Since bacterial plaque is by far the most important etiologic agent for the occurrence of periodontal diseases (for review see Kornman and Löe 1993), it is evident that the full-mouth assessment of the bacterial load must have a pivotal impact in the determination of the risk for disease recurrence. It has to be realized, however, that regular interference with the microbial ecosystem during periodontal maintenance will eventually obscure such obvious associations. In patients treated with various surgical and non-surgical modalities, it has been clearly established that plaque-infected dentitions will yield recurrence of periodontal disease in multiple locations, while dentitions under plaque control and regular supportive care maintain periodontal stability for many years (Rosling _et al_. 1976; Axelsson & Lindhe 1981a,b). Studies have thus far not identified a level of plaque infection compatible with maintenance of periodontal health. However, in a clinical set-up, a plaque control record of 20–40% might be tolerable by most patients. It is important to realize that the full-mouth plaque score has to be related to the host response of the patient, i.e. compared to inflammatory parameters.
### Percentage of sites with bleeding on probing
Bleeding on gentle probing represents an objective inflammatory parameter which has been incorporated into index systems for the evaluation of periodontal conditions (Löe & Silness 1963; Mühlemann & Son 1971) and is also used as a parameter by itself. In a patient's risk assessment for recurrence of periodontitis, bleeding on probing (BOP) reflects, at least in part, the patient's compliance and standards of oral hygiene performance. Although there is no established acceptable level of prevalence of BOP in the dentition above which a higher risk for disease recurrence has been established, a BOP prevalence of 25% has been the cut-off point between patients with maintained periodontal stability for 4 years and patients with recurrent disease in the same timeframe in a prospective study in a private practice (Joss _et al_. 1994) (Fig. 59-4). Further evidence of BOP percentages between 20% and 30% determining a higher risk for disease progression originates from studies of Claffey _et al_. (1990) and Badersten _et al_. (1990).
In assessing the patient's risk for disease progression, BOP percentages reflect a summary of the patient's ability to perform proper plaque control, the patient's host response to the bacterial challenge, and the patient's compliance. The percentage of BOP, therefore, is used as the first risk factor in the functional diagram of risk assessment (Fig. 59-3). The scale runs in a quadratic mode with 4, 9, 16, 25, 36, and >49% being the divisions on the vector.
Individuals with low mean BOP percentages (<10% of the surfaces) may be regarded as patients with a low risk for recurrent disease (Lang _et al_. 1990), while patients with mean BOP percentages >25% should be considered to be at high risk for reinfection.
### Prevalence of residual pockets greater than 4 mm
The enumeration of the residual pockets with probing depths greater than 4 mm represents, to a certain extent, the degree of success of periodontal treatment rendered. Although this figure _per se_ does not make much sense when considered as a sole parameter, the evaluation in conjunction with other parameters, such as BOP and/or suppuration, will reflect existing ecologic niches from and in which reinfection might occur. It is, therefore, conceivable that periodontal stability in a dentition would be reflected in a minimal number of residual pockets. Presence of high frequencies of deep residual pockets and deepening of pockets during supportive periodontal care has, in fact, been associated with high risk for disease progression (Badersten _et al_. 1990; Claffey _et al_. 1990). On the other hand, it has to be realized that an increased number of residual pockets does not necessarily imply an increased risk for reinfection or disease progression, since a number of longitudinal studies have established the fact that, depending on the individual supportive therapy provided, even deeper pockets may be stable without further disease progression for years (e.g. Knowles _et al_. 1979; Lindhe & Nyman 1984).
**Fig. 59-4** Distribution of "looser" sites (probing depth (PD) ≥4 mm) due to periodontal disease progression with or without concomitant recession, dependent on the mean bleeding on probing (BOP) percentage during an observation period of 4 years. Patients are sorted by decreasing mean BOP percentages. Patients with <20% BOP have a significantly lower risk for disease recurrence. (Data from Joss _et al_. 1994.)
Nevertheless, in assessing the patient's risk for disease progression, the number of residual pockets with a probing depth of ≥5 mm is assessed as the second risk indicator for recurrent disease in the functional diagram of risk assessment (Fig. 59-3). The scale runs in a linear mode with 2, 4, 6, 8, 10, and ≥12% being the divisions on the vector.
Individuals with up to four residual pockets may be regarded as patients with a relatively low risk, while patients with more than eight residual pockets may be regarded as individuals with high risk for recurrent disease.
### Loss of teeth from a total of 28 teeth
Although the reason for tooth loss may not be known, the number of remaining teeth in a dentition reflects the functionality of the dentition. Mandibular stability and individual optimal function may be assured even with a shortened dental arch of premolar to premolar occlusion, i.e. 20 teeth. The shortened dental arch does not seem to predispose the individual to mandibular dysfunction (Witter _et al_. 1990, 1994). However, if more than eight teeth from a total of 28 teeth are lost, oral function is usually impaired (Käyser 1981, 1994, 1996). Since tooth loss also represents a true end-point outcome variable reflecting the patient's history of oral diseases and trauma, it is logical to incorporate this risk indicator as the third parameter in the functional diagram of risk assessment (Fig. 59-3). The number of teeth lost from the dentition without the third molars (28 teeth) is counted, irrespective of their replacement. The scale runs also in a linear mode with 2, 4, 6, 8, 10, and ≥12% being the divisions on the vector.
Individuals with up to four teeth lost may be regarded as patients in low risk, while patients with more than eight teeth lost may be considered as being in high risk.
### Loss of periodontal support in relation to the patient's age
The extent and prevalence of periodontal attachment loss (i.e. previous disease experience and susceptibility), as evaluated by the height of the alveolar bone on radiographs, may represent the most obvious indicator of subject risk when related to the patient's age. In light of the present understanding of periodontal disease progression, and the evidence that both onset and rate of progression of periodontitis might vary among individuals and during different timeframes (van der Velden 1991), it has to be realized that previous attachment loss in relation to the patient's age does not rule out the possibility of rapidly progressing lesions. Therefore, the actual risk for further disease progression in a given individual may occasionally be underestimated. Hopefully, the rate of progression of disease has been positively affected by the treatment rendered and, hence, previous attachment loss in relation to patient's age may be a more accurate indicator during SPT than before active periodontal treatment. Given the hypothesis that a dentition may be functional for the most likely life expectancy of the subject in the presence of a reduced height of periodontal support (i.e. 25–50% of the root length), the risk assessment in treated periodontal patients may represent a reliable prognostic indicator for the stability of the overall treatment goal of keeping a functional dentition for a lifetime (Papapanou _et al_. 1988).
The estimation of the loss of alveolar bone is performed in the posterior region on either periapical radiographs, in which the worst site affected is estimated gross as a percentage of the root length, or on bite-wing radiographs in which the worst site affected is estimated in millimeters. One millimeter is equated with 10% bone loss. The percentage is then divided by the patient's age. This results in a factor. As an example, a 40-year-old patient with 20% of bone loss at the worst posterior site affected would be scored BL/Age = 0.5. Another 40-year-old patient with 50% bone loss at the worst posterior site scores BL/Age = 1.25.
In assessing the patient's risk for disease progression, the extent of alveolar bone loss in relation to the patient's age is estimated as the fourth risk indicator for recurrent disease in the functional diagram of risk assessment (Fig. 59-3). The scale runs in increments of 0.25 of the factor BL/Age, with 0.5 being the division between low and moderate risk and 1.0 being the division between moderate and high risk for disease progression. This, in turn, means that a patient who has lost a higher percentage of posterior alveolar bone than his/her own age is at high risk regarding this vector in a multi-factorial assessment of risk.
### Systemic conditions
The most substantiated evidence for modification of disease susceptibility and/or progression of periodontal disease arises from studies on type I and type II (insulin-dependent and non-insulin-dependent) diabetes mellitus populations (Gusberti _et al_. 1983; Emrich _et al_. 1991; Genco & Löe 1993).
It has to be realized that the impact of diabetes on periodontal diseases has been documented in patients with untreated periodontal disease, while, as of today, no clear evidence is available for treated patients. It is reasonable, however, to assume that the influence of systemic conditions may also affect recurrence of disease.
In recent years, genetic markers have become available to determine various genotypes of patients regarding their susceptibility for periodontal diseases. Research on the interleukin-1 (IL-1) polymor-phisms has indicated that IL-1 genotype-positive patients show more advanced periodontitis lesions than IL-1 genotype-negative patients of the same age group (Kornman _et al_. 1997). Also, there is a trend to higher tooth loss in the IL-1 genotype-positive subjects (McGuire & Nunn 1999). In a retrospective analysis of over 300 well maintained periodontal patients, the IL-1 genotype-positive patients showed significantly higher BOP percentages and a higher proportion of patients which yielded higher BOP percentages during a 1-year recall period than the IL-1 genotype-negative control patients (Lang _et al_. 2000). Also, the latter group had twice as many patients with improved BOP percentages during the same maintenance period, indicating that IL-1 genotype-positive subjects do indeed represent a group of hyper-reactive subjects even if they are regularly maintained by effective SPT (Lang _et al_. 2000). In a prospective study over 5 years on Australian white collar and blue collar workers on a University campus, the IL-1 geno-type-positive age group above 50 years showed significantly deeper probing depth than their IL-1 genotype-negative counterparts, especially when they were non-smokers.
In assessing the patient's risk for disease progression, systemic factors are only considered, if known, as the fifth risk indicator for recurrent disease in the functional diagram of risk assessment (Fig. 59-3). In this case, the area of high risk is marked for this vector. If not known or absent, systemic factors are not taken into account for the overall evaluation of risk.
Research on the association and/or modifying influence in susceptibility and progression of peri-odontitis of physical or psychologic stress is sparse (Cohen-Cole _et al_. 1981; Green _et al_. 1986; Freeman & Goss 1993). The hormonal changes associated with this condition, however, are well documented (Selye 1950).
### Cigarette smoking
Consumption of tobacco, predominantly in the form of smoking or chewing, affects the susceptibility and the treatment outcome of patients with adult peri-odontitis. Classical explanations for these observations have included the association between smoking habits and poor oral hygiene as well as lack of awareness of general health issues (Pindborg 1949; Rivera-Hidalgo 1986). More recent evidence, however, has established that smoking _per se_ represents not only a risk marker, but probably a true risk factor for peri-odontitis (Ismail _et al_. 1983; Bergström 1989; Berg-ström _et al_. 1991; Haber _et al_. 1993). In a young population (19–30 years of age), 51–56% of periodontitis was associated with cigarette smoking (Haber _et al_. 1993). The association of smoking and periodontitis has been shown to be dose-dependent (Haber _et al_. 1993). It has also been shown that smoking will affect the treatment outcome after scaling and root planing (Preber & Bergström 1985), modified Widman flap surgery (Preber & Bergström 1990), and regenerative periodontal therapy (Tonetti _et al_. 1995). Furthermore, a high proportion of so-called refractory patients has been identified as consisting of smokers (Bergström & Blomlöf 1992). The impact of cigarette smoking on the long-term effects of periodontal therapy in a population undergoing supportive periodontal care has been reported. Smokers displayed less favorable healing responses both at re-evaluation and during a 6-year period of supportive periodontal care (Baumert-Ah _et al_. 1994). In spite of the paucity of evidence relating cigarette smoking to impaired outcomes during supportive periodontal care, it seems reasonable to incorporate heavy smokers (>20 cigarettes/day) in a higher risk group during maintenance.
In assessing the patient's risk for disease progression, environmental factors such as smoking must be considered as the sixth risk factor for recurrent disease in the functional diagram of risk assessment (Fig. 59-3). While non-smokers (NS) and former smokers (FS) (more than 5 years since cessation) have a relatively low risk for recurrence of periodontitis, the heavy smokers (HS), as defined by smoking more than one pack per day, are definitely at high risk. Occasional (OS; <10 cigarettes a day) and moderate smokers (MS) may be considered at moderate risk for disease progression.
### Calculating the patient's individual periodontal risk assessment (PRA)
Based on the six parameters specified above, a multi-functional diagram is constructed for the PRA. In this diagram, the vectors have been constructed on the basis of the scientific evidence available. It is obvious that ongoing validation may result in slight modifications.
* A low periodontal risk (PR) patient has all parameters within the low-risk categories or at the most one parameter in the moderate-risk category (Fig. 59-3b).
* A moderate PR patient has at least two parameters in the moderate category, but at most one parameter in the high-risk category (Fig. 59-3c).
* A high PR patient has at least two parameters in the high-risk category (Fig. 59-3d).
Based on a 4-year prospective cohort study, the application of the multi-functional diagram for the subject-based PRA was validated (Persson _et al_. 2003) and, indeed, yielded complete periodontal stability after individually tailored recall intervals for all patients with a negative IL-1 gene polymorphism. For the IL-1 genotype-positive patients, however, the PRA resulted only in periodontal stability for 90% of the patients.
_Summary:_ The subject risk assessment may estimate the risk for susceptibility for progression of periodontal disease. It consists of an assessment of the level of infection (full-mouth bleeding scores), the prevalence of residual periodontal pockets, tooth loss, an estimation of the loss of periodontal support in relation to the patient's age, an evaluation of the systemic conditions of the patient, and finally, an evaluation of environmental and behavioral factors such as smoking and stress. All these factors should be contemplated and evaluated together. A functional diagram (Fig. 59-3) may help the clinician in determining the risk for disease progression on the subject level. This may be useful in customizing the frequency and content of SPT visits.
## Tooth risk assessment
### Tooth position within the dental arch
Early clinical surveys have associated the prevalence and severity of periodontal diseases with malocclusion and irregularities of tooth position (Ditto & Hall 1954; Bilimoria 1963). However, many subsequent studies using clinical evaluation methods could not confirm these conclusions (Beagrie & James 1962; Geiger 1962; Gould & Picton 1966). Although a relationship between crowding and increased plaque retention and gingival inflammation has been established (Ingervall _et al_. 1977; Buckley 1980; Griffith & Addy 1981; Hörup _et al_. 1987), no significant correlation between anterior overjet and overbite (Geiger _et al_. 1973), crowding and spacing (Geiger _et al_. 1974) or axial inclinations and tooth drifts (Geiger & Wasser-man 1980) and periodontal destruction, i.e. attachment loss subsequent to gingival inflammation, could be established. It is evident from the literature mentioned that crowding of teeth might eventually affect the amount of plaque mass formed in dentitions with irregular oral hygiene practices, thus contributing to the development of chronic gingivitis, but, as of today, it remains to be demonstrated whether tooth malposition within the dental arch will lead to an increased risk for periodontal attachment loss.
### Furcation involvement
It is evident that multi-rooted teeth with periodontal lesions extending into the furcation area have been the subject of intensive therapeutic studies for many years (Kalkwarf & Reinhardt 1988). Retrospective analyses of large patient populations in private periodontal practices of periodontal specialists (Hirschfeld & Wasserman 1978; McFall 1982) have clearly established that multi-rooted teeth appear to be at high risk for tooth loss during the maintenance phase. The most impressive long-term documentation maintained 600 patients for an average duration of 22 years, and 10% of these patients were even maintained for more than 30 years (Hirschfeld & Wasserman 1978). While 83% of the patients could be considered "well maintained" and had lost only 0–3 teeth during the observation period, a patient group of 4% (25) was identified with an extreme risk for disease progression and had lost between 10 and 23 teeth during a regularly scheduled maintenance program. Irrespective of the patient group of low, moderate, and high risk for disease progression during maintenance, the majority of the teeth lost were furcation-involved molars (Hirschfeld & Wasserman 1978). Similar results were obtained in a study on 100 treated periodontal patients maintained for 15 years or longer (McFall 1982).
Prospective studies on periodontal therapy in multi-rooted teeth have also revealed significant differences between non-molar sites and molar flat surfaces on the one hand and molar furcation sites on the other, when looking at the treatment outcomes evaluated as bleeding frequency, probing depth reductions, and levels of attachment (Nordland _et al_. 1987). Again, teeth with furcation involvement and original probing depths >6 mm had reduced treatment outcomes.
The assumption that the prognosis for single-rooted teeth and non-furcation-involved multi-rooted teeth is better than the prognosis for furcation-involved multi-rooted teeth was also confirmed by Ramfjord _et al_. (1987) in a prospective study over 5 years. It has to be realized, however, that these results are not intended to imply that furcation-involved teeth should be extracted, since all the prospective studies have documented a rather good overall prognosis for such teeth if regular supportive care is provided by a well organized maintenance program.
### Iatrogenic factors
Overhanging restorations and ill fitting crown margins certainly represent an area for plaque retention, and there is an abundance of association studies documenting increased prevalence of periodontal lesions in the presence of iatrogenic factors (for review see Leon 1977). Depending on the supragingival or subgingival location of such factors, their influence on the risk for disease progression has to be considered. It has been established that slightly subgingivally located overhanging restorations will, indeed, change the ecologic niche, providing more favorable conditions for the establishment of a Gram-negative anaerobic microbiota (Lang _et al_. 1983). There is no doubt that shifts in the subgingival microflora towards a more periodontopathic microbiota, if unaffected by treatment, represent an increased risk for periodontal breakdown.
### Residual periodontal support
Although many clinicians believe that teeth with reduced periodontal support are unable to function alone and should be extracted or splinted, there is clear evidence from longitudinal studies that teeth with severely reduced, but healthy, periodontal support can function either individually or as abutments for many years without any further loss of attachment (Nyman & Lindhe 1979; Nyman & Ericsson 1982; Brägger _et al_. 1990). Hence, successfully periodontally treated teeth can be maintained over decades and function as abutments in fixed bridge-work or as individual chewing units irrespective of the amount of residual periodontal support, provided that physiologic masticatory forces do not subject such teeth to a progressive trauma which may lead to spontaneous extraction. Obviously, by virtue of the already reduced support, should disease progression occur in severely compromised teeth, this may lead to spontaneous tooth exfoliation.
### Mobility
In light of the discussion of abutment teeth with severely reduced but healthy periodontal support, tooth mobility may be an indicator for progressive traumatic lesions, provided that the mobility is increasing continuously (Nyman & Lang 1994). When assessing tooth mobility, it has to be realized that two factors may contribute to hypermobility: (1) a widening of the periodontal ligament as a result of unidirectional or multidirectional forces to the crown, high and frequent enough to induce resorption of the alveolar bone walls; and (2) the height of the periodontal supporting tissues. If this is reduced due to prior periodontal disease, but the width of the periodontal ligament is unchanged, the amplitude of root mobility within the remaining periodontium is the same as in a tooth with normal height, but the leverage on the tooth following application of forces to the crown is changed. Therefore, it has to be realized that all teeth that have lost periodontal support have increased tooth mobility as defined by crown displacement upon application of a given force. Nevertheless, this hypermobility should be regarded as physiologic (Nyman & Lindhe 1976).
Since tooth mobility is probably more frequently affected by reduced periodontal height rather than unidirectional or multidirectional application of forces on the tooth, its significance for the evaluation of the periodontal conditions has to be questioned. Several studies have indicated that tooth mobility varies greatly before, during, and after periodontal therapy (Persson 1980, 1981a,b). From these studies it can be concluded that periodontally involved teeth show a decrease in mobility following non-surgical and/or surgical periodontal procedures. However, following surgical procedures, tooth mobility may temporarily increase during the healing phase and may resume decreased values later on. Provisional splinting as an adjunct to non-surgical or surgical therapy does not seem to affect the final result of tooth mobility.
_Summary:_ The tooth risk assessment encompasses an estimation of the residual periodontal support, an evaluation of tooth positioning, furcation involvements, presence of iatrogenic factors, and a determination of tooth mobility to evaluate functional stability. A risk assessment at tooth level may be useful in evaluating the prognosis and function of an individual tooth and may indicate the need for specific therapeutic measures during SPT visits.
## Site risk assessment
### Bleeding on probing
Absence of bleeding on probing (BOP) is a reliable parameter to indicate periodontal stability if the test procedure for assessing BOP has been standardized (Lang _et al_. 1990). Presence of bleeding upon standardized probing will indicate presence of gingival inflammation. Whether or not repeated BOP over time will predict the progression of a lesion is, however, questionable (Lang _et al_. 1986, 1990; Vanooteghem _et al_. 1987). Nevertheless, a 30% probability for attachment loss to occur in the future may be predicted for sites repeatedly positive for BOP (Fig. 59-5) (Badersten _et al_. 1985, 1990; Lang _et al_. 1986; Vanooteghem _et al_. 1987, 1990; Claffey _et al_. 1990).
Obviously, BOP is rather sensitive to different forces applied to the tissues. An almost linear relationship (R = 0.87) existed between the probing force applied and the percentage of bleeding sites in a study on healthy young adults (Fig. 59-6) (Lang _et al_. 1991). If the probing force exceeded 0.25 N (25 g), the tissues were traumatized and bleeding was provoked as a result of trauma, rather than as a result of tissue alterations due to inflammation. To assess the "true" percentage of bleeding sites due to inflammation, a probing force of 0.25 N or less should be applied, which clinically means a light probing force. This has also been confirmed for patients who have experienced loss of attachment, i.e. with successfully treated advanced periodontitis (Fig. 59-7) (Karayiannis _et al_. 1991; Lang _et al_. 1991).
**Fig. 59-5** Positive predictive values for loss of probing attachment of ≥2 mm in 2 years in sites which bled on probing 0, 1, 2, 3 or 4 times out of four SPT visits in a total of 48 patients following active periodontal therapy. (Data from Lang _et al_. 1986.)
**Fig. 59-6** Regression analysis between mean bleeding on probing (BOP) percentage and probing forces applied in young dental hygiene students with a healthy gingiva and normal anatomy. A very high correlation coefficient (R = 0.87) and an almost linear correlation between probing force and BOP percentage was found. (Data from Lang _et al_. 1991.)
**Fig. 59-7** Regression analysis between mean bleeding on probing (BOP) percentage and probing forces applied in subjects with successfully treated periodontitis: a reduced, but healthy, periodontium. (Data from Karayiannis _et al_. 1991.)
Since absence of BOP at 0.25 N indicated periodontal stability with a negative predictive value of 98–99% (Lang _et al_. 1990), this clinical parameter is the most reliable for monitoring patients over time in daily practice. Non-bleeding sites may be considered periodontally stable. On the other hand, bleeding sites seem to have an increased risk for progression of periodontitis, especially when the same site is bleeding at repeated evaluations over time (Lang _et al_. 1986; Claffey _et al_. 1990).
It is, therefore, advisable to register the sites with BOP in a dichotomous way using a constant force of 0.25 N. This allows the calculation of the mean BOP for the patient, and also yields the topographic location of the bleeding site. Repeated scores during maintenance will reveal the surfaces at higher risk for loss of attachment.
### Probing depth and loss of attachment
Clinical probing is the most commonly used parameter both to document loss of attachment and to establish a diagnosis of periodontitis. There are, however, some sources of error inherent in this method which contribute to the variability in the measurements. Among these are (1) the dimension of the periodontal probe; (2) the placement of the probe and obtaining a reference point; (3) the crudeness of the measurement scale; (4) the probing force; and (5) the gingival tissue conditions.
In spite of the recognized method errors inherent in clinical probing, this diagnostic procedure has not only been the most commonly used but is also the most reliable parameter for the evaluation of the periodontal tissues. It has to be realized that increased probing depth and loss of probing attachment are parameters which reflect the history of periodontitis rather than its current state of activity. In order to obtain a more realistic assessment of the disease progression or, more commonly, the healing following therapy, multiple evaluations should be performed. Obviously, the first evaluation prior to therapy will yield results confounded by greater measurement error than evaluations following therapy. The reference point (cemento-enamel junction) may be obstructed by calculus or by dental restorations, and the condition of the gingival tissues may allow an easy penetration of the periodontal probe into the tissues, even though the probe position and force applied are standardized. These biologic variables (tissue conditions and calculus) may be minimized following initial periodontal therapy, and hence, repeated periodontal evaluations using probing will improve the metric assessment. The first periodontal evaluation after healing following initial periodontal therapy should, therefore, be taken as the baseline for long-term clinical monitoring (Claffey 1994).
### Suppuration
In a proportion of periodontal lesions, pus will develop and may drain through the orifice of a pocket. This criterion of suppuration may be recognized while clinically probing the lesion, or preferably, by using a ball burnisher (Singh _et al_. 1977). Several longitudinal studies on the results of periodontal therapy have evaluated clinical parameters, including suppuration, for the prediction of future loss of attachment (Badersten _et al_. 1985, 1990; Claffey _et al_. 1990). In all these studies, the presence of suppuration increased the positive predictive value for disease progression in combination with other clinical parameters, such as BOP and increased probing depth. Hence, following therapy a suppurating lesion may provide evidence that the periodontitis site is undergoing a period of exacerbation (Kaldahl _et al_. 1990).
_Summary:_ The tooth site risk assessment includes the registration of BOP, probing depth, loss of attachment, and suppuration. A risk assessment on the site level may be useful in evaluating periodontal disease activity and determining periodontal stability or ongoing inflammation. The site risk assessment is essential for the identification of the sites to be instrumented during SPT.
## Radiographic evaluation of periodontal disease progression
As a consequence of the clinical risk assessments the decision may be made to gather radiographic information on the periodontal conditions as well (Hirschmann _et al_. 1994). The task may be related to a generalized pattern of disease progression or a localized monitoring. Not only periodontal aspects, but a comprehensive approach, should influence the choice of the radiographic technique (Rohlin & Akerblom 1992). Periodic radiographic surveys not based on clinical signs and symptoms should not be scheduled simply to confirm health.
Radiographic perception of periodontal changes is characterized by a high specificity, but a low sensitivity, with underestimation of the severity of a periodontal defect (Hämmerle _et al_. 1990; Åkesson _et al_. 1992). Undetectability of minute changes at the alveolar crest is related to overprojections and variations in projection geometry when taking repeated radio-graphs (Lang & Hill 1977; Goodson _et al_. 1984; Jenkins _et al_. 1992). This may result in mimicked variations in the alveolar bone height, obscured furcation status, etc. In addition, film processing variations may result in unreliable assessments of alveolar bone density changes (Rams _et al_. 1994).
The standard procedure for periodontal evaluations is based on a filmholder system with an alignment for long-cone paralleling technique (Rushton & Horner 1994). With the addition of simple pins to the filmholders as a repositioning reference, the methodologic error was impressively reduced (Carpio _et al_. 1994).
It is a fact that, in general, the standards in oral radiology related to agreement in the choice of a technique, the quality of film processing and the agreement in the diagnosis need to be improved (Brägger 1996).
## Clinical implementation
The _three levels_ of risk assessment presented represent a logic sequence of clinical evaluation to be performed prior to rendering treatment during maintenance. The information gathered from a stepwise evaluation should not impinge on, but should rather improve, the efficacy of secondary prophylactic periodontal care and treatment. A logical sequence of checks and examinations may be easily obtained in a short period of time and at no extra cost for laboratory tests. The information obtained from clinical monitoring and multi-level risk assessment facilitates an immediate appreciation of the periodontal health status of an individual and the possible risk for further infection and/or disease progression.
Most longitudinal studies published to date have been based on single-level, i.e. site or tooth, risk assessment, rather than accounting for the most evident factor in risk assessment: the patient. Ample evidence indicates that a minority of patients will continue to present problems and hence, differ completely from the maintenance pattern visualized in the majority of the patients. Even in the studies where this fact has been explicitly addressed (Hirschfeld & Wasserman 1978), the factors which determined whether or not a patient belonged to a well maintained group or to a group with continuous loss of periodontal attachment have not been identified.
_Summary:_ It is suggested that patients be evaluated on the _three different levels_ mentioned. At the patient level, loss of support in relation to patient age, full mouth plaque and/or bleeding scores, and prevalence of residual pockets are evaluated, together with the presence of systemic conditions or environmental factors, such as smoking, which can influence the prognosis. The clinical utility of this first level of risk assessment influences primarily the determination of the recall frequency and time requirements. It should also provide a perspective for the evaluation of risk assessment conducted at the tooth and site levels.
At the tooth and tooth site levels, residual periodontal support, inflammatory parameters and their persistence, presence of ecologic niches with difficult access such as furcations, and presence of iatrogenic factors have to be put into perspective with the patient overall risk profile (Fig. 59-8). The clinical utility of tooth and site risk assessment relates to rational allocation of the recall time available for therapeutic intervention to the sites with higher risk, and possibly to the selection of different forms of therapeutic intervention.
**Fig. 59-8** Continuous multiple level risk assessment. Subject, tooth, and site parameters are combined to establish the clinical risk for disease progression. Note that different sites in the same patient may have a different level of risk. Subject-based risk factors are used to put the tooth and/or site risk assessment in perspective.
# Objectives for SPT
The objective of maintenance care must be the continued preservation of gingival and periodontal health, obtained as a result of the active periodontal treatment. Irrespective of whether or not additional treatment such as prosthetic reconstructions or placement of implants has been rendered, the regular and adequate removal of supragingival plaque by the patient is, therefore, a prerequisite for a good long-term prognosis. In order to reach these goals, regular clinical re-evaluations with appropriate interceptive treatment, continued psychologic support and encouragement of the patient, and a lifelong commitment by the therapists are required.
General rules regarding frequency of maintenance care visits are difficult to define. However, there are a few aspects to consider in this respect: the patient's individual oral hygiene standard, the prevalence of sites exhibiting bleeding on probing, and the pre-therapeutic attachment level and alveolar bone height. This in turn means that patients with suboptimal plaque control and/or concomitant high prevalence of bleeding sites should be recalled more frequently than patients exhibiting excellent plaque control and healthy gingival tissues. Nevertheless, patients with healthy gingival conditions, but with a severely reduced height of periodontal support, should also be recalled with short time intervals (not exceeding 3–4 months) in order to exclude or at least reduce the risk of additional tooth loss. In most of the longitudinal studies referred to above, positive treatment results were maintained with regular maintenance care provided at 3–6-month intervals. It seems reasonable to commence post-therapeutic maintenance with recall visits once every 3–4 months and then shorten or prolong these intervals in accordance with the aspects discussed above.
Since clinical attachment levels are usually stable 6 months following active periodontal therapy, it has been suggested that the first 6 months after completion of therapy be considered a healing phase (West-felt _et al_. 1983b) during which frequent professional tooth-cleaning has been recommended. Following this healing phase, it is generally agreed to recall patients treated for periodontal disease at intervals of 3–4 months in a well organized system of SPT. It has to be realized that tissue contours may be subjected to remodeling processes despite stable clinical attachment levels and, hence, morphologic changes may still improve the accessibility of all tooth surfaces to oral hygiene practices for months and years. Proper oral hygiene practices appear to be the most important patient factor to guarantee long-term stability of treatment results (Knowles _et al_. 1979; Ramfjord _et al_. 1982, 1987; Lindhe & Nyman 1984). This, in turn, ne cessitates optimization of the patient's skills and continuous motivation and reinforcement to perform adequate mechanical oral hygiene practices, although chemical agents, such as the potent antiseptic chlorhexidine, may substitute and later complement the patient's efforts during the healing phase, when mechanical practices are difficult (Westfelt _et al_. 1983a). It is obvious that regular recall visits for SPT should be scheduled soon after completion of cause-related therapy, even if periodontal surgical procedures are still to be performed following a careful re-evaluation of the tissue response. To postpone the organization of a maintenance care program until corrective procedures such as surgery, endodontic, implant, operative or reconstructive therapy have been performed may reinforce a possible misconception of the patient that the professional visits to a therapist or hygienist guarantee positive treatment outcomes and optimal long-term prognosis rather than the patient's own regular performance of individually optimal and adequate oral hygiene practices.
# SPT in daily practice
The recall hour should be planned to meet the patient's individual needs. It basically consists of four different sections which may require various amounts of time during a regularly scheduled visit:
1. Examination, re-evaluation, and diagnosis (ERD)
2. Motivation, reinstruction, and instrumentation (MRI)
3. Treatment of reinfected sites (TRS)
4. Polishing of the entire dentition, application of fluorides, and determination of future SPT (PFD).
The SPT recall hour (Fig. 59-9) is generally composed of 10–15 minutes of diagnostic procedures (ERD) followed by 30–40 minutes of motivation, rein-struction, and instrumentation (MRI) during which time the instrumentation is concentrated on the sites diagnosed with persistent inflammation. Treatment of reinfected sites (TRS) may include small surgical corrections, applications of local drug delivery devices or just intensive instrumentation under local anesthesia. Such procedures, if judged necessary, may require an additional appointment. The recall hour is normally concluded with polishing of the entire dentition, application of fluorides and another assessment of the situation, including the determination of future SPT visits (PFD). Approximately 5–10 minutes have to be reserved for this section.
## Examination, re-evaluation, and diagnosis (ERD)
Since patients on SPT may experience significant changes in their health status and the use of medications, an update of the information on general health issues is appropriate. Changes in health status and medications should be noted. In middle-aged to elderly patients, especially, these aspects might influence the future management of the patient. An extraoral and intraoral soft tissue examination should be performed at any SPT visit to detect any abnormalities and to act as a screening for oral cancer. The lateral borders of the tongue and the floor of the mouth should be inspected in particular. An evaluation of the patient's risk factors will also influence the choice of future SPT and the determination of the recall interval at the end of the maintenance visit. Following the assessment of the subject's risk factors, the tooth site-related risk factors are evaluated. As indicated above, the diagnostic procedure usually includes an assessment of the following:
**Fig. 59-9** The SPT recall hour is divided into four sections. (1) Examination, re-evaluation and diagnosis (ERD) providing information on stable and inflamed sites. This segment uses 10–15 minutes. (2) Motivation, reinstruction of oral hygiene where indicated, and instrumentation (MRI) will use the bulk of the recall hour (30–40 minutes). Sites which were diagnosed as not stable are instrumented. (3) Treatment of reinfected sites (TRS) may require a second appointment. (4) Polishing all tooth surfaces, application of fluorides and determination of the future recall interval (PFD) conclude the recall hour (5–10 minutes).
1. The oral hygiene and plaque situation
2. The determination of sites with bleeding on probing, indicating persistent inflammation
3. The scoring of clinical probing depths and clinical attachment levels. The latter is quite time-consuming and requires the assessment of the location of the cemento-enamel junction as a reference mark on all (six) sites of each root. Therefore, an SPT evaluation usually only includes scoring of clinical probing depths
4. The inspection of reinfected sites with pus formation
5. The evaluation of existing reconstructions, including vitality checks for abutment teeth
6. The exploration for carious lesions.
All these evaluations are performed for both teeth and oral implants. Occasionally, conventional dental radiographs should be obtained at SPT visits. Especially for devitalized teeth, abutment teeth and oral implants, single periapical films exposed with a parallel and preferably standardized technique are of great value. Bite-wing radiographs are of special interest for caries diagnostic purposes. They also reveal plaque-retentive areas such as overhanging fillings and ill fitting crown margins. Since only approximately 10–15 minutes are available for this section, these assessments have to be performed in a well organized fashion. It is preferable to have a dental assistant available to note all the results of the diagnostic tests unless a voice-activated computer-assisted recording system is used.
## Motivation, reinstruction, and instrumentation (MRI)
This aspect uses most of the available time of the SPT visit. When informed about the results of the diagnostic procedures, e.g. the total percentage of the BOP score or the number of pockets exceeding 4 mm, the patient may be motivated either in a confirmatory way in the case of low scores or in a challenging fashion in the case of high scores. Since encouragement usually has a greater impact on future positive developments than negative criticism, every effort should be made to acknowledge the patient's performance.
Patients who have experienced a relapse in their adequate oral hygiene practices need to be further motivated. Especially if the personal life situation has influenced the performance, positive encouragement is appropriate. Standard "lecturing" should be replaced by an individual approach.
Occasionally, patients present with hard tissue lesions (wedge-shaped dental defects) which suggest overzealous and/or faulty mechanical tooth cleaning (Fig. 59-10). Such habits should be broken and the patient reinstructed in toothbrushing techniques which emphasize vibratory rather than scrubbing movements.
Since it appears impossible to instrument 168 tooth sites in a complete dentition in the time allocated, only those sites which exhibit signs of inflammation and/or active disease progression will be re-instrumented during SPT visits. Hence, all the BOP-positive sites and all pockets with a probing depth exceeding 5 mm are carefully rescaled and root planed. Repeated instrumentation of healthy sites will inevitably result in mechanically caused continued loss of attachment (Lindhe _et al_. 1982a).
Similar observations were made in clinical studies by Claffey _et al_. (1988) where loss of clinical attachment levels immediately following instrumentation was observed in 24% of the sites. It is also known from regression analyses of several longitudinal studies (e.g. Lindhe _et al_. 1982b) that probing attachment may be lost following instrumentation of pockets below a "critical probing depth" of approximately 2.9 mm. Instrumentation of shallow sulci is, therefore, not recommended. As it has been shown in several studies that non-bleeding on probing sites represent stable sites (Lang _et al_. 1986, 1990; Joss _et al_. 1994), it appears reasonable to leave non-bleeding sites for polishing only and concentrate on periodontal sites with a positive BOP test or probing depths exceeding 5 mm. To protect the hard tissues, root planing should be performed with great caution. The deliberate removal of "contaminated" cementum during SPT is no longer justified (Nyman _et al_. 1986, 1988; Mombelli _et al_. 1995). During SPT visits, root surface instrumentation should be aimed especially at the removal of subgingival plaque rather than "diseased" cementum. This may require a more differentiated approach than hitherto recommended. In this respect, the use of ultrasonics may have to be re-evaluated.
**Fig. 59-10** Wedge-shaped defects apical to the cemento-enamel junction following recession of the gingival tissues resulting from overzealous or faulty toothbrushing.
## Treatment of reinfected sites (TRS)
Single sites, especially furcation sites or sites with difficult access, may occasionally be reinfected and demonstrate suppuration. Such sites require a thorough instrumentation under anesthesia, the local application of antibiotics in controlled-release devices or even open debridement with surgical access. It is evident that such therapeutic procedures may be too time-consuming to be performed during the routine recall hour, and hence, it may be necessary to reschedule the patient for another appointment. Omission of thorough retreatment of such sites or only performing incomplete root instrumentation during SPT may result in continued loss of probing attachment (Kaldahl _et al_. 1988; Kalkwarf _et al_. 1989).
Treatment choices for reinfected sites should be based on an analysis of the causes most likely responsible for the reinfection.
Generalized reinfections are usually the result of inadequate SPT. Although not all sites positive for BOP may further progress and lose attachment, high BOP percentages call for more intensive care and more frequent SPT visits. Sometimes, a second visit 2–3 weeks after the recall may be indicated to check the patient's performance in oral home care. It is particularly important to supervise patients closely for advanced periodontitis if they have a high subject risk assessment (Westfelt _et al_. 1983b; Ramfjord 1987).
**Fig. 59-11** Flow sheet of supportive periodontal therapy (SPT) with strategic decision tree for the recall visit.
Local reinfections may either be the result of inadequate plaque control in a local area or the formation of ecologic niches conducive to periodontal pathogens. The risk assessment on the tooth level may identify such niches which are inaccessible for regular oral hygiene practices. Furcation involvements often represent special periodontal risk factors which may require additional therapy to be performed following diagnosis in the regular SPT visit.
## Polishing, fluorides, determination of recall interval (PFD)
The recall hour is concluded with polishing the entire dentition to remove all remaining soft deposits and stains. This may provide freshness to the patient and facilitates the diagnosis of early carious lesions. Following polishing, fluorides should be applied in high concentration in order to replace the fluorides which might have been removed by instrumentation from the superficial layers of the teeth. Fluoride or chlorhexidine varnishes may also be applied to prevent root surface caries, especially in areas with gingival recession. The determination of future SPT visits must be based on the patient's risk assessment.
_Summary_ : Figure 59-11 provides a flowchart for SPT. The SPT recall hour is divided into four sections. While the first 10–15 minutes are reserved for examination, re-evaluation and diagnosis, the second and most time-consuming section of 30–40 minutes is devoted to reinstruction and instrumentation of sites at risk identified in the diagnostic process. Some reinfected sites may require further treatment, and hence, the patient may have to be rescheduled for an additional appointment. The recall hour is concluded by polishing the dentition, applying fluorides and determining the frequency of future SPT visits.
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# Part 19: Halitosis
60 Halitosis Control
_Edwin G. Winkel_
# Chapter 60
# Halitosis Control
Edwin G. Winkel
* * *
Introduction
Epidemiology
Odor characteristics
Pathogenesis of intraoral halitosis
Pathogenesis of extraoral halitosis
Diagnosis
Flowchart in a halitosis practice
Before first consultation
At the first examination
Classification of halitosis
Therapy
Pseudo-halitosis and halitophobia
Temporary halitosis
Extraoral halitosis
Intraoral halitosis
Physiologic halitosis
Treatment planning
Adjustment of therapy
Future perspectives
* * *
# Introduction
Offensive body odor is one of the greatest taboos in our society. Conditions that are associated with body odors are bromidrosis, the secretion of foul-smelling sweat, body odor also known as osmidrosis or kakidrosis (Leyden 1981; Lukacs 1991; Guillet _et al_. 2000), flatulence, excessive production of bowel gases (Suarez _et al_. 1999; Bell 2000), and bad breath (Attia & Marshall 1982; Delanghe _et al_. 1997; van Steen-berghe 1997). One factor these conditions have in common is that bacteria play an essential role in the etiology.
This chapter will focus on bad breath. Several terms like breath malodor, oral malodor, _fetor ex ore_ , _fetor oris_ , bad or foul breath, and halitosis are used to prescribe noticeably unpleasant odors exhaled in breathing. Halitosis is a technical term for bad breath and originates from the Latin "halitus" meaning "breath" and the Greek "osis" meaning "abnormal" or "diseased". Knowledge of this condition dates back to ancient cultures. The Talmud, a collection of ancient rabbinical writings dating back more than 2 millennia, states that bad breath is a major disability. The marriage license (the Ketuba) may be legally broken in the case of halitosis of one of the partners (Shifman _et al_. 2002). The theme is also discussed in ancient writings from China, Greek, Roman, early Christian, and Islamic cultures. For example, Islamic theology stresses the importance of the Siwak or Miswak, a stick obtained from a plant called Salvadore Persica, to clean the teeth and the tongue. Prior to the late 1930s, most references pertaining to halitosis consisted mainly of anecdotal statements that have been perpetuated in the literature. In 1934, Fair and Wells developed the osmoscope, an instrument for measuring the intensity of odors. Later, this apparatus was used for breath analysis (Brening _et al_. 1938). During the last 40 years, our scientific knowledge about the source and causes of halitosis has become much greater.
Several nonoral pathologic conditions have been related to oral malodor, including infection of the upper and lower respiratory tracts, the gastrointestinal tract, and some metabolic diseases involving the kidneys and the liver (Manolis 1983). However, clinical surveys have shown that over 90% of all bad breath odors originate in the mouth (Delanghe _et al_. 1997; van Steenberghe 1997).
## Epidemiology
Information regarding the prevalence of oral halitosis is scarce due to the lack of epidemiologic studies. An early study from The Netherlands among 11 625 individuals revealed a prevalence of approximately 25% in subjects older than 60 years (de Wit 1966). In subjects under 20 years, the prevalence of oral halitosis was 10%, indicating that the prevalence of this condition increases with age. In Japan the prevalence of individuals with complaints of halitosis is approximately 14% (National Survey 1999). In the USA, it is estimated that 10–30% of the adult population have an appreciable problem with bad breath (Meskin 1996). Recently, in China the incidence of oral halitosis was surveyed in a sample of 2000 individuals aged 15–64 years. Oral halitosis was measured in 27.5% of the subjects with organoleptic measurements (Liu _et al_. 2006). However, only a few patients visit dental clinics to seek help for this condition.
**Table 60-1** Breath volatile sulphur compounds and some amines, together with some of their known odor characteristics
## Odor characteristics
Together with some of their known odor characteristics, the most common odorous volatile sulfur compounds and some amines found in the breath of patients with halitosis of different origin are shown in Table 60-1 (Verschueren 1983; Tangerman 2002). The 100% odor recognition threshold is the concentration at which 100% of the odor panel defined the odor as being representative of the odorant being studied. The unsaturated mercaptans (allyl mercaptan in garlic) and the unsaturated sulfides (allyl methyl sulfide in garlic) are the most odorous, followed by saturated mercaptans (propyl mercaptan in onion, methyl mercaptan in bad breath), disulfides (dimethyl disulfide), and sulfides (methyl propyl sulfide in onion and dimethyl sulfide and hydrogen sulfide in bad breath).
For a proper diagnosis and therapy and/or referral to a physician or specialist, it is important for the general practitioner to clearly differentiate between halitosis from oral and non-oral origin. Therefore, in this chapter the term _intraoral halitosis_ (oral malodor) will be used to define halitosis with a cause within the oral cavity, whereas _extraoral halitosis_ is used for halitosis of non-oral cause.
## Pathogenesis of intraoral halitosis
Intraoral halitosis may be indicative of either oral diseases, such as periodontal diseases, or the presence of excessive bacterial reservoirs on the tongue. The pathogenesis of intraoral halitosis is associated with the bacterial degradation of sulfur-containing amino acids (methionine, cystine, and cysteine) into volatile sulfur compounds (VSCs) of which methyl mercaptan (CH3SH) and hydrogen sulfide (H2S) are the major compounds. It appears that methyl mercaptan is the predominant causative factor of malodor (Tangerman 2002; Awano _et al_. 2004; Tangerman & Winkel 2007). Despite the strong evidence that VSCs are the major causative factors in intraoral halitosis, several research groups still suggest that other volatile compounds such as cadaverine, indole, skatole, and butyric acid may influence oral halitosis (Rosenberg & McCulloch 1992; Goldberg _et al_. 1994; Rosenberg 1996; Greenman _et al_. 2004). No data of the presence of smellable concentrations of such volatiles in mouth air have ever been shown. Therefore, no evidence exists of such a relationship. On the contrary, Tonzetich (1977) clearly showed that diamines, such as cadaverine, inhibited odor formation. It was also stated that indole and skatole, although emanating an objectionable odor in pure state, did not impart an odor to saliva under conditions approximating those of the oral cavity. He ascribed this to their extremely low volatility. The same holds for butyric acid. Due to their low volatilities these compounds have a low odor potential. This is in strong contrast with the VSCs which have a very high odor potential (Verschueren _et al_. 1983).
### Formation of volatile sulfur compounds
Gram-negative, proteolytic bacteria are believed to play an essential role in the formation of VSCs, although Gram-positive bacteria such as _Peptostreptococcus_ species have also shown ability to produce VSCs _in vitro_ (McNamara _et al_. 1972; Persson 1989; Claesson 1990; Persson _et al_. 1990). The most active producers of VSCs _in vitro_ are shown in Table 60-2. In our clinic we selected over 100 patients with halitosis but without a history of periodontitis. By culturing periodontal pathogens we found meanly _Fusobacterium_ species and low levels of _Prevotella intermedia_ (unpublished data), which was in accordance with findings of Loesche and Kazor (2002). This suggested that the indigenous tongue flora is distinct from the periodontal flora. Therefore, microbiologic information about patients with halitosis should clearly differentiate between patients with or without (a history of) periodontitis.
**Table 60-2** Microorganisms with a high capability of generating volatile sulfur compounds _in vitro_
## Periodontium
In patients with periodontal disease, methyl mercaptan was found to be the most abundant VSC (Yaegaki & Sanada 1992c). The role of hydrogen sulfide (H2S) and methyl mercaptan (MM) in the etiology of periodontitis is unclear. VSCs are potentially capable of altering the permeability of the gingival tissues, including inflammatory responses. By modulating the functions of gingival fibroblasts, VSCs may play a role in the pathogenesis of gingivitis and periodontitis (Ratkay _et al_. 1995; Ratcliff & Johnson 1999; Torresyap _et al_. 2003). In an _in vitro_ study, it was shown that MM had a more pronounced effect on the permeability of mucosa than a similar concentration of H2S (Johnson 1992; Ng 1984). MM has also been shown to act synergistically with both lipopolysaccharide (LPS) and interleukin 1-beta (IL-1β) to increase secretion of prostaglandin E2 and collagenase, important mediators of inflammation and tissue destruction (Ratkay _et al_. 1995). In fact, increased VSCs in mouth air are related to deep periodontal pockets (Coil & Tonzetich 1992; Yaegaki & Sanada 1992a,c). However, it has also become clear that intraoral halitosis may also occur in individuals with a healthy periodontium (Kaizu _et al_. 1978; Bosy _et al_. 1994; Winkel _et al_. 2003) _._ In patients with periodontitis, Yeagaki and Sanada (1992c) found six times more tongue coating than in those who were periodontally healthy.
### Tongue
The tongue has the largest bacterial load of any oral tissue and makes the greatest contribution to bacteria found in the saliva. It is believed that the bacterial mass located at the posterior dorsum of the tongue is the principal site where malodorous compounds are produced (Bosy _et al_. 1994; De Boever _et al_. 1994). Individuals that suffer from intraoral halitosis have a significantly higher bacterial load on the dorsum of the tongue in comparison to individuals without intraoral halitosis (De Boever & Loesche 1995; Yaegaki & Sanada 1992a) _._ In addition, the rough surface of the tongue provides an ideal habitat for anaerobic bacteria, which flourish under a continually forming tongue coating of food debris, dead cells, and hundreds of thousands of bacteria, both living and dead.
## Pathogenesis of extraoral halitosis
Approximately 10% of cases of halitosis are caused by extraoral halitosis (Delanghe _et al_. 1998; Tangerman & Winkel 2007).
Examples of extraoral halitosis of the upper respiratory tract are chronic sinusitis, nasal obstruction, nasopharyngeal abscess, and carcinoma of the larynx. Examples of the lower respiratory tract are bronchitis, bronchiectasis, pneumonia, pulmonary abscess, and carcinoma of the lungs (Attia & Marshall 1982; Lu 1982; Durham _et al_. 1993; McDowell & Kassebaum 1993).
Extraoral halitosis might also be a manifestation of a serious systemic disease, such as hiatus hernia, hepatic cirrhosis, or diabetes mellitus. These diseases may produce specific smells (Tangerman 2002) (Table 60-3). For example, _fetor hepaticus_ in liver cirrhosis is a type of severe bad breath caused by dimethyl sulfide (Tangerman _et al_. 1994). While intraoral halitosis is largely caused by MM and to a lesser extent by H2S (Tangerman 2002; Awano _et al_. 2004; Tangerman & Winkel 2007), these components cannot be found in blood-borne halitosis (Tangerman 2002). A new finding is outlined in a study by Tangerman and Winkel (2007) where they found that the majority of extraoral blood-borne halitosis was caused by a hitherto unknown metabolic disorder resulting in elevated odorous levels of dimethyl sulfide in blood and breath. Unpleasant odor from the lower gastrointestinal tract is only detectable during belching or vomiting, because the oesophagus is normally collapsed (Attia & Marshall 1982). The stomach is therefore not considered to contribute to halitosis, except in rare circumstances (Rosenberg 1996).
**Table 60-3** Odorous volatiles in the breath of patients with extraoral blood-borne halitosis
**Causes of blood-borne halitosis** | **Odorant**
---|---
**Systemic diseases** |
Hepatic failure/liver cirrhosis | Dimethyl sulfide
Uremia/kidney failure | Dimethylamine, trimethylamine
Diabetic ketoacidosis, diabetes mellitus | Acetone
**Metabolic disorders** |
Isolated persistent hypermethioninemia | Dimethyl sulfide
Fish odor syndrome, trimethylaminuria | Trimethylamine
**Medication** |
Disulfiram | Carbon disulfide
Dimethylsulfoxide | Dimethyl sulfide
Cysteamine | Dimethyl sulfide
**Food** |
Garlic | Allyl methyl sulfide
Onion | Methyl propyl sulfide
Adapted from Tangerman (2002).
**Table 60-4** Organoleptic scoring scale
**Score** | **Category** | **Description**
---|---|---
0 | Absence of halitosi | Odor cannot be detected
1 | Questionable halitosis | Odor is detectable, although the examiner could not recognize it as halitosis
2 | Slight halitosis | Odor is deemed to exceed the threshold of halitosis recognition
3 | Moderate halitosis | Halitosis is defi nitely detected
4 | Strong halitosis | Strong halitosis is detected, but can be tolerated by examiner
5 | Severe halitosis | Overwhelming halitosis is detected and cannot be tolerated by examiner (examiner instinctively averts the nose)
Adapted from Tangerman (2002).
# Diagnosis
## Flowchart in a halitosis practice
There are no accepted clinical protocols for the diagnosis of patients with halitosis.
In practice, the flowchart in Fig. 60-1 is suggested for patients with complaints of halitosis. The techniques and strategies for diagnosis and treatment that are described below have been drawn from the research methods and results of important workers in the field of halitosis (Tonzetich 1977; Preti _et al_. 1992; Rosenberg 1995; Richter 1996; van Steenberghe & Rosenberg 1996; Yaegaki & Coil 1999; Sanz _et al_. 2001; Coil _et al_. 2002; Quirynen _et al_. 2002b) and from the experience of the author in treating patients with chief complaints of halitosis for more than 10 years.
## Before first consultation
Before the first appointment all patients receive detailed medical and halitosis questionnaires as well as written instructions (Fig. 60-2). The general medical questionnaire, which includes questions about e.g. systemic diseases, allergy, asthma, rhinitis, sinusitis, and medication, has to be filled in before the appointment and can be discussed beforehand with the physician if needed. Additionally a specific halitosis questionnaire is given to the patient (Fig. 60-3).
## At the first examination
The questionnaires form the basis for the consultation. The various points and their implications are discussed with the patient. These points include the unreliability of the patient's self assessment. One's own breath odor is often undetectable due to habituation. Many patients link bad breath with bad taste (metallic, sour, fecal, etc.). From the start of the consultation it must be made clear to the patient that you are treating _bad breath_ and not _bad taste_ and that the presence of a bad taste does not mean that the patient also has bad breath. Nor does a fresh taste imply fresh breath. The opinion of the patient about the level of halitosis is thus unreliable.
It is important to start the examination by firstly carrying out both subjective and objective assessment of the degree of halitosis and then start the intraoral examination. In this way, the severity of the halitosis is assessed before any changes in the degree of halitosis can occur.
### Organoleptic measurements
Sniffing of expelled air of the patient by using the nose of the examiner, organoleptic scoring, is the usual technique for halitosis examination in daily practice (Schmidt _et al_. 1978; Rosenberg & McCulloch 1992; van Steenberghe 1997). Differentiation between intraoral and extraoral halitosis can easily be done by comparing mouth breath with nose breath (Durham _et al_. 1993; Richter 1996; Rosenberg 1996).
_Examination:_ For the organoleptic evaluation, participants are instructed to close their mouth for 1 minute, then to slowly exhale air out of the mouth at a distance of approximately 10 cm from the nose of the examiner (Fig. 60-4). For evaluation of extraoral halitosis, patients are also asked to slowly exhale air out of the nose, also at a distance of approximately 10 cm from the nose of the examiner. Full mouth and nose organoleptic odor assessments are used, on a scale of 0 to 5 (Table 60-4) (Rosenberg _et al_. 1991b; Yaegaki & Coil 2000).
**Fig. 60-1** Flowchart in a halitosis practice.
### Sulfide monitor
Dental practices and breath clinics now use portable sulfide monitors. For example the BreathtronTM (Sopapornamorn 2006) and the HalimeterTM (Rosen-berg _et al_. 1991a) can test the breath air for levels of sulphur emissions. The Halimeter (Fig. 60-5) has a high sensitivity for hydrogen sulfide but a lower sensitivity for methyl mercaptan, which is a significant contributor to halitosis. Certain foods such as garlic and onions produce sulfur in the breath for as long as 48 hours and may result in false readings. The Halimeter is also very sensitive to alcohol, so one should avoid drinking alcohol or using alcohol-containing mouthwashes for at least 12 hours prior to being tested.
The Halimeter is unsuitable for measuring patients with extraoral halitosis from dimethyl sulfide (Tangerman & Winkel 2007).
_Examination:_ The Halimeter needs to be calibrated to zero on ambient air prior to each measurement. First, the disposable straw, connected to the Halimeter, is placed in the opening of the nose of the patient. Then the patient is asked to blow slowly through to the nose. The maximum peak value of VSCs is recorded. Second, the patient is asked to close the mouth for 1 minute. Then the patient is asked to open the mouth and protrude the tongue. The straw is placed at the dorsal posterior mid part of the tongue and fixed until again the maximum peak value of VSCs is recorded. Peak VSC levels are registered in parts per billion (ppb) (Fig. 60-6a). According to the manufacturer, human standard ("normal") Halimeter readings range between 80 and 110 ppb (<http://www.halimeter.com/halcal.htm>). Values over 160 ppb are considered to identify a patient with true halitosis (Fig. 60-6b).
**Fig. 60-2** Instructions for first visit.
### Gas chromatography
Gas chromatography is by far the most appropriate method to detect halitosis of different origins and should be considered as the gold standard. It is an objective means of obtaining exact values for the various odorous volatiles (Tonzetich 1967; Furne _et al_. 2002; Tangerman 2002). New technology is now appearing in the form of portable gas chromatography machines such as the OralChromaTM (Fig. 60-7), which is specifically designed to digitally measure molecular levels of the three major VSCs (hydrogen sulfide, methyl mercaptan, and dimethyl sulfide) in a sample of breath air. It is extremely sensitive and produces visual results in graph form via computer interface (Fig. 60-8a).
_Examination_ : Insert the 1-ml plastic syringe half-way into the oral cavity and ask the patient to hold the syringe between the lips (Fig. 60-8b). Ask the patient not to touch the syringe with the tongue nor the palate. Wait 1 minute, then slowly pull the plunger, push it in again, and pull it for a second time before removing the syringe out of the oral cavity. Avoid saliva in the syringe. If the top of the syringe is wet, wipe it dry with a tissue, attach the needle and eject the air to 0.5 ml and then insert the needle in the injection port of the gas chromatograph (Fig. 60-8c). The apparatus will process the sample in 8 minutes.
### Oral inspection
During the first visit, extensive soft tissue, hard tissue, and periodontal examinations are performed in order to determine whether the patient has other oral health problems. Specific attention is paid to the tongue and the presence of tongue debris is noted using a tongue-coating index.
#### Index systems for tongue coating
A variety of index systems has been developed over the years (Miyazaki _et al_. 1995; Gomez _et al_. 2001; Winkel _et al_. 2003; Lundgren _et al_. 2007). Miyazaki _et al_. (1995) divides the tongue into three sections and the presence or absence of tongue coating is registered as follows: score 0 = none visible; 1 = less than one third of tongue dorsum is covered; 2 = between one and two thirds; 3 = more than two thirds. Gomez _et al_. (2001) divides the tongue into nine different sections, whilst Winkel _et al_. (2003) divides the tongue into six sections, three in the posterior and three in the anterior part of the tongue. Each sextant is categorized as: score 0 = no coating present; 1 = presence of a light coating; 2 = presence of a distinct coating. The resulting Winkel tongue coating index (WTCI) is obtained by adding all six scores (Winkel _et al_. 2003) (Fig. 60-9).
The tongue is normally pink (Fig. 60-10) but a very thin whitish coating can also be considered normal. Having a coating on your tongue does not necessarily mean that you have bad breath (Fig. 60-11), although heavy tongue coatings are usually positively related to halitosis (Fig. 60-12).
**Fig. 60-3** Halitosis questionnaire.
**Fig. 60-4** Organoleptic scores. Examiner at 10 cm distance from patient.
**Fig. 60-5** HalimeterTM.
**Fig. 60-6** (a) Halimeter computer readout from nose and mouth from patient with intraoral halitosis. (b) Halimeter computer readout from nose and mouth from patient with no halitosis, extraoral halitosis, or after successful therapy or with possible pseudo-halitosis or halitophobia.
**Fig. 60-7** OralChromaTM apparatus.
**Fig. 60-8** (a) OralChroma graphic from patient with intraoral halitosis. (b) Syringe in mouth for air collection with OralChroma. (c) Syringe in OralChroma.
**Fig. 60-9** Winkel Tongue Coating Index (WTCI).
**Fig. 60-10** Normal tongue (without coating).
## Classification of halitosis
In 1999, Miyazaki and co-workers classified halitosis as " _genuine_ " _halitosis_ , _pseudo-halitosis_ , and _halitophobia_ (see Fig. 60-1). One year later genuine halitosis was subclassified as _physiologic halitosis_ or _pathologic halitosis_. In physiologic halitosis there is no apparent disease or pathologic condition, whereas pathologic halitosis occurs as a consequence of an infection of the oral tissues. _Pseudo-halitosis_ is a condition in which halitosis is non-existent but the patients are convinced that they have halitosis. _Halitophobia_ can occur when there is no physical or social confirmation to suggest that halitosis is present, which can persist after therapy for either genuine halitosis or pseudo-halitosis (Yaegaki & Coil 2000).
_Temporary or transient halitosis_ is a term for a very common temporary condition caused by such things as oral dryness, hunger (ketosis), stress, eating certain foods such as garlic (Suarez _et al_. 1999) and onions, smoking, or poor oral hygiene. " _Morning bad breath_ " is a common example of temporary halitosis and is attributed to physiologic causes, such as reduced salivary Flow during sleep.
**Fig. 60-11** Tongue with light tongue coating.
**Fig. 60-12** Tongue with heavy tongue coating.
# Therapy
## Pseudo-halitosis and halitophobia
Pseudo-halitosis must be considered if halitosis cannot be detected organoleptically from the patient complaining of bad breath, if higher than normal VSCs cannot be demonstrated instrumentally and if the patient cannot provide reliable third-party verification (confidant) of an odor problem. If after treatment for genuine halitosis or pseudo-halitosis the patient still believes that he or she has halitosis, the diagnosis should be halitophobia (Yaegaki & Coil 2000) and the patient might be referred to a psychiatrist. The therapeutic recommendation is never to advise the patient to use certain products against halitosis, because the patient will think that this therapist has finally found something and the patient may be a constant problem in your practice. Patients with the experience of tonsilloliths also can develop a halitophobia. A tonsillolith, also called _tonsil stone_ or _calculus of the tonsil,_ is a calcified structure that develops in the tonsillar crypts (Fletcher & Blair 1988; Tsuneishi _et al_. 2006). These deposits break away from the tonsils and are coughed up as small stones that have an unpleasant smell. Patients often wrongly assume that they have halitosis based on this experience.
Patients with pseudo-halitosis and halitophobia might be advised to visit a clinical psychologist. However, few of these patients are willing to follow this advice. Again, it is very important that such patients are not treated for halitosis because there are no benefits in this course of action.
## Temporary halitosis
Temporary halitosis gradually disappears on its own by eating, by not smoking, and not using garlic, onions or spicy food.
## Morning bad breath
Morning bad breath in healthy subjects is a cosmetic problem analogous to body malodor. Morning bad breath develops during sleep when the saliva Flow rate and the oxygen availability are at their lowest, promoting anaerobic formation of VSCs. This would explain why halitosis is generally most severe upon arising in the morning.
To reduce morning bad breath one could advise the patient to use a tongue scraper in the evening before sleeping (Tonzetich & Ng 1976; Faveri _et al_. 2006). Mouth rinses (Roldan _et al_. 2003a) are also advocated to reduce morning bad breath (see below). After drinking and eating in the morning the halitosis will most likely disappear.
## Extraoral halitosis
### Nose and throat
Extraoral halitosis associated with respiratory problems, e.g. rhinitis, sinusitis, tonsillitis, pharyngitis or foreign bodies (unilateral), is characterized by bad breath arising from the nose and not or limited from the mouth, i.e. the organoleptic score for nose breath is higher than that for mouth breath. Halimeter and gas chromatographic scores are usually low. Chronic infection of the nasal cavity and paranasal sinuses leads to changes in the cleansing action of the respiratory epithelium, allowing bacterial overgrowth and stasis of the secretions to occur.
These patients should be sent to an ENT specialist. Postnasal drip may also give rise to unpleasant odors but seems to be difficult to treat. Dental treatment such as root canal therapy and dental extractions may violate the maxillary sinus and cause infections necessitating further dental intervention.
### Systemic conditions
Extraoral halitosis associated with pulmonary problems (blood-borne halitosis) is characterized by bad breath arising from both nose and the mouth, i.e. the organoleptic score for nose breath and mouth breath are about the same. The Halimeter readings are low in both cases because H2S and MM are not present. Gas chromatography may show high dimethyl sulfide (DMS) values and low or zero H2S and MM levels (Tangerman & Winkel 2007).
Table 60-5 Some drugs associated with halitosis
Tobacco
---
Alcohol
Chloral hydrate
Nitrites and nitrates
Dimethyl sulfoxide
Disulfiram
Cytotoxic agents
Phenothiazines
Amphetamines
Adapted from Porter & Scully (2006).
#### Medication
It is important to note that some medications for allergy and high blood pressure, antidepressants, and sinus medication can give rise to blood-borne halitosis (Table 60-5) (Porter & Scully 2006). Metabolites of many drugs have been found to be excreted via the lungs. A good example is disulfiram (Antabuse), a drug used in treating alcoholism, which is metabolized to carbon disulfide (Manolis 1983). Antineoplastic medications may indirectly contribute to halitosis due to mucosites, ulceration, and increased gingival inflammation. Some drugs may induce xerostomia (see below).
#### Trimethylaminuria: the fish malodor syndrome
The fish malodor syndrome, also known as the fish odor syndrome and trimethylaminuria, is a metabolic disorder characterized by the presence of abnormal amounts of dietary-derived trimethylamine, in the urine, sweat, expired air, and other bodily secretions. Trimethylamine itself has the powerful aroma of rotten fish, resulting in a highly objectionable body odor, which can be destructive to the personal, social, and work life of the affected individual. Therapy for this syndrome is limited. It appears that dietary management might be most effective in mild to moderate forms of fish odor syndrome but not in all cases (Mitchell 2005). Fortunately, cases of trimethylaminuria are very rare.
### Treatment planning
Patients with these forms of extraoral halitosis are referred to the appropriate specialist. Halitosis associated with medication need to be discussed with the patient's physician.
## Intraoral halitosis
In a halitosis practice most patients (±90%) have intraoral halitosis (Delanghe _et al_. 1998; Seemann _et al_. 2006). Intraoral halitosis is characterized by a low or non-existant score for nose breath combined with a high organoleptic score for mouth breath. The Halimeter gives similar results. The gas chromatograph shows high levels of H2S and MM and low levels of DMS. Occasionally, the levels of VSCs registered by the Halimeter are unusually low due to low levels of H2S whilst the organoleptic scores are high. This is usually associated with halitosis with high levels of MM.
### Pathologic halitosis
#### Periodontium
According to a majority of authors, halitosis is more closely associated with tongue coating than with the severity of periodontal disease (Tonzetich & Ng 1976; Bosy _et al_. 1994). Causes of halitosis such as periodontitis (Sulsur _et al_. 1939; Sato _et al_. 1980; Delanghe _et al_. 1998), pericoronitis, dry socket, necrotizing periodontitis, necrotizing ulcerative gingivitis (NUG), oral infection, and dental caries (Sulsur _et al_. 1939) should be treated accordingly by the dentist and/or periodontist.
#### Xerostomia
Xerostomia is defined as a subjective complaint of dry mouth that may result from a decrease in the production of saliva (Guggenheimer 2003). Studies have found this condition in approximately 20% of sampled populations (Nederfors 1997). There seems to be a strong correlation between medication (Table 60-6) and dry mouth (Guggenheimer 2003; Nederfors 1997). Dental caries is a major complication of xerostomia. Patients with symptoms associated with a dry mouth and/or medication require further investigation by the appropriate practitioner/specialist.
**Table 60-6** Some drugs associated with xerostomia
Anticholinergic agents
---
Antidepressant agents
Antipsychotic agents
Diuretic agents
Antihypertensive agents
Sedative agents
Muscle relaxant agents
Analgesic agents
Antihistamines
Anticonvulsants
Anorexiants
Anti-incontinence agents
Antiparkinsonian agents
Smoking cessation
Adapted from Guggenheimer (2003).
#### Menstrual cycles
Elevated VSCs were found in mouth air during midcycle and around menstruation (Tonzetich _et al_. 1978; Queiroz 2002).
#### Stress
Stressful situations can be a predisposing factor for the increase of VSCs in mouth air, but the mechanism cannot be simply explained by the reduction of the salivary Flow (Queiroz 2002).
## Physiologic halitosis
### Tongue coating
It has been shown that mechanical tongue cleaning has a significant reducing effect on the VSC levels in mouth air (Yaegaki & Sanada 1992a; Danser _et al_. 2003). Tongue scraping seems to be the most effective hygienic procedure to reduce morning bad breath in periodontally healthy subjects (Faveri _et al_. 2006), even more than interdental flossing. Tongue scrapers seem to be a little bit more effective than toothbrushes (Seemann _et al_. 2001; Outhouse _et al_. 2006). Cleaning the surface of the tongue with a hard toothbrush wetted with chlorhexidine also seems to be effective in reducing halitosis (Bosy _et al_. 1994; De Boever & Loesche 1995; Cicek _et al_. 2003).
## Treatment planning
### Tongue scraper
Mechanical cleansing is recommended in patients with tongue coating. Both tongue brushing (Gross _et al_. 1975) and tongue scraping (Fig. 60-13) have been advocated as a means of removing the tongue coating (Quirynen 2004). It is important to clean the back of the tongue as far as possible, because the posterior portion of the tongue is loaded with most coating. A recommended regime for patients with severe halitosis is to use five strokes of the tongue scraper twice a day. Care must be taken not to irreversibly damage the tongue. Tongue cleaning reduces the substrate for putrefaction (Gross _et al_. 1975; Quirynen 2004), rather than the bacterial load (Menon & Coykendall 1994; Quirynen 2004). Moreover, tongue scraping improved the taste sensation more than tongue brushing (Quirynen 2004).
**Fig. 60-13** Tongue scraping.
### Dentifrice
It was shown that brushing the dorsoposterior surface of the tongue with a dentifrice was more effective than brushing the teeth in reducing VSCs (Tonzetich & Ng 1976). In volunteers, dentifrices with triclosan have been shown to reduce organoleptic scores significantly (Gerlach _et al_. 1998; Niles _et al_. 1999; Sharma _et al_. 1999; Nogueira-Filho _et al_. 2002; Hu _et al_. 2003; Vazquez _et al_. 2003; Farrell _et al_. 2006). Also dentifrices with baking soda (Brunette _et al_. 1998), essential oils (Olshan _et al_. 2000), and stannous Fluoride (Gerlach _et al_. 1998) seem to be effective. The delivery of an antimicrobial agent via a dentifrice may not be as efficient in reducing intraoral halitosis as the same agent delivered in a mouth rinse (Loesche & Kazor 2002).
### Mouth rinses
In addition to tongue scraping, the use of mouth rinses has been advocated (Nachnani 1997; Roldan _et al_. 2003a). Active components in these rinses include antibacterial compounds such as: cetylpyridinium chloride (Yaegaki & Sanada 1992b; Rosenberg _et al_. 1992; Kozlovsky _et al_. 1996; Silwood _et al_. 2001; van Steenberghe _et al_. 2001; Borden _et al_. 2002; Quirynen _et al_. 2002a, 2005; Winkel _et al_. 2003; Carvalho _et al_. 2004; Roldan _et al_. 2004, 2005) ; chlorhexidine (Rosenberg _et al_. 1992; Bosy _et al_. 1994; De Boever & Loesche 1995; Quirynen _et al_. 1998, 2002a, 2005; van Steenberghe _et al_. 2001; Winkel _et al_. 2003; Roldan _et al_. 2003b, 2004, 2005; Carvalho _et al_. 2004) ; essential oils (Pitts _et al_. 1981, 1983; Rosenberg _et al_. 1992; Yaegaki & Sanada 1992b; Kozlovsky _et al_. 1996; Silwood _et al_. 2001; Borden _et al_. 2002; Carvalho _et al_. 2004) ; chlorine dioxide (Frascella _et al_. 1998, 2000; Silwood _et al_. 2001; Borden _et al_. 2002) ; metal ions, such as zinc lactate and zinc chloride (Schmidt & Tarbet 1978; van Steenberghe _et al_. 2001; Young _et al_. 2001; Borden _et al_. 2002; Quirynen _et al_. 2002a; Winkel _et al_. 2003; Codipilly _et al_. 2004; Roldan _et al_. 2004, 2005) ; triclosan (Carvalho _et al_. 2004) ; and hydrogen peroxide (Suarez _et al_. 2000). Most of these studies demonstrated that these products are effective in reducing oral malodor.
Despite the recommendations of the various manufacturers of these oral rinses, the efficacy of these products on intraoral halitosis is not clear. The main reason for this is that the duration and the number of controlled clinical trials is limited. The other problem with the studies which are available is that the patient groups in the studies are rarely patients with a definite diagnosis of intraoral halitosis. The mouth rinses are tested in students (Rosenberg _et al_. 1992; van Steenberghe _et al_. 2001; Quirynen _et al_. 2002a; Carvalho _et al_. 2004) and volunteers (Pitts _et al_. 1981, 1983; Yaegaki & Sanada 1992b; Kozlovsky _et al_. 1996; Suarez _et al_. 2000; Silwood _et al_. 2001; Borden _et al_. 2002; Codipilly _et al_. 2004; Roldan _et al_. 2004; Quirynen _et al_. 2005) without any complaints of halitosis. It is questionable if the results of these studies in "normal" patients and/or patients with Halimeter values within the normal range (80– 110 ppb) are applicable for the treatment of patients with real halitosis. Only a limited amount of studies were performed in subjects with a complaint of "bad breath" or with high objectionable levels of VSCs. These are case report studies with 0.2% chlorhexidine (Bosy _et al_. 1994), 0.12% chlorhexidine (De Boever & Loesche 1995), and 0.05% chlorhexidine, 0.05% cetylpyridinium chloride and 0.14% zinc lactate (Roldan _et al_. 2005) with a 3-month follow-up. A dual centre, placebo-controlled, double-blind, randomized controlled clinical trial with 0.05% chlorhexidine, 0.05% cetylpyridinium chloride, and 0.14% zinc lactate was performed by Winkel _et al_. (2003) and Roldan _et al_. (2003). The mouth rinse used in this study (Halita) was specifically formulated to treat halitosis. This mouth rinse contains ingredients with low concentrations of the active components without alcohol and has therefore limited side effects for long-term use. The results indicated significant improvements in organoleptic and VSC scores in the test group.
Quirynen _et al_. (1998) found a reduction in organoleptic scores in periodontitis patients with and without complaints of oral halitosis, after scaling and root planing of all pockets within 24 hours together with the application of chlorhexidine. Despite the demonstrated efficacy of 0.2% and 0.12% chlorhexi-dine, long-term use of these solutions cannot be recommended because of the side effects (Gagari & Kabani 1995). Some of these adverse effects are lost taste and discoloration of the teeth and the tongue. More suitable agents are mouth rinses with low concentrations of active ingredients. Based on the double-blind placebo-controlled study (Winkel _et al_. 2003) a recommended regime for severe halitosis patients is gargling twice a day for 1 minute with 15 ml of Halita with the tongue out. By gargling, instead of rinsing, the cleansing agents can reach the dorsal surface of the back of the tongue.
### Antibiotics
Currently, no research data are available about the use of antibiotics in patients with halitosis. In our clinic some patients with halitosis had used systemic antibiotics for other medical reasons. For a limited time there was a reduction of intraoral halitosis but after a few weeks, halitosis recurred. A possible explanation is that patients with intraoral halitosis based on tongue coating have commensal bacteria (Van Winkelhoff & Winkel 1997), e.g. _Fusobacterium nucleatum_. These commensal bacteria are suppressed by the antibiotics for a short period of time but recolonize up to a normal level after some weeks.
**Fig. 60-14** Instructions for recall visit.
### Use of a confidant
Previous research has demonstrated that patients with halitosis are generally unable to rate the intensity of their own halitosis (Rosenberg _et al_. 1995). Therefore, patients cannot reliably assess the effectiveness of the prescribed therapy. The recommended course of action is to ask them to use another person as a confidant. A confidant could be a spouse, a family member or close friend, who is willing to smell the patient's breath and provide straightforward feedback.
## Adjustment of therapy
All patients with the diagnosis of intraoral halitosis should come back for a recall visit and adjustment of therapy (Fig. 60-14). At the first visit, patients are seen in the "worst" condition to make a proper diagnosis. At the re-examination patients are asked to present themselves in the "best" condition, meaning proper oral hygiene and correctly following the advised treatment protocol for patients with halitosis. The purpose of the recall visit is to adjust the therapy based on the results of this re-examination. Organoleptic scores, measurement with the sulphide monitor and gas chromatography are performed. The first question to the patient is: "Did the therapy work?" Although, most of the time the therapy for intraoral halitosis is very successful, some patients will answer "No". The reason is that most of these patients still have a bad taste and think that the presence of a bad taste means that they have a bad breath, which is not necessarily the case. A confidant is of paramount importance for this group of patients. Another important question is about the "comfort range". The result is compared with the comfort range from the first examination. If the comfort range is the same and the halitosis is well treated, the patient could develop halitophobia and needs to seek professional help.
## Future perspectives
In a preliminary study, Burton _et al_. (2005) showed that replacement of bacteria implicated in halitosis by colonization with competitive bacteria (probiotica) such as _S. salivarius_ may provide an effective strategy to reduce the severity of halitosis.
### Conclusions
Social relationships are one of the pillars of the quality of life (Elias & Ferriani 2006). In that respect, halitosis can be a crippling social problem and therefore needs to be considered a serious problem. Extraoral halitosis might be a manifestation of a serious disease. It is of paramount importance to differentiate between extra- and intraoral halitosis.
Although there is an effective treatment of intraoral halitosis, many physicians, dentists, and dental hygienists do not recognize intraoral halitosis as a manageable condition. Since in most of the cases of halitosis the oral cavity is _the place of origin_ , health professionals in medicine and dentistry should be knowledgeable about diagnosis and therapy of this disorder. In most cases intraoral halitosis can be treated by tongue scraping and the use of chemical solutions with low concentrations of zinc ions, chlorhexidine, and cetylpyridinium chloride. The dental hygienist, dentist, and periodontist are the most appropriate professionals to diagnose and to treat this condition.
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Roldan, S., Herrera, D., O'Connor, A., Gonzalez, I. & Sanz, M. (2005). A combined therapeutic approach to manage oral halitosis: a 3-month prospective case series. _Journal of Periodontology_ **76** , 1025–1033.
Roldan, S., Herrera, D., Santa-Cruz, I., O'Connor, A., Gonzalez, I. & Sanz, M. (2004). Comparative effects of different chlor-hexidine mouthrinse formulations on volatile sulphur compounds and salivary bacterial counts. _Journal of Clinical Periodontology_ **31** , 1128–1134.
Roldan, S., Herrera, D. & Sanz, M. (2003a). Biofilms and the tongue: therapeutical approaches for the control of halitosis. _Clinical Oral Investigations_ **7** , 189–197.
Roldan, S., Winkel, E.G., Herrera, D., Sanz, M. & Van Winkel-hoff, A.J. (2003b). The effects of a new mouthrinse containing chlorhexidine, cetylpyridinium chloride and zinc lactate on the microflora of oral halitosis patients: a dual-centre, double-blind placebo-controlled study. _Journal of Clinical Periodontology_ **30** , 427–434.
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**Index**
Aae protein adhesin
abortion, spontaneous
abrasive agents
abscess
periapical
diabetes mellitus
drainage
_see also_ periodontal abscess
absorbable collagen sponge (ACS)
abutments
angulated
ceramic
implant-supported restorations
Zirconia
access therapy
distal wedge procedures
periodontal pocket surgery techniques
periodontal surgery guidelines
outcome
accessory canals
acellular freeze-dried dermal matrix (ADM) allografts
acetylsalicylic acid burn
aciclovir
_Actinobacillus actinomycetemcomitans see Aggregatibacter actinomycetemcomitans_
_Actinomyces_
biofilm composition
colonization
peri-implant infections
plaque formation
_Actinomyces naeslundii_
biofilm on implant surfaces
coaggregation
_Actinomyces viscosus_
active threshold determination
acute necrotizing ulcerative gingivitis (ANUG)
etiology
microbial invasion
smokers
spirochetes
adhesins
adhesion molecules
adolescents
palatal implants
periodontal tissue breakdown
plaque removal
prosthetic oral implant anchorage for orthodontics
_see also_ puberty
adrenal function disorders, surgery contraindication
advanced flap procedure, root coverage
advanced glycation end-products (AGEs)
afferent nerve fibers
age
aggressive periodontitis
attachment loss
chronic periodontitis risk
implant patient
necrotizing periodontal disease
periodontal disease
periodontal support loss
_see also_ adolescents; children
_Aggregatibacter actinomycetemcomitans_
aggressive periodontitis
elimination
antibiotics
local delivery
microbiologic tests
susceptibility
synergism
systemic
antibodies in aggressive periodontitis
antibody response
antibody titers
association studies
bacteriocin production
cardiovascular disease
carotid endarterectomy
clonal subset
connective tissue invasion
diabetes mellitus
elimination by extraction of all teeth
growth inhibition factors
HIV infection
immune response
interbacterial antagonism
invasion
leukotoxins
linear gingival erythema
metronidazole with amoxicillin combination
oral cavity colonization
peri-implant infection
periodontal disease history
periodontal infection
periodontal lesions in diabetes
polymicrobial microbiota
prevalence in periodontal disease
serotypes
smoking association
subgingival peri-implant infections
suppression
transmission
virulence
aggressive periodontitis
age at onset
_A. actinomycetemcomitans_
alveolar bone loss
antibodies
associated medical conditions
attachment loss
bacterial etiology
candidate genes
classification
clinical diagnosis
clinical syndromes
crevicular fluid prostaglandin E2 levels
dentition
permanent
primary
diabetes mellitus
diagnosis
differential diagnosis
drug-induced granulocytopenia
environmental factors
epidemiology
etiology
familial aggregation
aggressive periodontitis
forms
furcation involvement
generalized
genetic diagnosis
genetic factors
heritability
HIV infection
host defense evaluation
host response to bacterial pathogens
host susceptibility
hypophosphatasia
implants
planning
inheritance
leukemia
leukocyte adhesion deficiency
local inflammatory responses
localized
microbiologic diagnosis
microbiologic testing
orthodontic therapy
palmo-plantar keratitis
pathogenesis
pathogenic flora elimination/suppression
periodontal probing
periodontium rate of destruction
permanent dentition
polymorphonuclear leukocytes
_P. gingivalis_
primary dentition
prosthetic treatment
restorative therapy
restorative treatment
screening
sibling monitoring
smoking
surgery
therapeutic intervention
treatment
agranulocytosis, surgery contraindication
AIDS _see_ HIV infection
alcohol abuse, implant patient
alcohol consumption, necrotizing periodontal disease
alexidine, plaque control
allele frequencies
allergic reactions
oral mucosa
periodontium
alloplastic grafts
alveolar bone
blood vessels
dehiscence
gingival recession
deposition
destruction
fenestration
formation
healing
height
loss
aggressive periodontitis
children
diabetes mellitus
osseous surgery
_P. gingivalis_
radiographic assessment
risk assessment
smokers
trauma from occlusion
membrane barriers
necrosis
neurovascularization
orthodontic loading
osteoclast activity
osteoporosis
patient examination
radiographic analysis
regrowth
remodeling
renewal
repair
resorption
periodontitis
pulpal inflammatory response
turnover with orthodontic loading
alveolar bone proper
lamellar bone
periodontal ligament
fibers
resorption
Sharpey's fibers
tooth attachment
tooth extraction
tooth socket healing
alveolar crest
distance to cemento-enamel junction
fibers
outline
preparation for implant placement
recontouring
width determination
alveolar crestal height (ACH)
alveolar mucosa
necrotizing periodontal disease
transplanted
alveolar nerve, inferior
tooth extraction
alveolar plexus, superior
alveolar process
adaptation after tooth extraction
bone
cancellous
lamellar
loss
spongy
cortical plates
CT
edentulous alveolar ridge
formation
mineralization
resorption rate
tooth extraction
topography
alveolar pyorrhea, trauma from occlusion association
alveolar ridge
augmentation
clinical concepts
dehiscence defects
differentiation factors
extraction sockets
growth factors
horizontal defects
horizontal tooth movement
long-term results
materials
procedures
vertical defects
vertical tooth movement
defects
correction
dehiscence
horizontal
regeneration
soft tissue grafts
vertical
extraction sockets
healed following tooth loss
preservation
alveolar ridge, edentulous
atrophy following tooth loss
augmentation
bone gain
bone loss
bone marrow
bundle bone
classification of remaining bone
defect correction
deformed
extra-alveolar processes
free graft procedures
gingivoplasty soft tissue sculpting
implant placement
interpositional graft procedures
combined with onlay grafts
intra-alveolar processes
lamellar bone
onlay graft procedures
combined with interpositional grafts
osseointegration
pedicle grafts
pontic contours
pouch graft procedures
remaining bone
soft tissue collapse prevention
soft tissue grafts
surgical procedures for augmentation
topography
amalgam tattoo
ameloblasts
amine alcohols, plaque control
amine fluoride
amino acids, sulfur-containing
amoeba
amoxicillin
metronidazole combination
peri-implant lesions
amphotericin B
amyloglucosidase, plaque control
analgesia
anchorage
orthodontic
absolute
implants as temporary devices
indications for implants
length-reduced devices
skeletal systems
temporary devices
anchoring fibers
androgens
anemia, surgery contraindication
angina pectoris, surgery contraindication
angiogenesis
angular bone
defects
destruction
ankylosis
external inflammatory root resorption
functional
implants
maxillary anterior single-tooth replacement
replacement root resorption
antiadhesive agents, chemical plaque control
antibiotics
adjunctive systemic
adverse reactions
aggressive periodontitis
biofilm protection of bacteria
carriers
controlled delivery
controlled release
cumulative interceptive supportive therapy
delivery routes
evaluation
halitosis treatment
local delivery/application
clinical practice
clinical trials
microbiologic tests
minimal inhibitory concentration
necrotizing periodontal disease
peri-implant lesions
periodontal abscesses
periodontal dressings
periodontal therapy
plaque control
pre-operative prophylaxis
principles of therapy
prophylactic
bacterial endocarditis
patients on immunosuppressants
reconstructive therapy
reconstructive therapy
resistance
biofilms
systemic
clinical practice
clinical trials
antibodies
aggressive periodontitis
avidity
evasion by pathogens
innate defense systems
production
response
anticalculus agents
anticaries agents
anticoagulants
implants
surgery contraindication
treatment planning
anticonvulsants, gingival overgrowth
antigen presentation
antigen presenting cells
humoral immune response
antigingivitis agents
antimicrobial agents
plaque control
chemical
systemic
uptake measurements
_see also_ antibiotics
antimicrobial tests
antineoplastic drugs
antioxidants
antipathogenic agents, plaque control
antiplaque agents evaluation
antiseptics
cumulative interceptive supportive therapy
peri-implant lesions
plaque control
resistance
_see also_ chlorhexidine
alpha-1 antitrypsin
antiviral drugs, herpetic gingivostomatitis
anxiety
control
non-surgical therapy
apically repositioned flap
Arg1-protease
ARG-gingipain
arterial hypertension, surgery contraindication
articulation
implants
problems and oral stereognostic ability
aspirators
atheromatous plaque
atherosclerosis
risk with periodontitis
attachment
bony defect diagnosis
creeping
gingival augmentation
guided tissue regeneration
level changes
orthodontic intrusion
_see also_ clinical attachment level (CAL); probing attachment level (PAL)
attachment apparatus
loss
_see also_ alveolar bone proper; cementum; connective tissue, attachment re-establishment; periodontal ligament
attachment loss
age
aggressive periodontitis
chronic periodontitis
diabetes mellitus
endodontic lesions
gingival inflammation
incidental
intrusion of plaque-infected teeth
percentile plots
periodontitis
probing pocket depth
pulp infection
risk assessment
autoimmune disorders, implant patient
autoinducer-2
azathioprine
B cells
adaptive defense system
regulation process
smoking effects
bacteria/bacterial infections
adhesion
to calculus
antagonism
antibiotic resistance
attachment
bacterial endocarditis
bacterial vaginosis
beneficial species
bridging species
cardiovascular disease
cell-to-cell recognition
challenge to host
coaggregation
colonizing species
host defense mechanisms
commensal
in maxillary sinus
complex formation in biofilm
deposits on implants
endodontic origin lesions
fibrils
fimbriae
gingival disease
gingivitis
necrotizing
plaque-induced
halitosis
insulin resistance
interbacterial relationships
antagonism
intraoral transmission
invasion of periodontal tissue
linear gingival erythema
metabolic products
migration along stitch canal
mixed anaerobic
nutritional conditions
periodontitis
plaque
formation
rapid/slow formers
subgingival
pneumonia
primary colonization
root canal infection
smoking effects
tissue reactions around sutures
tongue
transmission
transport in dentinal tubules
volatile sulfur compound formation
_see also_ biofilms
bacteriocin
_Bacteroides_
black-pigmented group
fusiform
_Bacteroides forsythus see Tannerella forsythia_
_Bacteroides melaninogenicus see Prevotella intermedia_
barrier epithelium
barrier membranes
bioabsorbable materials
pedicle soft tissue graft for root coverage
ridge augmentation
combined procedures
furcation involvement
gingival dehiscence
intrabony defects
lateral bone augmentation for posterior implants
materials
regenerative surgery
maxillary anterior single-tooth replacement
modified papilla preservation technique
non-absorbable materials
pedicle soft tissue graft for root coverage
ridge augmentation
oral hygiene
pedicle graft procedure for root coverage
removal
ridge augmentation
basal cells
basal lamina
basement membrane
basic periodontal examination (BPE)
system code
Bass technique of toothbrushing
behavior, discrepancy development
behavioral change
counseling
oral hygiene
benign mucous membrane pemphigoid (BMMP)
benzalconium chloride
beta-lactamase
beveled flap
bioabsorbable materials
biofilms
antibiotic resistance
antimicrobial agents
bacteria
attachment
coaggregation
detection/enumeration
enzymes
growth rate
transmission
climax community
communication
complexity
composition
subgingival
supragingival
dental plaque
epithelial cell-associated
exopolymer matrix
exopolysaccharides
extracellular enzymes
formation
genetic information exchange
glycocalyx
health sites
host factors
implant surfaces
local environment
major perturbations
microbial complexes
microcolonies
nutrients
oral hygiene
orange complex species
adjunctive systemic antibiotics
peri-implant infections
periodontal infections
peri-implant infections
periodontal disease
status
PH
physiological heterogeneity
pioneer species
properties
protection against antibiotics
quorum sensing
red complex species
adjunctive systemic antibiotics
peri-implant infections
periodontal infections
shear force
structure
subgingival
composition
development
therapy effects
supragingival
composition
development
tooth cleaning
water channels
yellow complex species
bio-glass grafts
biologic width establishment
biologically active regenerative materials
modified papilla preservation technique
_see also_ enamel matrix derivatives (EMD)
Bio-Oss® grafts
bisbiguanide antiseptics
bisphosphonates
implant patient
osteonecrosis
bite force, implant-supported restorations
black triangle, interdental
bleaching agents
bleeding on probing (BoP)
basic periodontal examination
gingival
patient examination
peri-implant
risk assessment
_BMP4_ gene
body mass index (BMI), periodontitis
body odor
bonding of artificial tooth surfaces
bone
anti-resorptive agents
augmentation for implants
available for implants
biology
bundle
Contouring
cortical and orthodontic tooth movement
cyclic load reaction
dehiscence
gingival recession
destruction in periodontitis
diabetes mellitus
emergency type
endochondral formation
functional loading
healing
height for implants
residual
induction with autotransplantation of teeth
intramembranous formation
lamellar
edentulous alveolar ridge
osseointegration
loss
cyclic loading
endodontic lesions
horizontal
peri-implant
peri-implantitis
metabolic disorders
modeling
implant placement
osseointegration
parallel-fibered
preparation for implant placement
quality
reaction to orthodontic implant loading
recontouring for crown-lengthening
regeneration
autogenous grafts
peri-implant
trauma from occlusion
remodeling
adaptive
implant placement
osseointegration
repair inhibition
resorption
active
direct
endodontic lesions
indirect
therapeutic strategies
woven bone
smoking effects
static load reaction
surgical site
systemic loss
volume
width for implants
wound healing
woven
osseointegration
peri-implant loss
resorption
tooth socket healing
_see also_ alveolar bone; guided bone regeneration (GBR)
bone cells
regenerative capacity
bone chips
lateral bone augmentation for posterior implants
bone chisels
bone defects
angular
deep pocket probing depths
forced tooth eruption
iatrogenic root perforation
intrusion of plaque-infected teeth
trauma from occlusion
classification
diagnosis
horizontal
implant placement planning
morphology
periodontal attachment restoration
regenerative periodontal therapy
vertical
_see also_ intrabony defects
bone fill, angular bone defects
bone grafts
allogeneic
autogenous
cortico-cancellous
horizontal ridge defects
maxillary anterior single-tooth replacement
maxillary sinus floor elevation
materials
maxillary sinus floor elevation
osteoconductive
osteoinductive
osteoproliferative
regenerative therapy
ridge augmentation
simplified papilla preservation flap
tissue regeneration
types
vertical bone defects
vertical ridge defects
xenogeneic
bone lining cells
bone marrow
edentulous alveolar ridge
osseointegration
tooth socket healing
bone mineral density
bone morphogenetic proteins (BMPs)
alveolar bone healing
collagen carrier
expandable polytetrafluoroethylene membrane effect
ridge augmentation
bone multicellular unit (BMU)
bone removal instruments
bone replacement grafts, regenerative therapy
bone substitute materials
horizontal ridge defects
maxillary anterior single tooth replacement
maxillary sinus floor elevation
ridge augmentation
vertical bone defects
xenogenic
bone-added osteotome sinus floor elevation (BAOSFE)
bovine bone-derived biomaterials
Braun Oral-B Plaque Remover
BreathtronTM
bridges, tooth mobility
bridging, healing phenomenon
bruxism
implant failure
buccal artery
buccal bone plate, height reduction after extraction
buccal nerve
bucco-lingual thickness, gingival recession
Buerger disease, _Campylobacter rectus_ association
bundle bone _see_ alveolar bone proper
bupropion
burns, thermal
burs
burst hypothesis of disease progression
butyric acid
cadaverine
calcitonin
calcium
calcium channel blockers, gingival hyperplasia/overgrowth
calculus, dental
attachment to tooth surfaces/ implants
carbon fiber curettes
clinical appearance
clinical implications
composition
detection
diagnosis
distribution
formation rate
lipopolysaccharide
mineralization
periodontitis in adults
removal
complete
non-surgical root debridement
structure
subgingival
supragingival
Caldwell–Luc technique
modified
_Campylobacter rectus_
aggressive periodontitis
atherosclerosis association
cardiovascular disease
diabetes mellitus
fetal effects
growth restriction
leukotoxin
linear gingival erythema
periodontal infection
pregnancy adverse outcomes
smoking association
cancer chemotherapy
implants
cancrum oris
_Candida albicans_ (candidiasis)
chlorhexidine use
diabetes mellitus
gingival disease
linear gingival erythema
pseudomembranous
smoking association
canines, periodontal abscesses
cantilever units
extensions
fixed partial dentures
implant restorations
_Capnocytophaga_
aggressive periodontitis
periodontal lesions in diabetes
_CARD15 (NOD2)_ gene polymorphisms
cardiovascular disease
patient health protection
periodontitis
risk with
treatment
_Porphyromonas gingivalis_
surgery contraindication
treatment complications
caries, dental
high-risk patients
carotid artery, intima media thickness (IMT)
carotid endarterectomy
cathepsin C
gene mutations
CD4 lymphocyte count
HIV infection
necrotizing periodontitis
CD4-positive cells
CD8 marker
CD14–260 gene polymorphism
cellulase
cemented multiple-unit posterior implant prostheses
cementoblasts
cementum intrinsic fiber system
cementocytes
cemento-enamel junction
clinical attachment level
distance to alveolar crest
implant planning
implant shoulder sink depth
leveling
tissue regeneration
cementoid
cementum
acellular, extrinsic fiber
bone grafting
cellular
intrinsic fiber
mixed stratified
components
damage
dental pulp
infection
protection
deposition
extrinsic fiber system
formation of new
autogenous grafts
enamel matrix derivative use
incremental lines
intrinsic fiber system
lipopolysaccharide
mineralization
peri-implant mucosa
tooth attachment
types
_see also_ root cementum
central nervous system (CNS), sensitization
cephalosporins
cerebrovascular disease
cervical lymph nodes, deep
cetylpyridinium chloride
antimicrobial activity
halitosis treatment
plaque control
Charters technique of toothbrushing
checkerboard DNA–DNA hybridization
_Eubacterium_
peri-implant infection
_Tannerella forsythia_
Chediak–Steinbrinck–Higashi syndrome
chemical injury
chewing comfort
chewing gum
allergic reactions
chewing sticks
chickenpox
children
aggressive periodontitis
cemento-enamel junction distance to alveolar crest
gingival recession defects
necrotizing periodontal disease
palatal implants
prosthetic oral implant anchorage for orthodontics
chlorhexidine
anti-discoloration system
antimicrobial activity
chewing gum
clinical uses
full-mouth disinfection
gels
halitosis treatment
irrigation
irrigators
local application
mechanism of action
mouth rinses
side effects
mucosal desquamation induction
necrotizing periodontal disease treatment
oral hygiene
oral ulceration
plaque control
post-regenerative surgery
products
professional prophylaxis
professional tooth cleaning
regenerative surgery
safety
side effects
slow-release vehicles
sodium fluoride synergism
sprays
staining
structure
subgingival irrigation
toothpaste content
toxicology
use
chlorhexidine gluconate in gelatin chip
chorioamnionitis
chromosomes
chronic obstructive pulmonary disease
cigarette smoking _see_ smoking
ciprofloxacin
circular fibers
circumferential supracrestal fiberotomy (CSF) technique
citric acid demineralization
guided tissue regeneration combination
clavulanic acid
clear cells
clenching
implant failure
clindamycin
clinical attachment level (CAL)
regenerative therapy
supportive periodontal therapy
clinical trials
antibiotics
local
systemic
blindness
controls
plaque control
randomization
study groups
clonal expansion
_Clostridium difficile_
clotting mechanisms
cocaine burn
col region
collagen
bioabsorbable barrier membrane
formation after orthodontic extrusion
growth factor carriers
loss in gingivitis
collagen fibers
dento-alveolar
dento-gingival
lamina propria
orientation
periosteum
production
_see also_ periodontal ligament, principal fibers
collagen fibrils
collagenase
collagen-like platelet aggregation associated proteins (PAAP)
communication skills
Community Periodontal Index for Treatment Needs (CPITN)
complement
innate defense systems
computed tomography (CT)
alveolar process
confounding
congenital heart lesions, surgery contraindication
connective tissue
attachment re-establishment
periodontal ligament cells
dental pulp infection
diabetes mellitus
disorders in implant patients
fibers
gingiva
regenerative capacity
transplant
inflammatory cell infiltrate
invasion by _A. actinomycetemcomitans_
jiggling trauma
loss with orthodontic forces
matrix
osseointegration
papillae
peri-implant
smoking effects
supracrestal fiber severing
tooth socket healing
transmucosal attachment
connective tissue grafts
combined with coronally advanced flap
envelope technique
papilla reconstruction
trap door approach
tunnel technique
connectors for implants
contraceptives, periodontal effects
copper salts
coral skeleton
coronally advanced flaps
healing
coronary heart disease (CHD)
acute coronary syndrome with milleri streptococci
periodontal infection
_Prevotella intermedia_
cortisone
craters, interproximal
C-reative protein (CRP)
creeping attachment
critical probing depth
Crohn's disease
crown (s)
dental pulp diseases
displacement ( _see_ tooth mobility)
length-to-width ratio
crown length
increase
with gingivectomy
with orthodontic intrusion
orthodontic intrusion
crown-lengthening procedures
ectopic tooth eruption
excessive gingival display
exposure of sound tooth structure
sutures
crown–root ratio
crown–root–alveolar bone relationships, crown-lengthening
_CTSC_ gene mutation
cumulative implant survival rate (CISR)
cumulative interceptive supportive therapy (CIST)
curettes
carbon fiber
root debridement
cuticle
cyanoacrylates, periodontal dressings
cyclosporin, gingival hyperplasia/ overgrowth
cytokines
alveolar bone healing
diabetes mellitus
systemic bone loss
cytomegalovirus (CMV)
necrotizing periodontal disease
periodontal infection
debridement
peri-implant lesions
mechanical
non-surgical
_see also_ root debridement
decalcified freeze-dried bone allogeneic grafts
delmopinol
demineralization, root surface
demineralized bone matrix (DBM)
demineralized freeze-dried bone allografts
dental arch, shortened (SDA)
dental artery
dental follicle
dental lamina
dental nerve
dental organ
dental papilla
dental restorative materials allergic reactions
foreign body reactions
_see also_ restorative dentistry
dental status
stereognostic ability
tactile function
dental tape
dental team, infection protection
dental water jet
dentifrices
halitosis treatment
soft tissue abrasion
_see also_ toothpaste
dentilisin
dentin
abrasion
bone formation at surface
dehydration in root-filled teeth
etching by dietary components
formation
hypersensitivity
nerve fiber response to exposure
permeability to microorganisms
removal in periodontal treatment
reparative
dentinal tubules
bacteria transport
infection in root-filled teeth
invasion by subgingival bacteria
natural occlusion
open
pulp infection
dentin–pulp complex
dento-gingival epithelium
gingivitis
invasion by pathogens
proliferation in trauma from occlusion
dento-gingival fibers
dento-gingival interface probing
dento-gingival plexus
dento-gingival plexus, protein exudate
dento-gingival region
dento-periosteal fibers
denture stomatitis
chlorhexidine use
dentures
removable
partial
_see also_ fixed partial dentures (FPD); overdentures
denudation procedure
deproteinized bovine bone mineral (DBBM)
desensitizing agents
desmosomes
epithelial cell rests
detergents
plaque control
toothpaste
developing countries, necrotizing periodontal disease
dextranase
diabetes mellitus
aggressive periodontitis
alveolar bone loss
attachment loss
bone effects
chronic periodontitis
clinical symptoms
control
gingival disease
glycemic control
halitosis
host response effects
host susceptibility to disease
host–bacteria relationship
modification
implant patient
metabolic control
oral effects
periodontal effects
periodontal treatment
periodontitis
treatment effects
risk assessment
surgery contraindication
treatment considerations
type 1
type 2
diamines
diet, dentin etching
dietary habits, motivational interviewing
dietary proteins, allergic reactions
differentiation factors, ridge augmentation
digital volume tomography
dimethylsulfoxide
disclosing agents
discoid lupus erythematosus
disease predictors
disease-modifying genes
implant failures
peri-implant infections
periodontitis
disinfection, full-mouth
distal wedge procedures
distance between implant shoulder and mucosal margin (DIM measurements)
DNA
DNA hybridization
Down syndrome, implant patients
doxycycline
controlled delivery
regenerative surgery
doxycycline hyclate in biodegradable polymer
dressings
light-cured
periodontal
drug-induced disorders
chronic periodontitis
gingival
granulocytopenia
halitosis
mucocutaneous
_see also_ medications
dual energy X-ray absorptiometry (DXA)
ectomesenchyme
differentiation
_Eikenella corrodens_
aggressive periodontitis
elastase
elastic fibers
electric pulp testing
electric stimulation
empathy
enamel
matrix proteins
mesio-distal reduction
enamel matrix derivatives (EMD)
Bio-Oss® graft comparison
free soft tissue graft healing
furcation defects
intrabony defects
modified papilla preservation technique
outcomes
pedicle graft procedure for root coverage
regenerative therapy
simplified papilla preservation flap
endodontic lesions
bacteria
drainage
periodontitis differential
diagnosis
pulp vitality testing
vertical root fractures
endodontic treatment
iatrogenic root perforation
inflammatory exudate access to root canal
root separation and resection
endonucleases
endopeptidases
endo–perio lesions
diagnosis/treatment
endothelial dysfunction, periodontal therapy
endothelial leukocyte adhesion molecule 1 (ELAM-1)
endotoxins
enecrotizing periodontal disease
_Enterobacter agglomerans_
_Enterobacter cloacae_
enzyme-linked immunosorbent assay (ELISA)
enzymes, plaque control
epidemiology of periodontal disease
age
atherosclerosis
causal relationship
cigarette smoking
confounding
diabetes mellitus
exposure
frequency distribution
health survivor effect
HIV infection
index systems
initiation factors
methodology
microbiology
necessity of condition
non-modifiable background factors
obesity
osteopenia/osteoporosis
pregnancy complications
prevalence
progression factors
psychosocial factors
risk factors
selection bias
sufficiency of condition
systemic disease risk
epilepsy, surgery contraindication
epithelial cell rests of Mallassez
epithelial cells
gingivitis
pathogen invasion
_see also_ oral epithelium
epithelial rete pegs
gingivitis
epithelial ridges
epithelial root sheath
epithelial sheath of Hertwig
epithelial strands
epithelialized soft tissue graft, root coverage
Epstein–Barr virus (EBV)
epulis
erythema multiforme
erythrocytes, implant wound chamber
erythrosine
_Escherichia coli_ , smoking association
essential oils
halitosis treatment
plaque control
esthetics
anterior single-tooth replacement
cantilever pontics for fixed partial dentures
checklist
implant
direction
maxillary anterior restorations
multiple-unit anterior fixed restorations
patient
placement
scalloped design
segmented fixed restorations
tooth movement
implant-supported restorations
missing tooth replacement
objective criteria
orthodontic treatment
tooth movement
principles
single-tooth problem
treatment goal
treatment modality review
estradiol
estriol
estrogen
bone resorption treatment
chronic periodontitis
gingival disease
hormonal contraceptives
pregnancy
smokers
tissue response
ethnicity _see_ race/ethnicity
_Eubacterium_
exopeptidases
exopolysaccharides
Extent and Severity Index (ESI)
extraction of teeth
cortical plasticity
neuroplasticity
periodontal ligament receptors
phantom tooth phenomenon
sensory amputation
sensory nerve damage
extravascular circulation
facial artery
factor VIIc
factor XIIc
famciclovir
familial aggregation, aggressive periodontitis
Fc gamma receptors (FcγR) gene polymorphisms
_Fc_ γ _RIIa_ polymorphisms
fetal growth restriction, _Campylobacter rectus_
fetal–placental unit
fetor hepaticus
fever, necrotizing periodontal disease
fiberotomy
forced tooth eruption
with orthodontic treatment
fibrin
fibrinogen
fibroblast growth factor (FGF)
alveolar bone healing
ridge augmentation
fibroblasts
dental pulp infection
smoking effects
fibroplasia
osseointegration
fish malodor syndrome
fixed partial dentures (FPD)
abutments
fractures
avoidance with implants
cantilever pontics
cantilever units
cantilevered
cast post
cement-retained
complete-arch fixed complete denture
complications
diagnostic waxing
dowels
forces during function
full-arch tooth replacement
high risk
implant-supported
biomechanical risk reduction
clinical success assessment
immediate provisionalization
success/survival rate
implant-to-implant supported
long-term success
partially edentulous tooth replacement therapy
patient assessment
prosthesis design
retention loss
screw-retained
splinted metal–ceramic
straight
success/survival rate
support with implant and natural teeth combination
survival rate
tooth-implant supported
complications
implant loss risk
maintenance
natural tooth intrusion
tooth-supported
treatment planning
flap handling instruments
flap margin recession
flap procedures
apically positioned
ectopic tooth eruption
apically repositioned
beveled
clinical outcomes
coronally advanced flaps
envelope flap
hard tissue pockets
healing
implants
modified operation
mucoperiosteal flaps
maxillary anterior single-tooth replacement
maxillary sinus floor elevation
operation with/without osseous surgery
rotational
soft tissue lesion excision
soft tissue pockets
suturing
tension elimination
flexible spiral wire (FSW) retainer
floss holders
flossing
instruction
traumatic lesions
fluoride
anticaries action
chlorhexidine synergism
crystals in woodsticks
halitosis treatment
plaque control
toothpaste
foam brushes
foods, allergic reactions
forced tooth eruption
with fiberotomy
procedure
foreign body
impaction
reactions
formaldehyde dehydrogenase
formaldehyde lyase
free graft procedures, edentulous ridge
free soft tissue graft procedures
epithelialized
gingival augmentation
healing
interpositional grafts
pouch graft procedures
ridge augmentation
root coverage
thickness
freeze-dried bone allogeneic grafts (FDBA)
frenectomy
frenotomy with orthodontic treatment
fungal infection
chlorhexidine activity
gingival disease
linear gingival erythema
_see also Candida albicans_ (candidiasis)
furcated region
furcation
definition
incisors
mandibular molars
mandibular premolars
maxillary molars
maxillary premolars
probing
furcation defects
degree III
guided tissue regeneration
mandibular degree II
maxillary degree II
regenerative therapy
techniques
furcation entrance
exposure
molars
furcation fornix
furcation involvement
aggressive periodontitis
anatomy
assessment
automated probing systems
barrier membranes
basic periodontal examination
chronic periodontitis
classification
degree
diagnosis
differential diagnosis
extraction of tooth
guided tissue regeneration
implant planning
molar uprighting
occlusal interference
orthodontic treatment
papilla preservation flaps
prognosis
radiography
regeneration of defects
regenerative procedures
barrier membranes
risk assessment
root debridement
root separation and resection
root surface biomodification
terminology
trauma from occlusion
treatment
goal
tunnel preparation
furcation plasty
fusiforms
_Fusobacterium_
necrotizing gingivitis
necrotizing periodontal disease
plaque formation
root canal infection
_Fusobacterium nucleatum_
adherence
biofilm
content
implant surfaces
bridging species function
diabetes mellitus
HIV infection
linear gingival erythema
peri-implant infection
periodontal abscesses
plaque formation
smoking association
suppression by antibiotics
fusospirochetal infections
gas chromatography
gastrointestinal disease
gene(s)
gender in periodontal disease
disease-modifying
horizontal transfer
gene polymorphisms
aggressive periodontitis
chronic periodontitis
miscellaneous
periodontitis
genetic markers, risk assessment
genetic risk factors
aggressive periodontitis
chronic periodontitis
periodontal disease
genetic traits/disorders, implant patient
genotype frequencies
gingiva
abrasion by toothbrushes
adequate zone
after implants
attached
biologic width
biotypes
bleeding
damage from interdental cleaning
on probing
blood supply
buccal tissue dimensions
cleft removal
clinically healthy
connective tissue
inflammatory cell infiltrate
regenerative capacity
contour
dento-gingival epithelium
dimensions
biologic width
restorative therapy
width
enlargement
drug-induced
hereditary
leukemia-associated
epithelial mesenchymal interaction
excessive display
flat
free
health
height
increase
recession defects
root coverage
inadequate zone
innervation
interdental, cleaning
invagination removal
keratinization reduction in pregnancy
laceration
lamina propria
linear erythema
macroscopic anatomy
microbial challenge response
microscopic anatomy
oral epithelium
overgrowth
patient examination
periodontal mechanoreceptor activation
periodontal protection
pigmentation
pink tissue
probing
pronounced scallop
prosthesis
smokers
stippling
stretching in orthodontic treatment
transplanted
traumatic lesions
width
biologic
_see also_ gingival margin; gingival pocket/crevice
gingival augmentation
denudation procedure
grafting procedures
healing after
healing
indications
periosteal retention procedure
procedures
root coverage
split flap procedure
vestibular/gingival extension
healing after
gingival crevice fluid (GCF)
flow rate
gingivitis
immunoglobulins
innate mechanisms
prostaglandin E2 levels in aggressive periodontitis
smoking
_see also_ gingival pocket/crevice
gingival disease
allergic reactions
bacterial origin
candidosis
classification criteria
clinical signs
drug-induced
endogenous hormones
exudate alterations in gingivitis
fungal origin
genetic origin
pemphigus
hereditary fibromatosis
herpes virus infections
histoplasmosis
inflammation/inflammatory lesions
attachment loss
leukemia associated
non-plaque induced
plaque induced
prevalence
tooth loss
linear gingival erythema
malnutrition
mucocutaneous disorders
non-plaque-induced
plaque-induced treatment
pregnancy-associated
scurvy
sex steroid hormones
spectrum
systemic diseases
association
manifestations
ulcerative lesions
viral origin
_see also_ gingivitis
gingival graft, regenerated interdental tissue
gingival groove, free
gingival hyperplasia _see_ gingiva, enlargement
Gingival Index (GI)
gingival margin
apical displacement
endodontic lesion drainage
forced tooth eruption
free
maxillary anterior teeth
orthodontic intrusion
orthodontic treatment
plaque-induced gingivitis
position alteration
recession
limitation
orthodontic treatment
thickness
root coverage
sinus tracts
supra-erupted teeth
gingival pocket/crevice
biofilms
depth
incidence
innate mechanisms
leukocytes
microbial growth environment
neutrophils
probing
smokers
systemic humoral immune response
gingival recession
alveolar bone dehiscence
bucco-lingual thickness
children
defects
classification
orthodontic therapy
inflammation control
interdental
treatment options
labial
marginal tissue
limitation
orthodontic treatment
thickness
orthodontic forces
predictors
soft tissue thickness
tooth abrasion
tooth movement
direction
favorable
unfavorable
toothbrush trauma
treatment comparison
_see also_ root coverage
gingival sulcus
subgingival plaque
Gingival Sulcus Bleeding Index
gingivectomy
beveled
internal
healing
with orthodontic treatment
procedures
surgical technique
gingivitis
artefacta
bacterial flora
chronic
chronic periodontitis risk
clinical signs/symptoms
collagen loss
control agents
dento-gingival epithelium
diabetes mellitus-associated
diagnosis
epithelial cells
experimental studies
foreign body
histopathological features
hormonal contraceptive use
immune reactions
index systems
inflammation
inflammatory reaction
lesions
leukemia-associated
lymphocytes
menstrual cycle-associated
microbiology
necrotizing
acute form
chronic form
diagnosis
histopathology
host response
interproximal craters
lesion development
recurrent
traumatic ulcerative gingival lesion differential diagnosis
treatment
ulcerative
neutrophils
oral contraceptive-associated
periodontitis in adults
plaque removal
plaque-induced
plasma cells
polymorphonuclear leukocytes
pregnancy
prevalence
prevention in periodontitis prevention
progression to periodontal disease
puberty-associated
smoking
spectrum of disease
spirochetes
supportive periodontal therapy
supragingival plaque accumulation
susceptibility
treatment goal
_see also_ acute necrotizing ulcerative gingivitis (ANUG)
gingivoplasty
soft tissue sculpting
gingivostomatitis, herpetic
necrotizing periodontal disease differential diagnosis
primary
glucose intolerance
_see also_ diabetes mellitus
glucose oxidase, plaque control
glutathione
glycoprotein pellicle
glycoproteins
glycosaminoglycans
glycosyl-phosphatidyl-inositol (GPI)
Good Clinical Practice Guidelines
Gore Tex Periodontal Material®
grafting procedures
free gingival
gingival augmentation
interpositional
combined with onlay grafts
maxillary sinus floor elevation
onlay grafts
combined with interpositional grafts
roll flap procedure
soft tissue for ridge defects
_see also_ free soft tissue graft procedures; pedicle graft procedures
granulation tissue
interpositional grafts
peripheral inflammatory root resorption
tooth socket healing
growth factors
alveolar bone healing
delivery systems
osteoinductive/osteopromotive
ridge augmentation
tooth socket healing
growth hormone (GH)
guided bone regeneration (GBR)
augmentation materials
bone grafts
bone morphology
bone substitute materials
clinical concepts
long-term results
patient selection
soft tissue morphology
guided tissue regeneration (GTR)
aggressive periodontitis
attachment
barrier membranes
bioabsorbable materials
citric acid demineralization combination
clinical outcomes
combined procedures
with demineralized freeze-dried bone allograft
enamel matrix derivative comparison
evaluation
furcation
defect regeneration
involvement
healing
intrabony defects
membranes
oral hygiene
orthodontic tooth movement
pedicle soft tissue graft with barrier membrane for root coverage
peripheral inflammatory root resorption
post-operative morbidity
root coverage
healing
gum-wing profile
HalimeterTM
halitophobia
therapy
halitosis
blood-borne
chlorhexidine use for oral malodor
classification
confidant use
control
diagnosis
drug-induced
epidemiology
extraoral
instructions for patient
intraoral
morning
odor characteristics
oral inspection
organoleptic evaluation
organoleptic measurements
pathogenesis
pathologic
practice flowchart
prevalence
questionnaire
sulfide monitor
temporary
treatment
adjustment
planning
hand instruments, root debridement
hard tissue
replacement
resorption mechanisms
_see also_ alveolar bone; bone
Haversian canals
health education
health survivor effect
heart disease, postmenopausal women
heat necrosis, implants
hematologic disorders
chronic periodontitis
gingival manifestations
implant patient
surgery contraindication
hemidesmosomes
epithelial cell rests
junctional epithelium attachment
hemiseptal defects
hemoglobin, glycated (HbA1c)
hemostasis, local
hepatitis, dental team protection
hepatitis B infection, chlorhexidine activity
herb extracts, plaque control
hereditary gingival fibromatosis
herpes simplex virus (HSV)
dental team protection
erythema multiforme
gingival disease
periodontal infection
herpes virus infections
primary gingivostomatitis
herpes zoster
Hertwig's epithelial root sheath
fragmentation
remnants
hexetidine
high-strength all-ceramic implant restorations
histiocytosis X
aggressive periodontitis
chronic periodontitis
histoplasmosis, gingival disease
HIV infection
aggressive periodontitis
chlorhexidine activity
chronic periodontitis
herpetic gingivostomatitis
host susceptibility to disease
implant patient
linear gingival erythema
necrotizing periodontal disease
necrotizing stomatitis
periodontitis
plaque accumulation
homing
hormonal contraceptives
gingivitis
periodontal effects
hormone replacement therapy
periodontal effects
hormones
endogenous in gingival disease
sex steroid
_see also_ estrogen; progesterone
host defense mechanisms
adaptive defense system
enhancement for plaque control
humoral immune response
immune defense system
innate
pathogens overcoming
periodontal infections
host response
evaluation in aggressive periodontitis
necrotizing periodontal disease
pathogens
smoking
host susceptibility to disease
aggressive periodontitis
environmental factors
plaque formation
host-compatibility
Howship's lacunae
humoral immune response
antigen presenting cells
hyaline layer
hydrogen peroxide
bleaching
halitosis treatment
necrotizing periodontal disease treatment
plaque control
production by bacterial beneficial species
tooth whitening
hydrogen sulfide
hydroxyapatite
crystals
porous
hyperglycemia
hyperinsulinemia
hypoglycemia
hypophosphatasia
hypothiocyanite
I-Brush®
_IL1_ gene
_IL1_ gene polymorphisms
composite genotype
genetic marker
implant failures
implant patient
peri-implant bone loss
peri-implantitis
severe periodontal disease susceptibility
smoking
_IL1A_ gene
implant failures
_IL1B_ gene
implant failures
_IL1RN_ gene
implant failures
_IL10_ gene polymorphisms
iliac crest marrow grafts
illumination
loupes
microscope
microsurgery
image plate systems
image-guided surgery
immune memory
immune pathology
immune reactions
gingivitis
periodontal infections
protective role
immune receptors, innate
immune system
innate
gingival crevicular fluid antibodies/complement
microbial modulation
necrotizing periodontal disease
periodontal infections
smoking
suppression by pathogens
immunodeficient patients
herpetic gingivostomatitis
_see also_ HIV infection; immunosuppression
immunofluorescence techniques, biofilm bacterial detection/enumeration
immunoglobulin (s)
maxillary sinus
pemphigoid
immunoglobulin A (IgA)
immunoglobulin G (IgG)
Fc receptors
necrotizing periodontal disease
smoking effects
immunoglobulin M (IgM)
immunosuppressants
chronic periodontitis
gingival overgrowth
implants
prophylactic antibiotics
immunosuppression
chlorhexidine use
chronic periodontitis
implant patients
_see also_ HIV infection
implant (s)
abutment
material
for prosthetic appliances
abutment-level impression
adjacent teeth condition
aggressive periodontitis
alveolar bone loss in diabetes
anatomic landmarks with potential risk
anatomic structure avoidance
angle
angulation
ankylosis
anterior single-tooth replacement
articulation
bacterial deposits
biological differences from teeth
bone
apposition
augmentation
available
height/width
loss
modeling/remodeling
preparation
reaction to orthodontic loading
bony borders
buccal–lingual dimensions
calculus attachment
chewing comfort
classification
clinical inspection/examination
clinical test of mobility
color shades
completed soft tissue coverage of tooth socket
complications
connectors
crater-formed defects
cumulative implant survival rate
cutting
cyclic loads
dehiscence defects
direction
distally shortened arch
early stability
endosseous receptors
esthetic zone
extraction sockets
failures and disease-modifying genes
fixed prostheses
flap
closure
elevation
flapless insertion
function analysis
functional differences from teeth
furcation involvement
healing time
heat necrosis
horizontal defects
identification of presence
image-guided surgery
inclination
incorrectly placed
indications
infection
insertion torque
installation
interarch distance
interdental contact line
interdental space assessment
length
loading
excessive
functional
loss of osseointegration
maxillary anterior single tooth replacement
overloading
static
long axis
long-term performance
loss
malpositioned
marginal hard tissue defect
masticatory occlusal forces
materials
maxillary anterior restorations
multiple-unit fixed
mechanical stimuli perception
mechanical stress
mesio-distal orientation
model-based guided surgery
molars
multiple adjacent restorations
natural tooth substance preservation
neuropathies
non-cutting
number
oral mucosa
oro-facial position
orthodontic anchorage
advantages
direct
disadvantages
forces
growing patients
indications
indirect
length-reduced devices
loading
removal
stability
success rate
temporary devices
osteoporosis
outcomes
overloading
palatal
clinical procedures
growing patient effects
insertion sites
loading time schedule
palpation
papilla
assessment
dimensions
tissue loss
patient satisfaction
periodontally compromised patients
periosteal receptors
phonetics
disturbances
placement
alveolar ridge healing
clinical concepts
completed soft tissue coverage of tooth socket
fresh extraction sockets
guiding concept
planning
ridge corrections
substantial bone fill in extraction socket
therapy aims
timing
plaque formation
position
sites with limited vertical bone
posterior dentition
abutment-level impression
angulated abutments
cemented multiple-unit posterior implant prostheses
clinical applications
combination with natural tooth
support
concepts
controversial issues
distally shortened arch
distribution
early fixed restorations
fixed implant-supported prostheses
high-strength all-ceramic implant restorations
immediate fixed restorations
indications
lateral bone augmentation
multiple-unit tooth-bound restorations
number
occlusal considerations
orthodontic considerations
restoration with cantilever units
screw-retained restorations
shoulder-level impression
single-tooth replacement
sites with anterior sinus floor proximity
sites with extended horizontal bone volume deficiencies
size
splinted _versus_ single-unit restorations
technique
treatment planning
posterior segment
premolars
psychophysical testing
recipient site
re-innervation
rejuvenation at contaminated surface
removable prostheses
replacement of teeth
diseased
strategically important missing
resonance frequency analysis
restoration-driven
restorative dentistry
ridge augmentation procedures
risk indicators
risk predictors
rotation–symmetrical
safety zone
scalloped design
screw-retained suprastructure
screws
component complications
diameter
solid
segmented fixed restorations
self-tapping
sensory motor interactions
short
shoulder
depth in relation to labial mucosal margin
distance to plane of occlusion
microgap
sink depth
submucosal
shoulder-level impression
single-tooth
smoking risk
soft tissue
grafts
loss
stability
splinting
stability
placement immediately after extraction
static loads
submucosal shoulder position
success criteria
supportive care
surface quality
surgical site
survival rate
maxillary sinus floor elevation
system components
tactile capacity
technical failures
tilted
tissue biotype
tissue injury
titanium
tooth lengthening
trap door procedure
treatment spectrum
treatment success
vertical distance requirement
vertical ridge defects
vibrotactile capacity
wide-diameter/wide-platform
wound chamber
wound healing
_see also_ maxillary sinus floor
elevation; osseointegration; peri-implantitis
implant pass
implant patient
age
alcohol abuse
anamnestic information
autoimmune disorders
clinical conditions
clinical inspection
communication problems
connective tissue disorders
diabetes mellitus
endodontic infection
esthetic implication sites
esthetics and tooth movement
examination
clinical
components
extraoral
implant-supported restorations
intraoral
local
radiographic
expectations
failure-associated complications
history
immunosuppression
implant placement
lack of understanding
local conditions
medications
oral hygiene
oral infections
orthodontic pretreatment
osteoporosis
pass
periodontitis
post-surgical infection minimizing
post-treatment care/maintenance program
prognosis
psychiatric/psychological issues
questionnaire
radiography examination
treatment monitoring
risk assessment
behavioral considerations
clinical information
principles
risk factors
local
systemic
satisfaction
smoking
substance use/abuse
technical procedures to minimize risk
tissue damage minimization
treatment planning
radiographic monitoring
implant recognition software
implant stability quotient (ISQ)
implant-supported restorations abutments
materials
bite force
butt-joint interface
cement-retained
clinical inspection/examination
complications
abutment-related
biologic
clinical
implant screw-related
mechanical
overdenture
peri-implant
prosthetic
surgical
diagnostic waxing
esthetics
external hex
implants
angulation
loss
malpositioned
internal hex
load resistance
marginal defects
material failures
midline fracture
occlusal wear
one-piece implant designs
overdentures
patient examination
restorative veneer fracture
screw-retained
soft tissues
responses
success/survival rate
surgical guide
technical failures
treatment planning
_see also_ fixed partial dentures (FPD)
impressions, master model
incisive foramen width
incisors
crowded
furcations
overlapping
papillae
indole
infection
control for implant placement
self-performed
in surgery
dental pulp
dental team protection
dissemination
endodontic
focal
maxillary sinus
medical conditions predisposing
opportunistic
oral in implant patients
periodontium of endodontic origin
post-surgical
preterm birth
root-filled teeth
soft tissues around implants
systemic diseases
treatment complication
_see also_ bacteria/bacterial infections; fungal infection; gingivitis; pathogens; peri-implantitis; periodontal abscess; periodontitis; root canal infection; stomatitis; viral infections
infection plaque
inflammation gingival
attachment loss/tooth loss
gingivitis lesion
innate immune process
orthodontic therapy
periodontal tissue assessment
inflammatory cells
infiltrate
inflammatory mediators, preterm birth
inflammatory processes dental pulp
periodontal infections
inflammatory response aggressive periodontitis
clinically healthy gingiva
dental pulp
gingivitis
innate immune mechanism
leukocyte migration
peri-implant mucosa
peri-implantitis
periodontal infections
periodontium
smoking
sutures
infrabony defects
orthodontic tooth movement
infrabony pockets
orthodontic intrusion
trauma from occlusion
infraorbital artery
infraorbital nerve
initial tooth mobility (ITM)
innate defense systems
gingival crevicular fluid antibodies/complement
microbial modulation
innate immunity receptors, gene polymorphisms
insertion/deletion polymorphisms
instrument tray
instrumentation, hard tissue trauma
instruments
maxillary sinus floor elevation
microsurgery
root debridement
surgery
insulin
insulin resistance
bacterial infection
insulin-like growth factor (IGF)
alveolar bone healing
ridge augmentation
insulin-like growth factor 1 (IGF-1)
intercellular adhesion molecule 1 (ICAM-1)
leukocyte adhesion deficiency
intercellular adhesion molecule, soluble (sICAM)
interdental brushes
efficacy
hard tissue damage
interdental cleaning
efficacy
mechanical for plaque build-up prevention
interdental papilla _see_ papilla
interdental recession
prevention
interdental septum
interdental space, assessment
interdental support, root coverage
interferon γ (IFN-γ)
interleukin(s)
interleukin 1 (IL-1)
bone loss
peri-implant
systemic
late implant failures
_see also IL1_ gene
interleukin 1α (IL-1α)
interleukin 1β (IL-1β)
interleukin 2 (IL-2)
interleukin 6 (IL-6)
interleukin 10 (IL-10) gene polymorphisms
intermicrobial matrix
international normalized ratio (INR)
interpositional graft procedure
combined with onlay grafts
interproximal brushes
intrabony defects
barrier membranes
enamel matrix derivatives
guided tissue regeneration
membranes
papilla preservation flaps
regenerative therapy strategy
surgical access
intracellular adhesion molecule (ICAM-1)
intracoronal bleeding, peripheral inflammatory root resorption
intradental A-delta fibers
intraseptal artery
iodine tincture, vertical root fracture diagnosis
irradiation geometry
irrigation
full-mouth disinfection
subgingival
irrigators
pulsating
jaw
bone defects
implant placement planning
fixation and chlorhexidine use
shape variation
_see also_ mandible; maxilla
jiggling-type trauma
anchor teeth
orthodontic treatment
zones of co-destruction
jugulodigastric lymph nodes
junctional epithelium
Kaposi's sarcoma
keratin synthesis
keratinization
keratinocytes
cytotoxic immune reaction
differentiation
keratin-producing cells
keratohyalin bodies
_Klebsiella oxytoca_
_Klebsiella pneumoniae_
knives
Koch's postulates
lactoferrin
lamellar bone
edentulous alveolar ridge
osseointegration
lamina dura
lamina propria
Langerhans cells
laser therapy, ablative
leptin
leukemia
aggressive periodontitis
chronic periodontitis
gingival manifestations
gingivitis
necrotizing periodontal disease
necrotizing ulcers
surgery contraindication
leukocyte(s)
gingival crevice
implant wound chamber
migration
necrotizing periodontal disease
peri-implant mucosa
periodontal abscesses
pocket epithelium
recruitment
subgingival plaque
leukocyte adhesion deficiency (LAD)
aggressive periodontitis
leukoplakia, oral
leukotoxins
_A. actinomycetemcomitans_
aggressive periodontitis bacteria
lichen planus
lichenoid lesions, oral
lighting
linear gingival erythema
lingual artery
lingual nerve
block
linkage analysis, aggressive periodontitis inheritance
lipopolysaccharide
_A. actinomycetemcomitans_
in calculus
on cementum
host receptor recognition
preterm birth
lipopolysaccharide-binding protein
lipoteichoic acids
liver disease
fetor hepaticus
local anesthesia individual variability
mechanism of action
surgery
techniques
types
localized aggressive periodontitis (LAP)
_A. actinomycetemcomitans_
_Eikenella corrodens_
lesion long-term stability
long tooth syndrome
loupes
advantages
convergence angle
disadvantages
field of view
illumination
interpupillary distance
selection
viewing angle
working distance/range
low birthweight
periodontal disease
lupus erythematosus
lymph nodes
swelling
lymphatics, periodontium
lymphocytes
adaptive defense system
gingivitis
host defense
smoking effects
lymphogranulomatosis, surgery contraindication
lymphoreticular disorders, implant patient
LYS-gingipain
lysozymes
alpha-2 macroglobulin
macrophages
diabetes mellitus
host defense
implant wound chamber
migration
tooth socket healing
MadCAM-1 homing receptor
magnetic resonance imaging, functional (fMRI)
Maillard reactions
maintenance care visits
major histocompatibility complex (MHC)
malnutrition gingival disease
necrotizing periodontal disease
malocclusion, incisor crown shape
mandible
incisive canal bundle
local anesthesia
neuroanatomy
opening amplitude
premolars
_see also_ molars, mandibular
mandibular canal identification
implant planning
mandibular overdentures
marginal tissue
recession
mast cells
master model, impressions
matrix metalloproteinases (MMPs)
polymorphisms
maxilla
alveolar process
anterior teeth gingival margins
edentulous
local anesthesia
neuroanatomy
segmented fixed implant
restorations
width growth
_see also_ molars, maxillary; premolars
maxillary
maxillary anterior single-tooth replacement
sites with extended horizontal deficiencies
sites with localized horizontal deficiencies
sites with major vertical tissue loss
sites without significant tissue deficiencies
maxillary arch, length discrepancies
maxillary complex displacement
maxillary multiple-unit anterior fixed implant restorations
sites with extended horizontal deficiencies
sites with major vertical tissue loss
sites without significant tissue deficiencies
maxillary sinus
anatomy
blood supply
drainage
infection
membrane perforation
respiratory epithelium
septa
maxillary sinus floor elevation
augmentation
clinical decisions
crestal approach
implant placement
implant survival
indications
outcome
post-surgical care
success
surgical technique
delayed (two-stage)
grafting materials
lateral approach
complications
contraindications
implant survival
indications
outcome
post-surgical care
pre-surgical examination
success
techniques
one-stage with implant installation
osteotome technique
with grafting material
short implants
sinus membrane perforation
sinusitis
treatment options
two-stage
mechanical stimulation
mechanoreceptors
mechano-transduction mediators
medications
chronic periodontitis
drug interactions
gingival disease
gingival enlargement
implant patients
mucocutaneous disorders
patient examination
melanocytes
Melkersson–Rosenthal syndrome
membrane-associated CD14
menopause
chronic periodontitis
periodontal effects
menstruation
gingivitis
halitosis
periodontal effects
mental artery
Merkel's cells
mesio-distal enamel reduction
mesio-distal gap implant placement
optimization of dimensions
metal salts, plaque control
methicillin-resistant _Staphylococcus_ _aureus_ (MRSA)
methotrexate
methyl mercaptan
methylene blue, root fracture diagnosis
metronidazole
activity
amoxicillin combination
controlled delivery
gel
healing after guided tissue regeneration
peri-implant lesions
microarrays
microbe-associated molecular patterns (MAMPs)
microbiota, healthy sites
_Micromonas micros_
cardiovascular disease
peri-implant infections
microorganisms changing concepts
complex formation in biofilm
control
dentin permeability
endodontic
host-compatible
interactions
periodontal infections
persistence
regrowth
screw-retained implant restoration colonization
subgingival
subgingival plaque
_see also_ bacteria/bacterial infections; fungal infection; _named organisms;_ viral infections
micro-satellites
microscope, surgical
advantages
binocular tubes
disadvantages
eyepieces
lighting unit
magnification changer
objective lenses
microsurgery
clinical indications
comparison to conventional interventions
concepts
illumination
instruments
limitations
magnification
needle for suturing
practice requirements
root coverage
suture materials
sutures
teamwork
techniques
training
microsurgical triad
Miller class I–II defects
mineral trioxide aggregate (MTA)
minimal inhibitory concentration (MIC)
minimally invasive surgical technique (MIST)
miniplates, L-shaped
miniscrews
minocycline
microspheres
ointment
miscarriage
_MMP_ gene polymorphisms
modified flap operation
molars
accessory canals
banding
bonding
implants
mandibular
furcation defect regeneration
furcation entrance
furcation plasty
root separation and resection
vertical fractures
maxillary
furcation entrance
root separation and resection
periodontal abscesses
single-tooth restoration
uprighting and furcation involvement
vertical root fracture diagnosis
monocytes diabetes mellitus
implant wound chamber
necrotizing gingivitis
periodontal abscesses
motivational interviewing
advice giving
communication
definition
development
evidence for
implementation
oral hygiene
smoking cessation
mouth, hematoma of floor
mouth rinses
alcoholic
allergic reactions
halitosis treatment
home use studies
morning bad breath
plaque control
standards
triclosan
_see also_ chlorhexidine
mucocutaneous disorders
drug-induced
gingival disease
mucogingival junction
ectopic tooth eruption
mucogingival margin/line
mucogingival therapy
crown-lengthening procedures
deformed edentulous ridge
gingival augmentation
interdental papilla reconstruction
root coverage
mucoperiosteal flaps
deep dissection
maxillary anterior single-tooth replacement
maxillary sinus floor elevation
mucosa _see_ oral mucosa
mucositis
probing
_see also_ peri-implant mucositis
multiple sclerosis, surgery contraindication
mutanase
mutilated dentition treatment
_Mycobacterium chelonae_
_Mycoplasma pneumoniae_
myocardial infarction (MI)
_Peptostreptococcus micros_ association
risk with periodontitis
surgery contraindication
nasal–maxillary complex alteration
nasopalatine canals
bone augmentation
width
nasopalatine foramen
necrotizing periodontal disease
acute phase treatment
age
alcohol consumption
alveolar mucosa
clinical characteristics
communicability
diagnosis
endotoxins
fever
gingival defect elimination
gingivitis pre-existence
histopathology
HIV infection
host response
inadequate sleep
interproximal craters
lesion development
leukemia
lymph node swelling
maintenance phase treatment
malnutrition
microbiology
oral hygiene
pathogenesis
plaque control
predisposing factors
prevalence
previous history
racial factors
sequestrum formation
smoking
stress
systemic disease
treatment
necrotizing stomatitis
diagnosis
necrotizing ulcerative gingivitis (NUG)
chronic periodontitis
needle, microsurgical suturing
_Neisseria gonorrhoeae_ , gingival disease
nerve fibers, dentin exposure response
Neumann flap
neural crest
neurologic disorders, surgery contraindication
neutrophils
gingival crevice
gingivitis
necrotizing
implant wound chamber
peri-implant mucosa healing
periodontal abscesses
tooth socket healing
new attachment procedures
NF-kappa B pathway
nicotine
absorption
nicotine replacement therapy
nifedipine, gingival overgrowth
nitro-imidazoles
nociceptors
non-specific plaque hypothesis
nutritional deficiencies
chronic periodontitis
malnutrition
nystatin
obesity
biofilm composition
periodontitis
occlusal concept, implant-specific
occlusal interference
occlusal relationships, crown-lengthening
occlusion
assessment
masticatory forces
trauma
bone regeneration
orthodontic treatment
tooth mobility
octenidine, plaque control
octopinol
odds ratio
odontoblasts
odontoplasty
onlay graft procedures
combined with interpositional grafts
donor site/tissue
Onplant®
open flap curettage technique
opsonization
oral contraceptives
gingivitis
periodontal effects
oral epithelium
barrier function
basal layer
cell layers
clear cells
ento-gingival region
glycogen content in pregnancy
junctional
keratinized
keratin-producing cells
migration
progenitor cell compartment
reduced
stratum spinosum
subsurface
wound healing role
_see also_ dento-gingival epithelium
oral health
motivational interviewing
patient responsibility
oral hygiene
access for devices
adherence
adjunctive aids
barrier membranes
behavior change
biofilms
guided tissue regeneration
implant patient
instruction
interdental cleaning
motivation
motivational interviewing
necrotizing periodontal disease
orthodontic treatment of adults
patient examination
plaque build-up prevention
post-regenerative therapy
programs
psychosocial factors
public awareness
regenerative surgery
risk assessment
root coverage
self-performed plaque control
side effects
tongue cleaning
_see also_ chlorhexidine; toothbrushes; toothbrushing
oral hygiene products
allergic reactions
chemical injury
_see also_ dentifrices; mouth rinses; toothpaste
oral leukoplakia
oral lichenoid lesions
allergic reactions
oral malodor, chlorhexidine use
oral mucosa
allergic reactions
buccal soft tissue dimensions
keratinized
lining
margin
receding
masticatory
peri-implant
receding margins
periodontal mechanoreceptor activation
ridge
specialized
tissue-matched shades
_see also_ peri-implant mucosa oral sepsis
oral sulcular epithelium
oral tumors
maxillary sinus
periodontal abscess differential diagnosis
Oral-B Sonic Complete® toothbrush
OralChromaTM
organ transplantation, surgery contraindication
organic acids
organoleptic evaluation
oro-antral fissure, necrotizing stomatitis
orofacial granulomatosis
orofacial region neuroplasticity
orthodontic appliances bonding
chlorhexidine use
implants for abutment
periodontally compromised patients
retention
steel ligatures
orthodontic forces, root surface resorption
orthodontic loading, alveolar bone
orthodontic tilting movements
orthodontic trauma
orthodontic treatment aggressive periodontitis
anchorage
bodily tooth movement
esthetics
extrusion of single teeth
collagen formation
furcation involvement
gingival margins
gingival recession
hopeless teeth as anchorage
implant anchorage
intrusion
jiggling
legal aspects
minor surgery
oral hygiene
periodontal disease
peripheral inflammatory root resorption
recession defects
retention
risk management
splinting
tooth inflammation
tooth movement in adults
traumatic occlusion
_see also_ tooth movement, orthodontic
orthokeratinization
Orthosystem®
sseointegration
bone remodeling
definition
excessive occlusal load
failure
functional loading
loss
excessive loading
peri-implant
osteoporosis
process
quality assessment
wide marginal defects
wound chamber
wound cleansing
_see also_ implant (s); re-osseointegration
osseoperception
neurophysiology
peri-implant
osseous defects _see_ bone defects
ostectomy
osteitis, necrotizing stomatitis
osteoblasts
bone deposition
bone multicellular unit
one resorption
communication with osteocytes
differentiation
proliferation
osteocalcin, diabetes mellitus
osteoclasts
activation
bone multicellular unit
bone resorption
indirect
treatment
jiggling forces
osteoconduction
osteocytes
communication with osteoblasts
cytoplasmic processes
osteogenesis
malpositioned tooth movement
osteoid
formation
osteoinduction
osteoinductive factors
osteomyelitis
bisphosphonate-associated
periodontal abscess differential diagnosis
osteonecrosis
bisphosphonate-associated
implant failure
of the jaw
osteons
primary
secondary
tooth socket healing
osteopenia
periodontitis
osteoplasty
osteoporosis
chronic periodontitis
fractures
implant patient
periodontal effects
periodontitis
smoking
treatment
osteoprogenitor cells
osteoprotegrin
osteoradionecrosis, implant patient
osteotome, tapered
osteotome technique of maxillary sinus floor elevation
overdentures
implant angulation
implant-supported restoration complications
mandibular and occlusal force distribution patterns
oxidation–reduction potential (Eh)
pathogen growth conditions
periodontal infections
oxygen bacterial growth
pathogen requirements
oxygenating agents
oxytalan fibers
pain
control during treatment
non-surgical treatment
post-operative control
scaling and root planing
vertical root fracture
pain syndromes root dentin hypersensitivity
treatment goal
palatal nerve
block
greater
palate, hard
palatine artery, greater
palatine canal, greater
palmo-plantar keratitis, aggressive periodontitis
papilla
classification system
defects
dimensions
between adjacent implants
between teeth and implants
height
classification
loss
inter-implant
maxillary incisors
reconstruction
surgical techniques
tissue loss
papilla preservation flap
e-PTFE combination
intrabony defects
modified
outcomes
simplified
minimally invasive surgery
papilla preservation technique, modified
barrier membranes
biologically active regenerative materials
enamel matrix derivative
minimally invasive surgery
papillomavirus, periodontal infection
Papillon–Lefèvre syndrome (PLS)
aggressive periodontitis
implant patients
paraformaldehyde
parakeratinization
parathyroid hormone (PTH)
ridge augmentation
Parkinson's disease, surgery contraindication
parodontitis interradicularis
parodontitis profunda
parodontitis superficialis
passive threshold determination
pathogen-associated molecular patterns (PAMPs)
pathogenicity mechanisms
pathogen-related oral spirochetes
pathogens
adherence
antibiotic susceptibility
antibody evasion
bridging species
climax community complexity
coaggregation
colonization
antagonistic substances
host defense mechanisms
criteria for defining
elimination in aggressive periodontitis
genome sequences
host response
host-compatible
immune pathology
immune suppression
interbacterial relationships
interfamily transmission
intraoral transmission
invasion
mixed infections
multiplication
necrotizing periodontal disease
new putative
nutrient requirements
oxygen requirements
peri-implant infections
climax community complexity
edentulous subjects
implant exposure timing
periodontal
polymicrobial microbiota
prevalence in periodontitis patients
regulons
resistance to antiseptics/antibiotics
source
specific suppression
tissue damage
transmission
intraoral
types
virulence mechanisms
virulent
_see also_ bacteria/bacterial infections; fungal infection; viral infections
patient(s)
affirming
giving advice
health protection
history for implant therapy
reflection of communication
responsibility for oral health
_see also_ implant patient
patient examination
alveolar bone
chief complaint
compliance
dental history
expectations
implant success
family history
functional disturbance screening
furcation involvement assessment
gingiva
habits
hard tissue assessment
implant therapy
candidate
implant-supported restorations
medical history/medications
motivation
occlusion assessment
oral hygiene
periodontal disease
signs/symptoms
periodontal lesion diagnosis
periodontal ligament
radiographic
root cementum
smoking history
social history
tooth mobility assessment
pattern recognition receptors (PRRs)
pedicle graft procedures double
gingival augmentation
healing
roll flap procedure
root coverage
combined with barrier membrane
enamel matrix derivatives
peer-abutment
pemphigoid
pemphigus vulgaris
penicillins
adverse reactions
_Peptostreptococcus_ , root canal infection
_Peptostreptococcus micros_
peri-implant infection
smoking association
perception, periodontal tactile
neurophysiology
peri-implant osseoperception
psychophysical assessment
testing
periapical abscess diabetes mellitus
drainage
pericytes
bone multicellular unit
peri-implant crevicular fluid (PICF) analysis
peri-implant lesions
bone defects
cumulative interceptive supportive therapy
diagnosis
mechanical debridement
non-surgical debridement
regenerative therapy
resective therapy
resolution
surgical therapy
treatment strategies
peri-implant mucosa
barrier epithelium
biologic width
buccal soft tissue dimensions
collagen fibres
connective tissue quality
dimensions
healing
inflammatory response
morphogenesis of attachment
probing
thin/thick periodontal biotypes
vascular system
peri-implant mucositis
plaque formation
peri-implant tissues
load/loading
bone reactions to functional
cyclic
excessive occlusal
orthodontic
osseointegration loss
static
masticatory occlusal forces
osseoperception
tooth–implant supported
reconstructions
peri-implantitis
bone loss
climax community complexity
clinical features
disease-modifying genes
edentulous subjects
granulation tissue pathogens
histopathology
_IL1_ gene polymorphisms
implant exposure timing
implant-supported restorations
inflammatory response
management
microbiota of infection sites
_P. gingivalis_
partially edentulous subjects
periodontal disease history
pocket formation
prevalence
probing
progression
re-osseointegration
risk
risk factors
soft tissues around implants
treatment
periodontal abscess
classification
complications
diabetes mellitus
diagnosis
differential diagnosis
histopathology
infection dissemination
microbiology
non-periodontitis-related
pathogenesis
periodontitis-related
peripheral inflammatory root resorption
post-therapy
prevalence
signs/symptoms
sites
tooth loss
treatment
vertical root fracture
periodontal disease
age
animal experiments
assessment
biofilms
characteristics
definition
destructive
agents
gingival recession
examination methods
gender
genetic component
genetic risk factors
index systems
initiation
lesion diagnosis
low birthweight
maintenance care
orthodontic treatment
patient examination
peri-implant microbiota
plaque-associated
pre-eclampsia
preterm birth
prevalence
prevention
probing assessments
progression
radiographic evaluation
pulp influence
race/ethnicity
recurrent
screening
sibling relationship
signs/symptoms
smokers
susceptibility
systemic disease risk
tooth mobility
vaccines
volatile sulfur compounds
Periodontal Disease Index
periodontal dressings
Periodontal Index
periodontal innervation
neural feedback
periodontal ligament
blood supply
blood vessels
collagen fiber bundles
epithelial cells
fibroblasts
formation
innervation
mechanoreceptors
activation
patient examination
principal fibers
re-establishment in re-implanted roots
tooth attachment
trauma from occlusion
vascular plexus
widening
increased tooth mobility
periodontal ligament cells
periodontal regeneration
regenerative capacity
periodontal pockets
antibiotic actions
antibiotic delivery
bacterial infection
deep with peri-implant lesions
depth
reduction with forced tooth eruption
residual and regenerative surgery
distal wedge procedures
elimination
endodontic lesion
epithelium
flap procedures
gingivectomy procedures
hard tissue
iatrogenic root perforation
microbial growth environment
periodontal abscesses
probeable depth
regenerative procedures
residual
root debridement
soft tissue
spirochetes
subgingival bacterial deposit
subgingival calculus
surgery
healing
techniques
volatile sulfur compounds
periodontal probes
periodontal probing
aggressive periodontitis screening
automated systems
dento-gingival interface
depth
critical
non-surgical treatment
periodontal disease after scaling and root planing
smoking
furcation involvement assessment
peri-implant mucosa
peri-implantitis
periodontal tissue assessment
patient assessment
regeneration
periodontal receptors
activations
oral stereognosis
reduction
periodontal risk assessment (PRA) calculation
periodontal support
interdental
loss in relation to age
residual
periodontal tactile function
active threshold determination
passive threshold determination
periodontal tissues
breakdown and orthodontic tooth movement
fibrous reunion
regeneration
assessment
concepts
grafting procedures
growth regulatory factors
histologic studies
root surface biomodification
wound healing
periodontitis
adaptive defense system
adult
assessment for implants
advanced
age
alveolar bone resorption
alveolar process change
apical
attachment loss
biofilms
BMI
bone destruction
buccal migration of tooth
calculus association
cardiovascular disease
risk
treatment effects
characteristics
chronic
attachment loss
characteristics
clinical features
etiology
furcation involvement
gingivitis as risk
heritability
prevalence
progression
risk factors
single implant
stress
susceptibility
treatment
chronic obstructive pulmonary disease
classification
colonization
complexity
course
dental plaque association
diabetes mellitus
association
control
treatment effects
diagnosis
disease-modifying genes
early onset
endodontic lesion differential diagnosis
etiologic agents
etiology
_Fc_ γ _RIIa_ polymorphisms
fixed partial denture loss
frequency distribution
furcation area
gender
gene mutation
gene polymorphisms
genetic component
genetic risk factors
genetics role
glucose intolerance
heritability
aggressive disease
chronic disease
historical aspects
HIV infection
host defense processes
host factors
susceptibility
host–parasite relationship
modification in diabetes mellitus
immune defense system
immune reactions
implant patients
inflammatory processes
inflammatory reactions
initiation
factors
innate immune processes
invasion by pathogens
juvenile
lesions
ligature-induced
local environment
microbial invasion
microbiology
mixed infections
necrotizing
acute form
chronic form
diagnosis
interproximal craters
Kaposi's sarcoma
recurrent
obesity
osteopenia
osteoporosis
pathogenesis
pathogenicity mechanisms
pathogens
virulent
patients at risk
periodontic/orthodontic treatment
phenotype
population at risk
pregnancy adverse outcomes
prepubertal
prevalence
progression
factors
proteases
psychosocial factors
race/ethnicity
recurrent
regenerative periodontal therapy
respiratory infection risk
risk assessment
risk factors
severity
variability
sibling relationship
similarities to other infections
smoking
spirochetes
stress
supportive periodontal therapy
susceptibility
systemic disease risk
treatment impact
tooth loss
trauma from occlusion
triclosan-containing toothpaste
unique features
virulence factors
viruses
volatile sulfur compounds
_see also_ aggressive periodontitis
periodontium/periodontal tissue
allergic reactions
alveolar bone anatomy
anatomy
bacterial damage
bacterial invasion
blood supply
development
endodontic origin and infectious processes
enodontic treatment of lesions
extravascular circulation
function
gingiva anatomy
halitosis
healthy
jiggling-type trauma
reduced height
inflammation assessment
inflammatory lesions
lymphatic system
nerves
neural feedback
orthodontic single-tooth extrusion
overt lesions
periodontal ligament anatomy
potential infection
preservation
rate of destruction
regeneration
root cementum anatomy
smoking cessation
support loss assessment
toxic reactions
Periodontometer
periosteal retention procedure
periosteum
mechanoreceptors
activation
Periotest®
implants
peroxyborate/peroxycarbonate
pH
biofilms
pathogen growth conditions
periodontal infections
phagocytes defects in aggressive periodontitis
endodontic lesions
phagocytosis
pulp inflammatory response
subgingival plaque
phantom tooth phenomenon
phenols, plaque control
phenytoin gingival enlargement
surgery contraindication
phonetics with implants
disturbances
physically handicapped people, chlorhexidine use
plant extracts, plaque control
plaque, atheromatous
bacterial
plaque, dental
accumulation with orthodontic appliances
_Actinomyces_ -induced
bacteria
rapid/slow former
smoking effects
biofilms
mechanical debridement
plaque, dental ( _continued_ ) carbohydrate content
chemical control agents
evaluation
chronic periodontitis
risk
role
conditioning film
control
bacterial tests
clinical trials
instruction
motivation
self-performed
study methods
uptake measurements
etiology
experimental studies
fibrillar component
formation
gingival disease
treatment
gingival margin accumulation
gingival recession
gingivitis
glycoprotein pellicle
HIV infection
host susceptibility
immune response suppression
infection
association
non-specific plaque hypothesis
inflammatory response
inhibitory agents
intermicrobial matrix
lipids
mechanical debridement
microbial complexes
mineralization
non-specific plaque hypothesis of infection
oxygen levels
patient examination
peri-implant
peri-implant mucosa response
periodontitis in adults
reducing agents
removal
adolescents
agents
brushing force
gingivitis control
insufficient
peri-implant
self-performed
retentive factors
smoking effects on bacteria
structure
subgingival
biofilm
debridement
_Eubacterium_
pathogens
supragingival
biofilm
chemical agents
chemical control
control
debridement
mechanical control
removal
vehicles for delivery of chemical agents
treatment comparisons
Plaque Index (PLI)
plaque-inhibitory agents
evaluation
plasma cells
adaptive defense system
aggressive periodontitis
antibody production
gingival
gingivitis
necrotizing
plasma immunoglobulins
plasmatic circulation
plastic surgery _see_ microsurgery; mucogingival therapy
platelet-derived growth factor (PDGF)
alveolar bone healing
ridge augmentation
platelets
aggregation
tooth socket healing
pneumonia, bacterial
pocket probing depth (PPD)
endodontic lesions
angular bone defects
peri-implant lesions
regenerative therapy
risk assessment
single-tooth replacement
soft tissue around implants
polyethylene glycol (PEG)
hydrogel membranes
PTH carrier
polyglycolic acid
bioabsorbable barrier membrane
polylactic acid
bioabsorbable barrier membrane
polymer grafts
polymerase chain reaction (PCR)
biofilm bacterial detection/enumeration
polymorphonuclear leukocytes (PMNs)
aggressive periodontitis
chronic periodontitis risk
dental pulp infection
diabetes mellitus
gingival crevice
gingivitis
host defense
processes
migration
peri-implantitis
pocket epithelium
pulp inflammatory response
smoking
polyphosphates
polytetrafluoroethylene, expanded (e-PTFE)
BMP effects
lateral bone augmentation for posterior implants
maxillary anterior single-tooth replacement
papilla preservation flap combination
pedicle soft tissue graft for root coverage
ridge augmentation
pontic
central
contour refinement
porcelain-fused-to-metal alloys
_Porphyromonas_ , root canal infection
_Porphyromonas gingivalis_
adherence
aggressive periodontitis
alveolar bone loss
antibiotics
local delivery
microbiologic tests
susceptibility
systemic
antibody titers
Arg1-protease production
biofilm
composition
content
implant surfaces
cardiovascular disease
carotid endarterectomy
destructive periodontal disease
diabetes mellitus
elimination by extraction of all teeth
endothelial cell invasion
HIV infection
immune response
immunization studies
infection
mixed with _T. forsythia_
invasion
iron levels in environment
linear gingival erythema
pathogenic potential
peri-implant infection
periodontal disease history
subgingival
periodontal abscesses
periodontal lesions in diabetes
polymicrobial microbiota
pregnancy exposure
prevalence in periodontal disease
protease production
smoking association
suppression
transmission
virulence factors
posterior dentition implants
clinical applications
distally shortened arch
fixed implant-supported prostheses
multiple-unit tooth-bound restorations
screw-retained restorations
single-tooth replacement
potassium salts
desensitizing
root dentin hypersensitivity
pouch graft procedures
povidone iodine, plaque control
predentin
pre-eclampsia
periodontal disease
pregnancy
adverse outcomes with periodontitis
complications
gingival disease
gingival keratinization reduction
gingivitis
loss
medications
periodontal effects
periodontal treatment
periodontitis
treatment effects
plaque immune response suppression
pregnancy granuloma
pregnancy tumor
pre-medication
premolars
implants
mandibular
maxillary
root anatomy variation
root separation and resection
single-tooth restoration
vertical root fracture diagnosis
presbyopia
pressure zones
preterm birth
infection
periodontal disease
_Prevotella_
aggressive periodontitis
root canal infection
_Prevotella intermedia_
biofilm
content
implant surfaces
coronary heart disease
diabetes mellitus
HIV infection
linear gingival erythema
necrotizing periodontal disease
peri-implant infection
periodontal disease history
subgingival
periodontal abscesses
plaque formation
pregnancy gingivitis
prevalence in periodontal disease
pubertal gingivitis
smoking association
virulence
_Prevotella melaninogenica_
_Prevotella nigrescens_
peri-implant infection
prism loupes
probing _see_ periodontal probing
probing attachment level (PAL)
assessment
basic periodontal examination
inherent errors
measurement errors
peri-implant soft tissue
periodontal disease after scaling and root planing
periodontal tissue regeneration assessment
supportive periodontal therapy
probing pocket depth (PPD)
assessment
attachment loss
basic periodontal examination
inherent errors
measurement errors
reduction
treatment comparisons
trauma from occlusion
progesterone
hormonal contraceptives
pregnancy
tissue response
progestins, gingival disease
prognostic factors
pro-inflammatory mediators
prostaglandin E2
crevicular fluid levels in aggressive periodontitis
pregnancy
preterm birth
prostaglandins
prosthetic components of implants
protease inhibitors
proteases
periodontal infections
plaque control
proteoglycans
proteolytic enzymes
pseudo-halitosis
therapy
pseudomembrane
_Pseudomonas aeruginosa_
antibiotic resistance
biofilm
pseudopockets
psychiatric/psychological issues, implant patient
psychosocial factors, periodontitis
puberty
gingivitis
periodontal effects
_see also_ adolescents
pulp, dental
accessory canal communication
defense potential
disease
causes
processes
progression
dynamic events
exposure to oral environment
fibrosis
infection
inflammatory processes
root canal system infection
inflammatory responses
intra-pulpal mineralizations
necrosis
periodontal disease influence
periodontal treatment effects
sensibility
tissue necrosis
vitality
lost
testing
pulpal axons, terminal branch sprouting
pulpal pathosis
pyogenic granuloma pregnancy-associated
pyrophosphates
quaternary ammonium compounds
questions, open-ended
quorum sensing, biofilms
race/ethnicity
factors in necrotizing periodontal disease
periodontal disease
radiation detectors
radiation therapy, implant patient
radiographic analysis
alveolar bone
periodontal regeneration assessment
radiography
abutment placement
aggressive periodontitis
ALARA principle
alveolar crest for implant placement
bone loss
chronic periodontitis
condition of remaining teeth
dosage
furcation involvement
implant patient
treatment monitoring
implant planning
lower jaw imaging
lacement
upper jaw imaging
intraoral
radiation detectors
necessary information
osseointegration failure
osseous lesions
palatal implant insertion sites
panoramic
periodontal disease progression
reference
root resorption
surgical site
threaded implants
RANKL
reactive oxygen species
reattachment procedures
receptor activator of nuclear factor-kappa beta (RANK)
receptors for advanced glycation endproducts (RAGEs)
reduced dental epithelium
re-entry operations, periodontal regeneration assessment
reflection
regenerative periodontal surgery
bacterial contamination control
barrier materials
furcation involvement
barrier membranes
biologically active materials
bone replacement grafts
complications
coverage of regenerated tissue
crestal incision
furcation defects
barrier membranes
infection control regime
minimally invasive technique
modified papilla preservation technique
oral hygiene
orthodontic tooth movement
outcomes
papilla preservation flap
intrabony defects
modified
simplified
papilla preservation modified technique
post-operative morbidity
post-operative regime
suturing approach
regenerative periodontal therapy
barrier membranes
benefits
biologically active regenerative materials
bone grafts
replacement
clinical efficacy
clinical strategies
defect factors
effectiveness
enamel matrix derivatives
evidence-based strategy
indications
long-term effects
material selection
patient factors
PDGF
periodontal infection
prognostic factors
smoking
surgical approach
tooth factors
tooth survival
_see also_ root surface, biomodification
regulons
relative risk
removable partial dentures (RPD)
re-osseointegration
definition
implant surface quality
resonance frequency analysis, implants
respiratory burst
respiratory tract
infections and periodontitis
upper and extraoral halitosis
restorative dentistry
defective margins
dental pulp diseases
gingival dimensions
implants
shortened dental arch complex
treatment
concepts
goals
retainers
rete pegs
retention assessment
reticulin fibers
rheumatic endocarditis, surgery contraindication
ridge mucosa
risk assessment
alveolar bone loss
attachment loss
bleeding on probing
calculation
continuous multi-level
furcation involvement
iatrogenic factors
oral hygiene
periodontitis
pocket probing depth
process
clinical implementation
recall system compliance
relative risk
site
smoking
subject
systemic disease
tooth
loss
mobility
risk factors for periodontal disease
potential/putative
true
roll flap procedure
roll with resistance
rongeurs
root
coefficient of separation
degree of separation
development
divergence
iatrogenic perforation
sealing
intra-alveolar displacement
mechanical cleaning of surfaces
morphology alterations
resorption
clinical presentation
external
external inflammatory
forms
identification
peripheral inflammatory
replacement
surface
trigger mechanism
sensitivity with non-surgical treatment
stability
support remaining
trunk
length
vertical fractures
clinical expressions
diagnosis
incidence
mechanisms
treatment
_see also_ furcated region; furcation
root canal infection
bacteria
endodontic lesions
eriodontal tissue response
treatment
root canal system, accessory canals
root cementum
patient examination
periodontal ligament
root complex
root cones
divergence
fusion between
length
shape
root coverage
advanced flap procedure
clinical outcome
connective tissue graft
conventional surgery
coronally advanced flaps
healing
for multiple recessions
double papilla flap
epithelialized soft tissue graft
exposed root surface treatment
extent
flap tension elimination
free soft tissue graft procedure
epithelialized
healing
thickness
gingival margin position
guided tissue regeneration
healing
interdental support
microsurgery
pedicle graft procedures
combined with barrier membrane
with enamel matrix derivatives
healing
procedures
rotational flap procedure
semilunar coronally repositioned flap procedure
soft tissue healing
root debridement
ablative laser therapy
calculus removal
full-mouth disinfection
furcation involvement
hand instrumentation
method selection
non-surgical methods
reciprocating instruments
sonic scalers
subgingival biofilm influence
ultrasonic scalers
root dentin hypersensitivity
root planing
chlorhexidine use
_see also_ scaling and root planing
root separation and resection
mandibular molars
maxillary molars
maxillary premolars
periodontal surgery
prosthetic restoration
treatment sequence
root surface
biomodification
conditioning
demineralization
exposed
instrumentation
tetracycline biomodification
root-filled teeth
dentin dehydration
fracture propensity
infection
moisture content
rotational flap procedure, root coverage
salifluor
saline
antimicrobial activity
sterile physiologic
saliva, innate mechanisms
sanguinarine
sarcoidosis
saucerization
scalers
sonic/ultrasonic
scaling
necrotizing periodontal disease
periodontal abscesses
periodontal therapy
_Tannerella forsythia_ control
scaling and root planing
attachment gain
chronic periodontitis
full-mouth disinfection
furcation involvement
impaired access
local antibiotic delivery comparison
new attachment
pain
periodontal disease prevention
periodontal therapy
systemic antibiotics
_Tannerella forsythia_ control
scanograms
scars, dental pulp diseases
Schwartzman reaction
scleroderma, implant patient
screw-retained restorations
transocclusal
transverse
scurvy
chronic periodontitis
selection bias
selective estrogen receptor modulators (SERMs)
_Selenomonas_
necrotizing periodontal disease
self-efficacy, support
self-inflicted injuries
semilunar ganglion
sensibility tests
sex steroid hormones
chronic periodontitis
gingival disease
_see also_ estrogen; progesterone
Sharpey's fibers
alveolar bone proper
mineralization
shear force, biofilms
shortened dental arch (SDA)
simple tandem repeats (STRs)
single nucleotide polymorphisms (SNPs)
sinusitis
maxillary sinus floor elevation
size discrimination
Sjögren's syndrome
biofilm composition
implant patient
skatole
skeletal anchorage systems
sleep, inadequate
small-for-gestational-age births
smile line assessment
smoking
alveolar bone loss
antibiotic therapy regimens
biofilm composition
bone effects
cessation
motivational interviewing
counseling
estrogen levels
_Eubacterium_ infection
gingiva
gingival crevice fluid effects
gingivitis
healing effects
host response
host susceptibility to disease
_IL1_ gene polymorphisms
immune system effects
implant patient
implant risks
inflammatory system effects
inhalation
maxillary sinus floor elevation
osteoporosis effects
patient examination
periodontal disease
necrotizing
periodontitis
aggressive
chronic
probing depth
regenerative periodontal therapy
risk assessment
smoke composition/exposure
surgery contraindication
vascular effects
socioeconomic status in periodontitis
socket former
sodium chlorite, acidified
sodium fluoride, chlorhexidine synergism
sodium lauryl sulfate
antimicrobial activity
plaque control
sodium valproate, gingival overgrowth
soft tissue
damage from interdental cleaning
morphology for bone regeneration
recession
_see also_ gingiva
soft tissue curettage
soft tissues, peri-implant
evaluation
somatosensory system, oral
functional testing
specific plaque hypothesis
sphenopalatine nerve, long
spirochetes
biofilm
decrease with periodontal infection treatment
invasion
necrotizing gingivitis
peri-implant infection
periodontal abscesses
splinting
implants
orthodontic treatment
tooth mobility
split flap procedure
spongy bone
sprays
chlorhexidine
stannous fluoride
halitosis treatment
_Staphylococcus_ , peri-implant infections
_Staphylococcus epidermidis_
stereognosis, oral
compromising factors
receptor activation
stillbirth, periodontal treatment
stomatitis
denture
chlorhexidine use
necrotizing
diagnosis
stratum corneum
stratum germinativum
stratum granulosum
streptococci
bacterial coaggregation
biofilm formation
colonization
dental plaque development
"milleri"
_Streptococcus anginosus_
_Streptococcus constellatus_
_Streptococcus intermedius_
peri-implant microbiota
_Streptococcus mitis_
biofilm formation
_Streptococcus mutans_
_Streptococcus oralis_
_Streptococcus sanguinis_
coaggregation
growth inhibition
hydrogen peroxide production
plaque formation
virulence factors
stress
chronic periodontitis
dental procedures
halitosis
hypoglycemia
necrotizing periodontal disease
periodontitis
stripping, mesio-distal enamel reduction
stroke, periodontal infection
strontium salts
subepithelial plexus
subgingival irrigation
sublingual artery
sublingual nerve
sublingual region
submandibular lymph nodes
submandibular region
submental artery
submental lymph nodes
substance use/abuse, implant patient
sulfide monitor
Summers technique
supportive periodontal therapy
clinical attachment level
clinical implementation
continuous multi-level risk assessment
in daily practice
examination, re-evaluation and diagnosis (ERD)
gingivitis
lack in disease-susceptible individuals
maintenance care visits
motivation, reinstruction and instrumentation (MRI)
objectives
periodontitis
polishing, fluorides, determination of recall interval (PFD)
treatment of reinfected sites (TRS)
suppuration, risk assessment
suprabony defects
supraperiosteal blood vessels
gingiva
peri-implant mucosa
surgery
access therapy
aggressive periodontitis
attachment gain
bone fill in angular bone defects
chlorhexidine use
chronic periodontitis
comparison with non-surgical treatment
contraindications
distal wedge procedures
edentulous ridge augmentation
guidelines
healing
image-guided
indications
techniques
infection control
instrumentation
local anesthesia
minor with orthodontic treatment
objectives
osseous
outcomes
patient cooperation
periodontal abscesses
periodontal dressings
post-operative care
post-operative pain control
pre-operative chlorhexidine rinsing/irrigation
root separation and resection
root surface conditioning/biomodification
suturing
technique selection
visibility in field of operation
wound stability
_see also_ flap procedures; gingivectomy; grafting procedures; microsurgery; mucogingival therapy; regenerative periodontal surgery; sutures/suturing
surgical guide
surgical site for implants
anatomic landmarks with potential risk
clinical examination
healing time
implant placement
direction/inclination
position of implant
radiographic examination
sutures/suturing
bacteriostat-coated
continuous
interrupted dental
intraoral tissue reactions
microsurgery
modified mattress
needle
non-resorbable
removal
resorbable
suspensory
technique
swabs
systemic disease
aggressive periodontitis association
chronic periodontitis risk
extraoral halitosis
gingival disease association
halitosis
historical concepts
oral infections
periodontal disease
manifestation
necrotizing
risk
periodontitis
aggressive
chronic
treatment effects
risk assessment
treatment considerations
_see also_ diabetes mellitus; leukemia
systemic lupus erythematosus (SLE)
implant patient
T cell receptors (TCRs)
T cells
adaptive defense system
aggressive periodontitis
migration
smoking effects
T helper (Th) cells
tactile function
dental status
oral stereognosis
testing
_Tannerella forsythia_
aggressive periodontitis
biofilm
composition
cardiovascular disease
carotid endarterectomy
destructive periodontal disease
invasion
mixed infection with _P. gingivalis_
peri-implant infection
periodontal disease history
periodontal abscesses
polymicrobial microbiota
prevalence
serum antibodies
S-layer
smoking association
tea tree oil
temporary anchorage devices (TAD)
temporomandibular joint (TMJ) receptors
tension zones
tetracycline
activity
adverse reactions
controlled-release
non-resorbable plastic co-polymer
root surface biomodification
therapeutic alliance
thermal stimulation
thermoreceptors
thiocyanate
tin salts
titanium pins
_TNFA_ gene
_TNFA R_ -alleles
toll-like receptors (TLRs)
gene polymorphisms
tomography
conventional
incorrectly placed implants
lower jaw
vertical root fractures
_see also_ computed tomography (CT) ; digital volume tomography (CT)
tongue
bacterial load
cleaning
tongue cleaners
tongue coating
index systems
tongue scraper
tonofilaments
tonsilloliths (tonsil stone)
tooth
abrasion
autotransplantation
bodily movement
cleaning
biofilms
professional
eruption
ectopic
forced
hopeless
extrusion
orthodontic extraction
innervation
lengthening
periodontal infections
position within dental arch
pre-therapeutic single tooth prognosis
risk assessment
single and implant decisions
esthetic zone
strategically important missing
survival with regenerative periodontal therapy
total clearance
tooth bud
tooth extraction
alveolar process adaptation
alveolar ridge healing
bone resorption
implant placement immediately following
intra-alveolar processes
multiple
socket
bone fill
changes
completed soft tissue coverage
healing
soft tissue collapse prevention
tooth germ
tooth loss
alveolar ridge atrophy
gingival inflammation
periodontal abscesses
periodontal disease
prevalence
periodontitis
risk assessment
tooth mobility
automated probing systems
basic periodontal examination
bridges
mobility increase
clinical assessment
horizontal forces
increased
increased periodontal ligament width
normal periodontal ligament width
initial
mechanisms
pathologic
patient examination
periodontal disease
physiologic
rogressive
reduced periodontal ligament
regenerative periodontal therapy
risk assessment
secondary
splinting
trauma from occlusion
treatment
tooth movement
direction
gingival recession
implant esthetics
orthodontic
adults
adults with periodontal tissue breakdown
compromised bone areas
forced tooth eruption
infrabony pockets
regenerative procedures
single teeth extrusion/intrusion
through cortical bone
pathologic
periodontally compromised patient
root surface resorption
tooth powders
tooth size discrepancies (TSD) correction
tooth socket
bone fill
changes
completed soft tissue coverage
tooth socket healing
blood clot formation
bone marrow
bundle bone
connective tissue
edentulous alveolar ridge topography
fibrinolysis of blood clot
granulation tissue
hard tissue cap
lamellar bone
osteoid formation
osteons
tissue formation
wound cleansing
woven bone
tooth towelettes
toothbrush trauma
gingival recession
toothbrushes
abrasion
chemical
electric
efficacy
electrically active
end-tufted
filaments
end-rounding
tapering
wear
foam
instruction
ionic
manual
replacement
single-tufted
sonic
wear
toothbrushing
Bass technique
circular
duration
efficacy
force
frequency
gingival lesions
horizontal
ineffective
instruction
methods
modified Bass/Stillman technique
plaque build-up prevention
roll technique
scrubbing
sulcular
vertical
vibratory technique
tooth–implant supported reconstructions
toothpaste
abrasives
abrasivity
active ingredients
allergic reactions
chemical agent delivery
chlorhexidine
detergents
flavors
fluoride
home use studies
humectants
potassium-containing
standards
sweeteners
thickeners
triclosan-containing
_see also_ dentifrices
toothpicks
total tooth clearance
toxic reactions in periodontium
transeptal fibers
transforming growth factor β (TGF-β)
alveolar bone healing
hereditary gingival fibromatosis
ridge augmentation
transmucosal attachment
transpalatal arch (TPA)
transposon transfer
trauma
dental pulp diseases
foreign body reactions
gingival lesions
gingival recession
hard tissue
instrumentation
mechanical cleaning
non-surgical therapy
orthodontic
physical injury
root resorption
peripheral inflammatory
surface
self-inflicted injuries
thermal injury
toothbrush
ulcerative gingival lesion
_see also_ jiggling-type trauma
trauma from occlusion
alveolar bone loss
alveolar pyorrhea association
angular bony defects
animal experiments
bone regeneration
clinical trials
Glickman's concept
human autopsy material
infrabony pockets
jiggling-type
orthodontic treatment
orthodontic-type
peri-implant tissues
periodontal ligament
periodontitis
plaque-associated periodontal disease
primary
secondary
tooth mobility
Waerhaug's concept
zone of co-destruction
zone of irritation
treatment
aggressive periodontitis
allergic reactions
anxiety control
bleeding risk
cardiovascular disease effects
cardiovascular incidents
case presentation
cause-related
complications prevention
corrective phase
definitions
dentin removal
diabetes mellitus
drug interactions
effectiveness
evaluation of non-surgical therapy
furcation-involved teeth
gingival recession
goals
infectious complications
initial phase
maintenance phase
needs assessment
non-surgical
discomfort
outcome prediction
pain
probing measurements
re-evaluation
root debridement
root sensitivity
surgery comparison
tissue trauma
treatment evaluation
outcome parameters
pain control
planning
chronic periodontitis
implants in periodontally compromised patient
initial
pregnancy
outcomes
pre-medication
pre-therapeutic single tooth prognosis
prognosis
pulp effects
re-evaluation
after corrective phase
non-surgical therapy
spontaneous abortion
stillbirth
supportive
systemic disease
systemic phase
_Tannerella forsythia_ control
_see also_ supportive periodontal therapy; surgery
tremor, microsurgeons
_Treponema_ , necrotizing periodontal disease
_Treponema denticola_
biofilm
composition
implant surfaces
cardiovascular disease
peri-implant infection
periodontal disease history
peri-implant microbiota
periodontal disease
_Treponema pallidum_
_Treponema socranskii_
beta-tricalcium phosphate (β-TCP)
triclosan
antimicrobial activity
halitosis treatment
plaque control
suture coating
trigeminal nerve
neurophysiology
neurosensory pathway
trigeminal somatosensory evoked potentials (RSEP)
trimethylaminuria
tropocollagen
tuberculosis, dental team protection
tumor necrosis factor α (TNF-α)
diabetes mellitus
genes
pregnancy
preterm birth
tunnel preparation
two-point discrimination
ulcerative lesions gingival disease
recurrent
traumatic gingival
vaccines, periodontal disease
vaginosis, bacterial
valaciclovir
variable number of tandem repeats (VNTR)
varicella-zoster
varnishes
chlorhexidine
vasoconstrictors
_VDR_ gene polymorphisms
_Veillonella_ , plaque formation
verapamil, gingival overgrowth
vibrio corroders
Vincent's angina
_see also_ necrotizing ulcerative gingivitis (NUG)
viral infections
chlorhexidine activity
gingival disease
necrotizing periodontal disease
_see also_ HIV infection
virulence factors
aggressive periodontitis bacteria
environmental effects on expression
expression
immune pathology
killing other pathogens
periodontal infections
tissue damage
visual acuity
vitamin C deficiency
chronic periodontitis
vitamin D receptor gene polymorphisms
vitamin K
volatile sulfur compounds
formation
measurement
Volkmann's canals
water jet, dental
whitening agents
hydrogen peroxide
Widman flap
healing
modified
Winkel Tongue Coating Index (WTCI)
woodsticks
use
World Health Organization (WHO), periodontal treatment needs
wound cleansing
osseointegration
tooth socket healing
wound healing
bone cell regenerative capacity
enamel matrix derivatives
epithelium role
gingival connective tissue cells
impairment
implants
onlay graft procedures
PDGF
periodontal
periodontal ligament cells
root resorption
woven bone osseointegration
peri-implant loss
resorption
tooth socket healing
xenografts
xerostomia
halitosis
implant patient
zinc salts
Zirconia
zygomatic anchors
| {
"redpajama_set_name": "RedPajamaBook"
} | 3,964 |
\section{Introduction}
The QCD phase diagram is essential for understanding not only natural
phenomena such as compact stars and the early universe but also laboratory
experiments such as relativistic heavy-ion collisions.
Quantitative calculations of the phase diagram from the first-principle
lattice QCD (LQCD) have the sign problem at real quark chemical potential
($\mu_{\rm q}$).
Though several approaches have been proposed to circumvent the difficulty,
these are still far from perfection.
As an approach complementary to the first-principle LQCD, we can consider
effective models such as the Nambu--Jona-Lasinio (NJL) model and the
Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model.
The NJL model describes the chiral symmetry breaking, but not the confinement
mechanism. The PNJL model is constructed so as to treat both the mechanisms.
In the NJL-type models, the input parameters are determined at $\mu_{\rm q}=0$.
It is then highly nontrivial whether the models predict the dynamics of QCD at
finite $\mu_{\rm q}$ properly. This should be tested from QCD.
Fortunately, this is possible in some regions without sign problem,
such as imaginary $\mu_{\rm q}$, real and imaginary isospin chemical potential
($\mu_{\rm I}$).
In this paper, we consider two-flavor QCD and show the reliability of the PNJL
model by comparing the model result with LQCD data in their regions.
\section{Imaginary Quark Chemical Potential}
Roberge and Weiss~\cite{RW} found that the thermodynamic potential,
$\Omega_{\rm QCD}(\theta_{\rm q})$, of QCD at imaginary chemical potential
$\mu_{\rm q}=i\theta_{\rm q}T$ has a periodicity
$\Omega_{\rm QCD}(\theta_{\rm q}) = \Omega_{\rm QCD}(\theta_{\rm q} + 2\pi k/3)$, showing that $\Omega_{\rm QCD}(\theta_{\rm q} + 2\pi k/3)$ is transformed
into $\Omega_{\rm QCD}(\theta_{\rm q})$ by the $\mathbb{Z}_3$ transformation
with integer $k$.
This means that QCD is invariant under a combination of the $\mathbb{Z}_3$
transformation and a parameter transformation
$\theta_{\rm q}\rightarrow\theta_{\rm q}+2\pi k/3$.
We call this combination the extended $\mathbb{Z}_3$ transformation.
Thus, $\Omega_{\rm QCD}(\theta_{\rm q})$ has the extended $\mathbb{Z}_3$
symmetry, and hence quantities invariant under the extended $\mathbb{Z}_3$
transformation have the RW periodicity~\cite{Sakai-1}.
We reveal that the PNJL model has the RW periodicity~\cite{Sakai-1}.
The two-flavor PNJL Lagrangian~\cite{Fukushima} in Euclidean spacetime is
\begin{eqnarray}
{\cal L}=\bar{q}(i\gamma_\nu D_\nu-\gamma_4\mu_{\rm q}+m_0)q
-G_{\rm s}[(\bar{q}q)^2+
(\bar{q}i\gamma_5\vec{\tau}q)^2]+U_{\Phi}(\Phi[A],\Phi^*[A],T),
\label{Eq2-1}
\end{eqnarray}
where $q$ denotes the two-flavor quark field, $m_0$ does the current quark mass, and $D_{\nu}=\partial_{\nu}-iA_{\nu}\delta_{\nu 0}$ with the gauge field
$A_{\nu}$.
In the chiral limit ($m_0=0$), the Lagrangian density has the exact
$SU(2)_{\rm R}\times SU(2)_{\rm L}\times U(1)_{\rm v}\times SU(3)_{\rm c}$
symmetry.
The Polyakov potential $U_{\Phi}$~\cite{Rossner} is a function of the Polyakov
loop $\Phi=\frac{1}{3}{\rm tr_c}~L$ with $L=e^{iA_4/T}$ and its Hermitian
conjugate $\Phi^*$.
The PNJL thermodynamic potential $\Omega$ in the mean field approximation
(MFA) is
\begin{eqnarray}
\Omega=-4\int\frac{d^3{\bf p}}{(2\pi)^3}
\Bigl[3\epsilon({\bf p})+T\sum_{\lambda=\pm 1}
{\rm ln~det_c}(1+L^{\lambda}e^{-\epsilon({\bf p})/T+i\lambda\theta_{\rm q}})
\Bigr]+G_{\rm s}\sigma^2+U_{\Phi},
\label{Eq2-2}
\end{eqnarray}
where $\epsilon=\sqrt{{\bf p}^2+M^2}$, $M=m_0-2G_{\rm s}\sigma$,
and $\sigma=\langle\bar{q}q\rangle$.
The thermodynamic potential $\Omega$ is invariant
under the extended $\mathbb{Z}_3$ transformation,
\begin{eqnarray}
L\rightarrow e^{-i2\pi k/3}L,~~
\theta_{\rm q}\rightarrow\theta_{\rm q}+2\pi k/3.
\label{Eq2-3}
\end{eqnarray}
Therefore, $\Omega$ has the RW periodicity.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth,angle=-90]{Fig1.eps}
\end{center}
\caption{
Phase diagram in the real and imaginary $\mu_{\rm q}$ regions by
the PNJL model with the parameter set~\cite{Sakai-1} that reproduces
the LQCD data at imaginary $\mu_{\rm q}$.
The points ${\rm E_{RW}}$ and ${\rm E_{C}}$ are the endpoints
of the RW transition and the first-order chiral transition
respectively.
The solid line denotes the first-order chiral transition,
the dashed (dotted) line does the crossover deconfinement (chiral)
transition, and the dot-dashed line does the RW transition.
Lattice data ($\times$) are taken from~\cite{LQCD-1}.}
\label{Fig1}
\end{figure}
At the present stage, the PNJL model is only a realistic effective model that
possesses both the extended $\mathbb{Z}_3$ symmetry and the chiral symmetry
~\cite{Sakai-1}.
This property guarantees that the phase diagram evaluated by the PNJL model
has the RW periodicity in the imaginary $\mu_{\rm q}$ region, and therefore
makes it possible to compare the PNJL result with LQCD data
quantitatively in the imaginary $\mu_{\rm q}$ region.
Actually, the PNJL model succeeds in reproducing the LQCD data~\cite{LQCD-1}
by introducing the vector-type four-quark interaction and the scalar-type
eight-quark interaction~\cite{Sakai-1}.
The QCD phase diagram in the real $\mu_{\rm q}$ region is
predicted by the PNJL model with the parameter set~\cite{Sakai-1}
that reproduces the LQCD data at imaginary $\mu_{\rm q}$, as shown in
Fig.~\ref{Fig1}.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.4\textwidth]{Fig2-a.eps}
\includegraphics[width=0.4\textwidth]{Fig2-b.eps}
\end{center}
\caption{
Phase diagrams of the deconfinement and the RW phase transition
in the $\theta_{\rm q}-T$ plane
with RRW-type $U_{\Phi}$~\cite{Rossner}
(panel (a)) and F-type $U_{\Phi}$~\cite{Fukushima} (panel (b)).
The solid (dashed) line denotes the first-order (crossover) deconfinement
transition, and the dot-dashed line does the RW transition.
Point ${\rm E_{RW}}$ is the endpoint of the RW transition.
Lattice data (+) are taken from~\cite{LQCD-1}.}
\label{Fig2}
\end{figure}
The phase diagrams of the deconfinement and the RW phase transition in the
$\theta_{\rm q}-T$ plane by using the PNJL models with
RRW-type $U_{\Phi}$~\cite{Rossner} and F-type $U_{\Phi}$~\cite{Fukushima} are
shown in Fig.~\ref{Fig2} (a) and (b), respectively.
Thus, the PNJL model with RRW-type $U_{\Phi}$ reproduces
LQCD data~\cite{LQCD-1} at finite $\theta_{\rm q}$, but the model with F-type
$U_{\Phi}$ doesn't.
In this sense, the PNJL model with RRW-type $U_{\Phi}$ calculation is more
reliable.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.40\textwidth]{Fig3-a.eps}
\includegraphics[width=0.40\textwidth]{Fig3-b.eps}
\end{center}
\caption{
(a) The phase structure near ${\rm E_{RW}}$ with RRW-type $U_{\Phi}$
is magnified.
The solid (dashed) line denotes the first-order (crossover)
deconfinement transition, and the dot-dashed line does the RW transition.
Points ${\rm E_{RW}}$ and CP are an endpoint of the RW transition and critical
endpoints, respectively.
(b) $T$ dependence of
the chiral and Polyakov-loop susceptibilities, $\chi_{\sigma}$ and
$\chi_{\Phi}$, at the point CP.
}
\label{Fig3}
\end{figure}
The phase diagram for RRW-type $U_{\Phi}$ near ${\rm E_{RW}}$ is
magnified in Fig.~\ref{Fig3} (a).
The RW endpoint is first order for RRW-type $U_{\Phi}$, but it's second
order for F-type $U_{\Phi}$~\cite{Sakai-2}.
Thus, the order of the deconfinement phase transition near the RW endpoint
strongly depends on $U_{\Phi}$ taken.
The result of the PNJL calculation with RRW-type $U_{\Phi}$ is consistent with
the LQCD data~\cite{LQCD-2}
where the order of the RW phase transition at ${\rm E_{RW}}$ is first order
for small quark mass.
Point ${\rm E_{RW}}$ is the triple point where the three
first-order lines meet. Thus, there are two critical endpoints (CP) for each
triple point ; CP is a point where the crossover and the first order lines
meet.
Figure~\ref{Fig3} (b) shows the chiral and the Polyakov loop susceptibilities,
$\chi_{\sigma}$ and $\chi_{\Phi}$, as a function of $T$ near CP.
The susceptibilities are divergent at CP.
Hence, the chiral and deconfinement transitions are second order at CP.
\section{Imaginary Isospin Chemical Potential}
LQCD has no sign problem at both real and imaginary $\mu_{\rm I}$.
Recently, LQCD data were measured there and also in the case where both
$\mu_{\rm I}$ and $\mu_{\rm q}$ are imaginary~\cite{LQCD-3}.
In the chiral limit, QCD has the chiral $SU_{\rm L}(2)\times SU_{\rm R}(2)$
symmetry when $\mu_{\rm I}=0$.
However, at $\mu_{\rm I}\ne 0$ this symmetry is reduced to
$U_{\rm I_3}(1)\times U_{\rm AI_3}(1)$, where $U_{\rm I_3}(1)$ is the isospin
subgroup and $U_{\rm AI_3}(1)$ is the axial isospin subgroup.
In the case $m_u=m_d\ne 0$, only the $U_{\rm I_3}(1)$ symmetry survives.
When QCD vacuum keeps the $U_{\rm v}(1)$ and $U_{\rm I_3}(1)$ symmetries,
the baryon charge $B=V\langle\hat{B}\rangle$ is either zero or integer and the isospin
charge $I_3=V\langle\hat{I}_3\rangle$ is also
either zero or half-integer, where
$\hat{B}=\bar{q}\gamma_4 q, \hat{I}_3=\bar{q}\gamma_4 I_3 q$ and $V$ is the volume.
In the partition function $Z$, the baryon- and the isospin-charge operator appear
through the form $\exp[V(2i\theta_{\rm I}\hat{I}_3 + i \theta_{\rm q}\hat{B})]$
where $\mu_{\rm q, I}=iT\theta_{\rm q, I}$.
Therefore, $Z$ has the periodicity
$Z(\theta_{\rm q}, \theta_{\rm I})=Z(\theta_{\rm q}, \theta_{\rm I}+2\pi)$.
In the isospin symmetric limit $m_u=m_d$, $Z$ is invariant under the interchange
$u \leftrightarrow d$, i.e. $\theta_{\rm I}\rightarrow-\theta_{\rm I}$.
Hence, $Z$ is invariant under charge conjugation, both
$\theta_{\rm q}\rightarrow-\theta_{\rm q}$ and
$\theta_{\rm I}\rightarrow-\theta_{\rm I}$.
Furthermore we have proved that $Z$ has the RW periodicity at
$\theta_{\rm I}\ne 0$~\cite{Sakai-2}.
All the relations are summarized as
\begin{eqnarray}
Z(\theta_{\rm q}, \theta_{\rm I})=Z(\pm\theta_{\rm q}, \mp\theta_{\rm I})=
Z(\theta_{\rm q}, \theta_{\rm I}+2\pi)=Z(\theta_{\rm q}+2\pi/3, \theta_{\rm I}).
\label{Eq3}
\end{eqnarray}
Meanwhile, if the pion condensation occurs, the $U_{\rm I_3}(1)$ symmetry is
spontaneously broken and the isospin charge is neither zero nor
half-integer anymore. In this situation, QCD vacuum doesn't have the
periodicities (\ref{Eq3}).
We have proved that the pion condensation doesn't take place at imaginary
$\mu_{\rm I}$~\cite{Sakai-2}.
This can be understood intuitively.
For real $\mu_{\rm I}$, the Bose-Einstein distribution function has an
infrared divergence at $\mu_{\rm I}\ge m_{\pi}/2$.
This induces the Bose-Einstein Condensation, that is, the pion condensation.
For imaginary $\mu_{\rm I}$, such a divergence never happens and hence no pion
condensation occurs.
As a result of this fact, $Z$ has all the discrete symmetries (\ref{Eq3}).
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.32\textwidth]{Fig4-a.eps}
\includegraphics[width=0.32\textwidth]{Fig4-b.eps}
\includegraphics[width=0.32\textwidth]{Fig4-c.eps}
\includegraphics[width=0.32\textwidth]{Fig4-d.eps}
\includegraphics[width=0.32\textwidth]{Fig4-e.eps}
\includegraphics[width=0.32\textwidth]{Fig4-f.eps}
\end{center}
\caption{
$\Omega/T^4$, $n_{\rm q}/T^3$ and $n_{\rm I}/T^3$
as a function of $\theta_{\rm q}$ and $\theta_{\rm I}$.
Panels (a), (b) and (c) correspond to $T=175$~MeV,
while panels (d), (e) and (f) to $T=250$~MeV.}
\label{Fig4}
\end{figure}
The absence of the pion condensation at imaginary $\mu_{\rm I}$ is true in
the PNJL model~\cite{Sakai-2}.
The PNJL thermodynamic potential at $\mu_{\rm I}\ne 0$ in the MFA is
\begin{eqnarray}
\Omega=-2\int\frac{d^3{\bf p}}{(2\pi)^3}\sum_{f=\pm 1}
\Bigl[3\epsilon_{f}({\bf p}) + T\sum_{\lambda=\pm 1}
{\rm ln~det_c}
(1+L^{\lambda}e^{-\epsilon_{f}({\bf p})/T+i\lambda\theta_{\rm q}})
\Bigr]+G_{\rm s}(\sigma^2+\pi^2)+U_{\Phi},~~~
\end{eqnarray}
where $\epsilon_\pm=\sqrt{(\epsilon({\bf p})\pm\mu_{\rm I})^2+N^2}$,
$N=2G_{\rm s}\pi$.
The pion condensate $\pi=\langle\bar{q}i\gamma_5\tau_1q\rangle$ is an order
parameter of the spontaneous breakings of the $U_{\rm I_3}(1)$ symmetry.
When there is no pion condensation, $\Omega$ is reduced to a simpler form
\begin{eqnarray}
\Omega=-2\int\frac{d^3{\bf p}}{(2\pi)^3}
\Bigl[6\epsilon({\bf p}) + T\sum_{\lambda,~f=\pm 1}
{\rm ln~det_c}(1+L^{\lambda}e^{-\epsilon({\bf p})/T+i\lambda\theta_{\rm q}
+if\theta_{\rm I}})\Bigr]+G_{\rm s}\sigma^2+U_{\Phi},
\end{eqnarray}
which is invariant under the extended
${\mathbb Z}_3$ transformation (\ref{Eq2-3}), therefore $\Omega$ has the RW
periodicity.
The potential $\Omega$ has also the periodicity of
$\theta_{\rm I}\rightarrow\theta_{\rm I}+2\pi$.
Furthermore $\Omega$ is invariant under the transformation,
$\theta_{\rm I}\rightarrow-\theta_{\rm I}$, and
also under the transformation, $\theta_{\rm q}\rightarrow-\theta_{\rm q}$ and
$L^{\pm}\rightarrow L^{\mp}$.
These properties guarantee that
the PNJL model possesses all the symmetries in (\ref{Eq3}), and the model
reproduces LQCD data~\cite{LQCD-3} qualitatively at imaginary $\mu_{\rm I}$
and $\mu_{\rm q}$.
Figure~\ref{Fig4} shows $\Omega/T^4$, ${\rm Im}[n_{\rm q}]/T^3$ and
${\rm Im}[n_{\rm I}]/T^3$ as a function of $\theta_{\rm q}$ and
$\theta_{\rm I}$ in the cases of $T=175$ and $250$~MeV.
Symmetries (\ref{Eq3}) are seen in Fig.~\ref{Fig4}.
This result is consistent with LQCD ones~\cite{LQCD-3}.
If the pion condensate is nonzero, symmetries (\ref{Eq3}) break down.
Hence, the fact that LQCD has symmetries (\ref{Eq3}) means
that the pion condensation doesn't occur also in LQCD.
As shown in Fig.~\ref{Fig2} (a) for $\theta_{\rm I}=0$, at temperature above
$T_{\rm RW}=190$~MeV, there is the RW phase transition at
$\theta_{\rm q}=\pi/3$ mod $2\pi/3$, where
$n_{\rm q}=-{\rm d}\Omega/{\rm d}(iT\theta_{\rm q})$ is discontinuous.
In Fig.~\ref{Fig4}, $T=175$ and $250$~MeV are typical temperatures below
and above $T_{\rm RW}$, respectively.
For any temperature, the RW periodicity is seen.
Below $T_{\rm RW}$, these quantities are smooth at any $\theta_{\rm q}$ and
$\theta_{\rm I}$.
In contrast, above $T_{\rm RW}$,
$\Omega$ and $n_{\rm I}$ have cusps at $\theta_{\rm q}=\pi/3$ mod
$2\pi/3$, while $n_{\rm q}$ is discontinuous there.
The discontinuity means the RW phase transition.
Eventually, the transition occurs at $\theta_{\rm q}=\pi/3$ mod $2\pi/3$
when $0\le\theta_{\rm I}<\pi/2$ and $\pi<\theta_{\rm I}\le 2\pi$,
and at $\theta_{\rm q}=0$ mod $2\pi/3$ when $\pi/2\le\theta_{\rm I}\le3\pi/2$~\cite{Sakai-2}.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=0.23\textwidth,angle=-90]{Fig5-a.eps}
\includegraphics[width=0.23\textwidth,angle=-90]{Fig5-b.eps}
\includegraphics[width=0.23\textwidth,angle=-90]{Fig5-c.eps}
\end{center}
\caption{
Phase diagram of the deconfinement phase transition in the $\theta_{\rm I}-T$
plane. Panels (a), (b) and (c) correspond to $\theta_{\rm q}=0, \pi/6$ and
$\pi/3$, respectively.
The solid (dashed) line denotes the first-order (crossover) transition.
The area labeled by 'RW' between the two dot-dashed
lines represents the region where the RW phase transition occurs.}
\label{Fig5}
\end{figure}
Figure~\ref{Fig5} shows the phase diagram of the deconfinement phase
transition in the $\theta_{\rm I}-T$ plane.
Near $\theta_{\rm I}=\pi/2$ mod $\pi$, the deconfinement phase transition is
first order in all panel (a)-(c). Near $\theta_{\rm I}=\pi$ mod $\pi$,
the deconfinement phase transition is first order at $\theta_{\rm q}=0$,
but crossover at $\theta_{\rm q}=\pi/6$ and $\pi/3$.
The RW phase transition occurs in the area labeled by 'RW' between the two
dot-dashed lines.
Quantitative comparison of the PNJL model with LQCD data~\cite{LQCD-3} is
made at $T\le T_{\rm c}$ by using the hadron resonance gas (HRG) model that
can reproduce the LQCD data there.
We have shown~\cite{Sakai-2} that the PNJL model reproduces the LQCD data
for the oscillatory patterns.
For the magnitudes, meanwhile, the PNJL model underestimates the LQCD result.
This discrepancy is understandable as follows.
Below $T_{\rm c}$, hadronic excitations are important, but such
an effect is not included in the MFA.
By adding the hadronic correction to the PNJL model, the model agrees with the
LQCD~\cite{Sakai-2}.
The HRG model works well at $T<T_{\rm c}$, but not
at $T>T_{\rm c}$; especially the HRG model doesn't reproduce the RW phase
transition. In contrast, the PNJL model with the hadronic correction works
both below and above $T_{\rm c}$.
\section{Real Isospin Chemical Potential}
LQCD data are available at real $\mu_{\rm I}$ and $\mu_{\rm q}=0$
~\cite{LQCD-4}.
The scalar-type eight-quark interaction is necessary to reproduce LQCD data
at imaginary $\mu_{\rm q}$~\cite{Sakai-1}.
Figure~\ref{Fig4} (a) shows the phase diagram of the PNJL model with the
scalar-type eight-quark interaction in the $\mu_{\rm I}-T$ plane at
$\mu_{\rm q}=0$.
The PNJL model with the eight-quark interaction is also consistent with the
LQCD at $\mu_{\rm I}\ne 0$~\cite{Sasaki}.
There is a tricritical point (TCP) where the first-order pion-superfluidity
phase transition line is connected to the second-order phase transition.
The critical points such as CEP and TCP are important as indicators
of the chiral and pion-superfluidity phase transitions at compact stars and
laboratory experiments where $\mu_{\rm I}$ is nonzero generally.
The TCP in the $\mu_{\rm I}-T$ plane at $\mu_{\rm q}=0$ is connected to the
CEP in the $\mu_{\rm q}-T$ plane at $\mu_{\rm I}=0$ in the
$\mu_{\rm q}-\mu_{\rm I}-T$ space~\cite{Sasaki}, as shown
in Fig.~\ref{Fig6} (b).
\begin{figure}[htbp]
\begin{center}
\begin{minipage}{0.47\textwidth}
\includegraphics[width=0.90\textwidth]{Fig6-a.eps}
\end{minipage}
\begin{minipage}{0.47\textwidth}
\hspace{-0.5cm}
\includegraphics[width=1.20\textwidth]{Fig6-b.eps}
\end{minipage}
\end{center}
\vspace{-1cm}
\caption{
(a) Phase diagram in the $\theta_{\rm I}-T$ plane at $\theta_{\rm q}=0$
with the eight-quark interaction.
The thick-solid (dashed) line denotes a first-order
(second-order) pion-superfluidity phase transition.
The dot-dashed (dotted) line denotes a deconfinement (chiral) crossover
transition. Lattice data are taken from~\cite{LQCD-4}.
(b) Phase diagram in the $\mu_{\rm I}-\mu_{\rm q}-T$ space
with the eight-quark interaction. Line ABC denotes the chiral CEP, ABD line
does the pion-superfluid TCP.
The CEP and the TCP coexist on line AB.
The solid (dashed) line denotes the first (second) order transition.
}
\label{Fig6}
\end{figure}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,872 |
Tring Park School for the Performing Arts is an independent co-educational school in Tring, Hertfordshire, England, offering specialist courses in Dance, Commercial Music, Musical Theatre and Acting for 8–19 year olds. Originally known as the Arts Educational School, Tring Park, it was founded as the sister school of the Arts Educational School, London. In 2009 it became independent of the London school and was renamed Tring Park School for the Performing Arts.
Overview
Tring Park School for the Performing Arts is an independent, co-educational boarding and day school for pupils aged 8–19 years. It comprises a preparatory school, lower school, secondary school and sixth form and at a professional level. It is a specialist provider of vocational training in the performing arts, with a syllabus that includes Dance, Acting, Commercial Music and Musical Theatre. Vocational studies are supported by a full academic syllabus from Prep to A-level. As one of the leading schools for the performing arts in the United Kingdom, it is one of only twenty-one schools selected to allocate Government funded Dance and Drama Awards, a scholarship scheme established to subsidise the cost of professional dance and drama training for the most talented pupils at leading institutions.
History
The school was first founded in 1939 and was originally known as the Cone-Ripman School. It was formed as a result of a merger between the Cone School of Dancing founded in 1919 by Grace Cone, and the Ripman School founded in 1922 by Olive Ripman.
The schools were initially in two parts, the Cone studio located above Lilly & Skinner's shoe shop on Oxford Street and the Ripman in Baker Street. Cone-Ripman School was then based in premises at Stratford Place in London, but following the outbreak of World War II, it was relocated to Tring in Hertfordshire, using various rented buildings. In 1941, the school reopened in London, but a second school continued to operate in Tring. In 1945, the Rothschild Bank vacated the mansion at Tring Park, which had been its temporary base during the war, and the Rothschild family permitted the school to use the premises on a permanent basis. Tring Park remains the school's sole campus to this day and in 1947, the school was renamed the Arts Educational School, Tring Park, with the London school becoming the Arts Educational School, London. In 1970, the school acquired the freehold of the mansion and grounds and began a redevelopment of the site, financed by the sale of unused land. The refurbished building was officially opened in 1976 by the Duchess of Kent. The school was later extended in 1990, with the opening of the Markova Theatre by The Prince Edward. In 1993, the school purchased the former St Francis de Sales Convent for use as offsite boarding accommodation for senior pupils. A second house was purchased for use as boarding accommodation in 1994.
Later in 1994, the Arts Educational Schools Trust decided that it was in the best interests of both the London and Tring schools, for them to be run separately. This led to the formation of the AES Tring Park School Trust, which acquired the school and is now solely responsible for its ongoing management. In 2009, to further identify the school as an independent institution, it changed its name to Tring Park School for the Performing Arts. The London school continues to operate, and is commonly known as ArtsEd.
For many years, the school's president was the renowned Prima Ballerina Assoluta, Dame Alicia Markova. After her death, Leopold David de Rothschild CBE became president and the vice presidents are Irek Mukhamedov OBE and Howard Goodall CBE.
History of the mansion
The current Tring Park Mansion was built to a design of Sir Christopher Wren in 1685, for Sir Henry Guy.
Sir William Gore, Lord Mayor of London, bought the house in 1705 and it remained in his family for two subsequent generations. in 1786, it was sold to Sir Drummond Smith, a London banker, who refurbished the interior in Georgian style and remodelled the park in the fashion made popular by "Capability" Brown. William Kay, a Manchester textile magnate, bought the estate in 1823.
In 1838, Nathan de Rothschild began renting Tring Park as a summer residence. When the property was sold in 1872, Lionel de Rothschild bought it as a wedding present for his son, Sir Nathaniel (later Lord) de Rothschild. Lord Rothschild's family grew up and lived at Tring Park until the death of the dowager Lady Rothschild in 1935.
The house was used by the NM Rothschild & Sons bank during World War II before being taken over by the Arts Educational School in 1945.
Notable former pupils
Actors/presenters/writers
Dame Julie Andrews, DBE (The Cone-Ripman School, Tring site) Actress best known for films Mary Poppins and The Sound of Music
Joe Ashman, Actor, known for Free Rein, Doctors and Doctors
Dame Beryl Bainbridge, DBE (deceased), (The Cone-Ripman School, Tring site) Actress/writer In 2008, The Times newspaper named Bainbridge among their list of "The 50 greatest British writers since 1945".
Aeronwy Thomas, (deceased), (Arts Educational School, Tring site) Writer/translator of Italian poetry and daughter of Dylan Thomas. Patron of the Dylan Thomas Society
Jane Seymour, OBE (Arts Educational School, Tring site) Hollywood actress, best known playing Bond girl Solitaire in the film Live And Let Die and the TV series Dr. Quinn, Medicine Woman
Michael Learned, (Arts Educational School, Tring site) Actress, best known for her role in The Waltons
Thandie Newton, (Arts Educational School, Tring site) Hollywood actress and star of films such as; The Pursuit of Happyness, Run Fatboy Run, Mission: Impossible 2 and Crash
Bart Edwards, Actor, best known for TV series Lykkeland
Jessica Brown Findlay, Actress, best known for TV series Downton Abbey as a lead character: Lady Sybil Crawley (2010/11)
Amy Nuttall, Actress and singer, best known for West End musical Guys and Dolls, TV series Emmerdale & Downton Abbey (2011)
Emma Cunniffe, Actress, best known for BBC TV's series The Lakes
Caroline Quentin, Actress and comedian, best known for TV series Men Behaving Badly, Blue Murder and BBC's Life of Riley
Valerie Singleton, OBE, (Arts Educational School, Tring site) Former BBC TV co-presenter of Blue Peter, Nationwide, The Money Programme'.
Geraldine Somerville, Actress known for her role of; Lily Potter in the Harry Potter films and the film Gosford ParkLouise Griffiths, Songwriter/Singer/Actress, best known for BBC TV's Fame Academy (2003)
Claire Trévien, poet, author of The Shipwrecked HouseDaisy Ridley, actress best known for her leading role of 'Rey' in the Star Wars sequel trilogy
Aimee Kelly, actress best known in leading roles of 'Maddy Smith' in CBBC's Wolfblood and 'Kayla Richards' in 2011 movie, Sket''
Lily James, actress best known for Downton Abbey, Cinderella (2015 Disney film) and Baby Driver (2017) and War and Peace (2015)
Jordan Bolger, actor best known for Peaky Blinders, The 100, and The Woman King
Musical theatre
Sarah Brightman, (Arts Educational School, Tring site) Operatic singer, dancer and actress. Celebrated star of Lloyd Webber's Phantom
Stephanie Lawrence (deceased) (Arts Educational School, Tring site) Musical theatre actress, celebrated star of;Lloyd Webber's Evita and original cast lead of Starlight Express
Charlie Bruce (Charlotte), Jazz Dancer/West End performer (Dirty Dancing) and winner of BBC1's, So You Think You Can Dance (UK) Season 1, (2010)
Ballet/dance
John Gilpin (deceased) (The Cone-Ripman School, Tring site), Classical ballet dancer, 'arguably the finest male dancer England has yet produced, the most purely classical' founder member of Festival Ballet (now English National Ballet)
Rupert Pennefather, (Arts Educational School, Tring site), Principal Dancer of The Royal Ballet
Joshua Thew, Corps de Ballet, New York City Ballet
References
Bibliography
Ben Stevenson OBE 'most influential mentors' Eve Pettinger http://findarticles.com/p/articles/mi_m1083/is_12_83/ai_n45144389/
http://www.texasballettheater.org/?q=staff_stevenson
External links
Official website
https://web.archive.org/web/20110415083328/http://www.tring.gov.uk/info/artsed.htm
Private schools in Hertfordshire
Schools of the performing arts in the United Kingdom
Dance schools in the United Kingdom
Relocated schools
Tring
Member schools of the Independent Schools Association (UK)
Boarding schools in Hertfordshire | {
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The Indira Gandhi National Open University (Hindi: इंदिरा गाँधी राष्ट्रीय मुक्त विश्वविद्यालय), known as IGNOU, is a distance learning national university located in IGNOU road, Maidan Garhi, New Delhi, India. Named after former Prime Minister of India Indira Gandhi, the university was established in 1985 with a budget of ₹20 Million, when the Parliament of India passed the Indira Gandhi National Open University Act, 1985 (IGNOU Act 1985). IGNOU is run by the central government of India.
IGNOU, the largest university in the world with over 4 million students, was founded to impart education by means of distance and open education, provide higher education opportunities particularly to the disadvantaged segments of society, encourage, coordinate and set standards for distance and open education in India and strengthen the human resources of India through education. Apart from teaching and research, extension and training form the mainstay of its academic activities. It also acts as a national resource centre, and serves to promote and maintain standards of distance education in India. IGNOU hosts the Secretariats of the SAARC Consortium on Open and Distance Learning (SACODiL) and the Global Mega Universities Network (GMUNET) initially supported by UNESCO.
If you are a first time applicant you are advised to click the available programme tab on the homepage of the Online Admission System and select the desired programme and carefully read the details of programme including eligibility criteria, fee details, duration, etc. You are also requested to download the Common Prospectus 2016-17 and read carefully the rules of the University (Section 06) as mentioned in the common prospectus. You may also read section 1, 7, 8, 9, 12 and 13.
1.Click on "LOGIN" button from the homepage of Online admission system and then login with your UserName and password by clicking the "LOGIN" button given on the login screen.
If your subjects are different than the subjects mentioned; click the "OTHERS" check box.
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Last date for Certificate Programmes :15.06.2016 and 30.06.2016 with late fee of Rs 300. | {
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} | 4,030 |
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\section{Introduction}
\begin{table}[th]
\caption{Log of observations}
\vspace{-0.2cm}
\begin{tabular}{lllr}
\hline
\noalign{\smallskip}
Telescope$^{a}$ & ~~~Date & Energy Band & $T_{\rm int}$ \\
&& & (sec) \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\multicolumn{4}{c}{\bf X-ray} \\
ROSAT P & 1990 Dec 09--11 & 0.1--2.4 keV & 430 \\
ROSAT P & 1993 Nov 30--Dec 4 & 0.1--2.4 keV & 6760 \\
ROSAT P & 1994 Jun 01 & 0.1--2.4 keV & 2930 \\
ROSAT H & 1997 Dec 08 & 0.1--2.4 keV & 1800 \\
\noalign{\smallskip}
\multicolumn{4}{c}{\bf optical spectroscopy} \\
ESO 2.2 m & 1995 Mar 26 & 3000--9000 \AA & 1800 \\
\noalign{\smallskip}
\multicolumn{4}{c}{\bf optical photometry} \\
ESO 2.2 m & 1995 Mar 25--27 & B, R & 600, 180$\!\!$ \\
\noalign{\smallskip}
\hline
\noalign{\smallskip}
\end{tabular}
\noindent{\small $^{a}$ The abbreviations have the following meanings:
ROSAT P or H = PSPC or HRI detectors onboard the ROSAT satellite,
ESO = European Southern Observatory, La Silla/Chile.}
\label{log}
\end{table}
AM Her type variables are a subgroup of cataclysmic variables (CVs)
in which the magnetic field of the white dwarf controls the geometry
of the material flow between the main-sequence donor and the white dwarf
primary as well as synchronizes the white dwarf spin period
with the binary orbital period (see e.g. Warner 1995 for a detailed review).
The inflow of matter along the magnetic field lines (of one or
occasionally also two magnetic poles) is decelerated above the white dwarf
surface producing a shock front. This region is thought to emit hard X-rays
(usually modelled in terms of thermal bremsstrahlung of 10--20 keV)
and polarized cyclotron radiation (hence these systems are named also polars)
in the IR to UV range.
In addition, a strong soft component has been frequently observed from polars
which is thought to arise from the heated accretion pole
(usually modelled in terms of blackbody emission with 20--50 eV temperature).
It is this soft X-ray component which has led to the discovery of a few
dozen new polars by {\sl ROSAT}\ observations over the last 8 years,
most notably the {\sl ROSAT}\ all-sky survey (e.g. Beuermann \& Burwitz 1995
for a first summary). Based on these discoveries,
the strength of the soft component (or more precisely the ratio of the
blackbody and the bremsstrahlung component) has been found to increase with
the magnetic field strength of the white dwarf.
Since simple reprocession of the hard
component cannot produce the observed soft X-ray fluxes,
a scenario of high-$\dot{m}$, blobby accretion has been proposed as a
mechanism to explain the soft excess (Kujpers \& Pringle 1982).
In a different approach, bremsstrahlung emission is gradually replaced
by more efficient cyclotron cooling at high magnetic field strengths
(Woelk \& Beuermann 1996).
The source described here has been
discovered as a result of a systematic survey for supersoft X-ray sources in
the all-sky survey data (see Greiner 1996 for details of this survey)
which revealed a large number of CVs and single white dwarfs.
Other polars identified from this sample include
V844 Her = RX\,J1802.1+1804 (Greiner, Remillard and Motch 1995, 1998),
RS Cae = RX\,J0453.4--4213 (Burwitz {et\,al.}\ 1996), and
RX\,J1724.0+4114 (Greiner, Schwarz and Wenzel 1998).
In this paper we present photometric, spectroscopic
and X-ray observations (summarized in Tab.~\ref{log})
which led to the discovery of another polar, RX\,J1016.9--4103\
(henceforth referred to as RX\,J1016).
\begin{figure}
\vbox{\psfig{figure=rxj1016m41_fc.ps,width=8.7cm}}\par
\caption[fc]{A 10 min $B$-band CCD image of RX\,J1016.9--4103\ obtained with the
2.2 m telescope at ESO. The circle denotes the 3$\sigma$ X-ray
error circle derived from the HRI pointing (10\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi\ radius).
The optical position is measured as: R.A. (2000.0) = 10\h16\m58\fss9,
Decl. (2000.0) = --41$^\circ$ 03\ifmmode ^{\prime}\else$^{\prime}$\fi 45\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi\ ($\pm$1\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi).
The bright star at the left denoted with ``C'' has been used
as comparison star for the photometry.
}
\label{fc}
\end{figure}
\section{X-ray discovery and identification}
RX\,J1016\ was scanned during the {\sl ROSAT}\ all-sky-survey over a period of 4 days
in December 1990 for a total observing time of 430 sec.
Its mean count rate in the {\sl ROSAT}\
position-sensitive proportional counter (PSPC) was 0.13 cts/s,
and the hardness ratio $H\!R1=-0.95\pm0.12$ where $H\!R1$ is defined as
(H--S)/(H+S), with H (S) being the counts above (below) 0.4 keV over
the full PSPC range of 0.1--2.4 keV.
\begin{figure} [t]
\psfig{figure=rxj1016m41_f4.ps,width=0.98\columnwidth,%
bbllx=35pt,bblly=45pt,bburx=530pt,bbury=770pt,clip=}
\caption[perio]{
Results of the period-search using the analysis-of-variance method.
The adopted period of 134$\pm$3 min is marked as the shaded region.}
\label{perio}
\end{figure}
For the timing analysis the source photons were extracted with a radius of
4\ifmmode ^{\prime}\else$^{\prime}$\fi. The background was chosen at the same ecliptic longitude at
$\approx$1$^\circ$~ distance, corresponding to background photons collected
typically 15 sec before or after the time of the source photons. Standard
corrections were applied using the dedicated EXSAS software package
(Zimmermann {et\,al.}\ 1994). The RASS light curve folded
over the best-fit period as derived in section 3 is shown in
the upper panel of Fig. \ref{lc}.
The X-ray flux shows 100\% modulation with a peak count rate of $\sim$0.4
cts/s and a pronounced long faint-phase where the X-ray flux is nearly
zero (formal count rate of $0.05\pm 0.05$ cts/s).
The soft X-ray spectrum and strong variability immediately suggested
the cataclysmic variable nature. Indeed, using the best-fit X-ray coordinate
derived from the all-sky survey data only one optical object brighter than
20$^{\rm m}$ was found within the error circle (see Fig. \ref{fc}) which
later was identified spectroscopically as a polar (see section 4).
Dedicated follow-up pointed {\sl ROSAT}\ observations were performed in November
30 -- December 4, 1993 and June 1, 1994 with the PSPC and on December 8, 1997
with the high-resolution imager (HRI). Table \ref{xlog}
summarizes the relevant numbers of these measurements including the
total number of detected counts (column 3), the mean count rate (column 4),
the hardness ratio (column 5), the coverage of the orbital phases (column 6),
the off-axis angle (column 7) and the best-fit X-ray positions (column 8).
\begin{table*}
\caption{Basic numbers of the X-ray observations of RX\,J1016.9--4103}
\begin{tabular}{lccccccc}
\hline \noalign{\smallskip}
~~~~~~Date & Obs-ID$^{(1)}$ & N$_{\rm cts}$ & mean count & $HR1$ & phase
& offaxis & X-ray position \\
& & & rate (cts/s) & & coverage
& angle & (equinox 2000.0) \\
\noalign{\smallskip} \hline \noalign{\smallskip}
1990 Dec 09--12$^{(1)}$ & -- & ~\,57 & 0.13
& --0.95$\pm$0.12 & ~~\,5\% & 0\ifmmode ^{\prime}\else$^{\prime}$\fi--52\ifmmode ^{\prime}\else$^{\prime}$\fi
& 10\h16\m58\fss2\,--41\grad03\amin38\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi\ $\pm$ 15\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi \\
1993 Nov 30--Dec 4 & 201605p & 430 & 0.06
& --0.98$\pm$0.01 & ~\,55\% & 0\farcm50
& 10\h16\m59\fss8\,--41\grad03\amin52\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi\ $\pm$ 25\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi \\
1994 Jun 1 & 201605p-1 & 352 & 0.12
& --0.98$\pm$0.01 & ~\,30\% & 0\farcm32
& 10\h16\m59\fss2\,--41\grad03\amin44\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi\ $\pm$ 25\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi \\
1997 Dec 08 & 300580h & ~~\,3 & ~~~0.0019$^{(3)}$
& -- & ~\,20\% & 0\farcm21
& 10\h16\m58\fss9\,--41\grad03\amin40\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi\ $\pm$ 10\ifmmode ^{\prime\prime}\else$^{\prime\prime}$\fi \\
\hline
\noalign{\smallskip}
\end{tabular}
\noindent{\noindent\small $^{(1)}$ The letters after the number denote the
detector: h = HRI, p = PSPC.\\
$^{(2)}$ For the position determination only photons
in the energy range 0.25--0.5 keV have been
used to avoid position degradation due to
ghost images. \\
$^{(3)}$ Note the lower sensitivity of the
HRI at soft energies by a factor of 7.8 as
compared to the PSPC.
}
\label{xlog}
\end{table*}
\begin{figure}
\psfig{figure=rxj1016m41_f5.ps,width=0.98\columnwidth,%
bbllx=50pt,bblly=90pt,bburx=440pt,bbury=760pt,clip=}
\caption[olc]{
Optical and X-ray light curves of RX\,J1016\ plotted over orbital phase for
a period of $P=134.4$ min.
Note that the phase designation of the middle two panels is arbitrary
with respect to the all-sky survey (top panel) and optical (bottom panel)
data. Data are plotted twice for clarity and units are PSPC cts/s
for the upper three panels and $B$ magnitudes for the bottom panel.}
\label{lc}
\end{figure}
\section{Optical and X-ray variations}
CCD photometry was obtained during 3 nights in March 1995 with EFOSC II at
the 2.2 m telescope on La Silla (during MPI time).
Observations were performed mostly with the $B$ filter, though a few
exposures also were made with the $V$ and $R$ filters.
Exposure times ranged between 10--600 sec.
Observational details are listed in Tab. \ref{log}.
The images were processed using the profile-fitting scheme of the
{\sc DoPhot} reduction package (Mateo \& Schechter 1989)
to achieve high accuracy.
The optical light curve is characterized by a broad bright phase
and a shallow 0.3 mag deep faint phase.
In contrast, the X-ray intensity variations are much more pronounced
and show a clear on/off-like behaviour.
In order to derive an orbital period we carried out a period search using the
analysis-of-variance method (Schwarzenberg-Czerny 1989) for both, the
optical photometry data as well as the combined {\sl ROSAT}\ PSPC pointings
and the phase-dispersion method (Stellingwerf 1978) for the
{\sl ROSAT}\ all-sky survey data.
The resulting periodograms (Fig. \ref{perio}) show a variety of maxima
which are predominantly caused by the poor sampling rather than the
intrinsic variability.
A more closer look at the bottom two panels (optical and {\sl ROSAT}\ pointing
data) suggests that common periods of 123, 134 or 149 min are possible
(134 min is the most reliable period from the {\sl ROSAT}\ pointed data alone).
Inclusion of the {\sl ROSAT}\ all-sky survey data clearly favours the 134 min
period though we caution that due to the orbital motion of the {\sl ROSAT}\
satellite (96 min) the signal may be affected. We note also that the
actual best-fit period of the {\sl ROSAT}\ all-sky survey data is 132.5 min, thus
being slightly smaller than the period derived from the optical and
pointed {\sl ROSAT}\ data. Note that for each data set (corresponding to the three
panels in Fig. \ref{perio}) a slightly different best-fit period is obtained
though the errors (which we consider to correspond to the width of the peak)
overlap. Overall, based on the appearance of the folded light curves
(Fig. \ref{lc}) according to a criterion of ``greatest simplicity'' we feel
that $P_{\rm orb}$ = 134$\pm$3 min is our best estimate (shaded area in
Fig. \ref{perio}).
\section{A low resolution spectrum}
\subsection{Optical identification}
The identification spectrum of the likely counterpart was obtained on
March 26, 1995 with the ESO 2.2~m telescope at La Silla/Chile
and was exposed for 30 min. We used
the EFOSC II spectrograph equipped with a 1k$\times$1k Thomson CCD detector
with a 450 \AA/mm grism (corresponding to about 8.5 \AA/pixel)
covering the optical wavelength range from 3000--9000 \AA.
The observation was performed under stable photometric conditions and
accompanied by measurements of the standard star LT4816. We additionally
applied a correction using the $B$ magnitude derived from a direct image
taken just prior to the spectroscopic observation
to calibrate the flux with an accuracy of $\sim 10$\% (using standard
{\sc midas} procedures). By convolving the
original spectrum with functions representing the $BV\!R$ bandpasses we arrive
at $B=18\fm3$, $V=18\fm5$ mag and $R=18\fm0$ with a mean error of
$\pm$0.2 mag for RX\,J1016.
The resulting spectrum plotted in the upper panel of Fig.~\ref{ospec}
reveals strong emission lines with of the Balmer series and \ion{He}{ii}
typical for a CV. The high-excitation line \ion{He}{ii}
$\lambda 4686$~\AA\ is quite prominent. Its strength (2/3 of the H$\beta$-flux)
and the inverted decrement of the Balmer lines
clearly indicate a magnetic nature of the object.
\begin{figure}[t]
\psfig{figure=rxj1016m41_f3.ps,width=0.98\columnwidth,%
bbllx=60pt,bblly=70pt,bburx=520pt,bbury=790pt,clip=}
\caption[osp]{{\bf upper panel:} Low resolution optical spectrum of RX\,J1016.9--4103\
obtained on March 26, 1995. The dashed line represents a power-law with
$f_{\lambda}\propto \lambda^{-2}$ fitted in the range between
3800--5000 \AA. {\bf middle panel:} Residual spectrum after
subtraction of the blue continuum shown together with the spectrum of
the late M-dwarf Gliese 83.1 (M~4.5) scaled to match
the strength of the observed TiO features.
{\bf lower panel:} The spectrum after the removal of the contribution of
the secondary star. It
exhibits broad emission features at 5500 and 7400 \AA, tentatively
identified as 3rd and 4th harmonic of the cyclotron fundamental.
The solid line represents our favoured modell with $B=52$~MG,
$\theta=80\degr$ and for $kT=10$~keV. The alternative interpretation
for an $B=41$~MG field is also given (dashed line).}
\label{ospec}
\end{figure}
\subsection{The secondary star}
We further deconvolved the optical spectrum by fitting a power-law in the blue
range between 3800--5000 \AA. After subtracting this blue continuum
contribution the late-type companion is revealed by the slope of the
continuum in the near--IR and obvious flux depression due to the TiO
absorption throughs which
are best seen in the $\lambda\lambda$~7053 and 7667 \AA\ bandheads.
The faintness of the features prevents an accurate quantitative estimate of
the spectral type, but the low ratio $\la 0.5$
of the flux deficits $F_{\rm TiO}$(6165\AA) to $F_{\rm TiO}$(7667\AA) suggest
that it is later than dM~3. The expected parameters for a Roche-lobe
filling secondary in a 134 minute system are $M_{2}= 0.18$M$_{\odot}$,
$R_{2}=0.22$R$_{\odot}$ and a spectral type between M~4.5--5.5, for which
the ZAMS mass-radius and mass-spectral type relations
of Patterson (1984) and Kirckpatrick \& McCarthy (1994) were used.
The distance of RX\,J1016 can be estimated from the observed strength of the
M-dwarf using the method of Bailey (1981). In the following we take the
dM~4.5 star Gl 83.1 ($K=6\fm67$) as a template and assume that both M-stars
have the same colour $V-K=5\fm62$ (Leggett 1992).
By comparing the measured flux deficits in
the $\lambda 7667$-band in Gl 83.1 and that of RX\,J1016
(1800~10$^{16}$ and 0.2~10$^{16}$~\hbox{erg cm$^{-2}$ s$^{-1}$ }), we derive a $K$ magnitude
of 16\fm5 for the secondary in RX\,J1016 . If we take this value and
$S_{K}=4.43$ from the surface brightness
relationship of Beuermann \&\ Weichhold (1998) a distance of $615\pm150$ pc
is deduced. The error includes an uncertainty of 25\% for both, the
flux calibration and the scaling of the TiO band deficits.
\begin{figure*}
\psfig{figure=rxj1016m41_xsp.ps,width=10.9cm,%
bbllx=2.5cm,bblly=1.3cm,bburx=18.2cm,bbury=11.6cm,clip=}
\vspace*{-7.cm}\hspace*{11.cm}
\psfig{figure=rxj1016m41_cont.ps,width=7.cm,%
bbllx=1.9cm,bblly=1.1cm,bburx=13.5cm,bbury=12.1cm,clip=}
\vspace*{0.2cm}
\caption[xsp]{{\bf Left:} Phase-averaged X-ray spectrum of the two merged
PSPC observations of RX\,J1016\ unfolded with the sum of a blackbody and a
thermal bremsstrahlung spectrum with a temperature fixed at 20 keV
(see text for details). The lower
left panel shows the residua of the fit in units of $\sigma$.
{\bf Right:} The 68\%, 90\% and 95\% significance contours
of the blackbody model fit to the merged PSPC spectrum of RX\,J1016\
in the $N_{\rm H}-kT$ plane. Overplotted are the lines of constant
luminosity in units of (D /100 pc)$^2$ (dashed), as well as the value
of the total galactic absorbing column (vertical dotted line)
according to Dickey \& Lockman (1990). }
\label{xspec}
\end{figure*}
Detailed phase-resolved spectroscopic studies of selected systems,
e.g. AM Her (Davey \& Smith 1996), QQ Vul (Schwope {et\,al.}\ 1998) and
RX J0203.8+2959 (Schwarz {et\,al.}\ 1998)
have demonstrated that absorption features from the illuminated side
of the secondaries in magnetic CVs can be heavily suppressed due
to the strong X/UV irradiation from the accretion region.
We therefore caution that the distance derived from our single spectrum with
unknown viewing geometry of the binary system can serve as an upper limit only.
\subsection{A magnetic field estimate}
After subtraction of a suitably scaled spectrum of Gl 83.1 two broad
emission humps at $\lambda\lambda$ 5500 and 7400 \AA\ clearly stand out
in the red part of the spectrum (Fig.~\ref{ospec}, lower panel), which
we tentatively identify as cyclotron lines from the hot optically
thin post-shock region.
An unambiguous estimate of the magnetic field strength is difficult to
achieve with only two distinct humps observed. Their separation
favours an interpretation as the 3rd and 4th harmonic of the cyclotron
fundamental, in which case the field strength is 52$\pm2$~MG slightly
depending on the plasma temperature and the yet unknown field orientation.
An alternative interpretation as the 4th and 5th harmonics, in which
case $B$ is $\sim41$~MG, cannot not completely excluded but results in a
distinct mismatch of the expected humps with the shape of the continuum
between 6000--7000 \AA. Normalized cyclotron absorption coefficients for
both cases assuming $\theta = 80\degr$ and $kT = 10$~keV
shown in Fig.~\ref{ospec} illustrate this ambiguity.
\section{The X-ray spectrum}
The two pointed PSPC observations have resulted in the detection of nearly
800 photons thus enabling spectral investigation.
For the spectral analysis the source photons of the two PSPC pointings
were merged and then extracted with a radius of 1\farcm5. The background was
chosen from concentric circles around the source region with a radius of
3\ifmmode ^{\prime}\else$^{\prime}$\fi. Other nearby sources were cut out, and the background area
normalized to the source extraction area before the background subtraction.
Standard corrections were applied using the dedicated EXSAS software package
(Zimmermann {et\,al.}\ 1994).
As a first step, we have considered the total spectrum as collected
during each of the two observations (after merging).
Adopting a blackbody plus a thermal bremsstrahlung model (the temperature
of the latter fixed to 20 keV) we find that there
is no need at all for the inclusion of the bremsstrahlung component,
that is the spectral fit does not require any spectral component for hard
emission (Fig. \ref{xspec}). The resulting best-fit
temperature of the blackbody component is 10$\pm$7 eV and
the absorbing column $N_{\rm H}$=6.4$\times$10$^{20}$ cm$^{-2}$, e.g.
about 50\% of the total galactic absorbing column in this direction
(Dickey \& Lockman 1990). However, this gives an unrealistic high luminosity
for a cataclysmic variable due to the very low temperature.
If we fix the temperature at the canonical value of 20 eV, the best-fit
absorbing column is only $N_{\rm H}$=2.4$\times$10$^{20}$ cm$^{-2}$.
The difference in reduced $\chi^2$ is only marginal for all temperatures
in the 10--25 eV range.
As a second step we have investigated the emission during the off-state
phase intervals which has been observed for a total of 7340 sec.
Selecting time intervals where the 60 sec averaged X-ray intensity is
less than 0.05 cts/s, we find that the residual emission is consistent
with being background radiation. The mean count rate during the X-ray bright
phase (at $>$0.05 cts/s) is 0.38 cts/s in the PSPC.
Considering only the X-ray bright phase, the unabsorbed fluxes of the two
model components in the {\sl ROSAT}\ band (0.1--2.4 keV) are
$F_{\rm bbdy}$ = 5.1$\times10^{-11}$ \hbox{erg cm$^{-2}$ s$^{-1}$ }\ (using kT$_{\rm bbdy}$=20 eV
for comparison purposes) and
$F_{\rm thbr}$ $<$9.8$\times$10$^{-13}$ \hbox{erg cm$^{-2}$ s$^{-1}$ }, giving a small flux ratio
of $F_{\rm thbr}$/$F_{\rm bbdy} < 0.02$. The mean bolometric luminosity
during the X-ray bright phase is (again with kT$_{\rm bbdy}$=20 eV)
$L_{\rm X}$ = 2.4$\times$10$^{32}$ (D / 100 pc)$^2$ erg/s.
\section{Discussion and Conclusion}
The measured period of $P=134$ min places RX\,J1016\ in the 2--3 hr CV period gap
which is thought to be due to the transition from orbital angular momentum
loss by magnetic braking (P$>$ 3 hr) to gravitational radiation (P$<$ 2 hr)
(King 1988). Over the last years, more polars have been found with periods
in the 2--3 hr range thus re-initiating the debate on the existence and
significance of the period gap for magnetic systems (Wickramasinghe \& Wu 1994,
Wheatley 1995).
The shape of the X-ray light curve strongly argues for a self-eclipsing polar.
The length of the X-ray bright phase of $\la 0.5$ phase units suggests
(within our limited accuracy) an one pole accreting geometry such that
the accretion region passes behind the limb of the white dwarf for half
the orbital period. The lack of eclipses implies $i < 78\degr$.
Our tentative estimate of the magnetic field strength is 52$\pm2$~MG
and the strong soft X-ray excess are in good agreement with the
correlation found between these quantities (Beuermann 1998).
The strongly modulated soft X-ray emission, the seemingly synchronous rotation,
the strength and relative intensities of
the Balmer and \ion{He}{ii} emission lines as well as the cyclotron humps in
the optical spectrum clearly suggest the polar nature of RX\,J1016\ though
no polarimetric measurements have been made. More detailed optical
photometry and phase-resolved spectroscopy as well as polarimetry are
needed to determine the system parameters of this new polar.
\begin{acknowledgements}
We thank R. Egger for help during the ESO observing run and A.D. Schwope for
generously providing help and software for the cyclotron spectroscopy.
JG and RS are supported by the Deut\-sches Zentrum f\"ur Luft- und Raumfahrt
(DLR) GmbH under contract No. FKZ 50 QQ 9602\,3 and 50 OR 9206\,8.
The {\sl ROSAT}\ project is supported by the German Bundes\-mini\-ste\-rium f\"ur
Bildung, Wissenschaft, For\-schung und Technologie (BMBF/DLR) and the
Max-Planck-Society.
\end{acknowledgements}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,813 |
_A las mujeres buenas, ¡las mujeres fantásticas_!,
_las mujeres más extraordinarias que conozco_ :
_Beatrix, Sam, Victoria, Vanessa y Zara_.
_Cada una de ellas es especial y única_ ,
_valiente, cariñosa, sabia, resuelta_ ,
_creativa, constante, sincera, íntegra_ ,
_elegante y virtuosa_.
_Sois mis heroínas, mis modelos_ ,
_mi tesoro y mi alegría_.
_Gracias por las lecciones que me habéis enseñado_
_y por el amor infinito que compartimos_.
_Con todo mi amor_ ,
MAMÁ / D. S.
### 1
La mañana del 14 de abril de 1912, Annabelle Worthington leía tranquilamente en la biblioteca de la casa familiar, con vistas al extenso jardín tapiado. Empezaban a aparecer los primeros signos primaverales, los jardineros habían plantado muchas flores y todo estaría precioso cuando sus padres regresaran al cabo de unos días. El hogar que compartía con ellos y su hermano mayor, Robert, era una mansión imponente en la parte norte de la Quinta Avenida de Nueva York. Los Worthington, y la familia de su madre, los Sinclair, eran parientes directos de los Vanderbilt y los Astor, y de una forma más indirecta también estaban emparentados con todas las sagas más influyentes de Nueva York. Su padre, Arthur, era propietario y director del banco más prestigioso de la ciudad. Su familia llevaba varias generaciones en el negocio bancario, igual que ocurría con la familia materna en Boston. Su hermano Robert, de veinticuatro años, ya llevaba tres trabajando para su padre. Y, por supuesto, cuando llegara el día de la jubilación de Arthur, Robert pasaría a dirigir el banco. Su futuro, del mismo modo que su historia, era predecible, desahogado y seguro. Annabelle agradecía haberse criado bajo la protección de ese entorno.
Sus padres se querían mucho, y Robert y ella siempre se habían llevado bien y mantenían una relación muy cercana. Nunca había ocurrido nada que los hubiera disgustado ni entristecido de veras. Los problemas menores con los que se topaban eran despreciados o resueltos con facilidad. Annabelle había crecido en un mundo perfecto y dorado, había sido una niña feliz, rodeada de personas amables y cariñosas. Los últimos meses le habían resultado muy emocionantes, aunque habían quedado algo empañados por un pequeño contratiempo. En diciembre, justo antes de Navidad, la habían presentado en sociedad en un baile espectacular que sus padres habían dado en su honor. Era su puesta de largo y todo el mundo insistía en que era la debutante más elegante y carismática que Nueva York había visto en años. A su madre le encantaba celebrar fiestas por todo lo alto. Había mandado cubrir el jardín con una carpa y ponerle calefacción. Decoraron la sala de baile de la mansión con un gusto exquisito. La orquesta que habían contratado era la más cotizada de la ciudad. Asistieron cuatrocientas personas. Y el vestido que lució Annabelle la convirtió en una princesa de cuento.
Annabelle era una joven pequeña, delgada, delicada, más diminuta incluso que su madre. Era una muñequita rubia con el pelo largo, sedoso y dorado, y con unos ojos azules enormes. Era guapa, tenía las manos y los pies pequeños, y unas facciones perfectas. Cuando era niña, su padre no se cansaba de repetirle que parecía una muñeca de porcelana. A los dieciocho años, tenía una encantadora figura esbelta y bien proporcionada, y una gracia gentil. Todo en ella reflejaba la aristocracia de la que provenía y en la que habían nacido tanto Annabelle como sus antepasados y su círculo de amigos.
La familia había disfrutado de unas Navidades entrañables a los pocos días de su presentación en sociedad y, después de todas las emociones, las fiestas y las salidas nocturnas con su hermano y sus padres, en las que lucía vestidos finos a pesar del frío invernal, la primera semana de enero Annabelle contrajo una gripe muy fuerte. Sus padres se preocuparon mucho cuando vieron que la gripe se convertía rápidamente en bronquitis y, luego, casi en neumonía. Por suerte, su juventud y salud general la ayudaron a recuperarse. Aun con todo, estuvo enferma con fiebre por las noches durante casi un mes. El médico opinaba que era poco sensato que viajara estando todavía tan débil. Sus padres y Robert llevaban varios meses preparando un viaje en el que querían visitar a algunos amigos en Europa, y Annabelle seguía convaleciente cuando se marcharon en el _Mauretania_ a mediados de febrero. Habían viajado en ese mismo barco todos juntos varias veces, así que su madre se ofreció a quedarse en Nueva York con la muchacha, pero cuando llegó el momento de partir, Annabelle estaba lo bastante recuperada para quedarse sola en Nueva York. Había insistido en que su madre no se privara de ese viaje que había estado esperando durante tanto tiempo. A todos les dio pena dejarla sola y Annabelle también se sintió muy decepcionada de no poder ir, pero incluso ella admitió que, aunque ya se sentía mucho mejor, seguía sin verse con fuerzas para embarcarse en un periplo que duraría dos meses. Le aseguró a su madre, Consuelo, que cuidaría de la casa mientras estuvieran fuera. Sus padres confiaban plenamente en ella.
Annabelle no era de esa clase de chicas por las que uno tuviera que preocuparse, ni de las que se aprovechaban de la ausencia paterna. Lo único que lamentaban tremendamente sus progenitores era que no pudiese acompañarlos, igual que le pasaba a la propia Annabelle. Mantuvo el tipo mientras se despedía de ellos en el muelle Cunard en febrero, pero cuando volvió a casa se sintió abatida. Se entretenía leyendo y haciendo distintas tareas del hogar que satisfarían a su madre. Se le daban muy bien las labores, así que se pasaba horas remendando sábanas y manteles muy elegantes. Aún se sentía un poco débil para asistir a eventos sociales, pero su mejor amiga, Hortense, la visitaba con frecuencia. Hortense también había hecho su presentación en sociedad ese año, y las dos amigas eran inseparables desde la infancia. Hortie ya tenía un pretendiente y Annabelle había hecho una apuesta con ella, convencida de que James pediría su mano en Semana Santa. Annabelle ganó la apuesta, pues acababan de anunciar su compromiso hacía una semana. Annabelle se moría de ganas de contárselo a su madre, quien no tardaría en volver. Tenían que atracar en Nueva York el 17 de abril, tras haber partido de Southampton cuatro días antes en un barco nuevo.
Los dos meses sin su familia se le habían hecho largos, pues Annabelle los había echado mucho de menos a todos. No obstante, le habían dado la oportunidad de recuperarse totalmente y de leer infinidad de cosas. Después de terminar sus tareas domésticas, se pasaba las tardes y las noches en la biblioteca de su padre, inmersa en sus libros. Sus favoritos eran los que hablaban de hombres importantes o de temas científicos. Nunca le habían interesado mucho las novelas románticas que leía su madre, y todavía menos los libros que le prestaba Hortense, ya que le parecían insulsos. Annabelle era una joven inteligente, que absorbía los acontecimientos mundiales y la información actual como una esponja. Eso le daba mucho tema de conversación con su hermano e incluso él reconocía en privado que la profundidad del conocimiento de la muchacha lo ponía a veces en ridículo. Aunque Robert tenía madera para los negocios y era increíblemente responsable, le encantaba ir a fiestas y salir con amigos, mientras que Annabelle solo era sociable en apariencia, pues tenía un talante serio y una inmensa pasión por aprender, por la ciencia y los libros. Su sala predilecta de la casa era la biblioteca paterna, donde pasaba buena parte del tiempo.
La noche del 14 de abril, Annabelle se quedó leyendo en la cama hasta la madrugada, así que se levantó a una hora tan tardía que resultaba extraña en ella. Se lavó los dientes y se peinó nada más salir de la cama, se puso una bata y bajó adormilada a desayunar. Mientras bajaba la escalera, le dio la impresión de que en la casa reinaba un silencio poco común y no vio a ninguno de los sirvientes. Se asomó a la recocina y se encontró a varios de ellos arremolinados alrededor de un periódico, que doblaron al instante. Enseguida se dio cuenta de que su fiel ama de llaves, Blanche, había estado llorando. Era una mujer tan sensible que cualquier desgracia relacionada con un animal o con un niño en apuros conseguía que se deshiciera en un mar de lágrimas. Annabelle esperaba que le contaran una de esas historias cuando sonrió y les dio los buenos días, pero en cuanto lo hizo, William, el mayordomo, se echó a llorar y salió de la habitación.
—Dios mío, ¿qué ha pasado?
Annabelle miró a Blanche y a las otras dos sirvientas, muy sorprendida. Entonces se percató de que todas estaban llorando y, sin saber por qué, le dio un vuelco el corazón.
—Pero ¿qué pasa? —preguntó Annabelle, quien, de forma instintiva, alargó la mano hacia el periódico.
Blanche vaciló durante un largo instante y después se lo ofreció. Annabelle vio los gigantescos titulares en cuanto lo desdobló. El _Titanic_ se había hundido aquella noche. Era el barco recién estrenado que sus padres y su hermano habían tomado para regresar de Inglaterra. Annabelle abrió los ojos como platos mientras leía los detalles a toda velocidad. Todavía se sabían pocos datos; apenas que el _Titanic_ se había hundido, que los pasajeros habían subido a los botes salvavidas y que la embarcación _Carpathia_ , de la White Star Line, se había apresurado a acudir al lugar del siniestro. La noticia no decía nada sobre las víctimas ni los supervivientes, pero comentaba que, tratándose de un barco de semejante tamaño y tan nuevo, era de esperar que todos los pasajeros hubieran sido desalojados a tiempo y el rescate hubiera sido absoluto. El periódico informaba de que el enorme transatlántico había chocado contra un iceberg, y aunque tenía fama de ser imposible de hundir, lo cierto era que el barco se había hundido en el mar al cabo de unas horas. Había ocurrido lo inimaginable.
Annabelle pasó a la acción al momento y mandó a Blanche que hiciera llamar al chófer de su padre para que la esperara con el coche. Ya estaba en la puerta de la recocina, dispuesta a subir a su dormitorio para vestirse, cuando dijo que tenía que ir a las oficinas de la White Star cuanto antes para preguntar por Robert y sus padres. No se le ocurrió que cientos de personas harían lo mismo.
Le temblaban las manos mientras se vestía, presa del aturdimiento, con un sencillo vestido de lana gris; se puso medias y zapatos, agarró el abrigo y el bolso y corrió escaleras abajo, sin preocuparse siquiera de recogerse el pelo. Parecía una niña con la melena al viento cuando salió como un rayo por la puerta principal y la cerró de un portazo. La casa y todos sus moradores se quedaron congelados, como si empezaran a anticipar el duelo. Mientras Thomas, el chófer de su padre, la conducía a las oficinas de la White Star Line, que estaban al final de Broadway, Annabelle intentó contener una oleada de silencioso terror. Vio a un vendedor de periódicos en una esquina, gritando los titulares de las últimas noticias. Como tenía una edición más reciente del diario, le pidió al conductor que parase y compró uno.
El periódico decía que se había perdido un número indeterminado de vidas, y que el _Carpathia_ estaba radiando informes con las listas de supervivientes. Annabelle notó cómo se le llenaban los ojos de lágrimas mientras leía. ¿Cómo podía haber ocurrido algo así? Era el barco más grande y más nuevo que surcaba los mares. Era el viaje inaugural. ¿Cómo podía hundirse una embarcación como el _Titanic_? Y ¿qué les habría ocurrido a sus padres, a su hermano y a tantos otros?
Cuando llegaron a la empresa de transportes, había cientos de personas gritando que les dejaran entrar, y Annabelle no se imaginaba cómo iba a conseguir abrirse paso entre la muchedumbre. El corpulento chófer de su padre la ayudó, pero aun así le costó una hora entrar. Explicó que su hermano y sus padres viajaban en primera clase en el barco hundido. Un joven oficinista abrumado apuntó su nombre, mientras otros empleados iban a colgar listas de supervivientes en la fachada de las oficinas. La radio operadora del _Carpathia_ seguía transmitiendo los nombres, con la ayuda del encargado de radio del _Titanic_ , que se había salvado, y en la cabecera de la lista habían escrito con letras en negrita que estaba incompleta por el momento, cosa que daba esperanza a las personas que no veían los nombres tan esperados en ella.
Annabelle cogió una de las copias de la lista con manos temblorosas y apenas consiguió leer entre las lágrimas, pero entonces, casi al final de la enumeración, lo vio: un solo nombre. Consuelo Worthington, pasajera de primera clase. Su padre y su hermano no aparecían en la lista, así que, para calmar los nervios, se repitió que estaba incompleta. Le sorprendió la escasa cantidad de nombres que había enumerados.
—¿Cuándo se tendrán noticias sobre el resto? —preguntó Annabelle al empleado a la vez que le devolvía la lista.
—Esperemos que dentro de unas horas —contestó el joven mientras otras personas gritaban y preguntaban detrás de Annabelle. La gente gimoteaba, lloraba, discutía, y cada vez más personas se peleaban por entrar en la empresa. Era una escena de pánico y caos, terror y desesperación.
—¿Siguen rescatando supervivientes de los botes salvavidas? —preguntó Annabelle, obligándose a mantener la esperanza.
Por lo menos sabía que su madre estaba viva, aunque ignoraba en qué estado. Sin embargo, lo más seguro era que los demás también hubieran sobrevivido.
—Han recogido a los últimos esta mañana a las ocho y media —contestó el empleado con ojos sombríos.
Había oído relatos de cuerpos flotando en el agua, de gente que chillaba para que la rescataran antes de morir, pero él no era quien debía propagar esos rumores y tampoco tenía valor para contarle a la masa de familiares que se habían perdido centenares de vidas, tal vez más. Por el momento, la lista de supervivientes apenas contenía seiscientos nombres y el _Carpathia_ había comunicado que habían recogido más de setecientos, pero todavía no podían proporcionar todos los nombres. Si esa información era verídica, significaba que más de mil pasajeros y miembros de la tripulación habían perecido. El propio empleado se negaba a creérselo.
—Deberíamos haber recopilado todos los nombres dentro de unas horas —dijo intentando mostrarse comprensivo cuando un hombre con la cara enrojecida amenazó con pegarle si no le pasaba la lista, cosa que hizo de inmediato.
Todos corrían histéricos, asustados y descontrolados por las oficinas, pues se desesperaban por obtener información y apoyo. Los empleados preparaban y repartían tantas listas como podían. Y al final, Annabelle y el chófer de su padre, Thomas, volvieron al coche para esperar allí a que hubiera más noticias. Él se ofreció a llevarla a casa, pero Annabelle insistió en que prefería quedarse y volver a repasar la lista cuando estuviera completa, al cabo de unas horas. No le apetecía estar en ningún otro sitio.
Permaneció sentada en el coche en silencio, parte del tiempo con los ojos cerrados, pensando en sus padres y en su hermano, deseando que ellos también hubieran sobrevivido, a la vez que daba gracias por haber visto por lo menos el nombre de su madre en la lista. No comió ni bebió nada en todo el día, y cada hora se acercaba a comprobar la lista. A las cinco en punto les dijeron que la lista de supervivientes estaba completa, a excepción de algunos niños pequeños que todavía no se habían podido identificar con nombre y apellido. Salvo ellos, todas las demás personas recogidas por el _Carpathia_ aparecían enumeradas.
—¿Hay algún otro barco que haya recogido supervivientes? —preguntó alguien.
El empleado negó con la cabeza sin decir nada. Aunque había otros barcos recogiendo cadáveres de las aguas congeladas, la tripulación del _Carpathia_ era la única que había sido capaz de rescatar supervivientes, la mayoría subida a los botes salvavidas y unos cuantos en el mar. Casi todas las personas que habían caído al helado Atlántico habían muerto antes de la llegada del _Carpathia_ , a pesar de que los rescatadores habían acudido al lugar del desastre apenas dos horas después del hundimiento del _Titanic_. Había pasado demasiado tiempo para que alguien siguiera vivo a una temperatura tan baja dentro del océano.
Annabelle volvió a repasar la lista una vez más. Había 706 supervivientes. Leyó de nuevo el nombre de su madre, pero no había ningún otro Worthington en la lista, ni Arthur ni Robert, de modo que la única esperanza que le quedaba era confiar en que hubiera algún error. A lo mejor no los habían reconocido, o ambos estaban inconscientes y no podían decir cómo se llamaban a quienes elaboraban la lista. Era imposible proporcionar más información por el momento. Les dijeron que el _Carpathia_ tenía prevista la llegada a Nueva York tres días más tarde, el día 18. La muchacha tendría que mantener la fe hasta entonces, y dar gracias porque su madre hubiera sobrevivido. Se negaba a creer que su padre y su hermano estuvieran muertos. Era imposible.
Una vez en casa, se pasó la noche en vela y siguió sin probar bocado. Hortense fue a verla y se quedó a dormir con ella. Apenas hablaron, se limitaron a darse la mano y llorar sin parar. Hortie intentó animarla, y la madre de su amiga le hizo una visita breve también con la intención de consolarla. No había palabras que pudieran mitigar lo que había ocurrido. Todo el mundo estaba sobrecogido por la noticia. Era una tragedia de proporciones épicas.
—Gracias a Dios que estabas enferma y no pudiste ir —le susurró Hortie una vez que se metieron juntas en la cama de Annabelle, cuando la madre de su amiga se había marchado ya. Había aconsejado a su hija que se quedara allí a dormir y, es más, que le hiciera compañía a Annabelle hasta que regresara su madre. No quería que la joven estuviera sola.
Annabelle se limitó a asentir ante el comentario de Hortie, pero se sentía culpable por no haber estado con ellos, pues se preguntaba si su presencia habría ayudado de algún modo. Tal vez hubiera podido salvar por lo menos a uno de los dos, o a otra persona.
Durante los tres días siguientes, Hortie y ella vagaron por la casa como fantasmas. Hortie era la única amiga a quien quería ver o con quien quería hablar en esos momentos de conmoción y duelo. Annabelle no comía casi nada, a pesar de que el ama de llaves insistía en que lo hiciera. Todos los sirvientes lloraban sin cesar y, al final, Annabelle y Hortie salieron a dar un paseo y tomar un poco el aire. James las acompañó y fue muy amable con Annabelle, pues le dijo lo mucho que lamentaba lo ocurrido. La ciudad y el mundo entero no podían pensar en otra cosa.
Las noticias que llegaban del _Carpathia_ seguían siendo escasas. Lo único que habían confirmado era que el _Titanic_ se había hundido, de eso no cabía duda, y que la lista de supervivientes ya era definitiva y completa. Los únicos que no aparecían en ella eran los bebés y los niños aún no identificados, que tendrían que ser reconocidos por los familiares que se acercaran al puerto, en caso de que fueran de Estados Unidos. Si nadie los reconocía, tendrían que devolverlos a Cherbourg y Southampton, a sus angustiadas familias, que los estarían esperando allí. En total, había media docena de niños no emparentados con ninguno de los supervivientes y que eran demasiado pequeños para decir cómo se llamaban. Otras personas los cuidaban mientras tanto a falta de sus padres, pues era imposible saber a qué familia pertenecían. No obstante, todos los demás, incluso los enfermos o heridos, aparecían en la lista, según aseguraba la compañía.
Annabelle seguía sin poder creérselo mientras Thomas la conducía de nuevo al muelle Cunard la tarde del día 18. Hortie había preferido no acompañarla, porque no quería interferir en el encuentro, de modo que Annabelle se dirigió al embarcadero 54 sola.
La multitud expectante vio cómo el _Carpathia_ se acercaba lentamente a puerto, con unos remolcadores, pocos minutos después de las cinco. Annabelle notó que el corazón le latía desbocado mientras observaba la embarcación, que sorprendió a todo el mundo al dirigirse a los muelles de White Star, ubicados en los embarcaderos 59 y 60. Y allí, a la vista de todos los observadores, la tripulación bajó lentamente los botes salvavidas del _Titanic_ que habían recuperado, y que eran lo único que quedaba del barco recién estrenado, para devolverlos a la White Star Line antes de atracar el _Carpathia_. Los fotógrafos estaban hacinados en una flotilla de barcas pequeñas desde las que intentaban fotografiar los botes salvavidas, y los supervivientes del desastre se congregaron en la barandilla del barco. El ambiente que los rodeaba era medio funerario y medio circense, pues los familiares de los supervivientes esperaban en un silencio agónico para ver quién bajaba, mientras que los periodistas y fotógrafos gritaban y se daban codazos para colocarse en los mejores puestos y obtener las mejores instantáneas.
Tras depositar los botes salvavidas, el _Carpathia_ se desplazó lentamente hasta su embarcadero, el número 54, y los estibadores y otros empleados del Cunard se apresuraron a amarrar el barco. Y entonces, por fin, abrieron la compuerta y bajaron la plataforma. En silencio, y con una deferencia enternecedora, dejaron bajar primero a los supervivientes del _Titanic_. Los pasajeros del _Carpathia_ abrazaron a algunos de ellos y les estrecharon la mano. Se derramaron muchas lágrimas y se dijeron pocas palabras, mientras uno por uno todos los supervivientes desembarcaron, la mayor parte de ellos con lágrimas surcándoles la cara, algunos todavía en estado de shock por lo que habían visto y vivido aquella horrible noche del hundimiento. A ninguno le resultaría fácil olvidar los horripilantes gritos y gemidos desde el agua, las llamadas de auxilio en vano de personas que acabaron muriendo congeladas. Quienes se hallaban en los botes salvavidas tenían miedo de recoger a más pasajeros, por temor a que la embarcación pudiera volcarse por el peso y acabaran pereciendo todavía más personas de las que ya estaban entre las gélidas aguas. Las estampas de cuerpos flotando en el oscuro mar que habían presenciado mientras esperaban a que llegaran los refuerzos para recogerlos habían sido espeluznantes.
Quienes bajaron del _Carpathia_ eran en su mayoría mujeres con niños pequeños, algunas de ellas todavía vestidas de gala, con el atuendo que habían lucido la última noche pasada en el _Titanic_ , y cubiertas con mantas. Al parecer, varias mujeres estaban tan conmocionadas que ni siquiera se habían cambiado de ropa en los tres últimos días; se habían limitado a permanecer ovilladas en el espacio proporcionado dentro de los salones y comedores principales del _Carpathia_. Los pasajeros y los miembros de la tripulación habían hecho todo lo posible por ayudar a los supervivientes, pero ninguno de ellos había podido cambiar la voluntad del destino ni evitar la apabullante pérdida de vidas, en unas circunstancias que nadie habría predicho.
Annabelle contuvo la respiración hasta que distinguió a su madre en la plataforma. La joven observó cómo se acercaba a ella Consuelo desde la distancia, con prendas prestadas, el semblante demudado y el mentón alto, con una dignidad surcada por la tragedia. Annabelle lo adivinó todo en su rostro. No había ninguna otra silueta familiar a su lado. Su padre y su hermano no se veían por ninguna parte. Miró por última vez detrás de su madre, pero Consuelo estaba totalmente sola en medio de un mar de supervivientes, en su mayoría mujeres, más unos cuantos hombres que parecían algo avergonzados cuando descendieron junto a sus esposas.
Había una explosión continua de flashes, pues los periodistas querían captar tantos reencuentros como les fuera posible. Y entonces, de repente, su madre emergió delante de ella y Annabelle la abrazó con tanta fuerza que ninguna de las dos podía respirar. Consuelo sollozaba, y su hija también se echó a llorar mientras se aferraban la una a la otra y otros pasajeros y familiares deambulaban a su alrededor. Al cabo de un rato, con el brazo de Annabelle sobre los hombros de su madre, las dos se alejaron lentamente. Llovía, pero a nadie le importaba. Consuelo llevaba un grueso vestido de lana que no era de su talla y zapatos de fiesta, y todavía lucía el collar de diamantes con pendientes a juego que se había puesto la noche del naufragio. No tenía abrigo, así que Thomas se apresuró a darle a Annabelle la manta del coche para que se la pusiera sobre los hombros.
Apenas se habían alejado del embarcadero cuando Annabelle preguntó lo que tenía que preguntar. Podía imaginar la respuesta, pero era incapaz de seguir con la incertidumbre. Le susurró a su madre:
—¿Robert y papá...?
Esta se limitó a sacudir la cabeza y lloró todavía más fuerte mientras Annabelle la acompañaba al vehículo. De repente, su madre parecía muy frágil y mucho más vieja. Era una viuda de cuarenta y tres años, pero parecía una anciana cuando Thomas la ayudó con delicadeza a entrar en el coche y la cubrió con mucho cuidado con la manta de pieles. Consuelo se lo quedó mirando y siguió llorando, hasta que, en voz muy baja, le dio las gracias. Annabelle y ella se abrazaron en silencio durante el trayecto de vuelta. La mujer no volvió a pronunciar ni una palabra hasta que hubo llegado a la mansión.
Todos los sirvientes la estaban esperando en el recibidor para abrazarla, tocarla, darle la mano, y cuando vieron que llegaba sola, para darle el pésame por lo ocurrido. Al cabo de una hora, ya habían colocado un crespón negro en la puerta de entrada. Aquella noche fueron muchos los que colgaron ese complemento en sus casas, una vez que se hubieron disipado las dudas sobre quién no había regresado y no lo haría jamás.
Annabelle ayudó a su madre a bañarse y a ponerse el camisón, y Blanche se desvivió por ella como si fuera una niña. Había cuidado de Consuelo desde que era jovencita, y había asistido tanto al parto de Annabelle como al de Robert. Y ahora le había tocado esto. Mientras ahuecaba las almohadas de Consuelo, después de acompañarla hasta la cama, Blanche tuvo que limpiarse los ojos infinidad de veces a la par que emitía unos susurros reconfortantes. Le llevó una bandeja con té, copos de avena, tostadas, caldo y sus galletas favoritas, pero Consuelo no probó nada. Se limitó a quedarse mirando a su hija y al ama de llaves, incapaz de decir ni una palabra.
Annabelle se quedó a hacer compañía a su madre aquella noche, y por fin, bien entrada la madrugada, cuando Consuelo se estremeció de la cabeza a los pies y se desveló, le contó a su hija lo que había ocurrido. Ella se había montado en el salvavidas número 4, junto con su prima Madeleine Astor, cuyo marido tampoco había sobrevivido. Según dijo, el bote solo estaba medio lleno, pero su marido y Robert se habían negado a subir, pues querían quedarse en la retaguardia para ayudar a otras personas y dejar más espacio en los botes para las mujeres y los niños. Aun con todo, quedaba sitio de sobra para los dos.
—Ojalá se hubieran montado... —se lamentaba desesperada Consuelo.
Los Widener, los Thayer y Lucille Carter, todos ellos conocidos, también iban en el bote salvavidas. Pero Robert y Arthur habían seguido en sus trece y habían permanecido en el barco para ayudar a otras personas a montarse en los botes, aun a sabiendas de que iban a sacrificar su vida. Consuelo también le habló de un hombre llamado Thomas Andrews, que había sido uno de los héroes de la noche. Su madre insistió en que Annabelle supiera que su padre y su hermano habían sido muy valientes, aunque eso ahora no les suponía ningún alivio.
Hablaron durante horas, en las que Consuelo revivió los últimos momentos en el barco, y su hija la abrazó y lloró mientras la escuchaba. Al final, cuando el amanecer ya se colaba por la habitación, Consuelo concilió el sueño tras soltar un suspiro.
### 2
Esa semana se celebraron cientos de funerales en Nueva York y en otros muchos lugares. Los periódicos de todas partes estaban repletos de historias emotivas, de relatos estremecedores. La gente empezaba a asimilar que muchos de los botes salvavidas se habían alejado del barco medio vacíos, cargados únicamente con pasajeros de primera clase, y el mundo estaba conmocionado. El tan aclamado héroe era el capitán del _Carpathia_ , que había corrido al lugar del naufragio para recoger a los supervivientes. Seguían sin darse muchas explicaciones de por qué se había hundido el barco. Después de chocar contra el iceberg, había resultado imposible evitar el desastre. Sin embargo, la gente comentó largo y tendido, sin llegar a entenderlo, por qué el _Titanic_ se había adentrado en una zona de hielo después de haber recibido advertencias de que no lo hiciera. Por suerte, el _Carpathia_ había oído las súplicas desesperadas de ayuda por radio; de lo contrario, tal vez ninguno de los pasajeros se habría salvado.
El médico le había hecho un reconocimiento a Consuelo y había dicho que su salud era sorprendentemente buena, a pesar de que estaba acongojada y en estado de shock. Parecía haberse quedado sin vida. Por eso, Annabelle fue quien tuvo que encargarse de preparar hasta el último detalle del funeral de su padre y su hermano. La ceremonia conjunta se celebraría en la iglesia de Trinity, que era una de las favoritas de su padre.
El funeral fue sombrío y digno, y contó con centenares de personas que quisieron presentar sus respetos y darles el pésame a Consuelo y a Annabelle. Los dos ataúdes de los Worthington estaban vacíos, pues no se había recuperado ninguno de los cuerpos y, por triste que pareciera, nunca se recuperarían. De las 1.517 personas que habían fallecido, solo se habían encontrado 51 cadáveres. Los demás habían desaparecido en silencio en la tumba acuosa del mar.
Varios cientos de los asistentes a la ceremonia se acercaron después a la casa de los Worthington, donde se sirvió comida y bebida. Algunas celebraciones fúnebres tenían un aire festivo, pero esa no. Robert apenas tenía veinticuatro años, y su padre tenía cuarenta y seis; ambos estaban en la flor de la vida y habían muerto de una manera muy trágica. Tanto Annabelle como Consuelo se vistieron de luto riguroso. Annabelle se caló un elegante sombrero negro y su madre se puso un velo propio de una viuda. Y por la noche, cuando todos los invitados se hubieron marchado, Consuelo parecía destrozada. Era tal su abatimiento que su hija se preguntó a qué había quedado reducida su madre. Daba la impresión de que su espíritu había muerto con sus dos hombres y se preocupó muchísimo por ella.
Fue un gran alivio para Annabelle que su madre anunciara durante el desayuno dos semanas después del funeral que deseaba volver al hospital en el que solía hacer de voluntaria. Dijo que le parecía que sería positivo para ella pensar en otras personas y su hija le dio la razón.
—¿Seguro que te ves con fuerzas, mamá? —le preguntó Annabelle en voz baja, con cara preocupada. No quería que su madre enfermase, aunque ya estaban a principios de mayo y la temperatura era cálida.
—Estoy bien —contestó su madre con tristeza.
Todo lo bien que podría estar durante una buena temporada. De modo que esa tarde madre e hija se pusieron sendos vestidos negros y delantales blancos y se dirigieron al hospital de St. Vincent, donde Consuelo llevaba años haciendo tareas de voluntariado. Annabelle se había unido a su madre al cumplir los quince años. Por norma general, ayudaban a los indigentes y trataban problemas menores como heridas y lesiones, más que enfermedades infecciosas. Annabelle siempre se había sentido fascinada por esa labor y poseía un talento natural para ejercerla; por su parte, su madre era muy cariñosa y tenía un corazón muy tierno. Sin embargo, a Annabelle le atraía algo más que el cuidado a los enfermos: le fascinaban las cuestiones médicas, así que, cuando encontraba la ocasión, leía libros sobre medicina para entender las operaciones y curas que veía realizar. Nunca había sido aprensiva, a diferencia de Hortie, que se había mareado la única vez que Annabelle la había convencido para que las acompañara. Cuanto más complicada era una situación, más le gustaba. Su madre prefería servir las bandejas de comida, mientras que ella ayudaba a las enfermeras siempre que le dejaban, cambiaba vendas y limpiaba las heridas. Los pacientes decían con frecuencia que tenía unas manos de algodón.
Por la noche volvieron a casa agotadas, después de una tarde larga y fatigosa, y repitieron la visita al hospital al cabo de pocos días. Por lo menos, eso las mantenía entretenidas y les impedía pensar en la doble pérdida que habían sufrido. De repente, la primavera que prometía ser el período más emocionante de la vida de Annabelle, después de su presentación en sociedad, se había convertido en una época de soledad y duelo. No iban a aceptar ninguna invitación lúdica durante todo un año, cosa que preocupaba a Consuelo. Mientras su hija se quedaba en casa vestida de luto, todas las otras jovencitas que acababan de hacer la puesta de largo empezarían a comprometerse. Tenía miedo de que la tragedia que las había azotado también pudiera afectar al futuro de su hija de la manera más desafortunada, pero no había nada que pudieran hacer para remediarlo. De todas formas, Annabelle no parecía pensar mucho en lo que se estaba perdiendo. Como era lógico, le preocupaba más haberse quedado sin padre y sin hermano que su futuro o la ausencia de vida social.
Hortie seguía yendo a visitarlas a menudo y a mediados de mayo celebraron el decimonoveno cumpleaños de Annabelle. Consuelo estuvo muy triste durante toda la comida; comentó que ella se había casado a los dieciocho años, justo después de su presentación en sociedad, y que Robert había nacido cuando ella tenía la edad que ahora cumplía su hija. Pensar en eso provocó de nuevo las lágrimas de la mujer, que dejó a las dos jóvenes en el jardín y subió a su habitación para tumbarse a descansar.
—Ay, qué pena me da tu madre —dijo Hortie con empatía, y después miró a su amiga—. Y qué pena me das tú. Lo siento mucho, Belle. Todo esto es horrible.
Lamentaba tanto lo ocurrido a su mejor amiga que tardó otras dos horas en reconocer que James y ella habían puesto fecha para la boda, que se celebraría en noviembre, para cuyo enorme banquete tenían que hacer un montón de preparativos. Annabelle le dijo que estaba muy contenta por ella, y lo decía de corazón.
—¿De verdad no te importa no poder salir estos meses? —le preguntó Hortie.
Ella habría aborrecido tener que quedarse encerrada en casa un año entero, pero Annabelle lo había aceptado con resignación. Solo tenía diecinueve años y los meses que se avecinaban no iban a ser muy divertidos para ella. Pero ya había crecido a pasos de gigante en el breve mes que había transcurrido desde que su hermano y su padre habían muerto.
—No, no me importa en absoluto —contestó Annabelle con tranquilidad—. Mientras mi madre tenga ganas de colaborar en el hospital, la acompañaré y así tendré algo que hacer.
—Puaj, no me hables de eso. —Hortie dejó los ojos en blanco—. Me pongo mala... —Pero sabía que a su amiga le encantaba—. ¿A pesar de todo vais a ir a Newport este año?
Los Worthington poseían una casita preciosa allí, en Rhode Island, junto a la de los Astor.
—Mi madre dice que sí. A lo mejor podríamos ir pronto, en junio, antes de que empiece la temporada fuerte. Creo que le iría bien.
Lo único que preocupaba ahora mismo a Annabelle era el bienestar de su madre; a diferencia de Hortie, que tenía una boda que preparar, millones de fiestas a las que asistir y un prometido del que estaba locamente enamorada. Su vida era como debería haber sido la de Annabelle, pero ya no lo sería. Su mundo, tal como lo conocía hasta entonces, se había desintegrado, había cambiado para siempre.
—Por lo menos estaremos juntas en Newport —comentó alegre Hortie.
A las dos les encantaba ir a nadar cuando sus madres se lo permitían. Hablaron de los planes de la boda durante un rato y luego Hortie se marchó. Para Annabelle, había sido un cumpleaños muy tranquilo.
En las semanas que siguieron al funeral, Consuelo y Annabelle recibieron varias visitas, como era de esperar. Los amigos de Robert pasaban a saludar, algunas damas viudas iban a dar el pésame a Consuelo, dos empleados del banco de Arthur a quienes conocían bien se acercaron a prestar su apoyo, y por último se presentó un tercer empleado a quien Consuelo había visto algunas veces y que le caía muy bien. Se llamaba Josiah Millbank, tenía treinta y ocho años y era muy respetado en el banco de Arthur. Era un hombre apacible, de buenos modales, y le contó algunas anécdotas sobre Arthur que ella desconocía y que le hicieron reír. Se sorprendió de lo mucho que le había alegrado la visita de Josiah, y el hombre llevaba ya una hora en su compañía cuando Annabelle volvió de dar una vuelta en coche con Hortie. Recordaba haberlo visto antes, pero no lo conocía apenas. Estaba más próximo a la generación de su padre que a la suya, pues tenía catorce años más que su hermano mayor, así que, aunque lo hubiera visto en alguna fiesta, no se habría fijado en él porque no tenían nada en común. Sin embargo, igual que su madre, se sintió sorprendida por su amabilidad y sus buenos modales, y él se mostró también muy compasivo con ella.
Mencionó que iba a estar en Newport en julio, igual que todos los años. Allí tenía una casita sencilla pero cómoda. Josiah era originario de Boston, provenía de una familia tan respetable como la de los Worthington y su situación económica era similar. De todas formas, vivía de manera discreta y nunca se vanagloriaba de sus posesiones. Prometió ir a visitarlas cuando estuvieran en Newport, y Consuelo dijo que estaría encantada. Después de su partida, Annabelle se dio cuenta de que les había llevado un enorme ramo de lilas blancas, que la sirvienta ya había colocado en un jarrón. Consuelo se puso a hablar sobre él en cuanto se fue.
—Es un hombre muy simpático —dijo en voz baja mientras admiraba las lilas—. Tu padre lo apreciaba mucho, y ahora lo entiendo. Me pregunto por qué no se habrá casado.
—Hay personas que no se casan —contestó Annabelle sin darle mayor importancia—. No todo el mundo ha nacido para el matrimonio, mamá —añadió con una sonrisa.
Empezaba a preguntarse si ella sería una de esas personas. No se imaginaba dejando a su madre en esas circunstancias para irse a vivir con un hombre. No le gustaba la idea de dejar a su madre sola. Y el no casarse no le parecía una tragedia. Para Hortie sí habría sido un drama, pero para ella no. Ahora que faltaban su padre y su hermano, y que su madre estaba destrozada, Annabelle consideraba que tenía responsabilidades más importantes dentro del hogar y no lamentaba estar soltera ni un instante. Cuidar de su madre daba sentido a su vida.
—Si intentas decirme que no quieres casarte —le contestó su madre como si le hubiera leído el pensamiento, como solía hacer—, ya puedes ir quitándotelo de la cabeza. Cumpliremos el año de luto, como corresponde, y después te buscaremos marido. Eso es lo que tu padre querría.
Annabelle se dio la vuelta y la miró con seriedad.
—Papá no querría que te dejara sola —afirmó con la rotundidad propia de los adultos.
Consuelo sacudió la cabeza.
—Eso es una tontería, y lo sabes. Soy perfectamente capaz de cuidar de mí misma.
Pero mientras lo decía los ojos volvieron a llenársele de lágrimas, y su hija no se quedó muy convencida.
—Bueno, tiempo al tiempo —replicó la chica con firmeza, y salió corriendo de la habitación para mandar que prepararan una bandeja con la cena y se la subieran al dormitorio a su madre.
Cuando regresó, la rodeó con el brazo, la empujó con cariño para que subiera a la planta superior y se tumbara un rato, y la arropó en la cama, esa cama que había compartido con el marido al que tanto amaba y que había desaparecido, algo que le rompía el corazón a Consuelo.
—Eres demasiado buena conmigo, hija mía —dijo la mujer con aire avergonzado.
—No es verdad —contestó Annabelle con voz cantarina.
Era el único rayo de sol que quedaba en la casa. No le daba a su madre más que alegrías. Y ambas lo eran todo la una para la otra. Ahora solo estaban ellas dos. Annabelle le colocó un chal fino a Consuelo sobre los hombros y volvió a bajar para leer en el jardín, con la esperanza de que su madre estuviera lo bastante animada al día siguiente para ir al hospital. Era la única distracción que tenía Annabelle y le permitía volcarse en algo que le importaba.
Tenía muchas ganas de que llegara el mes de junio para marcharse a Newport.
### 3
Annabelle y su madre se marcharon a Newport un mes antes de lo habitual, en junio. El lugar estaba precioso en aquella época del año y, como siempre hacían, el servicio fue con antelación para abrir la casa. Por norma general, la temporada de eventos sociales en Newport era frenética, pero ese año madre e hija planeaban pasar unas vacaciones tranquilas. Habría quien fuera a visitarlas a su casa, pero dos meses después de la muerte de su padre y su hermano, era imposible que Annabelle y su madre salieran a socializar. Los crespones negros, a los que ya se habían acostumbrado, se colgaron también en la puerta de la casa de Newport, para indicar que estaban de luto.
Aquel año había varias familias en la misma situación en Newport, entre ellas los Astor. Madeleine Astor, que había perdido a su esposo John Jacob en el _Titanic_ , esperaba un hijo que nacería en agosto. La tragedia había sacudido con fuerza a la clase alta neoyorquina, pues era el viaje inaugural del navío y muchas personalidades destacadas y aristócratas de la ciudad se hallaban en el barco. Y las continuas noticias acerca de la ineptitud de la tripulación a la hora de desalojar a los pasajeros resultaban cada vez más inquietantes. Casi todos los botes salvavidas habían partido medio vacíos. Algunos hombres se habían abierto paso a la fuerza para montarse en ellos con las mujeres y los niños. Además, no se había salvado casi ningún pasajero de tercera clase. Cuando llegara el momento, los responsables tendrían que rendir cuentas ante las autoridades.
Newport estaba extremadamente tranquilo en junio, aunque empezó a animarse cuando algunas personas de Boston y Nueva York se instalaron en sus «casitas de campo» en julio. Para los profanos, lo que la gente llamaba «casitas» o «cabañas» en Newport en realidad habrían sido consideradas mansiones de proporciones colosales en cualquier otro sitio. Había caseríos con salón de baile, lámparas de araña imponentes, suelos de mármol, muebles antiguos de valor incalculable y unos jardines espectaculares que daban al mar. Se trataba de una comunidad muy especial formada por las altas esferas de la sociedad de toda la costa Este, un rinconcito con playa para los opulentos. Los Worthington estaban en su salsa. Su casa de verano era una de las más grandes y más encantadoras de la localidad.
Annabelle empezó a divertirse cuando llegó Hortie. Se escapaban al mar juntas, salían a pasear, y el prometido de Hortie, James, a menudo las acompañaba para comer juntos al aire libre. De vez en cuando, James invitaba a algún amigo, cosa que entretenía a Annabelle, y su madre fingía que no se daba cuenta. Mientras no asistieran a fiestas oficiales, no ponía objeciones a que su hija se relacionara con otros jóvenes. Era una persona tan buena y estaba tan volcada en el bienestar de su madre, que se lo merecía. Consuelo se preguntaba si alguno de los amigos de James, o de los antiguos compañeros de Robert, despertaría el interés de Annabelle. Cada vez le preocupaba más que el año de luto influyese en el destino de esta para siempre. Desde la época navideña, cuando todas las chicas de su quinta habían hecho la presentación en sociedad, se habían comprometido ya seis de las jóvenes de la edad de Annabelle. Y ella no iba a conocer a nadie si se quedaba todo el día en casa con su madre. Ahora, dos meses después de la tragedia, ya parecía mucho más madura y mayor que las demás chicas. Eso podía asustar a los posibles pretendientes. Y, por encima de todo, su madre quería que la muchacha se casara. Por su parte, Annabelle seguía sin preocuparse por el tema y se alegraba de ver a Hortie y a otros amigos, pero ninguno de los chicos que le presentaban le atraía lo más mínimo.
Josiah Millbank fue a verlas varias veces después de instalarse en Newport en julio. Nunca olvidaba darles un obsequio cuando las visitaba: flores en la ciudad y frutas o algún dulce en Newport. Se pasaba horas hablando con Consuelo, los dos sentados en el amplio porche de la entrada en sendas mecedoras y, tras su tercera visita, Annabelle empezó a bromear al respecto.
—Creo que le gustas, mamá —dijo la joven sonriendo.
—No seas tonta.
Consuelo se sonrojó ante el comentario. Lo último que deseaba era un pretendiente. Su intención era permanecer fiel a la memoria de su marido para siempre, y así se lo repetía a todo el que quería escucharla. No era una de esas viudas que pretenden volver a casarse, aunque sí se moría por encontrar marido para su hija Annabelle.
—Solo es amable con nosotras —añadió Consuelo con seguridad, convencida de lo que decía—. Además, es más joven que yo, y si hay alguien que pueda atraerle eres tú.
A pesar de sus palabras, no tenía pruebas que lo demostraran. El hombre parecía igual de cómodo hablando con la madre que con la hija, y nunca flirteaba con ellas; se limitaba a ser cortés.
—Yo no le atraigo, mamá —negó Annabelle con una amplia sonrisa—. Y solo tiene cinco años menos que tú. Creo que es una persona muy amable, pero tiene edad suficiente para ser mi padre.
—Muchas chicas de tu edad se casan con hombres de la suya —contestó su madre sin inmutarse—. No es tan viejo, por el amor de Dios. Si no me equivoco, apenas ha cumplido los treinta y ocho.
—A ti te iría mucho mejor.
Annabelle se marchó corriendo entre risas al encuentro de Hortie. Era un día cálido y soleado y querían ir a nadar; James había dicho que se les uniría más tarde. Aquella noche iba a celebrarse una gran fiesta en casa de los Schuyler, a la que James y Hortie, igual que todos sus amigos, iban a ir, aunque, por supuesto, Annabelle no los acompañaría. Ni se le pasaba por la cabeza pedirle permiso a su madre para eso; no deseaba disgustarla.
Sin embargo, por la noche, mientras estaban sentadas en el porche, les llegó el eco del jolgorio de la fiesta y la música a lo lejos. Vieron fuegos artificiales y Consuelo supo que eran para celebrar el compromiso de una de las hijas de los Schuyler. Se le rompió el corazón al pensar en Annabelle.
Para su sorpresa, Josiah se acercó a su casa en plena noche para llevarles un trozo de pastel que había sobrado de la fiesta. Se retiraba ya, y ambas mujeres se sintieron conmovidas por ese gesto tan gentil. El hombre se quedó a tomar una limonada con ellas y después dijo que debía marcharse, pues tenía un invitado esperándolo en casa. Les prometió que no tardaría en volver, cosa que le agradecieron. Incluso Annabelle se emocionó con aquella muestra de amistad. No tenía ningún interés romántico en él, sino que, por curioso que resultara, en cierto modo le parecía que era un sustituto de su hermano. Le gustaba hablar con él, y Josiah tenía la misma clase de humor que Robert, unas bromas que ella echaba mucho de menos.
—Me pregunto por qué no habrá llevado a su huésped a la fiesta —murmuró Consuelo mientras dejaba los vasos vacíos y la jarra de limonada en la recocina.
—A lo mejor es alguien con quien no quiere que lo vean en público —bromeó Annabelle—: una mujer estrafalaria que no le conviene. A lo mejor tiene una amante... —dijo, y soltó una carcajada cuando vio que provocaba las risas de su madre. Teniendo en cuenta el linaje del que provenía Josiah, y lo bien educado que era, les parecía poco probable. Y, de haber sido ese el caso, no habría mencionado que tenía a un invitado esperándolo.
—Tú sí que tienes una imaginación que no te conviene —se mofó su madre, y al momento las dos subieron a la planta superior, mientras charlaban con complicidad sobre Josiah y sobre lo amable que había sido al llevarles una porción de pastel de la fiesta.
Era la primera vez que Annabelle lamentaba de veras no haber podido salir. Todos sus amigos habían ido a la fiesta y, por el jaleo que habían oído, debía de haber sido una fiesta genial, con fuegos artificiales y todo. Iba a ser un verano muy tranquilo para Annabelle, quien solo vería a Hortie y Josiah, cuyas visitas eran frecuentes y puntuales, y a unos cuantos conocidos más.
Josiah reapareció al día siguiente y Consuelo lo invitó a comer de picnic con Annabelle y Hortie. El hombre parecía sentirse totalmente cómodo con ambas chicas, a pesar de que Hortie soltaba muchas risitas tontas y a menudo hacía comentarios infantiles en su presencia. Para explicar sus dotes de conversación con los jóvenes, les contó que tenía una hermanastra de su edad, del segundo matrimonio de su padre viudo. Annabelle seguía sin poder imaginársela como una mujer casada, cosa que sería al cabo de cuatro meses. Continuaba siendo una niña, pero a la vez estaba loca por James, y a menudo, cuando Annabelle y ella estaban solas, hacía comentarios picantes acerca de la noche de bodas y la luna de miel que conseguían que Annabelle se ruborizara. Por suerte, Hortie no dijo nada de eso delante de Josiah, y él comentó que su hermana se había casado en abril y estaba embarazada. Parecía totalmente familiarizado con las vidas, anhelos e intereses de las jovencitas, así que ambas disfrutaron mucho hablando con él.
Les mencionó quién era su invitado: un compañero de la Universidad de Harvard que iba a visitarlo todos los veranos. Dijo que era un tipo estudioso y reservado, que solía evitar los actos sociales y las fiestas.
Josiah se quedó con ellas hasta bien entrada la tarde y acompañó a Annabelle de vuelta a casa cuando Hortie se hubo marchado. Su madre estaba sentada en el porche, charlando con una amiga. Estaban muy entretenidas. Había mucha gente que pasaba a saludar y la vida parecía mucho más animada en el ambiente de Newport. El lugar era especialmente alegre para Annabelle, que temía el momento en que regresaran a la ciudad. Le había hablado a Josiah sobre la labor en el hospital que tanto le gustaba realizar y él había bromeado al respecto.
—Supongo que de mayor le gustaría ser enfermera —dijo, aunque sabía perfectamente, igual que ella, que eso no ocurriría jamás. Lo más cerca que estaría de ser enfermera en su vida sería la labor que desempeñaba como voluntaria, pero a pesar de todo Annabelle leía mucho sobre temas médicos. Era su pasión secreta.
—A decir verdad —contestó ella sincerándose, sin importarle parecerle ingenua—, me gustaría más ser doctora.
Tenía la sensación de que podía contarle cualquier cosa sin que él se burlara de ella. Desde que había muerto su padre y Josiah había empezado a visitarlas con asiduidad, se había convertido en un buen amigo. Sin embargo, en esa ocasión pareció perplejo. Lo había sorprendido. Annabelle era una persona mucho más madura de lo que él creía, y por la expresión de su rostro supo que la joven hablaba en serio.
—Es una ambición muy loable —contestó él después de asimilarlo—. ¿Se atrevería a hacerlo?
—Mi madre nunca me dejaría. Pero me encantaría ser médico si pudiera. Algunas veces cojo libros sobre medicina o sobre anatomía de la biblioteca. No comprendo todo lo que dicen, pero leyéndolos aprendo cosas muy interesantes. Opino que la medicina es fascinante. Y ahora hay muchas más doctoras que en el pasado.
Las mujeres llevaban más de sesenta años metiendo la cabeza en las facultades de medicina, pero, aun así, Josiah seguía sin imaginarse a Annabelle haciéndolo y sospechaba que ella tenía razón: a su madre le daría un ataque si se enteraba. Ella deseaba que Annabelle tuviera una vida mucho más tradicional, que se casara y tuviera hijos; de ahí su presentación en sociedad.
—Yo nunca soñé con ser médico —confesó él—. Pero sí me habría gustado unirme al circo cuando tenía diez o doce años. —Annabelle se rió al oírlo. Era muy divertido que admitiera algo así—. Me encantaban los animales, y de niño lo que quería era ser mago, para hacer desaparecer los deberes del colegio. No era muy buen estudiante.
—No sé si creerle, sabiendo que estudió en Harvard —dijo la joven riéndose de él—. Aunque seguro que habría sido divertido eso de unirse al circo. ¿Por qué no lo hizo?
—Porque su padre me ofreció empleo, pero eso fue más tarde. No sé, supongo que no tenía el valor necesario para trabajar en el circo. De todas formas, nunca tuve una ambición clara como usted, Annabelle. Solo de pensar en todos los años que hace falta estudiar para ser médico, se me quitan las ganas. Soy demasiado vago para la medicina.
—No le creo —insistió ella con amabilidad—. Pero sé que a mí me encantaría.
Sus ojos brillaron de emoción mientras lo decía.
—¿Quién sabe? A lo mejor llega el día en que pueda aplicar todo lo que ha aprendido en los libros y con la labor de voluntaria. Es una tarea muy noble.
El hecho de que dedicara su tiempo a ayudar en el hospital por lo menos ya era admirable.
—No nos dejan hacer mucho —contestó Annabelle algo decepcionada.
—¿Qué le gustaría hacer? —preguntó él con interés.
—Se me da muy bien la costura, todo el mundo lo dice. Me gustaría que me dejaran coserle unos puntos a algún enfermo. Seguro que sabría hacerlo.
Él se quedó sorprendido al oír sus palabras, y después dibujó una sonrisa de oreja a oreja.
—Recuérdeme que no me corte en su presencia, ¡o sacará aguja e hilo de bordar del bolso!
—Me encantaría... —admitió ella sonriéndole con picardía.
—Alguien tendrá que mantenerla ocupada, señorita Worthington, o tengo la impresión de que acabará haciendo alguna travesura.
—Sería feliz haciendo travesuras médicas. Piénselo, si no fuéramos quienes somos, yo podría ir a la facultad de medicina y hacer lo que quisiera. ¿No le parece un incordio? —preguntó, con aire infantil y adulto a la vez. Sin pensarlo dos veces, él la abrazó, igual que habría abrazado a su hermana pequeña.
Para él ella era eso, del mismo modo que ella sentía un vínculo con él similar al de un hermano. Entre ambos se estaba fraguando una relación muy bonita, una amistad.
—Si no fuera quien es, no podría permitirse ir a la facultad de medicina —replicó él siendo práctico, y ella asintió para darle la razón.
—Eso es cierto. Pero si fuera hombre, podría hacerlo. Robert podría haber estudiado, si hubiera querido, y mis padres le habrían dejado. Algunas veces es muy difícil ser mujer. Hay tantas cosas que no puedes hacer y que no se consideran apropiadas... Es aburridísimo —dijo Annabelle, y entonces dio una patada a una piedrecilla con la punta del zapato.
Josiah se rió de ella.
—No me diga que es una de esas mujeres que quieren luchar por los derechos y la libertad.
No le parecía una feminista empedernida, y le habría sorprendido que lo fuera.
—No. Soy muy feliz con las cosas tal como son. Solo me habría gustado poder ser doctora.
—Bueno, a mí me habría gustado ser el rey de Inglaterra, pero eso tampoco ocurrirá jamás. Algunas cosas están fuera de nuestro alcance, Annabelle, y tenemos que aceptarlo. Pero lleva una buena vida.
—Sí —reconoció ella—. Y quiero mucho a mi madre. No haría nada que pudiera disgustarla, y sé que eso la disgustaría horrores.
—Tiene razón.
—Ya ha superado suficientes desgracias este año: lo único que quiero es hacerla feliz.
—Lo sé —admitió él con afecto—. Ya lo he visto. Es una hija fantástica, y una persona muy dulce.
—No es verdad —contestó Hortie, que acababa de aparecer de la nada y se había acercado a ellos con sigilo—. Una vez diseccionó una rana. Leyó en un libro cómo se hacía. Fue la cosa más asquerosa que he visto en toda mi vida... Le aseguro que no es una persona muy dulce.
Y los tres se echaron a reír cuando lo dijo.
—Supongo que es verdad —dijo Josiah, que empezaba a conocer mejor a Annabelle. Era una joven muy especial en muchos sentidos.
—Sí, sí —respondió muy orgullosa Annabelle—. Lo hice tal como lo indicaba el libro. Fue muy interesante. Ojalá pudiera diseccionar a una persona de verdad. Me refiero a un cadáver, ¿sabe?, como hacen en la carrera de medicina.
—¡Ay, por Dios! —exclamó Hortie con cara de mareo, y Josiah se sorprendió, aunque le hizo gracia.
—Vamos, será mejor que vayan a nadar —comentó, y las azuzó para que se marcharan mientras él se acercaba al porche para despedirse de Consuelo.
—¿De qué hablaba con las muchachas, Josiah? —le preguntó la mujer muy interesada.
—Ah, de lo normal: fiestas, presentaciones, compromisos, bodas... —comentó, para cubrirle las espaldas a Annabelle, pues sabía que su madre se desmayaría si se enteraba de que Annabelle tenía ganas de diseccionar un cadáver. Josiah seguía riéndose para sus adentros cuando regresó a su modesta casa. Sin duda Annabelle Worthington era una joven muy interesante, totalmente distinta de las chicas de diecinueve años convencionales.
Justo cuando Josiah llegaba a la puerta de casa vio que su compañero de la universidad regresaba de comer fuera, así que lo saludó con la mano nada más verlo. Henry Orson era uno de sus amigos más antiguos y Josiah estaba encantado de compartir una parte de las vacaciones con él todos los veranos. Mantenían una estrecha amistad desde la época universitaria; además, Henry era un hombre acaudalado a quien todo el mundo admiraba.
—¿Qué tal la comida? —le preguntó Josiah.
Los dos eran hombres guapos que habrían podido tener tantas novias como desearan, pero su conducta era responsable. Nunca engañaban a las mujeres ni se aprovechaban de ellas. Henry se había comprometido hacía dos años y su decepción había sido mayúscula al enterarse de que su prometida se había enamorado de un hombre más joven, un chico de la edad de ella. Desde entonces, no había tenido ninguna relación seria, cosa que dejaba abierta la esperanza para las madres de Newport, igual que ocurría con Josiah.
—Aburrida —contestó Henry con sinceridad—. ¿Y la tuya?
Él consideraba que muchos encuentros sociales eran tediosos y prefería hablar de negocios con otros hombres serios en lugar de flirtear con las jovencitas.
—He comido al aire libre con una joven que quiere diseccionar un cadáver humano —dijo Josiah con una sonrisa, y Henry se rió en voz alta.
—Madre mía —exclamó, con aspecto divertido e impresionado, y fingió tener miedo—. Parece peligrosa. ¡Aléjate de ella!
—No te preocupes —lo tranquilizó Josiah entre risas mientras entraban juntos en la casa—. Lo haré.
Los dos hombres se pasaron el resto de la tarde jugando a las cartas y comentando la situación del mundo financiero, que era la pasión de Henry. Esa afición resultaba aburrida a ojos de las mujeres, pero interesante para los hombres, pues Henry poseía muchísimos conocimientos y hacía comentarios inteligentes, de modo que a Josiah le encantaba hablar con él. Había conseguido un puesto para Henry en el banco del padre de Annabelle hacía unos cuantos años y tanto sus compañeros como sus superiores lo respetaban tremendamente. A pesar de ser menos sociable que Millbank, también él había sabido manejarse bien en la empresa. Henry no conocía en persona a Annabelle ni a Consuelo, pero su amigo le prometió que se las presentaría durante su estancia en Newport, a lo que Henry asintió con la cabeza mientras fruncía el ceño pensando en las cartas.
—No sé si quiero conocerla si va a laminarme como a un fiambre... —dijo Henry con tono amenazador, y después sonrió mientras colocaba una carta con la que ganó la mano.
—Qué rabia —se lamentó Josiah al saberse perdedor, y luego le sonrió—: No te preocupes. No es más que una niña.
### 4
Josiah visitó con frecuencia a la familia Worthington durante julio y agosto, igual que hicieron Hortie y James, y varios amigos más. También les presentó a Henry, tal como había prometido, quien dio el pésame a Consuelo y le enseñó algunos juegos de cartas a Annabelle, con los que la joven se entretuvo muchísimo, sobre todo al ver que ganaba repetidas veces. La muchacha disfrutaba en compañía de los buenos amigos que tenía en Newport, y, aunque aquel verano madre e hija se vieron desgajadas de la vida social de todos los años, Annabelle se sintió menos aislada que en la ciudad. En la costa, la vida parecía casi normalizada, a pesar de la ausencia de su padre y su hermano, quienes, de todas formas, a menudo se quedaban en Nueva York porque seguían trabajando.
Para cuando se marcharon de Newport a finales de agosto, Annabelle tenía un aspecto sano, bronceado y feliz, y su madre también lucía mejor cara. Para las dos había sido un verano tranquilo y sin complicaciones, ideal después de la trágica primavera.
Una vez de regreso a la ciudad, Annabelle retomó la actividad en el hospital junto a su madre. Además, un día a la semana trabajaba como voluntaria por su cuenta en el Hospital de Nueva York para el Tratamiento de los Lisiados. La extraordinaria labor desempeñada en el centro la fascinaba. Le habló del tema a Josiah un día que fue a tomar el té con ellas.
—Todavía no te han puesto a abrir cadáveres, ¿verdad? —le preguntó fingiendo preocupación. Annabelle se rió de él.
—No, me limito a llevarles comida y jarras de agua a los pacientes, pero una de las enfermeras me ha dicho que a lo mejor algún día me dejan presenciar una operación.
—Eres una chica asombrosa, de verdad —dijo él con una amplia sonrisa afable.
Y, a finales de mes, Consuelo por fin tuvo la valentía de repasar las pertenencias de su marido y su hijo. Tiraron algunas cosas y dieron la mayor parte de la ropa, pero dejaron intactos el estudio de Arthur y el dormitorio de Robert. Ninguna de las dos se veía con agallas suficientes para desmontar esas habitaciones y no tenían necesidad de hacerlo. No les hacía falta utilizar esas estancias.
En septiembre apenas vieron a Josiah, en comparación con lo mucho que las había visitado en verano. Estaba muy atareado en el banco y ellas tenían gestiones que hacer para repartir la herencia. A pesar de que Arthur no tenía motivos para pensar que le fuera a pasar algo, había dejado todos los asuntos financieros atados y bien atados, y Annabelle y su madre se hallaban en una situación económica más que desahogada. Ambas podrían vivir fácilmente el resto de su vida con lo que él les había legado, y, aun así, seguiría quedando un patrimonio considerable para los futuros hijos de Annabelle, aunque eso era lo último que le preocupaba en aquellos momentos.
Durante ese mes, Annabelle tampoco vio apenas a Hortie. Faltaban solo seis semanas para la boda y esta tenía muchas cosas que hacer. Debía ir a probarse el vestido de novia, preparar el ajuar y comprar el mobiliario para la casa que les había regalado su padre a James y a ella. Pensaban viajar a Europa en su viaje de novios, que prolongarían hasta Navidad. Annabelle sabía que la echaría mucho de menos durante su ausencia. Una vez que estuviera casada, nada sería como antes. Annabelle ya lo había comprobado con otras amigas y empezaba a notar el distanciamiento de Hortie.
Octubre acababa de despuntar cuando Josiah retomó por fin sus visitas. Annabelle estaba en el Hospital para el Tratamiento de los Lisiados y Consuelo se hallaba en el jardín, disfrutando de una tarde soleada con una taza de té. Se sorprendió al ver a Josiah, pero el hombre siempre era bienvenido, y cuando ella se puso de pie para saludarlo, su expresión de alegría fue sincera.
—Hace siglos que no le veíamos, Josiah. ¿Qué tal está?
—Bien. —Le sonrió—. He pasado las últimas semanas en Boston. Mi familia tenía unos asuntos de los que quería que yo me encargara. ¿Qué tal están Annabelle y usted?
—Estamos bien, gracias. Annabelle ha vuelto a volcarse en la labor del hospital, pero por lo menos eso la mantiene entretenida. Aquí no hay mucho más que pueda hacer.
Todavía les quedaban otros seis meses de luto oficial y Consuelo sabía que, aunque Annabelle nunca se quejara, le resultaba duro. Llevaba seis meses sin salir con sus amigos, y eso era aburridísimo para una muchacha de diecinueve años. Necesitaba salir al mundo, pero por desgracia Consuelo no podía hacer nada para remediarlo.
—Imagino lo lento que debe de pasar el tiempo para las dos —comentó Josiah pensativo, mientras se sentaba en el jardín con ella y rechazaba una taza de té.
—A mí no me importa, pero lo siento por ella —admitió Consuelo—. Ya tendrá casi veinte años cuando vuelva a salir con sus amigos. No me parece justo, la verdad.
Sin embargo, lo que le había ocurrido a Consuelo tampoco había sido justo. A veces la vida era así.
—Se recuperará —le aseguró Josiah—. Annabelle es una de esas personas que sacan el mejor partido a cualquier situación. Ni una sola vez la he oído quejarse de no poder salir —dijo el hombre con sinceridad, y la madre asintió.
—Ya lo sé. Es un encanto. Qué lástima que no esté hoy en casa, le decepcionará saber que ha venido y no le ha visto. Siempre pasa los lunes por la tarde en el hospital.
Él asintió y vaciló un instante, perdió la mirada en el espacio y después volvió a posarla en Consuelo, con unos ojos sorprendentemente fijos.
—Lo cierto es que hoy no venía a ver a Annabelle. He venido a verla a usted, por un asunto que me gustaría comentarle a solas.
Puso el semblante serio y actitud empresarial mientras lo decía, como si hubiera ido para tratar algún tema del banco.
—¿Pasa algo con las propiedades de Arthur? ¿No puede solucionarlo con los abogados, Josiah? Ya sabe lo mal que se me dan estas cosas. Arthur se encargaba de todo. Para mí, es un misterio.
—No, no, todo está arreglado. El banco se ha puesto en contacto con los abogados y todo está en orden. Se trata más bien de un tema privado, y tal vez me precipite, pero quería comentarlo con usted. Confío en que sea discreta.
A Consuelo no se le ocurría de qué podía tratarse, ni conseguía entender por qué no debía estar Annabelle presente. Por una fracción de segundo, se preocupó al pensar que tal vez Annabelle hubiera estado en lo cierto hacía unos meses y el hombre tuviera intención de cortejarla. Esperaba que no. Apreciaba muchísimo a Josiah, pero si él tenía alguna clase de interés romántico en ella, Consuelo lo rechazaría. No tenía intención de entrar en ese terreno, ni con él, ni con ningún otro hombre. Por lo que respectaba a Consuelo, ese capítulo de su vida se había cerrado.
—Quería hablarle de Annabelle —dijo él sin tapujos, para que ninguno de los dos se llevara a equívoco. Josiah era consciente de que estaba más cerca de la edad de Consuelo que de la de su hija, pero no se había encendido la llama del amor con Consuelo; lo único que sentía por ella era respeto, admiración y una amistad muy cercana. La familia Worthington había sido increíblemente hospitalaria con él desde la muerte de Arthur, y él había disfrutado mucho de su compañía—. Sé que todavía les quedan seis meses de duelo y que eso hace que usted se preocupe mucho por Annabelle. Es una lástima que se haya perdido las actividades de todo este primer año después de su presentación en sociedad, con las oportunidades que eso habría podido brindarle. Al principio, pensé que no debía decirle nada a propósito de mis sentimientos. Annabelle es jovencísima, y yo creía firmemente que sería más feliz con alguien de su edad. Pero, para ser sincero, ya no estoy tan convencido.
»Annabelle es una joven muy especial en muchos sentidos: es inteligente, intelectual, ávida de conocimientos, y mucho más madura que las otras chicas de su edad. No sé qué le parecerá lo que voy a proponerle, pero me gustaría que, una vez que haya transcurrido el año de duelo, me permitiera pedir su mano en matrimonio para ver qué opina ella. Si ambos actuamos con discreción y mantenemos el secreto, le daremos otros seis meses a su hija para acostumbrarse a mí. Si está de acuerdo, Consuelo, puedo seguir visitándolas con frecuencia. Pero antes quería pedirle permiso.
Consuelo se quedó allí sentada mirándolo fijamente. A sus ojos, Josiah era la respuesta a sus oraciones, un sueño hecho realidad. Estaba consumida por la preocupación de pensar que la vida pasara por delante de Annabelle durante aquel año, temía que acabara convertida en una solterona. Y aunque él tenía diecinueve años más que su hija, Consuelo consideraba que Josiah era perfecto para Annabelle.
Josiah pertenecía a una familia excelente, tenía una buena educación, era increíblemente cortés, encantador, apuesto, y poseía un buen trabajo en el banco del padre de Annabelle. Y por lo que había observado, sobre todo a lo largo del verano, su hija y él habían entablado una gran amistad, algo que Consuelo consideraba una base mucho más sólida para el matrimonio que los romances ilusos de algunas chicas, que al final no perduraban. Así era como se habían conocido Arthur y ella. Él era amigo de la familia, le había pedido permiso a su padre para cortejarla, y siempre habían sido amigos además de esposos. No se le ocurría mejor partido para su hija e, igual que Josiah, pensaba que Annabelle podría encajar con un hombre mayor y más maduro.
—Espero no haberla sorprendido... o enojado —añadió el hombre con cautela a la vez que Consuelo se inclinaba hacia delante para darle un abrazo maternal.
—¿Cómo iba a enojarme? Estoy encantada. Creo que Annabelle y usted formarían una pareja magnífica.
Además, Consuelo consideraba que, así, el año de luto no sería una pérdida de tiempo al fin y al cabo. Era la manera perfecta de que ambos se conocieran mejor. Josiah no tendría que enfrentarse a distracciones como fiestas y bailes, en los que otros jóvenes tontorrones pudieran hacer que Annabelle se fijara en ellos. Josiah era un hombre sensato y bien asentado, y habría sido un marido fantástico para cualquier mujer, en especial para su hija. Además, Annabelle no parecía verlo con malos ojos, mejor dicho, era evidente que le gustaba mucho.
—¿Cree que sospecha algo sobre sus intenciones? —le preguntó con inocencia Consuelo.
La madre ignoraba si él se le había declarado, si la había besado o cortejado, o si le había dado alguna pista de sus sentimientos por ella. Annabelle no le había contado nada a su madre sobre el tema, algo que la llevaba a creer que no tenía ni idea de qué le pasaba por la cabeza a Josiah.
—Todavía no le he dicho nada —le confesó el hombre con sinceridad—. No quería hacerlo hasta haber hablado con usted. De todas formas, llevo pensándolo desde el verano, aunque me parecía demasiado pronto. Y, por desgracia, he estado fuera estas últimas semanas. No creo que Annabelle sospeche nada. Preferiría esperar un poco antes de sacar el tema, hasta que el año de duelo haya terminado, en abril. A lo mejor podría proponérselo en mayo.
Josiah sabía que, para entonces, Annabelle ya tendría veinte años y él, treinta y nueve, un hombre muy mayor en comparación con ella. Tenía miedo de que la joven tuviera reparos por la diferencia de edad, pero no estaba seguro. Annabelle no flirteaba con él, pero Josiah tenía la impresión de que se habían convertido en muy buenos amigos. E, igual que su madre, pensaba que la amistad era una base excelente para el matrimonio. Sería su primera vez. Nunca le había pedido matrimonio a ninguna mujer, pero confiaba en que no fuera demasiado tarde. Además, últimamente había empezado a plantearse la posibilidad de tener hijos con ella. Annabelle le parecía la compañera ideal para el resto de su vida. Consuelo estaba más que emocionada.
—No habría podido encontrar a una persona más adecuada para ella, aunque me lo hubiera propuesto —dijo, encantada, y de inmediato tocó la campanilla para que se presentara el mayordomo. Cuando apareció William, le pidió que les llevara dos copas de champán. Josiah se quedó algo sorprendido. No esperaba que resultase tan sencillo.
—No sé si deberíamos celebrarlo aún. Todavía tenemos que preguntárselo a Annabelle... A lo mejor a ella no le parece tan buena idea como a nosotros dos. Es muy joven, y yo le duplico la edad.
—Tranquilo, Annabelle es muy sensata y no pensará en eso —repuso Consuelo mientras el mayordomo regresaba y les entregaba sendas copas de champán. Arthur tenía unas bodegas fabulosas y aquel champán era excelente—. Además, le gusta, Josiah. Creo que congenian mucho.
—Yo también lo creo —admitió él con cara de felicidad. Ojalá hubiera podido contárselo aquella misma tarde a Annabelle, pero no sería apropiado pedirle que se casara con él tan poco tiempo después de la muerte de Arthur y Robert—. Confío en que esté de acuerdo —añadió esperanzado.
—Eso depende de usted —le recordó Consuelo—. Tiene los próximos seis meses para ganarse su corazón y cerrar el trato.
—Sin que ella sepa mis intenciones... —dijo él cauteloso.
—A lo mejor puede soltar alguna indirecta de vez en cuando —sugirió su futura suegra, y él se echó a reír.
—Annabelle es demasiado lista. Si empiezo a darle pistas, será mejor que se lo pregunte directamente. Y no querría precipitarme, pues temo asustarla.
—Dudo que convencerla sea tan difícil como imagina —replicó Consuelo con una sonrisa de oreja a oreja, iluminada por el sol moteado de esa tarde cálida de octubre. Gracias a él había sido un día perfecto. Lo único que lamentaba era no poder compartirlo con Arthur, pues sospechaba que él también habría estado encantado con la propuesta.
Seguían charlando de forma desenfadada acerca del plan de Josiah cuando Annabelle apareció en el jardín con paso garboso, todavía con el delantal del hospital puesto. Lo llevaba manchado de sangre y su madre hizo una mueca.
—Quítate eso ahora mismo —la reprendió—, y ve a lavarte las manos. Por el amor de Dios, Annabelle, has traído un cargamento de gérmenes a casa.
Con la mano le indicó que se marchara. Annabelle regresó cinco minutos más tarde, sin el delantal y con un vestido negro, de luto riguroso. Parecía una novicia. Su semblante estaba serio, pero se deshizo en sonrisas en cuanto vio a Josiah, y lo único que continuó siendo sombrío en ella fue su indumentaria. Estaba de un humor excelente.
—He tenido un día fantástico —les comentó, y entonces se fijó en el champán que estaban bebiendo. Era muy observadora y nunca se le escapaba un detalle—. ¿Por qué bebéis champán, mamá? ¿Qué se celebra?
—Josiah ha venido para contarme que acaban de ascenderle en el banco —respondió su madre con rapidez—. Le han asignado un montón de cuentas nuevas para que las gestione. Y se me ha ocurrido darle la enhorabuena así. ¿Te apetece una copita?
Annabelle asintió. Le encantaba el champán, así que fue a buscar una copa, para después felicitar a Josiah por su ascenso, aunque los asuntos del banco nunca le habían parecido muy emocionantes. Solía aburrirse cuando su padre y Robert hablaban de esos temas. Le interesaba mucho más la ciencia.
—¿Qué ha hecho hoy en el hospital, Annabelle? —le preguntó Josiah con afecto. De pronto le dio la sensación de que ya era su esposa y sintió una emoción muy tierna hacia ella, algo que no podía demostrar.
—Un montón de cosas interesantes —contestó la joven con una sonrisa sincera, y después bebió un sorbito de champán. Ignoraba por completo que estaba brindando por su futuro enlace matrimonial, y Consuelo y Josiah sonrieron también al pensarlo. Esa tarde se habían convertido en conspiradores—. Me han dejado mirar mientras curaban una herida muy asquerosa.
—Si sigues hablando de eso, me voy a marear —advirtió su madre, y Annabelle soltó una carcajada, así que cambiaron de tema—. Un día u otro tendrás que dejar ese voluntariado —añadió Consuelo misteriosamente—. Algún día te harás mayor y te casarás, y no podrás seguir paseándote por los hospitales para ver cómo cosen heridas.
—Es lo que haces tú —le recordó Annabelle sonriendo.
—No es verdad. Yo me limito a llevar bandejas de comida a los pacientes de un hospital mucho más civilizado, y cuando vosotros erais pequeños no tenía tiempo de hacerlo. Ya volverás a retomar tus aficiones con el tiempo.
—No veo por qué tendría que dejar de ir al hospital si me casara —objetó Annabelle—. Hay muchas mujeres con niños que siguen trabajando en el hospital. Además, a lo mejor no me caso. ¿Quién sabe?
—¡No quiero ni oírte decir eso! —exclamó su madre, con el entrecejo fruncido, y después se volvió hacia Josiah.
Se moría de ganas de que se casaran y empezaran a tener hijos. Así se abriría un capítulo totalmente nuevo en sus vidas, y sabía que Annabelle sería una madre magnífica. Era muy paciente y cariñosa, y Consuelo creía que sería una esposa estupenda para Josiah.
Entonces empezaron a hablar de la boda de Hortie, para la que solo faltaban unas semanas. La joven estaba tan atareada que apenas la veía últimamente. Josiah anunció que iría a la boda. Annabelle dijo en voz baja que ella no podía, y al instante se sorprendió con el comentario de su madre.
—No veo por qué no puedes asistir a la ceremonia religiosa —dijo Consuelo con aire benévolo—. No hay ninguna ley que diga que no podemos ir a la iglesia. De hecho, seguramente deberíamos ir más a menudo. Puedes volver a casa cuando termine y saltarte la recepción. Así, por lo menos verás cómo se casa Hortie. Al fin y al cabo, es tu mejor amiga y la conoces desde la infancia.
Y seguramente sería la dama de honor en la boda de Annabelle, pensó Consuelo, cuando se casara con Josiah.
—Me encantaría llevarlas a las dos —se ofreció enseguida Josiah, y se quedó mirando a su futura esposa, que no se imaginaba lo que le pasaba por la cabeza al banquero. Sería su primera oportunidad de acompañarla en público y se emocionaba solo de pensarlo.
—Creo que no estaría bien que yo fuera —dijo Consuelo con voz queda. Todavía no estaba preparada para aparecer en público—. Pero sería un detalle que acompañara a Annabelle a la ceremonia.
—¿Le apetecería? —preguntó Josiah directamente a Annabelle.
Ella esbozó una amplia sonrisa mientras asentía.
—Me encantaría.
Irían todos sus amigos. A Hortie le habría gustado que ella fuese la dama de honor, pero en esos momentos era imposible. Así que de esa forma por lo menos podría asistir a la boda. Y se divertiría en compañía de Josiah, sería un poco como ir con Robert. Su hermano la había acompañado a varias fiestas, aunque se trataba de fiestas pequeñas, antes de la presentación en sociedad de la joven. Y Hortie iba a celebrar una boda por todo lo alto. Habían invitado a ochocientas personas, y lo más probable era que la mayoría asistiera.
—Tendremos que buscarte algo que ponerte —manifestó su madre pensativa. Annabelle tendría que lucir un vestido negro apropiado a las circunstancias y no tenía nada formal en tonos tan oscuros.
—¡Va a ser muy divertido! —exclamó Annabelle dando palmadas como una niña mientras su madre y Josiah le sonreían.
—Todo será divertido de ahora en adelante —le dijo su madre con una mirada cariñosa. Se sentía francamente aliviada por los planes de compromiso de Josiah...
Y, dicho esto, Annabelle rodeó con los brazos a Josiah por el cuello y le dio un abrazo.
—Gracias por llevarme —le dijo muy contenta.
—Es uno de esos sacrificios que uno tiene que hacer a veces en la vida... —bromeó él—. Lo soportaré.
Se moría de ganas de que transcurrieran los siguientes seis meses para entonces, con suerte, poder celebrar su propia boda. Consuelo pensaba exactamente lo mismo en ese momento, y ella y Josiah intercambiaron una mirada por encima de la cabeza de Annabelle y sonrieron. Annabelle todavía no lo sabía, pero acababan de escribir su futuro. Era lo único que había deseado su madre para ella desde su nacimiento.
### 5
Annabelle estaba casi tan emocionada como la propia Hortie cuando se acicaló para ir a la boda de su amiga. Su madre había llamado a la modista, quien le había confeccionado un hermoso vestido de tafetán negro en tiempo récord. El cuerpo y el dobladillo estaban ribeteados con terciopelo negro. Y llevaba una chaquetilla a juego y un sombrero con un reborde de piel de marta, que servía para restar seriedad al atuendo y para iluminarle la cara. Annabelle parecía una princesa rusa. Y a pesar de que las normas dictaban que no había que ponerse joyas durante el período de duelo, su madre le prestó un par de pendientes de diamantes. Tenía un aspecto exquisito cuando Josiah fue a buscarla. Y él también, con frac y corbata blanca, y con un elegante sombrero de copa que le habían hecho a medida en París. Formaban una pareja espectacular, y Consuelo notó que se le humedecían los ojos mientras los miraba. Lo único que lamentaba era que Arthur no estuviera allí para presenciarlo. Sin embargo, de haber estado él, tal vez nunca se hubiera producido el romance. Josiah había empezado a visitarlas por compasión y empatía tras su desgracia. El destino daba giros curiosos y tomaba caminos extraños.
Consuelo había insistido en que utilizaran su coche, así que Thomas, el chófer, los condujo a la boda en el impecable Hispano-Suiza que su padre consideraba su trofeo más preciado y que solo se empleaba en las ocasiones especiales. En opinión de Consuelo, ese era un acontecimiento de proporciones destacadas. Era la primera vez que su futuro yerno sería visto en público con su única hija. ¿Qué otra ocasión podía ser más importante que aquella, salvo su boda?
Los observó con afecto mientras salían por la puerta y después subió al dormitorio, perdida en sus pensamientos. Recordaba la primera vez que había salido con Arthur, después de que él pidiera su mano a su padre. Habían ido juntos a la fiesta de puesta de largo de una amiga. Solo tenía un año menos que su hija ahora.
El coche los llevó a la iglesia episcopal de St. Thomas, en la Quinta Avenida, y el chófer dejó que Josiah se bajara el primero. Al instante rodeó el coche y ayudó a Annabelle a salir. La joven llevaba la melena rubia recogida por debajo del sombrero de terciopelo y marta, y un velo fino le tapaba la cara. Tenía tanto estilo como cualquier dama de París, y parecía mayor de lo que era debido al opulento vestido negro. Josiah nunca se había sentido tan orgulloso.
—¿Sabe una cosa? Para ser alguien que disfruta fregando suelos en el hospital y diseccionando cadáveres, está guapísima vestida de gala —le dijo él divertido, y Annabelle se echó a reír, lo que hizo que pareciera todavía más bella, pues los pendientes de diamantes de su madre resplandecieron por debajo del fino velo. Tenía un aspecto elegante, sensual y romántico, y Josiah se sintió cautivado por la mujer con la que esperaba casarse. Aún no se había dado plena cuenta de lo bella que era, pues no era muy pizpireta y, al estar de luto, nunca se ponía ropa atractiva ni se maquillaba. Josiah había asistido a su presentación en sociedad hacía un año, pero ni siquiera entonces la había visto tan guapa como en esos momentos. Se había convertido en toda una mujer a lo largo de ese año.
Un amigo del novio, con corbata blanca y frac, los acompañó a uno de los primeros bancos de la iglesia, en la parte de la novia. Los estaban esperando, y Josiah se dio cuenta de que la gente los miraba con silenciosa admiración. Formaban una pareja excelente. Annabelle estaba ajena a todo aquello, encandilada por el auténtico bosque de orquídeas que había encargado la madre de Hortie. Annabelle había visto el vestido de novia y sabía que Hortie estaría espectacular. Tenía un tipo fantástico. El vestido era de talle bajo, en tela de raso blanco cubierto con encaje también blanco, y con una cola que se extendía metros y metros. Había dieciséis damas de honor ataviadas con vestidos de satén en un tono gris pálido, que llevaban unas orquídeas pequeñitas en la mano. Como correspondía en una boda tan elegante, Hortie iba a llevar un enorme ramo de lirios del valle.
Tomaron asiento mientras Annabelle miraba a su alrededor. Conocía a todas las personas que había sentadas delante y detrás de ellos, y Josiah también conocía a la mayor parte. La gente sonreía y hacía gestos discretos a modo de saludo. Estaban encantados de verla con Josiah, y él se dio cuenta en ese momento de que la madre de Annabelle le había permitido pintarse los labios. En su opinión, en toda la iglesia no había ni una sola mujer más guapa que la joven a quien tenía sentada a su lado, ni siquiera la novia, que al cabo de unos minutos caminó hacia el altar al compás de la marcha nupcial de _Lohengrin_ de Wagner.
Todos los ojos estaban puestos en Hortie, y su padre jamás se había sentido más orgulloso en su vida. Fue entonces cuando Annabelle se percató de que, el día de su boda, no tendría a nadie que la acompañara al altar, ni su padre, ni su hermano. Al pensarlo, los ojos se le llenaron de lágrimas, y cuando Josiah se dio cuenta de que lloraba le dio unas palmaditas cariñosas en el brazo. Tenía la impresión de saber en qué pensaba la joven. Cada vez la conocía mejor y comenzaba a intuir qué sentía. Además, a pesar de que no hacía mucho tiempo que formaba parte de su vida, empezaba a amarla. Estaba encantado de poder sentarse junto a ella durante la ceremonia religiosa. Todo fue como la seda, y cuando la pareja de recién casados recorrieron juntos el pasillo después de la boda, al son de Mendelssohn, todos los invitados demostraron su emoción. Las dieciséis damas de honor, acompañadas de igual número de amigos del novio, caminaron con solemnidad detrás de ellos, así como un niño de cinco años que había llevado las alianzas y una niña de tres años que parecía una princesa, con un vestido de organza blanco, quien olvidó echar los pétalos de rosa a los novios y se quedó con ellos apretados en el puño.
Annabelle y Josiah saludaron a sus amigos entre la multitud que se congregó a la entrada de la iglesia. Todos fueron pasando en orden para dar la enhorabuena a los novios y a los padres de ambos, y por último, una hora después de la ceremonia, todo el mundo se marchó de la iglesia y se dirigió al banquete. A Annabelle le habría encantado poder ir con ellos, pues sabía que la fiesta sería fantástica y se prolongaría hasta la madrugada, pero no podía ni planteárselo. Josiah la acompañó a casa en el coche y la dejó en la puerta. Annabelle le dio las gracias por haber ido con ella a la ceremonia.
—Me lo he pasado de fábula —dijo la joven, y parecía encantada. Había sido divertido ver a sus amigos, aunque fuera de manera fugaz, así como conocer a alguno de los amigos de Josiah, que, por supuesto, eran mucho mayores que ella, pero parecían simpáticos.
—Yo también —confesó él con sinceridad. Había sido un honor para él poder acompañarla. Era una joven hermosísima.
—No se entretenga si no quiere llegar tarde al banquete —le advirtió Annabelle mientras se quitaba el sombrero, le daba un beso en la mejilla y lo empujaba hacia la puerta. Sin el velo todavía parecía más guapa, y los pendientes de su madre resplandecían.
—No tengo prisa —repuso él con aire espontáneo—. He rechazado la invitación al banquete.
Le sonrió.
—¿Sí? —Annabelle estaba aturdida—. ¿Por qué? Va a ser la boda del año.
Los padres de Hortie habían tirado la casa por la ventana y Annabelle no quería que Josiah se perdiera el evento. No se le ocurrió por qué podía haber rechazado la invitación.
—Ya he ido a muchas bodas del año —comentó él entre risas y añadió—: Desde hace años... Siempre quedarán bodas. ¿Por qué iba a ir al banquete si usted no puede? No me parece apropiado. La ceremonia en la iglesia ha estado bien. Hemos visto a mucha gente. Y puedo ir a fiestas en cualquier otro momento. ¿Por qué no vamos a la cocina y preparamos algo de cenar? Sé hacer unos bocadillos buenísimos y una triste tortilla.
Ninguno de los dos había cenado. El servicio se retiraba por las noches y su madre estaba en la planta superior, probablemente dormida.
—¿Habla en serio? ¿Seguro que no prefiere ir al banquete? —insistió Annabelle. Se sentía culpable por impedir que él fuera.
—Sería muy raro que me presentara ahora, después de haber rechazado la invitación. —Volvió a soltar una risa—. Pensarían que estoy loco, y, además, no tendría sitio. Así que, veamos qué hay en la nevera. Voy a asombrarla con mis dotes culinarias.
—¿Con ese traje?
Josiah aún llevaba el frac y la corbata blanca, con unos elegantes botones y gemelos de nácar y diamantes.
—A lo mejor me quito la chaqueta, si no le incomoda demasiado.
Llevaba la corbata clásica de piqué con el chaleco a conjunto, y también lucía botones de nácar en esa prenda, que le habían hecho a medida en París junto con el sombrero de copa. Tenía una planta excepcional, y parecía el hombre ideal para la joven.
—No me incomoda. Yo también voy a quitarme la chaqueta —dijo Annabelle mientras se sacaba la chaquetilla de terciopelo que iba a juego con el vestido y dejaba a la vista sus hombros, de un blanco cremoso, y un pecho bien torneado que él miró con disimulo.
—Qué vestido tan precioso —dijo él sonriéndole con admiración.
—Me alegro de que le guste —contestó ella con timidez.
De repente le pareció que la velada había adquirido un aire muy adulto. Su fiesta de presentación en sociedad había sido el único evento de ese tipo al que había asistido. Y había disfrutado muchísimo yendo a la boda de su amiga acompañada de Josiah.
Annabelle lo condujo hasta la cocina y encendió la luz. Todo estaba inmaculado y en un orden perfecto. Miraron dentro de la nevera y vieron huevos, mantequilla, verduras hervidas, medio pavo y algo de jamón cocido. Annabelle sacó la mayor parte de esas cosas y las dejó en la mesa de la cocina. También encontró lechuga y algunas hortalizas frescas en la despensa.
La joven puso la mesa con la vajilla del servicio, que contrastaba con su vestido de noche, mientras Josiah se quitaba la chaqueta del frac y preparaba la cena. Troceó el jamón y el pavo en láminas finas, hizo una ensalada y también una tortilla de queso estupenda. La cena estaba deliciosa, y ambos disfrutaron sentados a la mesa de la cocina mientras charlaban y comentaban a quiénes habían visto en la ceremonia. Josiah le contó chismorreos acerca de personas a quienes le había presentado, y ella le habló de algunos de sus amigos. Fue una conversación animada y se quedaron de sobremesa un buen rato después de terminar la cena. Annabelle no tenía la llave de la bodega, así que Josiah le dijo que le parecía perfecto acompañar los platos con un vaso de leche. Era la mejor velada que Annabelle pasaba desde hacía años.
Hablaron de las vacaciones y él le dijo que pensaba viajar a Boston para pasar el día de Acción de Gracias con su familia, pero le comentó que regresaría a Nueva York antes de Navidad. Ella comentó que tenía que acordarse de preguntarle a su madre si podían invitarlo a cenar en Nochebuena. Aquel año iban a ser unas fechas difíciles para ellas. Le costaba creer que un año después de su puesta de largo la vida de ambas hubiera cambiado de manera tan dramática, y así se lo contó a su amigo.
—En la vida nunca se sabe —observó él con tranquilidad—. Debe dar gracias por lo que tiene, mientras lo tenga. El destino es impredecible, y algunas veces no sabemos lo afortunados que somos hasta que la suerte nos da un revés.
Ella asintió y lo miró con tristeza.
—Yo sí sabía lo afortunados que éramos, y mi madre también. Todos lo sabíamos. Siempre consideré que tenía suerte de contar con unos padres y un hermano como los míos. Pero no puedo creer que ya no estén... —dijo en voz baja, y Josiah la miró y colocó una mano con delicadeza encima de la de ella.
—Algunas veces el destino provoca que ciertas personas salgan de nuestra vida y, cuando menos nos lo esperamos, otras personas entran en ella. Debe tener confianza en que las cosas van a marchar bien de ahora en adelante. Su vida acaba de empezar, Annabelle.
Ella volvió a asentir con la cabeza.
—Pero para mi madre ya ha terminado. No creo que se recupere nunca.
Annabelle se preocupaba mucho por ella.
—Nunca se sabe —dijo él con afecto—. También a ella pueden ocurrirle cosas buenas.
—Eso espero —susurró Annabelle, y le dio las gracias por preparar la cena. Había sido una velada estupenda. Él la ayudó a colocar los platos sucios en el fregadero, y después ella se volvió hacia Josiah con una sonrisa. La amistad florecía entre ambos—. Es muy buen cocinero.
—Espere a probar mis suflés. También preparo el pavo relleno para Acción de Gracias —contestó muy orgulloso.
—¿Cómo ha aprendido a cocinar?
Estaba intrigada. Ninguno de los hombres de su familia sabía cocinar, y Annabelle ni siquiera estaba segura de si sabían dónde se hallaba la cocina.
Él se rió a modo de respuesta.
—Si uno se queda soltero tantos años como yo, tiene que elegir entre morirse de hambre o aprender a alimentarse por sí mismo. O puede salir a cenar todas las noches, pero es agotador. Muchas veces, prefiero quedarme en casa y cocinar.
—Yo también, bueno, me refiero a lo de quedarme en casa. Como cocinera no soy nada buena.
—No le hace falta —le recordó él, y por un instante la joven sintió un poco de vergüenza. Toda su vida había tenido servicio. Igual que él.
—De todas formas, debería aprender un día de estos. A lo mejor lo hago.
Seguía admirada ante lo competente y organizado que era él entre los fogones.
—Podría enseñarle algunos trucos —se ofreció él, y a Annabelle le gustó la idea.
—Suena divertido —contestó muy entusiasmada. Siempre se lo pasaba bien en su compañía.
—Piense que es como la ciencia, así le parecerá más sencillo.
Ella se echó a reír mientras apagaba las luces y Josiah la siguió hacia la escalera. Después de subirla, cruzaron dos puertas y regresaron al distribuidor principal, iluminado por una lámpara de araña. El hombre llevaba en la mano la chaqueta del frac, y el sombrero de copa y los guantes se habían quedado en la mesita del recibidor. Los recogió, pasó los brazos por las mangas de la chaqueta y se caló el sombrero. Estaba más elegante que nunca, y nadie habría sospechado que acababa de preparar la cena.
—Tiene un aspecto imponente, señor Millbank. Me lo he pasado estupendamente con usted esta noche.
—Lo mismo digo —respondió él y le dio un beso casto en la mejilla. No quería precipitarse, tenían muchos meses por delante en los que serían solo amigos, a pesar de la bendición de su madre—. Nos veremos pronto. Gracias por ir a la boda de Hortie conmigo, Annabelle. Esas cosas pueden ser aburridísimas, a menos que uno tenga con quien divertirse.
—Sí, estoy de acuerdo —contestó ella—. Y lo mejor ha sido comentar todos los detalles después en la cocina.
Soltó una risita traviesa, y él también sonrió.
—Buenas noches, Annabelle —dijo Josiah.
Entonces abrió la puerta y se volvió para mirarla antes de cerrarla tras de sí. Ella recogió la chaqueta de la silla, volvió a ponerse el sombrero formando un ángulo divertido y subió la escalera que conducía a su habitación con una sonrisa y un tremendo bostezo. Había disfrutado muchísimo de la velada y se alegraba con todo su corazón de que Josiah y ella fueran amigos.
### 6
Para alegría de Consuelo, a petición de Annabelle invitaron a Josiah a cenar en Nochebuena. No se trataba de un gesto romántico por parte de Annabelle, sino que la joven consideraba que él había sido tan amable con ellas que tenían que agradecérselo de algún modo, y más sabiendo que iba a pasar solo la Navidad. Como solían hacer los Worthington, se vistieron de etiqueta para el banquete de Nochebuena. Annabelle y su madre lucían sendos vestidos de noche y, tal como le habían indicado, Josiah apareció con un frac hecho a medida con la camisa y el chaleco inmaculadamente almidonados, y como complemento, unos cubrebotones y gemelos de perla antigua y diamantes que habían pertenecido a su padre. Además, conmovió a madre e hija con unos obsequios.
Annabelle había comprado una bufanda de cachemir para Josiah, además de un libro de cocina a modo de broma, pero él dijo que le encantaba. Por su parte, la muchacha sintió un poco de apuro al descubrir que él le había comprado una preciosa pulsera de oro en Tiffany, y un elegante pañuelo de seda para su madre.
Los tres compartieron una encantadora velada cargada de afecto, y se sentaron junto a la chimenea después de cenar. Josiah se sirvió una copa de coñac, mientras que las dos damas bebieron licor de huevo con unas gotitas de ron, según una receta que solía hacer Arthur, y todos admiraron el árbol que Consuelo y Annabelle habían decorado. Como era lógico, ese año las Navidades se les hacían muy duras, así que Josiah evitó el tema de las últimas noticias publicadas acerca del _Titanic_. Sabía que, ocurriera lo que ocurriese, ellas no querrían saberlo. Nada mitigaría su pena.
Annabelle les comunicó que Hortie había regresado de la luna de miel esa misma tarde y que se había apresurado a contarle que ya estaba embarazada. Hortie no tenía dudas sobre su estado, y decía que tanto a James como a ella les hacía mucha ilusión, aunque a Hortie también le daba un poco de miedo. Acababa de convertirse en esposa y ya iba a pasar a ser madre. El bebé nacería aproximadamente a finales de agosto, si sus cálculos eran correctos. Le contó que había sido concebido en París, y entonces se rió con picardía y misterio, como la niña que seguía siendo a pesar de su nuevo estatus, e hizo toda clase de comentarios acerca de su vida sexual, unos detalles que Annabelle no quería ni oír. Hortie le contó que el sexo era fabuloso y que James era increíble en la cama, aunque era cierto que ella no tenía muchas experiencias con las que comparar, pero jamás en su vida se había divertido tanto. Por supuesto, Annabelle no comentó nada de todo eso delante de Josiah y de su madre, sino que les dijo que Hortie iba a tener un hijo y que estaba muy contenta. Al enterarse de la noticia, Consuelo fantaseó con la ilusión de que las Navidades siguientes Annabelle y Josiah tuvieran una buena nueva similar que compartir con ella, suponiendo que para entonces ya estuvieran casados, cosa que esperaba fervientemente. No veía ningún motivo para que la boda se retrasara mucho después de la petición de mano.
Antes de marcharse, Josiah les contó que iba a pasar unos días, hasta Año Nuevo, esquiando en Vermont con su antiguo compañero de universidad, Henry Orson. Como, según él, eran los únicos hombres solteros que quedaban de su edad, le encantaba contar con él para realizar esas actividades. Su escapada de esquí a Woodstock para esas fechas ya era una tradición que apalabraban todos los años, y a Josiah le hacía especial ilusión esa vez, pues sabía que habían añadido un nuevo trampolín de esquí a su pista favorita. Josiah le preguntó a Annabelle si sabía esquiar o ir con raquetas. Ella contestó que no, pero que le gustaría aprender. Consuelo y Josiah intercambiaron una mirada velada, y él le prometió que algún día le enseñaría. Propuso que tal vez Annabelle, su madre y él podrían hacer un viaje juntos a Vermont. A la muchacha se le iluminaron los ojos y dijo que sonaba divertido. Él les comentó que, además, en Woodstock también podían hacerse excursiones fantásticas en trineo.
Josiah se quedó con ellas hasta medianoche y, después, les agradeció una vez más los regalos y la exquisita cena, y Consuelo desapareció misteriosamente mientras la pareja se despedía. Annabelle volvió a darle las gracias a Josiah con mucha efusividad por la pulsera, que le encantaba, y que ya se había puesto.
—Me alegro de que te guste —dijo él con afecto. Ahora que se tenían más confianza, había empezado a tutearla—. Sé que se supone que durante el luto no debes llevar joyas, así que, si tu madre no te deja ponértela ahora, puedes hacerlo más adelante.
No quería ofender a Consuelo regalándole la pulsera a Annabelle todavía en el período de duelo, pero deseaba obsequiarle con algo que ella pudiera disfrutar durante mucho tiempo. Y tampoco quería regalarle algo demasiado ostentoso, pues ella podría haber sospechado de sus intenciones. Pensó que una sencilla pulsera de oro sería discreta, y Annabelle estaba emocionada con el obsequio.
—Que te diviertas esquiando —dijo Annabelle mientras lo acompañaba a la puerta. Josiah se cubrió el frac con un abrigo negro de corte impecable y una bufanda de seda blanca, con un sombrero de fieltro. Como siempre, lo encontró increíblemente elegante. Y ella estaba muy guapa y juvenil con su sencillo vestido de fiesta negro.
—Te llamaré cuando vuelva —le prometió Josiah—. Será después de Año Nuevo.
Le dio un beso tímido en la mejilla y ella se lo devolvió. Así se despidieron.
Annabelle encontró a su madre en la biblioteca, ojeando un libro. Era uno de los volúmenes de su padre que Annabelle había leído ya.
—¿Qué haces aquí metida? —preguntó, con aire sorprendido. Su madre no era muy aficionada a la lectura, y se volvió hacia su hija con una sonrisa cariñosa.
—Pensaba que Josiah y tú querríais estar a solas para despediros.
Miró a su hija con mucha intención, y esta se enojó por un momento.
—¿Josiah? ¡No seas tonta, mamá! Solo somos amigos. No empieces a formarte ideas raras sobre él. Eso lo estropearía todo. Me gusta la amistad que compartimos tal como es.
—Pero ¿y si él quisiera algo más? —preguntó Consuelo crípticamente, y su hija frunció el entrecejo.
—No quiere nada. Y yo tampoco. Las cosas nos parecen bien como están. Que Hortie se haya casado y vaya a tener un hijo no significa que yo tenga que hacer lo mismo. Ni siquiera puedo volver a salir hasta dentro de cuatro meses. Así que todavía tardaré una buena temporada en conocer a alguien, y además, quién sabe si alguna vez encontraré a un hombre que me guste y con quien quiera casarme. —Suspiró y puso los brazos alrededor de su madre—. ¿O es que intentas deshacerte de mí, mamá? —preguntó con cariño.
—Claro que no, lo único que quiero es que seas feliz. Y nada hace más feliz a una mujer que un marido y un hijo. Pregúntale a Hortie. Me apuesto lo que quieras a que se muere de ganas de tener a su bebé en brazos.
—Parece muy feliz, sí —admitió Annabelle con una sonrisa tímida—. Quería contarme un montón de detalles sobre la luna de miel. Por lo que me ha dicho, se lo han pasado muy bien.
Sobre todo en la cama, pero Annabelle no iba a decirle eso a su madre, ni siquiera ella quería saberlo.
—¿Cuándo tiene que nacer el bebé?
—A finales de agosto, creo. Hortie no está segura. Pero dice que pasó en París, y que James también está muy emocionado. Quiere que sea niño.
—Todos los hombres dicen lo mismo. Pero con quienes pierden la cabeza luego es con las niñas. Tu padre se quedó prendado de ti en cuanto te vio.
Ambas sonrieron ante el recuerdo. Había sido una Nochebuena difícil para las dos, pero tener la compañía de Josiah les había ayudado mucho. Todo era más sencillo y más agradable cuando él estaba presente.
Cogidas del brazo, subieron la escalera y se dirigieron a los respectivos dormitorios. Al día siguiente se dieron los regalos de Navidad. Consuelo le había comprado a su hija un abrigo de pieles magnífico, y Annabelle había elegido para su madre un par de pendientes de zafiros de Cartier. Había intentado comprarle el tipo de regalo que le habría hecho su padre, pero en una escala algo más modesta. Él siempre compraba regalos muy espléndidos para todos. Y, en cierto modo, Annabelle quería compensárselo a su madre ese año, aunque sabía que no podía mitigar de esa forma el dolor de la pérdida. Sin embargo, su madre se sintió muy conmovida por el gesto, y por lo hermoso que era el regalo de su hija, de modo que se puso los pendientes al instante.
Bajaron juntas a la planta inferior para tomar el copioso desayuno que les había preparado Blanche. Había nevado por la noche y una manta de color blanco cubría todo el jardín. Después del desayuno, se vistieron y salieron a pasear por el parque. Les iba a resultar difícil mantenerse todo el día entretenidas. Habían perdido a la mitad de la familia, y en fechas señaladas como aquella la ausencia de Arthur y Robert pesaba como una losa.
Al final, el día no resultó tan doloroso como habían temido. Las dos tenían mucho miedo a que llegara la Navidad y habían intentado por todos los medios estar ocupadas ese día. Consuelo y Annabelle habían comido juntas, habían jugado a las cartas por la tarde y, a la hora de cenar, ambas estaban fatigadas y listas para irse a dormir. Habían pasado el mal trago, eso era lo importante, y mientras Annabelle se desvestía por la noche, se descubrió pensando en Josiah, que estaría en Vermont. Se preguntó si Henry y él habrían llegado bien a las pistas y si se estarían divirtiendo. Le encantaría ir a esquiar algún día con ellos dos, tal como Josiah había propuesto. Seguro que era muy entretenido. Confiaba en tener la oportunidad de acompañarlos, tal vez al año siguiente, si podía convencer a su madre para que le diera permiso.
El resto de las vacaciones resultaron más llevaderas que el día de Navidad. Annabelle pasó algún rato con Hortie, aunque de lo único que le hablaba ahora su amiga era del bebé, igual que no había hablado más que de la boda durante los seis meses anteriores. Apenas tenía otras cosas en la cabeza. Consuelo le dio la enhorabuena cuando la vio, y Hortie se explayó durante media hora hablando de París y de toda la ropa que se había comprado allí, aunque al cabo de poco dejaría de caberle... Dijo que ese verano irían a Newport a pesar de todo, pues no le importaba dar a luz allí. De todas formas, pensaba tenerlo en casa, tanto si era en Newport como si era en Nueva York. Mientras escuchaba cómo Hortie le contaba todo esto a su madre, Annabelle se sintió excluida de la conversación. No tenía nada que aportar. Hortie se había convertido en una mujer casada y en una madraza de la noche a la mañana. Pero Annabelle seguía queriéndola mucho, tanto si era aburrida como si no. Hortie le había comprado un jersey precioso en París, con botones perlados. Era de un rosa muy pálido, y Annabelle se moría de ganas de que llegara el verano para ponérselo.
—No quería comprarte nada negro —dijo Hortie a modo de disculpa—. Me parecía muy tristón. Además, dentro de muy poco ya podrás ponértelo. Espero que te guste.
—¡Me encanta! —le confirmó Annabelle, y lo decía de corazón. Tenía un cuello de encaje finísimo y era de un rosa pálido muy elegante. A Annabelle le favorecía mucho, pues encajaba con su tono de piel y el color de su pelo.
Las dos jóvenes comieron juntas varios días esa semana y se sintieron como dos adultas cuando entraron en el restaurante Astor Court del hotel St. Regis. Hortie se tomaba su nuevo estatus muy en serio, se arreglaba mucho, lucía todas las joyas que James le había regalado y estaba fantástica. Cuando iban a comer, Annabelle se ponía el abrigo de pieles que le había regalado su madre en Navidad. Y tenía la sensación de jugar a disfrazarse de persona mayor con la ropa del armario de su madre. También lucía la pulsera de Josiah en la muñeca.
—¿Cuándo te la has comprado? —preguntó Hortie en cuanto la vio—. Me gusta mucho.
—A mí también —contestó espontáneamente Annabelle—. Me la regaló Josiah Millbank para Navidad. Fue un detalle muy bonito por su parte. A mamá le regaló un pañuelo de seda.
—Los dos estabais radiantes en nuestra boda. —De repente, los ojos de la joven se iluminaron, pues se le había ocurrido algo—: Oye, ¿qué me dices de él?
—¿Qué quieres que te diga? —Annabelle estaba perpleja.
—Me refiero a qué te parece... Ya sabes, como esposo.
Annabelle le respondió con una carcajada.
—No seas tonta, Hortie. Me dobla la edad. Hablas igual que mamá. Te lo aseguro: si pudiera, mi madre me casaría con el lechero.
—¿El lechero es guapo? —preguntó Hortie, que se rió al imaginárselo.
—No. Debe de tener unos cien años y no le queda ni un diente.
—Hablo en serio, ¿por qué no Josiah? A él le gustas. Siempre pulula a tu alrededor.
—Solo somos amigos. Nos gustan las cosas tal como están. Si entráramos en otro terreno se estropearía todo.
—Pues es una pulsera preciosa para regalársela a una amiga.
—Es solo un regalo, no es una petición de mano. Lo invitamos a cenar con nosotras para Nochebuena. Este año ha sido todo tan triste... —dijo, cambiando de tema.
—Claro —dijo Hortie comprensiva, y por un momento se olvidó de Josiah—. Lo siento mucho, Belle, debe de ser horrible.
Annabelle se limitó a asentir con la cabeza, así que se pusieron a hablar de otros temas, en concreto, de ropa. Hortie no sabía qué iba a ponerse cuando empezara a engordar. Tenía pensado ir a la modista de su madre para que le preparara algunos conjuntos en cuestión de semanas. Le contó que las prendas ya empezaban a apretarle por la cintura y que el corsé la aprisionaba. Le juró que tenía el pecho el doble de grande.
—A lo mejor tienes gemelos —se aventuró a decir Annabelle con una sonrisa.
—Sería divertido, ¿verdad? —contestó Hortie entre risas.
No se imaginaba todo lo que supondría cuidarlos, así que en esos momentos no era más que una posibilidad emocionante para ella.
Se sintió algo menos emocionada dos semanas más tarde, cuando empezó a sentir náuseas. Y durante los dos meses siguientes, apenas salió de la cama. Se sentía como un trapo. Para cuando empezó a notarse medio recuperada, ya estaban a mediados de marzo. Mientras tanto, Annabelle tuvo que ir a visitarla a su casa, pues Hortie no podía salir. Su amiga no había ido a ninguna fiesta desde Navidad, y ya no estaba tan contenta como al principio de estar embarazada. La mayor parte del tiempo se sentía gorda y mareada, y le dijo que no era nada divertido. Annabelle lo sentía mucho por ella, y le llevaba libros y flores, así como revistas para que se entretuviera. Su principal misión en la vida pasó a ser alegrar a su amiga. Y entonces, por fin, en abril Hortie se levantó de la cama. Para entonces el embarazo era más que evidente, pues ya estaba de cinco meses. Todas las mujeres de su familia aseguraron que solo llevaba un bebé, pero estaba inmensa, y su madre comentó que sería chico.
Era el único tema de conversación de Hortie y, la mayor parte del tiempo, se limitaba a quejarse desde la cama. Repetía que se sentía como una ballena. Y también decía que James ya casi no hacía el amor con ella, algo que la decepcionaba mucho. Casi siempre que salía con sus amigos, lo hacía sin ella, y le prometió que, cuando naciera el bebé, la compensaría saliendo con ella todo el tiempo. Sin embargo, su madre le recordó que entonces tendría que darle de mamar y que, aun cuando no le diera el pecho, tendría que cuidar del bebé en todo momento. Así pues, resultaba que ser adulta no era tan divertido. Annabelle tenía una paciencia infinita, escuchaba los lamentos y quejidos de su amiga, quien, además, por entonces lloraba a la mínima.
Consuelo solicitó una misa de aniversario para conmemorar que hacía un año del fallecimiento de Arthur y Robert. Volvieron a celebrarla en la iglesia de Trinity, y después ofrecieron algo de comer en su casa. Todos los amigos de su padre asistieron al acto, y también algunos primos de la familia, entre ellos Madeleine Astor, cuyo difunto esposo era primo de Consuelo. Josiah también las acompañó, por supuesto, así como todos los demás trabajadores del banco, incluido Henry Orson.
Josiah había pasado mucho tiempo con ellas en casa durante los últimos meses, siempre tan atento, siempre tan divertido, siempre con una broma o una sonrisa, o con un obsequio especial para ellas. Le había comprado a Annabelle una serie de libros de medicina, que le encantaron, y la obra _Anatomía de Gray_. Aparte de su querida Hortie, Annabelle consideraba que Josiah era el mejor amigo del mundo, y ahora la joven disfrutaba más de su compañía, pues él no estaba esperando un hijo ni se lamentaba de su suerte en todo momento. Siempre se divertía con él, y últimamente Josiah había empezado a llevarla a restaurantes elegantes para cenar. Una vez que hubo pasado la fecha del aniversario, Annabelle se emocionó pensando en que pronto podría ir a fiestas y otros eventos con él. No había salido a ninguna parte, salvo a la boda de Hortie, desde hacía más de un año. Antes del hundimiento del _Titanic_ , sus padres habían estado ausentes durante dos meses y ella había estado enferma el mes anterior a eso, de modo que hacía quince meses que no era vista en sociedad. A su edad, eso era una eternidad.
En mayo cumpliría veinte años. Y dos semanas después de la ceremonia en recuerdo de su padre y su hermano, Josiah la invitó a lo que prometía ser una cena muy especial en Delmonico's, un restaurante de lujo en el que Annabelle no había comido nunca y al que se moría de ganas de ir. Se compró un vestido nuevo para la ocasión, y su madre la peinó con esmero. Consuelo sospechaba lo que iba a ocurrir en aquella velada y, por el bien de todos, confiaba en que fuera un éxito.
Josiah fue a buscarla a las siete. Esta vez iba en su coche, y, en cuanto vio a Annabelle con su vestido nuevo, silbó admirado. Era de seda color marfil y tenía unos pliegues muy finos. Dejaba los hombros al descubierto, por encima de los cuales se había puesto un fino chal de seda blanco. Contrastaba tremendamente con la ropa negra que la muchacha había llevado durante tanto tiempo. Su madre seguía vestida de luto, porque decía que aún no se sentía preparada para dejarlo. Annabelle tenía miedo de que nunca se sintiera preparada. Pero ella estaba muy agradecida de haber podido apartar por fin sus vestidos negros. Ya era hora.
Llegaron al restaurante de lujo a las siete y media, y enseguida los condujeron a una mesa tranquila en un rincón. A Annabelle le parecía emocionante salir a cenar con Josiah. Allí sentada a la mesa, enfrente de él, se sintió increíblemente adulta, todavía más que en compañía de su amiga Hortie. Se quitó el chal que le cubría los hombros. Todavía llevaba puesta la pulsera de oro que Josiah le había regalado para Navidad. No se la quitaba nunca.
El camarero le preguntó si le apetecía un cóctel, pero ella lo rechazó muy nerviosa. Su madre le había advertido que no debía beber mucho, apenas una copita de vino. Según le dijo a Annabelle, no causaría muy buena impresión si se emborrachaba durante la cena. La joven se había reído al imaginárselo y le dijo a su madre que no tenía de qué preocuparse. Josiah pidió un whisky escocés con soda, algo que chocó un poco a Annabelle. Nunca le había visto beber licores fuertes hasta entonces, y se preguntó si él también estaba nervioso, aunque no se imaginaba por qué iba a estarlo, pues eran muy buenos amigos.
—¿No te apetece un poco de champán? —le preguntó Josiah cuando llegó su copa.
—No, gracias, estoy bien —contestó ella antes de soltar una risita—. Mi madre me ha dicho que no me emborrache ni te deje en ridículo.
Él también se echó a reír. No había nada que no pudieran contarse el uno al otro. Charlaron de mil temas interesantes y disfrutaron de la compañía mutua. Los dos pidieron el famoso plato de bogavante a la Newburg, especialidad de la casa, y tarta Alaska de postre.
La velada fue fantástica y, cuando llegó el postre, Josiah pidió champán para los dos. El camarero les llevó la botella a la mesa y la abrió delante de ellos, y Annabelle sonrió cuando dio el primer sorbo. Solo había bebido una copa de vino en toda la cena, así que no había incumplido la advertencia de su madre.
—Es delicioso —comentó Annabelle.
Josiah había pedido una botella especialmente buena. Él había bebido más que su acompañante, pero también seguía sobrio. Quería mantener la compostura para tener valor de decir lo que debía decir. Llevaba mucho tiempo esperando ese momento, que por fin había llegado. Se le formó un nudo en el estómago y sonrió nervioso mientras brindaban.
—Por usted, señorita Worthington, y por la maravillosa amistad que me ha brindado —dijo retomando las formalidades para halagar a Annabelle, y esta sonrió.
—Lo mismo digo —dijo ella con gentileza antes de dar otro sorbo a la copa de champán. No tenía ni la menor idea de lo que le pasaba por la cabeza a Josiah. Se le notaba en la cara. Annabelle era la inocencia personificada.
—Disfruto mucho en tu compañía, Annabelle —se limitó a decir Josiah, y era cierto.
—Yo también —se hizo eco ella—. Siempre nos divertimos mucho.
Entonces se puso a hablar de los libros de medicina que le había regalado, y él la interrumpió con educación, ante lo que ella se quedó sorprendida. Lo habitual era que la dejara hablar horas y horas sobre lo que había aprendido gracias a sus lecturas.
—Tengo algo que decirte. —La joven lo miró con ojos interrogantes; se preguntaba qué querría contarle. Esperaba que no hubiera ningún problema—. He esperado mucho tiempo. No me parecía adecuado hacerlo antes de abril, pues quería esperar al aniversario del funeral. Pero tu cumpleaños ya está cerca. Así que, aquí estamos.
—¿Hemos venido a celebrar algo? —preguntó ella con ingenuidad. Se sentía un poco achispada después del champán.
—Confío en que sí —contestó él con cariño—. Depende de ti. Tú eres quien debe decidir. Lo que llevo esperando a decirte desde el verano pasado es que estoy enamorado de ti. No me gustaría estropear nuestra amistad, ni incomodarte. Pero debo confesar que en algún momento me enamoré de ti, Annabelle. Creo que hacemos una pareja fantástica y no puedo seguir soltero toda la vida. Nunca he conocido a ninguna mujer que me haya animado a sentar la cabeza. Sin embargo, no se me ocurre ningún cimiento mejor para sellar este vínculo que la verdadera amistad, y nosotros somos como uña y carne. Así pues, me gustaría pedirte que me hicieras el honor de casarte conmigo, si lo deseas.
Cuando dijo esas palabras, vio que Annabelle lo miraba con una sorpresa mayúscula. Tenía la boca entreabierta y los ojos como platos.
—¿Hablas en serio? —le preguntó cuando por fin recuperó el aliento.
Josiah asintió.
—Sí, hablo en serio. Sé que para ti es una sorpresa, y puedes darle vueltas, si te hace falta. Annabelle, hace mucho tiempo que estoy enamorado de ti.
—¿Por qué no me lo habías dicho?
Josiah era incapaz de descifrar si ella estaba contenta o enfadada. La expresión más evidente era la de sorpresa.
—Pensaba que debía esperar hasta este momento.
Ella asintió. Era lo más adecuado, tenía sentido. Y Josiah siempre hacía las cosas bien. Era una de las cualidades que más le gustaban de él. Seguía mirándolo con incredulidad.
—¿Estás disgustada? —le preguntó él con aire de preocupación, y ella sacudió la cabeza. Tenía lágrimas en los ojos cuando lo miró a la cara.
—No, claro que no. Estoy emocionada —contestó, y alargó el brazo por encima de la mesa para tocarle la mano.
—Sé que soy mucho mayor que tú. Casi podría ser tu padre. Pero no quiero serlo. Quiero ser tu esposo, y prometo cuidar de ti para siempre.
Annabelle creyó sus palabras al escucharlas, y después le preguntó:
—¿Lo sabe mi madre?
Eso explicaría las discretas insinuaciones que había hecho algunas veces acerca de Josiah, cosas a las que Annabelle había restado importancia.
—Le pedí permiso para cortejarte en octubre, y me lo dio. Creo que considera que haríamos una excelente pareja.
—Yo también —susurró Annabelle con una sonrisa tímida—. Pero es que nunca habría esperado que ocurriera algo así. Creía que éramos solo amigos.
—Seguimos siendo amigos —respondió él también sonriendo—. Y si aceptas mi proposición, lo seremos siempre. Creo que los esposos deben ser los mejores amigos, aparte de todo lo demás. Me gustaría compartir unos hijos contigo, así como el resto de mi vida. Y siempre, siempre seré tu amigo.
—Yo también —dijo ella con aire confuso.
La mención de tener hijos con él la había sobresaltado un poco, pero había conmovido su corazón. Mientras lo escuchaba, procuraba no pensar en todos los detalles que Hortie le había descrito de su viaje a París. Lo que compartía con Josiah parecía mucho más puro. Aborrecería estropearlo. Aunque, claro, Hortie siempre había sido bastante alocada y, ahora que había descubierto el sexo, era todavía peor. Lo único que la frenaba un poco en esos momentos era el ir engordando día a día.
—¿Necesitas tiempo para pensarlo? Sé que te ha pillado por sorpresa. Llevo muchos meses mordiéndome la lengua. —Y entonces se echó a reír—. Por eso he pedido un whisky, he bebido media botella de vino y ahora el champán. Supongo que tu madre tendría que haberme advertido a mí que no me emborrachara. Necesitaba tener valor suficiente para decírtelo. No estaba seguro de si ibas a pegarme un bofetón o a decirme que sí.
—¿Solo tengo esas dos opciones? —preguntó ella mientras buscaba la otra mano de Josiah. Ya tenía una de ellas cogida—. ¿O pegarte un bofetón o decirte que sí?
—Básicamente.
Josiah le sonrió y apretó las dos manos de Annabelle entre las suyas.
—Entonces es muy fácil. La respuesta es sí. Si ahora te diera un bofetón, montaría un numerito. Es posible que nos echaran del restaurante. Y entonces a lo mejor dejarías de ser mi mejor amigo.
—No lo haría. —Y Josiah retomó la misma pregunta que ella le había hecho cuando él le había pedido matrimonio—. ¿Hablas en serio?
Se refería a su tímido «sí». Era sutil, pero sincero.
—Sí, hablo en serio. Nunca había pensado en nosotros dos en estos términos. Y cuando mi madre te lo sugirió, creo que hizo una locura. Pero, ahora que lo pienso, no se me ocurre ninguna otra persona en el mundo con quien me gustaría casarme. Salvo Hortie, tal vez, pero a veces puede ser insoportable. De modo que, si tengo que elegir a uno de mis mejores amigos para casarme, prefiero casarme contigo.
Los dos se rieron con ganas mientras ella explicaba sus motivos.
—¿Te he dicho que te amo? —le preguntó Josiah.
—Creo que sí. Pero puedes volver a decírmelo —dijo ella con remilgos y una sonrisilla encantadora.
—Te amo, Annabelle.
—Yo también te amo, Josiah. Te quiero muchísimo. Supongo que es la mejor manera de proteger nuestra amistad para siempre.
Y entonces, en cuanto lo hubo dicho, Josiah vio que a Annabelle se le llenaban los ojos de lágrimas y le temblaba el labio, y se dio cuenta de la tristeza que sentía.
—¿Qué te pasa? —le susurró.
—Ojalá pudiera contárselo a Robert y a mi padre. Es lo más importante que me ha pasado en la vida y no tengo a nadie a quien contárselo. Mi madre ya lo sabe. Y ¿quién me acompañará al altar?
Mientras lo decía, las lágrimas empezaron a resbalarle por las mejillas.
—Ya se nos ocurrirá algo —dijo él con afecto mientras le secaba las lágrimas con la mano—. No llores, cariño. Todo saldrá bien.
—Sí.
Estaba totalmente segura de que con Josiah siempre estaría en buenas manos. De repente, le pareció lo más lógico del mundo, aunque nunca se lo hubiera planteado antes. Sin embargo, ahora era una decisión de ellos dos, y no fruto de la insinuación alocada de una tercera persona que no sabía qué decía. Ahora todo cobraba sentido.
—¿Cuándo te gustaría celebrar la boda? —preguntó sin más la joven.
—No lo sé. Depende de ti. Estoy a tu disposición desde hoy mismo. Podemos casarnos cuando tú prefieras.
—¿Qué te parece en Newport este verano? —propuso ella con aire pensativo—. En el jardín. Eso sería menos formal que una iglesia. —Y no habría pasillo que recorrer, que era lo que tanto le preocupaba en esos momentos. No tenía tíos que la acompañaran al altar, nadie que pudiera actuar en representación de su padre o su hermano. No tenía a nadie. Tendría que subir al altar completamente sola—. Podríamos hacer una boda muy reducida y después dar una fiesta más numerosa. Ahora que papá y Robert no están, no me parece adecuado organizar un gran bodorrio, y creo que sería un golpe demasiado duro para mi madre. ¿Qué me dices de casarnos en Newport en agosto?
—Me parece fantástico. —Le sonrió de oreja a oreja. Las cosas iban todavía mejor de lo que había planeado, o de lo que se había atrevido a esperar desde el octubre anterior—. ¿Habrá tiempo suficiente para los preparativos?
—Creo que sí. No quiero una boda como la de Hortie. Además, ella es la única dama de honor que me gustaría tener, y para entonces estará embarazada de nueve meses...
—Ja, ja, más que una dama de honor, parecerá una «matrona de honor» —bromeó Josiah.
Ambos sabían que la mayor parte de la gente se quedaría perpleja si la veía aparecer en un acto social en semejante estado.
—Dice que es posible que el bebé nazca en Newport —añadió Annabelle.
—Tal vez lo tenga durante la boda... —Él chasqueó la lengua. Tenía la impresión de que con Annabelle, la vida siempre sería emocionante.
—¿Podré continuar haciendo mi tarea de voluntaria en el hospital? —preguntó Annabelle con cara de preocupación.
—Podrás hacer todo lo que quieras —se limitó a contestar él, y le sonrió de nuevo.
—Mi madre decía que tendría que olvidarme de eso cuando me casara.
—Por mí puedes continuar haciéndolo, salvo quizá cuando estés embarazada. Tal vez entonces sea aconsejable que lo dejes durante un tiempo.
Por sus palabras, Annabelle supo que sería un hombre razonable y que siempre estaría allí para protegerla. Le parecía el matrimonio ideal, y no se imaginaba cómo era posible que no se le hubiera ocurrido a ella antes. Todo lo que le decía Josiah era fantástico, igual que siempre.
Charlaron durante un rato más acerca de sus planes. La madre de él había muerto hacía años, y su padre había vuelto a casarse con una mujer que Josiah no veía con muy buenos ojos, pero pensaba que sería adecuado invitarlos, así como a su hermanastra y al marido de esta. También tenía dos tíos y un hermano. Su hermano vivía en Chicago, y Josiah no estaba seguro de si podría ir a la ceremonia. Dijo que su hermano era un poco excéntrico. Por lo tanto, dudaba que su familia sumara demasiados invitados. Por su parte, a Annabelle solo le quedaba su madre y una amplia variedad de primos lejanos. Dijo que le gustaría invitar a menos de cien personas, tal vez unas cincuenta. Y su madre podría celebrar una fiesta grande para todos ellos cuando volvieran a la ciudad, en otoño, cosa que a Josiah le pareció fantástica. Le gustaba la idea de que la boda fuese algo personal y privado, un momento tan especial para ellos dos, en lugar de un evento multitudinario. Nunca había deseado celebrar una boda de alto copete, bueno, hasta entonces nunca había pensado en casarse.
—¿Adónde te gustaría ir de luna de miel? —preguntó alegremente Josiah.
Agosto estaba a la vuelta de la esquina.
—A cualquier sitio al que no haya que ir en barco. Creo que no podría hacerle algo así a mi madre. Ni siquiera estoy segura de si a mí me apetecería.
—Ya se nos ocurrirá algo. A lo mejor California, o algún lugar de las Rocosas. O Canadá, o incluso podríamos ir a Maine. Nueva Inglaterra estará preciosa en esa época del año.
—No me importa adónde vayamos, Josiah —contestó ella con sinceridad—, mientras esté contigo.
Era exactamente lo que pensaba. Josiah llamó al camarero y pagó la cuenta. Todo había salido a la perfección, aunque le había pedido perdón por no tener todavía el anillo. Estaba tan nervioso que no había conseguido decidirse por cuál sería el más acertado.
La llevó a casa en coche, y vieron que Consuelo seguía levantada. Como sabía lo que iba a pasar, estaba demasiado agitada para dormir. Los miró con ojos expectantes cuando cruzaron la puerta y se fijó en que los dos sonreían de oreja a oreja.
—¿Tengo yerno? —preguntó casi en un susurro.
—Lo tendrás en agosto —contestó Josiah muy orgulloso, con el brazo alrededor de los hombros de su recién prometida.
—Será en Newport —añadió Annabelle levantando la cara y sonriendo embelesada a su prometido.
—Dios mío, una boda en Newport en agosto. Solo tenemos tres meses para prepararla. La cosa va en serio, ¿verdad?
—Queremos una boda muy discreta, mamá —dijo Annabelle con voz amable, y su madre entendió por qué. Oírlo también supuso un alivio para ella.
—Tendrás todo lo que quieras —dijo su madre, generosa.
—De verdad, nos gustaría invitar apenas a cincuenta o sesenta personas, cien como mucho, y celebrarla en el jardín.
—Sus deseos son órdenes para mí —contestó Consuelo en broma. Le habían entrado ganas de llamar a la florista en aquel preciso momento. En lugar de eso, se acercó a Josiah y lo abrazó. Le dio un beso a su hija—. Estoy muy contenta por los dos. Creo que vais a ser muy felices.
—Nosotros también —dijeron al unísono, y entonces los tres se echaron a reír.
Consuelo insistió en descorchar una botella de champán para celebrarlo, y de repente la joven se acordó de aquel día de octubre en el que había llegado a casa del hospital y se había encontrado a su madre y a Josiah bebiendo champán en el jardín.
—Dime la verdad: ¿te habías ganado un ascenso aquel día? —le preguntó Annabelle mientras su madre servía el champán.
—No, te había ganado a ti. Con el permiso de tu madre. Le dije que prefería esperar hasta mayo para pedirte la mano.
—Qué tramposos... —dijo entre risas Annabelle, y Consuelo brindó por los dos novios.
—Que seáis tan felices como fuimos Arthur y yo, que viváis muchos años y que tengáis salud y una docena de hijos.
Tanto Annabelle como Josiah alzaron las copas y tomaron un sorbito de champán, y a continuación Annabelle se acercó a su madre y la abrazó con fuerza. Sabía que en cierto modo la situación era difícil para ella. Las dos echaban de menos tremendamente a su padre y a su hermano.
—Te quiero mucho, mamá —dijo Annabelle en voz baja mientras Consuelo la estrechaba contra su cuerpo.
—Yo también te quiero mucho, hija mía. Y estoy muy contenta por ti. Y sé que, estén donde estén tu padre y Robert, ellos también se alegran mucho.
Ambas mujeres se secaron las lágrimas y Josiah carraspeó y se dio la vuelta, para que no vieran que él también lloraba. Sin lugar a dudas había sido la noche más feliz de su vida.
### 7
Consuelo se vio inmersa en una actividad frenética durante varias semanas. Tenía que organizar el cátering y los arreglos florales en Newport, apalabrar el enlace con el sacerdote, contratar a los músicos. Ya había decidido que abriría la casa en junio. El padre de Josiah accedió a encargarse del ensayo de la cena, que iba a celebrarse en el Club de Campo de Newport.
Consuelo también tenía que mandar las invitaciones. Y Annabelle necesitaba el vestido de novia y el ajuar. Había millones de detalles que planificar y organizar, y hacía un año que Consuelo no se sentía tan contenta. Lamentaba que Annabelle no tuviera cerca a su padre para que participara de los preparativos, y por eso deseaba que todo fuese todavía más hermoso para su hija; sería como una especie de compensación por la ausencia.
Anunciaron el enlace en el _New York Herald_ un día antes del cumpleaños de Annabelle y, al día siguiente, Josiah se presentó con el anillo de compromiso. Era un diamante de diez quilates que había pertenecido a su madre. Destacaba de forma espectacular en la mano de Annabelle. Josiah consideraba que regalarle el anillo de su madre era más significativo que comprar uno, y a Annabelle le encantó. Para entonces, Consuelo y ella ya andaban buscando el vestido de novia. Y, por pura casualidad, encontraron el vestido perfecto en la tienda B. Altman's el día 1 de junio. Era una prenda muy fina de exquisito encaje francés, cortado según un diseño del famoso Patou, y lo bastante sencillo como para no desentonar en una boda celebrada en el jardín en Newport. El vestido llevaba una larga cola vaporosa y un gigantesco velo de tul. Cuando se lo probó, Annabelle se vio magnífica. Y cuando le propuso a su amiga Hortie que fuera la dama de honor, la joven gritó:
—¿Estás loca? ¡No puedes casarte hasta que haya tenido el bebé! Si tu madre pensaba montar una carpa, que encargue dos, porque la voy a necesitar. Será lo único que pueda ponerme para entonces.
—Me da igual el aspecto que tengas o lo que diga la gente —insistió Annabelle—. Lo único que quiero es que estés allí conmigo.
Seguía siendo un tema peliagudo para su madre y para ella, pero había decidido que recorrería el pasillo nupcial a solas.
—Además, se supone que no debo aparecer en público una vez embarazada. Todas las alcahuetas de Newport hablarán de mí durante años.
Annabelle también pensaba que tenía razón en eso, y vio que Hortie estaba a punto de echarse a llorar.
—¿A quién le importa? Yo te quiero, tengas el aspecto que tengas. Y no nos apetece esperar más. Agosto es el mes perfecto para nosotros —intentó convencerla.
—Te odio. A lo mejor, si nado mucho, puedo dar a luz antes. Pero seguiré estando gorda...
Cuando se dio cuenta de que no iba a convencer a Annabelle de que pospusiera la boda, Hortie se rindió y le prometió que iría a la fiesta contra viento y marea. Era una semana antes de la fecha en la que salía de cuentas, y la joven estuvo a punto de pegarle un capón a Annabelle cuando esta insinuó que tal vez se retrasara el parto. Hortie quería que se adelantara. Ya estaba harta de sentirse fea y gorda.
Annabelle y Hortie fueron de compras juntas para buscar complementos para el ajuar. Y Annabelle y Josiah todavía tenían que decidir dónde iban a vivir. Josiah tenía una casita muy digna en Newport que había heredado de su madre, pero su apartamento de Nueva York podía resultar un poco pequeño una vez que tuvieran hijos. Habían acordado que buscarían un hogar más grande cuando regresasen de Wyoming, que era donde habían decidido pasar la luna de miel. En esas fechas era demasiado apresurado intentar encontrar un sitio nuevo en el que vivir. Por el momento, su apartamento era lo bastante grande para ellos dos. Y estaba cerca de donde vivía la madre de Annabelle, cosa que le encantaba. La joven aborrecía marcharse de casa y dejarla sola. Sabía perfectamente lo desolada que se sentiría su madre.
Sin embargo, por entonces Consuelo estaba demasiado ocupada para sentirse sola. Hizo dos viajes a Newport para empezar a organizar la boda e indicarle al jardinero qué quería que plantase. Y entre los dos habían logrado encontrar la carpa del tamaño ideal, que había sobrado de una boda celebrada el año anterior en la localidad.
Y para gran sorpresa de Annabelle y Josiah, a final de junio todos los cabos estaban atados y bien atados. Consuelo era un modelo de eficacia y deseaba que su hija tuviera la boda perfecta. Él se mostró adorable durante todo el proceso. No dio muestras de nerviosismo ni perdió la paciencia en ningún momento, a pesar de que había tenido que esperar mucho para casarse, hasta los treinta y nueve años. Una vez que se había decidido, estaba mentalizado y muy tranquilo con el tema. Más incluso que su prometida.
En cuanto su enlace matrimonial salió publicado en el _Herald_ , empezaron a invitarlos a infinidad de eventos, así que salían casi todas las noches. Hacían una pareja despampanante, y solo dos de las amigas de Consuelo comentaron con muy poco tacto que pensaban que Josiah era demasiado viejo para Annabelle. Consuelo les aseguró que era perfecto. Su primo, John Jacob Astor, se había casado con Madeleine cuando ella tenía dieciocho años y él pasaba de los cuarenta. Josiah le demostraba a diario que sería el marido perfecto para su hija. Y Annabelle había conseguido continuar haciendo sus tareas de voluntariado, con el beneplácito de él, hasta final de junio. Dejaría de realizarlas desde entonces hasta el otoño.
Lo único que Consuelo les pedía, y no se cansaba de repetirlo, era que le dieran nietos cuanto antes. Annabelle pensaba que, si volvía a oírselo decir otra vez, iba a soltarle un grito.
Por su parte, Hortie no dejaba de hablarle de las sorpresas que se le desvelarían al cabo de poco tiempo, y de lo genial que sería el sexo. Le ponían nerviosa todos esos consejos no solicitados por parte de su amiga de toda la vida, que no paraba de engordar. Hortie estaba enorme y Annabelle confiaba en que, cuando ella se quedara embarazada, no tuviera semejante aspecto. Un día se lo dijo tal cual a Josiah, y él se echó a reír.
—Cuando eso pase estarás preciosa, Annabelle, y nuestros hijos también serán preciosos.
Le dio un beso tierno. Tenían tantos planes por delante y tantas cosas que hacer en los próximos dos meses...
Parecía que todos sus conocidos quisieran prepararles una celebración. A los treinta y nueve años, por fin iba a casarse. Henry Orson le organizó una despedida de soltero. Todo el grupo de hombres tuvo resaca durante tres días después de la fiesta. Josiah admitió que se lo habían pasado en grande, aunque no entró en detalles. Ninguno de sus amigos soltó prenda.
Consuelo se marchó a Newport en junio y Annabelle se reunió con ella allí a mediados de julio. Josiah se apuntó a finales de mes, aunque se alojó en su propia casa. Henry Orson lo acompañó, para dar apoyo moral al novio, que parecía llevar muy bien la situación. Se quedaría en su casa mientras ellos estuvieran de luna de miel. Josiah había pedido tres semanas extras de vacaciones ese año, para celebrar el viaje de novios. El banco había sido comprensivo con su petición, sobre todo teniendo en cuenta que la novia era Annabelle.
Annabelle apreciaba mucho a Henry, el amigo de Josiah. Era muy inteligente, ingenioso, amable y un poco tímido. La muchacha se pasaba el día intentando decidir a cuál de sus amigas solteras debía presentárselo. Ya se lo había presentado a varias y el hombre había reconocido que dos de ellas le gustaban, aunque todavía no había surgido nada serio. De todas formas, Annabelle tenía esperanzas. Cuando Josiah y él se reunían, eran divertidos y ocurrentes, y multiplicaban las gracias de su repertorio. Henry siempre había sido muy gentil con ella. Era para Josiah lo mismo que Hortie para ella, su amigo más fiel desde el colegio. Y Annabelle lo admiraba inmensamente.
Para entonces, Hortie ya se había instalado en la casa de sus padres de Newport para pasar el verano, y James había ido con ella. Estaban casi seguros de que el niño nacería allí, y la joven iba a visitar a Annabelle a diario. Por su parte, esta ayudaba a su madre siempre que podía, aunque Consuelo insistía en que tenía todo bajo control. Annabelle había llevado consigo el vestido de novia. Sus amigos las invitaron a muchísimas fiestas en Newport. Y los Astor dieron un baile multitudinario en su honor. Consuelo se quejó de que nunca había salido tanto en su vida, pero, en el fondo, se divirtió mucho.
El número de invitados a la boda ya había superado la marca de la centena y se aproximaba a ciento veinte. Cada vez que alguien celebraba una fiesta para ellos, tenían que añadirlo a la lista. A pesar de todo, era evidente que la joven pareja se lo pasaba en grande. Un día, mientras comían en un picnic que habían organizado con su amigo Henry y las dos chicas, Josiah le comentó a Annabelle sin reparo que, si hubiera sabido que casarse era tan divertido, lo habría hecho muchos años antes.
—Pues menos mal que no lo hiciste —le recordó ella—, porque entonces no habrías podido casarte conmigo.
—Tienes toda la razón —dijo él y chasqueó la lengua, justo en el momento en que llegaba Hortie.
Estaba oronda y, cada vez que Annabelle la veía, no podía evitar reírse de ella. Costaba creer que al mes siguiente fuera a estar todavía más gorda que en esos momentos. Parecía a punto de explotar. Tanto Josiah como Henry tuvieron que ayudarla a sentarse en la hierba, e hizo falta mucho más esfuerzo y casi una grúa para levantarla después de la comida.
—No me hace gracia —dijo Hortie, mientras los otros tres se reían de ella—. Hace meses que no me veo los pies.
Tenía un aspecto monstruoso, e insistía en que se sentía como un elefante.
—¿Qué te pondrás para la boda? —le preguntó Annabelle con cara preocupada. No se imaginaba ningún vestido lo bastante ancho para que Hortie cupiera dentro.
—La colcha de la cama, supongo. O una carpa.
—En serio, ¿tienes algún vestido a medida? No pienses que vas a librarte de ir...
—No te preocupes, allí estaré —le aseguró—. No me lo perdería por nada del mundo.
Lo cierto era que había ido a la modista de su madre para que le hiciera el traje: un vestido gigantesco y con mucha caída en un tono azul pálido. Y se había comprado unos zapatos a juego. No era precisamente el vestido ideal para la dama de honor, pero era lo único que podía ponerse. Aborrecía reconocerlo, pero no le quedaba otra opción.
Consuelo se había hecho un vestido en color verde esmeralda con un sombrero a conjunto, y había pensado lucir las esmeraldas que Arthur le había regalado. El color le sentaba de maravilla y Annabelle sabía que la madre de la novia estaría guapísima.
Por fin llegó el gran día. El padre y la madrastra de Josiah llegaron de Boston, con la hermanastra de su futuro yerno, su marido y el hijo de ambos. A Annabelle le cayeron todos bien. Y el ensayo de la cena fue bastante fluido. Consuelo congenió con los parientes de su futuro yerno y los invitó a comer en su casa el día anterior a la boda. Ambas familias estaban muy emocionadas con el enlace. Era la unión de dos linajes muy respetables, y de dos personas a quienes todo el mundo quería. Tal como predijo Josiah, su alocado hermano George, quien vivía en Chicago, decidió no ir. Tenía que jugar un torneo de golf ese día. Así era su hermano, y Josiah no se sintió herido. De haber asistido, habría montado una escena, así que su ausencia era un alivio. Su familia nunca había sido tan normal, equilibrada y cohesionada como la de Annabelle. Y su madrastra lo ponía de los nervios. Tenía una voz chillona y se quejaba a la menor oportunidad.
Consuelo volvió a almorzar con los familiares de Josiah el mismo día de la boda, sin que estuvieran presentes los novios. Por pura superstición, Annabelle no quiso ver a su prometido antes de la ceremonia, así que él y su amigo Henry se quedaron en casa tranquilamente, para intentar relajarse. Hacía mucho calor ese día y Consuelo temía que las flores se marchitaran y la tarta nupcial se derritiera antes siquiera de que empezara la boda. La ceremonia en el jardín tendría lugar a las siete de la tarde y se sentarían a cenar a las nueve. Nadie dudaba de que la fiesta se alargaría hasta bien entrada la madrugada.
Al final había ciento cuarenta invitados, repartidos de forma casi equitativa entre el novio y la novia. Y Henry Orson, por supuesto, iba a ser el padrino de boda.
Hortie sería la dama de honor; bueno, eso si no tenía el bebé justo antes de la boda, cosa que podía ocurrir perfectamente. Con la intención de advertir a su amiga, le había confesado a Annabelle que hacía dos días que tenía contracciones y que rezaba para no romper aguas delante del altar. Ya era bastante bochornoso presentarse de semejante guisa. Sabía que todos se quedarían horrorizados cuando la vieran así en la boda y probablemente lo encontraran chocante. Pero no podía decepcionar a su mejor amiga. Annabelle le había dicho que ya era bastante triste para ella no poder contar con su padre y su hermano ese día, de modo que Hortie no podía ausentarse bajo ningún concepto.
Blanche había viajado a Newport con ellas para preparar la boda. Se pasó la tarde corriendo ajetreada por el dormitorio de Annabelle, atosigándola como si fuera una niña pequeña. Cuando llegó el momento, Consuelo y ella la ayudaron a ponerse el vestido de novia y le abrocharon los diminutos botoncillos. La cintura ceñida y la falda estrecha le quedaban fabulosas. Y después de tomar aire profundamente, Consuelo colocó la horquilla en el pelo rubio de Annabelle y le arregló el velo que le cubría la cara. Ambas mujeres retrocedieron para mirarla y las dos no pudieron reprimir las lágrimas. Sin lugar a dudas, Annabelle era la novia más guapa que habían visto jamás.
—Dios mío —susurró Consuelo cuando Annabelle les sonrió—. Estás increíble.
Annabelle era la mujer más feliz de la Tierra y se moría de ganas de que la viera Josiah. Todas lamentaban que su padre no pudiera estar presente. Consuelo sabía que, de haberla podido acompañar al altar, se le habría hecho un nudo del tamaño de un puño en la garganta. Annabelle siempre había sido su orgullo y máxima alegría.
Las dos mujeres la ayudaron a bajar la escalera mientras le recogían la larga cola. Entonces, una de las criadas le acercó el ramo de lirios del valle y, con él en la mano, Annabelle, acompañada de su madre y Blanche, se escabulló por una puerta lateral. La sirvienta avisó a los amigos de la pareja de que la novia estaba a punto de llegar. Los invitados estaban sentados donde les correspondía y Josiah y Henry estaban esperándola en el altar, con Hortie a su lado, que parecía un gigantesco globo de color azul celeste. Más de una viuda noble de Newport había exclamado sobresaltada al verla. Pero todo el mundo sabía que era una boda poco convencional. El novio tenía casi veinte años más que la novia y nunca se había casado, y la familia de la joven había hecho frente a una horrible tragedia hacía menos de un año. Era preciso hacer algunas concesiones.
Consuelo permaneció un momento más en el jardín lateral, contemplando a su hija, y después la estrechó en sus brazos y la abrazó muy fuerte.
—Que seas feliz, hija mía... Papá y yo te queremos muchísimo. —Y en ese instante, con las lágrimas resbalándole por las mejillas, corrió a sentarse en el lugar que tenía reservado, en la primera fila de sillas que habían colocado en el jardín principal para la ceremonia religiosa.
Los ciento cuarenta invitados estaban esperando y, en cuanto Consuelo tomó asiento, los músicos empezaron a tocar la marcha nupcial de _Lohengrin_ , la misma que habían tocado en la boda de Hortie. El gran momento había llegado. Se acercaba la novia. Consuelo levantó la mirada hacia Josiah y él le sonrió. Un brillo cálido se transmitió entre ambos. Y más que nunca, Consuelo supo que era el hombre adecuado. Estaba segura de que Arthur habría pensado lo mismo.
Todos los invitados de la boda se levantaron cuando el sacerdote hizo una señal, y todas las cabezas se volvieron hacia Annabelle. La tensión era palpable mientras, lenta y solemnemente, la exquisita novia recorría el jardín con pasos seguros, a solas. No había nadie para acompañarla, nadie que la llevara al altar, que la protegiera y entregara su mano al hombre con quien se iba a casar. Annabelle se aproximaba a él con orgullo y sigilo, con una certeza y una dignidad absolutas, por sí misma. Como no había quien la entregara a Josiah, ella misma se le entregaba, con el beneplácito de su madre.
Todos contuvieron la respiración a la vez al verla, y la fuerza de la tragedia que la había sacudido golpeó también a los invitados en cuanto vieron a la menuda y encantadora novia acercarse a ellos con un ramo de lirios del valle en la mano y el rostro cubierto por el velo.
Se colocó delante de Josiah y del sacerdote, mientras Henry y Hortie daban un paso atrás. La pareja de novios se quedó de pie, mirándose a través del velo, y el prometido tomó a la novia con delicadeza de la mano. Había sido muy valiente.
El sacerdote se dirigió a la multitud congregada y empezó la ceremonia. Cuando preguntó quién entregaba a esa mujer en matrimonio, su madre respondió con voz clara desde la primera fila «Yo la entrego», y el rito matrimonial continuó. En el momento correspondiente, Josiah levantó el velo con mucha ternura y la miró a los ojos. Se dijeron los votos el uno al otro, él le puso una estrecha alianza con un diamante a ella, y Annabelle le puso una sencilla alianza de oro a él. Los proclamaron marido y mujer, se besaron y a continuación, radiantes, volvieron a recorrer juntos el pasillo nupcial. Consuelo no dejaba de derramar lágrimas descontroladas mientras los observaba, y entonces, tal como había hecho su hija, recorrió el pasillo a solas detrás de Henry y Hortie, quien caminaba como un pato, feliz, del brazo de Henry. Él nunca había visto a una mujer tan increíblemente embarazada en público, igual que el resto de los asistentes. Pero Hortie había decidido que iba a disfrutar de la boda y estaba encantada de haber ido. No tardó en encontrar a James entre la multitud, y Consuelo, Annabelle y Josiah se pusieron en fila para saludar a los invitados, que querían felicitarlos.
Media hora después, todos se habían entremezclado y hablaban mientras disfrutaban de una copa de champán. Había sido una boda preciosa, tierna y muy emotiva. Annabelle estaba mirando con adoración a Josiah en el momento en que Henry se aproximó para darle un beso y dedicarle sus mejores deseos, así como para felicitar al novio.
—Bueno, ya lo has hecho —le dijo a Annabelle chasqueando la lengua—. Lo has civilizado. Decían que era imposible.
—Tú serás el próximo —bromeó ella mientras le daba un beso—. Ahora tenemos que encontrar a alguien para ti.
Henry se puso nervioso cuando le oyó decir eso y fingió estremecerse de miedo.
—No sé si estoy preparado —confesó—. Creo que preferiría seguir saliendo con vosotros dos y disfrutar de las maravillas del matrimonio desde la barrera. No os importa si me uno a vosotros, ¿verdad?
Lo decía medio en broma, pero Annabelle le dijo que sería siempre bienvenido. Sabía lo intensa que era la amistad entre él y Josiah, igual que la suya con Hortie. En su nueva vida había espacio para sus amigos de siempre.
Los recién casados saludaron a todos los invitados y entonces, justo después de las nueve, llegó el momento de sentarse a cenar. Annabelle y Consuelo habían sido muy meticulosas con la ubicación de los invitados, para asegurarse de que las personalidades más importantes de Newport eran tratadas con el debido respeto. Consuelo se había sentado con la familia de Josiah, y en la mesa de los novios habían colocado a Henry, a una de las amigas de Annabelle, a James y a Hortie, y otras tres parejas jóvenes que les caían muy bien. Casi todos los invitados eran personas que los novios deseaban de verdad que los acompañaran aquel día. Había muy pocos invitados de compromiso, a excepción de unos cuantos empleados del banco de Arthur, con quienes trabajaba Josiah. Les pareció adecuado incluirlos en la lista.
Josiah abrió el baile con Annabelle: un vals lento que ejecutaron a la perfección. A ambos les encantaba esa pieza y la habían bailado muchas veces. Los dos eran muy buenos bailarines y destacaban en la pista. Todo el mundo suspiró mientras los veía bailar. Y después el padre de Josiah bailó con la novia, y Josiah bailó con Consuelo, y a continuación el resto de los invitados se les unieron en la pista de baile. Casi eran las diez cuando los comensales empezaron a comer la suntuosa cena que Consuelo había encargado. Bailaron entre plato y plato, hablaron sin parar, se rieron, disfrutaron de la compañía, y muchos comentaron lo buena que estaba la comida, algo extraño en las bodas. La pareja de recién casados cortó la tarta nupcial a medianoche. Después siguieron bailando y los invitados no empezaron a marcharse hasta las dos de la mañana. La boda había sido todo un éxito y, cuando se dirigían al Hispano-Suiza de Arthur para ir al hotel New Cliff, donde iban a pasar la noche, Josiah se inclinó para besarla.
—Gracias por la velada más hermosa de mi vida —le dijo, mientras el arroz y los pétalos de rosa empezaban a bañarlos, e invitó a su flamante esposa a entrar en el coche. Ya habían dado las gracias con efusividad a la madre de Annabelle por ofrecerles la boda perfecta, y habían prometido que pasarían por su casa a despedirse por la mañana, antes de dirigirse a la ciudad para tomar el tren a Wyoming. Tenían las maletas hechas y preparadas en el hotel. Para el viaje, Annabelle pensaba ponerse un traje de lino de un azul pálido, con un enorme sombrero de paja con un estampado de flores también en azul pastel y unos guantes azules de cabritilla a juego.
Saludaron con la mano a los observadores mientras el coche se alejaba de la fiesta para llevarlos al hotel y, por un instante, Annabelle se preguntó qué le aguardaba. Lo último que vieron al marcharse fue la mastodóntica silueta de Hortie, que se despidió de ellos con la mano. Annabelle se rió mientras le devolvía el saludo, y confió en que, si se quedaba embarazada, no tuviera el aspecto de Hortie de ahí a nueve meses. Henry había sido el último en darle dos besos de despedida y estrecharle la mano a Josiah. Los dos hombres se habían mirado a los ojos y habían sonreído, y Henry les había deseado lo mejor. Era un buen hombre, Annabelle lo sabía, y Josiah lo consideraba un hermano, casi más próximo que el verdadero.
Se sentaron en la salita de la suite durante un rato, Annabelle todavía con el vestido de novia y él con el frac y la corbata blanca, y hablaron de la boda, de sus amigos, de lo bonito que había sido todo y de lo extraordinaria que había sido la labor de Consuelo. La ausencia de su padre y su hermano había sido dolorosa para Annabelle, pero incluso eso había sido tolerable. Ahora contaba con Josiah, y él la apoyaría, la amaría y la protegería. Y él tenía a Annabelle, quien lo alentaría y adoraría durante el resto de su vida. No podían pedir más.
Eran ya las tres de la madrugada cuando los novios se dirigieron a dos cuartos de baño diferentes y, al cabo de un rato, salieron. Él llevaba un pijama de seda blanca, que alguien le había regalado para la ocasión, y ella lucía un elegante camisón de chiffón blanco, con el corpiño incrustado de perlitas diminutas, y una bata a conjunto. Se rió como la adolescente que era en el fondo cuando se metió en la cama al lado de su marido. Josiah ya la estaba esperando, y la tomó en sus brazos. Sospechaba lo nerviosa que estaba ella, y ambos se notaban agotados después de una noche tan larga.
—No te preocupes, cariño —le dijo él en voz baja—, tenemos mucho tiempo por delante.
Y entonces, para alegría y sorpresa de ella, la abrazó con ternura hasta que se quedó dormida y soñó con lo bello que había sido todo. En sus sueños estaban en el altar, intercambiando los votos, y esta vez su padre y su hermano se hallaban a su lado, observándola. De todas formas, ella los había sentido cerca, así que continuó durmiendo mientras Josiah la abrazaba con sumo cuidado, como si fuera una piedra preciosa.
### 8
Tal como habían prometido, Annabelle y Josiah pasaron a despedirse de Consuelo justo antes de emprender el viaje. Thomas iba a llevarlos en el Hispano-Suiza familiar al centro de Nueva York, donde cogerían el tren por la tarde. En su primera etapa llegarían hasta Chicago y, una vez allí, cambiarían de tren y continuarían su viaje de novios hacia el oeste, en dirección a Wyoming, donde se alojarían en un rancho en el que Josiah había estado una vez y que le había encantado. Allí montarían a caballo, irían a pescar y harían caminatas en el increíble entorno de los Grand Tetons. Josiah le había dicho a su joven esposa que era más bello que los Alpes suizos, y no era preciso ir en barco. Se quedarían en el rancho casi tres semanas. Después regresarían a Nueva York y empezarían a buscar una casa lo bastante grande para ellos y los hijos que esperaban tener. Consuelo confiaba en que, igual que Hortie, Annabelle volviera embarazada después de la luna de miel.
Consuelo escudriñó la cara de su hija a la mañana siguiente, con la esperanza de encontrar algún cambio y una ternura nueva, propia de una mujer amada, pero lo que vio fue la niña resplandeciente a la que tanto había querido toda su vida. Nada había cambiado. Se alegró de ver que se había adaptado bien al cambio. No se veía arrepentimiento en ella, ni esa mirada de asombro asustadizo que a veces se observaba en el rostro de una recién casada después de la noche de bodas. Annabelle estaba tan contenta como siempre y seguía tratando a Josiah más como a un viejo amigo que como a un nuevo amor. Antes de despedirse de su madre, habían pasado también por la casita de Josiah para decirle adiós a su amigo Henry.
Consuelo estaba comiendo con el padre y la madrastra de Josiah cuando la pareja apareció en la casa de verano de los Worthington. Todo el mundo estaba de buen humor y recordaba lo deliciosa y bella que había sido la noche anterior. La madre de Annabelle volvió a abrazarla con fuerza, y los recién casados dieron las gracias al padre de Josiah por el ensayo de la cena. Al cabo de pocos minutos, se marcharon en el Hispano-Suiza.
A Annabelle le habría encantado ir a despedirse también de su amiga Hortie, pero su madre le contó que James le había mandado el recado de que estaba de parto. Había conseguido aguantar toda la boda, pero había roto aguas esa misma noche. Su madre y el médico estaban con ella, así que James había ido a comer con unos amigos. Annabelle confiaba en que todo saliera bien. Sabía que Hortie estaba preocupada por el tamaño del bebé, e imaginaba lo difícil que podía resultar el parto. Una de sus amigas, que había hecho su puesta de largo a la vez que ellas, había muerto dando a luz hacía unos meses. Había sido un golpe muy duro para todos. Esas cosas ocurrían, y a veces no podían evitarse, pues a menudo se producían infecciones después del parto, que casi siempre acababan con la vida de la madre. Así pues, Annabelle rezó en silencio por Hortie mientras se alejaban, preguntándose si su madre tendría razón y sería un niño. Era un pensamiento emocionante, que le hizo plantearse si ella también volvería embarazada del viaje de novios; tal vez tuviera un hijo concebido en los bosques de Wyoming.
Le estaba muy agradecida a Josiah por haber sido tan amable y respetuoso con ella la noche anterior. Añadir la novedad del sexo a una jornada tan emocionante habría sido demasiado para ella, aunque lo habría hecho si él hubiese insistido mucho. Sin embargo, tenía que admitir que se alegraba de que no la hubiese obligado. Era un marido perfecto, amable y comprensivo, y, tal como le había asegurado en un principio, seguía siendo su mejor amigo. Lo miró con adoración mientras entraban en coche en la ciudad y charlaban un poco más sobre la boda. Después, él volvió a describirle Wyoming. Le había prometido que la enseñaría a pescar. Annabelle creía que era la luna de miel perfecta. Y él estuvo de acuerdo cuando se lo dijo.
Llegaron a Nueva York a las cinco en punto, con tiempo más que suficiente de coger el tren de las seis, y se acomodaron en el compartimiento de primera clase más grande que había en el tren. Annabelle aplaudió con emoción al verlo.
—¡Qué divertido! ¡Me encanta! —dijo entre risitas mientras él se reía contento sin dejar de mirarla.
—Qué niña tan tonta... Y cuánto te quiero.
La abrazó y la besó mientras la estrechaba con fuerza contra su cuerpo.
Iban a pasar el día en Chicago antes de montarse en otro tren, esta vez nocturno, que los llevaría hacia el oeste. Josiah le había prometido que le enseñaría la ciudad durante la breve escala y había reservado una suite en el hotel Palmer House, para que pudieran descansar cómodamente entre un tren y otro. Había pensado en todos los detalles. Quería que Annabelle fuera feliz. Se lo merecía después de todo lo que había perdido y de todo lo que su familia había sufrido. Mientras el tren salía de la estación Grand Central, Josiah se juró a sí mismo que nunca la abandonaría. Y hablaba muy en serio. En su interior, lo veía como una promesa solemne.
A las seis de la tarde, cuando el tren en el que viajaban salió de la estación, el bebé de Hortie todavía no había nacido. Estaba siendo un parto arduo y agónico. El niño era enorme y ella era pequeña. Había gritado y se había retorcido durante horas. James había regresado a casa después de comer, y los alaridos de su mujer le habían resultado tan desgarradores y desconcertantes que se había servido un trago y había vuelto a salir a cenar con unos amigos. Aborrecía pensar que Hortie tuviera que pasar por aquello, pero no había nada que él pudiera hacer para remediarlo. Era lo que les tocaba hacer a las mujeres. Estaba seguro de que el médico, su madre y las dos enfermeras estaban haciendo todo lo que podían por ella.
Cuando regresó a casa a las dos de la madrugada estaba borracho, y se asombró al enterarse de que el bebé seguía sin salir. Estaba tan ebrio que no distinguió el semblante aterrado de la madre de Hortie. La joven estaba tan debilitada para entonces que sus gritos habían disminuido, para alivio de James, y un gemido animal y lastimero llenaba toda la casa. Él se puso una almohada encima de la cabeza e intentó dormir. Un repiqueteo nervioso en la puerta de la habitación de invitados donde se había acostado, pues era la más alejada del dormitorio en el que su esposa estaba dando a luz, lo despertó por fin a las cinco de la mañana. Era su suegra, quien le dijo que por fin había nacido el bebé, de casi cuatro kilos y medio. El niño había hecho picadillo a su hija, pero la mujer no le comentó eso a James. Si hubiera estado más sobrio, se habría dado cuenta por sí mismo. James le dio las gracias por la noticia y siguió durmiendo, tras prometerse que iría a ver a Hortie y al bebé por la mañana, en cuanto se despertara. De todas formas, no habría podido verla en aquel momento, porque el médico la estaba cosiendo después de los desgarros que le había ocasionado el alumbramiento.
Hortie había estado veintiséis difíciles horas de parto, y había dado a luz a un niño de cuatro kilos y medio. Seguía llorando desconsolada mientras el médico le ponía puntos con sumo cuidado, y al final optaron por darle cloroformo. Había sido un nacimiento complicado y ella habría podido morir en el parto. Es más, todavía quedaba el riesgo de infección, así que no estaba salvada del todo. Pero el bebé estaba sano. De Hortie no podía decirse lo mismo. Su iniciación en la maternidad había sido una prueba de fuego de la peor calaña. La madre de la muchacha se lo contaría entre susurros a sus amigas durante varios meses. Pero lo único que podría decirse en público sería que el bebé había nacido sano y que tanto la madre como el hijo estaban bien. El resto solo se confesaría en los corros de mujeres y con la puerta cerrada, pues las agonías del alumbramiento, y sus apabullantes riesgos, debían apartarse por todos los medios de los oídos masculinos.
Cuando Consuelo se enteró de todo al día siguiente por boca de la madre de Hortie, sintió mucho que la joven lo hubiera pasado tan mal. En el caso de Consuelo, Robert había nacido sin dificultad, pero Annabelle había supuesto un reto mucho mayor, pues estaba mal colocada y nació por los pies; había sido un milagro que ambas hubieran sobrevivido. Solo confiaba en que Annabelle tuviera un parto más sencillo que el de Hortie. Ahora iban a hacer todo lo posible para que no contrajera ninguna infección. Después de un parto tan difícil, muchas veces costaba impedir los contagios, aunque nadie sabía por qué.
Consuelo dijo que iría a verla al cabo de unos días, pero su madre reconoció que Hortie todavía no estaba recuperada, y que era posible que tardase bastante tiempo en estar bien del todo. Tenían previsto mantenerla encamada durante un mes entero. Le contó que James había visto a Hortie y al niño apenas unos minutos, y antes le habían puesto colorete en las mejillas a su esposa y la habían peinado, pero la joven no había dejado de llorar. Sin embargo, él solo tenía ojos para su hijito. Eso hizo que Consuelo pensara en Arthur, quien siempre había sido muy comprensivo después del nacimiento de sus dos hijos. Para ser un hombre joven, se había mostrado excepcionalmente compasivo y empático con ella. Y tenía la impresión de que Josiah también lo sería. Pero James era poco más que un adolescente y no tenía ni idea de lo que implicaba dar a luz a un hijo. En la boda había dicho que confiaba en poder tener otro pronto, y Hortie se había reído y había puesto los ojos en blanco. Consuelo sentía lástima por ella, pues sabía por el mal trago que acababa de pasar. Le mandó una cesta de fruta y un gigantesco ramo de flores por la tarde, y rezó para que se recuperase pronto. Era lo único que podía hacer. Hortie estaba en buenas manos. Y a ella no le cupo duda de que, después del parto, Hortie no volvería a ser la chica despreocupada que había sido hasta entonces. Había aprendido la lección.
Al final, resultó que Hortie consiguió levantarse de la cama en tres semanas en lugar de en un mes. El niño estaba estupendo, habían contratado a una nodriza para que lo amamantara y le habían vendado el pecho a Hortie para que dejara de generar leche. Todavía le temblaban un poco las piernas cuando se ponía de pie, pero tenía buen aspecto. Era una chica joven y sana, y había tenido la suerte de burlar a la infección, así que había salido de peligro. Consuelo había ido a visitarla varias veces. James estaba henchido de orgullo con su hijo tan rollizo, a quien habían llamado Charles. El niño engordaba por momentos. Y tres semanas después del parto, trasladaron a Hortie de vuelta a Nueva York en ambulancia, para que continuara recuperándose en casa. Estaba contenta de volver a su hogar. Consuelo se marchó de Newport ese mismo día.
Se sintió sola cuando se vio de vuelta en Nueva York. La casa estaba increíblemente silenciosa sin Annabelle, pues siempre derrochaba luz, vitalidad y diversión; siempre se preocupaba por su madre y se ofrecía a hacer cosas con ella. El peso de la soledad y del futuro que le esperaba explotó dentro de Consuelo como una bomba en cuanto entró en la mansión. Le costaría mucho seguir viviendo allí sola. Por lo menos, se alegraba de que los recién casados fueran a regresar del viaje de novios al cabo de dos días. Se había encontrado con Henry Orson por la calle y también él parecía tristón. Josiah y Annabelle emanaban tanta luminosidad y daban tanta alegría a quienes los rodeaban que, sin ellos, todos se sentían faltos de algo. Consuelo, Hortie y Henry se morían de ganas de que volvieran.
Y entonces, como una bocanada de aire fresco, regresaron del viaje. Annabelle insistió en parar en casa de su madre al volver de la estación, y Consuelo se emocionó al verla con ese aspecto sano, feliz y bronceado. Josiah también tenía buena cara. Todavía bromeaban el uno con el otro como niños en el patio de recreo, se tomaban el pelo, se reían y sacaban punta a todos los comentarios. Annabelle le contó que Josiah la había enseñado a pescar y que había atrapado una trucha enorme ella sola. Josiah parecía muy orgulloso de su esposa. Habían montado a caballo, habían hecho excursiones por la montaña y habían disfrutado de todos los aspectos de la vida en el rancho. Annabelle parecía una chiquilla que acabara de regresar de un campamento de verano. Costaba creer que fuera una mujer adulta y casada. Además, Consuelo no veía ninguna de las sutilezas e insinuaciones femeninas en su cara. No tenía ni idea de si habían concebido un niño, y no quería preguntarlo. Pero parecía la misma joven gentil, cariñosa y alegre que era cuando se marchó. Su hija le preguntó cómo se encontraba Hortie, y Consuelo le contestó que bien. No quería asustarla con historias sobre el parto y, de todas formas, no habría sido apropiado para los oídos de Josiah, así que se limitó a decir que la madre estaba bien y que el niño se llamaba Charles. Dejó en manos de Hortie el contarle (o no) el resto. En el fondo, confiaba en que no lo hiciera. La mayor parte de esos secretos podían asustar a una joven sin hijos. En especial, a una que podría verse en la tesitura de pasar por el mismo trance poco tiempo después. No tenía sentido aterrorizarla.
Se quedaron una hora más con ella y después se despidieron. Annabelle le prometió a su madre que le haría otra visita al día siguiente, aunque se verían antes, porque los recién casados irían a cenar con ella esa misma noche. A continuación, después de abrazar a Consuelo, la joven pareja se marchó. La mujer se había alegrado enormemente de verlos a ambos, pero la casa parecía aún más vacía después de su despedida. Últimamente apenas tenía apetito, y se sentía muy sola en el comedor sin nadie que la acompañara.
Tal como había prometido, Annabelle fue a comer con su madre al día siguiente. Se había puesto uno de los conjuntos comprados para el ajuar: un traje de lana en azul marino propio de una mujer hecha y derecha, aunque, a ojos de su madre, Annabelle seguía siendo una niña. A pesar de ir ataviada como una adulta y de lucir una alianza en el dedo, actuaba como una jovencita. Mientras charlaban durante la comida, se mostró muy alegre y le preguntó a su madre qué había hecho ella esas semanas. Su madre le dijo que no llevaba muchos días en la ciudad, pues se había quedado en Newport más tiempo del habitual, para disfrutar del clima costero en septiembre, y ahora estaba planteándose retomar su trabajo de voluntariado en el hospital. Confiaba en que Annabelle dijera que se uniría a ella, o que mencionara que iba a volver al Hospital para el Tratamiento de los Lisiados, pero la joven sorprendió a su madre y dijo que, en lugar de eso, quería trabajar como voluntaria en la isla de Ellis. Allí la labor sería más interesante y supondría un reto mayor para ella. Además, siempre les faltaban voluntarios que echaran una mano, de modo que tendría más oportunidades de colaborar en las tareas médicas, en lugar de limitarse a observar o a llevar las bandejas de alimentos. Al oírlo, su madre se disgustó.
—Pero muchas veces esos pacientes están muy enfermos; traen enfermedades de otros países. Las condiciones son pésimas. Creo que es una insensatez que te plantees eso. Acabarás pillando otra vez la gripe, o algo peor. No quiero que trabajes allí.
Sin embargo, ahora era una mujer casada y era Josiah quien tenía que aprobar lo que ella hacía. Le preguntó a su hija si él estaba al corriente de lo que se le había ocurrido. Annabelle asintió con la cabeza y sonrió. Josiah era muy comprensivo con esas cosas y siempre se había mostrado abierto y entusiasta ante el interés de Annabelle por la medicina y por las labores de voluntariado. La joven le había contado sus planes.
—A él le parece bien.
—Bueno, pues a mí no. —Consuelo frunció el entrecejo, muy enojada.
—Mamá, no olvides que la gripe más fuerte que he pasado en mi vida la pillé en los salones de baile, yendo a fiestas con vosotros. No me la contagiaron los pobres.
—Pues razón de más para no hacerlo —dijo su madre con firmeza—. Si eres capaz de ponerte enferma en una fiesta entre personas sanas y de buenos hábitos, imagínate lo mala que te pondrías si trabajaras con gente que vive en unas condiciones higiénicas pésimas y está cargada de enfermedades. Además, si te quedas embarazada, cosa que confío en que hagas (si no lo has hecho ya), sería una barbaridad que os pondría en peligro al bebé y a ti. ¿Ha pensado en eso Josiah?
Hubo algo que pasó por la mirada de Annabelle y que desconcertó a Consuelo, pero se desvaneció en un abrir y cerrar de ojos.
—No tengo prisa por fundar una familia, mamá. Josiah y yo deseamos divertirnos un poco antes.
Era la primera vez que Consuelo se lo oía decir tan claro y se sorprendió. Se preguntaba si estaría empleando uno de los métodos nuevos (o antiguos) para evitar quedarse embarazada. Pero no se atrevía a preguntárselo.
—¿Cuándo lo habéis decidido?
El comentario de su hija había respondido también a la duda de Consuelo de si Annabelle se había quedado encinta durante la luna de miel. Al parecer, no.
—Creo que soy demasiado joven. Y nos lo pasamos muy bien juntos sin tener que preocuparnos por un niño. Además, queremos viajar un poco más. Tal vez vayamos a California al año que viene. Josiah dice que San Francisco es precioso, y quiere enseñarme el Gran Cañón. No puedo hacer todo eso si estoy embarazada.
—El Gran Cañón puede esperar —le dijo su madre, con aire decepcionado—. Siento oír vuestros planes. Me hacía mucha ilusión tener nietos —añadió con tristeza.
En esos momentos no había nada que diera sentido a su vida, salvo las visitas de Annabelle, que ya no vivía con ella, cosa que echaba mucho de menos. Si hubiera tenido nietos, ellos habrían llenado ese vacío.
—Ya los tendrás —le confirmó su hija—. Pero todavía no. No tengas tanta prisa. Como dice Josiah, nos queda mucho tiempo por delante.
Su marido lo había dicho más de una vez durante el viaje de novios y a ella no le quedaba más remedio que darle la razón. Al fin y al cabo, era su esposo, y ella tenía que seguir su iniciativa.
—Bueno, pues continúa sin parecerme bien que trabajes en la isla de Ellis. Creía que te gustaba el trabajo de voluntaria que hacías hasta ahora.
El Hospital para los Lisiados ya era lo bastante horrendo, en opinión de Consuelo. La isla de Ellis era impensable.
—Me parece que trabajar en la isla de Ellis será más interesante, y allí tendré más opciones de mejorar mis habilidades —repitió Annabelle, y su madre se sobresaltó al oír esas palabras.
—¿Qué habilidades? ¿Qué escondes debajo de la manga?
Annabelle estaba siempre llena de ideas, sobre todo relacionadas con la medicina y la ciencia. Estaba claro que era su pasión, aunque no la hubiera ejercido de manera oficial.
—Nada, mamá —contestó Annabelle muy seria y con aspecto taciturno—. Es que me encantaría poder ayudar aún más a las personas, y creo que soy capaz de hacer más de lo que me permiten en los hospitales de aquí.
Su madre ignoraba que Annabelle quería ser médico. Era uno de esos sueños que la joven sabía que nunca se harían realidad, así que ¿para qué comentárselo si así iba a disgustarla? Pero, por lo menos, deseaba acercarse todo lo posible a ese sueño con su tarea de voluntaria. La isla de Ellis y sus profundas necesidades, pues el hospital estaba masificado y contaba con pocos profesionales, le darían la oportunidad de hacerlo. Había sido Henry Orson quien se lo había propuesto. Conocía a un médico que trabajaba en ese hospital y le había prometido que se lo presentaría. Y como había sido idea de Henry, a Josiah le había parecido bien el plan.
Después de comer, Annabelle y su madre fueron a visitar a Hortie. Todavía tenía que descansar en la cama algunas horas al día, pero se levantaba cada vez más. A Annabelle se le hizo un nudo en la garganta al ver lo flaca que se había quedado Hortie y lo fatigada que parecía. El bebé era guapo y estaba rollizo, pero Hortie tenía el aspecto de haber ido a la guerra, y le dijo que se sentía igual o peor.
—Fue horroroso —le dijo con sinceridad, con unos ojos que todavía reflejaban todo lo vivido—. Nadie me contó que sería así. Pensaba que me moría, y luego mi madre me dijo que estuve a punto de hacerlo. Para colmo, James dice que quiere otro hijo pronto. Me da la impresión de que tiene pensado empezar una dinastía, o montar un equipo de béisbol o algo así. Todavía me cuesta sentarme y tengo suerte de no haber pillado una infección. Eso habría acabado conmigo, igual que le ocurrió a Aimee Jackson el año pasado. —Parecía impresionada de verdad y muy conmocionada por lo que acababa de superar. Y Annabelle no podía dejar de preguntarse si el hijo compensaba todo aquello. Era adorable, pero no habría sido tan adorable si su llegada al mundo hubiera matado a Hortie, y daba la impresión de que había estado a punto. Le pareció aterrador cuando Hortie le describió cómo había sido el parto—. Creo que me pasé veintiséis horas chillando. Ni siquiera estoy segura de si quiero repetirlo. E imagínate si hubieran sido gemelos. Creo que me mataría antes de pasar por eso. ¡Imagínate tener dos la misma noche!
Estaba horrorizada, cuando apenas seis meses antes había pensado que tener gemelos sería divertido. Dar a luz había resultado ser un asunto mucho más serio de lo que pensaba antes. Y el relato asustó a su amiga. Tanto, que dio gracias de no estar embarazada.
—¿Y tú qué tal? —preguntó Hortie con una mirada pícara y retomando su carácter de siempre—. ¿Cómo fue la luna de miel? ¿No te parece que el sexo es fabuloso? Es una pena que tenga que terminar en un parto, aunque supongo que puede evitarse, si tienes suerte. ¿Crees que ya te habrás quedado embarazada?
—No —se apresuró a decir Annabelle—. No estoy embarazada. Y no tenemos prisa. Además, lo que acabas de contarme hace que se me quiten las ganas para siempre.
—Mi madre dice que no debería contarles estas cosas a las mujeres que no han dado a luz aún. —Puso cara de culpabilidad—. Siento haberte asustado.
—No pasa nada —contestó Annabelle quitándole hierro. No había comentado nada acerca de su vida sexual y no tenía intención de hacerlo—. Digamos que hace que me alegre de no estar embarazada.
Entonces Hortie se recostó en la cama con un suspiro cansado, justo cuando la nodriza les llevó al bebé para enseñarles lo lozano y guapo que era. Era un niño encantador, y dormía profundamente en brazos de la ama de cría.
—Supongo que valió la pena —comentó la madre de la criatura sin mucho convencimiento, cuando la nodriza se hubo marchado.
A Hortie no le gustaba demasiado cogerlo en brazos. La maternidad la asustaba y todavía no había perdonado al niño la agonía que le había provocado. Sabía que se acordaría durante meses y meses.
—Mi madre dice que con el tiempo me olvidaré. Pero no estoy tan segura. Fue una barbaridad —repitió—. El pobre James no tiene ni idea de lo que pasó, y no me dejan que se lo cuente. Se supone que los hombres no deben saber estas cosas.
A Annabelle le parecía un principio muy extraño, pues habrían tenido que comunicárselo si ella hubiera muerto. Pero supuso que, salvo en ese caso, todo lo demás debía permanecer en secreto y una debía fingir que todo había ido como la seda.
—No veo por qué no puede saberlo. Yo se lo contaría a Josiah. No hay nada que no pueda contarle. Y creo que, aunque no se lo contara, se preocuparía por mí.
—Algunos hombres son así. Pero James, no. Es un niño. Y Josiah es mucho mayor, casi como si fuera tu padre. Bueno, entonces, ¿os lo pasasteis bien?
—Fue genial —dijo Annabelle con una sonrisa—. Aprendí a pescar con anzuelo, montamos a caballo todos los días.
Le había encantado galopar por las laderas de las montañas con Josiah entre mares de flores silvestres.
—¿Y qué más aprendiste? —preguntó Hortie con mirada maliciosa, pero Annabelle hizo caso omiso—. Yo aprendí cosas muy interesantes de James durante nuestra luna de miel en París.
Todo el mundo sabía que, por lo menos antes del matrimonio, James frecuentaba el prostíbulo. Era un secreto a voces. Y seguramente las prostitutas le habían enseñado cosas que Annabelle no quería saber, aunque, por lo que parecía, a Hortie no le importaba. Ella prefería mil veces estar casada con Josiah, aunque tardaran más tiempo en fundar una familia. Además, antes tenían que encontrar casa, pues su apartamento era demasiado pequeño.
Hortie no le sacó nada de información con sus preguntas e insinuaciones, así que al final, agotada, se dio por vencida y se acostó para echar una siesta, de modo que Annabelle se despidió de ella y volvió a casa. Se alegraba de haberla visto y el bebé era precioso, aunque la historia sobre el parto la había sobrecogido. Deseaba tener un hijo, pero no le apetecía en absoluto pasar por todo aquello. Le habría gustado coger en brazos a Charles un momento, pero Hortie no se lo había ofrecido, y tampoco parecía sentir deseos de acunarlo ella. Aunque, teniendo en cuenta lo que le había ocurrido, pensó que era comprensible y se preguntó si haría falta tiempo para desarrollar el instinto maternal, del mismo modo que hacía falta tiempo para asimilar la idea del matrimonio. Ni Josiah ni ella se habían acostumbrado todavía a estar casados.
### 9
En noviembre, cuando la temporada de actividades sociales de Nueva York volvió a cobrar fuerza, Hortie ya estaba en pie y Josiah y Annabelle no dejaban de recibir invitaciones. Con frecuencia coincidían en las fiestas con James y Hortie, quien había recuperado su buen humor de siempre. El bebé ya casi tenía tres meses, y Annabelle y Josiah llevaban casados ese mismo tiempo.
De la noche a la mañana, Annabelle y Josiah se habían convertido en la pareja más deseada y popular de Nueva York. Juntos estaban radiantes, y además mantenían la relación sencilla y desenfadada del principio. Se gastaban bromas mutuamente sin cesar y jugueteaban como niños, aunque también entablaban serias discusiones sobre temas políticos e intelectuales, a menudo cuando Henry iba a cenar a su casa. Hablaban sobre libros y otras aficiones, y las conversaciones con Henry siempre eran muy animadas. Algunas veces, los tres jugaban a las cartas y se reían a carcajada limpia.
Josiah y Annabelle cenaban con Consuelo por lo menos dos veces por semana, y en ocasiones con mayor frecuencia. Annabelle intentaba pasar todo el tiempo posible con su madre durante el día, pues sabía lo sola que estaba, aunque Consuelo nunca se quejaba al respecto. Era una mujer elegante y cariñosa. Además, no presionaba a Annabelle para que formara una familia, aunque deseaba que lo hiciera. Y no podía evitar darse cuenta de que esta hablaba de su esposo en los mismos términos que empleaba antes para hablar de su hermano Robert. Había una parte de Annabelle que sencillamente no había crecido todavía, a pesar de todo lo que había ocurrido, pero Josiah parecía encantado con esa faceta y la trataba como a una niña.
Tal como le había prometido, Henry le presentó a su amigo, el médico de la isla de Ellis, y Annabelle empezó a colaborar allí de voluntaria. Trabajaba muchas horas y a destajo, a menudo con niños enfermos. Y su madre tenía razón, aunque Annabelle nunca lo reconocería delante de ella, cuando le dijo que la mayoría de los pacientes llegaban gravemente enfermos y las infecciones se propagaban como la pólvora. De todos modos, la labor era fascinante y le encantaba. Annabelle le daba las gracias a Henry por haberlo hecho posible siempre que lo veía. Josiah estaba muy orgulloso de lo mucho que trabajaba su esposa, aunque ella no solía compartir los detalles de su labor con él. A pesar de eso, Josiah sabía lo mucho que se volcaba Annabelle en el funcionamiento del hospital, en los inmigrantes y en la tarea en sí.
Se desplazaba a la isla de Ellis tres veces por semana, pasaba allí unas jornadas agotadoras pero reconfortantes, y a menudo volvía tarde a casa. Trabajaba en el complejo hospitalario con forma de U que había en la parte sur de la isla. Algunas veces la mandaban a la Gran Sala, en el Ala Principal. Las llamas la habían destruido hacía dieciséis años, y la zona en la que ella solía colaborar había sido reconstruida tres años después del incendio. En la Gran Sala, los inmigrantes eran retenidos en una especie de celdas gigantescas en las que los interrogaban para asegurarse de que sus documentos y cuestionarios estaban al día. La mayor parte de ellos eran trabajadores robustos, muchos con esposa e hijos pequeños, y otros solos. Algunos decían que los esperaba su futura esposa, a quien nunca habían visto o a quien apenas conocían. Annabelle solía ayudarles con el proceso de las entrevistas, aunque alrededor de un dos por ciento de los inmigrantes eran deportados, con lágrimas y desesperación, y enviados de vuelta a sus países de procedencia. Ante el terror de la deportación, muchas personas mentían al responder a las preguntas de los interrogadores. Como sentía una inmensa pena por ellos, más de una vez había apuntado como válida una respuesta vaga o incorrecta. No tenía agallas para convertirlos en candidatos a la deportación.
Cada mes llegaban a la isla de Ellis cerca de cincuenta mil personas, y si Consuelo las hubiera visto al entrar, habría temido todavía más por el bienestar de su hija. Muchas de las personas que recalaban allí habían superado penurias atroces y algunas habían contraído enfermedades por el camino; por eso debían ser enviadas al complejo hospitalario. Los afortunados abandonaban la isla de Ellis en cuestión de horas, pero aquellos cuyos papeles no estaban en regla, o quienes estaban enfermos, debían permanecer en cuarentena y podían ser retenidos durante meses o incluso años. Además, para salir de allí era preciso que contaran con veinticinco dólares. Y todo aquel cuya entrada en el país presentaba dudas era enviado a un centro comunitario para extranjeros, eso cuando no era expulsado. Los enfermos acababan en una de las salas del hospital, de 275 camas, a la que solía ser asignada Annabelle para desempeñar la labor que tanto le gustaba.
Faltaban médicos y enfermeras, así que los existentes debían trabajar jornadas larguísimas, y con frecuencia acababan delegando tareas en los voluntarios que Annabelle nunca habría tenido oportunidad de realizar en otras circunstancias. Ayudaba a dar a luz, cuidaba de los niños enfermos y, entre otras cosas, presenciaba análisis oculares para diagnosticar el tracoma, una afección que sufrían muchos inmigrantes. Algunos de ellos ocultaban los síntomas por miedo a que los deportaran. Por supuesto, también había pabellones de cuarentena para enfermos con paperas, fiebre escarlata y difteria, en los que Annabelle no podía entrar. Sin embargo, colaboraba en prácticamente todo lo demás, y los médicos con los que trabajaba solían quedar impresionados por su buen instinto para diagnosticar. A pesar de ser una persona sin formación, había adquirido una gran cantidad de conocimientos gracias a las lecturas que había realizado y poseía una habilidad innata para todo lo relacionado con la medicina, además de tener mucho tacto en el trato con los pacientes. Los enfermos la apreciaban y confiaban ciegamente en ella, quien, algunas veces, llegaba a ver a cientos de pacientes en un solo día para solucionar por sí misma dolencias menores, o para ayudar a médicos y enfermeras si los casos eran de mayor gravedad. Había tres edificios completos dedicados a las enfermedades contagiosas y muchos de los pacientes allí ubicados no abandonarían jamás la isla de Ellis.
El pabellón de los tuberculosos era el más triste del hospital, y Consuelo se habría puesto histérica de haber sabido que, con frecuencia, Annabelle se prestaba voluntaria para trabajar en él. Nunca se lo había dicho a su madre, ni siquiera a Josiah, pero los pacientes que más le interesaban eran los más graves, pues con ellos era con quienes consideraba que aprendía más acerca del tratamiento y la cura de las enfermedades serias.
Un día, después de haber estado ayudando en el pabellón de los tuberculosos hasta bien entrada la noche, se encontró al volver a casa a Henry y a Josiah charlando en la cocina. Este comentó que Annabelle llegaba muy tarde, así que ella se disculpó porque se sentía culpable. Le había costado mucho despedirse de los pacientes que había visto ese día, todos ellos niños con tuberculosis. Para entonces ya eran las diez, y Henry y Josiah estaban preparando la cena y hablando tranquilamente del banco. Josiah la abrazó muy fuerte. Annabelle estaba agotada y todavía no había entrado en calor después del trayecto en barca para regresar a la ciudad. Su marido le dijo que se sentara con ellos en la cocina, le acercó un cuenco de sopa y le preparó la cena a ella también.
Mientras cenaban, mantuvieron una conversación muy animada, como siempre que se reunían los tres. Eso sirvió para distraer a Annabelle, quien dejó de pensar por un rato en sus pacientes. Les encantaba debatir ideas nuevas y viejas, discutir sobre política y replantearse las normas sociales aceptadas desde hacía siglos dentro de su mundo; en general, se divertían mucho juntos. Eran tres personas inteligentes con mentes inquietas y parecían uña y carne. Annabelle había llegado a querer a Henry casi tanto como lo quería Josiah, y para ella se había convertido en otro hermano, pues echaba muchísimo de menos al suyo.
Esa noche estaba demasiado cansada para continuar conversando con ellos en la sobremesa, así que, cuando vio que ambos se enfrascaban en un acalorado debate sobre un tema político, les dio las buenas noches y se fue a dormir. Se preparó un baño caliente, se puso un camisón que abrigaba y se deslizó agradecida entre las sábanas, pensando en la labor que había realizado ese día en la isla de Ellis. Se había quedado profundamente dormida mucho antes de que Henry se marchase y Josiah se fuera a la cama. Cuando su marido entró en la habitación, se despertó y lo miró con ojos adormilados mientras él se deslizaba bajo las sábanas a su lado. Entonces alargó los brazos para recibirlo. Al cabo de pocos minutos, estaba totalmente despierta, pues ya había descansado durante varias horas.
—Siento no haberme quedado con vosotros. Estaba agotada —dijo con voz adormecida, disfrutando del calor que él le proporcionaba.
Le encantaba dormir abrazada a Josiah. Amaba todas las facetas de su marido y confiaba en que él la amara en igual medida. Algunas veces no estaba segura. Las relaciones con los hombres, y sus flaquezas, le resultaban desconocidas. Un marido era distinto de un padre o un hermano. Con un esposo, la dinámica era mucho más sutil y en ocasiones confusa.
—No seas tonta —le susurró él sin pensarlo—, es que hablamos demasiado. Y has tenido un día muy largo. Te entiendo.
Ella era una persona muy entregada y nunca dudaba en desvivirse por el bien de los demás. Era un ser humano increíble con un buen corazón, y él la amaba de verdad. No le cabía la menor duda.
A continuación se produjo un silencio incómodo entre los dos, pues Annabelle vaciló; deseaba preguntarle algo. Siempre le daba apuro sacar el tema.
—¿Crees que... a lo mejor... podríamos empezar a... tener familia? —le preguntó en un susurro, y durante un largo instante él no dijo nada, pero ella notó que se ponía tenso.
Se lo había preguntado una vez más, y en la otra ocasión tampoco le había sentado bien. Había momentos y temas sobre los que Josiah no quería que lo presionaran. Y ese era uno de esos temas.
—Tenemos mucho tiempo por delante, Annabelle. Solo llevamos casados tres meses. Las personas necesitan tiempo para acostumbrarse unas a otras. Ya te lo he dicho. Tiempo al tiempo, no presiones.
—No presiono. Solo pregunto...
No estaba ansiosa por pasar por el mismo mal trago que su amiga Hortie, pero quería tener un hijo con él y deseaba demostrarle lo valiente que era, por muy horrenda que fuera o pudiera ser la experiencia.
—Pues no preguntes, ya ocurrirá. Primero necesitamos asentarnos.
Sus palabras sonaron firmes, aunque Annabelle no quería discutir con su marido ni enojarlo. Siempre era muy cariñoso, pero cuando se enfadaba, se bloqueaba y se volvía muy frío con ella, algunas veces durante varios días. Y Annabelle no tenía el menor deseo de provocar una disputa entre ambos en ese preciso momento.
—Lo siento. No volveré a sacar el tema —susurró, sintiéndose reprendida.
—Por favor, no lo hagas —contestó él con una voz que de repente sonó gélida, y le dio la espalda.
Era un hombre afectuoso y comprensivo con el resto de los temas, pero no con ese. Era un asunto delicado para él. Unos minutos más tarde, sin decir ni una palabra más, se levantó. Annabelle se quedó despierta esperándolo durante un buen rato, y al final concilió el sueño antes de que regresara. Por la mañana, cuando se levantó, él ya estaba en pie y vestido. Sus discusiones casi siempre acababan así. Tal actitud reforzaba la petición de que no le molestara ni presionara, y le recordaba a Annabelle que no debía volver a tocar el tema.
A la semana siguiente fue a ver a Hortie y, cuando llegó a su casa, se la encontró hecha un mar de lágrimas. Estaba acongojada, pues acababa de descubrir que había vuelto a quedarse embarazada. El bebé nacería once meses después que Charles, en julio. James estaba encantado con la idea y esperaba que fuese otro chico. Pero el recuerdo del parto de su primer hijo estaba todavía demasiado fresco en la mente de Hortie, a quien daba pavor tener que pasar por lo mismo otra vez, así que no hacía más que llorar y apenas se levantaba de la cama. Annabelle intentó consolarla, pero no sabía qué decirle. Lo único que se le ocurría era que seguramente no fuese tan terrible la segunda vez. Hortie no estaba tan convencida.
—¡Y no quiero volver a ponerme como una vaca! —chilló—. James no se me acercó en todo el embarazo. Mi vida es una ruina, y además ¡a lo mejor esta vez me muero de verdad! —añadió entre gemidos—. Estuve a punto de morir en el otro parto.
—No te morirás... —le dijo Annabelle, con la esperanza de que fuera cierto—. Tienes un buen médico y tu madre te acompañará. No dejarán que te pase nada. —Sin embargo, las dos sabían que otras mujeres habían muerto mientras daban a luz, o justo después, a pesar de contar con unos cuidados excelentes—. No puede ser peor que la otra vez —insistió Annabelle, pero Hortie no se consolaba con nada.
—Ni siquiera me «gustan» los niños —le confesó—. Pensaba que un hijo sería como una hermosa muñeca gigante, pero lo único que hace es comer, cagar y llorar. Gracias a Dios que no le doy el pecho. ¿Por qué tengo que arriesgar mi vida a cambio de eso?
—¡Porque estás casada y eso es lo que tienen que hacer las mujeres! —le espetó su madre con sequedad mientras entraba en la habitación, y miró a su hija con ojos severos—. Deberías estar agradecida de ser capaz de concebir y hacer feliz a tu marido.
Todas ellas conocían a mujeres que eran incapaces de tener hijos, a quienes sus esposos abandonaban por otras que sí podían. No obstante, al escucharlas, Annabelle agradeció que ese tema no fuera problemático entre Josiah y ella, aunque creía que el bebé de Hortie era mucho más atractivo de lo que pensaba su madre. De todas formas, se pusiera como se pusiese, Hortie iba a tener dos hijos en julio del año siguiente, menos de dos años después de haberse casado.
—Eres una niña egoísta y malcriada —la reprendió su madre, y volvió a salir de la habitación, sin mostrar la menor empatía por su hija, aunque había estado presente en la agónica experiencia del parto. Lo único que dijo fue que ella había pasado por cosas peores, pues sus hijos habían sido igual de grandes, y además había tenido varios abortos y dos bebés que habían nacido muertos, así que Hortie no tenía ningún motivo para quejarse.
—¿Para eso estamos aquí? ¿Para parir? —le preguntó Hortie a su amiga, muy enfadada, una vez que su madre hubo salido del dormitorio—. Y ¿por qué es todo tan sencillo para los hombres, eh? Lo único que hacen es jugar contigo, y luego a ti te toca todo el sufrimiento y el trabajo, te pones gorda y fea y vomitas durante meses, y para colmo arriesgas tu vida para tener un hijo. Algunas mujeres mueren en el parto... Y ¿qué hacen los hombres mientras tanto? Nada, se limitan a hacerte otro hijo y después salen corriendo a divertirse con sus amigos.
Annabelle sabía, igual que Hortie, que en la ciudad corrían rumores de que James tonteaba demasiado y veía a otras mujeres además de a su esposa. Eso le recordó a Annabelle que ninguna vida ni ningún matrimonio eran perfectos. Josiah prefería esperar antes de fundar una familia, pero por lo menos estaba segura de que no la engañaba, no era de esa clase de hombres. De hecho, el único matrimonio perfecto que conocía era el de sus padres, y su padre había muerto y su madre era una viuda solitaria a los cuarenta y cuatro años. A lo mejor, en el fondo, la vida era injusta.
Escuchó las quejas y lamentos de Hortie durante varias horas y después regresó a casa con su marido, aliviada de que su vida fuese mucho más sencilla, aunque él siguió comportándose con frialdad aquella noche. No le habían gustado nada los comentarios que Annabelle había hecho la noche anterior. Salió a cenar con Henry al Club Metropolitan porque dijo que tenía que hablar de negocios con él. Annabelle se quedó en casa y se zambulló en sus libros de medicina. Al día siguiente volvería a la isla de Ellis. Leía todo lo que podía sobre enfermedades contagiosas, en especial sobre la tuberculosis. Aunque resultaba agotador y era un reto para ella, le encantaba todo lo que hacía en el hospital. Y, como solía ocurrir, ya estaba profundamente dormida cuando Josiah llegó a casa esa noche. Sin embargo, cuando se despertó de madrugada, notó que él la había abrazado. La joven sonrió y volvió a conciliar el sueño. Su mundo estaba a salvo.
### 10
Como Josiah no tenía muy buena relación con su familia, Annabelle y él pasaron tanto el día de Acción de Gracias como la Navidad con la madre de ella. Y como Henry estaba solo, a modo de deferencia hacia él lo invitaron también en ambas ocasiones. Era inteligente, encantador y muy atento con Consuelo, así que dio un poco de alegría al grupo.
Al final, Hortie se calmó y fue asimilando la idea de que iba a tener otro hijo. No estaba precisamente emocionada, pero no le quedaba otro remedio que aceptarlo. De todas formas, ella deseaba más descendencia, lo que ocurría era que simplemente no estaba preparada para dar a luz tan poco tiempo después de la odisea vivida en agosto. Pero confiaba en que esa vez fuese más sencillo, y de momento no tenía tantas náuseas.
Por su parte, Annabelle siguió volcada en su labor en la isla de Ellis, a pesar de las objeciones continuas de su madre. Consuelo no había vuelto a preguntarle a Annabelle por el tema de los nietos, pues había entendido el mensaje alto y claro de que la pareja no iba a tener hijos de manera inminente, y, aunque estaba ansiosa por ser abuela, no quería entrometerse sin motivos en la vida de la joven. Además, trataba a Josiah como a un hijo.
Todos se quedaron conmocionados cuando llegó abril y, con él, el segundo aniversario del hundimiento del _Titanic_. En algunos aspectos, parecía que hubiera ocurrido el dia anterior, y en otros, el episodio parecía mucho más lejano. Habían pasado tantas cosas desde entonces... Annabelle y su madre fueron a la iglesia ese día y celebraron una misa especial en memoria de su padre y su hermano. Consuelo se sentía sola, pero se había adaptado bien a esas grandes pérdidas y daba gracias porque Josiah y Annabelle pasaran tanto tiempo con ella. Eran muy generosos.
En mayo, esta cumplió veintiún años. Consuelo le preparó una fiesta reducida e invitó a algunos de sus amigos. Fueron James y Hortie, así como varias parejas jóvenes de su círculo, y Henry Orson, con una muchacha preciosa a quien acababa de conocer. Annabelle confiaba en que surgiera algo entre los dos.
Pasaron una velada estupenda y Consuelo incluso había contratado a unos músicos, así que después de la cena todos se pusieron a bailar. La fiesta fue fantástica. Y por la noche, cuando Josiah y Annabelle se fueron a dormir, ella volvió a plantearle a su marido la fatídica pregunta. No se lo había mencionado desde hacía meses. Josiah le había regalado una hermosa pulsera de diamantes para su cumpleaños, que todos los invitados admiraron y que era la envidia de todas sus amigas, pero ella quería otra cosa de él, algo que consideraba mucho más importante. El anhelo llevaba varios meses corroyéndola por dentro.
—¿Cuándo vamos a formar una familia? —le susurró cuando estaban en la cama, uno al lado del otro.
Lo dijo mirando hacia el techo, como si, por no mirarlo a la cara, a él le fuese a resultar más fácil darle una respuesta sincera. Cada vez había más cosas que se quedaban en el aire flotando entre los dos. Annabelle no quería disgustarlo pero, tras nueve meses de matrimonio, algunas cosas eran difíciles de explicar, y él no podía seguir diciéndole que «tenían tiempo» y que «no hacía falta correr». ¿Cuánto tiempo más debería esperar?
—No lo sé —contestó él con sinceridad y cara triste. Annabelle lo vio en sus ojos cuando volvió la cabeza para mirarlo—. No sé qué decirte —repitió él, a punto de echarse a llorar, y de repente Annabelle se asustó—. Necesito un poco de tiempo.
Ella asintió y con cariño le acarició la mejilla con la mano.
—No pasa nada. Te quiero —le susurró. Había muchas cosas que no comprendía y que no podía preguntarle a nadie—. ¿Hay algo que yo deba cambiar?
Él negó con la cabeza y se la quedó mirando.
—No eres tú. Soy yo. Intentaré solucionarlo, te lo prometo —dijo él mientras los ojos se le llenaban de lágrimas y la estrechaba entre sus brazos. Hacía meses que no se sentían tan próximos, y la joven sintió que Josiah por fin empezaba a derribar los muros que lo rodeaban para dejarla entrar.
Annabelle sonrió mientras lo abrazaba y le respondió con sus propias palabras.
—Tenemos tiempo.
Cuando lo dijo, una lágrima resbaló por la mejilla de Josiah.
En junio, Consuelo se marchó a Newport. Ahora que tenía menos cosas que hacer en la ciudad, le gustaba ir allí antes de que empezase la temporada estival. Annabelle le había prometido que se uniría a ella a principios de julio, y Josiah iría a finales de mes.
La mujer ya había abandonado la ciudad cuando las noticias desde Europa atrajeron la atención de todo el mundo. El 28 de junio de 1914, el archiduque Francisco Fernando, heredero del Imperio austro-húngaro, y su esposa Sofía, estaban de visita oficial en Sarajevo, en Bosnia, cuando los asesinó de un balazo un joven terrorista serbio llamado Gavrilo Princip. Este formaba parte de la Mano Negra, una organización terrorista serbia muy temida que quería terminar a toda costa con el dominio austro-húngaro en los Balcanes. El Gran Duque y su esposa habían muerto de un solo tiro disparado a bocajarro en la cabeza. La impactante noticia reverberó por todo el mundo, y sus consecuencias en Europa fueron rápidas y sobrecogedoras y dejaron de piedra a todos los habitantes de Estados Unidos.
Austria culpó al gobierno de Serbia y pidió ayuda a Alemania. Tras varias semanas de enfrentamientos diplomáticos, el 28 de julio, Austria-Hungría declaró la guerra a Serbia y abrió fuego en la ciudad de Belgrado. Dos días más tarde, Rusia movilizó sus tropas y se preparó para la guerra. Francia se vio entonces en una tesitura y, obligada por las condiciones del tratado firmado con Rusia, tuvo que apoyar sus planes bélicos. En cuestión de días, el castillo de naipes que mantenía la paz en Europa empezó a desmoronarse. Los dos disparos que habían matado al archiduque de Austria y a su mujer habían llevado a la guerra a los países más importantes de Europa. El 3 de agosto, a pesar de sus protestas, pues se trataba de un país neutral, las tropas alemanas marcharon por toda Bélgica para atacar Francia.
Al cabo de pocos días, Rusia, Inglaterra y Francia se aliaron y declararon la guerra a Alemania y al Imperio austro-húngaro. Los estadounidenses y su gobierno permanecían boquiabiertos ante lo ocurrido. El 6 de agosto, todas las grandes potencias de Europa estaban en guerra y en Estados Unidos no se hablaba de otra cosa.
Annabelle había retrasado su marcha a Newport a la espera de ver cómo se desarrollaban los acontecimientos en Europa. Deseaba quedarse en casa para estar cerca de Josiah. Aunque su país no había entrado en la contienda, sus aliados europeos estaban en guerra. Sin embargo, Estados Unidos no daba muestras de querer involucrarse. Y Josiah le aseguró que, incluso si el país entraba en guerra en algún momento, cosa harto improbable, Annabelle no tenía nada que temer pues, le recordó, estaba casada con un «hombre mayor». A los cuarenta y un años, no había ningún peligro de que lo mandaran al frente. El presidente Wilson repetía para tranquilidad de todos los ciudadanos estadounidenses que tenía intención de permanecer al margen de la guerra de Europa. De todas formas, la situación era increíblemente inquietante.
Al final, Annabelle viajó a Newport con Josiah a finales de julio, dos semanas más tarde de lo previsto. En la isla de Ellis había tenido tanto trabajo como siempre. Muchos de los inmigrantes sentían pánico por la seguridad de sus familiares. Era evidente que la guerra, declarada en muchos de los países de los que ellos procedían, afectaría a sus familias e impediría que algunos de los que tenían pensado reunirse con ellos en Estados Unidos pudieran desplazarse allí. Muchos de sus hijos, hermanos y primos ya habían sido llamados a filas.
En Nueva York, antes de marcharse, Annabelle, Josiah y Henry habían hablado largo y tendido sobre la guerra en Europa en varias de sus cenas compartidas en el jardín de los Millbank. E incluso en el idílico Newport corrían las noticias acerca de lo que estaba ocurriendo. Por una vez, la vida social de la localidad y la participación de los vecinos en ella habían pasado a un segundo plano y habían cedido protagonismo a las noticias de los acontecimientos mundiales.
En la fiesta del primer aniversario de bodas de Josiah y Annabelle, Consuelo se percató de que la pareja estaba más unida que nunca, aunque los encontró a ambos muy serios, cosa que era perfectamente comprensible, teniendo en cuenta lo que pasaba en el mundo. Henry se había desplazado desde Nueva York para celebrar el aniversario de bodas con ellos.
Para entonces, Hortie ya había tenido a su segundo hijo, que se retrasó dos semanas y nació el día 1 de agosto: esta vez fue una niña. El parto volvió a ser largo y complicado, pero ni la mitad de terrible que el de Charles. Y Louise, que fue el nombre que le pusieron, solo pesó tres kilos y ochocientos gramos. Hortie no pudo asistir a la cena de aniversario de Annabelle y Josiah en la casa de campo de Consuelo, porque todavía estaba recuperándose en la cama, atendida por su madre y una enfermera. Sin embargo, James sí que fue, por supuesto. Como tenía costumbre, ese verano asistió a todas las fiestas que se celebraron en Newport, algo que también hacía en Nueva York, con o sin Hortie.
Aquel agosto en Newport fue mucho más tranquilo que de ordinario, debido a las noticias de la guerra en Europa. El conflicto parecía un nubarrón que pendía sobre todos ellos, pues nadie dejaba de hablar de los Aliados al otro lado del Atlántico ni de preocuparse por sus amigos europeos. Annabelle y Josiah hablaban con frecuencia sobre el tema, incluso durante los tranquilos días que disfrutaron a solas después de la partida de Henry. Entre Josiah y Annabelle parecía haber un acuerdo tácito, pero Consuelo los veía más serios que en la primera etapa de su matrimonio. Le entristecía ver que seguían sin fundar una familia y Annabelle nunca le mencionaba el tema. En un momento dado, cuando vio que su hija tenía la mirada triste, Consuelo le preguntó si algo marchaba mal, pero Annabelle no compartió sus penas con ella, y parecía más entregada que nunca a su esposo. Consuelo seguía creyendo que formaban la pareja perfecta, y se divertía con ellos y sus amigos. Solo confiaba en que algún día le dieran un nieto y, a ser posible, pronto.
La joven pareja regresó a Nueva York a principios de septiembre: Josiah volvió a sus obligaciones en el banco y Annabelle a las suyas en la isla de Ellis. Cada vez se involucraba más en el hospital y sentía un profundo afecto y respeto por las personas a las que cuidaba y ayudaba, la mayor parte de ellas polacas, alemanas e irlandesas. Y su madre seguía preocupándose por su salud, pues no le gustaba que estuviera tan cerca de los enfermos. Sufrían muchas afecciones, y los niños solían estar muy enfermos; además, Consuelo sabía que la tuberculosis campaba a sus anchas... Lo que desconocía era que Annabelle no tenía miedo ni se preocupaba cuando se mezclaba con ellos. Ese otoño trabajó en el hospital más que nunca, a pesar de las advertencias y quejas de su madre.
Josiah también estaba muy ocupado en el banco, ya que debía solucionar algunos asuntos delicados. Como potencia neutral, el gobierno de Estados Unidos, pese a comprender su causa, se había negado a financiar o contribuir de manera oficial a los esfuerzos bélicos de los Aliados en Europa. En consecuencia, la empresa privada y algunos individuos muy acaudalados habían dado un paso adelante y habían ofrecido su ayuda a título personal. Enviaban dinero y fletaban alimentos, y no solo para los Aliados, sino a veces también para sus enemigos. Se estaba creando un gran revuelo, y controlar todas esas transferencias requería una discreción absoluta, en la que a menudo se veía inmerso el propio Josiah. Como hacía con la mayor parte de sus preocupaciones, le había confiado a Annabelle lo que tenía entre manos y había compartido con ella sus dudas. Le preocupaba horrores que ciertos clientes importantes del banco de su difunto padre enviaran material y fondos a Alemania, debido a los vínculos que dichos clientes tenían en el país germánico. Aborrecía tener que jugar en ambos bandos, pero debía cumplir las solicitudes de sus clientes.
Era un secreto a voces que se estaban realizando transacciones de tal naturaleza, y, para cortar de cuajo la llegada de provisiones a Alemania, Gran Bretaña había empezado a bombardear el Mar del Norte. Como represalia, los alemanes amenazaban con hundir cualquier barco que perteneciese a Gran Bretaña o a sus aliados. Además, los submarinos alemanes patrullaban el Atlántico bajo su superficie. Estaba claro que no era un buen momento para cruzar el océano, pero a pesar de ello seguía llegando a la isla de Ellis un torrente continuo de inmigrantes, decididos a encontrar una nueva vida en Estados Unidos.
Las personas a las que Annabelle trataba en esos momentos estaban más enfermas y en peores condiciones que las que había atendido en los años precedentes. En muchos casos, habían dicho adiós a unas condiciones penosas en sus países de origen y besaban el suelo cuando desembarcaban en Estados Unidos. Agradecían cualquier gesto amable que les ofreciera el personal médico y valoraban mucho todo lo que Annabelle hacía por ellos. Había intentado contarle a su madre, aunque en balde, lo necesitados que estaban de voluntarios como ella para que atendieran a los inmigrantes recién llegados. A pesar de eso, su madre seguía teniendo la firme convicción de que arriesgaba su vida cada vez que iba allí, y no se equivocaba del todo, por mucho que Annabelle no estuviera dispuesta a reconocerlo. Josiah era el único que parecía comprender y apoyar su labor. La joven había comprado más libros sobre medicina y solía estudiarlos todas las noches antes de irse a dormir. Eso la mantenía ocupada cuando Josiah tenía que trabajar hasta tarde o cuando salía con sus amigos a actos en clubes en los que no se aceptaban mujeres. A Annabelle no le importaba que saliera sin ella. Decía que así tenía más tiempo para leer y estudiar hasta bien entrada la madrugada.
Para entonces ya había visto realizar varias operaciones y había leído a conciencia todo lo que caía en sus manos acerca de las enfermedades contagiosas que se extendían como plagas entre los pacientes a los que atendía. Muchos de los inmigrantes morían, sobre todo los más ancianos, por culpa de las penurias del viaje o debido a las enfermedades que contraían cuando llegaban. En muchos sentidos, Annabelle era considerada entre el equipo médico del hospital como una especie de enfermera extraoficial y sin formación, que a menudo demostraba ser tan competente como el resto, o incluso más. Tenía un instinto muy certero y un talento aún mayor a la hora de diagnosticar a los pacientes, algunas veces con la rapidez necesaria para poder salvarles la vida. Josiah solía decir que era una santa, halago que ella rechazaba porque lo consideraba un piropo generoso pero inmerecido. Continuó trabajando con más ganas que nunca, y a menudo su madre pensaba que intentaba paliar así el vacío vital que habría llenado un hijo. Lamentaba la ausencia prolongada de descendencia en la vida de su hija, tal vez más que la propia Annabelle. La joven nunca mencionaba el tema de los hijos en su presencia.
Henry Orton volvió a celebrar la Navidad con Consuelo y ellos dos al año siguiente. Los cuatro compartieron una tranquila cena de Nochebuena. Era la tercera Navidad que pasaban sin Arthur y Robert, y los echaron mucho de menos, pues durante las vacaciones era cuando más les dolía su ausencia. Annabelle odiaba reconocerlo, pero notaba que una gran parte de la vitalidad y el talante alegre de su madre habían desaparecido después de la muerte de su esposo y su hijo. Consuelo siempre agradecía el tiempo que pasaba con ella y mostraba interés por lo que ocurría en el mundo, pero era como si, después de la terrible tragedia del _Titanic_ acaecida hacía más de dos años, ya no le importase el futuro. Henry era el único que todavía conseguía hacerla reír. Para Consuelo, la doble pérdida había sido excesiva. No le quedaba otra ilusión que vivir lo suficiente para conocer a sus nietos. Cada vez le preocupaba más que algo no marchase bien, o que su hija fuera incapaz de quedarse embarazada. No obstante, el vínculo entre Josiah y ella seguía pareciendo muy fuerte.
Y como siempre, incluso en Nochebuena, su conversación acabó versando sobre la guerra durante la sobremesa. Ninguna de las noticias era buena. Costaba creer que, en algún momento, aunque solo fuera por empatía, Estados Unidos no acabara entrando en la contienda y, en consecuencia, se perdieran muchas vidas de jóvenes estadounidenses. El presidente Wilson insistía con rotundidad en que no iban a verse involucrados, aunque Josiah empezaba a dudarlo.
Dos días después de Navidad, Annabelle hizo una visita improvisada a su madre y se sorprendió cuando el mayordomo le dijo que estaba en la cama. Se la encontró temblando metida entre las sábanas, con el semblante pálido y dos brillantes marcas rojas en las mejillas. Blanche acababa de llevarle una taza de té, que se había negado a tomar. Parecía muy enferma, y cuando Annabelle le tocó la frente con mano experta supo que tenía una fiebre altísima.
—¿Qué te pasa? —le preguntó, muy preocupada. Era evidente que se trataba de gripe, cuando no de algo peor. Era precisamente lo que su madre siempre temía que le pasase a ella. Pero Annabelle era joven y su resistencia a las enfermedades era excelente. Por el contrario, sobre todo desde hacía dos años, Consuelo se había vuelto muy frágil. La tristeza creciente por la pérdida familiar había mermado su juventud y su fortaleza.
—¿Cuánto hace que estás enferma? —La había visto apenas dos días antes y no tenía ni idea de que se encontrase mal. Consuelo había advertido a Blanche que no preocupara a su hija, pues estaba segura de que se pondría bien en cuestión de días.
—Desde ayer... —contestó su madre sonriéndole—. No pasa nada. Creo que cogí un poco de frío en el jardín el día de Navidad.
A Annabelle le parecía que su madre había cogido algo más que frío, y Blanche también estaba preocupada.
—¿Has llamado al médico? —preguntó Annabelle, y frunció el entrecejo cuando su madre negó con la cabeza—. Creo que deberías hacerlo.
Mientras lo decía, su madre empezó a toser y Annabelle se fijó en que tenía los ojos vidriosos.
—No quería molestarlo justo después de Navidad. Tiene cosas más importantes que hacer.
—No seas tonta, mamá —la reprendió con cariño Annabelle.
Salió de la habitación lentamente y fue a llamarlo por teléfono. Al cabo de unos minutos regresó al dormitorio con una sonrisa radiante que tenía más de voluntad que de sentimiento.
—Me ha dicho que vendrá enseguida.
Su madre no discutió con ella por haber llamado al médico, algo que también era inusual. Annabelle se dio cuenta de que debía de sentirse muy enferma. Y, a diferencia de cuando cuidaba con tanta diligencia a los enfermos de la isla de Ellis, se sentía impotente a los pies de la cama de su madre, y sin saber por qué le entró el pánico. No recordaba haberla visto nunca enferma. Y tampoco había oído que hubiese una epidemia gripal. El médico se lo confirmó en cuanto llegó a la casa.
—No tengo ni idea de cómo ha podido contraerla —dijo consternado—. He visto a unos cuantos pacientes con esta enfermedad durante las vacaciones, pero en su mayoría eran ancianos, que suelen ser más frágiles. Su madre todavía es joven y goza de buena salud —le aseguró a Annabelle. Estaba convencido de que Consuelo se sentiría mucho mejor al cabo de unos días. Así pues, le recetó unas gotas de láudano para ayudarla a dormir mejor, además de una aspirina para bajar la fiebre.
Sin embargo, a las seis de la tarde su madre estaba mucho peor, tanto que Annabelle decidió quedarse a pasar la noche con ella. Llamó a Josiah para comunicárselo y él se mostró muy comprensivo y le preguntó si había algo que pudiera hacer para ayudarla. Annabelle le aseguró que no y se reunió con su madre, quien había escuchado la conversación.
—¿Eres feliz con él? —le preguntó a su hija de pronto, una pregunta que Annabelle consideró muy extraña.
—Claro que sí, mamá. —Annabelle le sonrió y se sentó en una silla junto al lecho y alargó el brazo para darle la mano. Se quedó allí sentada, cogiéndola de la mano, igual que había hecho su madre cuando ella era una niña—. Lo quiero muchísimo —enfatizó—. Es un hombre maravilloso.
—Siento tanto que no tengáis hijos... ¿No ha pasado nada todavía?
Annabelle sacudió la cabeza con expresión seria y le dio la respuesta oficial.
—Tenemos tiempo.
Su madre confiaba en que no fuera una de esas mujeres incapaces de engendrar un hijo. Pensaba que sería una tragedia si no tenían descendencia, y Annabelle también lo creía así, aunque no quería reconocerlo ante su madre.
—Ahora lo importante es que te recuperes —dijo la joven para distraerla.
Consuelo asintió y, un ratito después, se acostó para intentar dormir. Parecía una niña, y ahora Annabelle era la adulta que se sentaba a su lado para velarla. La fiebre le subió aún más durante las horas siguientes, y a medianoche Annabelle empezó a cubrirle la frente con los paños húmedos que iba preparando Blanche. Tenían muchas más comodidades a su disposición que cuando trabajaba en la isla de Ellis, pero nada servía de ayuda. Se pasó la noche en vela junto al lecho de su madre, con la esperanza de que la fiebre bajara por la mañana, pero no lo hizo.
Durante los tres días siguientes, el médico fue a verla a primera hora y antes de acostarse, pues Consuelo seguía empeorando. Era el caso más grave de gripe que el doctor había visto desde hacía mucho tiempo, y bastante peor del que había sufrido Annabelle hacía tres años, cuando se había perdido el fatídico viaje en el _Titanic_.
Josiah fue a hacer compañía a su suegra una tarde, para que Annabelle pudiera dormir unas cuantas horas en su antigua habitación. Había salido antes del banco para llegar pronto, y se sorprendió cuando Consuelo se despertó y lo miró con unos ojos claros y brillantes. Parecía mucho más alerta de lo que había estado el día anterior, y Josiah confiaba en que estuviera mejorando. Sabía lo angustiada que estaba Annabelle por su madre, y con razón. Consuelo estaba muy, muy enferma, y no era la primera vez que alguna persona moría por culpa de una gripe, aunque no había motivos para que algo así le ocurriera a ella, con tan buenos cuidados. Annabelle no se había apartado de ella ni un instante, salvo para dormir media hora suelta aquí y allá, aprovechando los momentos en que Blanche o Josiah se sentaban junto a su madre. Consuelo no se había sentido sola ni un minuto. Además, el médico continuaba visitándola dos veces al día.
—Annabelle te quiere muchísimo —le dijo Consuelo a Josiah en voz baja desde la cama, sonriéndole. Estaba muy débil y pálida, como los moribundos.
—Yo también la quiero mucho —le aseguró él—. Es una mujer extraordinaria, y una esposa fantástica.
Consuelo asintió con la cabeza y se quedó satisfecha de oírselo decir. Con demasiada frecuencia, tenía la sensación de que él la trataba más como a una hermana menor o a una niña, en lugar de como a una esposa o una mujer adulta. Tal vez era su forma de comportarse, debido a que ella era mucho más joven que él.
—Tiene que descansar y ponerse bien —animó Josiah a su suegra, y ella perdió la mirada, como si supiera que en el fondo no importaba.
Entonces, lo miró a la cara con ojos intensos.
—Si me ocurre algo, Josiah, quiero que cuides bien de ella. Eres lo único que le queda. Y confío en que tengáis hijos algún día.
—Yo también —admitió él con afecto—. Sería una madre perfecta. Pero no debe decir esas cosas, seguro que se recupera.
Consuelo no parecía tan segura, y a Josiah le resultó evidente que la mujer creía que estaba en las últimas, aunque tal vez fuera solo miedo.
—Cuídala mucho —insistió la enferma, y entonces se le cerraron los ojos y volvió a conciliar el sueño.
No se despertó hasta que Annabelle regresó a la habitación una hora más tarde y le miró la fiebre. Para su desesperación, le había subido, y se lo comentó a su marido justo en el momento en que su madre abría los ojos.
—¿Te encuentras mejor? —preguntó Annabelle con una amplia sonrisa, pero Consuelo sacudió la cabeza, y su hija tuvo la aterradora sensación de que estaba tirando la toalla. Hasta ese momento, nada de lo que habían hecho por ella había surtido efecto.
Entonces Josiah volvió al apartamento y le dijo a Annabelle que lo llamara por la noche si había algo que estuviera en su mano. Annabelle le prometió que lo haría y, en cuanto se marchó de la casa de los Worthington, a Josiah le asaltaron las palabras que había pronunciado Consuelo. Tenía la firme intención de cuidar de Annabelle. Y era plenamente consciente de ser lo único que le quedaba en el mundo a la joven, aparte de su madre. En cierto modo, en especial si esta moría, eso pesaba sobre él como una losa.
En Nochevieja el médico les dijo que Consuelo tenía neumonía. Era lo que había temido desde el principio. Era una mujer sana y aún no estaba entrada en años, pero la neumonía era una enfermedad grave y el médico tenía la sensación de que a Consuelo no le importaba demasiado despedirse de la vida, y todos sabían por qué. Parecía que se les escapara de entre los dedos y no pudieran ganar la batalla sin su colaboración. Necesitaban que pusiera de su parte, e incluso entonces no era seguro que el desenlace fuera positivo. Annabelle, que seguía sentada junto a la cama de su madre, estaba aterrada. El único momento en que parecía alegrarse un poco era cuando su madre se despertaba; entonces intentaba convencerla para que comiera y bebiera, y le aseguraba que pronto se pondría bien. Consuelo no hacía comentarios, apenas comía lo suficiente para su sustento y se veía devorada por la fiebre. Dejaba pasar un día tras otro, mientras la fiebre se negaba a rendirse. Blanche parecía tan devastada como Annabelle mientras corría con bandejas que llevaba a la habitación de su señora, y la cocinera intentaba preparar platos para todos.
Y el día 6 de enero Consuelo se marchó sin hacer ruido. Se fue a dormir al anochecer, después de un día largo y difícil. Por la tarde había cogido de la mano a Annabelle y habían hablado un buen rato. Consuelo le había sonreído antes de acostarse y le había dicho a Annabelle que la quería. La joven estaba dormitando en la silla, junto al lecho de su madre, cuando a las ocho, de repente, notó que algo había cambiado y se despertó sobresaltada. Miró la expresión inmóvil del rostro de la yacente y al instante supo que no respiraba. Annabelle suspiró. Por primera vez desde hacía dos semanas tenía la cara fría, de un frío nada natural. La fiebre la había abandonado y se había llevado consigo la vida de Consuelo. Annabelle intentó sacudirla para despertarla, pero vio que era inútil. Se arrodilló ante el lecho de muerte de su madre, abrazó su cuerpo inerte y arrancó en sollozos. Era el último adiós que no había sido capaz de decirles a su padre y a su hermano, y lloró desconsolada.
Blanche se la encontró allí un rato después, y también se echó a llorar. Le acarició con ternura el pelo a Consuelo y después apartó de allí a Annabelle, mientras le pedía a Thomas que fuese a avisar a Josiah. Al cabo de pocos minutos su marido se presentó e hizo todo lo que pudo para consolar a su mujer. Sabía perfectamente lo grande que sería la pérdida para ella, pues quería muchísimo a su madre.
El médico fue aquella misma noche para firmar el certificado de defunción, y por la mañana el encargado de la funeraria fue a amortajarla. Depositaron el cuerpo de Consuelo en el salón y lo rodearon de numerosas flores. Durante todo el proceso, Annabelle permaneció de pie, destrozada, mientras su marido le daba la mano.
A lo largo del día siguiente, muchos amigos fueron a darle el pésame después de haber leído en el periódico la impactante noticia de que Consuelo Worthington había muerto. Su casa volvió a sumirse en un profundo duelo, tan poco tiempo después de la doble pérdida ocurrida casi tres años antes. Annabelle se dio cuenta de que se había quedado huérfana, y, tal como le había dicho su madre a su esposo, Josiah era lo único que le quedaba en el mundo. Se aferró a este durante los días que siguieron como si ella fuera un náufrago y él un salvavidas, y tampoco se separó de él en el funeral de su madre, celebrado en la iglesia episcopal de St. Thomas. Su esposo le colocaba el brazo por encima de los hombros en todo momento, y fue fiel a su palabra: no se apartó de ella en ningún momento, e incluso durmió con su esposa en la estrecha cama de su habitación infantil, en la casa familiar. Annabelle no quería regresar al apartamento e insistía en que él se quedase con ella en la mansión de sus padres. Le propuso que se mudasen allí, donde sin duda estarían mucho más amplios y cómodos, pero él opinaba que sería lúgubre y resultaría demasiado duro para ella. De todas formas, no quiso llevarle la contraria en esos momentos. La pérdida era casi insoportable. Por suerte, Henry los acompañaba con frecuencia y también le servía de apoyo a Annabelle. A menudo, Josiah y él hablaban en voz baja hasta tarde en la biblioteca o jugaban a las cartas, mientras ella dormía en la cama, conmocionada y afligida por el dolor.
Transcurrió un mes entero antes de que Annabelle saliera de la casa. No había tocado ni una sola cosa del dormitorio de su madre. Toda la ropa de Consuelo seguía allí. Josiah tramitó la herencia a través del banco. Ahora la enorme fortuna de sus padres le pertenecía a ella, incluida la porción que habría sido para Robert. Era una mujer muy rica, aunque eso no le proporcionaba alivio alguno. No le importaba. Y aunque a Josiah se le partió el corazón cuando lo hizo, en marzo le comunicó una oferta de compra para la casa, en la que estaba interesada una familia que conocía a la de Annabelle. La joven estaba horrorizada y no quería ni oír hablar de la venta, pero su marido le dijo con cariño que no creía que ella pudiera volver a ser feliz allí. Había perdido a todos sus seres más queridos en aquella casa, y esta estaba llena de fantasmas para ella. Además, era una buena oferta, probablemente mejor de la que obtendrían si decidía venderla más adelante. Sabía que a su esposa le resultaría muy doloroso, pero él consideraba que debía hacerlo.
—Pero ¿dónde vamos a vivir? —preguntó ella con angustia—. Tu apartamento se quedará pequeño cuando formemos una familia, y yo no quiero comprar otra casa.
Estaba bastante decidida a rechazar la oferta, aunque también sabía que su marido tenía razón. Josiah y ella todavía necesitaban una casa, pero habían dejado de buscar el día en que Josiah le había confesado que no estaba preparado para tener hijos, y era cierto que lo único que vería en la mansión familiar serían las imágenes de sus padres y su hermano, todos ellos desaparecidos ya. Por mucho que la llenaran de niños, estos nunca compensarían del todo la tristeza que Annabelle sentía al recordar a sus difuntos.
Lo habló con Hortie, quien para entonces estaba embarazada de su tercer hijo y volvía a tener náuseas. Se quejó de que James la había convertido en una fábrica de engendrar hijos, pero sus problemas le parecían mínimos en esos momentos en comparación con los de Annabelle, e intentó aconsejarla con algo de sentido común. Pensaba que Josiah tenía razón: debían vender la mansión de los Worthington y comprar una casa nueva para los dos, que no tuviera malos recuerdos para Annabelle ni reminiscencias tristes.
A Annabelle se le rompió el corazón al hacerlo, pero al cabo de dos semanas accedió. Ni siquiera se imaginaba cómo podía despedirse de la casa en la que había sido tan feliz de niña, pero era cierto que ahora estaba teñida de pérdida y dolor. Josiah prometió que se encargaría de todas las gestiones y le aseguró que encontrarían una casa que les convenciera o, de lo contrario, la mandarían construir. Sería un buen proyecto común. Todos los temas que pudiera haber pendientes entre ellos quedaron minimizados durante el período de duelo. A Annabelle ya no le preocupaba la familia que todavía no había fundado. No tenía ánimo para pensar en nada más que en su pena.
Annabelle se pasó el mes de abril recogiendo la casa y enviando las pertenencias importantes a un guardamuebles. Sacó a subasta todo lo que no era de interés o valor para ella. Los sirvientes, Josiah y Henry se desvivían por consolarla, pero, aun así, Annabelle se pasaba varias horas al día llorando. No había vuelto a la isla de Ellis desde la muerte de su madre. Lo echaba tremendamente de menos, pero estaba demasiado ocupada cerrando la casa de sus padres. Los últimos objetos fueron enviados al guardamuebles en mayo, el día del segundo aniversario del compromiso de la pareja. Iba a vender la mansión en junio, y entonces se instalarían en la casita de Newport, que Annabelle insistió en mantener. Josiah y ella pasarían allí el verano.
Seis días después de que se despidiera de la casa familiar, los alemanes hundieron el _Lusitania_ y mataron a 1.198 personas, en una desgracia marítima atroz que revivió todos los recuerdos del _Titanic_. Una vez más, la tragedia sacudió el mundo, además de llevarse a otro de los primos de su madre, Alfred Gwynne Vanderbilt, quien se había quedado rezagado para ayudar a otras personas a subir a los botes salvavidas, igual que habían hecho su padre y su hermano en el _Titanic_. E igual que ellos, Alfred había perdido la vida cuando el barco explotó y se hundió en menos de veinte minutos. Dos semanas más tarde, Italia entraba en guerra y se unía a los Aliados. Y llegaban noticias terroríficas que aseguraban que estaban empleando gas nervioso en el frente, que provocaba daños insospechados en los hombres que lo inhalaban. Toda Europa vivía una agitación continua, que parecía reflejar la desesperación y la angustia que sentía la propia Annabelle.
Hasta que se marcharon a Newport en junio, Annabelle pasó el resto del mes de mayo en el piso de Josiah. Se llevó a Newport a Blanche y al resto de los criados que aún estaban a su servicio para que la ayudaran. A finales de verano, la mayor parte de ellos se irían a trabajar a otros lugares, y la vida tal como Annabelle la había conocido hasta entonces habría cambiado para siempre. Blanche y William, el mayordomo, se quedarían en Newport junto a unos cuantos sirvientes más y le harían compañía.
Josiah le había prometido que iría a reunirse con ella a mediados de junio, pues tenía previsto pedir unas vacaciones más largas de lo habitual, ya que sabía que Annabelle necesitaba tenerlo cerca. Parecía descorazonada cuando se marchó de la ciudad. El hogar familiar que tanto había amado ya estaba en otras manos.
Una vez en Newport, Annabelle hizo algunas visitas a Hortie, quien se había instalado allí con su madre, sus hijos y la niñera. Aunque solo estaba embarazada de seis meses, volvía a estar inmensa, pero ahora Annabelle se sentía tan decaída que no podía pasar demasiado tiempo seguido en su compañía. Desde la muerte de su madre, estaba triste y angustiada, y se le hacía muy duro encontrarse en Newport sin ella. En cierto modo, era como una repetición del verano posterior al hundimiento del _Titanic_. Así pues, se alegró mucho cuando llegó Josiah.
Decidieron quedarse en la casa de su madre y se alojaron en la habitación de soltera de Annabelle. Daban largos paseos tranquilos junto al mar. Él estaba casi tan pensativo y silencioso como ella, pero ella nunca le preguntaba por qué. Había aprendido que algunas veces él se ponía así, malhumorado e incluso abatido. De hecho, ninguno de los dos estaba de muy buen humor. La joven le preguntó cuándo iría a visitarlos Henry, con la esperanza de que eso animara a Josiah, pero él fue impreciso al respecto y dijo que no estaba seguro.
Josiah llevaba casi una semana en Newport cuando por fin se dirigió a Annabelle una noche, mientras estaban sentados junto a la chimenea, y le dijo que tenía que hablar con ella. La joven sonrió, preguntándose qué querría contarle. Su tema de conversación más recurrente esos días era la guerra. Pero en aquella ocasión él suspiró profundamente y ella vio que tenía los ojos llenos de lágrimas cuando volvió la cara para mirarla.
—¿Estás bien? —le preguntó Annabelle, de repente preocupada.
Josiah se limitó a sacudir la cabeza con lentitud. El corazón de la joven se hundió como una piedra en el río ante su respuesta:
—No.
### 11
Nada en la vida de Annabelle la había preparado para lo que Josiah tenía que decirle. El impacto de sus palabras sobre ella fue tan devastador como el de la mañana en que había leído los titulares sobre el _Titanic_. Lo que le contó su marido la destrozó como una bomba. Al principio, Josiah no sabía por dónde empezar. Ella alargó el brazo y le tomó la mano entre las suyas.
—¿Qué ocurre? —le preguntó con ternura.
No podía imaginarse qué problema era capaz de provocarle una desesperación como la que veía en él. Parecía destrozado. Entonces, Josiah respiró hondo y empezó a hablar:
—No sé cómo decirte esto, Annabelle —la preparó mientras le apretaba la mano.
Sabía lo inocente que seguía siendo su esposa y lo mucho que le costaría comprenderlo. Tenía ganas de contárselo desde hacía seis meses, pero había pensado que lo mejor sería esperar hasta que pasaran las vacaciones de Navidad. Sin embargo, entonces había enfermado su madre. Y, claro, no podía decírselo después de la muerte de Consuelo. Annabelle estaba tan abatida por el fallecimiento de su madre que no habría soportado otra embestida, y mucho menos por parte de Josiah. Habían pasado casi seis meses desde que Consuelo había muerto y ahora la venta de la casa había supuesto otro shock para Annabelle. No obstante, Josiah no podía esperar más. Ella tenía que saberlo. Y él no podía seguir viviendo aquella pantomima, que, además, lo estaba volviendo loco.
—No te entiendo. ¿Qué pasa? —preguntó Annabelle también con los ojos llenos de lágrimas, y eso que aún no sabía lo que se avecinaba—. ¿He hecho algo que te haya molestado?
Él sacudió la cabeza con vehemencia.
—Claro que no. Siempre has sido maravillosa conmigo. Eres una esposa perfecta y entregada. No eres tú la que ha hecho algo malo, Annabelle, soy yo... Desde el principio. Te aseguro que pensaba que podría ser un buen marido para ti, que podría proporcionarte una buena vida. Yo quería...
Josiah deseaba seguir explicándose, pero ella lo cortó en seco, con la esperanza de apaciguar la tempestad. Sin embargo, la fuerza de la tormenta se había vuelto incontrolable, hasta el punto de que ni siquiera él podía detenerla. Debían afrontarlo.
—¿Por qué dices eso? Sí que eres un buen marido, y sí que me proporcionas una buena vida...
En su voz había un tono de súplica que a Josiah le rompió el corazón.
—No es verdad. Te mereces mucho más. Muchísimo más de lo que yo puedo darte. Creía que podría, al principio estaba seguro de que podría; de lo contrario, nunca te habría hecho esto. Pero no puedo. Te mereces un hombre que pueda darte todo lo que quieras, que cumpla todos los deseos de tu corazón y que pueda darte hijos.
—No tenemos prisa, Josiah. Siempre dices que nos queda tiempo por delante.
—Pero no es así —contestó él con rotundidad, y en su rostro se dibujó un rictus de tristeza.
Era mucho más difícil de lo que había temido. Lo peor de todo era que la amaba, pero sabía que en esos momentos no tenía derecho a hacerlo, ni lo había tenido antes. Además, se sentía culpable por romper la promesa que le había hecho a su madre de cuidar de Annabelle, pero la situación era mucho más complicada de lo que Consuelo habría podido imaginar.
—Llevamos casados casi dos años. Y nunca hemos hecho el amor. Te he dado mil excusas y te he rechazado como he podido.
Un par de veces, ella había llegado a preguntarse si su marido tenía un problema físico que le daba demasiada vergüenza reconocer. Sin embargo, siempre había tenido la sensación de que era algo emocional, una cuestión de adaptación, que esperaba que se arreglase con el tiempo, pero nunca lo había hecho. Ambos sabían que, tras casi dos años de matrimonio, ella seguía siendo virgen. Por supuesto, nunca se lo había confesado a nadie, ni siquiera a Hortie o a su madre. Le daba demasiada vergüenza y temía que fuese porque ella hacía algo mal, o porque Josiah no la encontraba atractiva. Había probado con todo lo imaginable, desde cambios de peinado hasta cambios de indumentaria, y había comprado camisones muy sugerentes, hasta que se había dado por vencida y había llegado a la conclusión de que él estaba ansioso y lo haría cuando tuviera que ser, cuando se hallara preparado. No obstante, Annabelle le había dado muchas vueltas al tema, aunque ahora tratase de quitarle hierro al asunto delante de él.
—Cuando me casé contigo, creía con todas mis fuerzas que sería capaz de actuar como un hombre para ti. Pero cada vez que pensaba en ello sabía que estaba mal, y no podía arrebatarte la virtud por una mentira.
—No es una mentira —dijo ella con valentía, luchando por su vida y por la de su matrimonio. Pero había perdido la batalla antes de comenzarla. No tenía opción de ganarla—. Nos amamos. No me importa que nunca quieras hacer el amor conmigo. Hay cosas mucho más importantes en la vida.
Él sonrió al ver lo inocente que seguía siendo. Muchas personas de ambos sexos no habrían estado de acuerdo con el comentario de Annabelle, entre ellas el propio Josiah. Pero ella no conocía otra realidad y, si permanecía a su lado, nunca la conocería.
—Te mereces algo mejor de lo que yo puedo darte. Annabelle, tienes que escucharme. Puede que te resulte difícil de comprender, pero quiero ser sincero contigo.
Sabía que tendría que haber sido honesto con ella desde el principio, pero por lo menos entonces debía serlo. Aunque con ello le arrebatara toda la inocencia a Annabelle en una sola noche, y tal vez incluso destruyera su fe en los hombres para siempre. No le quedaba otra opción. Había reflexionado largo y tendido sobre el tema y había aguardado más de lo aconsejable, por el bien de ambos. Ya no podía seguir haciéndolo. La amaba. Pero todo su matrimonio era un engaño.
Annabelle abrió los ojos como platos y lo miró fijamente. Le temblaron los dedos de la mano cuando se aferró a él con más fuerza, como si quisiera prepararse para la noticia. Todo su cuerpo se estremeció, aunque ella no se diera cuenta. Josiah se percató de que sacudía los hombros sin querer, expectante.
—No deseo hacer el amor con las mujeres —reconoció con voz ronca; era como una confesión—, sino con los hombres. Pensé que podría ser un buen marido para ti, que podría ir contra mi naturaleza, pero soy incapaz. Yo no soy así. Por eso no me había casado antes. Te amo con toda mi alma, quiero todos los aspectos de ti, pero no así. —Y entonces añadió, a modo de estocada definitiva—: Henry y yo estamos enamorados desde que éramos adolescentes.
Annabelle abrió tanto los ojos en ese momento que Josiah temió que fuera a desmayarse. Pero la joven era más valiente que todo eso, y se negó a ceder ante el mareo y las náuseas que la embargaban.
—¿Henry?
Su voz fue poco más que un gemido ahogado. ¿Henry, su compañero fiel, a quien ella consideraba el mejor amigo de ambos? Ese hombre la había traicionado y se había apoderado de la parte de su esposo que ella no tendría jamás. Josiah también la había traicionado.
—Sí. Comprendió que yo quisiera casarme y tener hijos contigo. Mi amor por ti era sincero y sentí mucha pena cuando murió tu padre. Quería serlo todo para ti: padre, hermano, amigo. Pero descubrí que había algo que no podía lograr, por más que lo intentara: ser tu marido. No era capaz de llevar tan lejos esta farsa. Y no podía ir contra mi naturaleza. Todo mi ser se negaba.
Ella asentía en silencio, intentando asimilar lo que él le había confesado. Eran demasiadas cosas para absorberlas de golpe. Todo lo que habían construido juntos durante su matrimonio, sus votos, su luna de miel, las promesas que se habían hecho el uno al otro, los dos años que habían transcurrido, todo había sido un fraude.
—Pensaba que podría obligarme a llevar una doble vida, pero no puedo. Y tampoco puedo continuar haciéndote esto, mientras tú buscas la manera de preguntarme con mucho tacto por qué nunca ha pasado nada entre nosotros. Ya no puedo más. Hace seis meses descubrí algo que lo cambió todo y ahora doy gracias por no haber superado nunca mis reservas. En diciembre me enteré de que tengo la sífilis. Bajo ningún concepto te pondría la mano encima sabiéndolo, ni intentaría darte los hijos que tanto deseas. No estoy dispuesto a arriesgar tu vida. Te amo demasiado para hacerlo.
Dos lágrimas solitarias resbalaron por las mejillas de Josiah mientras hablaba, y Annabelle lo rodeó con sus brazos y enterró la cabeza en su pecho. Sollozaba con histeria. Era la peor noticia que le había dado hasta ese momento, peor incluso que todo lo demás.
—Josiah... No puede ser...
Levantó la cara surcada por las lágrimas para mirarlo a los ojos. No veía nada raro en él, aunque tampoco conocía los síntomas. De momento, ninguno de ellos era visible, pero con el tiempo irían apareciendo. Al final, se quedaría ciego y acabaría muriendo. Su suerte estaba echada, y la de Henry también. Lo habían descubierto juntos, y por lo menos tenían el consuelo de saber que ninguno de los dos sobreviviría al otro. El suyo había sido un amor muy intenso que había durado veinte años, durante toda su vida adulta, y que ahora los acompañaría hasta la tumba.
—¿Estás seguro?
—Completamente. En cuanto me enteré, supe que tenía que ser sincero contigo, pero entonces tu madre se puso enferma... Me faltaron agallas para añadir más sufrimiento a eso. Sin embargo, ahora tenemos que hacer algo para remediarlo. No puedo dejar que esto siga así para siempre.
—Yo no quiero hacer nada para remediarlo —dijo ella con un amor incondicional. Soltó a Josiah y se secó las lágrimas con las manos—. Quiero seguir casada contigo hasta el final.
—No dejaré que lo hagas. No es justo para ti. Henry y yo queremos huir juntos y disfrutar del poco tiempo que nos queda por delante. —Ella se quedó de piedra al darse cuenta de que él no deseaba pasar sus últimos días con ella, sino que quería estar con el hombre a quien amaba. Era el rechazo más cruel del que sería objeto en toda su vida. Josiah volvió a tomar una bocanada de aire antes de contarle el resto—: He hablado con mi abogado en confianza. Ya ha preparado la documentación del divorcio. Lo haremos de la forma más discreta posible. Si alguien te pregunta, puedes decirle que fui un marido horrible, y que tenías que deshacerte de mí.
—Pero yo no quiero deshacerme de ti —replicó entre sollozos Annabelle, volviendo a aferrarse a él.
Ambos sabían que el adulterio era el único motivo de divorcio posible, así que, si él se divorciaba de ella, la gente imaginaría que Annabelle le había sido infiel pero no quería divorciarse de él. Ciertamente, ella no quería el divorcio. Y él lo sabía. Por eso, si quería liberarla por su propio bien, tendría que ser él quien solicitase el divorcio, para que ella no pudiera negarse.
—¿Por qué no podemos seguir casados? —preguntó Annabelle presa del pánico, pero él negó con la cabeza.
Josiah estaba decidido y nada le haría dar su brazo a torcer. Sabía cómo era su marido cuando se ponía así. Era un hombre de trato fácil la mayor parte del tiempo, salvo por esos arrebatos melancólicos que padecía de vez en cuando, pero era muy testarudo, un rasgo que él decía que había heredado de su padre.
—No podemos seguir casados, Annabelle —le contestó con dulzura—. Podríamos intentar pedir la anulación del matrimonio, pero no sin explicar los motivos, algo que resultaría bochornoso para ambos. Y, al cabo de dos años, ni siquiera estoy seguro de que pudiéramos hacerlo. Es mucho más sencillo y más rápido si nos divorciamos. Quiero que seas libre para reiniciar tu vida cuanto antes. Por lo menos, te debo eso. Mereces encontrar a otro hombre, casarte y tener la vida de pareja con la que soñabas. Necesitas un marido de verdad y un matrimonio de verdad. No este fraude.
—Pero yo no quiero reiniciar mi vida, ni casarme con otra persona —dijo ella sollozando.
—Ya, pero quieres tener hijos, y yo podría pasarme varios años enfermo, languideciendo. No quiero que estés atada a mí, malgastando tu vida todos estos años.
Josiah intentaba forzarla a renunciar a él para poder marcharse, que era precisamente lo que no quería ella. Lo único que deseaba Annabelle era tenerlo cerca. Lo amaba igual que al principio. No estaba enfadada con él, sino que tenía el corazón roto por lo que le había confesado. Y lo último que quería era el divorcio.
—Tienes que escucharme —insistió Josiah—. Yo sé lo que tengo que hacer. Cometí un error terrible y ahora debo corregirlo. Podríamos divorciarnos en Kentucky, algo que me parece absurdo y taimado. Creo que es mucho más lógico que lo hagamos en Nueva York, ya que vivimos allí. Nadie sabrá los pormenores. Lo haremos en privado y seremos muy discretos. —Entonces volvió a respirar hondo—. Mañana regresaré a la ciudad para reunirme de nuevo con mi abogado. Y después, Henry y yo nos marcharemos. Vamos a pasar una temporada en México.
Habrían preferido ir a Europa, pero ya no era razonable ni práctico pensar en algo así, de modo que habían optado por México. Allí no verían a nadie conocido y podrían desaparecer sin hacer ruido, que era lo único que deseaban para el tiempo que les quedaba de vida.
—¿Cuándo volverás? —preguntó Annabelle desfallecida. Después de perder a todos los demás, ahora iba a perderlo a él.
—Tardaré bastante —contestó Josiah, de un modo más brusco del que pretendía, pues no quería decir «Jamás». Al mismo tiempo, deseaba que ella aceptase que su relación había terminado. Para empezar, no tendría que haber surgido nunca, pero, dadas las circunstancias, lo único que podía esperar él era que la ruptura fuese rápida. Le parecía lo menos doloroso. Aunque, por el aspecto del rostro de Annabelle, supo que se equivocaba. Parecía completamente destrozada por lo que acababa de escuchar, en especial por la noticia de que iba a abandonarla al día siguiente.
La joven no se imaginaba cómo iba a sobrevivir sin él. Cuando su esposo se marchara, estaría completamente sola en el mundo. Él tenía a Henry, y por lo que parecía siempre lo había tenido, pero ella no tenía a nadie. Ni a sus padres, ni a su hermano, y ya tampoco a él.
—¿Por qué no podemos seguir casados? —volvió a preguntarle ella, a modo de súplica, igual que una niña pequeña—. Nada ha cambiado...
—Sí que ha cambiado. Ahora tú sabes la verdad, y yo también. Necesito liberarte, Annabelle. Es lo mínimo que puedo hacer. Te lo debo. Ya te he hecho perder dos años de tu vida.
Era peor que eso: se la había destrozado. A partir de ese momento no le quedaría nada, excepto su herencia. Ni siquiera contaba ya con la casa familiar en Nueva York. Se vería obligada a alojarse en un hotel, pues tampoco podía quedarse a vivir en el apartamento de Josiah si se divorciaban. De todas formas, él también había pensado en eso.
—Puedes quedarte en el apartamento hasta que te recompongas, hasta que decidas qué quieres hacer. Yo me marcharé dentro de unos cuantos días.
Henry y él ya habían hecho planes.
—Ojalá no hubiera vendido la casa —se lamentó Annabelle con voz débil, pero ambos sabían que era lo más apropiado.
Era demasiado grande para ella y no podía vivir allí sola, mucho menos sin marido. Necesitaba una vivienda más manejable para ella. Y Josiah estaba seguro de que, al cabo de poco tiempo, volvería a casarse. Era una joven guapa y apenas tenía veintidós años. Mantenía toda la inocencia y la frescura de la juventud. Por lo menos Josiah no había arrasado también con eso, aunque Annabelle se sentía como si hubiese envejecido una docena de años en una hora. En ese instante, Josiah se levantó y colocó los brazos alrededor de su mujer. La abrazó, pero no la besó. La farsa que había estado representando se había acabado. Ya no le pertenecía, y nunca lo había hecho. A decir verdad, siempre había pertenecido a Henry, y ambos iban a pagar caro su intento de fingir algo que no era. La amaba, pero no de la forma requerida para ser su esposo. Para él había sido muy triste reconocerlo. Y ahora para ella era devastador. De todas formas, Josiah no tenía otra opción. Se sintió aliviado de no haber hecho el amor con ella. Nunca se habría perdonado el haberla contagiado también. Lo que le había hecho ya era bastante atroz. Se sentía fatal por haberla engañado durante todo ese tiempo. Y peor aún se había engañado a sí mismo. La quería, pero sus votos matrimoniales estaban vacíos y no significaban nada.
La acompañó hasta el dormitorio, pero no quiso quedarse con ella a pasar la noche. Dijo que ya no le parecía adecuado. Josiah durmió en la habitación de invitados del piso inferior y Annabelle se tumbó en su cama y se pasó la noche llorando. Al final, bajó a trompicones la escalera e intentó acostarse con él, solo para que pudieran abrazarse, pero él no se lo permitió. Volvió a mandarla a la planta superior y le dijo que se quedara en el dormitorio, aunque se sentía como un monstruo y, una vez que ella se hubo ido, se tumbó en la cama de invitados y empezó a llorar. La amaba de verdad y le rompía el corazón abandonarla así, pero consideraba que no podía hacer otra cosa. Sabía lo atormentada que se sentía Annabelle por lo que nunca había ocurrido entre ellos, y no deseaba que siguiera a su lado entonces, para ver cómo él se deterioraba, lenta o rápidamente, hasta morir. No tenía derecho a hacerle eso y tenía pensado permanecer fuera de Nueva York hasta el final. La enfermedad avanzaba a pasos de gigante, sobre todo para Henry, que había empezado a manifestar algunos síntomas. Ambos habían tomado tratamientos de arsénico, pero no habían servido de nada. Querían alejarse cuanto antes de Nueva York y de todas las personas que conocían, para afrontar lo que vendría a continuación. Era el momento de abandonar a Annabelle y dejar que comenzara una nueva vida. Josiah sabía que, con el tiempo, cuando lo asimilara, la joven comprendería que era lo mejor para ella.
Annabelle se quedó llorando en los escalones de la entrada cuando él se marchó al día siguiente. Desde allí, vestida de luto por la muerte de su madre, observó con aire trágico cómo desaparecía el coche. Dejarla había sido lo más difícil que Josiah había hecho en su vida, y sintió náuseas y lloró de manera intermitente durante todo el trayecto de vuelta a Nueva York. Si la hubiera matado con sus propias manos no le habría resultado más difícil que lo que acababa de hacer, ni se habría sentido más rastrero.
### 12
Annabelle no quiso ver a nadie después de la huida de Josiah. Blanche sabía que había pasado algo terrible, pero no se atrevía a preguntar el qué. Annabelle se encerró en su habitación, donde le llevaban bandejas de comida que apenas probaba. Una vez al día, salía a dar un paseo por la playa, pero no veía a nadie ni hablaba con nadie. Hortie fue a visitarla una tarde, pero Annabelle se negó a recibirla. Le pidió a Blanche que le dijera que estaba enferma. Tenía el corazón tan destrozado que no tenía ganas de ver ni siquiera a su mejor amiga. Además, sentía demasiada vergüenza para contarle que iba a divorciarse, aunque no fuera por su culpa, pues no podía contarle los auténticos motivos. La verdad era impensable y Annabelle quería proteger a Josiah a toda costa. Le entraba el pánico cada vez que pensaba que no iba a volver a verlo jamás.
Sabía que, en cuanto la gente se enterase del divorcio, nadie la creería, y todo el mundo, tanto en Nueva York como en Newport, se sentiría conmocionado. Se preguntaba cuánto tardaría en propagarse la noticia. Como estaba de duelo por la muerte de su madre, nadie se extrañaría de que no saliera de casa, pero la gente empezaría a escamarse al no ver nunca a Josiah. Blanche ya sospechaba qué podía haber ocurrido, aunque pensaba que era una pelea entre enamorados y no tenía ni idea de que fuera a terminar en divorcio. El mayordomo y ella elucubraban que a lo mejor él tenía una amante, pero nadie podría haber imaginado que su amante fuese Henry, ni que su matrimonio con Annabelle hubiera terminado. Blanche trataba de consolarla diciendo que todo acabaría bien, pero como respuesta lo único que hacía Annabelle era llorar y sacudir la cabeza. Nada acabaría bien a partir de ese momento.
El abogado de Josiah fue a verla en julio. Para entonces, Josiah había dimitido de su puesto y ya se había marchado a México. Dos semanas antes, Henry había alegado que había alguien enfermo en su familia y también había dejado el trabajo. A nadie se le ocurrió relacionar ambos acontecimientos, pero la marcha de los dos empleados supuso una gran pérdida para el banco.
Josiah le había mandado una carta antes de irse, en la que volvía a pedirle perdón por su terrible perfidia y su traición. Dijo que cargaría con la culpa durante el resto de su vida, y le aseguró que el amor que había sentido por ella era sincero. De todas formas, ya había solicitado el divorcio en Nueva York y su abogado le presentó a Annabelle una copia de los documentos. El único motivo por el que había sido posible justificar aquel divorcio era la infidelidad, una acusación que devastó a Annabelle al leerla. Ya lo sabía, pero verlo escrito era mucho peor. La joven le había dicho a Josiah que ella no iba a pedir el divorcio, así que no le había quedado otro remedio que solicitarlo él.
—Todo el mundo pensará que lo he engañado —le dijo Annabelle al abogado con cara de angustia, pero él negó con la cabeza. Albergaba la esperanza de que Josiah no pidiese el divorcio, pero lo había hecho, alegando el único motivo posible.
—Nadie tendrá acceso a estos documentos —le aseguró el abogado—. Era la única opción viable, pues usted no estaba dispuesta a solicitar el divorcio.
Habría preferido morir antes que pedirle el divorcio. Lo amaba.
Al final, resultó que la confianza de Josiah y de su abogado en la confidencialidad del sistema distaba de la realidad. Un empleado del juzgado había vendido una copia de los documentos del divorcio a la prensa, y en agosto ya había salido publicada la noticia de que Josiah se había divorciado de su mujer por adulterio. Con un solo golpe habían arruinado la vida y la reputación de Annabelle para siempre. De la noche a la mañana, se convirtió en una paria.
Todavía se hallaba en Newport cuando le llegaron los rumores procedentes del banco de su padre, y la noticia se extendió como la pólvora. Allí todo el mundo hablaba del divorcio de Josiah y Annabelle. La joven tardó dos semanas enteras en reunir el coraje suficiente para ir a visitar a Hortie con la intención de contárselo, pero cuando lo hizo recibió otra bofetada. En lugar de permitirle subir de inmediato al dormitorio de Hortie, donde esta languidecía en la cama como siempre, el mayordomo le pidió que esperara en el salón, al que entró justo en el momento en que la madre de Hortie salía despavorida y pasaba rozándola con una mueca de desaprobación. No le dijo ni una palabra, y pasaron otros diez minutos antes de que apareciera Hortie, muchísimo más gorda que la última vez que la había visto. Parecía increíblemente nerviosa y ni siquiera se sentó. En lugar de eso, se quedó de pie mirándola con aspecto incómodo mientras las lágrimas resbalaban de sus ojos. Sin embargo, Hortie volvió la cabeza y fingió no haberla visto llorar.
—Supongo que ya te habrás enterado de la noticia. Todo el mundo lo sabe —comentó Annabelle con una tristeza infinita, y se sonó la nariz discretamente en el pañuelo de encaje que había heredado de su madre. También llevaba la sombrilla materna, pues había ido andando desde su casa y hacía un día muy caluroso.
—No tenía ni idea de que hubiera otra persona —dijo Hortie con voz ahogada, y no hizo ningún gesto por acercarse a su amiga, ni dijo nada para consolarla. Se quedó allí plantada, como una estatua, en el lado opuesto de la habitación, con los brazos rígidos y pegados al cuerpo.
—No hay otra persona, ni la ha habido nunca —dijo Annabelle sin tapujos—. El adulterio era el único motivo de divorcio que podía alegarse. Josiah quería el divorcio y yo no. Él creía que era lo mejor... No podía... No quería...
Sus palabras se convirtieron en un sollozo entrecortado. No se le ocurría cómo podía explicarlo, porque nada de lo que había ocurrido en realidad tenía sentido, y no podía contarle la verdad, ni siquiera a su mejor amiga. No quería traicionarlo, por muy grande que hubiera sido su traición hacia ella. No podía hacerle eso. La vida de él se iría al garete para siempre si ella reconocía que la había abandonado por un hombre, y no tenía agallas de decirle a Hortie que seguía siendo virgen, así que se limitó a sentarse en la silla y llorar. Para colmo, era impensable contarle a Hortie lo de la terrorífica enfermedad.
—No sé qué voy a hacer —dijo Annabelle deshecha en lágrimas—. Me quiero morir.
Hortie interpretó su angustia como culpabilidad. Su madre le había dicho que Annabelle se merecía todo lo que Josiah le hiciera, pues un hombre de su talla moral jamás se divorciaría de una mujer si no era por un buen motivo, así que Hortie podía estar segura, según decía su madre, de que fuera lo que fuese que hubiera hecho Annabelle, debía de ser imperdonable. De lo contrario, él habría continuado casado con ella. Y si se había divorciado de Annabelle por adúltera, entonces es que lo era. Su madre le dijo que lo sentía en el alma por Josiah, pero en absoluto por ella, quien no había hecho más que recibir su merecido. Para colmo, James había prohibido terminantemente a Hortie volver a ver a Annabelle, bajo ningún concepto. No quería que se expusiera a una influencia como esa.
—Siento mucho lo que ha pasado —se lamentó Hortie, claramente incómoda—. Debiste de cometer un tremendo error.
Intentaba ser compasiva con ella, pero en el fondo consideraba que su madre tenía razón. Josiah era un hombre demasiado bueno para hacer algo así a la ligera. Para que estuviera dispuesto a divorciarse de Annabelle, dejar el trabajo y marcharse de la ciudad, ella tenía que haberse comportado de manera abominable. Hortie jamás hubiera dicho que Annabelle fuese capaz de algo así, pero lo que había aprendido de esa situación era que uno no conoce ni siquiera a sus mejores amigos. Estaba francamente decepcionada con ella, y, por el mar de lágrimas que estaba derramando Annabelle, veía lo culpable que se sentía. Su madre y James estaban en lo cierto.
—Yo no he cometido ningún error —dijo entre hipidos Annabelle sin dejar de sollozar.
Tenía el aspecto y se sentía como una niña abandonada, y se quedó de piedra al ver que Hortie no era más cariñosa con ella, después de todo lo que habían vivido juntas desde la infancia. Se mostraba distante y sus palabras eran frías.
—Me parece que no quiero saber lo que pasó —le dijo Hortie mientras se acercaba a la puerta—. Lo siento, pero tienes que marcharte. James no me deja verte. Adiós, Annabelle, ahora tengo que subir a tumbarme un rato, no me encuentro bien.
Y, dicho esto, salió del salón y cerró la puerta tras de sí, sin pronunciar ni una palabra más. Annabelle se quedó allí sentada, mirándose los pies, incapaz de creer lo que acababa de ocurrirle. Temblaba de forma convulsa cuando se levantó, se marchó a la carrera de aquella casa y volvió a su hogar. Se le ocurrió tirarse al mar para suicidarse, pero no tenía coraje para hacerlo. Le habría gustado, porque estaba convencida de que así volvería a ver a sus padres y a Robert. No podía creer que Hortie la hubiera abandonado también y le hubiera dicho que no pensaba volver a verla. Entonces cayó en la cuenta de que todas las personas que conocía harían lo mismo. Todas las puertas de Newport y de Nueva York se cerrarían delante de sus narices cuando llegara el momento en que pudiera volver a salir a la calle.
Annabelle cerró dando un portazo en cuanto llegó a su casa y subió corriendo la escalera que conducía a su habitación. Se tiró encima de la cama, demasiado sobrecogida incluso para llorar. Seguía allí tumbada cuando Blanche entró en el dormitorio y habló con ternura a la mujer que conocía desde que era niña.
—Sé que no ha hecho usted lo que dice la gente, señorita Annabelle. La he visto casi a diario desde que era un bebé. Sé que ha sido una buena esposa para él. No sé lo que ha ocurrido entre los dos, pero sé que no ha tenido que ver nada con usted.
Y tras decir eso avanzó y colocó los brazos alrededor de Annabelle y ambas se echaron a llorar juntas. Annabelle no podía contarle la causa real del divorcio, pero por lo menos Blanche sabía que era incapaz de hacer aquello de lo que la acusaban. Y, mientras lloraban abrazadas, Annabelle echó de menos a su madre más que nunca. No podía imaginarse cómo iba a ser su vida en adelante. Se había negado a divorciarse de Josiah y él, pensando que la libraba de un destino peor, la había estigmatizado como adúltera para siempre.
Empezó a hacerse una idea de qué significaba eso durante las últimas semanas de agosto, cuando la temporada estival tocó a su fin. Fue a comprar al colmado unas cuantas veces, así como a la oficina de correos, y cada vez que lo hacía las personas que se encontraba por la calle volvían la cara y se negaban a hablar con ella. Los hombres la miraban con desaprobación y las mujeres la ignoraban por completo. De hecho, se había convertido en la paria que tanto temía ser, tal como le había advertido a Josiah. Él pensaba que era lo mejor para ella, y la había dejado en libertad por amor y remordimientos, pero al hacerlo la había condenado a una cadena perpetua de rechazo y desdén. Había sido desterrada por los suyos de su propio mundo. En esos momentos supo que su vida en Newport y en Nueva York había terminado, y entendió que nunca jamás volvería a ser bien recibida en las casas de alta alcurnia, ni en los círculos de sociedad. De ahora en adelante sería siempre la mujer adúltera de la que Josiah Millbank se había divorciado. Por el mismo precio, habría podido agarrarla y ahorcarla en la plaza mayor. La mujer decente que siempre había sido estaba más que muerta.
### 13
Annabelle regresó a Nueva York la primera semana de septiembre y pidió a Blanche, a William y a unos cuantos sirvientes más que se quedaran en la casa de Newport. Había dejado de ser la casa de sus padres, ahora era suya. Se llevó a Thomas consigo a Nueva York, aunque tenía intención de vender todos los coches de su padre, salvo uno.
Se instaló en el apartamento de Josiah; era consciente de que tenía que buscar casa, pero no se le ocurría por dónde empezar o cómo hacerlo, y además sabía que Josiah iba a tardar en volver, eso si volvía. Le había dicho que Henry y él pasarían muchos meses fuera, o incluso más tiempo, y lo cierto era que no había oído nada de su ex marido desde que se había marchado a México. La había abandonado de la noche a la mañana, igual que todos los demás. Y Josiah pensaba que lo había hecho por el bien de Annabelle...
La joven retomó su labor en la isla de Ellis mientras intentaba aclarar las ideas. Seguía llegando gente de Europa a pesar de que los británicos habían bombardeado el Atlántico y los alemanes seguían hundiendo barcos. Y, precisamente, mientras charlaba con una mujer francesa un día acerca de sus experiencias, fue cuando Annabelle supo qué debía hacer. Era la única cosa que se le ocurría, y tenía mucho más sentido que quedarse en Nueva York para ver cómo la despreciaban todos sus conocidos. No le importaba morir mientras cruzaba el Atlántico, ni perecer una vez que estuviera en Europa. De hecho, habría aceptado gustosa tal liberación del destino al que Josiah la había condenado, aun sin proponérselo, mediante el divorcio.
Habló con distintas personas de la isla de Ellis acerca de sus intenciones. El médico con el que había trabajado le preparó una carta de recomendación en la que detallaba sus habilidades, que Annabelle confiaba en poder emplear en un hospital de Francia. El médico le habló de un hospital que habían instalado en una abadía en Asnières-sur-Oise, cerca de París, en el que trabajaban únicamente mujeres. Lo había abierto el año anterior una escocesa, la doctora Elsie Inglis, quien había propuesto la misma iniciativa en Inglaterra pero no había obtenido autorización para llevarla a cabo. El gobierno francés la había recibido con los brazos abiertos, así que ella se había puesto manos a la obra y había adaptado personalmente la abadía para convertirla en un hospital. Luego había contratado a un equipo casi totalmente femenino, tanto para el ejercicio de la medicina como para la enfermería, a excepción de unos cuantos cirujanos, que eran hombres. El médico y amigo con el que Annabelle trabajaba en la isla de Ellis la había animado a que fuese allí en cuanto le había contado sus planes.
Elsie Inglis era una mujer sufragista y adelantada a su tiempo, que había estudiado en la facultad de medicina de la Universidad Femenina de Edimburgo. Había montado su propia escuela de medicina y había dado clases en el Nuevo Hospital para Mujeres. El médico que había dado referencias a Annabelle para que fuese a su encuentro estaba convencido de que cualquier centro médico que Inglis dirigiera contaría con los últimos avances técnicos y tendría una gestión impecable. Había conseguido poner en funcionamiento el hospital de la abadía de Royaumont en diciembre de 1914, justo después del estallido de la guerra. Y por las noticias que le habían llegado al médico de la isla de Ellis, su centro estaba realizando una labor fantástica en el cuidado de los soldados heridos que eran trasladados desde los hospitales de campaña que había cerca del frente. Todo lo que Annabelle oyó al respecto la convenció de que era allí donde quería estar; además, era muy probable que la recibieran con una sonrisa. No le importaba si la mandaban conducir una ambulancia o trabajar en el hospital. Estaba más que dispuesta a hacer cualquier cosa para echar una mano.
No tenía motivos para quedarse en Estados Unidos. No tenía hogar, ni familia, ni marido, e incluso su mejor amiga le había dicho que no podía volver a verla. Los amigos de sus padres y los de Josiah se quedarían todavía más escandalizados con la noticia. Y como él se había marchado de la ciudad, todo el mundo daría por hecho que Annabelle le había roto el corazón. La desgracia había caído sobre ella de todas las formas posibles, y nadie sabría jamás la verdad de lo que había ocurrido. No tenía absolutamente ningún motivo para quedarse y todos los posibles para marcharse.
Annabelle dedicó los días siguientes a empaquetar todo lo que deseaba guardar almacenado, además de a tramitar un pasaporte nuevo, pues hacía seis años que no viajaba, desde que tenía dieciséis. Reservó una plaza en el _Saxonia_ , que viajaba a Francia, y compró ropa gruesa y resistente, que le sería muy útil una vez allí. Ya no le hacían falta los volantes ni los vestidos de fiesta. Asimismo, dejó todas sus joyas y las de su madre en una caja fuerte en el banco de su padre, y realizó diversas gestiones bancarias para asegurarse la liquidez cuando estuviera en Europa. No le dijo a nadie lo que iba a hacer, y a finales de septiembre regresó a Newport para despedirse de Blanche y del resto del servicio. Quedaban cinco sirvientes en la casa, que pasarían allí el invierno con el fin de cuidarla y atender los terrenos. Eran suficientes, teniendo en cuenta el tamaño de la propiedad, pero no eran demasiados. Le contó a Blanche lo que pensaba hacer y le confesó que era posible que tardase mucho tiempo en regresar.
La anciana lloró por todo lo que había ocurrido y se lamentó del destino de su joven señora. No quería ni pensar en las cosas terribles que podían acontecerle en Francia. Todos eran conscientes de que tal vez no sobreviviera a la travesía, teniendo en cuenta los campos de minas y los submarinos alemanes que peinaban los mares. Blanche también era plenamente consciente de que a Annabelle aquello no le importaba en absoluto. No tenía nada que perder y nadie por quien vivir. Por lo menos, en el frente, tendría un objetivo en la vida. Pensaba llevarse todos sus libros de medicina, pues creía que podría necesitarlos. Cuando se marchó de Newport dos días más tarde, todos lloraron a lágrima viva mientras se despedían, preguntándose si volverían a verla algún día.
Una vez de vuelta en Nueva York, Annabelle fue a decir adiós a los médicos y enfermeras con quienes había trabajado en la isla de Ellis, y también se despidió de sus pacientes favoritos, en especial de los niños. Todos se entristecieron mucho al saber que se iba, aunque ella no les contó por qué. Solo informó al jefe del departamento médico de que se marchaba de voluntaria a un hospital de campaña en Francia. Le rompía el corazón dejar atrás la isla de Ellis.
Para entonces, ya había mandado a un guardamuebles todas las posesiones que compartía con Josiah, y lo único que le quedaba eran las maletas que iban a acompañarla, en las que había metido las prendas gruesas que había comprado para el viaje, algunas chaquetas de invierno y varios abrigos. Había conseguido introducirlo todo en tres maletas grandes, y tenía intención de quedarse en el camarote durante la travesía, así que no incluyó ningún vestido de noche en el equipaje. Había renovado el pasaporte y había reservado el billete con su nombre de soltera, en lugar de con el apellido de Josiah. En su último día en Nueva York, dio un paseo muy largo, hasta llegar a casa de sus padres. Era la única cosa de la que todavía no se había despedido. Permaneció frente a la mansión por unos instantes, pensando en todo lo que había perdido y, mientras estaba allí, vio que uno de sus antiguos vecinos salía del coche, se fijaba en ella y la miraba con maldad. Le dio la espalda sin saludarla siquiera, subió los peldaños que conducían a su hogar y cerró la puerta con firmeza después de entrar. Mientras regresaba andando al apartamento de Josiah y reflexionaba sobre el episodio, lo único que consiguió Annabelle fue afianzar su decisión. Ya no le quedaba nada en Nueva York.
Thomas llevó a Annabelle en coche al muelle de Cunard a la mañana siguiente, con tiempo de sobra para meter las tres modestas maletas a bordo. El _Saxonia_ era un barco grande de quince años de antigüedad pensado para pasajeros y mercancía, con cuatro palos imponentes y una chimenea altísima. Lo que primaba en la embarcación era el tamaño y no la velocidad, así que recorrería el Atlántico a quince nudos. No era un barco lujoso, pero sí cómodo, y salía muy rentable a la compañía de transportes gracias a las mercancías, que reducían la zona de pasajeros de forma considerable. La primera clase había sido eliminada por completo desde el estallido de la guerra. No era ni la mitad de prestigioso que los otros barcos en los que había viajado Annabelle con anterioridad acompañada de sus padres, pero no le importaba, y eligió uno de los camarotes más amplios de segunda clase.
Dos marineros jóvenes la acompañaron a su camarote y Thomas le dio un cálido abrazo cuando se despidió de ella. Iba a dejar el coche de su padre en un aparcamiento alquilado hasta que se cumplieran las instrucciones que tenía el banco de venderlo. Thomas ya había empezado a buscar otro empleo, pues Annabelle ignoraba cuándo iba a regresar.
Se quedó de pie en el muelle, saludándola con la mano mientras el barco se alejaba lentamente de los amarres, hasta que desapareció de su vista al cabo de media hora. Las personas que iban a bordo tenían el semblante serio, pues conocían los riesgos que corrían al aventurarse en el Atlántico. Quienes viajaban en esa época tenían buenos motivos para hacerlo. Ya nadie surcaba esas aguas por placer. Era demasiado peligroso con toda Europa en guerra.
Annabelle permaneció en la cubierta hasta que dejaron atrás la estatua de la Libertad. Se despidió de la isla de Ellis y sintió que se le desgarraba el corazón, y entonces se metió en su camarote. Tomó uno de los libros sobre medicina y empezó a leerlo, procurando no pensar en lo que ocurriría si los torpedeaban. Era el primer viaje transoceánico que hacía desde que su padre y su hermano habían perecido en el _Titanic_ , y se puso tensa cuando oyó cómo gruñía el barco, pues se preguntaba a qué distancia de las aguas estadounidenses se hallarían los submarinos y si los atacarían o no. Todos los pasajeros del barco pensaban en lo mismo.
Cenó sola en su cabina y por la noche se tumbó en el catre, totalmente despejada. Empezó a preguntarse si llegarían sanos y salvos, y qué se encontraría cuando atracaran en Francia. Tenía intención de desplazarse hasta la zona en la que le habían dicho que su ayuda sería más requerida. Como Estados Unidos no participaba en la guerra, Annabelle no había tenido opción de presentarse como voluntaria en representación de su país, a pesar de que sabía que sus primos Astor habían financiado un hospital de campaña y que uno de sus primos por la parte de los Vanderbilt había ido de voluntario a la contienda. No obstante, después de que se propagara la noticia del divorcio, no se atrevía a contactar con ellos. Tendría que buscar su propio camino cuando llegara a Francia. Allí averiguaría qué le esperaba.
Una vez instalada en el hospital al que se dirigía, haría cualquier tarea que le asignasen. Estaba dispuesta a aceptar las labores más insignificantes, pero, por lo que había oído, las trincheras estaban llenas a rebosar y los hospitales todavía más repletos de heridos. Estaba segura de que alguien la pondría a trabajar al instante, si lograban sobrevivir a la travesía.
Había aprendido una barbaridad de los médicos y enfermeras de la isla de Ellis, y continuaba estudiando sus libros de medicina todos los días. Además, aunque no le dejasen hacer nada más que conducir una ambulancia, por lo menos sabía que sería de más utilidad que en Nueva York, donde tendría que esconderse de las miradas de todo un universo de personas en otro tiempo afectuosas, del que ahora la habían excluido.
Aunque Josiah lo había hecho con buena intención, lo cierto era que toda la respetabilidad, la reputación, el decoro y la capacidad para rehacer la vida de Annabelle habían quedado destrozados por el divorcio. Él no se lo había planteado. Para ella era como estar condenada por un delito imperdonable. Y la sentencia sería a cadena perpetua, pues nadie tendría dudas de su culpabilidad. Aun así, bajo ningún concepto se atrevería a divulgar el secreto de Josiah. Lo amaba demasiado para hacerle eso y lo que él escondía era mucho más escandaloso que el divorcio. La revelación de su larga historia de amor con Henry y de la sífilis que habían contraído habría hecho que la gente lo dilapidara. Annabelle no podía hacerle eso. Seguía queriéndolo, de modo que se llevaría el secreto a la tumba. Sin proponérselo, él la había sacrificado.
Le parecía un alivio viajar a Francia, donde nadie la conocería. Al principio no sabía si era mejor decir que era viuda o que nunca había estado casada. Pero si alguien conocía a Josiah, cosa que podía ocurrir incluso en Europa, sabrían que estaba vivo y que ella era una mentirosa, una acusación que sumaría a todo lo demás. Al final, decidió que diría que nunca se había casado. Era más sencillo así, por si daba con alguien que conociese a Josiah. Volvía a ser Annabelle Worthington, como si los dos años vividos con él no hubieran transcurrido nunca, aunque sí lo habían hecho y ella había llegado a amarlo profundamente. Tanto que le perdonaba las debilidades que no podía evitar y la enfermedad que terminaría con su vida.
Mientras el barco navegaba sin problemas durante la primera noche de travesía, Annabelle se planteó que a lo mejor moría en Francia y así no tenía que sufrir otra pérdida y otro duelo. Sabía que, incluso después del divorcio, se le rompería el corazón otra vez cuando él muriese. Lo único que deseaba era una vida con él, un matrimonio feliz y unos hijos. Hortie no sabía la suerte que tenía de contar con un marido normal, y todos esos niños. Además, en esos momentos Annabelle ni siquiera la tenía a ella. La habían repudiado y abandonado todos sin excepción. El rechazo de Hortie era el que más le había dolido después del de Josiah. Y lo que todo ello significaba para Annabelle: mientras el _Saxonia_ avanzaba con cautela por el Atlántico rumbo a Francia, la joven se hallaba total y absolutamente sola en el mundo. Era un pensamiento aterrador para una muchacha que había estado protegida toda su vida, primero por su familia y después por su marido. Y ahora todos ellos se habían esfumado, junto con su buen nombre y su reputación. Siempre sería tildada de adúltera. Cuando volvió a pensar en eso, las lágrimas le resbalaron de los ojos y mojaron la almohada.
Esa noche el barco navegó sin complicación. Habían duplicado el personal de vigilancia para controlar que no hubiera ninguna mina en su senda. Era imposible saber dónde podían estar escondidas, o lo mucho que se atreverían a acercarse a aguas estadounidenses los submarinos alemanes. Habían realizado un simulacro de desalojo en los botes salvavidas una hora después de salir del muelle. Todo el mundo sabía a qué bote debía dirigirse y contaba con un chaleco salvavidas, que habían dejado bien visible en cada camarote. En épocas de paz, los chalecos salvavidas se almacenaban en un lugar mucho más discreto, pero desde el hundimiento del _Lusitania_ en mayo, la línea de transportes de Cunard no quería arriesgarse. Preferían tomar cualquier precaución a su alcance en pro de la seguridad, aunque con ello consiguieran tensar todavía más el ambiente dentro del barco.
Annabelle no hablaba con nadie. Había mirado la lista de pasajeros y había visto que había dos conocidos de sus padres a bordo. Teniendo en cuenta la marea de escándalos que había despertado en Nueva York su divorcio de Josiah, no tenía el menor deseo de encontrárselos y arriesgarse a que le hicieran un desplante, o algo peor. Prefería quedarse en su camarote la mayor parte del día y salir a dar un paseo en solitario por la cubierta al caer la noche, mientras los demás pasajeros se cambiaban para ir a cenar. Después, cenaba sola en la cabina. A pesar de todos los libros que había llevado consigo para distraerse, tenía muy presente el fallecimiento de su padre y su hermano en el _Titanic_. Y los relatos que le habían llegado del hundimiento del _Lusitania_ eran casi peores. Se pasaba casi todo el día tensa y ansiosa, aunque consiguió estudiar mucho durante sus largas horas de vigilia.
La camarera asignada a su camarote intentaba por todos los medios que fuera a cenar al salón del barco, pero era en vano. Y el capitán la había invitado a sentarse a su mesa para cenar la segunda noche de travesía. Era un honor que la mayor parte de los pasajeros habrían recibido con entusiasmo, pero Annabelle le envió una nota pidiendo disculpas por rechazar la invitación, alegando que no se encontraba bien. El mar había estado revuelto ese día, así que era plausible que, si no había viajado mucho en barco, se hubiese mareado (lo cual no era el caso). Se encontró de maravilla durante todo el trayecto.
Tanto el camarero como la camarera que la atendían se preguntaban si estaría recuperándose de algún tipo de pérdida. Era hermosa y joven, pero muy solemne, y se fijaron en que vestía siempre de negro, pues todavía estaba de luto por la muerte de su madre. Dudaban si sería viuda o habría perdido un hijo. Era evidente que algo grave le había ocurrido. Parecía una figura trágica y romántica cuando contemplaba el atardecer durante sus paseos. Se quedaba de pie en la cubierta mirando el mar, pensando en Josiah, y se preguntaba si volvería a verlo algún día. Intentaba no pensar en Henry, para no odiarlo.
Con frecuencia, cuando volvía a su camarote, que constaba de una amplia salita y de un dormitorio, tenía aspecto de haber llorado. Muchas veces se ponía un velo para esconder el rostro, que quedaba todavía más oculto gracias a los grandes sombreros que se calaba. No deseaba en absoluto que la reconocieran, ni que la vieran siquiera. Estaba desapareciendo de su mundo, despojándose del caparazón protector que en otra época había lucido y de la identidad que había formado parte indisoluble de su vida. Deseaba desprenderse de todas esas cosas familiares que le daban seguridad, para desvanecerse en una vida de servicio en el frente. Eso era lo único que deseaba en estos momentos.
Se sobresaltó al caer en la cuenta de que, aparte de la casita de verano de sus padres en Newport, no tenía otro hogar. Casi todas sus pertenencias estaban en el guardamuebles, y el resto lo llevaba en aquellas tres maletas, que podía transportar ella sola. No llevaba ni un solo baúl para ropa, cosa de lo más extraña, tal como había comentado la camarera al sobrecargo, para una mujer de su categoría. Incluso desprovista de los abrigos de pieles, de las joyas y de los vestidos de gala, por su forma de hablar y sus modales, por su porte y sus movimientos, era fácil ver que Annabelle provenía de una buena familia. Y al ver la aflicción que reflejaban sus ojos en todo momento, la joven doncella sintió pena por ella. Tenían casi la misma edad, y Annabelle siempre era muy amable con la empleada.
El cuarto día de navegación, en el que ya se aproximaban a Europa, el barco aminoró la marcha de forma brusca. Apenas se desplazaban por las aguas, porque el capitán de ese turno de vigilancia había visto algo sospechoso y le preocupaba que pudiese haber un submarino alemán en las inmediaciones. Todos los pasajeros se alarmaron y algunos se pusieron el chaleco salvavidas, aunque no había sonado la sirena. Por primera vez, Annabelle salió a cubierta a plena luz del día para ver qué pasaba. Uno de los oficiales se lo explicó con tranquilidad y se quedó prendado de la belleza de la joven, escondida tras el sombrero y el velo. Se preguntó si sería una actriz famosa, que viajaba de incógnito, o alguien conocido. Vestía un traje negro hecho a medida y, cuando se quitó uno de los guantes, el marinero se dio cuenta de que tenía las manos finísimas. La tranquilizó y Annabelle, que deseaba apartarse de los grupitos de personas que charlaban o jugaban a las cartas sentadas en la cubierta, decidió dar un breve paseo por el barco, y después regresó a su habitación.
El joven oficial llamó a su puerta esa misma tarde y Annabelle abrió con cara de sorpresa. Tenía un libro en la mano y la melena larga y rubia le caía por los hombros. Parecía una chiquilla, y el hombre se admiró aún más de lo guapa que era. Se había quitado el traje de chaqueta y vestía una blusa negra y una falda larga también negra. Igual que la camarera, sospechaba que era una viuda joven, pero no tenía la menor idea de por qué viajaba a Europa. Le dijo que quería asegurarse de que Annabelle estaba bien, pues la había visto preocupada por la mañana y seguían desplazándose a poca velocidad. Ella le confirmó con una sonrisa tímida que se encontraba bien. Él bajó la mirada para ver qué leía y se sorprendió al descubrir de qué se trataba. Era un libro de medicina del doctor Rudolph Virchow, y vio tres tomos más del doctor Louis Pasteur y del doctor Claude Bernard, las eminencias médicas del momento, en la mesa que había detrás de la joven. Eran sus libros sagrados.
—¿Estudia medicina? —preguntó con inusitada admiración.
Era muy peculiar que una mujer leyera esos libros, y se preguntó si sería enfermera. Aunque parecía poco probable, teniendo en cuenta su evidente estatus social.
—Sí... No... Bueno, no exactamente —contestó ella algo azorada—. Me gusta leer sobre medicina. Es mi pasión.
—Mi hermano es médico —dijo él orgulloso—. Él es el listo de la familia. Mi madre es enfermera.
Se quedó quieto un momento, buscando excusas para seguir hablando con ella. Había algo increíblemente misterioso en esa mujer y no podía evitar preguntarse qué la había llevado a viajar a Francia. Tal vez tuviera familia allí. En esa época, cada vez escaseaban más las mujeres que viajaban solas en barco.
—Si hay algo que pueda hacer por usted, señorita Worthington, no dude en decírmelo.
Ella asintió, sorprendida de que la llamaran por su nombre de soltera por primera vez en dos años. Todavía no se había acostumbrado. Era como retroceder a la infancia y viajar en el tiempo. Con lo mucho que se enorgullecía de que la llamaran señora Millbank... La entristecía volver a apellidarse Worthington, como si ya no mereciese el apellido de Josiah. Ambos habían acordado que ella recuperase el nombre de soltera. Josiah habría podido solicitar al tribunal que le permitieran mantener el de él, pero los dos consideraban que era mejor si no lo hacía. A Annabelle le resultaría más fácil empezar de cero con su propio apellido, aunque todavía echaba de menos el de su marido.
—Muchas gracias —contestó ella con educación.
Él hizo una reverencia, y Annabelle cerró la puerta y retomó la lectura. No volvió a abandonar el camarote hasta el anochecer. Estaba impaciente por llegar. Estar confinada en su cabina todo el tiempo hacía que el trayecto pareciese muy largo. Y como habían aminorado tanto la marcha, tardarían un día más en atracar, pero todo el mundo coincidía en que era mejor ser cautelosos y tomar precauciones, aunque eso implicase retrasarse.
El día siguiente fue todavía más estresante que el anterior. Los vigilantes del turno matutino habían avistado un campo de minas a lo lejos, por estribor. Esta vez sí sonaron las sirenas y todo el mundo salió a la cubierta para que la tripulación explicara qué ocurría. Los pasajeros aparecieron con los chalecos salvavidas puestos y la tripulación les aconsejó que se los dejaran durante todo el día. Annabelle había salido del camarote sin sombrero ni velo, y notó que hacía un cálido día veraniego con una suave brisa. El pelo se le ondulaba ligeramente por la espalda, que tenía cubierta por un vestido de lino negro. El mismo oficial del día anterior se acercó a ella con una sonrisa.
—No hay de qué preocuparse —la tranquilizó—. Es solo por precaución. Nos mantendremos alejados de las minas. Nuestros hombres son muy listos. Las han descubierto a la primera.
Se sintió aliviada, aunque, de todos modos, la situación era inquietante. Sin que deseara compartirla con él, a la joven se le escapó un ápice de información personal.
—Mis padres y mi hermano viajaban en el _Titanic_ —comentó en voz baja, y casi sintió un escalofrío al decirlo y mirarlo a la cara con los ojos muy abiertos.
—Lo siento mucho —dijo él con afecto—. Aquí no va a pasar nada parecido. No se preocupe, señorita. El capitán lo tiene todo bajo control.
Sin embargo, la presencia de un campo de minas en la distancia implicaba otro día meciéndose lánguidamente en el agua. Y a lo largo de las dos jornadas siguientes tendrían que prestar todavía más atención, pues el _Saxonia_ se aproximaba a Francia.
Al final, la travesía duró siete días. Llegaron a Le Havre a las seis de la madrugada y el barco atracó mientras la mayoría de los pasajeros dormía. Sirvieron el desayuno a las siete, y los que desembarcaban allí tuvieron que presentarse en cubierta a las nueve. El barco se dirigía a continuación a Liverpool, pues Southampton había sido tomado por fuerzas militares. Además, en esa ocasión habían atracado primero en Francia porque, debido a los campos de minas, habían tenido que modificar considerablemente el rumbo. Annabelle ya estaba en la cubierta vestida de la cabeza a los pies cuando llegaron a puerto. El joven oficial la vio y se acercó a ella. Parecía emocionada y totalmente despierta. En su rostro se dibujaba la expresión más feliz que había observado en ella en toda la travesía, y se preguntó si su aspecto sombrío se había debido simplemente al miedo de estar en el barco, ya que sus familiares habían viajado en el que se había hundido. Y los campos de minas y los submarinos alemanes habrían alarmado a cualquiera. Todo el mundo se alegró mucho cuando llegaron sanos y salvos a Francia.
—¿Está contenta de haber llegado a París? —le preguntó él por darle conversación.
Era evidente que sí, y de pronto el oficial se planteó que tal vez la estuviera esperando su prometido. Annabelle le dedicó una sonrisa amplia cuando asintió bajo el sol de primera hora de la mañana. Llevaba puesto el sombrero, pero no llevaba velo, así que la miró directamente a los ojos azules.
—Sí, pero no me quedaré mucho tiempo —contestó ella sin dar más explicación.
Él se sorprendió. Nadie viajaba a Europa para poco tiempo, teniendo en cuenta los riesgos que suponía, y mucho menos para un viaje relámpago de vacaciones.
—¿Piensa regresar?
—No. Confío en poder trabajar en un hospital al norte de París, a unos cincuenta kilómetros del frente.
—Es usted muy valiente —comentó él, impresionado.
Era tan guapa y tan joven que no quería ni imaginársela en la carnicería propia de los hospitales en tiempos de guerra, pero quedaba patente que estaba emocionada con la idea. Eso explicaba por qué la había encontrado leyendo libros de medicina en el camarote cuando había ido a saludarla.
—¿Cree que estará a salvo? —preguntó el marinero con preocupación. Pero ella sonrió.
—Lo suficiente.
Annabelle habría preferido poder trabajar más cerca de las trincheras, pero le habían dicho que en los hospitales de campaña solo aceptaban a personal médico y militar con formación. El hospital instalado en la abadía de Royaumont, en Asnières-sur-Oise, era peculiar y, por lo tanto, sería mucho más fácil que la aceptaran en el equipo.
—¿Se dirigirá allí hoy mismo? —preguntó él con interés, a lo que ella negó con la cabeza.
—He pensado que pasaré la noche en París y encontraré la forma de llegar al hospital mañana.
Solo estaba a cincuenta kilómetros hacia el norte de París, pero Annabelle no estaba segura de qué tipo de transporte podría conseguir.
—Demuestra ser muy valiente viajando sola —insistió él con admiración, pues había supuesto, y con acierto, que se trataba de una mujer que había estado cobijada y protegida toda su vida y que no estaba acostumbrada a tener que ingeniárselas por sí misma. Sin embargo, ahora no le quedaba otra opción. Annabelle sabía que viajar a Francia era como hacer borrón y cuenta nueva o, por lo menos, como escapar del ostracismo que acababa de empezar a saborear en su tierra y que, con el tiempo, solo habría empeorado.
El joven oficial tenía que ir a atender sus obligaciones, así que Annabelle volvió a su camarote a cerrar las maletas. A las siete, ya estaba preparada para desembarcar. Dio las gracias a la camarera por sus amables atenciones durante el viaje, le entregó una generosa propina en un sobre discreto y se dirigió al salón principal para desayunar. Era la primera y única vez que comía en público durante toda la travesía. Pero todos estaban demasiado atareados para prestarle atención. Se dedicaban a despedirse de sus amigos recién conocidos, y disfrutaban del último desayuno copioso antes de bajar del barco.
Annabelle fue de los primeros pasajeros en desembarcar. Y se despidió del joven oficial cuando este fue a decirle adiós y desearle buena suerte. A continuación se montó en el compartimiento que tenía reservado en el tren. Sabía muy bien que esos eran los últimos lujos de los que disfrutaría en mucho tiempo. Al día siguiente, con un poco de suerte, estaría trabajando a pleno rendimiento y viviría como todos los demás miembros del equipo médico de la abadía.
Al bajar del tren, consiguió apañárselas sola con las tres maletas y encontró un taxi que la llevara a la estación de trenes Gare du Nord de París. Había comido algo en el tren y no tenía hambre, así que fue directa al hotel. Había reservado una habitación en el hotel de Hollande, en el noveno distrito, cerca de Montmartre. Mientras el taxista la conducía allí, se fijó en unos hombres con gorra azul montados en bicicleta, en su mayoría en grupos de cuatro, que patrullaban la ciudad. Habían eliminado todas las terrazas de los cafés de París, algo que suponía un gran cambio respecto de la vez anterior en que había estado en la ciudad con sus padres, de jovencita. No había vuelto desde los dieciséis años. Se respiraba un ambiente tenso y se percató de que apenas se veían hombres por la calle. Casi todos habían sido llamados a filas y estaban luchando por su país y por su vida en el frente. A pesar de todo, la ciudad seguía siendo tan hermosa como la recordaba. La Place de la Concorde era tan majestuosa como siempre, igual que los Campos Elíseos. El clima era templado y, cuando el taxi la dejó en la puerta del hotel, pensó que hacía un día de otoño espléndido.
No le extrañó que el recepcionista del hotel fuese un hombre ya anciano, quien le mostró dónde estaba su habitación, en la primera planta. Era un espacio pequeño, pero luminoso y soleado, que daba al jardín del hotel, donde habían colocado unas cuantas sillas alrededor de unas mesas, en las que algunos huéspedes comían en ese momento. Le preguntó al recepcionista cómo podía desplazarse a Asnières al día siguiente. Deseaba saber si el empleado podía buscarle un chófer y algún tipo de vehículo. Le habló en un francés fluido que había aprendido con la institutriz, como parte de sus refinados estudios, y que ahora le resultaría muy útil.
—¿Para qué quiere ir a Asnières? —le preguntó el hombre frunciendo el entrecejo, como si la reprendiera.
En su opinión estaba demasiado cerca del frente, pero Annabelle no pensaba lo mismo. Había intentado insinuar, sin ser grosera, que recompensaría económicamente con creces al conductor que la llevara allí sin viaje de regreso, eso suponiendo que el hospital le permitiese quedarse, cosa que todavía estaba por ver. De todas formas, era optimista y contaba con la carta de recomendación del médico de la isla de Ellis, que había guardado en el bolso.
—Voy a ir a la abadía de Asnières —le informó.
—Pero ya no es una abadía —rectificó el hombre—. Ahora es un hospital. Lo llevan solo mujeres.
—Sí, lo sé —respondió Annabelle con una sonrisa—. Por eso voy allí.
—¿Es usted enfermera?
Ella negó con la cabeza a modo de respuesta. El recepcionista no pudo evitar pensar que era un hotel demasiado elegante para una enfermera, pero incluso con la ropa modesta que llevaba, la joven parecía aristocrática.
—No, no soy más que una voluntaria. Me gustaría ayudar a los médicos con lo que me dejen hacer —dijo con humildad, y él le sonrió con una mirada de asombro.
—¿Ha viajado hasta aquí para ayudar a nuestros chicos en el hospital?
Esta vez ella asintió sin dudarlo. Por la noche, el hombre le sirvió la cena en la habitación y añadió una botellita de vino que había reservado para sí mismo.
—Es usted una mujer buena —le dijo cuando volvió a verla.
—Gracias —contestó ella con un hilo de voz, pues sabía que toda Nueva York y todo Newport habrían discrepado.
Más tarde, el anciano encargado de la recepción le dijo que le había pedido a su sobrino que la llevara a Asnières al día siguiente. Lo habían herido en el frente el año anterior y había perdido varios dedos, pero le aseguró que Jean-Luc conducía muy bien, aunque se disculpó al decirle que el joven la llevaría a su destino en camioneta. Era el único vehículo que tenían. Ella le aseguró que le parecía perfecto.
Apenas consiguió dormir aquella noche, pues estaba muy alterada. No tenía la menor idea de qué sorpresas le depararía el día siguiente; ni siquiera sabía si le permitirían quedarse en la abadía. Lo único que podía hacer era rezar para que así fuera.
### 14
Annabelle y el sobrino del recepcionista del hotel, Jean-Luc, emprendieron el viaje a las seis de la mañana, en cuanto el sol salió en París. Hacía un día asombrosamente bello, pero el hombre le dijo que había estallado una batalla atroz en Champagne el día anterior, en la que todavía combatían. Dijo que era la segunda batalla que tenía lugar en ese enclave, y que ya habían muerto o resultado heridos ciento noventa mil soldados. Annabelle lo escuchaba con silencioso horror y pensaba en esa cifra tan astronómica. Era inconcebible.
Precisamente por eso estaba ella allí. Para ayudar a sanar a sus hombres y para hacer todo lo que pudiera por salvarlos, si es que era capaz de curarlos de algún modo, o por lo menos de consolarlos. Se había puesto un ligero vestido de lana de color negro, y botas y medias del mismo color. Llevaba todos sus libros de medicina en las maletas y también llevaba consigo un delantal blanco limpio, metido en el bolso. Era el que se ponía en la isla de Ellis, aunque allí lo combinaba con faldas y vestidos más vistosos y alegres cuando no estaba de luto como en esa época, debido a la trágica muerte de su madre. Casi todas las prendas que había llevado a Europa eran negras.
Tardaron tres horas por carreteras secundarias en llegar al hospital. Estas estaban en mal estado y presentaban profundos surcos, además de socavones por doquier. Nadie tenía tiempo de arreglarlas, ni había hombres para que lo hicieran. Todos los varones no lisiados estaban en el ejército, y no quedaba nadie en las casas para reparar y mantener en pie el país excepto los ancianos, las mujeres, los niños y los hombres tullidos a quienes habían mandado de regreso a sus hogares. A Annabelle no le importó que las abruptas carreteras hicieran saltar la camioneta de Jean-Luc, que, según le dijo, solía emplear para transportar aves de corral. La joven sonrió cuando vio que había plumas adheridas a sus maletas. Se descubrió mirándose las manos un momento y notó la estrecha marca que le había dejado el anillo de bodas en el dedo. Se sintió conmovida durante un momento. Se lo había quitado en agosto y todavía lo echaba de menos. Lo había dejado en el banco, dentro de la caja fuerte de las joyas, junto con el anillo de compromiso, que Josiah había insistido en que se quedara. Sin embargo, en esos momentos no tenía tiempo de pensar en esas cosas.
Pasaban unos minutos de las nueve cuando por fin llegaron a la abadía de Royaumont, un edificio eclesiástico del siglo XIII algo deteriorado. Era una estructura hermosa con arcos muy estilizados y una laguna debajo. Hervía de actividad. Había enfermeras con uniforme que empujaban a hombres en sillas de ruedas por el patio, otras entraban apresuradas en las distintas alas del centro, mientras que otros heridos se movían con ayuda de muletas o eran transportados en ambulancias conducidas por mujeres. Las que llevaban las camillas también eran mujeres. Allí no había nada más que mujeres trabajando, incluido el cuadro médico. Los únicos hombres que se veían eran los heridos. Bueno, al cabo de unos minutos vio a un médico que entraba a toda prisa por la puerta. Era una rareza en medio de aquella población femenina. Y como Annabelle miraba a su alrededor, sin saber hacia dónde ir, Jean-Luc le preguntó si deseaba que la esperara.
—Sí, por favor. Si no le importa... —dijo ella, abrumada por un momento, pero muy consciente de que, si no la admitían como voluntaria, ignoraba por completo adónde podría ir o qué otra cosa iba a hacer. Estaba decidida a quedarse en Francia para colaborar, a menos que fuera como voluntaria a Inglaterra. Lo que estaba claro era que, pasara lo que pasase, no pensaba volver a casa. Por lo menos, no durante una buena temporada, o tal vez nunca. No quería pensar en eso—. Tengo que hablar con las encargadas para ver si quieren aceptarme —añadió en voz baja.
Y si no permitían que se quedara, necesitaría un lugar en el que alojarse. No le importaba dormir en una barraca o en un garaje si hacía falta.
Annabelle cruzó el patio y siguió los carteles que indicaban las distintas secciones del hospital instalado en la abadía, hasta que vio una flecha que señalaba hacia unas oficinas que había debajo de los arcos y en la que ponía «Administración».
Cuando entró, se encontró con una fila de mujeres detrás de un escritorio manejando documentos, mientras las conductoras de las ambulancias les entregaban solicitudes de admisión. Abrían historiales de todos los pacientes a quienes trataban, algo que no siempre se cumplía en los hospitales de campaña, donde en ocasiones tenían que trabajar bajo mucha mayor presión. Allí había una sensación de actividad frenética, pero al mismo tiempo se palpaba la claridad y el orden. Las mujeres del mostrador eran en su mayor parte francesas, aunque Annabelle oyó que varias eran inglesas. Y todas las conductoras de las ambulancias eran jóvenes francesas. Eran chicas del pueblo a quienes habían formado en la abadía, y algunas de ellas no parecían tener más de dieciséis años. Todo el mundo tenía que colaborar. A sus veintidós años, Annabelle era bastante mayor que muchas, aunque no lo parecía. Sin duda era lo bastante madura para llevar a cabo ese trabajo si se lo permitían, y mucho más experimentada que la mayoría de las voluntarias.
—¿Con quién podría hablar sobre el voluntariado? —preguntó en un francés perfecto.
—Conmigo —contestó sonriendo una mujer que tendría más o menos su edad. Llevaba un uniforme de enfermera, pero trabajaba en la administración. Como todas las demás, hacía turnos dobles. Algunas veces, las conductoras de ambulancia, o las doctoras y enfermeras de los quirófanos, tenían que trabajar veinticuatro horas seguidas. Hacían todo lo que era necesario. Y el ambiente era agradable, muy alegre y rebosaba energía. Annabelle estaba francamente impresionada.
—A ver, ¿qué sabes hacer? —le preguntó la joven del escritorio mirándola de arriba abajo.
Annabelle se había puesto el delantal para parecer más profesional. Con ese serio atuendo de luto, parecía una mezcla entre monja y enfermera, cuando en realidad no era ninguna de las dos cosas.
—Traigo una carta —dijo nerviosa, mientras la pescaba del bolso. Le preocupaba que no la admitieran. ¿Y si solo contrataban a enfermeras?—. He realizado tareas relacionadas con la medicina desde los dieciséis años, como voluntaria en distintos hospitales. He trabajado con inmigrantes en la isla de Ellis, en Nueva York, durante los dos últimos años, y he adquirido bastante experiencia en el tratamiento de enfermedades contagiosas. Antes de eso, había trabajado en el Hospital para el Tratamiento de los Lisiados de Nueva York. Supongo que eso estará más relacionado con lo que hacen aquí... —añadió Annabelle, casi sin aliento pero esperanzada.
—¿Tienes formación médica? —quiso saber la joven enfermera cuando leyó la carta de recomendación del médico de la isla de Ellis. La había halagado mucho y decía que era la ayudante médica sin formación más habilidosa que había tenido jamás, mejor que muchas enfermeras e incluso que algunos médicos. Annabelle se había sonrojado al leerla.
—En realidad, no —contestó Annabelle con sinceridad, reconociendo su falta de estudios. No quería mentirles y fingir que sabía hacer cosas que desconocía—. Pero he leído muchos libros sobre medicina, sobre todo acerca de enfermedades contagiosas, cirugía ortopédica y heridas gangrenosas.
La enfermera asintió y la miró con atención. Le caía bien. Parecía impaciente por empezar a trabajar, como si aquella labor significara mucho para ella.
—Caray, menuda carta de recomendación —dijo con admiración—. Supongo que eres de Estados Unidos...
Annabelle asintió. La otra joven era británica, pero hablaba un francés perfecto, sin rastro de acento inglés. El francés de Annabelle también era bueno.
—Sí —dijo ella como respuesta a la pregunta sobre su nacionalidad—. Llegué ayer.
—¿Por qué has venido aquí? —preguntó curiosa la enfermera, tras lo cual Annabelle vaciló y se ruborizó mientras sonreía con timidez.
—Por vosotras. El médico de la isla de Ellis que escribió mi recomendación me habló de este hospital. Cuando lo oí, me pareció fantástico, así que se me ocurrió venir a ver si podía aportar mi granito de arena. Haré cualquier cosa que me manden. Poner cuñas a los enfermos, limpiar palanganas del quirófano, lo que sea.
—¿Sabes conducir?
—Todavía no —contestó Annabelle con timidez. Siempre la había llevado el chófer—. Pero puedo aprender.
—Admitida —se limitó a decir la enfermera británica.
No hacía falta ponerla a prueba con una carta de recomendación como aquella, y saltaba a la vista que tenía madera. Su cara estalló en una amplia sonrisa cuando la mujer de detrás del escritorio dijo la palabra. Era el propósito de su viaje a Francia. Había valido la pena la travesía larga, solitaria y aterradora que había realizado, a pesar de los campos de minas y los submarinos enemigos, y a pesar de sus propios temores por culpa del _Titanic_.
—Preséntate en el Pabellón C a las trece horas.
Faltaban veinte minutos.
—¿Hace falta uniforme? —preguntó Annabelle todavía con la sonrisa en la cara.
—Así estás bien —contestó la enfermera mirándole el delantal. Y entonces se le ocurrió algo—. ¿Tienes alojamiento? ¿Sabes dónde vas a dormir?
Intercambiaron una sonrisa.
—Aún no. ¿Podría quedarme en alguna habitación del hospital? Dormiré donde sea. En el suelo, si es preciso.
—No le digas eso a nadie —le advirtió la enfermera—, o te tomarán la palabra. Aquí las camas van muy escasas y cualquiera estaría encantada de quitarte la tuya. La mayoría compartimos cama, me refiero a que utilizamos la misma que otras personas que tienen turnos laborales diferentes. Quedan algunas libres en las antiguas celdas de las monjas, y hay un dormitorio en el monasterio, pero está bastante abarrotado. Yo en tu lugar cogería una de las celdas, o preguntaría si alguien quiere compartirla contigo. Indaga por ahí. Seguro que alguien te acoge.
Le dijo en qué edificio se hallaban y, a la carrera, Annabelle fue en busca de Jean-Luc. Su misión había sido un éxito, iban a permitirle que trabajara allí. Le costaba creer la buena suerte que había tenido y seguía sonriendo cuando encontró a Jean-Luc, de pie junto a su furgoneta de reparto de pollos, tanto para vigilarla como para que ella lo viera fácilmente. Los vehículos escaseaban y tenía pavor a que alguien se lo robara con el fin de utilizarlo de ambulancia.
—¿Se queda? —le preguntó cuando vio que la joven se le acercaba con una sonrisa.
—Sí, me han aceptado —dijo ella, aliviada—. Empiezo a trabajar dentro de veinte minutos y todavía tengo que encontrar habitación.
Metió los brazos en la parte posterior de la camioneta, sacudió las plumas de las maletas y las sacó. Él se ofreció a llevárselas, pero ella pensó que sería mejor que lo hiciera por sí misma. Volvió a darle las gracias y se despidió, pues ya le había pagado por la mañana. Él la abrazó con afecto, la besó en las mejillas, le deseó buena suerte, se metió en el vehículo y se marchó.
Annabelle se dirigió a la abadía cargando con las maletas y encontró la zona en la que la enfermera le había dicho que estaban las antiguas celdas de las monjas. Había filas y filas de celdas, todas ellas oscuras, pequeñas, mohosas y con aspecto de ser tristemente incómodas, con un mugriento colchón en el suelo y una colcha, en muchos casos sin sábanas. Solo unas pocas tenían ropa de cama y Annabelle supuso, acertadamente, que las mujeres alojadas en ellas habían traído sus propias sábanas. Había un cuarto de baño comunitario cada cincuenta celdas más o menos, pero Annabelle dio gracias al saber que por lo menos contaría con un aseo en el interior del edificio. Era evidente que las monjas no vivían con ninguna clase de lujo ni comodidad, ya fuera en el siglo XIII o en tiempos recientes. La abadía había sido comprada a la orden religiosa hacía muchos años, a finales del siglo anterior, y ya era propiedad privada cuando Elsie Inglis la había solicitado para convertirla en hospital. Era un edificio antiguo precioso, y, aunque no estaba en las mejores condiciones, resultaba perfecto para sus propósitos. Era el hospital ideal para todas ellas.
Mientras Annabelle miraba a su alrededor, una joven salió de una de las celdas. Era alta y delgada y parecía claramente inglesa, con la piel pálida y el pelo tan moreno como rubio era el de Annabelle. Vestía uniforme de enfermera y sonrió a la recién llegada con una expresión azorada. Parecía una niña. La afinidad entre ambas fue instantánea.
—No es precisamente el Claridge's —dijo con el acento propio de las clases altas británicas, porque había adivinado al instante que Annabelle pertenecía a su mismo entorno. Era algo que se percibía aunque no se viera, pero ninguna de las dos jóvenes estaba impaciente por anunciar a los cuatro vientos su sangre azul. Habían ido allí a trabajar de sol a sol, y estaban encantadas de estar en la abadía—. Supongo que buscas habitación —le dijo la chica antes de presentarse—. Soy Edwina Sussex. ¿Sabes qué turno te ha tocado?
Annabelle le dijo cómo se llamaba y añadió que no conocía aún su turno.
—Todavía no sé qué querrán que haga. Me han dicho que tengo que presentarme en el Pabellón C dentro de diez minutos.
—Pues qué suerte. Es uno de los pabellones quirúrgicos. No eres aprensiva, ¿verdad?
Annabelle sacudió la cabeza, mientras Edwina le explicaba que ya había dos chicas con quienes compartía la celda, pero le señaló la que había en la puerta contigua y dijo que la que se alojaba allí se había marchado a casa el día anterior porque su madre estaba enferma. Era evidente que nadie estaba tan lejos de su hogar como Annabelle. Las chicas de Gran Bretaña podían ir a visitar a su familia sin problemas y regresar al cabo de un par de días, si era necesario, aunque cruzar el canal de la Mancha tampoco era fácil en aquella época. De todas formas, nada era tan peligroso como atravesar el Atlántico. Annabelle le contó que había llegado de Estados Unidos el día anterior.
—Qué valiente —contestó Edwina con admiración.
Las dos jóvenes eran exactamente de la misma edad. Edwina dijo que se había comprometido con un joven que por entonces estaba luchando en la frontera italiana, a quien no veía desde hacía seis meses. Mientras se lo contaba, Annabelle dejó las maletas en la celda contigua a la suya. Era tan pequeña, oscura y fea como las otras, pero no le importó, y Edwina dijo que no pasaban ni un momento en las celdas, salvo para dormir.
Annabelle apenas tuvo un minuto para dejar el equipaje y correr escaleras abajo para encontrar el Pabellón C. Y tal como le había informado Edwina, cuando llegó vio que se trataba de un enorme pabellón quirúrgico. Había una sala gigantesca con aspecto de haber sido una capilla en otra época, abarrotada con unas cien camas. La habitación no tenía calefacción y los hombres estaban cubiertos con varias mantas para intentar que entraran en calor. Sus dolencias eran muy variadas, aunque muchos habían perdido alguna extremidad en un bombardeo o habían tenido que amputársela en el quirófano. La mayor parte de ellos gemía, algunos lloraban y todos estaban muy enfermos. Varios deliraban por culpa de la fiebre y, mientras Annabelle recorría el pabellón en busca de la jefa de enfermería para presentarse, fueron muchas las manos que se agarraron a su vestido. Además de la estancia principal había otras dos salas grandes que servían de quirófanos, donde oyó gritar a más de un hombre. Era una escena impresionante; si Annabelle no hubiese desempeñado su trabajo como voluntaria en los anteriores seis años, a buen seguro se habría desmayado al instante. Sin embargo, parecía serena mientras recorría la sala y pasaba por delante de decenas de camas.
Encontró a la jefa de enfermería cuando salía de uno de los quirófanos improvisados, con aspecto frenético y sujetando una palangana con una mano dentro. Annabelle le contó que acababa de entrar a trabajar allí. La enfermera jefe le alargó la palangana y le dijo dónde debía desechar el contenido. Annabelle no titubeó y, en cuanto regresó a su puesto, la enfermera la puso a trabajar durante las siguientes diez horas. Annabelle no paró ni un segundo. Fue su prueba de fuego y, cuando terminó, se había ganado el respeto de la enfermera de mayor edad.
—Servirás —le dijo la mujer con una fría sonrisa, y alguien comentó que había trabajado con la doctora Inglis en persona, quien ya había regresado a Escocia para entonces. Tenía intención de abrir otro hospital en Francia.
Cuando Annabelle volvió por fin a su celda, ya era medianoche. Se sentía demasiado agotada para deshacer las maletas, e incluso para desvestirse. Tal cual estaba, se tumbó en el colchón, se tapó con la colcha y cinco minutos más tarde estaba profundamente dormida con el semblante lleno de paz. Sus oraciones habían sido escuchadas. Y en ese momento se sintió como en casa.
### 15
Los primeros días de Annabelle en la abadía de Royaumont fueron agotadores. Los heridos de la segunda batalla de Champagne llegaban a toda velocidad. La joven prestaba ayuda durante las operaciones, vaciaba bandejas quirúrgicas y contenía hemorragias, se deshacía de las extremidades amputadas, vaciaba las bacinillas de los enfermos, les daba la mano a los moribundos y bañaba a quienes tenían fiebres muy altas. Nada de lo que había visto hasta entonces se parecía ni remotamente a aquello. Nunca había trabajado con tanto ahínco en su vida, pero era justo lo que deseaba. Allí se sentía útil y aprendía sin cesar.
Apenas veía a Edwina. Su compañera trabajaba en otra parte del hospital y hacían turnos diferentes. Alguna que otra vez se encontraban en el cuarto de baño o se cruzaban por los pasillos entre pabellones, y se saludaban con la mano. Annabelle no tenía tiempo de entablar amistades, había demasiado trabajo por hacer, y el hospital estaba hasta la bandera de hombres agonizantes. Todas las camillas estaban ocupadas y algunos pacientes esperaban el turno tumbados en colchones en el suelo.
Por fin, un día encontró unos minutos libres para ir al banco del pueblo, desde donde mandó un mensaje a su propio banco, en Nueva York, para informar de que había llegado sana y salva a Francia. No había nadie más a quien comunicárselo o a quien le importase. Llevaba dos semanas en Asnières y le daba la sensación de que llevara allí un año. Los ingleses y los franceses habían llegado a Salónica, en Grecia, y las fuerzas austríacas, alemanas y búlgaras habían invadido Serbia y expulsado al ejército serbio de su país. En Francia, los hombres caían como moscas en las trincheras. El frente, a cincuenta kilómetros del hospital, apenas había variado, pero se perdían vidas continuamente. A pesar de que se habían habilitado hospitales en las iglesias más próximas a la contienda, seguían desviando a la abadía de Asnières tantos hombres como era posible, pues allí podían recibir un tratamiento mejor. El personal lidiaba con casos de todo tipo, desde disentería hasta dolencias en los pies, y varios de sus pacientes habían contraído el cólera. Annabelle consideraba que todo aquello era aterrador, pero al mismo tiempo estaba emocionada de poder ayudar.
En una de sus escasas mañanas libres, una de las mujeres alojadas en las celdas de las monjas le enseñó a conducir una camioneta que empleaban como ambulancia, que no era muy distinta de la furgoneta para pollos de Jean-Luc. Al principio le había costado ponerla en marcha, pero para cuando tuvo que volver a sus obligaciones, ya casi le había cogido el tranquillo. La mandaban al quirófano con más frecuencia que al resto de las voluntarias, porque era precisa, atenta, meticulosa y muy obediente, pues seguía las indicaciones de los cirujanos al pie de la letra. Algunos de los médicos se habían fijado en ella y se lo habían comentado a la jefa de enfermería, quien coincidía en que su labor era excelente. Consideraba que sería una enfermera estupenda y le aconsejó a la joven que estudiara la carrera después de la guerra, aunque el cirujano jefe de la abadía pensaba que podía aspirar a más. Se paró a hablar con ella un día después de la última operación de la jornada, bien entrada la noche. Annabelle ni siquiera parecía cansada mientras fregaba el suelo del quirófano y ponía un poco de orden. Había sido un día especialmente agotador para todos ellos, pero Annabelle no había desfallecido ni un momento.
—Parece que te diviertes con tu labor —le dijo el médico mientras se limpiaba las manos en el delantal ensangrentado.
El de Annabelle tenía un aspecto similar. Pero a ella no parecía importarle, ni se había dado cuenta de que tenía una mancha de sangre de otra persona en la cara. El médico le acercó un retal de tela para que se lo limpiase y ella le dio las gracias con una sonrisa. Era un cirujano francés procedente de París, y por supuesto era uno de los pocos hombres con los que contaban. La mayor parte del personal médico eran mujeres, pues esa había sido la intención de Elsie Inglis al fundar el hospital. Sin embargo, hacían excepciones, ya que necesitaban muchas manos. Les llegaban tantos heridos que a esas alturas agradecían la ayuda de todos los médicos dispuestos a colaborar.
—Sí, es verdad —contestó Annabelle con sinceridad, mientras dejaba el retal sucio con los otros retazos de tela que las chicas de la lavandería recogerían más tarde. Algunos de ellos tendrían que ir directos a la basura—. Siempre me ha encantado este trabajo. Lo que lamento es que los soldados tengan que sufrir tanto. Esta guerra es horrible.
Él asintió. Ya había cumplido los cincuenta años y nunca jamás había visto una carnicería semejante.
—La jefa de enfermeras considera que deberías estudiar enfermería —le expuso para tantear el terreno, y no dejó de mirarla mientras salían juntos del quirófano. Era imposible no fijarse en lo guapa que era Annabelle, aunque esa no era su única virtud. Desde su llegada, había impresionado a todo el mundo con sus habilidades para el ejercicio de la medicina. El médico que había escrito la carta de recomendación no había exagerado: la joven era mejor aún de lo que había expresado con sus elogiosas palabras—. ¿Es eso lo que te gustaría hacer? —le preguntó el cirujano.
Además, estaba impresionado por el buen francés que hablaba la joven, que había mejorado de forma asombrosa durante las últimas dos semanas. Podía hablarle en ese idioma con toda naturalidad y ella le respondía con la misma soltura.
Recapacitó un momento antes de contestarle. Ya no estaba casada con Josiah y sus padres habían muerto. Podía hacer todo lo que quisiera, no tenía que rendir cuentas a nadie. Si quería ir a la escuela de enfermería, podía hacerlo. Sin embargo, cuando levantó la cara para mirarlo a los ojos, Annabelle se sorprendió tanto como el médico de su propia respuesta.
—Preferiría estudiar medicina —respondió casi en un susurro, temerosa de que se riera de ella.
La doctora Inglis, que había fundado el hospital, era una mujer, pero seguía siendo poco frecuente ver chicas estudiando medicina. Algunas lo hacían, pero era muy extraño. El cirujano asintió antes de responder.
—Eso mismo pensaba yo. Creo que deberías hacerlo. Tienes talento. Eso se nota. —Él había dado clases en la facultad de medicina de París durante años antes de la guerra, y había enseñado a hombres mucho menos capacitados que ella. Le parecía una idea excelente—. ¿Hay algo que pueda hacer por ti?
—No lo sé —contestó Annabelle aún aturdida. Nunca se había permitido plantearse esa ilusión como una posibilidad real. Y ahora ese hombre tan amable la tomaba en serio y le ofrecía su ayuda. No pudo evitar que los ojos se le llenaran de lágrimas—. ¿Sería posible?
—Claro. Todo es posible si uno lo desea con todas sus fuerzas y está dispuesto a pelear por ello. Y algo me dice que tú estarías dispuesta. ¿Por qué no lo piensas un poco y volvemos a hablar del tema otro día?
Era el doctor Hugues de Bré, y sus caminos no volvieron a cruzarse hasta un mes más tarde. Annabelle se enteró de que había ido a trabajar a uno de los hospitales de campaña más cercanos al frente durante un tiempo y regresó a la abadía en noviembre. Sonrió en cuanto la vio y dejó que ella administrara el cloroformo al paciente. La joven fue delicada y eficiente, y consiguió dormir al hombre que sollozaba. A continuación, un joven médico la sustituyó para ayudar durante la operación. El doctor De Bré habló con ella esa noche antes de marcharse.
—¿Has vuelto a pensar en nuestro plan? Me gustaría comentarte otra cosa —dijo con cautela—. La facultad de medicina es cara. ¿Podrías permitírtelo?
Algo en el porte de la joven le decía que sí, pero no quería darlo por supuesto. Había estado dándole vueltas a cómo podía pedir una beca para sus estudios. Sin embargo, le habría costado conseguirla, pues no era francesa.
—Creo que puedo arreglármelas —dijo ella discretamente.
—¿Qué te parecería ir a la facultad de medicina de la doctora Inglis en Escocia? —le propuso, pero Annabelle negó con la cabeza.
—No sé, preferiría quedarme en Francia.
Aunque el tema del idioma sería más sencillo en Escocia, se desenvolvía bien en francés, y la perspectiva de pasar varios años en el terrible clima escocés no la atraía mucho.
—Lo cierto es que yo quizá podría ayudarte más si te quedas aquí. Se me ha ocurrido que podrías ir a una facultad de medicina pequeña que siempre me ha gustado; está en el sur de Francia, cerca de Niza. Y no creo que debas esperar a que termine la guerra. Te resultaría más fácil entrar ahora. El número de estudiantes se ha reducido y necesitan llenar las clases. Muchos de los hombres jóvenes están en el frente, así que hay menos demanda de admisión. Te recibirían con los brazos abiertos. Con tu permiso, me gustaría escribirles para ver qué opinan.
Annabelle le dedicó una sonrisa estupefacta y agradecida. No podía creer que estuviera ocurriéndole aquello. A lo mejor era el destino. Seis meses antes estaba casada, confiando en fundar una familia algún día, y llevaba una vida segura y predecible a caballo entre Newport y Nueva York. En esos momentos estaba sola, en Francia, planteándose ir a la facultad de medicina, y todos los aspectos de su vida habían cambiado. Josiah estaba en México con Henry, y ella no tenía que responder ante nadie. Si ese era su sueño, ahora podía hacerlo realidad. No había nadie que se lo impidiera. Lo único que la entristecía era que no tenía a una sola persona a quien consultarle sus dudas, aparte de al doctor De Bré.
Todavía les llegaban oleadas de heridos del frente, pues el clima había empeorado y hacía mucho frío, y cada vez más hombres morían por culpa de alguna infección, de las heridas o de la disentería. Otro día, en el que Annabelle había perdido a dos de los hombres a quienes había atendido por la mañana, el doctor De Bré se paró a hablar con ella de nuevo. Faltaban dos semanas para Navidad y era la primera vez que la joven sentía añoranza desde que había llegado. Pensaba que, hacía apenas un año, su madre aún seguía viva. El doctor De Bré interrumpió su ensueño para decirle que había recibido una carta de la facultad de Niza. La miró con aire solemne y ella contuvo la respiración, esperando oír las noticias.
—Han dicho que estarán encantados de aceptarte con una recomendación por mi parte. Tendrás que pasar un período de prueba durante el primer trimestre y después, si lo haces bien, te aceptarán como estudiante para todo el curso. —Sonrió a la muchacha y vio su cara de sorpresa—. Por lo visto, les gustaría que te incorporases el 15 de enero, si te apetece.
Annabelle abrió mucho los ojos y la boca, incrédula, y se lo quedó mirando.
—¿Habla en serio?
Estuvo a punto de saltarle a los brazos. Parecía una chiquilla y el médico empezó a reírse de ella. Había sido un placer ayudar a una joven con tanto talento. En su opinión, el mundo necesitaba médicos como ella. Y por mucho que precisaran de su ayuda en la abadía, él consideraba que era mucho más importante que se formase tan pronto como le fuera posible. Podría hacer muchas más buenas obras en el mundo si era doctora.
—Me temo que sí estoy hablando en serio. ¿Qué piensas hacer? —volvió a preguntarle, todavía inseguro de si Annabelle iría o no.
Ni ella estaba segura. Se había tomado la solicitud del médico como una especie de prueba, para ver qué decían. Annabelle no esperaba que acceder a la universidad fuera tan sencillo ni tan rápido. Pero la facultad necesitaba estudiantes desesperadamente y, vista la fe que De Bré tenía en ella, como quedó patente en su carta de recomendación, tenían plena confianza en que la estudiante respondería.
—Dios mío —exclamó Annabelle mirándolo a la cara mientras abandonaban el pabellón y salían al aire fresco de la noche—. Dios mío... ¡Tengo que ir!
Era un sueño hecho realidad, algo que nunca había esperado que ocurriera, con lo que nunca se había atrevido a fantasear, y en ese instante esa fantasía estaba al alcance de su mano. Ya no tendría que limitarse a leer libros sobre medicina por su cuenta, intentando averiguarlo todo por sí misma. Podría estudiarlos y convertirse exactamente en lo que deseaba ser. Él no podía ni imaginar el regalo que le había concedido. A Annabelle no se le ocurría cómo podía darle las gracias, así que lanzó los brazos alrededor del cuello del hombre y le besó en la mejilla.
—Vas a ser una doctora magnífica, ya lo verás. Y quiero que estés en contacto conmigo y vayas a verme cuando haya terminado esta guerra y la vida vuelva a normalizarse, si es que lo hace algún día.
Justo en esa época era difícil de creer. El número de víctimas mortales en Europa había rebasado los tres millones. Ya se había perdido una cantidad exagerada de vidas y, de momento, no se había conseguido nada. Todos los países de Europa estaban en guerra unos contra otros y Estados Unidos seguía en sus trece de no intervenir.
Annabelle lamentaba horrores tener que marcharse de la abadía. Sabía que allí la necesitaban, pero el doctor De Bré había hecho un comentario muy acertado: era el momento ideal para que se matriculara en la facultad de medicina. En época de paz, cuando hubiera más hombres que solicitaran el acceso, tal vez no se mostraran tan dispuestos a aceptarla. Le habían dicho al doctor que en el siguiente trimestre sería la única chica de la clase, aunque no era la primera mujer que se matriculaba en la escuela. En total, sus estudios durarían seis años. El primero consistiría en su mayor parte en clases teóricas, y en los cinco restantes compaginaría las clases y el trabajo con pacientes en un hospital cercano a la facultad. Tenían un acuerdo con uno de los mejores de Niza. Obtendría mucha experiencia y, además, Niza era una ciudad muy buena para vivir. De ordinario era más segura que París, más pequeña y provinciana, es decir, mejor para ella ahora que no tenía quien la protegiera. El médico le informó de que había una residencia para estudiantes dentro de la universidad y comentó que le asignarían una habitación propia, debido a que era la única mujer matriculada ese curso. También le sugirió que, una vez terminados sus estudios, regresara a París, donde tal vez pudiera trabajar para él. Tenía mucha fe puesta en ella y Annabelle estaba dispuesta a no defraudarlo.
Esa noche, cuando se metió en la cama de su celda, Annabelle flotaba: el doctor De Bré le había dicho que escribiría a la facultad en su nombre para aceptar la plaza. La joven tenía que mandar algo de dinero a principios de enero, pero eso no suponía ningún problema. Podía pagar el resto de los estudios del primer curso una vez que estuviera en la universidad. El cerebro iba a explotarle de tanta emoción y tantos planes. La cabeza le daba mil vueltas y se pasó la mayor parte de la noche en vela, pensando en todo aquello. Se acordó de la vez en que le había dicho a Josiah que le gustaría diseccionar un cadáver. Ahora lo haría, y nada ni nadie podrían impedírselo. Ya había aprendido muchísimo sobre anatomía tras haber trabajado en el quirófano de la abadía, en especial de la mano del doctor De Bré. Él se había esmerado en explicarle todo lo que hacía, siempre que el caso no fuera demasiado complicado. Y simplemente verlo operar ya era un honor.
No le contó a nadie sus planes hasta el día anterior a Navidad, cuando por fin se lo comunicó a la jefa de enfermería, quien se quedó anonadada, aunque le pareció una idea excelente.
—Cielo santo —le dijo sonriéndole—, yo pensaba que serías enfermera. Nunca pensé que querías ser médico. Pero ¿por qué no? La doctora Inglis es una de las mejores. Tú podrías seguir sus pasos algún día —sentenció la mujer muy orgullosa, como si se le hubiera ocurrido a ella la idea—. Lo que ha hecho el doctor De Bré es fantástico. Lo apoyo de todo corazón.
Para entonces Annabelle ya llevaba tres meses allí y había demostrado su valía en todos los sentidos. No había tenido mucho tiempo para entablar amistades, puesto que trabajaba de sol a sol, incluso cuando no era su turno. Pero es que había tantos heridos, y tanto que hacer para ayudarlos a todos... Incluso había conducido la ambulancia alguna que otra vez, en los casos en que había sido imprescindible. Estaba encantada de colaborar de la manera que fuese. Cuando se había acercado al frente en la ambulancia para recoger a los soldados de los hospitales militares y llevarlos a la abadía, el sonido de las detonaciones la había impresionado y le había recordado lo próxima que estaba la contienda. En cierto modo, se sentía culpable por abandonarlos para ir a la facultad de medicina en Niza, pero era un proyecto tan emocionante que no se atrevía a rechazarlo. Le daba algo más que vértigo el pensar que, para cuando terminase la carrera, ya habría cumplido veintiocho años. Le parecía una eternidad, pero sabía que debería aprender mucho durante ese período. No imaginaba cómo iba a poder asimilarlo todo en seis cursos.
Se encontró por casualidad con Edwina en la puerta de la celda la mañana del día de Navidad, se abrazaron muy fuerte y ella le contó que iba a marcharse al cabo de tres semanas. Edwina no disimuló la decepción instantánea.
—Vaya, cuánto lo siento. Siempre me ha apetecido pasar más tiempo contigo para charlar, pero nunca encontraba el momento. Y ahora te vas.
Albergaba la esperanza de que pudieran ser amigas, pero ninguna de las dos tenía tiempo para esas cosas. Siempre había demasiado trabajo. La situación hizo que Annabelle pensara en Hortie y en la última vez que se habían visto, y en la terrible sensación de traición que la había embargado entonces. Hortie no había sentido reparos en dar la espalda a su amiga de la infancia más querida, alegando que James no le permitía seguir viéndola. Era parte del motivo por el que había decidido viajar a Francia. Había perdido a demasiadas personas y Hortie había sido la gota que había colmado el vaso. Todo ello hizo que mirase a Edwina con una sonrisa tierna, mientras lamentaba haberse quedado sin una amistad tan apreciada.
—A lo mejor puedo volver a trabajar con vosotras cuando terminen las clases. Bueno, no sé si en las facultades de medicina hacen vacaciones, pero supongo que sí —dijo Annabelle esperanzada.
Deseaba volver a ver a todas sus compañeras. En cierto modo, no quería marcharse. Había sido muy feliz allí los últimos tres meses, tan feliz como podía ser alguien entre tantos hombres gravemente heridos. La camaradería dentro del equipo era tremenda.
—¿Vas a estudiar medicina? —Edwina estaba asombrada. No tenía la menor idea.
—El doctor De Bré lo ha arreglado todo —le informó Annabelle con ojos danzarines. Cada día se emocionaba más al pensarlo—. Nunca creí que pudiera pasarme algo así —añadió con una mezcla de alegría y aturdimiento.
—¿Qué te ha dicho tu familia? —preguntó Edwina con interés, pero justo entonces una nube enturbió el rostro de Annabelle, cosa que aquella no comprendió—. ¿No les importa que te quedes aquí? Deben de estar muy preocupados si saben que estás tan cerca del frente.
Si las líneas de ataque se modificaban y los conquistaban, todas ellas podrían acabar siendo prisioneras. Era un riesgo en el que no se permitían pensar una vez que entraban en el hospital, pero la amenaza era real. Los padres de Edwina se habían puesto muy nerviosos cuando les había dicho que quería ir de voluntaria, en especial su madre, pero ella había ido de todos modos. Sus dos hermanos estaban luchando en la guerra y ella deseaba participar también.
—No tengo familia —respondió Annabelle en voz baja—. Los he perdido a todos. Mi madre murió hace un año, y mi padre y mi hermano en el hundimiento del _Titanic_.
No mencionó a Josiah, quien había supuesto otra pérdida vital, porque allí nadie sabía que había estado casada, así que no tenía modo de explicarlo y, además, no tenía ganas de hacerlo. Era un dolor que acarreaba en silencio, como haría toda su vida.
—Cuánto lo siento —contestó con cariño Edwina—. No lo sabía.
Ninguna de ellas había tenido tiempo de compartir sus historias, ni muchas otras cosas, apenas una taza de té de vez en cuando, y un saludo aquí y allá. Había tanto por hacer que quedaban pocos momentos para las confesiones, o para la clase de oportunidades que, en otras circunstancias, permitían que se estrecharan los lazos de amistad. Las jóvenes se limitaban a trabajar codo con codo hasta caer extenuadas, y entonces se iban a dormir a sus colchones en el suelo o en esas diminutas celdas para las monjas. Lo más emocionante que hacían en todo el día era hurtar un cigarro entre risitas en alguna ocasión. Annabelle los había probado varias veces, solo para ser sociable, pero no le gustaba el sabor.
Charlaron unos cuantos minutos más y Edwina le deseó una feliz Navidad y mucha suerte en la escuela. Se prometieron que pasarían algún rato juntas, o que quedarían en el comedor antes de que Annabelle se marchase, pero ninguna de las dos estaba segura de si iba a ser posible. Y entonces continuaron cada una por su camino, hacia los respectivos pabellones en los que trabajaban. Para ellas, el día de Navidad no era más que otro día en el que cuidar de los enfermos y heridos. No hubo celebraciones, ni villancicos, ni regalos. Se había pactado un alto el fuego, pero a las seis de la tarde los alemanes lo habían interrumpido, de modo que aquella noche llegaron más hombres con alguna extremidad amputada. Sin importar el día del año, aquello era un torrente interminable de sufrimiento humano.
Annabelle estaba agradecida por haber trabajado tanto aquel día. Eso evitó que pensara en todas las personas que había amado y perdido, dos de ellas en el último año. No estaba dispuesta a permitirse pensar en la Nochebuena vivida en casa de su madre el año anterior. Le dolía demasiado. Y no tardaría en empezar una nueva vida en Niza. Se obligó a concentrarse en eso cada vez que tenía un descanso, algo que no ocurría a menudo. Se concentraba en cómo sería la facultad de medicina, aunque era inevitable que, en alguna que otra ocasión, se colaran en su mente imágenes de su madre, o el sonido de su voz... o la última vez que la había visto... Y en eso pensaba cuando se tumbó en el jergón aquella noche, preguntándose qué habría opinado Consuelo de todo lo que había ocurrido en el último año. Confiaba en que, estuviera donde estuviese, observándola, se sintiera orgullosa de ella cuando se convirtiera en doctora. Sabía que lo más probable era que su madre no hubiese aprobado la decisión. Pero ¿qué otra cosa le quedaba en esos tiempos? Y ¿quién le quedaba? Ser médico era el único sueño de Annabelle, su única esperanza para una vida completamente nueva.
### 16
Nadie se percató de que Annabelle se marchó del hospital de la abadía de Royaumont, en Asnières. El día anterior ya había ido a despedirse del doctor De Bré y a darle las gracias, y también se había despedido de la jefa de enfermería. Aparte de eso, no tenía a nadie más a quien decirle adiós, salvo a Edwina, a quien vio unos instantes esa misma mañana. Se desearon buena suerte la una a la otra y dijeron que confiaban en volver a verse. Y entonces Annabelle se montó en la furgoneta que tenía que llevarla a la estación. Viajaría en tren hasta Niza, un trayecto largo y lleno de obstáculos. Todas las rutas que se hallaban demasiado cerca del frente habían sido desviadas para esquivarlo, y la mayor parte de los trenes estaban controlados por el ejército debido a la coyuntura.
Tardó un día entero, con su consiguiente noche, en llegar a Niza, y cuando por fin se encontró allí vio dos taxis delante de la estación de ferrocarril, ambos conducidos por mujeres. Se montó en uno y le dio a la conductora la dirección de la facultad de medicina. Estaba a las afueras de Niza, en una colina desde la que se contemplaba el océano, en un castillo pequeño propiedad de la familia del fundador de la escuela, el doctor Graumont. Con sus apacibles jardines y huertos alrededor, costaba creer que se estuviera librando guerra alguna en el mundo, por no hablar del gas nervioso, los cuerpos destrozados y las personas moribundas. Allí se sintió completamente protegida del mundo real. Era el lugar más apacible que había visto desde Newport y, en cierto modo, le recordó a él.
Un administrador de semblante serio le enseñó dónde estaba su habitación, le entregó unas sábanas para que se hiciera la cama y le dijo que debía presentarse en la planta inferior a las ocho en punto si quería cenar. Los estudiantes del primer curso de medicina se alojaban en el dormitorio comunitario de la residencia. Los estudiantes de cursos superiores, todos ellos hombres, contaban con habitaciones individuales. Sin embargo, como era la única mujer, le habían reservado una de esas habitaciones, un cuarto cómodo desde el que se veía el mar. En total, había cuarenta y cuatro estudiantes viviendo en el castillo, todos ellos exentos de realizar el servicio militar por uno u otro motivo. Había un joven inglés, otro escocés, dos italianos y el resto eran franceses. Annabelle era la única estadounidense. Le habían dicho que, una vez terminados sus estudios, podría ejercer la medicina en Estados Unidos si hacía un examen allí, pero no había hecho planes a tan largo plazo. Durante los siguientes seis años estaría allí, y le parecía el lugar ideal para ella. En cuanto lo vio, no le cupo la menor duda. Se sintió segura y protegida.
Se lavó la cara y las manos, se puso un vestido negro limpio, uno de los más bonitos que se había llevado, y se recogió el pelo en un discreto moño. Inmaculada, bajó a cenar puntualmente a las ocho.
Todas las noches, los universitarios se reunían en el gran salón del castillo antes de cenar. Hablaban tranquilamente, por lo general sobre temas médicos, pues todos ellos llevaban en la facultad desde el mes de septiembre. Annabelle era la intrusa que había llegado tarde y, cuando entró en la sala, todas las miradas se posaron en ella. Al cabo de un momento, los estudiantes volvieron la cabeza y continuaron charlando o fingieron no haberla visto. Se quedó anonadada ante la fría bienvenida, pero se sentó en silencio a solas hasta la hora de cenar, sin intentar irrumpir en sus conversaciones. Se percató de que la miraban de reojo, pero ninguno de los jóvenes se acercó a hablar con ella. Era como si no existiera, o como si creyeran que, si no reconocían su presencia, acabaría por desaparecer.
Un hombre viejo con un frac todavía más viejo los avisó de que era la hora de la cena, y a continuación los grupos de estudiantes se desplazaron al comedor y se sentaron repartidos en las tres largas mesas de refectorio, que parecían tan antiguas como el castillo. Todo el mobiliario estaba desgastado y raído, pero poseía una especie de decadente grandeza que resultaba muy propia de la antigua Francia.
El doctor Graumont, el director de la facultad, fue a saludarla y la invitó a sentarse a su lado. Fue increíblemente educado al presentarse, pero después dedicó la mayor parte del tiempo a charlar con el joven que tenía al otro lado, quien parecía tener unos treinta años. Comentaron una operación que habían presenciado aquel día y no hicieron ademán alguno de incluir a Annabelle en la conversación. La joven se sentía como un fantasma, invisible para todos.
En otro momento de la velada, el doctor Graumont habló con ella brevemente acerca del doctor De Bré y le preguntó cómo estaba el médico, pero la conversación no fue mucho más allá, pues al instante le deseó buenas noches e, igual que todos los demás, se marchó a su dormitorio. Ni uno solo de sus compañeros de clase se había presentado a Annabelle ni le había preguntado cómo se llamaba. Subió a su habitación sola y se sentó encima de la cama; no sabía muy bien qué hacer y había dejado de sentirse tan segura de haber tomado la decisión acertada. Esos seis años se le iban a hacer muy largos si nadie hablaba con ella en el castillo. Saltaba a la vista que no les apetecía que una mujer entrara en su círculo, así que habían decidido ignorarla por completo. De todas formas, ella no había ido a la facultad a socializar, había ido a aprender.
A la mañana siguiente se presentó en el comedor a las siete en punto, tal como le habían mandado. El desayuno era escaso debido a la guerra, y Annabelle comió muy poco. Los otros estudiantes llegaron y se marcharon sin decirle ni una sola palabra, así que se dedicó a buscar el aula, pues quería llegar con tiempo a la clase de las ocho. La facultad ocupaba todas las estancias del castillo que, gracias a ello, había podido continuar en manos de la familia propietaria, pues contribuía a su mantenimiento. Y en cuanto empezó la clase, Annabelle recordó por qué estaba allí. Era fascinante. Les hablaron de las enfermedades del riñón y les enseñaron diagramas de distintas operaciones. Además, al día siguiente iban a ir al hospital de Niza, donde observarían en directo algunas intervenciones y trabajarían con los pacientes. Se moría de ganas de ir.
Todavía estaba emocionada con la clase cuando fueron a comer, y agradeció más que nunca al doctor De Bré lo que había hecho por ella. Además, olvidando lo antipáticos que habían sido sus compañeros de clase, entabló conversación con el joven inglés e hizo un comentario sobre la clase. Él se la quedó mirando igual que si Annabelle acabara de quitarse la ropa allí mismo.
—Perdona, ¿te he molestado? —preguntó ella con inocencia.
—No recuerdo haberle dirigido la palabra —contestó él, muy maleducado, mientras la miraba por encima del hombro con unos ojos gélidos, que le dejaron claro como el agua que no le interesaban en absoluto sus comentarios.
—No, pero yo sí te he hablado —replicó ella sin inmutarse.
Se negaba a darse por vencida. En otro momento lo había oído decir que provenía de una familia con cuatro generaciones de médicos. Era evidente que estaba muy pagado de sí mismo pero, igual que ella, no era más que un estudiante de primer curso, aunque bastante mayor que Annabelle. También oyó que le mencionaba a otra persona que había estudiado en Eton y después en Cambridge, cosa que explicaba la diferencia de edad. Era evidente que se consideraba mucho mejor que Annabelle, y no tenía la menor intención de perder el tiempo hablando con ella. El hecho de que fuera tan hermosa parecía dejarlo indiferente. Es más, ponía todo su empeño en ser antipático para ponerla en evidencia.
—Me llamo Annabelle Worthingon —añadió con muy buenos modales, pues se negaba a dar su brazo a torcer. Annabelle tenía ganas de darle un porrazo en la cabeza con el plato, pero se limitó a sonreír con educación y después se dirigió al estudiante que había sentado al otro lado, con intención de presentarse. Este miró al compañero que tenía enfrente, como si esperara la aprobación del resto, y después sonrió a su pesar.
—Yo soy Marcel Bobigny —dijo él en francés, y cuando lo hizo, todos los demás lo miraron como a un traidor, y, acto seguido, continuaron comiendo.
Annabelle y Marcel charlaron un poco acerca de la clase que habían tenido esa mañana, aunque durante la mayor parte de la comida la sala estuvo inmersa en el silencio. Nadie disimulaba que no era bienvenida, e incluso el director de la facultad hizo caso omiso de la muchacha. Annabelle agarró el cuaderno y la pluma y fue directa a su siguiente clase, después de darle las gracias a Marcel por haber hablado con ella. Este hizo una reverencia cortés y Annabelle oyó que sus compinches se burlaban de él por haberle dirigido la palabra. Sin embargo, ella pasó por delante de todos con la cabeza bien alta.
—Me importa un bledo si es guapa —oyó que susurraba uno de ellos al corro de jóvenes—. Este no es sitio para ella.
Sin embargo, tenía tanto derecho como los demás a estar allí. Había pagado la matrícula del curso y estaba igual de ansiosa por convertirse en médico, probablemente incluso más. Pero no había duda de que entre todos habían acordado hacerle el vacío.
Ese trato despreciable por parte de sus compañeros se prolongó durante las siguientes cuatro semanas de clase, y en las visitas que realizaban tres veces por semana al hospital de Niza, donde asistían a clases magistrales y veían a los pacientes, se dio cuenta de que tanto los estudiantes como los profesores la observaban con especial detenimiento. Era consciente de que, si cometía un error o pronunciaba una afirmación equivocada, por nimia que fuera, su fallo sería utilizado en su contra, así que prestaba sumo cuidado a todo lo que decía. De momento, no había cometido errores visibles y los dos trabajos que había presentado sobre enfermedades del tracto urinario y del riñón habían obtenido calificaciones sobresalientes.
Y era justo cuando visitaban a los pacientes, y cuando hablaban con ellos, cuando los celos de sus compañeros de clase crecían hasta convertirse en odio. Annabelle los trataba de una manera amable y compasiva, les hacía preguntas inteligentes acerca de sus síntomas y conseguía que se sintieran cómodos con ella al instante. Los pacientes preferían con diferencia hablar con la joven, y sin duda mirarla, en lugar de a sus compañeros, y aquellos a quienes atendía más de una vez estaban encantados de volver a contar con su presencia. Sus compañeros de carrera se subían por las paredes.
—Te tomas demasiadas confianzas con los pacientes —la criticó un día el estudiante inglés, que era sistemáticamente rudo con ella.
—Qué curioso —contestó Annabelle muy tranquila—. Yo creo que tú eres demasiado seco.
—¿Qué sabrás tú? ¿Acaso habías pisado un hospital alguna vez?
—Bueno, acabo de pasar tres meses trabajando en uno cercano al frente, en Asnières, y también he colaborado como voluntaria en hospitales durante seis años, los dos últimos ayudando a inmigrantes recién llegados a Estados Unidos en la isla de Ellis, en Nueva York.
El hombre no le dijo nada más, porque no estaba dispuesto a admitir que admiraba que hubiese trabajado tres meses en Asnières. Le habían llegado rumores de que era un lugar extenuante. Marcel Bobigny se acercó a ella después de la clase y le preguntó cómo había sido la experiencia de colaborar en la abadía de Royaumont. Fue la primera conversación real que mantenía con alguien desde hacía un mes. Y estaba agradecida de tener al fin a alguien con quien hablar.
—Fue muy duro —reconoció Annabelle—. Trabajábamos turnos de dieciocho horas al día, algunas veces más. Las encargadas del hospital son mujeres, pues ese era el propósito inicial, aunque ahora, además de todas las empleadas, han aceptado también a algunos hombres recién llegados de París. Cualquier ayuda es bienvenida.
—¿Qué tipo de casos viste allí? —le preguntó el joven con interés.
Creía que los demás estudiantes se equivocaban al darle la espalda. A él le gustaba. Era una chica alegre, muy inteligente y trabajadora, y carecía de las pretensiones de algunos de ellos.
—Lo más habitual eran casos de amputaciones de miembros, muchas gangrenas, heridas causadas por explosiones, daños por gas nervioso, disentería. Más o menos lo que uno espera encontrar tan cerca del frente.
Lo dijo con sencillez, sin intención de impresionarlo o de alardear delante del estudiante.
—¿Qué te dejaban hacer?
—De vez en cuando aplicaba cloroformo antes de las operaciones. Casi siempre me encargaba de vaciar las palanganas del quirófano, aunque el jefe de cirujanos era muy amable y me enseñaba muchas cosas mientras practicaba las operaciones. El resto del tiempo lo pasaba en el pabellón de cirugía, cuidaba de los enfermos en el postoperatorio, y un par de veces llevé una ambulancia para recoger lesionados.
—No está nada mal para alguien que no tiene formación médica.
Estaba impresionado.
—Necesitaban ayuda.
Él asintió, pues le habría gustado haber ido también. Se lo dijo a Annabelle y ella sonrió. Era el único de sus compañeros de clase que había sido cordial con ella, incluso simpático. La mayor parte de ellos seguían ignorándola.
Una noche de febrero, un mes y medio después de su llegada a la facultad, todos estaban muy animados mientras cenaban, pues se habían puesto a hablar de la batalla de Verdún, que había tenido lugar unos días antes y ya había provocado una pérdida de vidas enorme para ambos bandos. Había sido un episodio atroz que los entristecía a todos, y Marcel la introdujo en la conversación. Los otros estaban tan enfrascados en la discusión que se olvidaron de hacer un mohín o prestar oídos sordos cuando ella habló.
La batalla de Verdún se convirtió en el tema de conversación principal durante la cena, hasta que dos semanas más tarde, a principios de marzo, la quinta batalla del Isonzo, en Italia, contra Austria-Hungría, tomó el relevo. La conversación saltaba continuamente de los temas médicos a la guerra. Era algo que provocaba un profundo malestar en todos los estudiantes.
Al final, el joven inglés le preguntó a Annabelle cuándo iba a intervenir Estados Unidos en la contienda. El presidente Wilson seguía asegurando que no entraría, pero era un secreto a voces que Estados Unidos proporcionaba armamento a ambos bandos, y era muy criticado por tal práctica. Annabelle no tuvo empacho en admitir que le parecía mal esa conducta, y todos le dieron la razón. Pensaba que Estados Unidos debía entrar en la guerra y desplazarse a Europa para ayudar a los Aliados. Entonces la conversación se desvió hacia el _Lusitania_ , pues todos creían que lo habían bombardeado porque llevaba un cargamento secreto de municiones, algo que nunca había sido desmentido de manera oficial. Al hablar del _Lusitania_ , sin saber cómo acabaron hablando del _Titanic_ , y en ese momento Annabelle se quedó callada y empalideció. Rupert, el inglés, se dio cuenta e hizo un comentario.
—Vaya mal trago —reconoció con una sonrisa.
—Para mí, desde luego —contestó ella en voz baja—. Mis padres y mi hermano viajaban en él —dijo, mientras toda la mesa se quedaba callada y la miraba.
—¿Consiguieron salir con vida? —preguntó uno de los estudiantes franceses, a lo que ella negó con la cabeza.
—Mi madre se montó en uno de los botes salvavidas, pero mi padre y mi hermano se hundieron con el barco.
Se produjo un coro de frases de apoyo y, con mucho tacto, Marcel redirigió la conversación hacia otros temas para intentar que ese doloroso momento le resultara menos incómodo. Le gustaba Annabelle y quería protegerla del resto de los estudiantes. Sin embargo, poco a poco los demás también iban suavizando sus modales hacia ella. Costaba mucho resistirse a la amabilidad, sencillez, inteligencia y humildad de la joven.
Dos semanas después, el barco de pasajeros francés _Sussex_ fue torpedeado, desgracia que volvió a hacer aflorar el tema bélico. Para entonces, la situación en el frente había empeorado y ya habían muerto casi cuatro millones de personas. El número de víctimas crecía por momentos. Había ocasiones en las que la guerra los distraía de sus estudios por completo y no eran capaces de hablar de otra cosa. De todas maneras, se esforzaban mucho. Ninguno de los estudiantes estaba allí para calentar la silla y, con un número tan reducido de ellos en las aulas, todos destacaban.
Sin proponérselo, en abril todos habían mejorado el trato que daban a Annabelle, y cuando llegó mayo muchos deseaban en secreto dirigirle la palabra, mantener conversaciones con ella e incluso reírse juntos. Habían aprendido a respetar sus preguntas inteligentes aunque formuladas con voz baja, y reconocían que tenía mucha mejor mano para tratar a los pacientes que ellos. Todos sus profesores se habían percatado y hacía tiempo que el doctor Graumont había escrito al doctor De Bré para confirmarle que no se había equivocado. Le dijo que Annabelle Worthington era una alumna brillante y que algún día llegaría a ser una excelente médico. Y para Annabelle, comparado con la abadía de Asnières, el hospital de Niza era increíblemente básico, aunque interesante al fin y al cabo. Además, por fin se cumplió su deseo. Habían empezado a diseccionar cadáveres, cosa que le pareció tan fascinante como siempre había creído que sería.
Las noticias sobre la guerra seguían distrayéndolos, si bien continuaron con las clases durante el verano. El 1 de julio estalló la batalla del Somme, en la que se produjo el mayor número de víctimas mortales de la guerra hasta ese momento. Al terminar el día, había sesenta mil muertos y heridos. Las cifras eran horripilantes. Y conforme avanzaba el verano, no hacían más que aumentar. Eso hacía que algunas veces costara mucho concentrarse en los estudios. La pérdida de vidas crecía sin cesar con el transcurso de la guerra, y no se vislumbraba un final a corto plazo. Para entonces Europa ya llevaba dos años en guerra.
En agosto, Annabelle intentó no pensar mucho en el aniversario de boda que habría celebrado con Josiah. Habría sido su tercer año juntos, pero ella ya llevaba once meses en Europa. Era difícil de creer. Desde que había llegado a la facultad de medicina en Niza, el tiempo había pasado volando. Hacían infinidad de cosas e intentaban aprender de cada experiencia. Cada vez trataban a los pacientes con mayor asiduidad e invertían tres días completos de su formación en prácticas en el hospital de Niza. Los heridos de guerra empezaron a llegar incluso allí, pues los soldados lesionados que no podrían regresar al frente habían sido trasladados a hospitales más próximos a su lugar de origen. Annabelle se encontró por casualidad con dos pacientes a quienes había atendido en Asnières. Se emocionaron al verla, así que ella procuraba ir a visitarlos siempre que podía.
A esas alturas, Marcel y Annabelle ya eran muy buenos amigos. Charlaban todas las noches después de cenar y a menudo estudiaban juntos. Y los otros compañeros de clase la habían aceptado por fin como a uno más. Todos tenían una buena impresión de ella, la apreciaban y respetaban. Algunos de los estudiantes se reían incluso de lo desagradables que habían sido con la muchacha al principio, y Rupert, el pomposo inglés que había sido el más antipático de todos, había ido entablando amistad con ella poco a poco. Les costaba encontrar fallos en la forma de proceder de Annabelle, y ella se esforzaba por ser simpática siempre con todos y cada uno de los alumnos. Marcel solía decir que era como la madrina del grupo.
Un día, mientras paseaban por los jardines de la facultad, después de las clases, Marcel se dirigió a Annabelle con una mirada curiosa.
—¿Por qué no se ha casado una joven tan guapa como tú? —le preguntó.
Annabelle sabía que no intentaba cortejarla, pues acababa de comprometerse con una muchacha de Niza. Era una amiga de la infancia que siempre había mantenido relación con su familia. Marcel provenía de Beaulieu, no muy lejos de allí, y solía ir de visita el fin de semana, o incluso escaparse a comer, siempre que podía. Su prometida iba a verlo a veces a la facultad y a Annabelle le caía muy bien.
—No creo que el matrimonio sea compatible con mi deseo de ser médico, ¿no te parece? —le respondió ella, desviando la pregunta. En su opinión, para una mujer no era igual que para un hombre. Una mujer precisaba mucho más sacrificio y compromiso si quería llegar a ser médico.
—¿Por qué me da la sensación de que viniste a Europa con el corazón roto? —Era un hombre inteligente y sabía leer en su mirada—. No estoy seguro de si lo que quieres es sacrificar tu vida personal por la vida profesional o tal vez, por miedo a tener una vida personal, deseas refugiarte en la medicina. Creo que puedes tener las dos cosas —le dijo con cariño mientras la miraba fijamente a los ojos.
Annabelle evitó responderle durante unos cuantos minutos y dio un mordisco a una manzana. Ese mes de mayo había cumplido veintitrés años. Era hermosa y vital, pero le aterraba que volvieran a romperle el corazón. Marcel tenía razón. La conocía al dedillo.
—Detrás de esa sonrisa y esas palabras amables —continuó el joven— se esconde algo muy triste, y no creo que sea por lo de tus padres. Las mujeres solo tienen esa mirada cuando un hombre les ha roto el corazón.
Lamentaba que algo así le hubiera ocurrido a su amiga. Ella, más que ninguna otra persona que él conociera, merecía encontrar a un hombre atento y cariñoso.
—Deberías haberte hecho adivino en lugar de médico —bromeó la joven con una sonrisa grácil, y se echó a reír.
Sin embargo, él supo, aunque ella no se lo confirmara, que estaba en lo cierto. Pero ella no tenía la menor intención de decirle que se había divorciado. No estaba dispuesta a reconocerlo delante de nadie, ni siquiera de Marcel, aun ahora que eran amigos. Le daba demasiada vergüenza.
El mes anterior había recibido una carta de su banco, en la que le informaban de que habían llegado los documentos definitivos del divorcio. Josiah y ella estaban oficialmente divorciados. En todo ese tiempo, había recibido una única carta por su parte, escrita en Navidad, para decirle que Henry y él seguían en México. Annabelle ignoraba si a esas alturas continuaban allí, pero confiaba en que estuvieran bien. Por lo que le había escrito, pudo deducir que ambos se hallaban muy enfermos. Ella le había contestado, preocupada por Josiah, pero no había vuelto a tener noticias suyas. Su carta no había obtenido respuesta.
—¿Tengo razón? —insistió Marcel.
Le caía muy bien Annabelle y, a menudo, se arrepentía de no saber más cosas sobre ella. Nunca hablaba de su infancia ni de su historia en general. Era como si no tuviera una vida anterior. Lo único que deseaba era hacer borrón y cuenta nueva y empezar otra vez en Europa. Siempre que hablaba con ella, notaba que guardaba secretos sobre su pasado.
—No importa. Lo importante es que ahora estoy aquí, con el corazón roto o no.
—¿Crees que regresarás algún día? —Siempre mostraba curiosidad.
Annabelle se quedó callada mientras cavilaba, y después le respondió con sinceridad:
—No lo sé. Allí no me queda nada, salvo una casa de verano en Rhode Island. —Los sirvientes de sus padres seguían allí, cuidando de la vivienda y confiando en que ella volviera. Annabelle escribía a Blanche de vez en cuando, pero a nadie más—. Ya no tengo familia. No veo ningún motivo para regresar.
—Seguro que tienes amigos —dijo Marcel mientras la miraba con tristeza. Aborrecía imaginársela sola. Era una persona tan cariñosa, gentil y amable que no le cabía en la cabeza que no tuviera amistades, por muy tímida que fuese—. Creciste rodeada de gente. Alguien tiene que quedarte.
Lo que dijo la hizo pensar en Hortie, y negó con la cabeza. No le quedaban amigos. Por muy buenas que fueran sus intenciones, Josiah había provocado esa ruptura. Había sido un ingenuo al pensar que hacía lo más adecuado para ella al liberarla. Lo que había conseguido era convertirla en una marginada dentro de su mundo. El único amigo que tenía ahora era Marcel.
—No. Mi vida dio un vuelco. Por eso vine aquí.
Aun con todo, no estaba segura de si iba a quedarse. En esos momentos no pertenecía a nadie ni a ningún sitio. Su única vida era la de la facultad de medicina, y así sería a lo largo de los siguientes cinco años. Su hogar era el castillo. Su única ciudad, Niza. Y los hombres con los que estudiaba eran los únicos amigos que tenía, en especial, él.
—Me alegro de que lo hicieras —se limitó a decir Marcel, pues no quería indagar demasiado ni reabrir heridas antiguas.
—Yo también.
Ella le sonrió y juntos regresaron caminando al castillo. A Marcel le asombraba que ninguno de sus compañeros de carrera se hubiera encaprichado de Annabelle de forma romántica. Pero era cierto que la joven transmitía un mensaje implícito de «No te acerques». Se había construido un muro alrededor. Marcel lo percibía, pero no sabía a qué se debía, y pensaba que era una lástima. Su actitud distante provocaba que se desperdiciara una mujer encantadora. Él creía que Annabelle merecía encontrar marido y esperaba que lo hiciera con el tiempo.
El verano en el castillo fue largo y caluroso, y lo dedicaron a estudiar y hacer prácticas en el hospital, hasta que en agosto les dieron dos semanas libres para ir a casa o marcharse de vacaciones. Annabelle fue la única estudiante que se quedó en el castillo. No tenía ningún otro sitio adonde ir. Se dedicó a dar largos paseos y a ir de compras en Niza, aunque no quedaban demasiadas cosas en las tiendas, debido a la guerra. Adquirió algunas prendas para abastecer su ropero, pues la mayor parte de lo que se había llevado era de color negro y ya había terminado el período de duelo por la muerte de su madre. Y una tarde, en la que le prestaron una vieja camioneta que tenían en la facultad, salió a dar una vuelta hasta Antibes y sus alrededores, donde encontró una antigua iglesia muy hermosa del siglo XI, y se quedó mirando las vistas de la ciudad desde lo alto. Fue una tarde perfecta, en la que disfrutó de un paisaje espectacular.
Entró a cenar en un pequeño café y regresó de noche a la escuela. Incluso el doctor Graumont se había marchado de vacaciones, así que Annabelle se quedó a solas en el castillo con las dos criadas. Fueron dos semanas muy tranquilas y se alegró cuando los otros estudiantes regresaron, en especial Marcel. Todos dijeron que se habían divertido, aunque su amigo inglés llamado Rupert, quien la había atormentado al principio, volvió desolado porque había perdido a su hermano en el frente. Varios de ellos habían perdido ya a hermanos, primos o amigos. Era un duro recordatorio de la agitación y la angustia que devoraba Europa, y que parecía interminable.
Cuando volvieron a empezar las clases en septiembre, la batalla del Somme continuaba cobrándose vidas, tal como llevaba haciendo desde hacía dos meses. Y el número de víctimas mortales crecía día tras día. Por fin, a mediados de noviembre, terminó la batalla, lo que supuso un gran alivio para todos. Durante algo más de una semana reinó la paz después de una serie de combates terrible, en la que más de un millón de hombres habían muerto o resultado heridos. Sin embargo, apenas diez días después de la tregua, los alemanes atacaron Gran Bretaña desde el aire por primera vez. Acababan de introducir un aspecto totalmente nuevo en la guerra, cosa que los aterraba a todos. Cuando llegó la Navidad, los estudiantes estaban desmoralizados por las derrotas aliadas y los continuos ataques del enemigo. Dos alumnos más habían perdido a sus hermanos en el frente. A finales de mes, el doctor Graumont los reunió en el salón de actos porque quería leerles una carta del gobierno francés. Era una llamada a todo el personal médico con formación para que prestaran sus servicios en el frente. Se los necesitaba desesperadamente en los hospitales de campaña de toda Francia. Tras leer el escrito se quedó callado, y luego dijo que ellos eran quienes debían decidir qué hacer. Les comunicó que la escuela les permitiría ir, si lo deseaban, sin que sus estudios se resintieran, y los readmitiría de forma automática en cuanto regresaran. Hacía meses que llegaban cartas de distintos hospitales, entre ellas el de un centro recién fundado por Elsie Inglis, esta vez en VillersCotterêts, al nordeste de París, más cerca del frente que Asnières y la abadía de Royaumont en la que había colaborado Annabelle. Como en los otros casos, los equipos médicos del establecimiento estaban formados únicamente por mujeres, así que Annabelle habría sido más que bienvenida allí.
Todos los estudiantes hablaron del asunto durante la cena y la conversación fue agitada. A la mañana siguiente, la mitad ya había tomado una decisión, así que fueron a ver al doctor Graumont uno por uno. Se marcharían al cabo de pocos días. Para colmo, el invierno había sido muy duro en las trincheras, y los soldados de toda Europa morían tanto por culpa de las heridas como por las enfermedades y el frío. Muchos habían decidido marcharse porque no podían hacer oídos sordos a la petición de socorro. Al final, todos salvo cuatro estudiantes decidieron ir a colaborar. Annabelle se decidió el primer día. La entristecía interrumpir sus estudios de medicina, pero sentía que, en el fondo, no le quedaba otra opción. Le habría parecido muy egoísta quedarse en la universidad.
—¿También tú nos dejas? —le preguntó el doctor Graumont con una sonrisa triste, pero no le sorprendió. A lo largo del curso anterior había llegado a apreciarla y respetarla enormemente. Algún día sería una médico excelente, y en muchos sentidos ya lo era.
—Tengo que ir —contestó ella con añoranza. Aborrecía tener que marcharse de la escuela y el castillo—. Pero volveré.
—Espero que sí —dijo él de todo corazón—. ¿Adónde vas a ir?
—Al hospital de Inglis en Villers-Cotterêts, si me aceptan.
Con la formación que habían adquirido los estudiantes, todos podían ser buenos auxiliares de medicina. Annabelle sabía mucho más que cuando había colaborado en Asnières, de modo que resultaría mucho más útil para los enfermos y heridos.
—Ten cuidado, Annabelle. Cuídate mucho. Allí te esperarán con los brazos abiertos —le aseguró el director.
—Muchas gracias —repuso ella en voz baja, y le dio un sentido abrazo.
Hizo las maletas esa misma noche y dejó dos en el castillo, pues pensó en llevarse únicamente una consigo. Al día siguiente, la mayoría de los alumnos, salvo los cuatro estudiantes que iban a quedarse, había emprendido el viaje.
Todos se abrazaron, se desearon buena suerte y se prometieron que volverían a verse. Las despedidas que le brindaron a Annabelle fueron especialmente fraternas y afectuosas, y todos le recordaron que tuviera mucho cuidado; ella les deseó lo mismo.
Marcel la acompañó al tren, pues ella se iba antes que él. Juntos caminaron por el andén, Annabelle con la pequeña maleta en la mano. Marcel era su único amigo de verdad, y había sido cordial con ella desde el principio. Aún sentía gratitud hacia él por ese gesto.
—Cuídate mucho —le dijo Marcel mientras le daba un último abrazo y la besaba en ambas mejillas—. Confío en que todos volvamos a vernos pronto —añadió con mucho convencimiento. Él tenía pensado marcharse esa misma tarde.
—Yo también.
Annabelle siguió despidiéndose con la mano hasta que dejó de ver a Marcel, quien había esperado para decirle adiós. Se lo quedó mirando hasta que desapareció de su campo de visión. Sería la última vez que lo viera con vida. Dos semanas más tarde, mientras conducía una ambulancia, pisó una mina. Fue la primera víctima de la facultad del doctor Graumont, y con él Annabelle había perdido a otro amigo.
### 17
Annabelle llegó por fin al hospital que Elsie Inglis había fundado en Villers-Cotterêts, unos cincuenta kilómetros al nordeste de París. Distaba apenas veinticinco kilómetros del frente. Si uno prestaba atención, podía oír las explosiones a lo lejos. El hospital acababa de abrir y era una iniciativa mayor y más arriesgada que la abadía de Asnières, en la que Annabelle había trabajado el año anterior. Tanto el personal como las encargadas del hospital eran mujeres, pues tal era la intención de la doctora Inglis. Sus nacionalidades representaban a muchos de los países aliados, aunque se dividían casi a partes iguales entre inglesas y francesas, mientras que Annabelle era una de las tres estadounidenses voluntarias. Esta vez le dieron una habitación en condiciones, aunque diminuta, que compartía con otra mujer. Y sus pacientes llegaban directos desde el frente. La tragedia que veían a diario era espeluznante: cuerpos despedazados, mentes destrozadas y un apabullante número de vidas agostadas.
Las conductoras de ambulancia se pasaban el día yendo y viniendo del frente, de cuyas trincheras sacaban a rastras a los soldados, mutilados, heridos o moribundos. En cada trayecto, a la conductora de la ambulancia la acompañaba una doctora o estudiante de medicina, que debía tener formación y conocimientos suficientes para realizar labores hercúleas durante el trayecto con el fin de salvar la vida de los hombres que transportaban. Si los soldados estaban tan malheridos que no podían moverlos, los dejaban en los hospitales de campaña improvisados cerca de las trincheras. Pero siempre que les era posible, trasladaban a los heridos al hospital de VillersCotterêts para operarlos y someterlos a cuidados intensivos.
Con un curso de medicina a sus espaldas, además de sus años de voluntariado, Annabelle fue asignada a la unidad de ambulancias, y le dieron el uniforme oficial de los médicos. Trabajaba dieciocho horas al día, soportaba los traqueteos del vehículo por las abruptas carreteras, y algunas veces se limitaba a coger en brazos a los hombres cuando no había nada más que pudiera hacer por ellos. Luchaba con todas sus fuerzas por salvarlos con el escaso material que tenía a su disposición y con las técnicas que había aprendido. En ocasiones, a pesar de todos sus esfuerzos, y de la carrera a toda velocidad de vuelta al hospital, los hombres estaban tan graves que no lograban sobrevivir y acababan pereciendo de camino.
Llegó a Villers-Cotterêts el día de Año Nuevo, que allí no era más que otro día laborable. Para entonces, a consecuencia de la contienda ya habían muerto seis millones de personas. Durante los dos años y medio que habían transcurrido desde el comienzo de las hostilidades, Europa se había visto diezmada y había ido perdiendo a todos sus jóvenes por culpa del monstruo que era la guerra, que los devoraba a millares. Annabelle se sentía a veces como si intentaran vaciar el océano con una taza, o peor aún, con un dedal. Había tantos cuerpos que curar, algunos de ellos en un estado lamentable, tantas mentes que jamás se recuperarían de las brutalidades que habían presenciado... Para el personal médico las cosas tampoco eran fáciles, y todas las mujeres voluntarias estaban exhaustas y terminaban rendidas al caer la noche. Sin embargo, por muy difícil que fuera, y por muy desmoralizadora que resultase la tarea, algunos días Annabelle estaba más segura que nunca de su decisión de convertirse en médico. Aunque le partía el corazón en muchos momentos, amaba su trabajo y lo desempeñaba muy bien.
En enero, el presidente Wilson trató de lograr el final de la guerra empleando la neutralidad de Estados Unidos para animar a los Aliados a concentrar sus esfuerzos en la consecución de la paz. Pero sus intentos no habían dado fruto y seguía decidido a mantener al país al margen de la confrontación. En Europa nadie comprendía cómo era posible que los estadounidenses no se unieran a las fuerzas aliadas, y en enero de 1917 nadie creía ya que continuaran ajenos al conflicto bélico durante mucho más tiempo. Y no se equivocaban.
El 1 de febrero, Alemania arremetió de nuevo sin compasión con las armas submarinas. Dos días después, Estados Unidos rompió las relaciones diplomáticas con Alemania. Al cabo de tres semanas, el presidente pidió permiso al Congreso para armar los buques mercantes en previsión de un ataque de los submarinos alemanes. El Congreso denegó el permiso, pero el 12 de marzo, por orden del ejecutivo, Wilson anunció que, a partir de ese momento, los buques mercantiles llevarían armamento. Ocho días más tarde, el 20 de marzo, su gabinete de guerra votó de forma unánime a favor de declarar la guerra a Alemania.
El presidente entregó el comunicado de guerra al Congreso el 2 de abril. Y cuatro días después, el 6 de abril, Estados Unidos declaró la guerra a Alemania. Por fin entraban en el conflicto los estadounidenses, en una coyuntura en que los malogrados Aliados de Europa los necesitaban desesperadamente. Durante las semanas y meses que siguieron, miles de jóvenes estadounidenses dejarían su hogar, se despedirían de sus familias, sus esposas y sus novias, y empezarían a recibir instrucción militar. Iban a mandarlos a la otra orilla del océano dos meses después. De la noche a la mañana, todo había dado un vuelco en su patria.
—Ya era hora —le dijo a Annabelle una de las mujeres estadounidenses que trabajaban en Villers-Cotterêts, cuando se reunieron en el comedor para cenar. Ambas habían estado desempeñando sus respectivas labores durante diecinueve horas. Tanto ella como las otras norteamericanas eran enfermeras, aunque sabía que Annabelle trabajaba de auxiliar de medicina.
—¿Estudiabas para enfermera antes de la guerra? —le preguntó con interés.
Era una hermosa joven del sur que tenía un marcado acento de Alabama. Se llamaba Georgianna y en otro tiempo había sido una belleza sureña, algo que ya no significaba nada allí, del mismo modo que la refinada educación de Annabelle en la elegante mansión familiar de Nueva York no tenía relación alguna con su vida diaria. Lo único que le había proporcionado su cuna era una formación decente, buenos modales y la posibilidad de aprender francés. El resto no importaba ya.
—El año pasado empecé a estudiar medicina en una facultad del sur de Francia —contestó Annabelle antes de tomar un sorbo de un caldo muy claro. Intentaban estirar las raciones de alimentos tanto como les era posible, por el bien del equipo médico y de los pacientes. Por lo tanto, ninguna de ellas había degustado una comida en condiciones desde hacía meses, aunque no podían quejarse. Annabelle había perdido bastante peso en los cuatro meses que llevaba en el hospital. Incluso a ella le costaba creer que ya estuvieran en abril de 1917, es decir, que llevara diecinueve meses en Francia.
Georgianna se quedó impresionada al enterarse de que su compatriota estudiaba medicina, y se pusieron a hablar de ello durante unos minutos. Ambas estaban molidas. La enfermera era una muchacha guapa con grandes ojos verdes y el pelo de un brillante color rojizo, y se rió mientras reconocía ante Annabelle que, a pesar de llevar dos años allí, hablaba un francés lamentable. No obstante, Annabelle sabía, por las referencias que había oído de ella, que a pesar de todo desempeñaba muy bien su trabajo. Jamás había conocido a tantas personas serias, competentes y dedicadas como allí. Se desvivían y lo daban todo por los demás.
—¿Crees que terminarás la carrera de medicina? —le preguntó Georgianna, y Annabelle asintió con aire pensativo.
—Espero que sí.
No se imaginaba qué podía impedir que lo hiciera, salvo la muerte.
—¿No tienes intención de regresar a casa cuando todo esto termine? —Georgianna no podía imaginarse viviendo siempre en Francia. Tenía familia en Alabama, tres hermanas más jóvenes y un hermano. Ella, en cambio, no quería volver a Nueva York. Allí no le aguardaba nada, salvo el castigo y el dolor.
—La verdad es que no. No tengo gran cosa esperándome allí. Creo que voy a quedarme.
Últimamente había pensado mucho en la cuestión y se había decidido. Todavía tenía cinco años de carrera universitaria por delante y, al terminar, deseaba buscar trabajo en París. Con suerte, tal vez incluso lograra colaborar con el doctor De Bré. Ya no había nada que la atase a Nueva York. Y si volvía tendría que estudiar un año más para poder ejercer. Estaba casi convencida de que su vida en Estados Unidos era historia. Su único futuro estaba allí. Era una vida totalmente nueva, en la que nadie conocía su pasado, ni la vergüenza de su divorcio. Al cabo de unas semanas cumpliría veinticuatro años. Y algún día, con mucho esfuerzo y un poco de suerte, sería médico. Lo único que lograría en Nueva York era ser desgraciada, aunque no tuviera la culpa de nada.
Las dos mujeres se despidieron al salir del comedor y cada una se dirigió en solitario a la correspondiente barraca, con la promesa de quedar en otro momento cuando tuvieran un día libre, cosa que, las pocas veces que se les brindaba, no solían aceptar. Annabelle no se había tomado ni un día libre desde que había llegado.
La tercera batalla de Champagne terminó en un absoluto desastre para los franceses a finales de abril y provocó una avalancha de pacientes nuevos en el hospital, algo que las mantuvo a todas muy atareadas. Annabelle no hacía más que trasladar soldados desde el frente. La única noticia alentadora que les llegó fue la victoria canadiense en la batalla de Vilma Ridge. Y debido a la enorme desmoralización entre sus filas, se produjeron varios intentos de motín entre los franceses durante las primeras semanas de mayo. También leyeron artículos acerca de la Revolución rusa: el zar había abdicado en marzo. Sin embargo, todo lo que ocurría más allá de las trincheras y del frente más próximo resultaba remoto para todas las trabajadoras de Villers-Cotterêts. Estaban demasiado involucradas en la tarea que tenían entre manos para preocuparse de mucho más.
Annabelle se olvidó por completo de su cumpleaños. Un día daba paso al siguiente y al final no sabía ni en qué día vivía. No se dio cuenta hasta una semana más tarde, cuando leyó el periódico que alguien había traído de París, de que había cumplido veinticuatro años. Un mes después, en junio, todo el mundo se emocionó al enterarse de que las primeras tropas de Estados Unidos habían desembarcado en Francia.
Fue al cabo de tres semanas, a mediados de julio, cuando un batallón de soldados norteamericanos llegó a Villers-Cotterêts y montó el campamento a las afueras de la ciudad. Una semana más tarde se les unieron las fuerzas británicas, pues todos ellos se preparaban para una ofensiva en Ypres. Tener tropas británicas y estadounidenses pululando por todas partes avivó la zona considerablemente. Se entretenían en seducir a todas las mujeres del pueblo y la policía militar no hacía más que sacarlos a rastras de los bares y de las calles, borrachos, para llevarlos de vuelta al campamento. Por lo menos, les proporcionaba un poco de distracción a las voluntarias. Además, a pesar de los inevitables soldados alborotadores, algunos eran muy simpáticos. Un día, Annabelle vio a un grupo de soldados estadounidenses que paseaban de la mano de unas chiquillas francesas, mientras ella regresaba con la ambulancia de un hospital de campaña cercano. No estaba de humor para charlar con ellos, pues el hombre que trasladaban al hospital de Villers-Cotterêts había muerto en la carretera. Sin embargo, cuando la ambulancia pasó por delante de los norteamericanos, estos gritaron y saludaron con la mano al ver dos jóvenes tan guapas unidas a la causa. Y durante un instante doloroso, Annabelle sintió el intenso anhelo de oír el acento de su país. Les devolvió el saludo y sonrió. Uno de los hombres de uniforme corrió hacia donde estaban y la joven no pudo reprimirse y dijo:
—Hey, hola.
—¿Sois de Estados Unidos? —preguntó él asombrado, y la conductora de la ambulancia se detuvo y sonrió. Le parecía que el soldado era guapo. Ella era francesa.
—Sí —contestó Annabelle, con aspecto fatigado.
—¿Cuándo habéis llegado? Creía que no mandaban a las enfermeras hasta el mes que viene.
Habían tardado más en organizar las unidades de mujeres voluntarias que a los hombres llamados a filas.
Annabelle se rió ante su pregunta. Notó el acento de Boston en su voz y, tenía que admitirlo, se alegró de oírlo. Le recordaba a su hogar.
—Ya llevo dos años aquí —anunció la joven con una sonrisa de oreja a oreja—. Chicos, llegáis tarde.
—¡Ya lo creo! Pero vamos a echar a patadas a esos alemanuchos y los meteremos en el redil. Han reservado lo mejor para el final.
Parecía un crío y, como buen bostoniano, era tan irlandés como el que más, cosa que le recordó sus visitas a Boston y los veranos en Newport. De pronto, Annabelle sintió nostalgia de su hogar por primera o segunda vez en veintidós meses. Ni siquiera recordaba la última ocasión en que se había sentido así.
—¿De dónde eres? —le preguntó el soldado, mientras uno de sus amigos charlaba con la conductora de la ambulancia, aunque ambas sabían que tenían que regresar al hospital. No estaba bien quedarse allí de cháchara con ellos cuando transportaban a un hombre muerto en la parte trasera. De todas formas, había chicas que hacían cosas mucho peores. Llegaba un punto en que los horrores de la guerra ya no te sobresaltaban tanto como al principio.
—De Nueva York —contestó Annabelle en voz baja.
—Yo soy de Boston —dijo él, y cuando lo hizo, ella percibió el alcohol que desprendía su aliento.
En cuanto salían del campamento militar en el que se alojaban, la mayoría de ellos bebía muchísimo. Tenían motivos para hacerlo. Bebían y perseguían a cualquier chica que se cruzara en su camino.
—Ya me había dado cuenta —dijo ella refiriéndose a su acento de Boston, mientras le hacía una señal a su compañera para que pusiera el motor en marcha—. Buena suerte —le deseó a él y al resto de los soldados.
—¡Para vosotras también! —contestó el joven dando un paso atrás.
Mientras la ambulancia regresaba al hospital, la invadió una oleada de nostalgia hacia su país de origen; nunca había añorado tanto su hogar como en ese momento. Echaba de menos todas las cosas familiares que no había visto o en las que no se había permitido pensar durante dos años.
Suspiró cuando entre las dos trasladaron hasta la morgue, en una camilla, el cuerpo del soldado fallecido. Lo enterrarían en la colina con innumerables hombres más y después se lo notificarían a su familia. No había forma de devolver los cadáveres a sus casas. Eran demasiados. Y los cementerios improvisados cubrían ahora el paisaje.
Sin quitarse de la cabeza a los estadounidenses que había visto por la tarde, Annabelle salió a dar un paseo esa noche cuando terminó el turno de trabajo, antes de regresar a su habitación. Habían perdido a todos los hombres que habían recogido esa jornada. Era deprimente y seguía entristeciéndola aunque, por desgracia, ocurría con frecuencia. Todos los soldados eran tan jóvenes..., muchos de ellos más jóvenes incluso que ella. Y no solo eso, también muchas de las enfermeras eran más jóvenes que Annabelle. A sus veinticuatro años, con un curso de medicina a sus espaldas, ya no se sentía una jovencita. Había pasado por demasiados malos tragos a lo largo de los últimos años y había visto demasiado sufrimiento.
Emprendió el camino de vuelta después del paseo. Deambulaba sin prisa no muy lejos de las barracas, pensando en la vida que había dejado atrás en Estados Unidos, con la cabeza gacha. Pasaba de la medianoche y había estado trabajando desde las seis de la mañana. Estaba cansada y no prestaba mucha atención a lo que la rodeaba, así que dio un respingo cuando oyó una voz británica detrás de ella.
—Hola, guapa —dijo un joven zalamero—. ¿Qué haces aquí fuera tan sola?
Annabelle se dio la vuelta y vio a un oficial británico paseando por el mismo camino que ella. Era evidente que había estado bebiendo con sus amigos, a quienes acabaría de dejar en algún bar. Imponía con su uniforme, aunque parecía bastante borracho. Era un muchacho apuesto, más o menos de su edad, y no le dio miedo, menos aún cuando vio que se trataba de un oficial. A lo largo de los últimos dos años había visto a muchos hombres ebrios y siempre había sabido cómo mantenerlos a raya.
—Creo que necesita que lo lleven a casa —advirtió Annabelle con una sonrisa natural—. Vaya en esa dirección. —Y señaló uno de los edificios de la administración en los que estaban acostumbrados a lidiar con esa clase de situaciones, pues ocurrían con frecuencia. Al fin y al cabo, estaban en tiempos de guerra y en el hospital trataban con miles de hombres al día, muchos de ellos con ganas de juerga por la noche—. Alguien lo acompañará al campamento militar.
Teniendo en cuenta que se trataba de un oficial, nadie haría preguntas. Algunas veces les ponían las cosas un poco más complicadas cuando los alborotadores eran soldados rasos. Sin embargo, los oficiales siempre eran tratados con el respeto que merecía su rango. Por los galones de su uniforme vio que era un teniente, y por su acento supo que se trataba de un aristócrata. Eso no impedía que fuera tan baboso como cualquier otro hombre cuando estaba borracho y que se tambaleara ligeramente mientras la contemplaba.
—No quiero volver al campamento —protestó como un niño testarudo—. Preferiría irme a casa contigo. ¿Qué me dices? ¿Te apetece que vayamos a tomar un trago? Además, ¿tú qué eres? ¿Enfermera?
La miraba por encima del hombro con cierta altivez, a la par que intentaba enfocarla con los ojos vidriosos.
—Soy médico, y tengo la sensación de que, si no se acuesta enseguida, usted va a terminar necesitando los cuidados de alguien como yo.
Daba la impresión de que el hombre fuera a desplomarse en cualquier momento.
—Una idea fantástica. ¿Por qué no te acuestas conmigo?
—No me refería a eso.
Annabelle lo miró con frialdad, preguntándose si lo más acertado sería alejarse de él y dejarlo allí solo. No había nadie más en las inmediaciones, aunque no estaban lejos de las barracas. A esas horas, todas las demás voluntarias se habían ido a dormir, salvo las que tenían turno de noche en las ambulancias o en los pabellones del hospital.
—Pero, vamos a ver, ¿quién te crees que eres? —preguntó el oficial mientras alargaba la mano para agarrarla, y Annabelle retrocedió un paso. Él se tambaleó y estuvo a punto de caerse, y cuando se reincorporó, su semblante parecía airado—. No eres nadie, eso es lo que eres... —le espetó, perdiendo todos los modales de repente—. Mi padre es el conde de Winshire. Y yo soy lord Harry Winshire. Soy vizconde —dijo con grandilocuencia, aunque arrastrando las palabras.
—Es bueno saberlo, señor lord —dijo ella con educación, para responder a su rango y a su título nobiliario—. Pero le aconsejo que vuelva al campamento antes de que termine mal. Yo regreso a las barracas. Buenas noches.
—¡Puta! —la insultó como si le escupiera con la palabra, y Annabelle lo dejó atrás con paso garboso.
La conversación ya había durado demasiado y no quería demorarse más. Saltaba a la vista que estaba borracho como una cuba y se iba poniendo cada vez más insolente por culpa de las grandes cantidades de alcohol que había ingerido. Annabelle no le tenía miedo, pues había salido de cosas peores, pero no quería tentar a la suerte. Sin embargo, antes de que pudiera dar un solo paso más por el camino solitario, él la agarró con fuerza y la obligó a darse la vuelta de forma violenta, atrapándola entre sus brazos e intentando besarla. Ella lo apartó con firmeza e hizo lo posible por zafarse del oficial. Era sorprendentemente fuerte a pesar de estar ebrio.
—¡Basta ya! —gritó ella con seguridad. Aunque lo disimuló, la abrumaba la fuerza de él y la firmeza de sus brazos.
De repente se dio cuenta de que no podría escapar de sus garras. El teniente le cubrió la boca con una mano y con la otra la arrastró a una puerta oscura que había en una de las barracas cercanas. No había nadie a la vista, y le tapaba la boca con tanta fuerza que Annabelle ni siquiera podía gritar. Le mordió los dedos, pero eso no lo detuvo, y peleó como un gato enfurecido, mientras él la lanzaba al suelo y se arrojaba encima de ella con todo su peso. La dejó semiinconsciente al tirarla al suelo, y con la mano que no le tapaba la boca, le subió la falda y le bajó la ropa interior. Annabelle era incapaz de creer lo que le estaba pasando y empleó todas sus fuerzas para resistirse, pero era una mujer menuda y él un hombre alto y corpulento. Además, lo había invadido la rabia y el alcohol, y estaba dispuesto a dominarla por las buenas o por las malas. Ella lo había enojado con su desplante y ahora se lo iba a hacer pagar a la fuerza. Lo único que veía era la furia negra en los ojos del soldado mientras continuaba agarrándola y empujándola contra el suelo. En ningún momento le quitó la mano de la boca, así que apenas podía emitir sonidos guturales que nadie oyó.
La noche estaba en calma, salvo por las risas de las mujeres y los gritos ebrios de los hombres que salían de las tabernas. Los gritos amortiguados de Annabelle eran tan flojos que no llegaban a oídos de nadie, y sus ojos reflejaban el terror que sentía. Para entonces él se había desabrochado los pantalones con la mano libre y Annabelle notaba su erección pegada al cuerpo. Lo que Josiah no había sido capaz de arrebatarle en sus dos años de matrimonio iba a quitárselo por la fuerza aquel desconocido borracho. Hizo todo lo que pudo para detenerlo, pero fue en vano. El oficial le abrió las piernas violentamente con las suyas, y en un instante se le metió dentro y empezó a empujar y a gemir como un animal mientras ella intentaba forcejear, pero él la aprisionaba contra el suelo, y cada vez que embestía para introducirse más, ella cerraba los ojos por el dolor, y él seguía aprisionándole la espalda contra el pavimento. Todo acabó en un momento, el hombre soltó un grito al eyacular y entonces la apartó de él tirándola como una muñeca vieja. Ni siquiera entonces consiguió Annabelle chillar ni emitir sonido alguno. Estaba demasiado aterrada. Se dio la vuelta, vomitó y se atragantó entre sollozos. Él se puso de pie, se abrochó los pantalones y la miró con petulancia.
—Si le cuentas a alguien lo que ha pasado, vengo y te mato. Te encontraré. Y será tu palabra contra la mía.
Sabía que lo más probable fuera que hablase en serio: él era un oficial del ejército y no solo de alta cuna sino, en teoría, un vizconde. Independientemente de lo que Annabelle dijera o hiciera, nadie se atrevería a poner en entredicho al teniente, y mucho menos a castigarlo por un incidente como ese. Para él no significaba nada, mientras que para ella, la virtud que había conservado toda su vida, que había mantenido aun después de estar dos años casada con un hombre a quien amaba, le había sido arrebatada y tirada como si fuera un despojo, que era justo como la había tratado él. Annabelle se recolocó la falda mientras él empezaba a caminar. Se quedó un rato más sentada en el peldaño de la puerta contigua a donde la había tirado, llorando, hasta que al final se puso de pie algo mareada. Además de violarla, le había golpeado la cabeza contra el escalón de piedra.
Aún aturdida, se dirigió hacia las barracas y se detuvo una vez más a vomitar, dando gracias de que nadie la viera. Tenía ganas de esconderse en un rincón y morirse, pues sabía que jamás olvidaría el rostro de aquel hombre ni las ansias asesinas que desprendían sus ojos mientras la forzaba. Él se desvaneció en la noche y ella acabó de recorrer la distancia hasta su alojamiento casi a gatas, y se metió en el cuarto de baño comunitario, aliviada de no encontrarse a nadie allí. Se limpió lo mejor que pudo. Tenía sangre entre las piernas y en la falda, pues era virgen, algo que no había importado lo más mínimo a su agresor; no era más que una puta a la que se había beneficiado después de una noche de juerga. Y sentía un temblor horroroso entre las piernas, que acompasaba el dolor de espalda y de cabeza, ocasionado por la contusión fruto del impacto contra el peldaño de piedra. Sin embargo, todo eso no era nada en comparación con el dolor de su corazón.
Y él tenía razón, si Annabelle intentaba contárselo a alguien, nadie la escucharía ni la tomaría en serio. Casi a diario había chicas que aseguraban que los soldados las habían violado, y nadie hacía nada para solucionarlo. Si insistían mucho y se lo contaban a las autoridades o al tribunal militar, solo conseguían que las humillaran y repudiaran, y nadie creía su versión. Al instante las acusaban de ser unas rameras que habían incitado a sus atacantes. Además, si Annabelle alegaba que quien había cometido el crimen era un lord británico, se reirían de ella en cualquier oficina militar. Y no solo eso: estaban en tiempos de guerra, así que el hecho de que una estudiante de medicina fuera violada por un teniente británico era una de las preocupaciones más insignificantes que tenía la gente. Lo único que podía hacer en esos momentos era rezar para no quedarse embarazada. No podía imaginarse un destino más cruel que ese. Cuando se metió en la cama y repasó mentalmente lo ocurrido, no dejó de repetirse que nada ni nadie podía ser tan cruel como había sido el vizconde con ella. Sin poder evitarlo, tumbada entre sollozos, empezó a pensar en Josiah. Su único deseo había sido compartir la vida con él y engendrar sus hijos. Y, en lugar de eso, aquel desgraciado oficial había convertido un acto de amor en una farsa y la había violado. Y lo peor de todo era que no había absolutamente nada que ella pudiera hacer para remediarlo, salvo intentar olvidar.
### 18
En septiembre, los alemanes tenían acorralados a los rusos. Y en Villers-Cotterêts, Annabelle sentía náuseas a diario. Había ocurrido lo peor. No había tenido la menstruación desde julio y sabía que estaba embarazada. La situación la superaba. No había nadie a quien pudiera contárselo, ni tenía forma de interrumpirlo. La espalda, la cabeza y otras partes de su cuerpo habían tardado semanas en dejar de dolerle, pero las secuelas psicológicas de lo que le había hecho aquel hombre la acompañarían siempre. Se le ocurrió buscar algún sitio donde le provocaran un aborto, pero no sabía a quién preguntar; además, conocía muy bien los peligros que eso comportaba. Durante el tiempo que llevaba en el hospital, dos de las enfermeras habían muerto mientras intentaban abortar. Annabelle no se atrevía a correr ese riesgo. Habría preferido suicidarse directamente, pero tampoco tenía coraje suficiente para hacerlo. Y, desde luego, no deseaba alumbrar al hijo de ese monstruo. Si sus cálculos no fallaban, saldría de cuentas a finales de abril, y tendría que marcharse del hospital en cuanto el embarazado fuera evidente. Por suerte, de momento no se le notaba. Así que se volcó en su trabajo más que nunca: transportaba heridos y material pesado, daba botes en la ambulancia con los socavones de las carreteras maltrechas... Rezaba para que la naturaleza tuviera compasión de ella y le provocara un aborto natural, pero conforme pasaban las semanas se fue haciendo a la idea de que no sería así. Y cuando empezó a ensanchársele la cintura y el cuerpo, hurtó vendas de lino del quirófano y se vendó el torso para comprimirlo al máximo. Apenas podía respirar, pero estaba decidida a seguir trabajando mientras fuera capaz. No tenía ni idea de adónde podría ir cuando tuviera que marcharse del hospital.
En Navidad seguía sin notársele la barriga, pero para entonces Annabelle ya percibía los movimientos del bebé dentro de su cuerpo. Intentaba resistirse a sus encantos y se repetía que tenía mil motivos para aborrecer a esa criatura, pero no podía. El niño era tan inocente como ella, aunque Annabelle odiara al padre. Pensó en localizarlo para contarle lo que había ocurrido y obligarle a tomar responsabilidades, pero sabía que, teniendo en cuenta lo que había visto aquella noche, el oficial se limitaría a negarlo. Y ¿quién sabía a cuántas mujeres había violado antes que a ella, o después? Annabelle no era más que un resto de un naufragio que había pasado rozándolo en el mar del conflicto bélico, y el teniente no tendría reparos en rechazarla como había hecho aquella noche, igual que a su bebé. No tenía a quién acudir, pues no era más que una mujer con un hijo ilegítimo en tiempos de guerra y a nadie le importaría que la hubieran violado o no.
En enero continuaba trabajando. Ya estaba embarazada de seis meses y procuraba cubrirse la creciente barriga con el delantal. A simple vista, apenas abultaba, porque seguía aprisionándola con vendas tirantes, y entre la preocupación y los escasos alimentos a su alcance, apenas comía. No había ganado peso desde la concepción; es más, tal vez hubiera adelgazado un poco. Estaba sumida en una profunda depresión desde el mes de julio, cuando había ocurrido aquello. Y aún no se lo había contado a nadie.
Hasta que un día helador y lluvioso de finales de ese mes, mientras estaba trabajando en el pabellón quirúrgico una tarde para cubrir el turno de otra voluntaria, oyó a dos hombres que hablaban. Ambos eran británicos, uno de ellos oficial y el otro sargento. Los dos habían perdido alguna extremidad en las trincheras durante la sangrienta batalla más reciente. Y Annabelle se quedó petrificada en el sitio cuando oyó que mencionaban a un tal Harry. Al principio no supo por qué, podría haberse tratado de cualquier hombre, pero al instante el oficial dijo que era una auténtica lástima que Harry Winshire hubiera muerto. Hablaron de lo buen hombre que era y de lo mucho que lo echarían de menos. A Annabelle le entraron ganas de darse la vuelta y gritarles que no era un buen hombre, sino un monstruo. Salió a trompicones del pabellón y se quedó temblando en el quicio de la puerta. Intentó tomar una bocanada de aire frío, pues se sentía como si alguien la estrangulara. No solo la había violado, sino que ahora había muerto. Su hijo no tendría padre; es más, nunca lo había tenido. A fin de cuentas, sabía que probablemente fuera lo mejor y que el oficial se lo merecía, pero mientras la magnitud de todo lo que le estaba ocurriendo volvió a apoderarse de ella, de pronto se vio tan sobrecogida por un sentimiento de terror puro que empezó a tambalearse, mecida como un sauce llorón con la brisa, y se desmayó en el barro que la rodeaba. Dos enfermeras vieron cómo se caía al suelo y fueron corriendo a socorrerla, mientras uno de los cirujanos que salía entonces del edificio se detuvo y se arrodilló a su lado. Como era lógico, todos tenían un miedo atroz al cólera, pero cuando la tocaron comprobaron que no tenía fiebre. Sospechaban que había sido culpa del exceso de trabajo y la falta de comida o de sueño, unas penurias que todos ellos llevaban años soportando.
El médico ayudó a las enfermeras a introducirla en el pabellón y Annabelle recuperó el conocimiento justo cuando la subían a una camilla. Estaba empapada de sudor, tenía el pelo aplastado contra la cara por la lluvia y el delantal pegado al cuerpo. Se deshizo en disculpas por haber montado semejante alboroto e intentó levantarse y escapar. Pero en el momento en que se incorporó, volvió a desmayarse, y esta vez el médico empujó la camilla hasta una consulta pequeña y cerró la puerta. No la conocía mucho, pero la había visto varias veces por allí.
En voz baja le preguntó si padecía disentería, pero ella insistió en que estaba bien y le contó que llevaba trabajando desde primera hora de la mañana y no había comido nada desde el día anterior. Annabelle intentó sonreírle con simpatía, pero el médico no se lo tragó. Tenía la cara del mismo color que el delantal. Le preguntó cómo se llamaba y ella se lo dijo.
—Señorita Worthington, tengo la impresión de que sufre fatiga de combate. A lo mejor le convendría salir de aquí unos días e intentar recuperarse. —Ninguno de ellos se había tomado un descanso desde hacía meses, y Annabelle no deseaba hacerlo, pero sabía que sus días en el hospital estaban contados. La barriga le crecía de manera exponencial y cada vez le costaba más esconderla, por mucho que se apretase las vendas—. ¿Hay algo más que quiera contarme relativo a su salud? —le preguntó el médico con aspecto preocupado.
Lo último que necesitaban era que el personal médico fuera propagando enfermedades contagiosas o desencadenara una epidemia, o sencillamente que muriera por exceso de trabajo y alguna enfermedad escondida. Todos estaban tan comprometidos con la causa que muchas enfermeras y médicos ocultaban si se ponían enfermos. El cirujano tenía miedo de que fuera el caso de Annabelle. Tenía un aspecto demacrado.
Ella intentó negar con la cabeza, pero él vio que tenía los ojos llenos de lágrimas.
—Estoy bien, de verdad —insistió la joven.
—Sí, tan bien que acaba de desmayarse dos veces —repuso él con cariño.
Tenía la sensación de que había algo más, pero ella no estaba dispuesta a contárselo, y parecía igual de malnutrida que muchas otras voluntarias. Le pidió que se tumbara en la camilla para que pudiera hacerle una palpación con la ropa puesta pero, en cuanto se tumbó, vio el leve bulto que surgía de su barriga y la miró a los ojos. Incluso le colocó las manos con delicadeza encima del vientre y notó la hinchazón que Annabelle había ocultado con tanta determinación durante todos esos meses, y al instante supo de qué se trataba. No era la primera joven que se quedaba embarazada de un soldado en tiempos de guerra. Mientras la miraba, esta empezó a llorar.
—Creo que esto lo explica todo —dijo el médico a la vez que la joven se sentaba, tomaba un pañuelo y se sonaba la nariz. Se moría de vergüenza, y se sentía desesperada—. ¿Cuándo sale de cuentas?
Ella estuvo a punto de atragantarse con sus palabras, y sintió ganas de contarle cómo había ocurrido, pero no se atrevía. La verdad era horrorosa y seguramente él, como cualquier otra persona, la culparía a ella, o nunca la creería. Estaba segura de que ocurriría eso porque lo había visto en otras ocasiones. Había mujeres que decían que las habían violado cuando en realidad habían tenido una aventura extramatrimonial. ¿Por qué iba a creerla precisamente a ella aquel médico? Así pues, igual que había salvaguardado el secreto de Josiah para protegerlo cuando él la había abandonado, ahora iba a guardar el secreto del vizconde Winshire. Aunque la que pagara el precio de todo eso fuera ella.
—En abril —contestó con desesperación.
—Ha logrado ocultarlo durante mucho tiempo.
Le desató el delantal, deshizo las vendas que le cubrían el vientre y le levantó la blusa. Se quedó horrorizado al ver lo fuerte que se había apretado el vendaje, y era evidente que llevaba varios meses así.
—Es un milagro que pueda respirar.
Le iba mucho más ceñido que cualquier corsé: una crueldad tanto para la madre como para el hijo.
—No puedo... —se lamentó ella entre sollozos.
—Tiene que dejar de trabajar ahora mismo —le indicó el médico, aunque Annabelle ya lo sabía—. ¿Y el padre? —preguntó con delicadeza.
—Muerto —susurró ella—. Acabo de enterarme hoy.
No le dijo que odiaba a Harry y que se alegraba de que lo hubieran matado. Se lo merecía. Sabía que el médico se habría quedado anonadado de haberlo oído.
—Ya. Y ¿cuándo piensa volver a casa?
—No puedo volver —se limitó a decir la joven, por motivos que el médico no podía ni imaginar. Ya no era bien recibida en Nueva York ni en Newport, y regresar embarazada solo habría servido para acabar de hundirla para siempre.
—Pues tendrá que encontrar un lugar en el que vivir. ¿Quiere que la ayude a buscar alguna familia con la que pueda alojarse? A lo mejor puede echarles una mano cuidando de sus hijos.
Annabelle negó con la cabeza. Le había dado muchas vueltas al tema durante las últimas semanas, mientras le crecía la barriga. Tampoco podía regresar a la facultad de medicina; por lo menos de momento. De hecho, el único lugar que le venía a la cabeza era la zona que rodeaba Antibes, cerca de la iglesia antigua, donde se había refugiado algunas veces cuando se tomaba un respiro entre clase y clase. Tal vez encontrara una casita modesta allí en la que poder cobijarse hasta que el niño naciera y entonces, o bien volvería al frente o bien retomaría los estudios. Aunque le costaba imaginarse volviendo al frente con un bebé, y tampoco tenía a nadie con quien dejarlo. Le quedaban muchos cabos por atar. De todas formas, rechazó el ofrecimiento del médico. Quería solucionar las cosas por sí misma. Y él no podía saber que ella poseía una situación económica acomodada y que tenía medios para alquilar o comprar una casa si lo deseaba.
—Muchas gracias, me las arreglaré —respondió con tristeza mientras él la ayudaba a bajar de la camilla.
—No espere mucho —le aconsejó. Todavía intentaba asimilar cómo había conseguido esconder el embarazo durante seis meses.
—No, tranquilo —le prometió—. Gracias de nuevo —añadió Annabelle con lágrimas en los ojos mientras él le daba una palmadita en la espalda para darle ánimos. Ambos salieron de la consulta. Las dos jóvenes enfermeras estaban esperando fuera, para ver qué tal se encontraba.
—Está bien —les dijo el médico con una sonrisa—. Aquí todo el mundo trabaja demasiado. Le he recomendado que se tome un descanso antes de que pille el cólera y propague una epidemia.
Les sonrió a todas para dar más fuerza a sus palabras y, tras mirar a Annabelle con ojos cargados de intención, se marchó. Las otras dos mujeres la acompañaron a su habitación y ella se tomó el resto de la tarde libre.
Se tumbó en la cama y empezó a pensar. El médico tenía razón. Pronto tendría que marcharse, y lo sabía. Debía hacerlo antes de que se enteraran todos y volvieran a repudiarla por algo que no era en absoluto culpa suya.
Annabelle consiguió aguantar en Villers-Cotterêts hasta el 1 de febrero y entonces, muy a su pesar, dijo que debía marcharse. Le contó a su supervisora que iba a retomar sus estudios en la facultad de medicina de Niza. Nadie podía reprochárselo. Llevaba allí catorce meses y se sentía una traidora por huir de esa forma, pero no le quedaba otra opción.
El día en que se despidió del hospital y de las personas con quienes había trabajado fue muy triste para ella. Se montó en el tren a Niza, adonde tardó dos días en llegar, pues muchos trenes habían sido desviados y tenían que esperar largo y tendido entre estación y estación para permitir que los vehículos militares los adelantaran, ya que eran los que transportaban las provisiones para el frente.
Lo primero que hizo cuando llegó a Niza fue entrar en una joyería pequeña y comprar una alianza de oro. Se la puso en el dedo anular y el joyero la felicitó. Era un anciano muy amable, que le deseó que fuese muy feliz. Annabelle salió de la tienda llorando en silencio. Había inventado una historia plausible para su situación: era una viuda de guerra, cuyo marido había sido asesinado en Ypres. No había motivos para que la gente no la creyera. Parecía respetable y, a esas alturas, el país estaba repleto de viudas, muchas de ellas con bebés que habían nacido después de la muerte de sus progenitores. Annabelle no era más que otra víctima en un mar de pérdidas y tragedias provocadas por la guerra.
Se registró en un hotelito de Niza y se compró varios vestidos negros de tallas más grandes. Le sorprendió mucho constatar que, ahora que ya no llevaba las vendas que la constreñían, tenía la barriga sorprendentemente voluminosa. No podía compararse con Hortie, por supuesto, pero saltaba a la vista que iba a tener un hijo, y ahora ya no había razones para ocultarlo. Con un anillo de boda en el dedo y el atuendo negro propio de una viuda, había recuperado el aspecto de mujer respetable, que es lo que era, y la tristeza que reflejaban sus ojos era más que real.
Le habría gustado ir a la facultad de medicina para visitar al doctor Graumont, pero no se veía con ánimos de hacerlo. Más adelante, se presentaría con el bebé en brazos y contaría la historia del hombre con quien se había casado antes de que lo mataran en combate. Pero, de momento, todo le resultaba aún muy reciente. No se sentía preparada para enfrentarse a nadie hasta haber dado a luz al bebé. Y tampoco estaba muy segura todavía de cómo podría explicar que no había cambiado de apellido, como era costumbre. Ya se le ocurriría algo. Por el momento, lo primordial era encontrar un lugar en el que vivir, así que uno de esos días regresó a Antibes y se acercó a la pequeña iglesia que tanto admiraba. Era una capilla de pescadores desde la que se veía perfectamente el puerto y los Alpes Marítimos. Justo antes de salir de la iglesia, preguntó a la sacristana si conocía alguna casa libre en la zona, a ser posible de alquiler. Pero la mujer sacudió la cabeza y la inclinó un poco, como si reflexionara.
—Me parece que no —contestó con un marcado acento del sur de Francia. Para entonces, el francés que hablaba Annabelle era tan fluido que nadie habría sospechado que no provenía de París, o de cualquier otra ciudad del norte del país—. Había una familia que vivía aquí antes de la guerra. Regresaron a Lyon, pero sus dos hijos murieron en combate. No han vuelto desde entonces y dudo que vuelvan a acercarse. A sus chicos les encantaba esto. Les rompería el corazón.
Le indicó a Annabelle dónde estaba la casa. Fue andando desde la iglesia y vio que se trataba de una preciosa casita de campo, con aspecto de residencia de verano. Había un hombre de edad avanzada cuidando de las tierras, que la miró cuando se dirigió a él y le preguntó si había posibilidades de que la casa estuviera en alquiler. El jardinero dijo que lo dudaba, pero que estaría encantado de escribir a los propietarios para preguntarles. Le advirtió que todos los muebles y pertenencias seguían en la casa, por si eso le resultaba un problema. Ella le aseguró que no le importaba, es más, lo prefería así.
Él se dio cuenta de que le faltaba poco para dar a luz, pues para entonces ya estaba de siete meses, y también se percató de que era viuda. Annabelle le dijo que estaba dispuesta a alquilarla el tiempo que la familia prefiriera, tal vez hasta finales de año. Confiaba en poder regresar a la universidad para cuando empezara el trimestre de otoño, o en enero como muy tarde. En septiembre su hijo tendría cinco meses y ella podría retomar los estudios de medicina, eso si conseguía encontrar a alguien que cuidara de él mientras tanto. A lo mejor incluso podía ir y venir a diario suponiendo que tuviera un vehículo para los desplazamientos. Dejó el nombre y la dirección del hotel, y el encargado de la casa le dijo que se pondría en contacto con ella cuando tuviera noticias de los propietarios, en un sentido o en otro. Annabelle confiaba en haberle dado suficiente pena para que presionara a los dueños con el fin de que le alquilaran la casa.
Mientras regresaba a Niza, se le ocurrió que podía quedarse un tiempo más en el hotel si hacía falta; aunque no era el entorno ideal para un bebé, por lo menos estaba limpio y aseado. Lo más adecuado en su situación sería vivir en una casa pero, si no encontraba ninguna, se quedaría donde estaba.
Durante las semanas siguientes se dedicó a pasear por Niza. Caminaba por la playa, comía lo mejor que podía y dormía mucho. A través del hospital localizó a un médico y fue a verlo para contarle la historia inventada de que era una viuda de guerra. El hombre fue amable y comprensivo, y Annabelle le dijo que le gustaría dar a luz en su domicilio. No quería correr el riesgo de toparse con alguno de los médicos con quienes había trabajado en el hospital durante las prácticas de la universidad. No le contó los motivos, pero insistió en que prefería dar a luz en casa.
Un día de marzo, al regresar de un paseo, se encontró con un recado de Gaston, el cuidador de la casa de Antibes. El hombre quería que fuese a verlo, cosa que hizo. Tenía buenas noticias para ella. Los propietarios habían sentido lástima por Annabelle y se alegraban de poder ayudarla alquilándole la casa. Incluso tal vez estuvieran interesados en vendérsela más adelante, aunque todavía no lo habían decidido. Tal como sospechaba, le dijeron que tenían demasiados recuerdos de sus hijos allí y les resultaba increíblemente triste regresar. Por el momento, deseaban alquilársela durante seis meses; ya decidirían qué hacer una vez pasado ese período. El jardinero y cuidador se ofreció a enseñarle las dependencias, y la joven se quedó encantada con lo que vio. Había un dormitorio principal muy soleado de proporciones bastante amplias, y dos habitaciones individuales más pequeñas cerca de él. Los tres dormitorios compartían un solo lavabo, cosa que no le importó. Las baldosas del cuarto de baño eran antiguas y había una bañera enorme que le llamó mucho la atención. En la planta baja había un salón-comedor y una galería acristalada pequeña que daba a un porche. Era del tamaño perfecto para ella y su hijo, e incluso podría contratar a una niñera que la ayudara a cuidar del bebé más adelante. De momento, lo único que deseaba era estar sola.
Escribió una carta de agradecimiento a los dueños de la casa y les dijo que indicaría al banco que hiciera la transferencia necesaria. Gaston estaba emocionado y le dio la enhorabuena. Le parecía fantástico volver a tener vida dentro de la casa, y su mujer estaría encantada de ir a limpiar para ella y, tal vez, ayudarla a cuidar del recién nacido. Annabelle le dio las gracias y se marchó, y esa misma tarde fue a un banco de Niza. Se presentó ante el director de la oficina y le pidió que mandara un telegrama de su parte al banco de Estados Unidos, para informar de dónde se hallaba. Lo único que les hacía falta saber era adónde transferirle el dinero, pues había cerrado la cuenta que tenía en Villers-Cotterêts antes de marcharse del hospital. Sus empleados de Nueva York no tenían ni idea de por qué se encontraba en Niza ni de lo que estaba a punto de ocurrir allí, y Annabelle no pudo evitar preguntarse cuántos hijos más habría tenido Hortie para entonces. Seguía echando mucho de menos a su amiga de la infancia. Por grande que hubiera sido su traición hacia ella, Annabelle sabía que lo había hecho por debilidad. Aquello no había impedido que continuara preocupándose por ella, aunque jamás volvieran a ser amigas. Aun suponiendo que regresara algún día a Estados Unidos, habían ocurrido demasiadas cosas en el entreacto para retomar el pasado.
Annabelle se instaló en la casa ubicada en el cabo de Antibes el 4 de abril. El médico dijo que el niño podía nacer en cuestión de días, aunque no podía precisar cuándo. Para entonces ya se había engordado mucho, y se dedicaba a dar tranquilos paseos diarios por las colinas, además de visitar la iglesia que tanto le encantaba y admirar el paisaje desde allí. Florine, la esposa de Gaston, limpiaba la casa y cocinaba para ella algunos días. Y Annabelle pasaba muchas noches en vela leyendo sus antiguos libros de medicina. Seguía sintiendo emociones contradictorias respecto del bebé. Había sido concebido con tanta violencia y angustia que le costaba imaginarse que no fuera a recordarlo cada vez que lo viera. Pero el destino había querido que el bebé y Annabelle fueran el uno para el otro. Se había planteado contactar con la familia del vizconde para comunicarles su existencia, pero no les debía nada, y si eran tan despiadados y deshonrosos como su vástago, no quería saber nada de ellos. Annabelle y su hijo se tendrían mutuamente, y no necesitarían a nadie más.
La tercera semana de abril, salió a dar un paseo largo, se detuvo en la iglesia como solía hacer y se sentó dejando caer el peso sobre un banco para admirar el paisaje. Había encendido una vela en recuerdo de su madre y había rezado por Josiah. No había tenido noticias suyas desde hacía más de dos años, y no tenía ni idea de dónde podían estar ahora Henry y él: si seguían en México o habían regresado a Nueva York. La había abandonado y no había mantenido ningún contacto con ella. La intención de Josiah era que Annabelle fuera libre para empezar una nueva vida, pero jamás se le habría pasado por la cabeza, por mucho que lo hubiera intentado, la cantidad de reveses y golpes del destino que había tenido que soportar la joven.
Regresó a paso lento a la casa bañada por la luz moteada de la tarde mientras pensaba en todos ellos: Josiah, Hortie, su madre, su padre, Robert... Era como si notara que todos la acompañaban. Cuando llegó a la casa, subió a su dormitorio y se tumbó en la cama. Florine ya se había marchado y Annabelle concilió un sueño ligero. Para su sorpresa, pasaba de medianoche cuando se despertó. Un calambre en la espalda fue lo que la desveló, y de repente notó un dolor punzante en la parte baja del vientre, y supo al instante de qué se trataba. No había nadie en la casa para llamar al médico y carecía de teléfono, pero aun así no sintió miedo. Estaba segura de que sería un proceso sencillo que podría llevar a cabo ella sola. Sin embargo, conforme avanzaba la noche y los dolores de las contracciones se agudizaban, dejó de estar tan segura. Le parecía increíblemente cruel que, después de todo lo que había sufrido para concebir a ese niño, ahora tuviera que volver a sufrir para alumbrar a un hijo sin padre, al que ni siquiera deseaba. En todos esos años en los que había anhelado tener un hijo con Josiah, jamás se le había ocurrido que un niño pudiera entrar de semejante forma en su vida.
Se retorcía con cada contracción y se aferraba con fuerza a las sábanas. Vio cómo salía el sol del amanecer, y para entonces estaba sangrando muchísimo. Los dolores eran agónicos y empezaba a sentirse como si se ahogara y fuera a morir en cualquier momento. Aquello le hizo pensar en las historias atroces que Hortie le había contado y en los terribles alumbramientos que había padecido su amiga. Empezaba a entrarle el pánico cuando Florine apareció en la puerta del dormitorio. La había oído desde la planta inferior y había corrido escaleras arriba. Annabelle estaba tumbada en la cama con los ojos desorbitados, incapaz de hablar por culpa de todo el sufrimiento que había soportado durante la noche. Llevaba ya ocho horas de parto.
Florine entró a toda prisa en el dormitorio, y con cariño levantó la colcha que la cubría y colocó sábanas viejas debajo de su cuerpo, que ya había reservado hacía unos días con tal propósito. Emitió unos sonidos reconfortantes, como si meciera a Annabelle, y le garantizó que todo saldría bien. Miró y le informó de que ya veía la cabeza del bebé.
—Me da igual —dijo Annabelle desesperada—. ¡Quiero que salga ya...!
En ese momento soltó un grito y el bebé pareció avanzar unos centímetros hacia abajo, pero después retrocedió. Florine corrió a la planta de abajo para ir a buscar a Gaston, y le dijo que llamara al médico inmediatamente. Sin embargo, nada de lo que vio hizo que se alarmara: todo iba bien. Y por otros partos que había presenciado, sabía que podía quedar un buen trecho aún. Lo peor todavía estaba por llegar, pues la superficie de la cabeza del niño que había visto apenas era del tamaño de una moneda.
Annabelle no paraba de llorar, tumbada en la cama, mientras Florine le enjugaba la frente con paños fríos con aroma de lavanda; aunque, al final, Annabelle ni siquiera le dejaba que hiciera eso. No deseaba que nadie la tocara y lloraba sin cesar de tanto dolor. Cuando llegó el médico, le pareció que había pasado una eternidad. Venía directo de otro parto, en el que una mujer había dado a luz a gemelos. Llegó a casa de Annabelle a las dos de la tarde y vio que las cosas no habían progresado mucho, aunque los dolores empeoraban por momentos.
Pareció muy satisfecho cuando la estudió después de lavarse las manos.
—Esto va viento en popa —dijo para animar a su paciente, que gritaba a pleno pulmón con cada contracción—. Creo que tendremos al bebé aquí antes de la hora de cenar.
Ella lo miró con auténtico pánico en los ojos, pues sabía que no podría soportar ni un minuto más la agonía en la que estaba sumida. Y al final, mientras soltaba lastimeros sollozos, el médico le pidió a Florine que la incorporase un poco con almohadones y la sujetase de los pies. Annabelle manoteaba y gritaba con cada empujón, y no dejaba de llamar a su madre, así que el médico tuvo que ponerse serio para decirle que debía colaborar. La parte de la coronilla del bebé que quedaba a la vista era mucho más grande, así que le repitió una y mil veces a Annabelle que empujara. Llegó un punto en que se recostó en los almohadones, demasiado agotada para seguir empujando, pero en ese momento él le dijo que empujara todavía más fuerte que antes y que no desfalleciera. Se le puso la cara de un rojo encendido en el instante en que la parte superior de la cabeza del bebé asomó por su cuerpo, con la carita arrugada, y Annabelle chilló y miró hacia abajo, al niño que emergía de su vientre.
Empujó con todas sus fuerzas y por fin se oyó un llanto largo y bajo que llenó la habitación, y un rostro diminuto con los ojos brillantes los miró a todos, mientras Annabelle lloraba y reía, y Florine exclamaba muy emocionada. El bebé tenía los bracitos y las piernecillas enredados en el cordón umbilical, que el médico cortó enseguida, y la anciana lo envolvió con una manta y se lo tendió a la madre. Era una niña.
—Ay... Es preciosa... —dijo Annabelle con lágrimas resbalándole por las mejillas.
Aquella diminuta criatura era perfecta, tenía unas facciones exquisitas, unas extremidades graciosas, y manos y pies muy chiquitines. El médico tenía razón: apenas pasaban de las seis de la tarde, lo que, según dijo, era rápido para un primer parto. Annabelle no podía dejar de mirar y hablar a su hija mientras el hombre terminaba de realizar su labor. Florine lavaría bien a Annabelle más tarde; de momento, la cubrieron con una manta. Y con una ternura infinita, esta se llevó a la niña al pecho, con auténtico instinto maternal. El angelito que tenía en brazos era el único familiar vivo que le quedaba en el mundo, y entonces supo que habían merecido la pena todos y cada uno de los momentos de dolor, que ahora le parecían insignificantes.
—¿Cómo se va a llamar? —le preguntó el médico mientras le sonreía. Sentía lástima por Annabelle, pues sabía que era viuda, pero por lo menos tenía al bebé.
—Consuelo —contestó Annabelle en voz baja—. En honor de mi madre.
Y entonces se inclinó con cuidado hacia delante y le dio un beso en la cabeza a su hija.
### 19
La niña era perfecta en todos los sentidos. Estaba sana, contenta, y le ponía las cosas fáciles a Annabelle. Era como un angelito caído del cielo que hubiera aterrizado en los brazos de su madre. Annabelle jamás se había imaginado que pudiera querer tanto a su recién nacida. Todo vínculo con el hombre que la había forzado se desvaneció en el momento en que nació la niña, quien pertenecía única y exclusivamente a ella.
La joven fue a visitar al doctor Graumont a la facultad de medicina en julio, justo después del estallido de la segunda batalla del Marne. El número de víctimas mortales había aumentado de forma vertiginosa desde que Annabelle se había marchado de Villers-Cotterêts. Y después del nacimiento de Consuelo, se dio cuenta de que no podía regresar al frente. No quería llevarse a la niña al hospital, ni pasar tantas horas separada de ella, ni arriesgarse a que contrajera alguna enfermedad. Aunque se sentía culpable por no seguir colaborando en el esfuerzo bélico, Annabelle sabía que ahora mismo su lugar estaba junto a su hija. Florine se había ofrecido a cuidar de la niña si ella decidía ir al frente, pero no soportaba imaginarse lejos de su pequeña ni una sola hora al día, y mucho menos dejarla durante varios meses al cargo de otra persona. Así pues, había decidido quedarse en Antibes por el momento.
Seguía teniendo ganas de estudiar medicina y esperaba poder organizarse para regresar a la facultad. Para cuando fue a ver al doctor Graumont, ya había interiorizado la historia fabricada por ella misma. Le contó que se había casado con un oficial británico poco después de mudarse a Villers-Cotterêts. Habían mantenido la boda en secreto ante la familia de él, pues deseaban anunciarlo cuando el oficial regresara a Inglaterra pero, antes de que tuvieran oportunidad de hacerlo, lo habían matado. Y como nadie estaba al corriente de su matrimonio, Annabelle había decidido conservar el apellido de soltera, y mucho más en esos tiempos que la familia de su difunto esposo había quedado sin herederos. Es decir, en honor a ellos había preferido seguir apellidándose Worthington. La historia se aguantaba con pinzas, pero al parecer el médico se la creyó, o estaba dispuesto a creer cualquier historia que ella deseara contarle. Le dijo que la niña era guapísima y le aseguró que, cuando Annabelle retomara sus estudios en septiembre, madre e hija podrían alojarse en la casita para el jardinero, entonces desocupada, que había en los terrenos de la universidad. En esos momentos había nueve estudiantes en la facultad de medicina, más tres alumnos nuevos que empezarían el mismo trimestre que ella. Por desgracia, le comunicó que siete de sus compañeros de clase habían muerto desde que todos se habían marchado como voluntarios. El profesor se sintió muy aliviado al ver que Annabelle estaba sana y salva, y más hermosa aún después del parto. Ahora tenía un aspecto todavía más femenino, y esa primavera había cumplido ya veinticinco años. Saltaba a la vista que estaba preparada para retomar sus estudios y no le daba vértigo pensar que tendría treinta años cuando se graduara y se convirtiera oficialmente en médico. Lo único que deseaba era ponerse en marcha cuanto antes. Apenas faltaban seis semanas para que comenzara el curso.
Decidió mantener el alquiler de la casita de Antibes porque tenía intención de ir siempre que le fuese posible. De todas formas, necesitaba que alguien cuidara de Consuelo mientras ella iba a clase, así que contrató a una muchacha, Brigitte, que viviría con ellas en la casita de las inmediaciones del castillo. A partir de septiembre las tres habitarían juntas en la vivienda que el doctor Graumont le había facilitado a cambio de un alquiler simbólico. Las aguas volvían a su cauce.
Así pues, el día convenido de septiembre, Annabelle, su hija y Brigitte se presentaron en el castillo que albergaba la facultad de medicina y se instalaron en la casita para el jardinero. Annabelle empezó las clases al día siguiente. Le pareció más emocionante que nunca, pues no cabía en sí de alegría. Tenía a Consuelo, a quien amaba con toda su alma, y había conseguido retomar sus estudios de medicina. Además, en esa época le resultaba más sencillo trabajar en el hospital de Niza. Después de todo lo que había aprendido en la abadía y en el hospital de Villers-Cotterêts como auxiliar de medicina, estaba mucho más preparada para la práctica sanitaria que cuando se había marchado.
La guerra siguió bramando todo el mes de septiembre, y al mismo tiempo una terrible epidemia de gripe se extendió y sacudió tanto a Europa como a Estados Unidos, diezmando tanto a los civiles como al personal militar. Miles de personas murieron por esa causa, sobre todo niños y ancianos.
Y por fin, a finales de mes, las tropas franco-estadounidenses comenzaron la ofensiva de Meuse-Argonne. En cuestión de días, las fuerzas armadas del general Douglas Haig alcanzaron la Línea de Hindenburg y se abrieron paso a través de ella. Seis días más tarde, Austria y Alemania se pusieron en contacto con el presidente Wilson para pactar un armisticio, pues las fuerzas británicas, estadounidenses y francesas continuaban machacando a sus oponentes: se habían invertido las tornas. La lucha continuó durante cinco semanas más, en las cuales Annabelle y sus compañeros de la facultad no podían hablar de otra cosa.
Finalmente, el 11 de noviembre, a las once de la mañana, cesó el enfrentamiento. Así acababa la guerra que había saqueado Europa durante más de cuatro años y había costado quince millones de vidas.
Annabelle estaba de pie, con la niña en brazos, cuando oyó la buena noticia, y no pudo contener las lágrimas que le resbalaban por las mejillas.
### 20
Con el fin de la guerra, las personas empezaron a recuperar poco a poco sus vidas. Los soldados regresaron a sus lugares de origen, se casaron con las novias que habían dejado allí, o con otras nuevas que habían conocido durante los años de la contienda. Volvieron a sus ocupaciones y costumbres anteriores. Se veían lisiados y heridos por todas las calles: con muletas, en sillas de ruedas, algunos con miembros amputados o con prótesis. En ocasiones daba la sensación de que la mitad de los hombres de Europa estaban mutilados, aunque por lo menos seguían vivos. Y quienes no llegaron a regresar jamás eran llorados y recordados por sus familiares. Annabelle pensaba con frecuencia en sus compañeros de clase que habían desaparecido. Todos los días echaba de menos a Marcel, e incluso a Rupert, que le había hecho la vida imposible los primeros meses en el castillo, pero con quien había terminado siendo muy amiga.
No dejaban de llegar alumnos nuevos a la facultad y, cuando empezó la primavera, ya eran sesenta los estudiantes del castillo: jóvenes formales, comprometidos, decididos a hacerse médicos y servir al mundo. Ella seguía siendo la única mujer de la clase, y todos estaban enamorados de Consuelo. Celebró su primera fiesta de cumpleaños con sesenta y un estudiantes de medicina adorables, y empezó a andar justo al día siguiente. Era la favorita de todos ellos e incluso enternecía el corazón del doctor Graumont, que podía ser tan severo algunas veces. La niña tenía diecisiete meses cuando su madre empezó el tercer curso de la carrera. Procuraba por todos los medios que no entrara en contacto con desconocidos, pues la epidemia de gripe seguía azotando el mundo entero. Para entonces, ya habían fallecido varios millones de personas enfermas.
La facultad de medicina se convirtió en el hogar ideal tanto para Annabelle como para Consuelo, con sesenta encantadores tíos que no dejaban de hacerle monerías siempre que tenían ocasión. Le regalaban detalles, jugaban con ella, y en cuanto uno la soltaba, otro la cogía en brazos o la columpiaba en sus rodillas. La niña vivía muy feliz.
Al final, Annabelle se vio obligada a prescindir de la casa en Antibes cuando los propietarios decidieron venderla, y tuvo que despedirse de Gaston y Florine. Sin embargo, Brigitte se quedó con ellas, pues en la casita dependiente del castillo había sitio de sobra para las tres.
De vez en cuando, mientras veía cómo crecía su preciosa Consuelo, pensaba en contactar con la familia del vizconde. Ahora que sabía lo que era tener un hijo, se preguntaba si los padres del oficial desearían mantener una especie de último vínculo afectivo con su hijo a través de la niña. Sin embargo, no se veía con fuerzas para hacerlo. No deseaba compartir a Consuelo con nadie. La niña era clavadita a ella, como si nadie más hubiese contribuido a su concepción. Todos los que la veían decían que era el vivo retrato de Annabelle en todos los sentidos.
Los años en la universidad pasaron ante ella a la velocidad del rayo. Estaba tan ocupada y volcada en lo que hacía que tuvo la sensación de que todo acababa en un abrir y cerrar de ojos, aunque se había esforzado mucho para llegar hasta allí.
Cumplió treinta años el mismo mes en que se graduó en la facultad de medicina del doctor Graumont. Y Consuelo había cumplido los cinco en abril. Dejar la universidad y abandonar también la casita de los terrenos del castillo, en la que habían vivido un lustro, era como volver a marcharse de casa. Le resultaba a la vez emocionante y doloroso. Annabelle había decidido viajar a la capital, pues había pedido una colaboración con el hospital Hotel-Dieu de París, cerca de Notre Dame, en la Île de la Cité. Era el hospital más antiguo de la ciudad. Tenía intención de abrir una consulta de medicina general. Siempre había albergado la esperanza de trabajar para el doctor De Bré, pero este había muerto la primavera anterior. Y el último vínculo que tenía con su país natal se había cortado de cuajo un mes antes de su graduación. Recibió una carta del director del banco de su padre en la que le comunicaba que Josiah había muerto en México en febrero, y que Henry Orson había fallecido poco después. El encargado de los asuntos financieros de Annabelle dentro del banco pensó que querría saberlo y, de paso, adjuntó una carta que Josiah le había dejado. Cuando murió, tenía cuarenta y nueve años.
Su muerte y su última carta desencadenaron un alud de recuerdos en ella, así como una oleada torrencial de tristeza. Habían pasado ocho años desde que la había abandonado y ella había viajado a Europa, y siete años desde el divorcio. La carta que le había dedicado era tierna y nostálgica. La había escrito hacia el final de sus días. Le decía que había sido feliz con Henry en México, pero que siempre la había recordado con amor y con arrepentimiento por lo mucho que la había hecho sufrir. Confiaba en que ella hubiera encontrado también la felicidad y algún día pudiera perdonarlo. Mientras leía la carta, Annabelle tuvo la sensación de que el mundo en el que había crecido y que compartía con él ya no existía. No tenía ninguna clase de lazo que la uniera a él. Su vida estaba en Francia, con su hija, con su profesión. Hacía mucho tiempo que había quemado los puentes. Lo único que le quedaba en Estados Unidos era la casa de Newport, que llevaba ocho años desocupada, todavía en manos de los fieles sirvientes de sus padres, que la cuidaban con esmero. Dudaba de que algún día volviera a ella, pero no se había sentido con fuerzas para venderla, y además no le era imprescindible. Sus padres le habían legado más que suficiente para vivir de forma holgada y asegurar el futuro de Consuelo y el suyo propio. Algún día, cuando aunara el valor necesario, vendería la residencia de verano familiar. Lo que ocurría era que aún no se veía con ánimo de hacerlo. De la misma manera que tampoco se veía con ánimo de contactar con los padres del vizconde. Consuelo y ella eran las únicas habitantes de su universo particular.
Le costó mucho despedirse de la facultad de medicina y de los amigos que había hecho allí. Todos sus compañeros de promoción iban a dispersarse por distintas partes de Francia. Muchos pensaban quedarse en el sur del país, y la joven nunca había sentido especial afinidad con el único de ellos que iba a mudarse a París también. En todos los años que llevaba en Europa no había mantenido ninguna relación amorosa. Primero había estado demasiado volcada en su voluntariado, y después había estado absorbida por sus estudios y su hija. Era una joven viuda muy digna y ahora sería una médico igual de entregada. No quedaba espacio en su vida para nada más, y deseaba que siguiera siendo así. Josiah le había roto el corazón y el padre de Consuelo había destrozado el resto de su ser. No quería a ningún hombre en su vida, ni a nadie más que a su hija. Esta y su trabajo eran todo lo que necesitaba.
Ambas tomaron el tren hacia París en junio con Brigitte, quien estaba muy emocionada de acompañarlas a la capital. Hacía años que Annabelle no visitaba París y descubrió que en esos momentos estaba mucho más animada. Llegaron a la Gare de Lyon y llamaron a un taxi que las llevó al hotel en el que Annabelle había reservado habitación, en la ribera izquierda del Sena. Era un establecimiento pequeño que le había recomendado el doctor Graumont, pues decía que era muy apropiado para dos mujeres y una niña. Le había advertido de los peligros que acechaban en París. Annabelle se dio cuenta de que el taxista era ruso, y tenía aire distinguido. A causa de la Revolución bolchevique y el asesinato de la familia del zar, muchos rusos blancos de la nobleza habían emigrado a París, donde se dedicaban a trabajar de taxistas o desempeñar empleos poco cualificados.
Sintió una gran satisfacción cuando se registró en el hotel como la _docteur_ Worthington. Se le iluminaron los ojos como a una niña. Seguía siendo la bella joven que era cuando había llegado a Europa, y en los momentos en que jugaba con Consuelo volvía a la infancia. Sin embargo, detrás de ese espíritu juvenil había una mujer seria y responsable, alguien en quien los demás podían confiar, en cuyas manos podían poner su salud y sus vidas. Su sensibilidad con los pacientes había sido la envidia de sus compañeros de facultad y de prácticas, y gracias a ella se había ganado el respeto de todos sus profesores. El doctor Graumont sabía que sería una excelente profesional, además de un orgullo para la escuela.
Dejaron las maletas en el hotel. El doctor Graumont se encargaría de enviarles sus pertenencias más adelante, cuando hubieran encontrado casa. Annabelle deseaba instalarse en un lugar en el que pudiera abrir también la consulta médica para visitar a los pacientes.
Un día después de su llegada a París, fue al hospital Hôtel-Dieu, para preguntar si le darían permiso para desviar a los pacientes graves a ese centro. Mientras tanto, Brigitte se llevó a Consuelo a ver los Jardines de Luxemburgo. La hermosa niñita rubia aplaudió muy emocionada cuando se reunió de nuevo con su madre en el hotel.
—¡Mamá, hemos visto un camello! —exclamó, y acto seguido se lo describió, mientras Brigitte y su madre se reían—. Yo quería montarme en él, pero no me han dejado —se lamentó, y al instante volvió a soltar una risita contagiosa. Era una niña encantadora.
En el hospital Hôtel-Dieu le dieron permiso sin dudarlo en cuanto los encargados vieron la carta de recomendación del doctor Graumont. Era un paso importante para Annabelle. Llevó a Consuelo y a Brigitte a cenar al hotel Meurice para celebrarlo, y otro taxista ruso las llevó a dar una vuelta por París para ver los puntos más emblemáticos de la ciudad iluminados. Qué distinto era del día en que Annabelle había llegado allí durante la guerra, con el corazón destrozado y después del rechazo social sufrido en Nueva York. Ahora comenzaba una vida totalmente nueva, por la que se había esforzado mucho.
Cuando por fin regresaron al hotel eran las diez de la noche. Consuelo se había quedado dormida en el taxi y Annabelle la llevó en brazos a la habitación y la dejó con cuidado encima de la cama. A continuación, se dirigió a su parte de la suite y miró por los ventanales para contemplar París _la nuit_. Hacía años que no se sentía tan joven y exaltada. Se moría de ganas de empezar a trabajar, aunque antes tenía que encontrar una casa en la que vivir.
Durante las tres semanas siguientes Annabelle tuvo la sensación de recorrer todas las casas de París, tanto en la ribera derecha como en la izquierda, mientras Brigitte llevaba a Consuelo a todos los parques de la ciudad —el Bagatelle, los Jardines de Luxemburgo, el Bois de Boulogne...— y se montaban en el carrusel. Las tres salían a cenar fuera todas las noches. Hacía años que Annabelle no se divertía tanto, y aquella nueva vida de adulta le parecía completamente novedosa.
Entre una visita y otra, iba de compras porque quería renovar su vestuario: buscaba cosas lo bastante serias para dar buena impresión como médico, pero lo bastante estilosas para estar a la altura de las mujeres parisinas. Le recordaba a cuando había ido con su madre a comprar la ropa para el ajuar, y se lo contó a Consuelo. A la niña le encantaba escuchar historias sobre sus abuelos y su tío Robert. Eso le daba la sensación de pertenecer a un grupo más grande que el formado únicamente por su madre y ella, aunque siempre provocaba una leve punzada en el corazón de Annabelle, que recordaba la familia que no podía ofrecerle. No obstante, se tenían la una a la otra, y la joven siempre le repetía a su hija que no necesitaban nada más. Consuelo añadía con semblante serio que también necesitaban un perro. En París todo el mundo tenía perro, así que Annabelle le prometió que, cuando por fin encontraran casa, le compraría un perro. Fueron unos días muy felices para las tres, pues Brigitte también se divertía flirteando con uno de los botones del hotel. Acababa de cumplir veintiún años y era una muchacha muy guapa.
A finales de julio, Annabelle empezó a desanimarse tremendamente. Seguían sin encontrar una casa adecuada. Todo lo que veían era o demasiado grande o demasiado pequeño, o bien no tenía la disposición adecuada para montar una consulta médica. Tenía la impresión de que nunca iban a hallar lo que necesitaban. Y entonces, por fin, Annabelle dio con el lugar idóneo en una callecita estrecha del decimosexto distrito. Era una casita pequeña pero elegante con un patio delantero y un jardín posterior, y una extensión con entrada independiente donde podría atender a los pacientes. Estaba en perfectas condiciones y la había puesto a la venta el banco. Además, a Annabelle le encantaba que tuviera ese aire distinguido. Era la ubicación perfecta para una profesional de la medicina. Y para colmo, vio un parquecillo muy cerca en el que Consuelo podría jugar con otros niños.
Manifestó su interés por la casa de inmediato, aceptó el precio que había estipulado el banco y tomó posesión del inmueble a finales de agosto. Mientras tanto, se dedicó a encargar el mobiliario, la ropa de cama, la vajilla, algunas antigüedades adorables para decorar la habitación de Consuelo, unos muebles preciosos para su dormitorio y algo un poco más sencillo para la habitación de Brigitte. Compró muebles serios para el despacho, y empleó el mes de septiembre en adquirir el equipo médico que precisaba tener antes de abrir la consulta. Fue a la imprenta y encargó material de oficina con su membrete. Asimismo, contrató a una secretaria y auxiliar de medicina que decía haber trabajado también en la abadía de Royaumont, aunque Annabelle no había coincidido con ella. Hélène era una mujer mayor bastante tranquila, que había colaborado con diversos médicos antes de la guerra y que estaba encantada de ayudarla a montar el negocio.
A principios de octubre, Annabelle estaba preparada para abrir las puertas de su consulta. Había tardado más de lo que esperaba, pero quería que todo estuviera a punto antes de la inauguración. Con manos temblorosas colgó su placa, y esperó a ver qué pasaba. Lo único que le hacía falta era que una persona atravesara esa puerta, y después el engranaje empezaría a rodar gracias al boca a boca. De haber estado vivo el doctor De Bré, habría podido recomendársela a algunos pacientes, pero ahora era imposible. Por suerte, el doctor Graumont había escrito a distintos médicos que conocía en París para pedirles que enviaran a Annabelle a varios de sus pacientes, pero de momento su petición no había obtenido frutos.
Durante las tres primeras semanas no ocurrió nada. Annabelle y Hélène, su secretaria y auxiliar de medicina, se pasaban el día mirándose la una a la otra y viendo cómo pasaban las horas. Annabelle tenía por costumbre volver al edificio principal de la casa al mediodía para comer con Consuelo. Hasta que, por fin, a principios de noviembre, entró en la consulta una mujer con la muñeca dislocada y un hombre con un corte muy grande en el dedo. A partir de entonces, como por arte de magia, empezó a haber una corriente continua de pacientes que entraban en la sala de espera de la consulta. Un paciente se la recomendaba a otro. No eran casos muy complicados, sino cosas pequeñas que no le costaba solucionar. Sin embargo, su seriedad y su experimentada gentileza con los pacientes consiguieron que se los metiera en el bolsillo de inmediato. Al cabo de poco tiempo, varias personas cambiaron de médico de cabecera para que ella los atendiera, o bien enviaban a sus amigos, llevaban a sus hijos y le consultaban dolencias menores y problemas mayores. En enero, la consulta estaba siempre llena. Annabelle desempeñaba la labor para la que se había formado y disfrutaba con cada minuto de su trabajo. Se esmeraba en dar las gracias a los colegas que la recomendaban, y siempre respetaba sus opiniones anteriores, para no hacerlos quedar como unos incompetentes delante de los pacientes, aunque algunos de ellos lo habrían merecido. Era meticulosa, poseía una gran formación y siempre se mostraba encantadora en el trato con los enfermos. A pesar de su belleza y su aspecto juvenil, no cabía duda de que se tomaba su profesión muy en serio, y sus pacientes confiaban en ella plenamente.
En febrero, mandó hospitalizar al hijo de una de sus pacientes. El muchacho solo tenía doce años y padecía un caso grave de neumonía. Annabelle iba a visitarlo al hospital dos veces al día y se preocupaba mucho por el chico, sobre todo cuando vio que su salud empeoraba, pero por fortuna consiguió remontar y su madre se lo agradeció eternamente. Annabelle había puesto en práctica algunas técnicas nuevas que habían empleado en el hospital de Villers-Cotterêts con los soldados, y siempre hacía gala de su creatividad al combinar métodos nuevos con otros antiguos. Continuaba leyendo y estudiando con avidez por las noches, para aprender más sobre las últimas investigaciones. Su apertura de mente hacia las ideas novedosas le resultaba muy útil en su labor diaria, y leía sobre todos los temas recogidos en las revistas médicas. Muchas noches se quedaba despierta hasta tarde leyendo esas publicaciones, a menudo mientras abrazaba a Consuelo en la cama, quien había empezado a decir que ella también quería ser médico. Otras niñas de su edad querían ser enfermeras, pero en la familia de Annabelle el listón estaba muy alto. En ocasiones, esta no podía evitar preguntarse qué habría pensado su madre de aquello. Sabía que no era lo que habría deseado para su hija, pero confiaba en que hubiera estado orgullosa de ella igualmente. Era plenamente consciente de que Consuelo se habría deprimido de haber presenciado el divorcio provocado por Josiah, y se preguntaba si su ex marido también la habría abandonado de no haber muerto su madre. De todas formas, todo eso era agua pasada. Además, ¿de qué le habría servido seguir casada con él toda la vida si estaba enamorado de Henry? Annabelle no habría podido hacer nada para evitarlo. Saberlo no la enojaba, sino que la entristecía. Siempre que pensaba en el tema, la embargaba un amargo dolor que sospechaba que acarrearía durante toda su existencia.
La única cosa que no la entristecía nunca era Consuelo. Era la niña más alegre, risueña y divertida del mundo, y adoraba a su madre. Pensaba que el sol salía y se ponía con ella, y Annabelle había creado un padre imaginario para ella, con el propósito de que no se sintiera falta de afecto. Le decía que su padre era inglés, que había sido una persona magnífica procedente de una familia muy buena, y que había muerto como un valiente héroe de guerra antes de que ella naciera. A la niña nunca se le ocurría preguntar por qué no veía en ninguna ocasión a la familia de su difunto padre. Sabía que todos los parientes de su madre habían muerto, pero Annabelle nunca le había dicho que los de Harry también hubieran desaparecido. Consuelo nunca lo mencionaba, se limitaba a escuchar con interés a su madre, hasta que un día se dirigió a ella a la hora de comer y le preguntó si su «otra» abuela podía ir a visitarla algún día; se refería a la que vivía en Inglaterra. Annabelle se quedó mirando a la niña desde el otro lado de la mesa, como si hubiera visto explotar una bomba, pues no sabía qué contestarle. Nunca se había planteado que ese día llegaría, y no estaba preparada para afrontarlo. Consuelo tenía seis años y todos sus amigos del parque tenían abuelas. Entonces, ¿por qué no podía ir a verla la suya?
—Eh... bueno, es que vive en Inglaterra. Y hace mucho tiempo que no hablo con ella... Esto, en realidad —aborrecía mentirle a su hija—, no hemos hablado nunca... No la conozco. Tu papá y yo nos enamoramos y nos casamos durante la guerra, y como luego él murió, nunca llegué a conocer a su familia.
Intentaba salir del paso como podía mientras Consuelo la miraba atentamente.
—¿Es que no quiere verme? —Consuelo parecía decepcionada, y Annabelle sintió que se le encogía el corazón.
Se había metido en un embrollo ella sola y, a menos que le dijera a su hija que sus abuelos no sabían de su existencia, no se le ocurría qué otra cosa podía añadir. Sin embargo, tampoco quería verse obligada a contactar con ellos. Menudo dilema.
—Seguro que le gustaría verte, si pudiera, cariño... Me refiero a que a lo mejor está enferma o algo... A lo mejor es muy anciana. —Y entonces, con un suspiro y el corazón en un puño, le prometió—: Pero le escribiré, a ver qué dice.
—Muy bien.
Consuelo le sonrió desde el otro lado de la mesa y, mientras Annabelle regresaba a la consulta, maldijo a Harry Winshire como no lo había hecho en años.
### 21
Fiel a la palabra que le había dado a Consuelo, Annabelle se sentó a escribir una carta a lady Winshire. Ignoraba qué decirle o cómo enfocar la cuestión. Contar la verdad, que su hijo la había violado y ella había tenido una hija ilegítima como consecuencia, no le parecía una manera muy adecuada de presentarse, y dudaba de que a lady Winshire le hiciera demasiada gracia. Sin embargo, no quería mentirle. Al final, le escribió una versión increíblemente suavizada y simplificada, edulcorada. En el fondo, no quería ver a lady Winshire, ni siquiera quería que conociera a Consuelo, pero por lo menos quería decirle a su hija que lo había intentado.
Le escribió que Harry y ella se habían conocido durante la guerra en Villers-Cotterêts, en el hospital en el que Annabelle trabajaba. Eso era cierto, aunque habría sido mucho más preciso decir que él la arrojó sobre el suelo y la violó. Entonces añadió que apenas se habían visto y que no eran amigos, cosa que también era cierta, pero que había ocurrido un desafortunado incidente, algo más que cierto, a consecuencia del cual ella había tenido una hija, que había cumplido ya seis años. Le confesó que no había contactado antes con los familiares porque no deseaba pedirles nada. Le explicó que era estadounidense y había ido a Francia como voluntaria, y que su encuentro con Harry, y el embarazo consiguiente, había sido uno de esos horribles episodios propios de la guerra, pero que su hijita era una niña maravillosa y que acababa de preguntarle por su abuela por parte de padre, una situación que resultaba muy violenta para Annabelle. Reconoció que no quería seguir mintiendo, como había hecho hasta entonces. Le dijo que la niña creía que ella y su padre habían estado casados, cosa que no era cierta. Por eso, le proponía a lady Winshire que, si lo deseaba, le enviara por favor una carta o una notita a Consuelo en la que le mandase alguna foto de su padre o algo similar. Con eso bastaría. Firmó la carta como «Doctora Annabelle Worthington», para que viera que era una persona respetable, como si eso importara algo. Había sido su hijo quien había demostrado ser de todo menos respetable y quien debería haber ido a la cárcel, pero en su lugar había engendrado a la niña más encantadora de la Tierra, y Annabelle no podía odiarlo por eso. En cierto modo, le estaría siempre agradecida por el resultado, pero sus recuerdos de él no eran nada buenos.
En cuanto envió la carta, se olvidó del tema. El mes de mayo estuvo muy atareada, pues la sala de espera estaba continuamente llena. No había recibido respuesta de lady Winshire y, por el momento, Consuelo parecía haberse olvidado de su abuela. Había empezado a ir al colegio ese invierno y pasaba allí todas las mañanas, cosa que le dejaba tiempo a Brigitte para echar una mano en la consulta médica.
Annabelle acababa de regresar de ver a un paciente en el hospital cuando Hélène le dijo que había una mujer esperándola. Llevaba dos horas allí plantada y se negaba a contarle el motivo de su visita. Annabelle supuso que probablemente se tratara de algún problema embarazoso. Se puso la bata blanca, se sentó junto al escritorio y le indicó a Hélène que la hiciera pasar.
Dos minutos más tarde, Hélène entró acompañada de una señorona muy voluminosa. Era una mujer corpulenta con la voz fuerte, que lucía un sombrero enorme, un collar de perlas de unas seis vueltas y un bastón de plata. Cuando entró en la consulta, dio la impresión de querer golpear a alguien con ese bastón. Annabelle se puso de pie para saludarla y tuvo que contenerse para no sonreír. La mujer pasó por alto la mano extendida de Annabelle y se quedó de pie, mirándola fijamente. No parecía enferma, así que esta no tenía la menor idea de qué hacía en su consulta. Fue directa al grano.
—¿A qué viene esa ocurrencia absurda de que tengo una nieta? —le espetó a Annabelle en inglés—. Mi hijo no tenía descendencia, ni cargas, ni mujeres importantes en su vida cuando murió. Y si alega que esa hija es suya, ¿puede saberse por qué ha esperado seis años para escribirme y contármelo?
Mientras lo decía, se sentó en la silla que había al otro lado del escritorio de Annabelle y siguió mirándola con la misma fijeza. Era igual de amable que su hijo, y a ella no le hizo ninguna gracia descubrir a qué se debía todo ese alboroto: en lugar de responder a su carta, la madre se había presentado allí con toda la artillería.
—He esperado seis años a contactar con usted —contestó con frialdad Annabelle— porque no deseaba hacerlo, y punto.
Ella podía ser igual de brusca que lady Winshire si se lo proponía. Aparentaba unos setenta años, que era una edad bastante plausible, teniendo en cuenta que para entonces Harry habría estado en la treintena. Annabelle calculaba que el oficial debía de tener más o menos su edad la noche que la violó.
—Le escribí porque mi hija estaba triste de no tener abuelos. La niña no entendía por qué nunca veíamos a su abuela. Y le dije que su padre y yo habíamos estado casados muy poco tiempo, durante la guerra, y luego él había muerto. Le conté que por eso nunca había tenido oportunidad de conocerla a usted. Esta situación también es muy violenta para mí.
—¿Se casó con mi hijo? —Lady Winshire parecía apabullada.
Annabelle negó con la cabeza.
—No, no nos casamos. Solo nos vimos una vez.
Dicho así, ella quedaba como una chica fácil, pero Annabelle pensó que, por muy desagradable que fuera la señora, no hacía falta que se enterara de que su hijo era un violador. Creía que tanto Consuelo como la anciana merecían mantener sus ilusiones, así que pensaba ahorrarle el bochorno a lady Winshire, aun en su propio perjuicio.
—Pero preferiría que mi hija siguiera creyendo que sí estuvimos casados.
—¿En aquella época ya era médico? —preguntó entonces lady Winshire, de repente muy interesada.
Annabelle volvió a negar con la cabeza.
—No. Entonces era auxiliar de medicina. Y colaboraba con el servicio de ambulancias.
—¿Cómo lo conoció?
Algo se suavizó en su mirada. Había perdido a sus dos hijos en la guerra y conocía muy bien lo que eran el luto y el dolor.
—En el fondo no importa —se limitó a contestar, lamentando que la mujer hubiera ido a verla—. Apenas llegamos a conocernos. Mi hija fue un accidente.
—¿Qué clase de accidente?
Era como un perro que roe un hueso. Y Annabelle era el hueso.
Suspiró antes de responder, mientras intentaba dilucidar hasta dónde estaba dispuesta a contar. Desde luego, no la verdad.
—Él había bebido mucho.
Lady Winshire no parecía sorprendida.
—Siempre igual... Harry siempre bebía mucho, y hacía un montón de estupideces cuando estaba borracho. —Sus ojos penetraron en los suyos—. ¿Hasta dónde llegó la estupidez que cometió con usted?
Annabelle sonrió, preguntándose si la dama pensaba que intentaba chantajearla, y decidió volver a insistir.
—No quiero nada de usted.
—Esa no es la cuestión. Si mi hijo fue descortés, tengo derecho a saber hasta dónde llegó su mal comportamiento.
—¿Por qué? ¿Qué más da eso ahora? —Annabelle hablaba con una pausada dignidad.
—Es usted una mujer muy generosa —dijo sin alterarse lady Winshire, mientras se recostaba en la silla. Daba la impresión de estar dispuesta a quedarse allí hasta haber escuchado la verdad—. Pero sé muy bien cómo eran mis hijos. Mi hijo Edward era casi un santo. Y Harry era como el demonio hecho persona. Adorable de niño y maleducado de adulto. Algunas veces, «peor» que maleducado. Su actitud no mejoraba con el alcohol. Creo que estoy al corriente de la mayor parte de sus pillerías. —Entonces suspiró—. Quería venir a verla porque nadie me había dicho nunca que hubiera tenido un hijo suyo. Cuando leí su carta desconfié de usted. Pensaba que querría obtener algo a cambio. Y ahora he visto que es una mujer honesta y se han invertido los papeles: usted desconfía de mí tanto como yo desconfiaba de usted. —La anciana esbozó una sonrisa glacial y se pasó una mano por las perlas—. Dudé en si presentarme o no —admitió—. No deseaba verme involucrada en la historia de alguna mujer increíblemente vulgar que hubiera tenido un hijo bastardo y que ahora alegara que lo había engendrado mi hijo. Sin embargo, salta a la vista que usted no es de esa clase de personas, y tengo el fuerte convencimiento de que su encuentro con mi hijo fue desagradable, o peor, y no desearía ser quien se lo recuerde.
—Gracias —dijo Annabelle, pues valoraba todo lo que acababa de escuchar.
Pero entonces lady Winshire la sobresaltó al preguntar sin tapujos:
—¿La violó?
Al parecer, conocía muy bien a su hijo. Se produjo un silencio eterno en la sala, y al final Annabelle asintió con la cabeza, lamentando tener que decirle la verdad.
—Sí.
—Lo siento... —se lamentó la anciana con más afecto—. No es la primera vez que me cuentan algo así —continuó con una voz que reflejaba el arrepentimiento de una madre—. No sé en qué nos equivocamos... —Sus ojos se llenaron de tristeza cuando Annabelle y ella se miraron—. ¿Y ahora qué hacemos? Debo admitir que tenía miedo de qué podía encontrarme aquí, pero al mismo tiempo no lograba resistirme a la tentación de ver a mi propia nieta, si de verdad existía. Mis dos hijos están muertos. Mi marido murió de neumonía la primavera pasada. Y ninguno de mis hijos se había casado ni tenía hijos. Hasta que apareció usted.
Se le habían llenado los ojos de lágrimas y Annabelle la miró con compasión.
—¿Le gustaría conocer a Consuelo? —Entonces le advirtió, aunque no importaba, porque no pretendía reclamar su herencia—: No se parece a él. Se parece mucho a mí.
—Me atrevería a decir que eso sería una gran bendición —dijo la anciana con una sonrisa.
Se levantó con cierta dificultad y se apoyó en el bastón.
Annabelle también se puso de pie, rodeó la mesa y acompañó a lady Winshire hasta la puerta del despacho, después de decirle a Hélène que se marchaban. Por suerte, tenía un hueco libre entre unos pacientes y otros. Las dos mujeres recorrieron juntas el patio en dirección a la entrada principal de la casa. Annabelle sabía que Consuelo ya habría vuelto del colegio a esa hora, así que entró sin llamar, empleando la llave que siempre llevaba encima, y sin quitarse la bata de médico. Lady Winshire subió los peldaños exteriores de la casa y estudió con atención el recibidor una vez dentro.
—Tiene una casa preciosa —señaló muy educada.
Estaba impresionada por todo lo que veía. Annabelle tenía buen gusto, y era evidente que provenía de un entorno en el que se valoraban las cosas refinadas.
—Gracias —contestó ella, y la condujo al salón principal.
A continuación corrió escaleras arriba para buscar a su hija. Le dijo que tenían una invitada y que le gustaría que bajara a saludarla. No quería anticiparle nada más.
Annabelle y Consuelo bajaron la escalera charlando muy animadamente y cogidas de la mano. En el último peldaño la pequeña se detuvo, sonrió con timidez a su invitada, hizo una reverencia y fue a darle la mano. Era evidente que estaba muy bien educada y tenía excelentes modales, y lady Winshire miró con aprobación a Annabelle por encima de la cabeza de la niña.
—¿Cómo estás, Consuelo? —le preguntó mientras la niña se fijaba en el enorme sombrero y en las numerosas cuentas de perlas.
—Me gusta mucho su sombrero. Es precioso —observó la niña sin dejar de mirarlo mientras la señora le sonreía.
—Muchas gracias por el cumplido. Es un poco viejo, pero a mí me gusta. Tú también eres una niña preciosa. —No tenía más nietos, y hacía años que no hablaba con un niño—. He venido desde Inglaterra para verte —siguió diciendo sin que Consuelo le quitara ojo de encima—. ¿Sabes quién soy? —preguntó con afecto, pero Consuelo sacudió la cabeza—. Soy la abuela que no conocías: la madre de tu padre. —La niña abrió los ojos como platos cuando miró por encima del hombro hacia su madre y después volvió a fijarse en su abuela—. Siento que hayamos tardado tanto en vernos. No volverá a pasar —dijo muy solemne lady Winshire. Nunca había visto a una niña tan encantadora, y sus modales eran impecables—. Te he traído unas fotos de tu padre cuando era niño. ¿Te apetecería verlas?
Consuelo asintió y se sentó junto a ella en el sofá, a la vez que lady Winshire sacaba un manojo de fotografías descoloridas del bolso. Por su parte, Annabelle se marchó discretamente para pedirle a Brigitte que preparara el té.
Lady Winshire prolongó su visita más de una hora, y cuando la niña volvió a subir a su habitación con la sirvienta, le dio la enhorabuena a Annabelle por tener a una niña tan fabulosa.
—Sí, es un primor —corroboró su madre.
—Mi hijo no sabía la suerte que había tenido al topar con alguien como usted, y al dejar a una niña tan dulce como ella en el mundo.
Miraba a Annabelle con gratitud y compasión. La pequeña le había robado el corazón nada más verla. Era difícil que no ocurriera algo así, y por primera vez Annabelle se alegró de que la mujer se hubiera presentado en su casa en lugar de limitarse a escribir una carta. Para Consuelo había sido un gran regalo.
—Siento mucho que se comportara tan mal con usted. Mi hijo también tenía un lado bueno. Lamento que no llegara a verlo. Al principio la situación debió de resultarle increíblemente dura.
Annabelle asintió.
—Me quedé en el hospital todo el tiempo que pude, y después me mudé a Antibes. Allí fue donde nació Consuelo.
—¿Y su familia sigue en Estados Unidos?
Le parecía curioso que Annabelle hubiera empezado a ejercer la medicina en París en lugar de volver a su país, aunque estaba claro que la niña debía de haberle complicado las cosas.
—No me queda familia —se limitó a decir Annabelle—. Todos murieron antes de que viniera aquí. Solo estamos Consuelo y yo.
Lady Winshire también estaba sola en el mundo. Y en cierto modo, por extraño que pareciera, ahora se tenían la una a la otra.
Por fin se levantó y tomó la mano de Annabelle entre las suyas.
—Gracias por ofrecerme el más extraordinario de los regalos —le dijo la dama con lágrimas en los ojos—. Es como una parte de Harry a la que puedo aferrarme. Además, Consuelo es una niña muy especial.
Y, dicho esto, abrazó a la joven y le dio un beso en la mejilla. Esta la ayudó a bajar los peldaños de la entrada y la acompañó hasta el coche, cuyo chófer la había esperado en la puerta. La anciana sonrió a Annabelle una vez más antes de marcharse, y con delicadeza le deslizó algo en la mano.
—Esto es para usted, querida mía. Se lo ha ganado. Es muy poca cosa.
Annabelle intentó rechazarlo sin mirarlo siquiera, pero lady Winshire insistió. Las dos mujeres se dieron un abrazo y Annabelle sintió que había encontrado a una nueva amiga, una especie de maravillosa tía anciana y excéntrica. Ahora se alegraba de haberle escrito. Había sido positivo para todas ellas.
Se despidió con la mano mientras lady Winshire se alejaba en el coche y no se atrevió a mirar el objeto que tenía en la palma hasta que la anciana se hubo marchado. Le había dado la impresión de que se trataba de un anillo, pero no estaba preparada para la clase de anillo que era: una hermosa esmeralda antigua muy grande engarzada en un aro de diamantes igual de antiguo. Annabelle estaba anonadada. Le recordó a los anillos que solía llevar su abuela, que continuaban en la caja fuerte del banco, en Nueva York. Sin embargo, no dudó en colocarse el anillo en el dedo en el que ya llevaba la alianza de boda que ella misma se había comprado. Se sintió conmovida por el gesto. Algún día se lo regalaría a Consuelo, pero hasta entonces lo luciría. Y mientras regresaba a la consulta, pensó para sus adentros que a partir de ese momento tendrían abuela. Consuelo y ella ya no estaban solas en el mundo.
### 22
El verano llegó a París con un tímido brote de gripe, algunos creían que provocado por el calor, así que Annabelle tuvo que mandar a varios pacientes al hospital. Iba a visitarlos dos veces al día, pero confiaba en poder marcharse de vacaciones con Consuelo y Brigitte en agosto. No acababa de decidirse entre ir a Dordogne, a Bretaña o al sur. Al final, resultó que no pudieron ir a ninguno de los tres sitios. Tenía tantos enfermos a los que atender que le era imposible ausentarse. En lugar de eso, optaron por pasar unos cuantos días en Deauville, en la costa de Normandía, una vez que sus pacientes se hubieran recuperado.
Poco después de su regreso de las vacaciones, dos pacientes más tuvieron que ser hospitalizados porque tenían neumonía. Un día, a última hora de la tarde, salió del hospital ensimismada, pensando en la paciente que acababa de visitar, una anciana cuyo pronóstico no era nada bueno. Annabelle estaba intentando dar con alguna solución nueva para sus numerosas complicaciones, cuando se chocó de frente en la escalera del hospital con otra persona, que subía en el momento en que ella bajaba. Se golpearon tan fuerte que el hombre estuvo a punto de tirarla al suelo, así que hizo un rápido ademán para agarrarla antes de que cayera rodando por la escalera.
—Perdón, lo siento mucho —dijo ella azorada—. No miraba por dónde iba.
—Yo tampoco. —Él también se disculpó y le dedicó una sonrisa radiante—. ¿Ha venido a visitar a un amigo?
Era una confusión lógica, que hizo reír a Annabelle.
—No, soy médico.
Por lo menos el hombre no le había preguntado si era enfermera.
—Qué grata coincidencia —dijo él devolviéndole la risa—. Yo también. ¿Por qué nunca había tenido la suerte de conocerla?
Era francamente encantador y Annabelle no estaba acostumbrada a tratar con hombres tan zalameros. Hacía años que se había cobijado detrás de su papel de médico, viuda y madre de Consuelo. Los hombres nunca flirteaban con ella. Sin embargo, este en cuestión parecía bastante ocurrente y divertido, y no cabía duda de que era apuesto.
—¿Cuál es su especialidad? —le preguntó a Annabelle con mucho interés, sin importarle lo más mínimo que no hubieran realizado las presentaciones formales reglamentarias. Le dijo que él se llamaba Antoine de St. Gris, y le preguntó su nombre, a lo que Annabelle contestó. Se negaba a creer que fuera de Estados Unidos, pues hablaba francés sin una pizca de acento.
—La medicina de familia —respondió ella con modestia, algo apurada por estar hablando con un desconocido.
—Yo soy cirujano ortopédico —la informó él con mucho garbo.
Annabelle sabía que la mayoría de los cirujanos ortopédicos poseían un ego enorme, salvo durante la guerra, cuando habían tenido que arrimar el hombro y reconocer sus limitaciones como todos los demás, pues, después de ver tantas atrocidades, sabían que el daño que podían paliar era apenas ínfimo.
La acompañó hasta el pie de la escalera, según dijo, para asegurarse de que no se caía, y esperó hasta que se hubo montado en el coche, que conducía ella.
—¿Seré lo bastante afortunado de volver a verla? —le preguntó guiñándole un ojo, y Annabelle se echó a reír.
—Si me rompo la pierna, lo llamaré.
—No espere tanto. O tendré que pillar la neumonía para poder visitarla. Y sería una lástima. Preferiría volver a verla cuando ambos estemos sanos.
Se despidió de ella con la mano mientras la joven ponía en marcha el coche y acto seguido subió apresurado la escalera del hospital. Que un hombre así charlara con ella le había alegrado el día. Le ocurría muy pocas veces; es más, casi nunca.
Pasó una velada tranquila leyendo en voz alta para su hija Consuelo y después la acompañó a la cama. Y al día siguiente, en la consulta, estaba en medio de un reconocimiento de un paciente cuando Hélène le dijo que había un médico en la sala de espera que solicitaba verla inmediatamente. Decía que tenía que hacerle una consulta sobre un caso. En cuanto terminó con el enfermo, salió del despacho, confundida. No se imaginaba quién podía ser. Y allí estaba Antoine de St. Gris, con un elegante abrigo azul, creando un revuelo en la sala de espera y entreteniendo a los pacientes, que en su mayoría reían sin parar. Siguió contándoles chistes hasta que Annabelle le dijo que pasara a la consulta un momento.
—¿Qué está haciendo aquí? —le preguntó una vez dentro con una sonrisa azorada. Se alegraba de volver a verlo, pero estaba en plena jornada laboral—. Tengo pacientes que atender.
—No sé qué me ha pasado. Creo que ayer pillé un resfriado tremendo. Me duele mucho la garganta.
Sacó la lengua para que le examinara la garganta después de decirlo. Annabelle se rió de él. Era atrevido, irreverente y vergonzosamente encantador.
—Yo la veo bien.
—¿Y qué tal su pierna? —quiso saber entonces.
—¿Mi pierna? Bien. ¿Por qué?
—Creo que se le ha roto. Deje que le eche un vistazo.
Hizo ademán de tocarle el dobladillo de la falda, y Annabelle se alejó de él entre risas.
—Doctor, debo pedirle que se marche. Tengo que atender a mis pacientes.
—Bueno, no se preocupe. En ese caso, mejor quedemos para cenar.
—Eh... No puedo. Es que...
—Ni siquiera se le ocurre una excusa decente. —Se rió él—. Es patético, de verdad. Pasaré a buscarla a las ocho.
Y, dicho esto, volvió a la sala de espera, saludó a los pacientes y se marchó.
Era completamente arrollador, muy descarado y, a pesar de eso, o precisamente debido a eso, muy atractivo; casi irresistible, para ser sinceros.
—¿Quién era? —le preguntó Hélène con una mirada reprobatoria antes de indicar al siguiente paciente que pasara.
—Un cirujano ortopédico.
—Ya, eso lo explica todo —masculló Hélène entre dientes, y se percató de la expresión infantil en el rostro de su jefa. Nunca la había visto con esa mirada—. Está loco —añadió, y después sonrió a su pesar—. Aunque es un loco muy guapo. ¿Piensa volver a verlo?
Annabelle se ruborizó.
—Esta noche. Para cenar.
—Oh, oh... Tenga cuidado con él —le advirtió.
—Lo haré —le aseguró ella, y entonces continuó con las visitas.
Volvió a casa más tarde de las siete, después de haber atendido al último enfermo y haber cerrado la consulta. Consuelo estaba en la bañera, riéndose con Brigitte. Annabelle miró el reloj y se dio cuenta de que tenía menos de una hora para arreglarse para la cena con el atrevido del doctor St. Gris. Fue a darle un beso a su hija, quien quería jugar a las cartas con su madre después del baño.
—No puedo, cariño —le dijo para disculparse—. Voy a salir.
—¿De verdad? —Consuelo parecía sorprendida.
Era algo de lo más inusual. De hecho, no ocurría nunca, salvo una vez cada muchos meses, si Annabelle iba a una reunión de facultativos o a una conferencia para mujeres médicos. Aparte de esos casos, no salía jamás, pues carecía de vida social, por lo menos desde que se había marchado de Nueva York nueve años antes. Por eso, su respuesta tuvo las mismas consecuencias que si hubiera lanzado una granada de mano en pleno cuarto de baño.
—¿Adónde vas a ir?
—A cenar con un médico —concretó Annabelle con aire inocente.
—Ah. Y ¿adónde? —Consuelo quería saberlo todo, y su madre parecía algo avergonzada.
—No lo sé. Va a pasar a buscarme a las ocho.
—¿Es un hombre? Y ¿cómo es?
—Pues normal, como todas las personas —dijo Annabelle tirando pelotas al aire. No quería decirle que era muy guapo.
En ese momento salió del lavabo y fue a cambiarse de ropa. Esa noche hacía calor. Se puso un traje de lino blanco que se había comprado en Deauville y un sombrero muy bonito que había encontrado a juego. Se sentía un poco rara arreglándose tanto para una cita, pero no ocurría a diario que la invitaran a cenar, y no podía ponerse ese traje ni ese sombrero para trabajar.
Antoine de St. Gris llegó a las ocho en punto, y Brigitte lo invitó a pasar. Le indicó que se sentara en la salita y entonces vio que, aprovechando que la habían dejado sola cinco minutos, Consuelo bajaba la escalera a toda velocidad con el camisón puesto. Entró en la sala de estar y sonrió, mientras Brigitte trataba sin éxito de convencerla para que regresara a su habitación.
—Hola —saludó la niña muy alegre—. ¿Es usted el médico que va a cenar con mi madre?
En esa época le faltaban dos de los dientes frontales, cosa que le daba un aspecto todavía más gracioso.
—Sí. ¿Qué ha pasado con tus dientes? —le preguntó Antoine mirándola fijamente.
—Se me han caído —respondió ella muy orgullosa.
—Vaya, lo lamento —dijo él con seriedad—. Confío en que sepas dónde están y puedas volver a ponértelos. Sería un rollo quedarte sin dientes, ¿no crees? ¿Cómo muerdes una manzana?
Ella soltó una risita al oír sus palabras.
—No, no sé dónde están. Los puse debajo de la almohada y se los llevó el Ratoncito Pérez. Me los cambió por un caramelo. Pero pronto me saldrán dientes nuevos. Ya los noto... ¿Los ve?
Inclinó la cabeza formando un ángulo extraño y le mostró los diminutos bultitos blancos que empezaban a perforarle las encías.
—Pues cuánto me alegro —repuso él con una amplia sonrisa en el momento en que Annabelle entraba en la habitación. Vio cómo su hija conversaba tan tranquila con el médico.
—Vaya, ya os conocéis —comentó con cierto nerviosismo.
—Bueno, no nos hemos presentado oficialmente —confesó él, y entonces hizo una elegante reverencia dirigida a Consuelo—. Soy Antoine de St. Gris —le dijo con formalidad—. Me siento honrado de haberte conocido, y más ahora que sé que van a salirte dientes nuevos.
La niña soltó otra risita. Annabelle presentó a su hija, quien le hizo la reverencia correspondiente a Antoine.
—¿Lista? —le preguntó el médico a Annabelle, y ella asintió.
Le dio un beso a Consuelo antes de mandarle que subiera a su habitación y se preparara para irse a la cama, pues ya había cenado antes de darse el baño. Esta subió de dos en dos los peldaños después de saludar con la mano al invitado, mientras Annabelle lo acompañaba a la puerta.
—Lo siento —dijo muy serio, mientras la conducía al precioso Ballot Open Tourer de color azul que había dejado aparcado en la puerta. Era un coche muy elegante que encajaba con él a la perfección. Todo lo que rodeaba a aquel hombre denotaba estilo, decisión y seguridad—. No debería invitarte a cenar. Acabo de comprometerme. Me he enamorado ciegamente de tu hija. Creo que es la niña más adorable que he visto en mi vida.
Annabelle sonrió ante su comentario.
—Tienes muy buena mano con los niños.
—Hace mucho tiempo yo también fui niño. Y mi madre insiste en que sigo siéndolo, porque dice que nunca he madurado...
Annabelle entendía por qué debía de decirlo su madre, pero ese aire infantil era parte de su encanto. Se preguntó cuántos años tendría y calculó que unos treinta y cinco, es decir, unos cuatro años más que ella. Eran casi de la misma edad; sin embargo, el porte de Annabelle era mucho más serio y reservado. Él era una especie de bufón guapo y encantador. A ella le gustaba que fuera tan despreocupado y que tuviera tanto sentido del humor. A los pacientes de la sala de espera de su consulta también los había cautivado. Igual que a sus propios pacientes.
Charlaron de manera desenfadada mientras su pretendiente la llevaba en coche a Maxim's. Annabelle nunca había estado allí, pero sabía que era uno de los mejores restaurantes de París, y un sitio que siempre estaba de moda. Llevaba siglos en funcionamiento.
Cuando llegaron, quedó patente que lo conocían mucho en el local. El maître lo saludó y él reconoció a varios de los comensales del restaurante, a quienes les presentó a Annabelle con mucho orgullo. La presentó como doctora Worthington, cosa que siempre la hacía sentir importante. Se había esforzado mucho para ser merecedora de ese título.
Él propuso algunos platos que creía que podían gustarle a Annabelle y pidió la cena para los dos, así como una botella de champán. Ella no bebía casi nunca, pero el champán hacía que la velada pareciese una celebración. No había salido a cenar con un hombre desde que vivía con Josiah, hacía diez años. Su vida había sido totalmente distinta en Francia: en el frente, en la facultad de medicina y, en esos momentos, como madre de Consuelo. Sin embargo, de repente se veía allí, cenando en Maxim's con Antoine. Era algo totalmente inesperado, casi un capricho.
—¿Hace cuánto tiempo que eres viuda? —le preguntó él con delicadeza mientras cenaban.
—Desde que nació Consuelo —se limitó a contestar.
—Vaya, es demasiado tiempo sola, suponiendo que lo hayas estado —le preguntó con doble intención. Sentía curiosidad por ella. Era una mujer muy poco corriente: hermosa, distinguida, claramente de buena cuna y, además, médico. Nunca había conocido a nadie así, y se sentía muy atraído por ella.
—Sí que lo he estado —confirmó. De hecho, había estado sola mucho más tiempo. Nueve años, desde que Josiah la había abandonado, pero no podía decirle eso.
—Supongo que no llevabas mucho casada... —señaló él pensativo.
—Apenas unos meses. Mataron a mi marido en el frente, justo después de que nos casáramos. Nos conocimos mientras yo trabajaba en Villers-Cotterêts, en el hospital que montó Elsie Inglis, con personal médico femenino.
—¿Ya eras médico por aquel entonces? —Estaba confuso, pues eso significaba que era mayor de lo que aparentaba. Le parecía muy joven.
—No. —Annabelle sonrió—. Sólo era auxiliar. Aparqué los estudios de medicina para ir de voluntaria. Antes había trabajado en la abadía de Royaumont, en Asnières. Regresé a la universidad después de que naciera Consuelo.
—Eres una mujer emprendedora y muy valiente —dijo él claramente impresionado. Mientras tanto iban cenando; todo estaba delicioso. Él había pedido bogavante y ella tomó un plato de ternera muy fino—. ¿Qué te hizo decantarte por la medicina?
Quería saberlo todo sobre ella.
—Supongo que lo mismo que a ti. Desde que era niña, me encantaba la ciencia y la medicina. Pero nunca pensé que tendría la oportunidad de ejercerla. ¿Y en tu caso?
—Tanto mi padre como mis dos hermanos son médicos. Y mi madre debería haberlo sido. Siempre nos corrige cuando nos equivocamos. Y odio admitirlo, pero algunas veces tiene razón. —Se echó a reír—. Lleva muchos años ayudando a mi padre con la consulta. Pero ¿por qué ejerces aquí y no en Estados Unidos?
Seguía sin poder creer que no fuera francesa, ya que hablaba el idioma como una nativa. Jamás habría sospechado que era estadounidense.
—No sé. Las cosas salieron así. Vine como voluntaria para contribuir al esfuerzo bélico. Y después una circunstancia llevó a la otra. Uno de los cirujanos de Asnières me ayudó a entrar en la facultad de medicina de Niza. Además, no habría podido estudiar de haber estado vivos mis padres. A mi madre nunca le gustó mi fascinación por la medicina. Pensaba que acabaría contrayendo alguna enfermedad. Antes había trabajado con inmigrantes en Nueva York.
—Vaya, pues qué suerte he tenido de que vinieras a Europa. ¿Crees que regresarás a Estados Unidos algún día?
Ella negó con la cabeza, muy solemne.
—No me queda nadie allí. Toda mi familia ha desaparecido.
—Qué triste... —dijo él intentando ser empático—. Yo tengo una relación muy estrecha con los míos. Me sentiría perdido sin ellos. Somos como una tribu. —A Annabelle le gustaba ese aspecto de él. Parecía un hombre cercano y afable y, si todos sus familiares eran tan divertidos como él, debía de ser un grupo muy animado—. Y ¿qué me dices de la familia de tu difunto esposo? ¿Los ves a menudo?
—Muy poco. Viven en Inglaterra. Aunque la abuela de Consuelo vino a vernos no hace mucho. Es una mujer encantadora.
Sin embargo, no le dijo que era la primera visita que les hacía.
Había infinitos aspectos de su pasado que Annabelle no podía contarle. Que su verdadero esposo la había abandonado porque estaba enamorado de otro hombre. Que se había divorciado por esa causa. Que la habían violado y nunca se había casado con el padre de su hija... La verdad era mucho más impactante que la versión que solía relatar. Lo peor de todo era que Annabelle debía pagar por unos pecados que no había cometido, y así sería toda su vida. Él era tan abierto de mente que ella suponía que la verdad no le escandalizaría tanto como a otras personas. Pero, de todas formas, no podía contársela. La historia que había inventado era de una respetabilidad absoluta. Además, él no tenía motivos para sospechar lo contrario. Todo lo que la joven decía era francamente verosímil, y parecía tan educada y correcta que nadie sospecharía otra cosa de ella.
Durante la cena, Antoine comentó que nunca se había casado. La especialización en cirugía ortopédica lo había mantenido recluido en la facultad de medicina durante muchos años. Había estudiado en la Faculté de Médecine de París. Más adelante había hecho prácticas en el hospital Pitié-Salpêtrière, y había tenido que interrumpir sus estudios durante un tiempo debido a la guerra. De una forma espontánea, dejó caer que lo habían condecorado dos veces durante la contienda. A pesar de su estilo desenfadado, le parecía una persona impresionante, y era evidente que él pensaba lo mismo de ella. Mientras hablaban y degustaban los platos, Annabelle tuvo la sensación de que había aterrizado en su vida como un regalo caído del cielo. Se alegraba de que se hubiera chocado con ella en la escalera del hospital, porque de lo contrario no lo habría conocido. Y él parecía igual de encantado de haberse topado con Annabelle.
Cuando la acompañó a casa en coche le preguntó cuándo podría volver a verla. Ella no tenía ningún otro compromiso que le impidiera quedar; de hecho, no tenía ningún compromiso a la vista para el resto de su vida, salvo las cenas y veladas con su hija Consuelo, así que él le prometió que la llamaría al día siguiente para concertar una cita. Y, para gran asombro de la joven, la llamó.
Estaba en el despacho, rellenando los historiales de los pacientes que había visto esa mañana, cuando Hélène le dijo que el médico estaba al aparato. La invitó a cenar el sábado siguiente, es decir, al cabo de dos días. Era como un placer inesperado en su vida. De paso, Antoine le preguntó si a Consuelo y a ella les apetecería ir a comer el domingo con sus dos hermanos y los niños en casa de sus padres. La invitación le resultó muy atrayente. Así pues, se lo comentó a su hija por la noche. La niña se emocionó. Pensaba que el hombre había sido muy gracioso cuando le había hablado de sus dientes. Entonces miró a su madre muy pensativa y, de manera espontánea, le dijo que era muy simpático. Annabelle le dio la razón.
El sábado, Antoine la llevó a cenar a La Tour d'Argent, que era todavía más elegante que Maxim's. Ella se puso un sencillo vestido negro hecho a medida y el anillo de esmeraldas de lady Winshire. No tenía ninguna otra joya en Francia, pero no le hacía falta: derrochaba estilo incluso sin joyas. Su belleza natural era mucho más llamativa que cualquier complemento que pudiera ponerse. Y volvieron a pasárselo en grande, hablaron casi hasta medianoche de muchísimas cosas: la guerra, la cirugía, la medicina, la reconstrucción de Europa. Era el acompañante ideal para una velada, además de muy divertido.
El día que pasaron juntos con su familia fue todavía mejor. Al final, resultó que la casa de sus padres estaba a apenas unas manzanas de la de Annabelle. Sus hermanos eran tan entretenidos como él, y sus esposas eran muy dulces. Los niños tenían más o menos la misma edad que Consuelo, y toda la familia se pasaba el rato hablando de medicina, así que ella estaba en su salsa. La madre de Antoine era una especie de tirana benévola que los gobernaba a todos. Reprendía con frecuencia a Antoine y ponía los ojos en blanco, disgustada, cada vez que repetía que no entendía por qué no se había casado aún. En apariencia, aprobaba a Annabelle como futura nuera, y aseguró que le parecía increíble que no fuera francesa sino estadounidense y que se hubiera criado en Nueva York.
La abuela dejó que Consuelo se sentara en su regazo antes de sentar también por turnos a todos sus nietos, y después los persiguió por el jardín y jugó con ellos al pilla-pilla. Para cuando Antoine las llevó a casa, ambas estaban agotadas pero felices, porque habían pasado un día fantástico.
—Gracias por congeniar con mi madre —dijo Antoine con una sonrisa—. No suelo llevar a nadie a las comidas familiares de los domingos. La mayoría de las mujeres saldrían huyendo en cuanto vieran el percal...
—A mí me ha encantado —dijo Annabelle con sinceridad. Echaba tanto de menos a su familia que la de él le parecía una bendición, y para Consuelo era una maravilla rodearse de entornos familiares como ese, con tías, tíos, primos, abuelos... Era todo lo que les faltaba a ellas. Además, Consuelo disfrutó de cada minuto de la jornada, incluso más que su propia madre—. Gracias por invitarnos.
—Lo repetiremos —le prometió Antoine—. Te llamaré para organizar algunas cenas más la semana que viene.
No una, sino «algunas cenas»... De repente, Antoine se había convertido en una pieza angular de su vida, y Annabelle tenía que admitirlo: le hacía muy feliz. Y, a su modo de ver, que tuviera una familia así sumaba puntos.
La llamó el martes para invitarla a cenar el viernes por la noche y le propuso que comieran juntos el sábado en La Cascade, uno de los restaurantes más antiguos y elegantes de París, además de con su familia el domingo, si ella se veía con ánimos. Estaba claro que no perdía el tiempo.
Por suerte, todas y cada una de sus citas fueron absolutamente perfectas. La cena del viernes en el Ritz fue exquisita, igual que las otras dos cenas anteriores. La comida en La Cascade fue suntuosa y relajada a la vez, y luego fueron a pasear por los jardines de Bagatelle y admiraron los pavos reales. Cuando la acompañó a casa después de pasar la tarde juntos, ella lo invitó a quedarse a cenar con Consuelo y ella en la cocina. Luego, el médico estuvo jugando a las cartas con la niña, que gritó emocionada al ver que ganaba, aunque Annabelle sospechó que la partida estaba amañada.
Aquel domingo en familia fue todavía mejor que el primero. Eran un clásico ejemplo de la burguesía francesa, con sus particulares puntos de vista, sus opiniones políticas, sus reglas tácitas y sus normas de etiqueta, así como con sólidos valores familiares. A Annabelle le encantaba ese modo de pensar. Era tan tradicional como ellos y se divirtió mucho hablando con las dos cuñadas de Antoine antes de comer, mientras comentaban anécdotas sobre sus hijos.
Después de la comida entabló conversación sobre medicina con sus hermanos, pues uno de ellos había trabajado de cirujano en Asinères, aunque nunca habían coincidido, ya que Annabelle ya había vuelto a la facultad de medicina para cuando él fue trasladado allí. Todos parecían tener mil cosas en común, y Annabelle encajaba a la perfección en ese entorno.
El fin de semana siguiente, Antoine invitó a Annabelle y Consuelo a pasar un par de días con él en Deauville. Había reservado dos habitaciones separadas y su conducta demostró que deseaba ser francamente cauto. Consuelo estaba emocionada con la idea del fin de semana, y Annabelle también. Se alojaron en un hotel magnífico, anduvieron por el paseo marítimo, recogieron conchas, entraron en todas las tiendas y comieron un marisco delicioso. Al regresar a París, Annabelle le dijo que no sabía cómo agradecérselo. Consuelo subió adormilada a su habitación con Brigitte, pues el largo trayecto en coche la había dejado rendida, y ambos se quedaron un rato en el patio delantero, mientras él la contemplaba con ternura. Le rozó el rostro con delicadeza con sus largos dedos de cirujano y después le dio un beso. Entonces, la estrechó entre sus brazos.
—Me he enamorado de ti, Annabelle —le dijo en un susurro. Incluso él mismo se había sorprendido de su confesión, y Annabelle se emocionó al oír sus palabras.
Sin embargo, ella sentía lo mismo. Nunca había conocido a nadie tan maravilloso como él, ni tan atento con su hija y con ella. Jamás había sentido lo mismo por otra persona, ni siquiera por Josiah, quien siempre había sido más parecido a un amigo que a un amante, con una relación mucho menos romántica. Antoine la había levantado por los aires y subido a una nube; Annabelle estaba igual de enamorada que él. Además, todo había ocurrido muy deprisa. En ese momento volvió a besarla y se dio cuenta de que esta temblaba.
—No tengas miedo, cariño mío —la tranquilizó. Y entonces añadió—: Ahora ya sé por qué no me había casado. —Bajó la mirada hacia ella y le dedicó una sonrisa larga y pausada. Era el hombre más feliz del mundo, y ella era la mujer más feliz—. Te esperaba a ti —le susurró meciéndola en sus brazos.
—Yo también —dijo ella, y se fundió en su abrazo.
Se sentía total y absolutamente segura con él. Lo único que sabía a ciencia cierta sobre Antoine, lo único que creía a pies juntillas, era que jamás le haría daño. Nunca en su vida había confiado tan ciegamente en nadie.
### 23
Las semanas y los meses posteriores que Annabelle disfrutó con Antoine fueron como un sueño hecho realidad para ambos. El médico pasaba buena parte de los fines de semana con Annabelle y Consuelo. Dejaba que Annabelle presenciara algunas de sus operaciones. Por su parte, ella le consultaba dudas sobre el diagnóstico de algunos pacientes y respetaba su opinión y sus valoraciones, en ocasiones más que las propias. Antoine la invitó a todos los restaurantes buenos de París, y después de la cena solía llevarla a bailar. Cuando el clima se suavizó un poco, empezaron a dar largos paseos por el parque. Le gustaba llevarla a los jardines de Versalles, y allí estaban, besándose cogidos de la mano, cuando cayeron los primeros copos de nieve del invierno. Cada momento que compartían era mágico, pues ningún hombre había sido tan atento y cariñoso con ella en su vida, ni siquiera Josiah. Su relación con Antoine era más madura, mucho más romántica, y además tenían en común su profesión. Él era increíblemente detallista, con frecuencia se presentaba en su casa con un ramo de flores para Annabelle, y le regaló a Consuelo la muñeca más bonita que la niña había visto. Todo era poco para él. Además, madre e hija pasaban los domingos con la familia de Antoine. Annabelle tenía la impresión de que Consuelo y ella habían sido adoptadas y bien recibidas en todos los sentidos por los suyos.
Annabelle preparó una auténtica cena de Acción de Gracias en honor de Antoine, con el pavo relleno y otros detalles característicos, e intentó explicarle en qué consistía la festividad, que a él le pareció conmovedora. Pasaron la Nochebuena con la familia De St. Gris, y todos se intercambiaron regalos. Annabelle también había elegido un obsequio para cada uno de ellos: un cálido chal de cachemir para la madre de Antoine, unas elegantes plumas doradas para sus dos hermanos, una primera edición de un libro de medicina muy difícil de encontrar para su padre, preciosos jerséis para sus cuñadas y juguetes para todos los sobrinos. La familia fue igual de generosa con ella.
El día de Navidad, Annabelle los invitó a todos a su casa con el fin de agradecerles los numerosos domingos que Consuelo y ella habían compartido con ellos. Antoine todavía no había hecho oficial la relación, pero saltaba a la vista que tenía intenciones a largo plazo. Ya había empezado a hacer planes con ella para el verano siguiente. Y Hélène no dejaba de bromear con la médico sobre el tema.
—¡Oigo campanas de boda! —le dijo un día sonriendo.
Al final la secretaria había terminado por apreciarlo, pues notaba que era muy atento con Annabelle, que parecía pletórica de felicidad.
En Nochevieja, Antoine la llevó a bailar al Hôtel de Crillon. La besó con ternura a medianoche y la miró a los ojos. Y entonces, sin preámbulos, se arrodilló y la miró suplicante, mientras ella se mantenía de pie, con su vestido de noche de satén blanco, con pedrería plateada. Bajó la vista hacia él, asombrada. El hombre habló con solemnidad y una gran emoción en la voz.
—Annabelle, ¿me harías el honor de casarte conmigo?
No había ninguna otra persona a quien pudiera pedirle la mano, así que, con lágrimas en los ojos, la joven asintió con la cabeza antes de decir que sí. Antoine se levantó y la estrechó entre sus brazos, y las personas que los rodeaban en la sala de baile vitorearon a los recién comprometidos. Eran la pareja de oro allá donde fueran, dos personas guapas que además tenían talento, inteligencia, estilo y dignidad. Nunca se llevaban la contraria en nada, y él siempre se mostraba cariñoso y amable con ella.
Anunciaron su compromiso a la familia de Antoine el día de Año Nuevo. Su madre se echó a llorar y los besó a los dos, y después todos brindaron con champán. Se lo dijeron a Consuelo esa misma noche. Después de la boda, Antoine se mudaría a casa de ellas, donde vivirían todos juntos. Ya habían hablado incluso de los hijos que les gustaría tener. Él deseaba tenerlos con todas sus fuerzas, y ella también. Y esta vez todo saldría bien: Annabelle no volvería a estar sola. Era el matrimonio ideal que siempre había merecido tener, pero que se le había resistido hasta ese momento. Ahora todo sería perfecto. Todavía no se habían acostado juntos, pero él era tan sensual y apasionado con ella que no tenía dudas de que sería fantástico.
Lo único que le preocupaba era que Antoine seguía sin conocer su pasado. Nunca le había hablado de Josiah, ni de la naturaleza de su matrimonio, ni de por qué se había divorciado de ella o por qué motivo había huido de Nueva York. No le había contado que, de haberse quedado allí, la habrían apedreado y echado a patadas por ser una desgraciada, pues todos ignoraban los oscuros secretos de Josiah, y ella nunca los había propagado, ni lo haría mientras viviera.
No sabía nada acerca de la concepción de Consuelo, la violación de Harry Winshire en Villers-Cotterêts. Al principio, Annabelle creyó que no había motivos para compartirlo con él. Y, cuando se tomaron más confianza, deseó que lo supiera todo y pensó que era lo más adecuado, pero nunca encontró el momento idóneo. Y ahora que le había pedido si quería casarse con ella y había aceptado, le resultaba incómodo contarle todas esas cosas; daba la impresión de que era demasiado tarde. Sin embargo, Annabelle era una mujer de honor y consideraba que debía confesárselo. Había muchas posibilidades de que él nunca se enterara por otros medios, pero incluso en el caso de que no lo descubriera, Annabelle seguía pensando que se merecía saber la verdad. Había estado casada con un hombre y había sido violada por otro. Y lo que Antoine no habría podido imaginar jamás era que, salvo por la violación, Annabelle había permanecido virgen toda su vida. Tenía treinta y un años, y había estado casada dos de ellos, pero nunca había hecho el amor con un hombre; solo había sufrido aquel violento abuso sexual sobre el suelo en la oscuridad. Y, en cierto modo, a Annabelle le parecía importante que él lo supiera. Consideraba que lo que había vivido y experimentado formaba parte de su personalidad. Y aunque ambas historias eran dramáticas, no le cabía la menor duda de que Antoine sabría comprenderla.
El día después de Año Nuevo empezaron a hacer planes para la boda. Como para él eran sus primeras nupcias, deseaba una boda grande y, además, tenía muchos amigos a quienes invitar. Annabelle habría preferido algo más discreto, pues oficialmente era «viuda» y tenía muy pocos amigos en París, y ni un solo pariente aparte de Consuelo. No obstante, quería hacer lo que a él le hiciera feliz y lo que él considerase mejor.
Hablaron sobre la lista de invitados y su ubicación, así como de cuántos niños les gustaría tener, mientras terminaban de comer en Le Pré Catalan, en el Bois de Boulogne, y después fueron a dar un paseo. Hacía un día fresco y despejado. Y de repente, mientras ella paseaba con la mano engarzada en el brazo de él, supo que era el momento adecuado, tanto si le gustaba como si no. No podían comentar los pormenores de la boda, o el número de hijos que les gustaría tener juntos, sin que él supiera algunos detalles de su vida. Sabía que eso no cambiaría las cosas entre ellos, pero sentía que su honor la obligaba a contárselo.
Se produjo un lapso de pacífico silencio mientras caminaban, que ella aprovechó para volverse hacia su prometido con expresión seria.
—Tengo que contarte una cosa —le anunció casi en un susurro.
Sentía un hormigueo en el estómago, como si le bailara una mariposa dentro, pero quería quitarse el peso de encima cuanto antes y dejar volar la mariposa.
—¿De qué se trata? —preguntó él sonriéndole.
Era el hombre más feliz del universo.
—De mi pasado.
—Ah, sí, claro. Para pagarte los estudios en la facultad de medicina tuviste que trabajar como bailarina de cabaret en el Folies Bergère, ¿verdad?
—No va por ahí.
Ella sonrió. Le alivió saber que la haría reír durante el resto de su vida.
Pasaron por delante de un banco y Annabelle propuso que se sentaran. Eso hicieron y Antoine le colocó un brazo alrededor de los hombros y la acercó hacia su cuerpo. Le encantaba que lo hiciera. Por primera vez desde hacía años, se sentía amada, protegida y segura.
—Hay algunos aspectos de mi vida que no te he contado —le dijo con total sinceridad—. No estoy segura de si son importantes, pero aun así creo que deberías saberlos. —Respiró hondo y empezó a hablar. Era más duro de lo que había imaginado—. En otro tiempo estuve casada.
Él sonrió de oreja a oreja.
—Sí, amor mío, ya lo sé.
—Bueno, es que no fue exactamente lo que piensas, o con quien piensas.
—Qué misterioso suena eso...
—En cierto modo, lo es. O lo fue para mí... durante mucho tiempo. Me casé con un hombre llamado Josiah Millbank cuando tenía diecinueve años. Fue en Nueva York. Él trabajaba para el banco de mi padre. Ahora que lo veo con distancia, supongo que sentía lástima por mí después de la muerte de mi padre y de mi hermano. En realidad era más como un amigo, pues tenía diecinueve años más que yo. Pero un año después del accidente en el que murieron, me pidió en matrimonio. Proviene de una familia muy respetable, o mejor dicho, provenía. Y en aquel momento, todo parecía de lo más lógico. Sin embargo, nos casamos y no pasó nada.
»O dicho en plata: nunca nos acostamos juntos. Yo pensaba que era por mi culpa, que yo tenía algún defecto. El caso es que cuando se daba la ocasión, él siempre la posponía. Solía decir que teníamos "mucho tiempo por delante".
Antoine no dijo ni una palabra, y a Annabelle se le llenaron los ojos de lágrimas al recordar aquella decepción y aquella pena tan honda y tan olvidada ya. Continuó:
—Dos años después de que nos casáramos, me confesó que él pensaba que podría estar casado conmigo y llevar una doble vida. Pero, al parecer, no era capaz. Estaba enamorado de un hombre, un amigo íntimo de la universidad que siempre venía con nosotros. Yo no sospechaba nada. También lo tenía por amigo. Después de muchos rodeos, Josiah terminó por contarme que estaba enamorado de él y que llevaba veinte años amándolo. Pensaban marcharse juntos a México, es decir, iba a abandonarme. Lo que le hizo decidirse por fin fue que había descubierto que los dos tenían sífilis. No volví a verlo jamás. Murió a principios de este año. Pero, tranquilo, nunca corrí el riesgo de contagiarme, pues, como te he dicho, no nos acostamos juntos ni una vez. Cuando se disolvió nuestro matrimonio, yo seguía igual de virgen que cuando había jurado los votos. Sinceramente, yo estaba dispuesta a seguir casada con él a pesar de todo. Lo amaba y no me importaba renunciar a otro tipo de vida o de futuro personal. Sin embargo, él se negó. Dijo que tenía la obligación de dejarme libre, pues merecía algo mejor que lo que él podía darme: un marido de verdad e hijos, y todo lo que él me había prometido y no podía cumplir.
En ese momento del relato, las lágrimas empezaron a resbalarle a borbotones por las mejillas.
—Solicitó el divorcio porque yo me negué a hacerlo. Cuando lo hizo, pensaba que era lo mejor para mí. Pero en Nueva York, el único motivo de divorcio aceptado era acusar al otro de adulterio. Así pues, se divorció de mí alegando que le era infiel. Alguien filtró la historia a los periódicos y me convertí en una paria de la noche a la mañana. Todos me retiraron la palabra, incluso mi mejor amiga. Si me hubiera quedado, habría tenido que soportar el desprecio de todos aquellos que conocía en Nueva York. Era una marginada, una vergüenza. Entonces fue cuando me marché rumbo a Francia. Pensé que no me quedaba otra opción. Y fui a trabajar a la abadía de Royaumont. Así fue como recalé aquí.
—¿Y entonces fue cuando volviste a casarte? —Antoine reflejaba una increíble sorpresa. La única reacción que podía interpretar Annabelle en su rostro era la confusión absoluta.
La mujer sacudió la cabeza.
—No, no volví a casarme. No volví a mantener ninguna relación afectiva con ningún hombre. Estaba demasiado conmocionada por todo lo que había ocurrido en Nueva York. Me limité a trabajar día y noche. Ni siquiera miraba a los hombres.
—¿Y Consuelo es hija de una virgen? —preguntó él, todavía más confundido.
—Más o menos —admitió ella. Respiró hondo y le contó el resto—. Me violaron una noche en Villers-Cotterêts. Fue un oficial británico borracho, que resultó ser de una familia decente, aunque él era abominable, peor que la oveja negra. No lo vi más que esos minutos en los que abusó de mí, ni una sola vez más. Lo mataron poco después. Entonces descubrí que me había quedado embarazada. Trabajé casi hasta el séptimo mes de embarazo, porque me ataba la barriga con vendas para ocultarlo.
Aquellos detalles le resultaban muy dolorosos y le costaba mucho admitirlos ante él. Pero no le quedaba otro remedio. Una vez que lo supiera todo, Annabelle no volvería a tener secretos para él. Y la verdad de lo ocurrido era esa:
—Nunca me casé con él, pues ni siquiera lo conocía. Lo único que sabía era cómo se llamaba. Me quedé sola con Consuelo. No me puse en contacto con su familia hasta este año. Su madre vino a visitarnos y fue muy amable. Se mostró muy dulce, tanto con la niña como conmigo. Al parecer, no era la primera vez que su hijo hacía algo así. No se sorprendió. —En ese momento se volvió para mirar a Antoine a la cara, con el rostro surcado de lágrimas—. Así que estuve casada, pero no con él. Técnicamente, Consuelo es una hija ilegítima, por eso le puse mi apellido. Y no soy viuda. Soy divorciada, de un matrimonio con otro hombre. Y ahí se acaba la historia —dijo entonces, aliviada por fin.
—¿Ahí se acaba la historia? —preguntó él con tensión en la mirada—. ¿No has estado en la cárcel ni has matado a nadie?
Ella sonrió ante su pregunta y negó con la cabeza.
—No.
Lo miró con mucho cariño y se enjugó las lágrimas. Había sido duro contárselo todo, pero se alegraba de haberlo hecho. Quería ser totalmente sincera con él. Sin embargo, cuando volvió a mirarlo a la cara, él se puso de pie de un brinco y empezó a caminar. Parecía disgustado, casi en estado de shock. Incluso Annabelle tenía que reconocer que la historia era impactante.
—A ver si lo he entendido bien: estuviste casada con un hombre con sífilis, pero aseguras que nunca te acostaste con él.
—Eso es —confirmó ella en un susurro, preocupada por el tono de voz de Antoine.
—Se divorció de ti por un adulterio que tú insistes en que no cometiste, a pesar de que nunca te hizo el amor. Fuiste repudiada por la sociedad neoyorquina por culpa de un adulterio que no existió, pero que tu marido alegó para divorciarse de ti porque tú te negabas a divorciarte, a pesar de que él te había engañado con un hombre. Entonces huiste justo después del divorcio. Y, una vez aquí, te quedaste embarazada de forma ilegítima, de un hombre que aseguras que te violó. No te casaste con él ni volviste a verlo. Diste a luz a su hija bastarda, pero fingiste que eras viuda en lugar de divorciada, y no contaste a nadie que te había rechazado tu ex marido porque prefería acostarse con otro hombre. Y luego llevaste a esa hija bastarda a la casa de mis padres y dejaste que jugara con mis sobrinos, mientras actuabas como si fueras viuda tanto delante de mi familia como de mí, cosa que es otra mentira. Por el amor de Dios, Annabelle, ¿hay una sola cosa que sea verdad de todo lo que me has dicho desde el principio de nuestra relación? Y, para colmo, me aseguras que, aparte de esa oportuna violación, que dio como fruto a tu hija bastarda, casi eres virgen todavía. Pero ¿es que crees que soy imbécil?
La atravesó con la mirada, mientras sus palabras perforaban el corazón de Annabelle como un puñal. Jamás en su vida había visto a nadie tan enojado, aunque ella también estaba dolida. Rompió a llorar otra vez mientras se acurrucaba hecha un ovillo en el banco, y él caminaba en círculos cada vez más furioso. Annabelle ni siquiera se atrevía a alargar el brazo para tocarlo, pues temía que, si lo hacía, él le devolviera la caricia con un bofetón. Lo que Antoine le había dicho era imperdonable.
—Tienes que reconocer —dijo él con frialdad— que cuesta un poco de creer. Tu santa inocencia a lo largo de toda la vida, tu falta de responsabilidad sobre lo ocurrido..., cuando en realidad sospecho que engañaste a tu marido y que, para colmo de males, es probable que tengas la sífilis. Gracias a Dios que no me he acostado contigo. Me pregunto cuándo pensabas contarme este secretito. En Nueva York te trataron como a la ramera que obviamente demostraste ser, y luego vas y tienes una hija bastarda con alguien que aseguras que pertenece a la nobleza británica... Pero, vamos a ver, ¿quién se traga eso? Te has comportado como una zorra desde el principio hasta el final. Y por favor, ahórrate ese cuento de tu virginidad —la atacó—. Sabiendo que corro el riesgo de contraer la sífilis, no tengo intención de ponerla a prueba.
Si la hubiera golpeado con los puños no le habría hecho más daño que con sus insultos. En ese momento, Annabelle se puso de pie para mirarlo a la cara, temblando toda ella. Antoine acababa de demostrarle aquello que tanto había temido Annabelle: que tendría que cargar con los pecados de los demás y que nadie aceptaría nunca su inocencia, ni siquiera un hombre que aseguraba que la amaba, pero que no la creía cuando ella le confesaba la verdad.
—Todo lo que acabo de contarte es cierto —dijo Annabelle entre lágrimas—, desde la primera palabra hasta la última. Y no se te ocurra volver a llamar a mi hija «bastarda». Ella no tiene la culpa de que me violaran, y yo tampoco. Podría haber abortado, pero me daba tanto miedo que al final decidí tenerla de todos modos, y camuflarlo de la mejor manera posible para que las personas no la llamaran justo lo que tú acabas de llamarla. Puede que la sífilis sea contagiosa, pero desde luego la ilegitimidad, no. No tienes por qué preocuparte de que tus sobrinos se contagien de ella. Te aseguro que no corren ningún peligro con mi hija.
En esos momentos Annabelle estaba furiosa, y herida por la crueldad de las palabras de Antoine.
—¡No puedo decir lo mismo de ti! —volvió a insultarla sin piedad. Sus ojos quemaban como el fuego al hielo—. ¿Cómo se te ha ocurrido pensar que podrías engatusarme para que me casara contigo fingiendo ser viuda, olvidando mencionarme todo esto a propósito? Y me refiero a todo: desde la sífilis al adulterio, y por supuesto lo de tu hija bastarda. ¿Cómo has podido presentarte ante mi familia como algo que no eres? Y además ahora intentas convencerme de todas estas mentiras flagrantes. Por lo menos ten las agallas de reconocer lo que eres.
Estaba lleno de rabia. Se sentía como si ella le hubiera robado algo: su fe, su confianza y la santidad de su familia. Lo que acababa de confesarle era impensable, y no volvería a creer ni una sola palabra dicha por Annabelle. Y, por supuesto, no se tragaba esa patraña con la que ahora intentaba lavar su imagen.
—¿Y qué es lo que crees que soy, eh, Antoine? ¿Una ramera? ¿Qué ha pasado con el amor y la fe en mí que deberías sentir si tanto me quieres? No tenía por qué explicarte nada de esto. Lo más probable es que nunca te hubieras enterado. Pero deseaba contarte la verdad porque te amo y creo que tienes derecho a saberlo todo sobre mí. Las cosas malas que me han ocurrido fueron provocadas en su mayor parte por los demás, y ya he pagado un precio muy alto por ellas. Me abandonó un marido al que quería disolviendo un matrimonio que era una farsa, y por ese motivo me dio la espalda el único mundo que conocía hasta entonces. Perdí a todos mis seres queridos y viajé aquí sola a los veintidós años. Me violaron cuando todavía era virgen. Y tuve una hija, que no deseaba, también yo sola. ¿Cuántas penalidades más tengo que soportar para que te comportes como un ser humano y tengas un poco de compasión y fe en mí?
—Eres una fresca y una mentirosa, Annabelle. Lo llevas escrito en la cara.
—Entonces, ¿por qué no te habías dado cuenta antes? —preguntó ella, sin dejar de llorar mientras lo decía.
Se estaban gritando el uno al otro en medio del Bois de Boulogne, aunque por suerte no había nadie cerca que pudiera oírles.
—No me había dado cuenta antes porque mientes muy bien. Es más, eres la persona que mejor miente de todas las que conozco. Me tenías completamente engañado. Has contaminado a mi familia y mancillado todo lo que tanto quiero —la acusó él, con aire pomposo y tono cruel—. No tengo nada más que decirte —añadió, y entonces se apartó de ella cuanto pudo—. Me voy a casa, y no pienso acompañarte a la tuya. A lo mejor puedes pedirle a un soldado o a algún marinero que te lleve, y de paso darte una alegría en el camino de vuelta. No me atrevería a tocarte ni con la punta de la bota.
Se volvió para darle la espalda, antes de empezar a andar con zancadas largas, mientras ella se quedaba allí plantada mirándolo y temblando de la cabeza a los pies, e incapaz de creer lo que acababa de oír o lo que él había hecho. Un momento después, Annabelle oyó el motor del coche de Antoine y empezó a andar para salir del Bois de Boulogne. Se sentía igual que si su mundo se hubiese derrumbado, y sabía que no volvería a confiar en nadie jamás. Ni en Hortie. Ni en Antoine. Ni en ninguno de sus conocidos. De ahora en adelante, sus secretos serían solo suyos, y Consuelo y ella vivirían sin necesidad de ninguna otra persona. Estaba tan destrozada y abstraída que casi la atropelló un coche cuando por fin llegó a la carretera.
Llamó a un taxi y le dio la dirección al conductor. Estaba congelada hasta el tuétano cuando se sentó sin dejar de sollozar en el asiento posterior del vehículo. El amable ruso que iba al volante acabó por preguntarle si podía hacer algo para ayudarla. Pero ella se limitó a sacudir la cabeza. Antoine acababa de hacer realidad sus peores pesadillas: que nadie creería jamás en su inocencia y que la condenarían para siempre por lo que le habían hecho los demás. Lo poco que quedaba de su corazón acababa de romperse en mil pedazos a sus pies. Antoine le había demostrado que no existía el concepto del amor, ni del perdón. Y la idea de que Consuelo pudiera contaminar a su familia, o cómo la había insultado, hacía que le entraran ganas de vomitar.
Cuando llegaron a la casa del decimosexto distrito en la que vivía Annabelle, el caballeroso ruso blanco se negó a cobrarle la carrera. Sacudió la cabeza repetidas veces y volvió a ponerle el dinero en la mano.
—Nada puede ser tan horrible, señora —le dijo.
Él también había pasado muy malos tragos en los últimos años.
—Sí, sí que puede... —contestó Annabelle, y se atragantó en un sollozo.
Le dio las gracias y entró corriendo en casa.
### 24
Annabelle vagó por la casa como un alma en pena durante tres días. Canceló todas las visitas médicas, no fue a la consulta y le dijo a todo el mundo que estaba enferma. En realidad, lo estaba. Estaba enferma por dentro, le dolía el corazón por todo lo que Antoine le había reprochado y por todo lo que había destruido para siempre. Si la hubiera apedreado en la calle o le hubiera escupido a la cara, no le habría hecho tanto daño. En cierto modo, había hecho ambas cosas. Y algo peor: le había roto el corazón.
Le pidió a Brigitte que llevara a Consuelo al colegio y al parque, pues también a ellas dos les dijo que estaba enferma. La única que no se lo creyó fue Hélène, su ayudante. La mujer notaba que había ocurrido algo terrible, y temía que tuviera que ver con Antoine.
Annabelle estaba tumbada en la cama, pensando en la ruptura y en todo lo que le había dicho su prometido, cuando sonó el timbre. No tenía ganas de levantarse para responder, y Brigitte había salido. No quería ver a nadie. Después de todo lo que le había echado en cara el médico, a Annabelle no le quedaba nada que decir a nadie, y mucho menos a él. No había sabido de él desde que la había dejado tirada en el parque. Y no tenía intención de volver a dirigirle la palabra. De todos modos, dudaba que volviera a oír su voz algún día.
El timbre siguió sonando con insistencia al menos durante diez minutos, así que, al final, se puso una bata encima del camisón y bajó a la planta inferior. A lo mejor había una emergencia y alguien del barrio requería a un médico urgentemente. Abrió la puerta de par en par sin molestarse siquiera a ver quién era el visitante y se topó de bruces con Antoine. No se le ocurría nada que decir. Y por una fracción de segundo, él tampoco supo qué hacer.
—¿Me dejas pasar, por favor? —preguntó por fin con solemnidad.
Annabelle dudó, pues no estaba segura de si deseaba que aquel hombre volviera a entrar en su casa, pero después se apartó del paso poco a poco. Se quedó un momento rezagada antes de cerrar la puerta y no le invitó a sentarse. Permaneció de pie, mirándolo, en el recibidor.
—¿Te importaría que nos sentásemos un momento? —preguntó él de forma cautelosa.
Por suerte, Antoine todavía no había tenido tiempo de regalarle el anillo de compromiso, de forma que no tenía nada que devolverle.
—Preferiría no hacerlo —contestó ella con voz de ultratumba—. Creo que el otro día ya dijiste más que suficiente. Dudo que quede mucho más que añadir.
Él se sobresaltó al ver la mirada de ella. Era como si algo hubiese muerto en su interior.
—Annabelle, soy consciente de que fui demasiado severo contigo. Pero lo que me contaste era increíblemente difícil de asimilar. Me habías ocultado un matrimonio, y no sabía que tu hija era ilegítima. Incluso has estado expuesta a una enfermedad letal que podrías haberme transmitido una vez que estuviéramos casados.
Sus palabras fueron como otra bofetada en la cara, ya que le demostraron de nuevo que no había creído ni una sola palabra de lo que le había dicho. Desgarraron el corazón ya maltratado de Annabelle.
—Ya te dije que nunca estuve expuesta a la sífilis. De haberlo estado, jamás habría aceptado salir a cenar contigo. No me habría arriesgado a enamorarme de ti si me hubiera visto expuesta a una enfermedad que podía matarte. Te amo, Antoine. O te amaba. Ya te lo dije: nunca me acosté con Josiah.
—Cuesta un poco de creer. Estuviste dos años casada con ese hombre.
—Sí, y él se acostaba con su mejor amigo —contestó ella con la misma voz fantasmal—. Pero yo no lo sabía. Pensaba que el problema lo tenía yo, cuando resultó que quien tenía muchos problemas era él. Y lo único que conseguiste con tu reacción fue demostrarme que no tendría que haberte contado nada de todo esto.
Cuando lo miró a los ojos, estaba destrozada.
—¿Habrías preferido continuar mintiéndome, como habías hecho desde el principio? Entonces te habrías casado conmigo de manera fraudulenta. Y te recuerdo que eso es un delito.
—Por eso te lo conté. Lo que quería decir es que no debería haberme molestado en intentar compartirlo contigo. Es más, no debería haber entablado una relación sentimental contigo...
—¿Cómo puedes decir eso? Yo te amo —dijo él con pomposidad.
Annabelle ya no se sentía cautivada por sus encantos.
—Perdona, pero ya no me lo creo; y más teniendo en cuenta todo lo que me dijiste hace unos días. No se trata de ese modo a alguien a quien se ama.
—Estaba disgustado.
Annabelle no respondió a eso, sino que apartó la mirada. Él no se acercó más a ella. Tenía miedo de que, si lo hacía, la mujer le diera una bofetada. Sus ojos emanaban odio.
—Lo que dijiste de Consuelo es imperdonable. No volveré a dejar que te acerques a ella. Mi hija no tiene la culpa de ser ilegítima. La culpa es mía por haberla parido, por haber elegido tenerla a pesar de todo. Y ni siquiera tengo yo la culpa. El culpable fue un lunático borracho que me tiró al suelo y me violó. Y tú serías capaz de culparme a mí toda tu vida en lugar de creerme.
Los fríos ojos de Annabelle reflejaban lo dolida que estaba.
—Por eso he venido a hablar contigo. He estado dándole vueltas —dijo él con prudencia—. Lo admito, no es lo que esperaba de ti. Y no es exactamente lo que deseaba saber de mi esposa. Pero te quiero, y estoy dispuesto a hacer la vista gorda y perdonar todos tus errores del pasado. Lo único que te pido es que te hagas la prueba de la sífilis y me demuestres que no eres portadora de la enfermedad.
—No hará falta —contestó ella antes de volver a abrir la puerta de entrada. Empezó a temblar con el viento frío que soplaba esa tarde de enero—. No tendrás que perdonar mis errores ni los de otras personas, ni siquiera tendrás que pasarlos por algo. Consuelo no contaminará a tus sobrinos ni mancillará tus reuniones familiares, porque no volveremos a estar en ellas. Y no es necesario que me haga ninguna prueba, porque jamás volverás a ponerme la mano encima.
—Eso significa que tienes la enfermedad —dedujo él achinando los ojos.
—¿Es que quieres que te recuerde que me dijiste que no te atreverías a tocarme ni con la punta de la bota? Me acuerdo perfectamente de esas palabras. De hecho, recuerdo al dedillo todo lo que me dijiste, y siempre lo recordaré. Tal vez tú seas capaz de perdonarme, pero yo seré incapaz de perdonarte a ti.
—¿Cómo te atreves a decirme eso después de todo lo que has hecho? —De repente la ira se reavivó en él—. ¡Tienes suerte de que esté dispuesto a aceptarte con semejante historial! Una mujer como tú, que Dios sabe con cuántos hombres se habrá acostado, además de tener maridos sifilíticos, hijos ilegítimos y vete tú a saber qué aventuras más entre esas dos perlas, ¡o después!
Annabelle sintió ganas de abofetearlo, pero no merecía la pena. Ya no.
—Muy bien, Antoine. Ya he oído todo lo que querías decirme. Y nunca lo olvidaré. Ahora, sal de mi casa. Fuera.
Ambos temblaban por el frío invernal, y él se la quedó mirando, incrédulo.
—Estás de broma, ¿verdad? ¿Quién más crees que querrá estar contigo después de todo lo que has hecho en el pasado?
Tenía un porte erguido y majestuoso, y estaba muy guapo. Sin embargo, lo que ya no le gustaba a Annabelle era el hombre que había dentro de ese traje a medida.
—Tal vez nadie —dijo Annabelle como respuesta a su pregunta—. Y en el fondo no me importa. He estado sola desde que Josiah me abandonó hace nueve años, casi diez ya. Tengo a Consuelo, mi hija «bastarda», como tú la llamaste. No necesito a nadie más. Y a ti ya no te quiero. —Señaló la puerta abierta una vez más—. Muchas gracias por su generoso ofrecimiento, doctor, pero me temo que tengo que rechazarlo. Ahora, márchese, por favor.
Annabelle había erguido el cuerpo y él se dio cuenta de que hablaba en serio. Él era incapaz de creérselo.
Se quedó a unos centímetros de ella y después la miró por encima del hombro con desprecio.
—Estás chalada. Nadie te querrá si le cuentas la verdad.
—No te apures, no tengo intención de volverme a ver en esa tesitura. Me has dado una buena lección. Gracias, ya la he aprendido. Siento que todo esto haya sido tan decepcionante para los dos y que te resultara tan difícil creer y aceptar la verdad cuando te la conté.
—Ya te lo he dicho —repitió Antoine—, estoy dispuesto a perdonarte, o por lo menos a tolerar tus defectos. Solo hace falta que te hagas la prueba que te he pedido. Tienes que admitir que es justo.
—Nada de todo esto es justo. Nunca lo ha sido, ni antes de conocerte, ni ahora. Y no quiero que me toleren. Quiero que me amen. Creía que tú me amabas. Pero, al parecer, los dos estábamos muy equivocados.
Se quedó allí plantado, mirándola, y entonces sacudió la cabeza y, sin decir ni una palabra más, salió de la casa. Annabelle cerró de un portazo tras él, se apoyó en la puerta y tembló de la cabeza a los pies. Ningún hombre había sido tan atento con ella como él al principio de su relación, ni tan cruel al final.
Se dirigió a la sala de estar y se sentó allí sola, mirando al infinito. Seguía sin lograr asimilar todas las cosas que le había reprochado sobre Consuelo, como lo de que era una bastarda que podía contaminar a su familia, ni podía creer que Antoine insistiera en que ella era una especie de ramera solo porque estaba divorciada, o que no quisiera aceptar que la habían violado.
Seguía allí sentada cuando Brigitte y la niña regresaron del parque. Esta, que estaba preocupada por su madre, se le subió al regazo y le puso los brazos alrededor del cuello. Eso era lo único que necesitaba en esos momentos Annabelle. Su hija era la única persona en quien podía confiar, o en quien confiaría de ese momento en adelante.
—Te quiero, mamá —dijo la niña al ver que se le llenaban los ojos de lágrimas.
—Yo también te quiero mucho, mi vida —contestó Annabelle abrazándola muy fuerte.
Y, a pesar de que se sentía fatal y tenía el aspecto de que le hubieran dado una paliza, lo que, en cierto modo, era cierto, Annabelle se reincorporó al trabajo al día siguiente. No le quedaba otro remedio. Tenía que continuar con su vida. Antoine le había dado una buena lección acerca de lo estrecha de miras que podía ser la gente, y de las presuposiciones que hacía todo el mundo. A decir verdad, ya había aprendido esa lección en Nueva York, cuando todos pensaron lo peor de ella. Pero el francés había traicionado su confianza y destruido su fe en la raza humana de una vez por todas.
En la consulta, Hélène se preocupaba mucho por ella, y siguió angustiada durante varias semanas. Annabelle no volvió a saber de Antoine. Él pensaba que ella era tonta por no estar dispuesta a que la «toleraran» y la «perdonaran» por pecados que aseguraba no haber cometido. Era evidente que el médico solo estaba dispuesto a imaginarse lo peor.
La joven volvió a concentrarse en sus pacientes y en su hija, y se olvidó de los hombres. A lo largo de los meses siguientes mostró un aire taciturno, aunque cuando llegó marzo ya se sentía mejor. Es más, empezaba a sonreír de nuevo, pasaba los domingos por la tarde en el parque con Consuelo... Al principio, la niña se había llevado una decepción cuando dejaron de ir a comer los domingos a casa de la familia De St. Gris, pues se divertía mucho con los sobrinos de Antoine. Su madre le contó que este y ella creían que se habían equivocado y que habían dejado de ser amigos. Y cada vez que Annabelle pensaba en cuando el hombre había acusado a Consuelo de poder contaminar a su familia, porque era indigna de estar con ellos, se repetía por qué estaba sola y por qué tenía intención de seguir así para siempre. Su última visita, además de decepcionarla y de destrozar toda esperanza que pudiera quedarle en la decencia de la humanidad, había conseguido convencerla de lo que ya sabía: que nunca podría eludir el destino al que Josiah la había condenado y que Harry Winshire había remachado. Lo único que verían en ella serían las etiquetas que los demás le colgaran, por las que la hacían responsable de sus malas experiencias. Ahora estaba convencida de que nadie creería jamás en su inocencia, nadie confiaría en ella ni la amaría, independientemente de lo que dijera. Antoine había hecho realidad todos y cada una de sus peores pesadillas.
### 25
Annabelle recibió dos cartas a principios de primavera. Ambas le dieron mucho que pensar. Una de ellas la había enviado lady Winshire, quien invitaba a Consuelo y a ella a pasar unos días juntas en Inglaterra. Le decía que pensaba que sería beneficioso para la niña el ver de dónde procedía la otra mitad de su familia y cómo vivían, pues eso formaba parte de sus raíces. Confiaba en que fueran a verla en cuanto pudieran. Le dio vueltas a la propuesta, pero no estaba segura. Harry Winshire seguía siendo un recuerdo terrible para ella, pero, al mismo tiempo, lo que decía su madre era cierto. La cuestión no era Harry, sino Consuelo y la abuela que por fin había conocido. Tenía la sensación de que a su hija le haría ilusión ir a visitarla.
La segunda carta era del empleado del banco de su padre que seguía al cargo de sus asuntos financieros. Durante todo ese tiempo, habían ido transfiriéndole dinero para sus gastos en Francia, pero el grueso de su fortuna continuaba en Estados Unidos. Por primera vez en mucho tiempo, el empleado le preguntaba qué quería hacer con la casa de Newport. Hacía diez años que no la pisaba, pero nunca se había visto con ánimos de desprenderse de ella. Tenía muchos recuerdos asociados a esa casa, aunque tampoco se imaginaba regresando allí, ni siquiera de visita. Y también formaba parte de la herencia familiar de Consuelo, mucho más que los terrenos de lady Winshire, pues el padre de Consuelo nunca había entrado en sus vidas.
El empleado del banco le había escrito para contarle que le habían hecho una oferta más que razonable para comprar la casa de verano. Blanche, William y los demás sirvientes continuaban viviendo allí y manteniéndola en perfecto estado, pero habían perdido toda esperanza de volver a ver a Annabelle. No podía decir que se equivocaran. Durante todos esos años, ella no había sentido deseos de regresar. De vez en cuando lo echaba de menos, pero también conocía el sufrimiento y el ostracismo que sufriría si volvía, aunque fuese unos días. No le quedaba nadie a quien visitar en su país. Y temía que, si regresaba, se reabrirían las antiguas heridas causadas por la pérdida de su familia y de todos sus seres queridos, incluido Josiah. No quería verse obligada a revivir ese dolor. A pesar de todo, tampoco se sentía preparada para venderla, aunque el banquero tenía razón, la oferta que le habían hecho era buena. Era incapaz de tomar una decisión.
Se centró primero en la propuesta de lady Winshire y se la comentó a Consuelo esa misma noche, durante la cena. La niña se entusiasmó al instante y dijo que ella quería ir. Y, aunque pareciera extraño, a Annabelle también le apetecía. Pensaba que a las dos les sentaría bien salir un poco. Su hija le había pedido varias veces que volvieran a Deauville, pero ella no quería, después de la amarga experiencia con Antoine. Tenía la impresión de que los malos recuerdos la acechaban por todas partes, y no hacía más que esconderse de sus propios fantasmas.
Respondió a la carta de lady Winshire al día siguiente para decirle que les encantaría ir a verla. En cuanto leyó su respuesta, lady Winshire contestó inmediatamente y les propuso distintas fechas para elegir. Escogieron el fin de semana del cumpleaños de Consuelo. Cumpliría siete años. Para entonces haría mejor tiempo. Annabelle le pidió a su ayudante Hélène que comprara los billetes e hiciera los preparativos del viaje. Primero tomarían el tren a Calais, cruzarían el canal de la Mancha hasta Dover, y luego lady Winshire mandaría que alguien las fuera a buscar. Desde allí solo había dos horas de coche hasta su finca.
Cuando llegó el fin de semana en cuestión, Consuelo estaba tan nerviosa que no podía dejar de moverse ni un momento. Brigitte iba a quedarse en París, donde había pensado disfrutar del fin de semana con su nuevo novio. Annabelle se subió al tren con las dos maletas en la mano y guió a la niña para que no se perdiera, y ambas se acomodaron en el compartimiento de primera clase que Hélène les había reservado. Era la mayor aventura que Consuelo vivía desde que se habían mudado a París dos años antes, aparte del fin de semana en Deauville con Antoine. Ya no hablaban de él. Aunque todavía era pequeña, había entendido que el tema resultaba doloroso para su madre, así que evitaba mencionarlo. Annabelle se lo había encontrado una vez en el hospital, pero en cuanto lo había visto, se había dado la vuelta y había corrido por la escalera de servicio para llegar por otro camino a la habitación del paciente al que iba a visitar. No quería volver a hablar con él en la vida. Su traición había sido demasiado grande.
Mientras el tren salía de la Gare du Nord, Consuelo lo observaba todo con fascinación y Annabelle sonreía. Comieron en el vagón-restaurante «como dos damas», tal como dijo su hija, y después se deleitaron con el paisaje que pasaba ante ellas, hasta que la niña acabó por dormirse en el regazo de su madre. Esta apoyó la cabeza en el asiento y recapacitó sobre los últimos meses transcurridos. Habían sido muy duros. Era como si Antoine no solo le hubiera arrebatado el sueño que le había ofrecido, sino también la esperanza de que cambiaran sus condiciones de vida.
En esos momentos Annabelle tenía la impresión de que siempre la castigarían por su pasado. Había sido víctima de las decisiones de otras personas, de sus debilidades y sus mentiras. Era deprimente asimilar ese sentimiento, como si la verdad no fuera a salir a la luz jamás y ella nunca fuera a ser capaz de limpiar su nombre. No importaba cuántas cosas hubiera vivido desde entonces, o qué logros hubiera conseguido, lo que parecía pender en el aire eternamente, igual que un tatuaje que no pudiera borrarse, eran los pecados con los que la habían hecho cargar, aunque se trataran de los pecados de otras personas. Era una buena madre y una excelente médico, una mujer decente, y a pesar de todo siempre sería estigmatizada por su pasado. Y el caso de Consuelo era mucho peor: estaba marcada desde la cuna. Antoine era el único que se había atrevido a pronunciar la palabra. Era un apelativo cruel para una niña inocente.
Apenas tres horas más tarde llegaron a Calais y se subieron al barco. Annabelle temía ese momento. Le gustaba navegar, pero el canal de la Mancha siempre estaba agitado y tenía miedo de que Consuelo se marease con el vaivén. Al final resultó que la travesía fue muy accidentada, pero la pequeña disfrutó de cada minuto del trayecto. Cuanto más subía y bajaba el ferry y más se tambaleaba entre las olas bravas, más reía y más gritaba, completamente emocionada. Para cuando llegaron a Dover, en la otra orilla, Annabelle empezaba a sentirse mareada, pero su hija estaba más contenta que nunca. Bajó de un salto de la embarcación, dándole una mano a su madre y con su muñeca preferida en la otra.
El chófer de lady Winshire las esperaba en un Rolls de época en el muelle, tal como les había prometido la señora. El trayecto de dos horas recorría una zona campestre, que describía curvas suaves entre granjas con vacas y fincas inmensas, salpicadas por algún que otro castillo antiguo. Para Consuelo, aquello era una aventura increíble. Y ahora que habían bajado del barco, Annabelle también empezaba a disfrutar del viaje.
Sin embargo, ninguna de las dos estaba preparada para la magnificencia de la propiedad de los Winshire, ni para el esplendor de la enorme mansión. Había árboles centenarios altísimos que bordeaban el largo camino que conducía a la vivienda principal, y gracias a la fortuna de lady Winshire, independiente de la del difunto conde, la propia mansión, construida en el siglo XVI, lucía un aspecto impecable. Incluso los establos eran más grandes, más limpios y más hermosos que muchas casas corrientes. Lady Winshire había destacado como jinete cuando era joven, y aún le gustaba mantener el establo con unos cuantos caballos de pura raza, que media docena de mozos de cuadra montaban a diario.
Cuando salió a recibirlas a la escalinata de la entrada, lucía un aspecto más imponente que nunca, con un vestido azul oscuro, resistentes zapatos para caminar, las consabidas perlas y otro sombrero enorme. Blandía el bastón de plata como si fuese una espada, con la que señaló sus maletas antes de mandarle al chófer que se encargara de llevarlas a sus habitaciones. Y, acto seguido, con una amplia sonrisa y después de haber abrazado tanto a Annabelle como a Consuelo, quien miraba con los ojos como platos todo lo que veía, les indicó que la acompañaran dentro.
Recorrieron una galería interminable, en la que se sucedían decenas de retratos de familia con semblante serio; después pasaron por un salón gigantesco con una lámpara de araña magnífica, una biblioteca abarrotada de libros antiguos, una sala de música con dos arpas y un majestuoso piano, y un comedor con una mesa lo bastante grande para acomodar a cuarenta comensales, que era donde solían dar las cenas de sociedad en otros tiempos. Las habitaciones para recibir a los invitados se sucedían sin descanso, hasta que por fin llegaron a una salita de estar más pequeña y acogedora, donde a la condesa le gustaba sentarse para contemplar los jardines. Cuando Annabelle observó los alrededores y el esplendor de aquella mansión, pensó que costaba mucho creer que alguien que hubiera crecido en ese entorno pudiera llegar a violar a una mujer, para después amenazarla de muerte si contaba lo sucedido. Encima de un tapete había fotos de ambos hijos de la familia Winshire. Y, después de tomar un té con bollitos, acompañados de nata espesa y mermelada, lady Winshire le pidió a una de las sirvientas que le enseñara los establos a Consuelo. Había mandado que ensillaran un poni, para que si, le apetecía a la niña, pudiera montarlo y dar una vuelta con él. Annabelle le agradeció su amabilidad y su cálida bienvenida en cuanto Consuelo desapareció para ver el poni.
—Tengo mucho que compensar... —se limitó a decir la anciana, y Annabelle sonrió.
No la hacía responsable de los delitos de su hijo. Además, ¿cómo podía seguir considerando un delito lo que le había hecho cuando había resultado en Consuelo, a pesar del modo en que hubiera sido concebida? Compartió este pensamiento con lady Winshire, quien agradeció a Annabelle tal generosidad de espíritu, y le dijo que, a pesar de lo mucho que lo había amado, su hijo no merecía a alguien como ella. Le confesó con tristeza que había sido un hijo irresponsable y malcriado.
Charlaron un rato más y después salieron a pasear por los jardines, y al cabo de unos minutos vieron aparecer a uno de los mozos de cuadra, con Consuelo montaba en el poni. Parecía flotar en una nube. Saltaba a la vista que la niña se lo estaba pasando en grande, gracias a la abuela que acababa de recuperar. Lady Winshire le preguntó a Annabelle si a ella también le apetecía montar a caballo. La joven le respondió que hacía años que no montaba, pero tal vez se animara a la mañana siguiente. Todos esos lujos y caprichos habían desaparecido de su vida en cuanto había abandonado Estados Unidos. Pensó que tal vez fuera divertido volver a montar a caballo. De jovencita lo hacía con frecuencia, sobre todo en verano, cuando estaban en Newport.
Después de que Consuelo y el mozo de cuadra regresaran a los establos, Annabelle mencionó que estaba planteándose vender la casa de campo de Newport.
—¿Por qué quiere venderla? —le preguntó la anciana, casi como un reproche—. Me dijo que había pertenecido a su familia desde hacía generaciones. Es preciso que la conserve, es parte de su historia. No la venda.
—No estoy segura de si voy a regresar. Hace diez años que no la piso. Está allí plantada, olvidada y vacía, atendida por cinco sirvientes.
—Debería volver —dijo lady Winshire con rotundidad—. Además, también es parte de la historia de Consuelo. La niña tiene derecho a eso, a todas sus cosas, y a todas las nuestras. Toda su herencia define quién es, y en quién se convertirá algún día. Del mismo modo que es parte de usted.
Era evidente que tener todas esas pertenencias le había hecho un flaco favor a Harry, pensó Annabelle para sus adentros, pero no se atrevía a contestarle algo así a su madre, quien, a fin de cuentas, ya lo sabía, así que lo guardó para sí misma.
—No puede huir eternamente de la persona que es, Annabelle. No puede negarlo. Y Consuelo debería ver la casa. Tendría que llevarla algún día de visita.
—Todo eso es agua pasada para mí —contestó Annabelle con aire testarudo, mientras lady Winshire negaba con la cabeza.
—Para ella solo es el principio. Consuelo necesita algo más que París en su vida, igual que usted. Necesita que nuestras historias se entrelacen y le sean ofrecidas como un ramo de flores.
—Me han hecho una oferta muy buena. Y siempre podría comprarme alguna propiedad en Francia.
Sin embargo, nunca lo había hecho. Lo único que tenía en París era una casa muy modesta en el decimosexto distrito. No poseía ninguna casita en el campo, y tenía que reconocer, al ver cómo se divertía allí Consuelo, que a su hija le sentaría de fábula algo similar.
—Sospecho que podría hacerlo igualmente —supuso acertadamente la dama.
Annabelle había heredado una inmensa fortuna de su padre, y otra casi igual de grande de su madre, de las que apenas había gastado nada en años. Ya no encajaba con su nuevo estilo de vida ni con su labor como médico, y había puesto mucho esmero en que ningún rasgo opulento se reflejara en ella durante los últimos diez años. Eso decía mucho en su favor, pero en esos momentos, a punto de cumplir los treinta y un años, tenía edad suficiente para empezar a disfrutar de su fortuna.
Entonces lady Winshire se dirigió a ella con una sonrisa:
—Confío en que vengan a verme con frecuencia. Todavía viajo a Londres de vez en cuando, pero la verdad es que paso aquí la mayor parte del tiempo. —Era la casa familiar de su difunto esposo, cosa que le recordó otro tema que quería comentarle a Annabelle cuando Consuelo no estuviera presente. No estaba segura de si le parecería un poco precipitado, pero llevaba dándole vueltas desde hacía tiempo—. He pensado mucho en la situación de Consuelo, provocada por el hecho de que su padre y usted no estuvieran casados. Eso podría suponer un gran lastre para la niña dentro de unos años, cuando crezca un poco. No puede mentirle toda la vida, y algún día es posible que alguien ate cabos. He hablado con nuestro abogado, y no tiene mucho sentido que yo la adopte a estas alturas. Además, es su hija. Por otra parte, Harry no puede casarse con usted de manera póstuma, lo cual es una pena. Pero lo que sí puedo hacer es reconocer a Consuelo oficialmente, lo cual mejoraría las cosas en cierto modo, pues podría añadir nuestro apellido al suyo, si le parece adecuado, por supuesto —le sugirió con mucho tacto.
No deseaba ofender a la madre de la niña, que tan valiente había sido al afrontar todas las responsabilidades de su crianza en solitario. Sin embargo, Annabelle le respondió con una sonrisa. Desde que había tenido que aguantar los insultos de Antoine, especialmente el de que Consuelo era una bastarda, ella también estaba muy sensibilizada con ese tema. Solo de pensarlo volvía a sentirse dolida.
—Me parece una idea fantástica —dijo Annabelle muy agradecida—. Podría facilitarle las cosas en el futuro.
—¿No le importaría, Annabelle? —Lady Winshire parecía esperanzada.
—Al contrario, me encantaría. —Asociaba el apellido con lady Winshire, no con su malvado hijo—. De ese modo, mi hija se convertiría en Consuelo Worthington-Winshire, o a la inversa, lo que usted prefiera.
—Creo que lo mejor sería Worthington-Winshire. Puedo pedir a nuestros abogados que empiecen a preparar los documentos ahora mismo.
Sonrió de oreja a oreja a Annabelle, quien se inclinó hacia delante y la abrazó.
—Qué amable es con nosotras —le dijo ella para agradecérselo de nuevo.
—¿Y por qué no iba a serlo? —preguntó la anciana restándole importancia—. Es usted una buena mujer. Me he dado cuenta de que ha sido una madre fabulosa para la niña. No sé muy bien cómo, pero, a pesar de todo, ha logrado llegar a ser doctora en medicina. Y por las referencias que me han llegado, bastante buena en su trabajo. —El médico particular de la señora había hecho algunas discretas averiguaciones a través de colegas de profesión que conocía en Francia—. Pese a todo lo que le hizo mi hijo, no le ha reprochado nada a la niña, ni siquiera a mí. Y empiezo a pensar que ha dejado de reprochárselo incluso a él. No estoy segura de lo que habría hecho yo en su lugar.... Es una mujer respetable, responsable, decente y muy trabajadora. Se dejó la piel por ayudar a los demás durante la guerra. No tiene familia que la apoye. Lo ha hecho todo por sí misma, sin que nadie le echara una mano. Fue lo bastante valiente para tener una hija ilegítima y asimilar la situación lo mejor posible. No se me ocurre una sola cosa por la que no debería respetarla o apreciarla. De hecho, es una mujer extraordinaria y estoy orgullosa de haberla conocido.
Sus palabras sinceras provocaron las lágrimas de Annabelle. Era el antídoto contra todo lo que le había dicho Antoine.
—Ojalá yo supiera verlo desde ese prisma —dijo con tristeza—. Lo único que veo son mis errores. Y lo único que la gente parece ver, salvo usted, son las etiquetas que los demás me han colgado.
En ese momento le confesó uno de sus secretos mejor guardados, pues le contó que se había divorciado antes de marcharse de Estados Unidos, y le explicó los motivos. Con ello solamente consiguió que lady Winshire la admirase todavía más.
—Es una historia asombrosa —comentó la anciana después de recapacitar durante unos instantes. No se escandalizaba con facilidad, y el relato del matrimonio de Annabelle con Josiah no había hecho más que aumentar su lástima por la joven—. Qué tonto fue al creer que podría compaginarlo todo.
—Creo sinceramente que pensaba que podría, pero luego descubrió que era imposible. Y su amigo nos acompañaba a todas partes. Eso debió de dificultarle todavía un poco más las cosas.
—A veces las personas somos muy bobas —insistió lady Winshire sacudiendo la cabeza—. Y lo más ingenuo de todo fue que él creyera que divorciándose de usted no emborronaría su apellido. Es muy bonito eso de decir que deseaba dejarla libre para que pudiera rehacer su vida. Cuando se divorció por adulterio con el fin de liberarla no hizo más que arrojarla a los perros. Por el mismo precio, también podría haberla quemado en la hoguera en la plaza mayor, si me permite la expresión. De verdad, qué ignorantes y egoístas pueden ser a veces los hombres. Supongo que no es fácil enmendar ese error a estas alturas. —Annabelle sacudió la cabeza—. Pero tiene que repetirse que le es indiferente. Usted conoce la verdad. Y eso es lo que importa.
—Pero no evitará que la gente siga cerrándome la puerta en las narices —dijo Annabelle con nostalgia—. Igual que a Consuelo.
—¿Tanto le importa esa gente en el fondo? —preguntó con sinceridad lady Winshire—. Si realmente son personas lo bastante malvadas para hacerle eso a usted y a la niña, son ellas quienes no se merecen a ninguna de las dos, y no al contrario.
Annabelle le contó la experiencia, todavía reciente, que había vivido con Antoine, y la dama se indignó.
—¿Cómo se atrevió a decirle cosas como esas precisamente a usted, Annabelle? No hay nada más estrecho de miras y más pervertido que las pretensiones de superioridad moral de quienes se hacen llamar burgueses. Querida, la habría hecho desdichada, créame. Hizo muy bien en no dejar que volviera con usted. No la merecía.
Annabelle sonrió al oírle decir eso y le dio la razón. Estaba muy triste por todo lo que había pasado, pero una vez que había descubierto cómo era en realidad Antoine, no lo echaba de menos. Lo único que añoraba era la ilusión y la esperanza acerca de cómo podría haber sido la vida a su lado, algo que, evidentemente, nunca tendría lugar. Había sido una fantasía. Un sueño hermoso que se había convertido en una pesadilla a raíz de sus feas palabras y sus prejuicios. Había dejado patente que estaba dispuesto a creer lo peor de ella, tanto si era cierto como si no.
En ese momento, Consuelo entró dando saltos en la sala de estar, emocionada de haber visto tantos caballos en el establo y de haber dado una vuelta en poni. Y su entusiasmo fue todavía mayor cuando vio su dormitorio. Era una habitación grande y soleada, decorada con telas de seda y chintz con estampado de flores, y contigua a la habitación de su madre, que era prácticamente igual que la suya. Esa misma noche, durante la cena, le contaron la idea de darle un doble apellido.
—Es un poco difícil de escribir —dijo Consuelo, preocupada por los aspectos prácticos, y tanto su madre como su abuela se echaron a reír.
—Ya te acostumbrarás —le contestó Annabelle.
Estaba más agradecida que nunca a lady Winshire por reconocer legalmente a su hija. Tal vez eso evitara que volviera a llamarla «bastarda» alguien tan cruel como Antoine.
Jugaron a las cartas después de cenar y, al cabo de un rato, las tres se fueron a la cama. Para entonces, Consuelo ya estaba medio dormida y apoyada contra su madre. Al final, durmió en la cama de esta. Y, a la mañana siguiente, fue directa al establo una vez más en cuanto se hubo vestido.
Las dos mujeres se pasaron el día charlando tranquilamente acerca de temas muy variados, desde política hasta medicina, pasando por literatura. La dama era inteligente e increíblemente leída. Su conversación le recordó a Annabelle a las que había mantenido tiempo atrás con su madre. Además, le había dado mucho que pensar con sus comentarios del día anterior, cuando le había dicho que no debía amedrentarse por los apelativos que otras personas le hubieran adjudicado de manera injusta. Durante todo el fin de semana no cesó de repetirle que era una mujer buena. Eso consiguió que se sintiera orgullosa de sí misma y dejara de considerarse la paria en que la habían convertido cuando se marchó de Nueva York. Las palabras de Antoine habían conseguido avivar esa hoguera y habían sido incluso peores, porque provenían de alguien a quien ella amaba, y de quien creía que la amaba.
El último día, mientras comían en el jardín, la condesa les dijo que tenía una sorpresa para la niña. Pidió que uno de los mozos de cuadra se reuniera con ellas a la hora del postre, cuando sirvieron la tarta de cumpleaños de Consuelo, y el muchacho llegó con una caja de sombreros atada con un enorme lazo de color rosa. Tanto la pequeña como su madre pensaron que se trataba de un casco de montar para que aquella lo usara cuando volvieran de visita. Pero entonces Annabelle se percató de que la caja se sacudía ligeramente y empezó a sospechar qué debía de esconder. El mozo de cuadra sujetó la caja con firmeza mientras Consuelo desataba el lazo y levantaba la tapa con mucho cuidado. Y en cuanto lo hizo, una carita negra se la quedó mirando y saltó de la caja a sus brazos. Era un cachorro de doguillo de color negro y beige, igual que los perros que tenía lady Winshire, y la niña estaba tan emocionada que no le salían las palabras de la boca mientras el cachorro le lamía la cara. Las dos mujeres sonrieron y Consuelo miró a su abuela y le rodeó el cuello con los brazos.
—¡Gracias! ¡Es precioso! ¿Qué nombre le pongo?
—El que tú quieras, cariño. —Lady Winshire no dejaba de sonreír. Esa nieta inesperada se había convertido en una gran alegría que llenaba su vida.
Las tres se quedaron muy tristes cuando llegó el momento de despedirse y Consuelo y su madre se montaron en el coche que las llevaría de nuevo a Dover, para emprender allí la larga travesía en barco y después el viaje en tren hasta París. Lady Winshire les repitió que volvieran pronto a verla. Su nieta le dio las gracias de nuevo por el cachorrillo, que seguía sin tener nombre, pero estaba encantado de partir de viaje. Y lady Winshire le recordó discretamente a Annabelle que le enviaría los documentos sobre Consuelo en cuanto los tuviera redactados.
Se quedó de pie en la escalinata de la entrada mientras madre e hija se alejaban, y Consuelo no dejó de jugar con el doguillo en todo el camino de vuelta a París. Le dijo a su madre que aquel viaje había sido el mejor regalo de cumpleaños que había tenido en su vida, y para Annabelle también había sido positivo.
Al día siguiente de su regreso, esta escribió a sus abogados y les dijo que no vendieran la casa de verano de Newport. Y, una vez en la consulta, le pidió a Hélène que reservara pasaje para dos personas en junio en un barco con destino a Nueva York, con la vuelta a París en julio. Había seguido al pie de la letra todos los consejos de lady Winshire.
### 26
La tercera semana de junio, Annabelle, Consuelo y Brigitte emprendieron el viaje a bordo del _Mauretania_. Era el mismo barco en el que habían navegado sus padres y Robert rumbo a Europa en aquel último y fatídico viaje. La coincidencia resultaba dolorosa para Annabelle. Salieron de Le Havre un día despejado y bastante cálido, y se acomodaron en dos camarotes contiguos muy bonitos en la cubierta superior.
El _Mauretania_ era uno de los barcos más grandes, veloces y lujosos que surcaban los mares. Annabelle también había navegado en él dieciséis años antes, junto con sus padres. Esta vez había reservado dos de los camarotes más grandes del imponente barco. Los viajeros habituales adoraban las cabinas tan espaciosas que ofrecía, incluso en segunda clase, que era muy escasa, y sobre todo en primera.
Consuelo no cabía en sí de la emoción. Brigitte, por su parte, estaba nerviosa por tener que cruzar el océano. Uno de sus parientes lejanos había sufrido el hundimiento del _Titanic_ y no había sobrevivido. Por eso, empezó a llorar y a santiguarse en cuanto subieron a bordo, y se puso a hablar sin parar de aquel desastre marítimo, cosa que enojó a Annabelle. No quería que asustara a la niña con sus temores, ni que le recordara cómo habían muerto su propio abuelo y su tío. Brigitte no escatimaba en detalles de todo lo que había oído y leído acerca del hundimiento; ni siquiera obvió los gritos de los moribundos en medio del mar.
—¿Es verdad, mamá?
La niña levantó la mirada hacia ella con los ojos abiertos como platos. No le cabía en la cabeza cómo podía hundirse un barco tan grande. Consuelo conocía la historia, pero no los pormenores.
—En parte, sí —dijo Annabelle con sinceridad—. Algunas veces ocurren desgracias, aunque no son frecuentes. Eso pasó hace mucho, mucho tiempo, y desde entonces cientos de barcos han ido y venido a través del océano sin ningún tipo de problemas. Este en el que vamos lleva viajando de manera segura desde hace dieciocho años, y en nuestra travesía no nos toparemos con ningún iceberg en medio del camino, ya lo verás. Mira qué bonito y soleado está el mar, y mira lo grande que es el barco. Te prometo que todo irá bien —la tranquilizó Annabelle con cariño, y fulminó con la mirada a Brigitte por encima de la cabeza de Consuelo.
—El _Titanic_ era más grande aún... Y ¿qué me dice del _Lusitania_? —insistió la sirvienta, y Annabelle sintió ganas de estrangularla por asustar a su hija.
—¿Qué es el «lupimania»? —preguntó esta, que no había entendido bien el nombre.
—No le hagas caso. Brigitte está asustada y por eso dice bobadas. Te prometo que el viaje será fantástico. Y vamos a hacer un montón de cosas divertidas cuando lleguemos a Nueva York. Además, veremos mi antigua casa de Newport.
Por motivos diferentes, estaba igual de nerviosa que Brigitte. No le preocupaba la posibilidad de que el barco se hundiera en esa ocasión, mucho menos en época de paz, pero iba a ser la primera vez que regresara a Nueva York desde hacía diez años, y estaba inquieta por cómo sería todo, y porque temía enfrentarse con los fantasmas y los traumas que había dejado allí. Sin embargo, estaba de acuerdo con lady Winshire. Todo aquello formaba parte de las raíces de Consuelo, y la niña tenía derecho a verlo y a saber más cosas sobre su familia materna, igual que en el caso de la rama de los Winshire. Además, Annabelle no podía esconderse de su pasado toda la vida. Había tardado mucho tiempo en regresar. La guerra había sido una buena excusa para no volver durante una temporada, y después había tenido que acabar los estudios de medicina. Pero hacía ya siete años que había terminado la contienda, desde el nacimiento de Consuelo. Había pasado tiempo más que suficiente. Aun con todo, no le hacía falta oír los detalles escabrosos sobre el hundimiento del _Titanic_ por cortesía de Brigitte, incluidos los gritos de los moribundos desde las aguas; gracias, pero no. Así mismo se lo dijo a la niñera con rotundidad y sin rodeos aprovechando que Consuelo había ido a acariciar al perro de otro pasajero. Había muchos perros en el barco. Y también había muchos niños con quienes Consuelo podría jugar.
Le pidió a Brigitte que empezara a deshacer el equipaje para mantenerla entretenida, mientras ella se llevaba a Consuelo a ver la piscina, el espectacular comedor, las salas de juegos y las casetas para los perros, que se hallaban en otra cubierta. Habían dejado el doguillo en París al cuidado de Hélène, quien lo adoraba. La niña lo había llamado Coco.
Cuando la embarcación zarpó y se fue alejando del puerto, las tres se asomaron por la cubierta y vieron cómo Francia desaparecía poco a poco detrás de ellas. Consuelo insistía en que la dejaran ir a jugar a las cartas, y Annabelle le prometió que jugarían una partida por la tarde. Ya de noche, su madre y ella cenaron en el regio salón-comedor del barco. Era un viaje muy diferente del que había realizado Annabelle hacía diez años rumbo a Europa, cuando apenas había salido de su camarote e ignoraba por completo qué le esperaba al llegar a puerto. Lo único que había deseado entonces era huir de la gente que la había repudiado en Nueva York. Y en esos momentos, diez años más tarde, por fin emprendía el regreso.
Todo fue como la seda hasta el tercer día de travesía, cuando Annabelle vio a una pareja de ancianos que estaban de pie observando cómo otros pasajeros jugaban a los naipes, al lado de una pareja más joven que, sin duda, eran su hija y su yerno. Los ancianos se la quedaron mirando, pero Annabelle fingió no reconocerlos cuando Consuelo y ella pasaron por delante. Sin dudarlo, se enfrascó de inmediato en una animada conversación con su hija, para no tener que saludar a unas personas que había reconocido a la primera. Eran unos conocidos de sus padres. Mientras la niña y ella pasaban junto a la familia neoyorquina, oyó que la anciana hablaba con su marido entre murmullos, que se propagaron con facilidad por la cubierta.
—... Sí, casada con Josiah Millbank... ¿No te acuerdas?... La hija de Arthur Worthington... Un escándalo bochornoso... Tuvo una aventura y él se divorció... Huyó con su amante a Francia...
Así que eso era lo que pensaban, descubrió Annabelle con sobresalto. Y todavía se acordaban del episodio. Se preguntó si todo el mundo lo recordaría. Había sido una auténtica condena a cadena perpetua: nunca la perdonarían ni condonarían la pena. Sería una adúltera para el resto de sus días.
Le chocó enterarse de que algunas personas creyeran que se había fugado a Francia con un hombre. En cuanto lo oyó, le entraron ganas de correr a esconderse en su camarote y no volver a salir de allí. Pero entonces pensó en los consejos que le había dado lady Winshire. «Mantenga la cabeza bien alta, Annabelle. Es una buena mujer. No debe importarle lo que digan.» Mientras escuchaba el eco de esas palabras en su interior, se dio cuenta de que la dama tenía razón; bueno, hasta cierto punto. Sí que le importaba lo que decían los demás, no quería ser una marginada y aborrecía los apelativos con que la calificaban... El peor de todos ellos, el de «adúltera»... Pero ella no era una adúltera y nunca lo había sido. Siempre había sido fiel a su marido, había sido una buena mujer en aquella época y seguía siéndolo entonces. Nada había cambiado, tanto con divorcio como sin él. Y después de todos aquellos años, ¿a quién le importaba por qué se había marchado a Europa, o con quién? Ninguna de esas personas había estado allí para echarle una mano, para apoyarla, para consolarla, ni para abrazarla con el propósito de aliviar la pena por todas las pérdidas que había sufrido. Tal vez su vida hubiera sido diferente si la hubieran aceptado. Pero de haberlo hecho, nunca habría viajado a Europa, ni habría estudiado medicina, ni tendría a Consuelo junto a ella. Así que, al fin y al cabo, era ella la que había salido ganando.
Cuando regresaban de otra visita a las casetas de los perros, entre los que Consuelo había descubierto un simpático doguillo negro como el suyo, Annabelle volvió a pasar con su hija de la mano junto a la pareja de conocidos. Y esta vez miró a la mujer directamente a los ojos y dejó patente que la reconocía saludándola con la cabeza. Annabelle lucía un casquete muy chic a conjunto con el traje de seda gris que se había comprado para el viaje, y tenía un aire muy estiloso; ya no parecía norteamericana, sino francesa. En cuanto Annabelle hizo ademán de reconocerla, la mujer se apresuró a acercarse a ella con una amplia sonrisa falsa, desviviéndose en palabras de bienvenida.
—Por el amor de Dios, Annabelle, ¿eres tú? ¡Después de tantos años! ¿Cómo estás? Ay, qué niña tan guapa. Es tuya, ¿verdad? Es tu vivo retrato... ¿Tu marido también está a bordo?
—No —respondió Annabelle, y les estrechó la mano a ambos con educación—. Soy viuda. Y esta es mi hija. Consuelo Worthington-Winshire.
Consuelo hizo una reverencia, tan educada como siempre, con el precioso vestido que había elegido ponerse ese día. También llevaba unos guantes blancos y un sombrero.
—Ah, qué tierno... Le has puesto el nombre de tu madre. Era una mujer fabulosa. ¿Sigues viviendo en Francia?
—Sí, en París —dijo con indiferencia Annabelle.
—Nunca viajas a Nueva York, ¿verdad? Hacía siglos que no te veíamos.
—Sí, esta es la primera vez que vuelvo desde que me marché —le habría gustado añadir: «Por culpa de lenguas viperinas como la suya, de personas que mantienen los rumores vivos durante años y años, cuelgan sambenitos a los demás y no dejan que el resto de la gente se olvide de ellos».
—Vaya, parece mentira. ¿Y la casita de Newport?
—Allí es donde vamos a pasar unas semanas. Quiero que Consuelo la conozca. —La niña hablaba inglés con algo de acento francés, que resultaba encantador—. Y tenemos millones de cosas que ver en Nueva York —añadió sonriendo a su hija, pues estaban a punto de ponerse a caminar otra vez.
Por lo menos, la mujer le había dirigido la palabra. Aunque pequeño, era un logro. Diez años atrás no lo habría hecho. Se habría limitado a dejarla plantada y no le habría dado ni los buenos días. Por lo menos en esos momentos fingía ser cordial, independientemente de lo que pensara o de lo que dijera a sus espaldas.
—A lo mejor nos vemos en Newport —dijo la anciana, a quien todavía picaba la curiosidad, porque no dejaba de mirar de reojo el caro traje con sombrero a juego de Annabelle y el precioso vestido de Consuelo—. Y ¿con qué te entretienes en París? —le preguntó para cotillear, sin duda porque quería más detalles acerca de la vida de Annabelle, con el fin de chismorrear cuando regresara a la ciudad. Se le notaba en la cara. La anciana también se había fijado en el imponente anillo de esmeraldas de lady Winshire que lucía junto con el anillo de boda que aún llevaba, el que se había comprado ella misma antes de que naciera Consuelo. No era más que una estrecha alianza de oro, pero nunca se la quitaba del dedo anular.
—Soy médico —dijo Annabelle, sonriéndole, mientras volvía a recordar las palabras de lady Winshire, y esta vez estuvo a punto de echarse a reír. Qué nimia e insignificante era aquella gente, qué provinciana; parecían urracas que buscaran cosas brillantes entre la basura, para poder mostrárselas a los demás, o para intercambiarlas por la buena reputación de las personas decentes, quienes valían diez veces más que esos pajarracos.
—¿De verdad? ¡Es asombroso! —Casi se le salieron los ojos de las cuencas—. Pero ¿cómo has podido lograr algo así?
Annabelle sonrió con benevolencia.
—Estudié en una facultad de medicina en Francia, después de la muerte de mi marido.
—¿Él también era médico?
—No —se limitó a decir Annabelle. Ese difunto marido no existía—. El padre de Consuelo era el vizconde de Winshire. Lo mataron en la guerra, en Ypres. —Todo eso era cierto. No había dicho ni una sola mentira acerca del padre de Consuelo. Y no era asunto de aquella mujer, ni lo sería jamás, si habían estado casados o no. Eso no restaba importancia a sus logros, ni a las buenas acciones que había hecho en su vida.
—Ah, claro —dijo la mujer arrugando la nariz, mucho más impresionada de lo que deseaba admitir, aunque no podía aguantarse las ganas de que Annabelle se marchara para poder contárselo a su hija, a quien Annabelle apenas había reconocido, pues había engordado una barbaridad, y la había visto pocas veces antes de marcharse de Nueva York. Estaba jugando una partida de cartas con varias amigas.
Un segundo después, Annabelle y Consuelo reemprendieron la marcha.
—¿Quién era esa señora? —preguntó Consuelo con curiosidad.
—Nadie, una conocida de mis padres de Nueva York —contestó, y hacía meses que no se sentía tan bien. Antoine la había golpeado con fuerza. Y quienes la habían atacado antes que él también habían hecho mella. Pero, de repente, todo eso había dejado de afectarla.
—Tenía ojos de mala persona —observó Consuelo con gran sabiduría, y su madre se echó a reír.
—Sí, es verdad. Y lengua de mala persona también. Antes conocía a muchos como ella.
—¿En Nueva York todo el mundo es así, mamá? —Parecía preocupada.
—Espero que no —respondió Annabelle risueña—. Pero no vamos a Estados Unidos por ellos. Vamos por nosotras.
Además, ya no tenía ganas de seguir escondiéndose de toda esa gente. No eran los dueños de Newport ni de Nueva York. En esos momentos Annabelle tenía su propio universo, con su vida en París, sus pacientes, su consulta y su hija. Lo único que le faltaba era un hombre, pero si tenían que ningunearla, humillarla y «perdonarla» hombres como Antoine, quien no había confiado en ella ni la había respetado, entonces prefería seguir sola. Estaba bien así.
La travesía transcurrió sin ningún otro percance. Se lo pasaron muy bien. Annabelle y Consuelo cenaban mano a mano en el comedor todas las noches, y cuando el capitán la invitó a sentarse a su mesa una noche, ella rechazó el ofrecimiento con educación. Prefería cenar con su hija que en medio de personas absurdas e hipócritas como esos conocidos de sus padres con quienes había coincidido en el barco.
Cuando atracaron echando humo en el puerto de Nueva York, ayudados de los remolcadores, Annabelle sintió un nudo en la garganta al ver la estatua de la Libertad, erguida con orgullo con su antorcha en lo alto. Fue un instante conmovedor, como si la estatua hubiera estado esperándolas precisamente a ellas. Señaló la isla de Ellis para que la viera su hija y le explicó que había ayudado allí antes de estudiar medicina, un sueño que le parecía imposible en aquella época.
—¿Por qué, mamá? ¿Por qué aquí no podías ser médico?
La niña no lo entendía. Que su madre ejerciera la medicina le resultaba lo más natural del mundo. De hecho, ella también quería serlo de mayor, y tal vez lo fuese algún día.
—Antes había pocas mujeres que estudiaran medicina. Y ahora todavía son escasas. La gente piensa que las mujeres deberían casarse, tener hijos y quedarse en casa para cuidarlos.
—¿No se pueden hacer las dos cosas? —Consuelo la miró con expresión confundida.
—Yo creo que sí —contestó Annabelle, y volvió a mirar la estatua de la Libertad.
Su propósito era recordar a todo el mundo que la llama de la libertad no se apagaba nunca. Aunque uno cerrara los ojos, seguía ahí, iluminando el camino para todos, hombres y mujeres, ricos y pobres. La libertad pertenecía a toda la humanidad, y ahora también a Annabelle.
La niña se quedó pensativa.
—Y si te casaras con un hombre, no sé, con Antoine o alguien parecido, ¿dejarías de ser médico?
—No, cariño.
No hizo ningún comentario a propósito de Antoine, quien había llamado «bastarda» a su hija. Nunca le perdonaría semejante insulto. Y, por el momento, tampoco había sido capaz de perdonarle el resto.
Después de desembarcar y pasar por la aduana, encontraron dos taxis que las llevaron a ellas y a su equipaje al hotel Plaza. Poseía una estupenda vista de Central Park, y desde allí se podía ir andando hasta su antigua casa. Annabelle se sorprendió muchísimo al ver cuánto había cambiado Nueva York, cuántos edificios nuevos habían construido, así como lo abarrotada que parecía. Consuelo estaba fascinada con todo lo que veía y, en cuanto se hubieron instalado y comido, su madre y ella se pusieron en camino dispuestas a explorar la ciudad.
Era inevitable que en primer lugar fuesen a su casa familiar. Annabelle no pudo contenerse. Tenía que verla. Seguía en buen estado, aunque los postigos estaban cerrados y parecía desocupada. Supuso que los dueños actuales habían ido a veranear a otro sitio. Annabelle se quedó mirando la fachada durante un buen rato sin soltar a Consuelo de la mano.
—Aquí es donde vivía yo de pequeña. —Estuvo a punto de decir «hasta que me casé», pero se reprimió. Nunca le había hablado a Consuelo de Josiah, aunque sabía que algún día tendría que hacerlo.
—Seguro que fue muy triste cuando murieron tu papá y tu hermano —dijo Consuelo con aire serio, como si estuviera delante de su tumba, cosa que, en cierto modo, era cierta. También era la tumba de su madre. La mujer había muerto en esa misma casa. Y Annabelle había nacido allí.
—Tu abuela Consuelo también vivía aquí.
—¿Era simpática? —preguntó la niña con mucho interés mientras su madre sonreía.
—Mucho. Y también era muy guapa, igual que tú. Era una mujer magnífica y muy buena. Y yo la quería mucho.
—Seguro que la echas un montón de menos —comentó la pequeña en voz baja.
—Sí, es verdad.
Allí de pie, Annabelle recordó la mañana en que se enteró de que se había hundido el _Titanic_ , así como el día en que había muerto su madre. Sin embargo, también le vinieron a la mente los recuerdos felices. Los días infantiles en los que todo era fácil y favorable para ella. Había tenido una infancia de ensueño, rodeada de personas cariñosas que la habían protegido de todo sufrimiento. Y en los años posteriores había pagado con creces por todo lo que tenía en esos tiempos.
Se alejaron poco a poco y Annabelle llevó a Consuelo a ver otros lugares representativos de su vida. Le contó dónde había celebrado la puesta de largo. Y visitaron el banco de su abuelo, donde Annabelle presentó a su hija al director y a los distintos empleados que todavía conocía. Esta los saludó estrechándoles la mano y haciendo reverencias. Al caer la tarde, regresaron al restaurante Palm Court del Plaza para cenar. Era de lo más impresionante, y vieron a varias mujeres vestidas con mucho estilo y primor, que lucían sombreros extravagantes y joyas exageradas, y que charlaban y disfrutaban de la cena bajo el enorme tragaluz.
A Consuelo le encantó Nueva York y Annabelle estaba más contenta de lo que esperaba. Era agradable volver a estar allí, y le resultaba divertido enseñarle todos aquellos lugares a su hija. Lady Winshire tenía razón, era una parte de su propia historia y de la de su hija, y era importante que esta viera dónde se había criado su madre. Permanecieron allí una semana, en la que Annabelle no vio a nadie conocido. De hecho, no había ni una sola persona a quien deseara ver. Cuando terminó la semana en la ciudad, estaba más que impaciente por llegar a Newport y a la casa de campo. Sabía que a Consuelo le encantaría, igual que le había gustado a ella de niña. Al no participar de la vida social que era tan esencial para los residentes, el océano, la playa y todas las bellezas naturales resultaban todavía más atractivas para ellas que las casas de veraneo que tanto valoraban sus propietarios y todos sus conocidos.
Tras abandonar el hotel Plaza, tomaron un tren a Boston, donde el antiguo chófer de su padre, William, ya las estaba esperando en la estación con uno de los coches de la familia, que todavía conservaban en Newport. El hombre se echó a llorar en cuanto la vio, e hizo una gran reverencia al conocer a Consuelo, quien estaba muy impresionada al ver que un hombre tan anciano era tan respetuoso con ella. Y le dio tanta pena cuando vio que el señor lloraba que se puso de puntillas para darle un beso. En el momento de saludarse, tanto Annabelle como él tenían los ojos vidriosos por las lágrimas. Los sirvientes sabían de Consuelo a través de las cartas enviadas por Annabelle a Blanche, pero no tenían del todo claro quién era el padre o cuándo había tenido lugar la boda. Por lo que habían entendido, el padre había muerto en el frente poco después de que Annabelle y él se casaran. William miró a Consuelo con los ojos llorosos y una expresión nostálgica.
—Es igual que usted cuando tenía su edad. Y también me recuerda un poco a la señora Worthington.
Las ayudó a acomodarse en el coche y se pusieron en marcha. Les esperaba un trayecto de siete horas hasta Newport, que Consuelo pasó observando y comentando todo lo que iban viendo. William le explicaba qué era cada cosa. E, igual que le había ocurrido en Nueva York, Annabelle pensó que aquel entorno también había cambiado mucho, aunque el propio Newport seguía como siempre. Cuando entraron en el pueblo, vio que tenía el mismo aspecto venerable que antes. Y los ojos de Consuelo se abrieron todavía más al contemplar la casa de verano y la gran extensión de terreno que la rodeaba. Era una finca imponente y los sirvientes la habían conservado en perfecto estado.
—Es casi tan grande como la casa de la abuela en Inglaterra —dijo la niña, sin apartar los ojos de la impresionante vivienda.
Su madre sonrió. Estaba exactamente igual que como la recordaba, y la transportó a su infancia con un salto vertiginoso.
—Bueno, no tanto —rectificó Annabelle—. La casa de la abuela es más grande. Pero aquí yo pasé unos veranos fantásticos.
Salvo el último. Regresar a Newport hacía aflorar muchos recuerdos de Josiah, así como del terrible final de su matrimonio. No obstante, también la hacía pensar en lo feliz que había sido el principio de su relación, cuando ella era joven y miraba al futuro con esperanza. Ahora tenía ya treinta y dos años, y muchísimas cosas habían cambiado. Pero, en el fondo, aquel seguía siendo su hogar.
En cuanto se detuvo el coche, Blanche y los demás salieron corriendo de la casa. Blanche se tiró en brazos de Annabelle sin dejar de llorar. Parecía muy envejecida, y cuando vio a Consuelo también la abrazó. E, igual que había hecho William, le dijo a Annabelle que su hija era su vivo retrato.
—¡Y además es médico! —Blanche seguía sin poder creérselo. Y tampoco podía creer que por fin hubiera vuelto a casa.
Los criados pensaban que no regresaría jamás. Y tenían mucho miedo a que terminara por vender la casa. También se había convertido en su hogar. Y habían mantenido todo en unas condiciones inmejorables para ella. Daba la impresión de que se hubiera marchado el día anterior, en lugar de diez años antes. Esa década le parecía una vida entera, pero al mismo tiempo, en cuanto volvió a pisar la casa de verano, el lapso transcurrido desde la última vez que había estado allí se esfumó, reducido a nada.
Annabelle volvió a echar de menos a su madre cuando pasó por delante de su dormitorio. Pensaba alojarse en una de las habitaciones de invitados, mientras que les había asignado a Consuelo y a Brigitte su antiguo dormitorio infantil, para que la niña pudiera jugar a sus anchas. De todas formas, seguro que pasaba la mayor parte del tiempo al aire libre, como solía hacer ella cuando tenía su edad. Se moría de ganas de llevar a su hija a nadar, cosa que hicieron esa misma tarde.
Annabelle le contó que ella había aprendido a nadar allí, igual que la pequeña había aprendido a hacerlo en Niza y Antibes.
—Aquí el agua está más fría —comentó esta, pero le gustaba. Le encantaba jugar con las olas y pasear por la playa.
Esa misma tarde, cuando regresaron a casa después de estar en la playa, Annabelle dejó a su hija con Brigitte. Quería salir a dar un paseo sola. Había determinados recuerdos que no deseaba compartir. Pero justo cuando iba a salir de casa, Consuelo bajó a toda prisa la escalera para reunirse con ella, y Annabelle no tuvo valor para decirle que no podía acompañarla. La niña estaba emocionada en aquel lugar, descubriendo el antiguo universo de su madre, que era tan distinto del entorno en el que vivían ahora, con su casita minúscula pero acogedora en el decimosexto distrito. Visto en retrospectiva, todo lo relacionado con su antiguo mundo le parecía enorme, igual que a su hija.
La casa que quería ver no estaba lejos de allí, y cuando llegó, vio que los árboles estaban muy altos y abandonados, que los postigos estaban cerrados y toda la casa se hallaba en mal estado. Blanche le había dicho que la habían vendido hacía un par de años, pero daba la impresión de que allí no vivía nadie, es más, parecía que no la hubieran ocupado desde hacía una década. Estaba desierta. Era la antigua casa de Josiah, donde Annabelle había pasado sus veranos de casada, y donde Henry y él habían continuado con su historia de amor; pero en esos momentos no quería pensar en esas cosas. Se limitó a pensar en él. Y Consuelo se dio cuenta de que aquella casa significaba mucho para su madre, aunque era pequeña y oscura, y parecía triste.
—¿Conocías a las personas que vivían aquí, mamá?
—Sí, hija —contestó Annabelle en voz baja.
Casi pudo percibirlo a su lado mientras decía esas palabras, y confiaba en que descansara en paz. Hacía mucho tiempo que lo había perdonado. Ya no le quedaba nada que perdonar. Josiah había hecho las cosas lo mejor que había podido y, a su manera, la había amado. Ella también lo había amado. No sentía hacia él la cruda decepción y el dolor de la traición que sentía por Antoine, una herida mucho más reciente. Las cicatrices de lo que había ocurrido con Josiah habían palidecido varios años antes.
—¿Y se han muerto? —preguntó Consuelo con tristeza. A juzgar por el estado de la casa, era la sensación que le daba.
—Sí.
—¿Vivía algún amigo tuyo? —Consuelo sentía curiosidad, pues su madre parecía lejana y muy conmovida mientras observaba la casa.
Annabelle dudó unos segundos. A lo mejor había llegado el momento. No quería seguir mintiéndole sobre su pasado para siempre. El engaño de que había estado casada con el padre de Consuelo ya era suficiente, y algún día tendría que contarle la verdad sobre ese tema también; no el hecho de que la hubiera violado, claro, sino de que no se hubieran casado. Ahora que lady Winshire la había reconocido, no sería tan bochornoso, aunque seguía siendo difícil de explicar.
—Esta casa era de un hombre que se llamaba Josiah Millbank —dijo en voz baja Annabelle mientras se asomaban al jardín. Había malas hierbas por todas partes y parecía totalmente abandonada, lo cual era cierto. Se volvió hacia su hija y continuó—: Fue mi marido. Nos casamos aquí, en Newport, cuando yo tenía diecinueve años. —Consuelo la miró con los ojos como platos, mientras se sentaba junto a ella en un tronco caído—. Estuve dos años casada con él, y fue un hombre maravilloso. Lo quería mucho.
Deseaba que su hija conociera también esa parte de la historia, no solo que había terminado mal.
—Y ¿qué le pasó? —preguntó Consuelo con un hilillo de voz. Cuántas personas habían muerto en la vida de su madre. Todo el mundo desaparecía...
—Se puso muy enfermo y decidió que ya no quería seguir casado conmigo. Pensó que sería injusto para mí, porque su enfermedad era muy grave. Así que se marchó a México y se divorció de mí, lo que significa que puso fin a nuestro matrimonio.
—Pero ¿no querías estar con él aunque estuviera muy enfermo? ¿No querías cuidar de él? —La niña parecía abrumada, y Annabelle le sonrió mientras asentía.
—Claro que sí quería. Pero no era lo que él deseaba. Él pensó que hacía lo mejor para mí, porque yo era muy joven. Y él era mucho mayor. Lo bastante mayor para ser mi padre. Consideró que yo tenía que casarme con alguien que no estuviera enfermo y con quien pudiera tener muchos hijos.
—Como mi padre —contestó Consuelo muy orgullosa, pero al instante una nube le enturbió la mirada—. Pero él también murió.
Toda la historia era muy triste, y, a pesar de que solo tenía siete años, se dio cuenta de cuántos escollos había tenido que superar su madre para asomar la cabeza por el otro extremo del océano, entera y viva, e incluso convertirse en médico.
—Bueno, el caso es que se divorció de mí y se marchó a México. —No le habló de Henry. No hacía falta que la niña lo supiera—. Y aquí todo el mundo se sorprendió muchísimo. Pensaban que se había divorciado de mí porque yo había hecho algo malo. Nunca le contó a nadie que estaba enfermo, y yo tampoco lo dije. Así que creyeron que yo había hecho algo imperdonable, y por eso me puse muy triste. Me marché a Francia y empecé a trabajar de voluntaria durante la guerra. Y entonces conocí a tu padre, y te tuve a ti. Y todos fueron felices y comieron perdices —añadió con una sonrisa, mientras tomaba la mano de Consuelo entre las suyas.
Ahora su matrimonio con Josiah había dejado de ser un misterio. Le parecía mejor así. No quería seguir guardando tantos secretos, ni tener que mentir para encubrirlos. Había sido justa con él en su relato de la historia. Siempre había sido justa con él.
—Pero ¿por qué se portaron todos tan mal contigo cuando él se marchó?
A Consuelo aquello le parecía horroroso, además de muy injusto para su madre.
—Porque no lo entendían. No sabían qué había ocurrido en realidad. Así que empezaron a inventar chismes sobre mí.
—¿Y por qué no les contaste la verdad?
Esa parte no tenía ningún sentido a ojos de la niña.
—Josiah no quería que la contara. Él no quería que nadie supiera que estaba enfermo.
Ni por qué, cosa que era mucho más comprensible. Por no mencionar la presencia de Henry Orson.
—Pues qué tonto —repuso la niña, mirando la casa vacía por encima del hombro.
—Sí, hija, qué tonto.
—¿Volviste a verlo alguna vez?
Annabelle negó con la cabeza.
—No. Murió en México. Yo ya estaba en Francia para entonces.
—¿Y ahora la gente sabe la verdad? —preguntó la pequeña, que continuaba pensativa.
No le gustaba nada esa parte de la historia, cuando la gente había sido mala con su madre. Seguro que se había puesto muy triste al pasar aquel mal trago. Incluso parecía triste ahora con solo recordarlo.
—No. De eso hace mucho tiempo —contestó Annabelle.
—Gracias por contármelo, mamá —exclamó Consuelo muy orgullosa.
—Tenía intención de contártelo de todos modos, cuando fueras un poco mayor.
—Siento mucho que se portaran mal contigo —le dijo la niña en voz baja—. Y espero que no vuelvan a hacerlo.
La única persona que había sido mala con ella últimamente había sido Antoine. No solo mala, sino cruel. Había sido la peor traición de todas, porque había reabierto todas sus antiguas heridas. Hablar con lady Winshire sobre el tema le había ayudado mucho. Ahora veía qué insignificante y ridículo era él en el fondo, si no era capaz de amarla a pesar de su pasado. Ella no le habría hecho lo mismo. Era una persona mucho más íntegra.
—En este momento eso no importa. Te tengo a ti —le recordó Annabelle, y era cierto. Consuelo era todo lo que le hacía falta.
Se levantaron y regresaron paseando a su casa, y durante las tres semanas siguientes jugaron y nadaron e hicieron todas las cosas que Annabelle había hecho de niña y que tanto le habían divertido.
Fue durante su última semana en la localidad cuando llevó a su hija a comer al Club de Campo de Newport. Era una de las pocas actividades «adultas» que habían hecho en toda la estancia. Por lo general, Annabelle había evitado los lugares en los que podía toparse con viejas amistades. Habían permanecido la mayor parte del tiempo dentro de los terrenos de la casa, que eran lo bastante extensos. Pero ese día habían decidido salir a comer fuera, algo muy valiente por parte de Annabelle.
Y justo cuando iban a marcharse después de la sobremesa, esta vio a una mujer corpulenta que entraba en el restaurante. Parecía sofocada, tenía la cara enrojecida e iba acompañada de una niñera. Intentaba controlar a seis niños pequeños y tenía un bebé cogido en brazos. Mientras reprendía a uno de ellos, el bebé se puso a llorar y el sombrero se le torció. Y hasta que no estuvieron a apenas unos centímetros la una de la otra, Annabelle no reconoció a su antigua amiga Hortie. Ambas se quedaron boquiabiertas y dejaron de caminar. Se miraron mutuamente.
—Eh... ¿qué haces «tú» aquí? —preguntó la recién llegada como si Annabelle no tuviera derecho a estar en aquel lugar.
Y entonces intentó enmascarar la incómoda situación con una sonrisa nerviosa. Consuelo frunció el entrecejo sin dejar de observarla. La mujer ni siquiera se había percatado de la presencia de la niña, pues miraba fijamente a su madre como si hubiera visto un fantasma.
—He venido de visita con mi hija. —Annabelle sonrió a su antigua amiga y sintió lástima por ella—. Veo que la fábrica de niños sigue en funcionamiento —bromeó.
Hortie puso los ojos en blanco y soltó un bufido. Por un instante le recordó a la amiga a quien Annabelle tanto habría apreciado, y a quien nunca habría dejado en la estacada.
—¿Te volviste a casar? —preguntó aquella con interés, y después desvió la mirada hacia Consuelo.
—Soy viuda.
—Y es médico —añadió Consuelo muy orgullosa. Ambas mujeres se echaron a reír.
—¿De verdad? —Hortie miró a Annabelle, impresionada ante la noticia, aunque sabía que le habían gustado los temas médicos desde jovencita.
—Sí. Vivimos en París.
—Eso he oído. Me contaron que fuiste una especie de heroína durante la guerra.
Annabelle se echó a reír.
—Qué va. Era auxiliar de medicina, y conducía una ambulancia con la que íbamos a los hospitales de campaña a recoger soldados heridos. No es nada heroico.
—A mí sí me parece heroico —dijo Hortie mientras su bandada de niños revoloteaba a su alrededor y la niñera intentaba mantenerlos bajo control, con escaso éxito. No le pidió disculpas por haberla traicionado ni le dijo que la había echado de menos, aunque se le notaba en la mirada—. ¿Os vais a quedar mucho tiempo? —preguntó con cierta nostalgia.
—Unos cuantos días más.
Sin embargo, Hortie no la invitó a su casa, ni le dijo que se pasaría por la de los Worthington. Sabía que James no se lo permitiría. Pensaba que Annabelle era una mala influencia para ella. Las divorciadas y adúlteras no eran bien recibidas en su casa, aunque las historias que corrían sobre él eran mucho peores que eso.
Por un instante, Annabelle tuvo ganas de decirle que la había echado de menos, pero no se atrevió. Era demasiado tarde para ambas. Y darse cuenta la puso triste. Hortie parecía vulgar, agotada y superada por las circunstancias, y no estaba envejeciendo bien. Se había convertido en una mujer de mediana edad con una camada de hijos que había dado la espalda a su mejor amiga. Ella siempre la echaría de menos. Toparse con ella había sido como ver un fantasma. Se despidieron sin abrazarse, y Annabelle permaneció callada cuando salieron del restaurante.
Consuelo no habló hasta que se montaron en el coche y se dirigieron de vuelta a casa. Entonces miró a su madre y le dijo en voz baja:
—¿Era una de esas personas que dijeron cosas malas sobre ti?
—Más o menos. De pequeña era mi mejor amiga; es más, lo fue hasta que pasó lo que te he contado. A veces la gente hace tonterías —explicó Annabelle sonriendo a su hija—. Cuando teníamos tu edad, éramos como hermanas, y continuamos siéndolo hasta que nos hicimos mayores.
—Pues es fea —dijo Consuelo, cruzándose de brazos y arrugando la frente. Estaba enfadada porque quería defender a su madre—. Y gorda.
Ella se echó a reír aunque no hizo ningún comentario.
—Cuando era joven era muy guapa. Y ha tenido muchos hijos.
—Sí, también son feos, y alborotan un montón —replicó Consuelo con severidad, y se acurrucó contra su madre.
—Ya lo creo que sí —comentó esta.
Hortie nunca había sido capaz de controlar a sus hijos, ni siquiera cuando solo tenía uno o dos. Parecía que James la había mantenido embarazada desde entonces.
El resto de su estancia en Newport transcurrió tal como las dos habían confiado en que lo hiciese. Para Annabelle fue como una vuelta al hogar, y enterneció su corazón. Y mientras preparaban las maletas para marcharse, Consuelo le preguntó a su madre si volverían algún día. Annabelle se había planteado lo mismo y se alegró de no haber vendido la casa. Una vez más, lady Winshire estaba en lo cierto. Muchas de las cosas que le había dicho eran muy acertadas. Y su esmeralda no se separaba jamás del dedo de Annabelle. Era un regalo que apreciaba muchísimo, sobre todo ahora que eran amigas.
—Creo que sería una buena idea venir todos los veranos aquí a pasar unas semanas. O incluso un mes. ¿Qué te parece? —le preguntó a Consuelo mientras Brigitte cerraba las maletas.
—Me encantaría —dijo la niña sonriendo de oreja a oreja a su madre.
—A mí también.
Eso mantendría vivos los vínculos de Annabelle con Estados Unidos y afianzaría los de su hija. El tiempo lo cura todo. Annabelle se había dado cuenta mientras estaba en Newport. Aunque siguieran hablando de ella, y recordaran el escándalo que había protagonizado tantos años antes, si Annabelle mantenía su postura firme el tiempo suficiente, la gente se olvidaría. O, por lo menos, esas etiquetas tan feas se difuminarían y los demás no se molestarían en leerlas tan a menudo. Justamente entonces ya no le importaba demasiado. Habían pasado tantas cosas desde entonces... Se había forjado una vida completamente nueva en otro lugar, tenía un hogar, una profesión y una hija a quien quería con locura. Pero al mismo tiempo notó que le había sido devuelta una antigua parte de sí misma. Y era una parte de una vida anterior que había echado de menos durante todos esos años.
William las llevó de vuelta a Boston, donde cogieron el tren con destino a Nueva York. Solo tenían pensado quedarse dos días allí esta vez, para hacer las pocas cosas que les habían quedado pendientes en la estancia anterior.
—Cuídese mucho, señorita Annabelle —le dijo William con los ojos llenos de lágrimas de nuevo—. ¿Cree que volverá pronto?
Todos se habían dado cuenta de lo mucho que había disfrutado de la visita. En ciertos momentos, en la playa, o corriendo por el césped con Consuelo, la propia Annabelle parecía una niña.
—El verano que viene. Lo prometo.
La despedida de Blanche también había sido muy emotiva y le había hecho la misma promesa.
William abrazó y besó tanto a Consuelo como a Annabelle, y se quedó de pie en el andén, saludándolas con la mano, hasta que desaparecieron de su vista.
Y entonces madre e hija se acomodaron en el compartimiento y emprendieron el viaje a Nueva York. Se lo habían pasado en grande en Newport. Las vacaciones habían superado todas las expectativas de Annabelle.
### 27
Los dos últimos días que pasaron en Nueva York fueron acelerados pero muy divertidos. Annabelle llevó a Consuelo al teatro a ver un musical, que encantó a la pequeña. Cenaron en el Sardi's y en el Waldorf Astoria, a lo grande. Dieron una vuelta en ferry alrededor de Manhattan, y Annabelle volvió a señalarle dónde estaba la isla de Ellis y le contó más cosas sobre aquel lugar. Y la última tarde pasaron caminando por delante de su antigua casa una vez más, solo para despedirse. Se quedó allí de pie durante un buen rato, para rendir homenaje tanto a la mansión como a todos los que habían vivido allí, incluida la parte inocente de sí misma que había perdido. Ya no tenía nada en común con la niña que había sido cuando vivía en aquella casa. Había madurado.
Consuelo y ella se alejaron en silencio, cogidas de la mano. Aquella había aprendido muchas cosas sobre su madre a lo largo de ese viaje, así como sobre sus abuelos, su tío Robert e incluso sobre algunos de los amigos de su madre. No le había caído bien esa amiga que habían visto en Newport, la que tenía tantísimos hijos. Le había dado mucha rabia que hubiera sido antipática con su madre y la hubiera disgustado. Y sentía pena por el hombre que había muerto en México. Se había dado cuenta de que su madre lo quería mucho.
Esa vez, Brigitte estaba un poco menos nerviosa cuando embarcaron en el _Mauretania_ para emprender el regreso. El barco le había parecido tan cómodo y lujoso durante la ida que se había relajado bastante. Annabelle tuvo una sensación extraña cuando pasó por delante de los antiguos muelles de White Star y de Cunard. De repente, se acordó de cuando había ido a buscar a su madre hacía trece años, después del hundimiento del _Titanic_. Sin embargo, no se lo mencionó a su hija, y mucho menos a Brigitte, quien, de todos modos, se las ingenió para sacar el tema. Annabelle la miró con el entrecejo fruncido y la niñera se calló.
Cuando volvieron a pasar por delante de la estatua de la Libertad, sintió que se desprendía de una parte de su corazón. Hacía muchísimo tiempo que no se sentía tan vinculada a su país, así que la reconfortó pensar que regresarían al verano siguiente. Consuelo no había dejado de repetirlo durante su breve estancia en Nueva York: le había encantado Newport y se moría de ganas de volver.
En esa ocasión no había nadie conocido en el barco; Annabelle había repasado la lista de pasajeros. De todas formas, no le habría importado. No tenía nada que temer. Había salido airosa de su exposición en público en Newport y Nueva York y ya no le quedaban secretos que proteger. Incluso si alguien descubría lo que escondía su pasado, ¿qué daño podría hacerle? Nadie podría arrebatarle su casa, ni su vida, ni su trabajo, ni a su hija. Lo único que podrían hacer los demás sería hablar mal de ella, y ya había pasado por eso. Aquella gente no tenía nada que ella deseara. Incluso la dolorosa traición de Hortie le había parecido más pequeña cuando se la había encontrado durante su estancia en Newport. Todos aquellos que tanto daño le habían hecho en otro tiempo se habían esfumado, y ya no quería saber nada de ellos. Tampoco podían robarle nada. Se había forjado una vida propia, y era una buena vida.
Annabelle y Consuelo volvieron a echar un vistazo a las casetas de los perros, igual que en el viaje de ida. Esta vez no había ningún doguillo, pero sí varios pequineses y caniches. La niña había echado mucho de menos a Coco y tenía unas ganas locas de volver a ver a su mascota. Además, su madre le había prometido que pasarían un fin de semana en Deauville cuando volvieran a casa. Incluso el impacto de Antoine sobre Annabelle se había amortecido durante esas vacaciones. No era más que un hombre desagradable y estrecho de miras que vivía en un mundo diminuto lleno de gente cargada de prejuicios. En ese mundo no había sitio para ella. Y en el suyo no había sitio para él.
Cuando regresaban de ver a los perros, se detuvieron junto a la barandilla para contemplar el mar. La melena larga y rubia de Consuelo se meció con la brisa y a Annabelle se le voló el sombrero, que empezó a dar vueltas como una rueda por la cubierta del barco, mientras las dos lo perseguían entre carcajadas. Seguía teniendo el pelo igual de rubio que su hija, y el sombrero se detuvo por fin a los pies de un hombre que lo recogió y se lo entregó con una amplia sonrisa.
—Gracias —dijo ella sin resuello luciendo una sonrisa infantil.
Habían corrido un buen trecho para atrapar el sombrero. Ella tenía la tez morena por el sol de Rhode Island. Volvió a calarse el sombrero formando un ángulo un poco torcido.
—Creo que se le va a volar el sombrero otra vez —le advirtió el hombre.
Ella asintió y se lo quitó, mientras Consuelo entablaba conversación con el señor.
—Mi abuelo y mi tío murieron en el _Titanic_ —le comunicó, para romper el hielo, y el hombre la miró muy serio.
—Lo siento muchísimo. Mis abuelos también. A lo mejor se conocían. —Era una idea intrigante—. Pero de eso hace mucho tiempo. Fue antes de que tú nacieras, diría yo.
—Tengo siete años —dijo la niña, cosa que lo confirmaba—. Y me llamo igual que mi abuela. También está muerta. —El hombre se contuvo para no sonreír ante el comentario de la niña, pues parecía que toda su familia se hubiera extinguido—. Igual que mi padre —añadió la pequeña, como colofón—. Murió antes de que yo naciera, en la guerra.
—¡Consuelo! —la reprendió Annabelle. Nunca la había oído dar tanta información seguida, y confiaba en que no lo hiciera muy a menudo—. Lo siento —añadió dirigiéndose al desconocido que le había recogido el sombrero del suelo—. No era nuestra intención darle las noticias necrológicas.
Sonrió al hombre, quien le devolvió la sonrisa.
—Seguro que es porque has notado que soy periodista —le dijo a Consuelo con amabilidad.
—¿Qué es eso? —la niña mostró mucho interés.
—Escribo para el periódico. Bueno, mejor dicho, soy el editor de un periódico: el _International Herald Tribune_ de París. Ya lo leerás cuando seas mayor.
Volvió a sonreír, esta vez mirándolas a las dos.
—Pues mi madre es médico.
La niña dirigía la conversación a su territorio con total desenvoltura, y Annabelle puso cara de apuro.
—¿De verdad? —preguntó él con interés antes de presentarse. Dijo que se llamaba Callam McAffrey, era originario de Boston y en esos tiempos vivía en París.
Annabelle también se presentó y Consuelo añadió muy contenta que ellas también vivían en París, en el decimosexto distrito. Él le contó que vivía en la rue de l'Université, en la ribera izquierda. Estaba cerca de la facultad de bellas artes, y Annabelle conocía muy bien la zona.
Las invitó a las dos a tomar un té con él, pero Annabelle le dijo que tenían que volver al camarote para cambiarse antes de cenar. El caballero les sonrió mientras se alejaban. Pensó que la niña era adorable y la madre era muy guapa. No encajaba en su imagen de una médico. Había entrevistado a Elsie Inglis hacía varios años, y Annabelle no se parecía en nada a ella, por decirlo de una manera elegante. Le había divertido que la pequeña fuera tan pródiga en información sobre su familia, aunque su madre se hubiera sentido algo incómoda.
Las localizó en el comedor por la noche, pero no se acercó a saludar. No quería entrometerse. Sin embargo, al día siguiente vio a Annabelle sola en la cubierta, paseando tranquilamente. Consuelo había ido a nadar con Brigitte, y esta vez llevaba un sombrero atado con un lazo por debajo de la barbilla.
—Veo que hoy se ha ajustado bien el sombrero —dijo él con una sonrisa tras detenerse un momento en la barandilla, junto a ella.
Annabelle se volvió hacia el caballero también sonriendo.
—Hay más brisa ahora que cuando llegamos hace un mes.
Estaban ya a finales de julio.
—A mí me encantan estos viajes oceánicos —comentó el hombre—, a pesar de que ambos hayamos perdido a seres queridos en el mar y hayamos sufrido tragedias familiares. Estar aquí me da la oportunidad de tomar aliento y permanecer entre dos vidas y dos mundos. Me gusta encontrar momentos tranquilos para la reflexión de vez en cuando. ¿Han pasado todo el mes en Nueva York? —preguntó con interés. Daba gusto conversar con él.
—Solo unos días. También hemos estado unas cuantas semanas en Newport.
Él sonrió.
—Yo he estado en Cape Cod. Me gusta veranear allí todos los años. Me devuelve a la infancia.
—Era la primera vez que mi hija venía.
—¿Y qué le ha parecido?
—Le ha encantado. Dice que quiere volver todos los veranos. —Y entonces añadió un dato sobre sí misma—. Hacía diez años que yo no regresaba.
—¿A Newport? —No le sorprendía demasiado.
—No, a Estados Unidos. —Eso lo sorprendió bastante más.
—Vaya, eso es mucho tiempo.
Era un hombre alto y enjuto, con el pelo entrecano, unos ojos marrones muy cálidos y las facciones marcadas. Debía de tener poco más de cuarenta años. Parecía más inteligente que guapo, aunque tenía encanto.
—Supongo que habrá estado muy atareada, si no ha tenido ocasión de regresar antes. O muy enfadada por algo —añadió, como buen periodista que era, y Annabelle se echó a reír.
—No estaba enfadada. Tenía ganas de cortar por lo sano. He rehecho mi vida en Francia. Primero me marché como voluntaria al frente, a trabajar en un hospital, y allí me quedé. Pensaba que no lo echaba de menos. Pero tengo que admitir que ha sido agradable volver a casa y enseñarle los lugares de mi infancia a mi hija.
—¿Es viuda? —preguntó el caballero.
Era fácil de suponer, pues Consuelo le había dicho que su padre llevaba muerto tantos años como ella tenía. Annabelle empezó a asentir con la cabeza, pero entonces se detuvo en seco. Estaba cansada de decir mentiras, sobre todo aquellas que eran innecesarias, solo para proteger a otras personas o a sí misma del daño ajeno.
—Divorciada.
Él no reaccionó ante su respuesta, aunque estaba confundido. A algunas personas les habría parecido una confesión escandalosa. Pero él no parecía darle demasiada importancia.
—Creía que su hija había dicho que su padre había muerto.
Annabelle se lo quedó mirando unos segundos y entonces decidió sacar toda la artillería. No tenía nada que perder. Si el hombre se escandalizaba y se apartaba de ella, le daba igual; no pasaba nada si no volvía a verlo. En el fondo, tampoco lo conocía.
—No me casé con su padre —dijo en voz baja pero con firmeza.
Era la primera vez que se lo contaba a alguien sin tapujos. En los círculos en los que se había criado, habría sido motivo más que suficiente para dar la conversación por concluida y para hacerle el vacío de ahí en adelante.
Él tardó un instante en contestar, pero al cabo de unos segundos asintió y la miró con una sonrisa.
—Si espera que me desmaye o me tire por la borda en lugar de hablar con usted, lamento decepcionarla. Soy periodista. He oído infinidad de historias. Y vivo en Francia. Allí es bastante frecuente, aunque haya personas que no lo reconozcan. Muchos hombres tienen hijos con las esposas de otros. —Ella se echó a reír, cosa que llevó al hombre a preguntarse si ese había sido el motivo de su divorcio. Era una mujer interesante—. Y sospecho que ocurre más a menudo de lo que sabemos o queremos creer, incluso en nuestro país. También hay personas que tienen hijos con quienes aman, aunque no se casen. Mientras no se haga daño a nadie, ¿quién soy yo para decir que no está bien? Nunca me he casado.
Era un hombre muy abierto de miras.
—Bueno, yo no lo amaba —añadió Annabelle—. Es una historia muy larga. Pero acabó bien. Consuelo es lo mejor que me ha pasado en la vida.
Él no hizo comentario alguno, pero parecía de acuerdo con lo que acababa de oír.
—¿Qué clase de médico es?
—De las buenas —contestó ella con una sonrisa, y él se rió como respuesta.
—Eso lo daba por supuesto. Me refería a cuál es su especialidad.
Annabelle le había entendido a la primera, pero le gustaba bromear con él. Su conversación era natural. Y le parecía un hombre abierto, afectuoso y de trato fácil.
—Medicina general.
—¿Trabajó en el frente? —No creía que tuviera edad para haber estudiado antes de la guerra.
—Como auxiliar de medicina, aunque solo había estudiado un curso en la universidad. Terminé la carrera después de la guerra.
Le pareció curioso que no hubiera querido ejercer en Estados Unidos, aunque podía imaginarse por qué. A él también le encantaba París. Tenía una vida mucho más plena que la que habría llevado en Nueva York o Boston.
—Yo me marché para trabajar de reportero para los británicos al principio de la guerra. Y llevo en Europa desde entonces. Viví en Londres durante dos años cuando acabó el conflicto y ahora hace cinco años que me instalé en París. Dudo que pudiera volver a vivir en Estados Unidos. Me gusta demasiado la vida que llevo en Europa.
—Yo tampoco podría regresar —coincidió Annabelle.
Y no tenía motivos para hacerlo. Ahora su vida estaba en París. Únicamente su historia seguía en Estados Unidos, así como su casa de verano.
Charlaron un rato más y después ella fue a buscar a Consuelo y a Brigitte, que seguían en la piscina. Volvieron a verlo por la noche, cuando salían del comedor después de una cena temprana. Él entraba en ese momento y le preguntó si le apetecería tomar una copa con él más tarde. La mujer dudó, mientras Consuelo los miraba a los dos, y al final le dijo que sí. Quedaron en el Verandah Café a las nueve y media. Consuelo ya estaría durmiendo a esas horas, así que Annabelle estaría libre.
—Le gustas —le dijo la niña a su madre como si tal cosa, mientras regresaban al camarote—. Es simpático.
Annabelle no hizo ningún comentario. Lo mismo había pensado de Antoine y se había equivocado. Sin embargo, Callam McAffrey era otra clase de hombre, y Annabelle tenía más cosas en común con él. Se preguntó por qué no se habría casado nunca, y él la sacó de dudas aquella misma noche, mientras bebían champán en el Verandah Café, que tenía una terraza desde donde se disfrutaba de la brisa marina.
—Me enamoré de una enfermera en Inglaterra durante la guerra. La mataron una semana antes de que se firmara el armisticio. Íbamos a casarnos, pero ella no quería hacerlo hasta que hubiera acabado el conflicto. Tardé mucho tiempo en recuperarme (en concreto, seis años y medio). Era una mujer muy especial. Provenía de una familia adinerada, pero nunca alardeaba de ello. Tenía los pies en el suelo, y trabajaba más que cualquiera que yo haya conocido. Nos divertíamos muchísimo juntos. —No lo dijo con sensiblería, sino más bien como si todavía se deleitara con el recuerdo—. De vez en cuando visito a su familia.
—El padre de Consuelo era británico. Pero me temo que no era un hombre muy recomendable, la verdad. Aunque su madre es fantástica. Seguramente iremos a verla en agosto.
—Cuando los británicos son buenos, son increíbles —dijo él con sinceridad—. Pero no siempre me llevo igual de bien con los franceses. —Annabelle se rió con sorna mientras pensaba en Antoine, pero no dijo nada—. Sí, a veces no sé de qué pie calzan. Tienden a ser más retorcidos.
—Creo que tiene razón, por lo menos en algunos casos. Como amigos y compañeros de trabajo son maravillosos. Pero en el terreno amoroso, es otro cantar.
Por lo poco que ella había comentado, él intuyó que había sufrido algún desengaño, era de suponer que por culpa de un francés. Aunque el padre inglés de Consuelo tampoco parecía una perla. Le daba la sensación de que Annabelle había tenido ración más que suficiente de manzanas podridas. Y en su juventud, él también había tenido más de una mala experiencia, sin tener en cuenta a Fiona, por supuesto, la enfermera de la que se había enamorado. Ahora llevaba una temporada solo. Se había tomado un descanso en el amor. De ese modo su vida era más sencilla, que era la misma conclusión a la que había llegado Annabelle.
Hablaron de la guerra durante un rato, luego sobre la política en Estados Unidos, de algunas de sus experiencias como periodista y de las de Annabelle en el campo de la medicina. Por lo menos, ella pensó que sería un buen amigo. El hombre la acompañó a su camarote y le deseó las buenas noches de forma afectuosa pero educada.
Volvió a invitarla a tomar una copa al día siguiente, y también se divirtieron mucho. Además, jugó a las cartas con ella y Consuelo el último día de travesía, y esa noche Annabelle lo invitó a cenar con ellas. La niña y él hicieron muy buenas migas y la pequeña le contó con pelos y señales cómo era su perrito, e incluso lo invitó a ir a verlo un día, a lo que Annabelle no hizo comentario alguno.
Tomaron una última copa juntos aquella noche y, de improviso, mientras la acompañaba al camarote una vez más, le dijo que le gustaría ir a ver el perro de su hija. Él también tenía un labrador. Annabelle se rió ante el comentario de él.
—Puede venir a ver el perro de mi hija cuando quiera. Será usted bienvenido —le dijo—. También puede venir a vernos a nosotras.
—Bueno, digamos que lo que más me interesa es ver el perro —puntualizó él guiñándole un ojo—, pero supongo que no me importaría verlas de paso a las dos, si al perro no le importa.
En ese momento miró con ternura a Annabelle. Había averiguado muchas cosas sobre ella durante el trayecto, más de las que ella creía. En eso consistía su trabajo. Percibía el dolor y las dificultades que había tenido que superar. Las mujeres de su estatus social no solían marcharse de casa a los veintidós años para trabajar como voluntarias a cinco mil kilómetros de su hogar, con el fin de contribuir a una guerra que no era la suya. Y tampoco se quedaban en un país extranjero después del conflicto, ni se volcaban en una profesión como la que había elegido ella, a menos que en su patria les hubieran sucedido cosas terribles. Además, tenía la impresión de que, después de eso, le habían pasado unas cuantas desgracias más. Estaba convencido de que no era de esa clase de mujeres que tienen un hijo ilegítimo así como así, sino que debió de hacerlo porque no le quedó otro remedio. Y saltaba a la vista que había sacado adelante a Consuelo de la mejor manera posible, y había sabido ver el lado positivo de todo lo que le había ocurrido. Era una gran mujer. Lo llevaba escrito en la cara. Confiaba en poder volver a verla.
—Me gustaría mantener el contacto una vez que estemos en París —le propuso él muy correcto.
Annabelle no era arrogante, pero sí muy fina y distinguida, y eso también le gustaba de ella. En cierto modo le recordaba a Fiona, aunque era más joven y más guapa. No obstante, lo que más le había gustado de Fiona en su momento, y ahora de Annabelle, era lo que veía en su interior. Era evidente que se trataba de una mujer con determinación e integridad, con grandes valores morales, un corazón enorme y una mente avispada. No se podía pedir más, y si una mujer como Annabelle se cruzaba en el camino, no había que malgastar la oportunidad de conocerla mejor. Las mujeres de su talla no aparecían muchas veces en la vida de alguien. Él ya había tenido la suerte de contar con una en su vida, y sabía que, si alguna vez tenía la buena fortuna de conocer a una segunda mujer tan especial, no dejaría pasar la oportunidad.
—Muy bien, allí me encontrará —le dijo ella—. Aunque puede que vayamos unos días a Deauville. Le prometí a Consuelo que la llevaría a la playa. Y es posible que viajemos a Inglaterra a ver a la familia de su padre. Pero no tardaremos en volver a estar por París. Tengo que abrir la consulta antes de que mis pacientes se olviden de que existo.
Al periodista le resultaba imposible imaginar que alguien que la hubiese conocido pudiera olvidarse de ella. Y desde luego, él no tenía intención de perderle la pista.
—A lo mejor podríamos hacer algo los tres juntos este fin de semana —propuso él—, con el perro, por supuesto. No me gustaría herir sus sentimientos...
Annabelle sonrió ante su respuesta. Faltaban pocos días para que llegara el fin de semana, y la idea le gustó. De hecho, le gustaba todo lo que había descubierto sobre él durante el viaje en barco. Y le daba buena espina. Le inspiraba solidez, integridad, afecto y amabilidad. El respeto del uno hacia el otro era mutuo, por lo menos, hasta el momento. Era un buen punto de partida, mejor que muchos de los que había tenido Annabelle. Su amistad fraterna con Josiah debería haberle dado pistas de algo que en aquella época no había sabido ver. Y los ademanes exagerados y gustos ostentosos de Antoine no habían hecho más que encubrir un corazón vacío. Callam era un hombre completamente distinto.
Se despidieron en la puerta del camarote. Y a la mañana siguiente, Annabelle se levantó y se vistió muy temprano, igual que había hecho al llegar a Europa diez años antes, cuando había huido de Nueva York a la desesperada. No obstante, esta vez no sintió desesperación, ni dolor, mientras permanecía de pie junto a la barandilla de cubierta, contemplando el amanecer. A lo lejos distinguió Le Havre, donde atracarían al cabo de dos horas.
Mientras observaba el mar abierto, tuvo una increíble sensación de libertad, de haber roto por fin todas las cadenas que la aprisionaban. Ya no la oprimía el yugo de las opiniones ajenas, ni de las mentiras que dijeran sobre ella. Era una mujer libre, una buena mujer, y lo sabía.
Mientras el sol se alzaba en el cielo matutino, oyó una voz a su lado, se dio la vuelta y vio que era de Callam.
—Tenía el presentimiento de que la hallaría aquí —dijo él en voz baja. Sus ojos se encontraron y los dos sonrieron—. Una mañana estupenda, ¿verdad? —comentó sin más.
—Sí —respondió Annabelle, y su sonrisa se ensanchó.
Era una mañana estupenda. Ambos eran buenas personas. Y la vida era un placer.
## UNA BUENA MUJER
### DANIELLE STEEL
Danielle Steel es sin duda una de las novelistas más populares en todo el mundo. Sus libros se han publicado en cuarenta y siete países, con ventas que superan los quinientos ochenta millones de ejemplares. Cada uno de sus lanzamientos ha encabezado las listas de bestsellers de _The New York Times_ , y muchos de ellos se han mantenido en esta posición durante meses.
PRIMERA EDICIÓN VINTAGE ESPAÑOL, MAYO 2014
_Copyright de la traducción © 2011 por Ana Mata Buil_
Todos los derechos reservados. Publicado en coedición con Penguin Random House Grupo Editorial, S. A., Barcelona, en los Estados Unidos de América por Vintage Español, una división de Random House LLC, Nueva York, y en Canadá por Random House of Canada Limited, Toronto, compañías Penguin Random House. Originalmente publicado en inglés en EE.UU. como A Good Woman por Delacorte Press, una division de Penguin Random House, Nueva York. Copyright © 2008 por Danielle Steel. Esta traducción fue originalmente publicada en España por Penguin Random House Grupo Editorial, S. A., Barcelona, en 2011. Copyright de la presente edición en castellano para todo el mundo © 2011 por Penguin Random House Grupo Editorial, S. A.
Vintage es una marca registrada y Vintage Español y su colofón son marcas de Random House LLC.
Esta novela es una obra de ficción. Los nombres, personajes, lugares e incidentes o son producto de la imaginación de la autora o se usan de forma ficticia. Cualquier parecido con personas, vivas o muertas, eventos o escenarios es puramente casual.
Información de catalogación de publicaciones disponible en la Biblioteca del Congreso de los Estados Unidos.
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**Vintage ISBN en tapa blanda: 978-0-8041-7172-4**
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Índice
Una buena mujer
Capítulo 1
Capítulo 2
Capítulo 3
Capítulo 4
Capítulo 5
Capítulo 6
Capítulo 7
Capítulo 8
Capítulo 9
Capítulo 10
Capítulo 11
Capítulo 12
Capítulo 13
Capítulo 14
Capítulo 15
Capítulo 16
Capítulo 17
Capítulo 18
Capítulo 19
Capítulo 20
Capítulo 21
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Capítulo 23
Capítulo 24
Capítulo 25
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Capítulo 27
Acerca de la autora
Créditos
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} | 532 |
{"url":"http:\/\/wpedia.goo.ne.jp\/enwiki\/Alpha_Centauri","text":"Alpha Centauri\n\n\"Toliman\" redirects here. For other uses, see Toliman (disambiguation).\nObservation data Characteristics Epoch J2000.0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Equinox J2000.0 \u03b1 Centauri and \u03b2 Centauri, with Proxima circled in red Constellation Centaurus Alpha Centauri A Right ascension 14h\u00a039m\u00a036.49400s[1] Declination \u201360\u00b0\u00a050\u2032\u00a002.3737\u2033[1] Apparent magnitude (V) +0.01[2] Alpha Centauri B Right ascension 14h\u00a039m\u00a035.06311s[1] Declination \u201360\u00b0\u00a050\u2032\u00a015.0992\u2033[1] Apparent magnitude (V) +1.33[2] G2V[3] +0.24[2] +0.71[2] K1V[3] +0.68[2] +0.88[2] Radial velocity (Rv) \u221221.4\u00b10.76[4] km\/s Proper motion (\u03bc) RA:\u00a0\u22123679.25[1]\u00a0mas\/yr Dec.:\u00a0473.67[1]\u00a0mas\/yr Parallax (\u03c0) 754.81\u00a0\u00b1 4.11[1] mas Distance 4.37[5] ly Absolute\u00a0magnitude\u00a0(MV) 4.38[6] Radial velocity (Rv) \u221218.6\u00b11.64[4] km\/s Proper motion (\u03bc) RA:\u00a0\u22123614.39[1]\u00a0mas\/yr Dec.:\u00a0802.98[1]\u00a0mas\/yr Parallax (\u03c0) 754.81\u00a0\u00b1 4.11[1] mas Distance 4.37[5] ly Absolute\u00a0magnitude\u00a0(MV) 5.71[6] Mass 1.100[7]\u00a0M\u2609 Radius 1.227[8]\u00a0R\u2609 Luminosity 1.519[7]\u00a0L\u2609 Surface gravity (log\u00a0g) 4.30[9]\u00a0cgs Temperature 5,790[7]\u00a0K Metallicity [Fe\/H] 0.20[7]\u00a0dex Rotation 22[8] days Age \u22484.4[10]\u00a0Gyr Mass 0.907[7]\u00a0M\u2609 Radius 0.865[8]\u00a0R\u2609 Luminosity 0.5002[7]\u00a0L\u2609 Surface gravity (log\u00a0g) 4.37[9]\u00a0cgs Temperature 5,260[7]\u00a0K Metallicity 0.23[7] Rotation 41[8] days Age \u22486.5[10]\u00a0Gyr Primary A Companion B Period (P) 79.91\u00b10.011 yr Semi-major axis (a) 17.57\u00b10.022\" Eccentricity (e) 0.5179\u00b10.00076 Inclination (i) 79.205\u00b10.041\u00b0 Longitude of the node (\u03a9) 204.85\u00b10.084\u00b0 Periastron epoch (T) 1875.66\u00b10.012 Argument of periastron (\u03c9) (secondary) 231.65\u00b10.076\u00b0 Toliman, Bungula, Gliese\u00a0559, FK5\u00a0538, CD\u221260\u00b05483, CCDM\u00a0J14396-6050, GC\u00a019728 \u03b1 Cen A: Rigil Kentaurus, Rigil Kent, \u03b11\u00a0Centauri, HR\u00a05459, HD\u00a0128620, GCTP\u00a03309.00, LHS\u00a050, SAO\u00a0252838, HIP\u00a071683 \u03b1 Cen B: \u03b12\u00a0Centauri, HR\u00a05460, HD\u00a0128621, LHS\u00a051, HIP\u00a071681 SIMBAD AB A B Exoplanet Archive data ARICNS data Extrasolar Planets Encyclopaedia data\n\nAlpha Centauri (\u03b1 Centauri, abbreviated Alpha Cen, \u03b1 Cen) is the closest star system to the Solar System at a distance of 4.37 light-years (1.34\u00a0pc).[5] It consists of three stars: the pair Alpha Centauri A (also named Rigil Kentaurus[12]) and Alpha Centauri B together with a small and faint red dwarf, Alpha Centauri C (also named Proxima Centauri[12]), that may be gravitationally bound to the other two.[13] To the unaided eye, the two main components appear as a single point of light with an apparent visual magnitude of \u22120.27, forming the brightest star in the southern constellation of Centaurus and the third-brightest star in the night sky, outshone only by Sirius and Canopus.\n\nAlpha Centauri A (\u03b1 Cen A) has 1.1 times the mass and 1.519 times the luminosity of the Sun, while Alpha Centauri B (\u03b1 Cen B) is smaller and cooler, at 0.907 times the Sun's mass and 0.445 times its visual luminosity.[14] During the pair's 79.91-year orbit about a common centre,[15] the distance between them varies from about that between Pluto and the Sun to that between Saturn and the Sun.\n\nProxima Centauri (\u03b1 Cen C) is at the slightly smaller distance of 4.24 light-years (1.30\u00a0pc) from the Sun, making it the closest star to the Sun, even though it is not visible to the naked eye. The separation of Proxima from Alpha Centauri AB is about 15,000 astronomical units (0.24\u00a0ly; 0.07\u00a0pc),[16] equivalent to 500 times the size of Neptune's orbit. Proxima Centauri b, an Earth-sized exoplanet in the habitable zone of Proxima Centauri, has been detected[17] and may be a destination of future interstellar spacecraft, including a fleet of StarChip spacecraft currently being developed for a flyby mission by the Breakthrough Starshot project.[17]\n\nNomenclature\n\n\u03b1 Centauri (Latinised to Alpha Centauri) is the system's Bayer designation. It bore the traditional name Rigil Kentaurus, which is a latinisation of the Arabic name \u0631\u062c\u0644 \u0627\u0644\u0642\u0646\u0637\u0648\u0631\u0633 Rijl al-Qan\u1e6d\u016bris, meaning \"Foot of the Centaur\".[18][19]\n\nAlpha Centauri C was discovered in 1915 by the Scottish astronomer Robert Innes, Director of the Union Observatory in Johannesburg, South Africa,[20] who suggested that it be named Proxima Centauri[21] (actually Proxima Centaurus).[22] The name is from Latin, meaning \"nearest [star] of Centaurus\".[23]\n\nIn 2016, the International Astronomical Union organized a Working Group on Star Names (WGSN)[24] to catalog and standardize proper names for stars. The WGSN states that in the case of multiple stars the name should be understood to be attributed to the brightest component by visual brightness.[25] The WGSN approved the name Proxima Centauri for Alpha Centauri C on 21 August 2016 and the name Rigil Kentaurus for Alpha Centauri A on 6 November 2016. They are now both so entered in the IAU Catalog of Star Names.[12]\n\nNature and components\n\nview\u00a0\u2022\u00a0discuss\u00a0\u2022\u00a0edit\n-13\u00a0\u2014\n-12\u00a0\u2014\n-11\u00a0\u2014\n-10\u00a0\u2014\n-9\u00a0\u2014\n-8\u00a0\u2014\n-7\u00a0\u2014\n-6\u00a0\u2014\n-5\u00a0\u2014\n-4\u00a0\u2014\n-3\u00a0\u2014\n-2\u00a0\u2014\n-1\u00a0\u2014\n0\u00a0\u2014\nAxis scale: billions of years.\nAlso see: Human timeline and Life timeline\nThe relative sizes and colours of stars in the Alpha Centauri system, compared to the Sun\n\nAlpha Centauri is the name given to what appears as a single star to the naked eye and the brightest star in the southern constellation of Centaurus. At \u22120.27 apparent visual magnitude (calculated from A and B magnitudes), it is fainter only than Sirius and Canopus. The next-brightest star in the night sky is Arcturus. Alpha Centauri is a multiple-star system, with its two main stars being Alpha Centauri\u00a0A (\u03b1 Cen A) and Alpha Centauri\u00a0B (\u03b1 Cen B), usually defined to identify them as the different components of the binary \u03b1 Cen AB. A third companion\u2014Proxima Centauri (or Proxima or \u03b1 Cen C)\u2014has a distance much greater than the observed separation between stars A and\u00a0B and is probably gravitationally associated with the AB system. As viewed from Earth, it is located at an angular separation of 2.2\u00b0 from the two main stars. Proxima Centauri would appear to the naked eye as a separate star from \u03b1 Cen AB if it were bright enough to be seen without a telescope. Alpha Centauri\u00a0AB and Proxima Centauri form a visual double star. Direct evidence that Proxima Centauri has an elliptical orbit typical of binary stars has yet to be found.[26] Together, the three components make a triple star system, referred to by double-star observers as the triple star (or multiple star), \u03b1 Cen AB-C.\n\nTogether, the bright visible components of the binary star system are called Alpha Centauri\u00a0AB (\u03b1 Cen AB). This \"AB\" designation denotes the apparent gravitational centre of the main binary system relative to other companion star(s) in any multiple star system.[27] \"AB-C\" refers to the orbit of Proxima around the central binary, being the distance between the centre of gravity and the outlying companion. Some older references use the confusing and now discontinued designation of\u00a0A\u00d7B. Because the distance between the Sun and Alpha Centauri\u00a0AB does not differ significantly from either star, gravitationally this binary system is considered as if it were one object.[28]\n\nAsteroseismic studies, chromospheric activity, and stellar rotation (gyrochronology), are all consistent with the \u03b1 Cen system being similar in age to, or slightly older than, the Sun, with typical ages quoted between 4.5 and 7 billion years (Gyr).[10] Asteroseismic analyses that incorporate the tight observational constraints on the stellar parameters for \u03b1 Cen A and\/or B have yielded age estimates of 4.85\u00b10.5\u00a0Gyr,[7] 5.0\u00b10.5\u00a0Gyr,[29] 5.2\u20137.1\u00a0Gyr,[30] 6.4\u00a0Gyr,[31] and 6.52\u00b10.3\u00a0Gyr.[32] Age estimates for stars A and B based on chromospheric activity (Calcium H & K emission) yield 4.4\u20136.5\u00a0Gyr, whereas gyrochronology yields 5.0\u00b10.3\u00a0Gyr.[10]\n\nAlpha Centauri A\n\nAlpha Centauri A, also known as Rigil Kentaurus, is the principal member, or primary, of the binary system, being slightly larger and more luminous than the Sun. It is a solar-like main-sequence star with a similar yellowish colour,[33] whose stellar classification is spectral type G2\u00a0V. From the determined mutual orbital parameters, Alpha Centauri\u00a0A is about 10 percent more massive than the Sun, with a radius about 23 percent larger. The projected rotational velocity ( v\u00b7sin i ) of this star is 2.7\u00b10.7\u00a0km\/s, resulting in an estimated rotational period of 22\u00a0days,[34] which gives it a slightly faster rotational period than the Sun's 25 days. When considered among the individual brightest stars in the sky (excluding the Sun), Alpha Centauri\u00a0A is the fourth brightest at an apparent visual magnitude of +0.01, being fractionally fainter than Arcturus at an apparent visual magnitude of \u22120.04.\n\nAlpha Centauri B\n\nAlpha Centauri B is the companion star, or secondary, of the binary system, and is slightly smaller and less luminous than the Sun. It is a main-sequence star of spectral type K1\u00a0V, making it more an orange colour than the primary star.[33] Alpha Centauri\u00a0B is about 90 percent the mass of the Sun and 14 percent smaller in radius. The projected rotational velocity ( v\u00b7sin i ) is 1.1\u00b10.8\u00a0km\/s, resulting in an estimated rotational period of 41\u00a0days. (An earlier, 1995 estimate gave a similar rotation period of 36.8\u00a0days.)[35] Although it has a lower luminosity than component\u00a0A, star B emits more energy in the X-ray band. The light curve of B varies on a short time scale and there has been at least one observed flare.[36] Alpha Centauri\u00a0B at an apparent visual magnitude of 1.33 would be twenty-first in brightness if it could be seen independently of Alpha Centauri A.\n\nAlpha Centauri C (Proxima Centauri)\n\nAlpha Centauri C, also known as Proxima Centauri, is of spectral class M6\u00a0Ve, a small main-sequence star (Type\u00a0V) with emission lines. Its B\u2212V colour index is\u00a0+1.82 and its mass is about 0.123\u00a0solar masses (M), or 129 Jupiter masses.\n\nObservation\n\nLocation of Alpha Centauri in Centaurus\n\nThe two Alpha Centauri AB binary stars are too close together to be resolved by the naked eye, because the angular separation varies between 2 and 22\u00a0arcsec,[37] but through much of the orbit, both are easily resolved in binoculars or small 5\u00a0cm (2\u00a0in) telescopes.[38]\n\nIn the southern hemisphere, Alpha Centauri forms the outer star of The Pointers or The Southern Pointers,[38] so called because the line through Beta Centauri (Hadar\/Agena),[39] some 4.5\u00b0 west,[38] points directly to the constellation Crux\u2014the Southern Cross.[38] The Pointers easily distinguish the true Southern Cross from the fainter asterism known as the False Cross.[40]\n\nThe two bright stars at the lower right are Alpha (right) and Beta Centauri (left, above antenna). A line drawn through them points to the four bright stars of the Southern Cross, just to the right of the dome of La Silla Observatory.[41]\n\nSouth of about 29\u00b0 S latitude, Alpha Centauri is circumpolar and never sets below the horizon.[42] Both stars, including Crux, are too far south to be visible for mid-latitude northern observers. Below about 29\u00b0 N latitude to the equator (roughly Hermosillo, Chihuahua City in Mexico, Galveston, Texas, Ocala, Florida and Lanzarote, the Canary Islands of Spain) during the northern summer, Alpha Centauri lies close to the southern horizon.[39] The star culminates each year at midnight on 24 April or 9 p.m. on 8 June.[39][43]\n\nAs seen from Earth, Proxima Centauri is 2.2\u00b0 southwest from Alpha Centauri AB.[44] This is about four times the angular diameter of the Full Moon, and almost exactly half the distance between Alpha Centauri AB and Beta Centauri. Proxima usually appears as a deep-red star of an apparent visual magnitude of 13.1 in a sparsely populated star field, requiring moderately sized telescopes to see. Listed as V645 Cen in the General Catalogue of Variable Stars (G.C.V.S.) Version 4.2, this UV Ceti-type flare star can unexpectedly brighten rapidly by as much as 0.6 magnitudes at visual wavelengths, then fade after only a few minutes.[45] Some amateur and professional astronomers regularly monitor for outbursts using either optical or radio telescopes.[46]\n\nObservational history\n\nView of Alpha Centauri from the Digitized Sky Survey 2\n\nEnglish explorer Robert Hues brought Alpha Centauri to the attention of European observers in his 1592 work Tractatus de Globis, along with Canopus and Achernar, noting \"Now, therefore, there are but three Stars of the first magnitude that I could perceive in all those parts which are never seene here in England. The first of these is that bright Star in the sterne of Argo which they call Canobus. The second is in the end of Eridanus. The third [Alpha Centauri] is in the right foote of the Centaure.\"[47]\n\nThe binary nature of Alpha Centauri AB was first recognized in December 1689 by astronomer and Jesuit priest Jean Richaud. The finding was made incidentally while observing a passing comet from his station in Puducherry. Alpha Centauri was only the second binary star system to be discovered, preceded by Alpha Crucis.[48]\n\nBy 1752, French astronomer Nicolas Louis de Lacaille made astrometric positional measurements using state-of-the-art instruments of that time.[49] Its large proper motion was discovered by Manuel John Johnson, observing from Saint Helena, who informed Thomas Henderson at the Royal Observatory, Cape of Good Hope of it. The parallax of Alpha Centauri was subsequently determined by Henderson from many exacting positional observations of the AB system between April 1832 and May 1833. He withheld his results, however, because he suspected they were too large to be true, but eventually published them in 1839 after Friedrich Wilhelm Bessel released his own accurately determined parallax for 61 Cygni in 1838.[50] For this reason, Alpha Centauri is sometimes considered as the second star to have its distance measured because Henderson's work was not fully recognized at first.[50] (The distance of Alpha is now reckoned at 4.396\u00a0ly or 41.59\u00a0trillion\u00a0km.)\n\nLater, John Herschel made the first micrometrical observations in 1834.[51] Since the early 20th century, measures have been made with photographic plates.[52]\n\nCompared to the Sun, Alpha Centauri A is of the same stellar type G2, while Alpha Centauri B is a K1-type star.[53]\n\nBy 1926, South African astronomer William Stephen Finsen calculated the approximate orbit elements close to those now accepted for this system.[54] All future positions are now sufficiently accurate for visual observers to determine the relative places of the stars from a binary star ephemeris.[55] Others, like the Belgian astronomer D. Pourbaix (2002), have regularly refined the precision of any new published orbital elements.[15]\n\nAlpha Centauri is inside the G-cloud, and the nearest known system to it is Luhman 16 at 3.6\u00a0ly (1.1\u00a0pc).[56]\n\nScottish astronomer Robert T. A. Innes discovered Proxima Centauri in 1915 by blinking photographic plates taken at different times during a dedicated proper motion survey. This showed the large proper motion and parallax of the star was similar in both size and direction to those of Alpha Centauri AB, suggesting immediately it was part of the system and slightly closer to Earth than Alpha Centauri AB. Lying 4.24\u00a0ly (1.30\u00a0pc) away, Proxima Centauri is the nearest star to the Sun. All current derived distances for the three stars are from the parallaxes obtained from the Hipparcos star catalogue (HIP)[57][58][59][60] and the Hubble Space Telescope.[61]\n\nBinary system\n\nApparent and true orbits of Alpha Centauri. The A component is held stationary and the relative orbital motion of the B component is shown. The apparent orbit (thin ellipse) is the shape of the orbit as seen by an observer on Earth. The true orbit is the shape of the orbit viewed perpendicular to the plane of the orbital motion. According to the radial velocity vs. time [11] the radial separation of A and B along the line of sight had reached a maximum in 2007 with B being behind A. The orbit is divided here into 80 points, each step refers to a timestep of approx. 0.99888 years or 364.84 days.\n\nWith the orbital period of 79.91\u00a0years,[15] the A and B components of this binary star can approach each other to 11.2\u00a0AU (1.68\u00a0billion\u00a0km), or about the mean distance between the Sun and Saturn; and may recede as far as 35.6\u00a0AU (5.33\u00a0billion\u00a0km), approximately the distance from the Sun to Pluto.[15][62] This is a consequence of the binary's moderate orbital eccentricity e\u00a0=\u00a00.5179.[15] From the orbital elements, the total mass of both stars is about 2.0\u00a0M[63]\u2014or twice that of the Sun.[62] The average individual stellar masses are 1.09\u00a0M and 0.90\u00a0M, respectively,[64] though slightly higher masses have been quoted in recent years, such as 1.14\u00a0M and 0.92\u00a0M,[65] or totalling 2.06\u00a0M. Alpha Centauri A and B have absolute magnitudes of +4.38 and +5.71, respectively. Stellar evolution theory implies both stars are slightly older than the Sun at 5 to 6 billion years, as derived by both mass and their spectral characteristics.[44][64]\n\nViewed from Earth, the apparent orbit of this binary star means that its separation and position angle (PA) are in continuous change throughout its projected orbit. Observed stellar positions in 2010 are separated by 6.74\u00a0arcsec through the PA of 245.7\u00b0, reducing to 6.04\u00a0arcsec through 251.8\u00b0 in 2011.[15] The closest recent approach was in February 2016, at 4.0\u00a0arcsec through 300\u00b0.[15][66] The observed maximum separation of these stars is about 22\u00a0arcsec, while the minimum distance is 1.7\u00a0arcsec.[67] The widest separation occurred during February 1976 and the next will be in January 2056.[15]\n\nIn the true orbit, closest approach or periastron was in August 1955, and next in May 2035. Furthest orbital separation at apastron last occurred in May 1995 and the next will be in 2075. The apparent distance between the two stars is rapidly decreasing, at least until 2019.[15]\n\nProxima Centauri\n\nMain article: Proxima Centauri\n\nThe much fainter red dwarf Proxima Centauri, or simply Proxima, is about 15,000 astronomical units (AU) away from Alpha Centauri AB.[27][44][52] This is equivalent to 0.24\u00a0ly or 2.3\u00a0trillion\u00a0km\u2014about 5% the distance between Alpha Centauri AB and the Sun. Proxima is likely gravitationally bound to Alpha Centauri AB, orbiting it with a period between 100,000 and 500,000 years.[44] However, it is also possible that Proxima is not gravitationally bound and thus moving along a hyperbolic trajectory[68] with respect to Alpha Centauri AB.[27]:72 The main evidence for a bound orbit is that Proxima's association with Alpha Centauri AB is unlikely to be coincidental, because they share approximately the same motion through space.[44] Theoretically, Proxima could leave the system after several million years.[69] It is not yet certain whether Proxima and Alpha Centauri are truly gravitationally bound.[70] In a pre-print published 10 November 2016 P. Kervella and F. Th\u00e9venin showed that based on new high precision radial velocity measurements Proxima and Alpha Centauri are in fact gravitationally bound with a high degree of confidence.[71] The orbital period of Proxima is approximately 550,000 years, with an eccentricity of 0.50\u00b10.08. Proxima comes within 4.3+1.1\n\u22120.9\nkAU of Alpha Centauri AB at periastron, and the apastron occurs at 13.0+0.3\n\u22120.1\nkAU.\n\nRelative positions of Sun, Alpha Centauri AB and Proxima Centauri. Grey dot is projection of Proxima Centauri, located at the same distance as Alpha Centauri AB.\n\nProxima is a red dwarf of spectral class M6 Ve with an absolute magnitude of +15.60, which is only a small fraction of the Sun's luminosity. By mass, Proxima is calculated as 0.123\u00b10.06\u00a0M (rounded to 0.12\u00a0M) or about one-eighth that of the Sun.[72]\n\nKinematics\n\nStars closest to the Sun, including Alpha Centauri (25 April 2014).[73]\n\nAll components of Alpha Centauri display significant proper motions against the background sky, similar to the first-magnitude stars Sirius and Arcturus. Over the centuries, this causes the apparent stellar positions to slowly change. Such motions define the high-proper-motion stars.[74] These stellar motions were unknown to ancient astronomers. Most assumed that all stars were immortal and permanently fixed on the celestial sphere, as stated in the works of the philosopher Aristotle.[75]\n\nEdmond Halley in 1718 found that some stars had significantly moved from their ancient astrometric positions.[76] For example, the bright star Arcturus (\u03b1 Boo) in the constellation of Bo\u00f6tes showed an almost 0.5\u00b0 difference in 1800 years,[77] as did the brightest star, Sirius, in Canis Major (\u03b1 CMa).[78] Halley's positional comparison was Ptolemy's catalogue of stars contained in the Almagest[79] whose original data included portions from an earlier catalogue by Hipparchos during the 1st century BCE.[80][81][82] Halley's proper motions were mostly for northern stars, so the southern star Alpha Centauri was not determined until the early 19th\u00a0century.[67]\n\nScottish-born observer Thomas Henderson in the 1830s at the Royal Observatory at the Cape of Good Hope discovered the true distance to Alpha Centauri.[83][84] He soon realized this system displayed an unusually high proper motion,[85] and therefore its observed true velocity through space should be much larger.[86][67] In this case, the apparent stellar motion was found using Nicolas Louis de Lacaille's astrometric observations of 1751\u20131752,[87] by the observed differences between the two measured positions in different epochs. Using the Hipparcos Star Catalogue (HIP) data, the mean individual proper motions are \u22123678\u00a0mas\/yr or \u22123.678\u00a0arcsec per year in right ascension and +481.84\u00a0mas\/yr or 0.48184\u00a0arcsec per year in declination.[88][89] As proper motions are cumulative, the motion of Alpha Centauri is about 6.1\u00a0arcmin each century, and 61.3\u00a0arcmin or 1.02\u00b0 each millennium. These motions are about one-fifth and twice, respectively, the diameter of the full Moon.[69] Using spectroscopy the mean radial velocity has been determined to be around 20\u00a0km\/s towards the Solar System.\n\nAs the stars of Alpha Centauri approach the Solar System, the measured proper motion and trigonometric parallax slowly increase.[44][69][69][88] Changes are also observed in the size of the semi-major axis of the orbital ellipse, increasing by 0.03\u00a0arcsec per century.[27] This small effect is gradually decreasing until the star system is at its closest to Earth, and is then reversed as the distance increases again.[27] Consequently, the observed position angles of the stars are subject to changes in the orbital elements over time, as first determined by W. H. van den Bos in 1926.[90][91][92] Some slight differences of about 0.5 percent in the measured proper motions are caused by Alpha Centauri AB's orbital motion.[88]\n\nApparent motion of Alpha Centauri relative to Beta Centauri\n\nBased on these observed proper motions and radial velocities, Alpha Centauri will continue to gradually brighten, passing just north of the Southern Cross or Crux, before moving northwest and up towards the celestial equator and away from the galactic plane. By about 29,700\u00a0AD, in the present-day constellation of Hydra, Alpha Centauri will be 3.26\u00a0ly or 1.00\u00a0pc away.[69] Then it will reach the stationary radial velocity (RVel) of 0.0\u00a0km\/s and the maximum apparent magnitude of \u22120.86v (which is comparable to present-day magnitude of Canopus). Even during the time of this nearest approach, however, the apparent magnitude of Alpha Centauri will still not surpass that of Sirius, which will brighten incrementally over the next 60,000 years, and will continue to be the brightest star as seen from Earth for the next 210,000 years.[93]\n\nThe Alpha Centauri system will then begin to move away from the Solar System, showing a positive radial velocity.[69] Because of visual perspective, about 100,000\u00a0years from now, these stars will reach a final vanishing point and slowly disappear among the countless stars of the Milky Way. Here this once bright yellow star will fall below naked-eye visibility somewhere in the faint present day southern constellation of Telescopium. This unusual location results from the fact that Alpha Centauri's orbit around the galactic centre is highly tilted with respect to the plane of the Milky Way.[69]\n\nIn about 4000 years, the proper motion of Alpha Centauri will mean that from the point of view of Earth it will appear close enough to Beta Centauri to form an optical double star. Beta Centauri is in reality far more distant than Alpha Centauri.\n\nPlanets\n\nThe Alpha Centauri planetary system\nCompanion\n(in order from star)\nMass Semimajor axis\n(AU)\nOrbital period\n(days)\nBc (unconfirmed) 0.141 20.4 <0.24 0.92\u00a0R\nCb 1.27+0.19\n\u22120.17\nM\n0.0485+0.0041\n\u22120.0051\n11.186 <0.35\n\nProxima Centauri b\n\nMain article: Proxima Centauri b\n\nIn August 2016, the European Southern Observatory announced the discovery of a planet slightly larger than the Earth orbiting Proxima Centauri.[94] Proxima Centauri b was found using the radial velocity method, where periodic Doppler shifts of spectral lines of the host star suggest an orbiting object. From these readings, the radial velocity of the parent star relative to the Earth is varying with an amplitude of about 2 metres (6.6\u00a0ft) per second.[94] The planet lies in the habitable zone of Proxima Centauri, but it is possible that the planet is tidally locked to the star,[94] resulting in temperature extremes that would be difficult for life to overcome.[95]\n\nAlpha Centauri Bb\n\nMain article: Alpha Centauri Bb\n\nIn 2012, a planet around Alpha Centauri B was announced, but in 2015 a new analysis concluded that it almost certainly does not exist and was just a spurious artefact of the data analysis.[96][97][98]\n\nAlpha Centauri Bc\n\nOn 25 March 2015, a scientific paper by Demory and colleagues published transit results for Alpha Centauri B using the Hubble Space Telescope for a total of 40 hours.[99] They evidenced a transit event possibly corresponding to a planetary body with a radius around 0.92\u00a0R. This planet would most likely orbit Alpha Centauri B with an orbital period of 20.4 days or less, with only a 5 percent chance of it having a longer orbit. The median average of the likely orbits is 12.4 days with an impact parameter of around 0\u20130.3. Its orbit would likely have an eccentricity of 0.24 or less. If confirmed, this planet would be called Alpha Centauri Bc. Like the probably spurious Alpha Centauri Bb, it likely has lakes of molten lava and would be far too close to Alpha Centauri B to harbour life.[100]\n\nPossible fourth stellar object\n\nMain article: U (TNO)\n\nIn images taken on 7 July 2014 (343.5\u00a0GHz) and 2 May 2015 (445\u00a0GHz), researchers discovered a source in the far infrared located within 5.5 arcseconds of \u03b1 Cen AB. Based on its proper motion, it was at first thought to be a part of the Alpha Centauri system. Further analysis, however, found that the object must be closer to the Solar System, and that it may be gravitationally bound to the Sun. The researchers suggest that the object may be an extreme trans-Neptunian object (ETNO) beyond 100\u00a0AU (15\u00a0billion kilometres), a super-Earth at around 300\u00a0AU (45\u00a0billion kilometres), or a very cool brown dwarf at around 20,000\u00a0AU (3.0\u00a0trillion kilometres).[101][102]\n\nThe discovery of planets orbiting other star systems, including similar binary systems (Gamma Cephei), raises the possibility that additional planets may exist in the Alpha Centauri system. Such planets could orbit Alpha Centauri\u00a0A or Alpha Centauri\u00a0B individually, or be on large orbits around the binary Alpha Centauri AB. Because both the principal stars are fairly similar to the Sun (for example, in age and metallicity), astronomers have been especially interested in making detailed searches for planets in the Alpha Centauri system. Several established planet-hunting teams have used various radial velocity or star transit methods in their searches around these two bright stars.[103] All the observational studies have so far failed to find any evidence for brown dwarfs or gas giants.[103][104]\n\nIn 2009, computer simulations (then unaware of the close-in planet Bb) showed that a planet might have been able to form near the inner edge of Alpha Centauri B's habitable zone, which extends from 0.5 to 0.9 AU from the star. Certain special assumptions, such as considering that Alpha Centauri A and B may have initially formed with a wider separation and later moved closer to each other (as might be possible if they formed in a dense star cluster) would permit an accretion-friendly environment farther from the star.[105] Bodies around A would be able to orbit at slightly farther distances due to A's stronger gravity. In addition, the lack of any brown dwarfs or gas giants in close orbits around A or B make the likelihood of terrestrial planets greater than otherwise.[106] Theoretical studies on the detectability via radial velocity analysis have shown that a dedicated campaign of high-cadence observations with a 1-meter class telescope can reliably detect a hypothetical planet of 1.8\u00a0M in the habitable zone of B within three years.[107]\n\nRadial velocity measurements of Alpha Centauri B with High Accuracy Radial Velocity Planet Searcher spectrograph ruled out planets of more than 4\u00a0M to the distance of the habitable zone of the star (orbital period P = 200 days).[108]\n\nCurrent estimates place the probability of finding an earth-like planet around Alpha Centauri A or B at roughly 85%, although this number remains uncertain.[109]\n\nTheoretical planets\n\nEarly computer-generated models of planetary formation predicted the existence of terrestrial planets around both Alpha Centauri A and\u00a0B,[107][110][111] but most recent numerical investigations have shown that the gravitational pull of the companion star renders the accretion of planets very difficult.[105][112] Despite these difficulties, given the similarities to the Sun in spectral types, star type, age and probable stability of the orbits, it has been suggested that this stellar system could hold one of the best possibilities for harbouring extraterrestrial life on a potential planet.[6][106][113][114]\n\nIn the Solar System both Jupiter and Saturn were probably crucial in perturbing comets into the inner Solar System. Here, the comets provided the inner planets with their own source of water and various other ices.[115] In the Alpha Centauri system, Proxima Centauri may have influenced the planetary disk as the Alpha Centauri system was forming, enriching the area around Alpha Centauri A and B with volatile materials.[116] This would be discounted if, for example, Alpha Centauri\u00a0B happened to have gas giants orbiting Alpha Centauri\u00a0A (or conversely, Alpha Centauri\u00a0A for Alpha Centauri\u00a0B), or if the stars B and A themselves were able to perturb comets into each other's inner system as Jupiter and Saturn presumably have done in the Solar System. Such icy bodies probably also reside in Oort clouds of other planetary systems, when they are influenced gravitationally by either the gas giants or disruptions by passing nearby stars many of these icy bodies then travel starwards.[69] There is no direct evidence yet of the existence of such an Oort cloud around Alpha Centauri\u00a0AB, and theoretically this may have been totally destroyed during the system's formation.[69]\n\nTo be in the star's habitable zone, any suspected planet around Alpha Centauri\u00a0A would have to be placed about 1.25\u00a0AU away\u00a0[citation needed] \u2013 about halfway between the distances of Earth's orbit and Mars's orbit in the Solar System\u00a0\u2013 so as to have similar planetary temperatures and conditions for liquid water to exist. For the slightly less luminous and cooler Alpha Centauri\u00a0B, the habitable zone would lie closer at about 0.7\u00a0AU (100\u00a0million\u00a0km), approximately the distance that Venus is from the Sun.[115][117]\n\nWith the goal of finding evidence of such planets, both Proxima Centauri and Alpha Centauri\u00a0AB were among the listed \"Tier\u00a01\" target stars for NASA's Space Interferometry Mission (SIM). Detecting planets as small as three Earth-masses or smaller within two astronomical units of a \"Tier\u00a01\" target would have been possible with this new instrument.[118] The SIM mission, however, was cancelled due to financial issues in 2010.[119]\n\nView from this system\n\nLooking towards the sky around Orion from Alpha Centauri with Sirius near Betelgeuse, Procyon in Gemini, and the Sun between Perseus and Cassiopeia generated by Celestia\n\nViewed from near the Alpha Centauri system, the sky would appear very much as it does for an observer on Earth, except that Centaurus would be missing its brightest star. The Sun would be a yellow star of an apparent visual magnitude of +0.5 in eastern Cassiopeia, at the antipodal point of Alpha Centauri's current right ascension and declination, at 02h\u00a039m\u00a035s +60\u00b0\u00a050\u2032 (2000). This place is close to the 3.4-magnitude star \u03b5 Cassiopeiae. Because of the placement of the Sun, an interstellar or alien observer would find the \\\/\\\/ of Cassiopeia had become a \/\\\/\\\/ shape[note 1] nearly in front of the Heart Nebula in Cassiopeia. Sirius lies less than a degree from Betelgeuse in the otherwise unmodified Orion and with a magnitude of \u22121.2 is a little fainter than from Earth but still the brightest star in the Alpha Centauri sky. Procyon is also displaced into the middle of Gemini, outshining Pollux, whereas both Vega and Altair are shifted northwestward relative to Deneb (which barely moves, due to its great distance), giving the Summer Triangle a more equilateral appearance.\n\nView from Proxima Centauri b\n\nFrom Proxima Centauri b, Alpha Centauri AB would appear like two close bright stars with the combined apparent magnitude of \u22126.8. Depending on the binary's orbital position, the bright stars would appear noticeably divisible to the naked eye, or occasionally, but briefly, as a single unresolved star. Based on the calculated absolute magnitudes, the visual apparent magnitudes of Alpha Centauri A and B would be \u22126.5 and \u22125.2, respectively.[120]\n\nView from a hypothetical A or B planet\n\nArtist's rendition of the view from a hypothetical airless planet orbiting Alpha Centauri A\n\nAn observer on a hypothetical planet orbiting around either Alpha Centauri\u00a0A or Alpha Centauri\u00a0B would see the other star of the binary system as an intensely bright object in the night sky, showing a small but discernible disk while near periapse: A up to 210 arc seconds, B up to 155 arc seconds. Near apoapse, the disc would shrink to 60 arc seconds for A, 43 arc seconds for B, being too small to resolve by naked eye. In any case, the dazzling surface brightness could make the discs harder to resolve than a similarly sized less bright object.\n\nFor example, some theoretical planet orbiting about 1.25 AU from Alpha Centauri\u00a0A (so that the star appears roughly as bright as the Sun viewed from the Earth) would see Alpha Centauri\u00a0B orbit the entire sky once roughly every one year and three months (or 1.3(4) a), the planet's own orbital period. Added to this would be the changing apparent position of Alpha Centauri\u00a0B during its long eighty-year elliptical orbit with respect to Alpha Centauri\u00a0A (The average speed, at 4,5 degrees per Earth year, is comparable in speed to Uranus here. With the eccentricity of the orbit, the maximum speed near periapse, about 18 degrees per Earth year, is faster than Saturn, but slower than Jupiter. The minimum speed near apoapse, about 1,8 degrees per Earth year, is slower than Neptune.). Depending on its and planet's position on their respective orbits, Alpha Centauri B would vary in apparent magnitude between \u221218.2 (dimmest) and \u221221.0 (brightest). These visual apparent magnitudes are much dimmer than the apparent magnitude of the Sun as viewed from the Earth (\u221226.7). The difference of 5.7 to 8.6 magnitudes means Alpha Centauri\u00a0B would appear, on a linear scale, 2500 to 190 times dimmer than Alpha Centauri\u00a0A (or the Sun viewed from the Earth), but also 190 to 2500 times brighter than the full Moon as seen from the Earth (\u221212.5).\n\nAlso, if another similar planet orbited at 0.71\u00a0AU from Alpha Centauri\u00a0B (so that in turn Alpha Centauri B appeared as bright as the Sun seen from the Earth), this hypothetical planet would receive slightly more light from the more luminous Alpha Centauri\u00a0A, which would shine 4.7 to 7.3 magnitudes dimmer than Alpha Centauri\u00a0B (or the Sun seen from the Earth), ranging in apparent magnitude between \u221219.4 (dimmest) and \u221222.1 (brightest). Thus Alpha Centauri\u00a0A would appear between 830 and 70 times dimmer than the Sun but some 580 to 6900 times brighter than the full Moon. During such planet's orbital period of 0.6(3) a, an observer on the planet would see this intensely bright companion star circle the sky just as humans see with the Solar System's planets. Furthermore, Alpha Centauri\u00a0A's sidereal period of approximately eighty years means that this star would move through the local ecliptic as slowly as Uranus with its eighty-four year period, but as the orbit of Alpha Centauri\u00a0A is more elliptical, its apparent magnitude will be far more variable. Although intensely bright to the eye, the overall illumination would not significantly affect climate nor influence normal plant photosynthesis.[115]\n\nAn observer on the hypothetical planet would notice a change in orientation to very-long-baseline interferometry reference points commensurate with the binary orbit periodicity plus or minus any local effects such as precession or nutation.\n\nAssuming this hypothetical planet had a low orbital inclination with respect to the mutual orbit of Alpha Centauri\u00a0A and B, then the secondary star would start beside the primary at \"stellar\" conjunction. Half the period later, at \"stellar\" opposition, both stars would be opposite each other in the sky. As a net result, both the local sun and the other star would each be in sky for half a day, like sun and moon are both above horizon for half a day. But during stellar conjunction, the other star being \"new\" would be in sky in daytime, while during the opposition, the other star being \"full\" would be in sky for the whole night. In an Earth-like atmosphere, the light of the other star would be appreciably scattered, causing the sky to be perceptibly blue though darker than in daytime, like during twilight or total solar eclipse. Humans could easily walk around and clearly see the surrounding terrain, and reading a book would be quite possible without any artificial light.[115] Over the following half period, the secondary star would be in sky for a progressively decreasing part of night (and increasing part of day) until at the next conjunction the secondary star would only be in sky in daytime near the primary star.\n\nFrom a planet orbiting Alpha Centauri A or B, Proxima Centauri would appear as a fourth to fifth magnitude star, as bright as the faint stars of the Little Dipper. [121] [122]\n\nOther names\n\nDistances of the nearest stars from 20,000 years ago until 80,000 years in the future\n\nIn modern literature, Rigil Kent[123] (also Rigel Kent and variants;[note 2] \/\u02c8r\u0259l \u02c8k\u025bnt\/)[19][124] and Toliman,[125] were cited as colloquial alternative names of Alpha Centauri.\n\nRigil Kent is short for Rigil Kentaurus,[126] which is sometimes further abbreviated to Rigil or Rigel, though that is ambiguous with Beta Orionis, which is also called Rigel. Although the short form Rigel Kent is often cited as an alternative name, the star system is most widely referred to by its Bayer designation Alpha Centauri.\n\nThe name Toliman originates with Jacobus Golius' edition of Al-Farghani's Compendium (published posthumously in 1669). Tolim\u00e2n is Golius' latinization of the Arabic name \u0627\u0644\u0638\u0644\u0645\u0627\u0646 al-\u1e92ulm\u0101n \"the ostriches\", the name of an asterism of which Alpha Centauri formed the main star.[127]\n\nDuring the 19th century, the northern amateur popularist Elijah H. Burritt used the now-obscure name Bungula,[128] possibly coined from \"\u03b2\" and the Latin ungula (\"hoof\").[19]\n\nTogether, Alpha and Beta Centauri form the \"Southern Pointers\" or \"The Pointers\", as they point towards the Southern Cross, the asterism of the constellation of Crux.[38]\n\nIn Standard Mandarin Chinese, \u5357\u9580 N\u00e1n M\u00e9n, meaning Southern Gate, refers to an asterism consisting of \u03b1 Centauri and \u03b5 Centauri. Consequently, \u03b1 Centauri itself is known as \u5357\u9580\u4e8c N\u00e1n M\u00e9n \u00c8r, the Second Star of the Southern Gate.[129]\n\nTo the Australian aboriginal Boorong people of northwestern Victoria, Alpha and Beta Centauri are Bermbermgle,[130] two brothers noted for their courage and destructiveness, who speared and killed Tchingal \"The Emu\" (the Coalsack Nebula).[131] The form in Wotjobaluk is Bram-bram-bult.[130]\n\nExploration\n\nThe Very Large Telescope and star system Alpha Centauri.[132]\n\nAlpha Centauri is envisioned as a likely first target for manned or unmanned interstellar exploration. Crossing the huge distance between the Sun and Alpha Centauri using current spacecraft technologies would take several millennia, though the possibility of nuclear pulse propulsion or laser light sail technology, as considered in the Breakthrough Starshot program, could reduce the journey time to a matter of decades.[133][134][135]\n\nBreakthrough Starshot is a proof-of-concept initiative to send a fleet of ultra-fast light-driven nanocraft to explore the Alpha Centauri system, which could pave the way for a first launch within the next generation. An objective of the mission would be to make a fly-by of, and possibly photograph, any planets that might exist in the system.[136][137] Proxima Centauri b, announced by the European Southern Observatory (ESO) in August 2016, would be a target for the Starshot program.[136][138]\n\nIn January 2017, Breakthrough Initiatives and the ESO entered a collaboration to enable and implement a search for habitable planets in the Alpha Centauri system.The agreement involves Breakthrough Initiatives providing funding for an upgrade to the VISIR (VLT Imager and Spectrometer for mid-Infrared) instrument on ESO's Very Large Telescope (VLT) in Chile. This upgrade will greatly increase the likelihood of planet detection in the system.[132][139]\n\nDistance\n\nAlpha Centauri AB distance estimates\nSource Parallax, mas Distance, pc Distance, ly Distance, Pm Ref.\nHenderson (1839) 1160\u00b1110 0.86+0.09\n\u22120.07\n2.81+0.29\n\u22120.24\n26.6+2.8\n\u22122.3\n[83]\nHenderson (1842) 912.8\u00b164 1.10+0.08\n\u22120.07\n3.57+0.27\n\u22120.23\n33.8+2.5\n\u22122.2\n[140]\nMaclear (1851) 918.7\u00b134 1.09\u00b10.04 3.55+0.14\n\u22120.13\n33.6+1.3\n\u22121.2\n[141]\nMoesta (1868) 880\u00b168 1.14+0.10\n\u22120.08\n3.71+0.31\n\u22120.27\n35.1+2.9\n\u22122.5\n[142]\nGill & Elkin (1885) 750\u00b110 1.333\u00b10.018 4.35\u00b10.06 41.1+0.6\n\u22120.5\n[143]\nRoberts (1895) 710\u00b150 1.41+0.11\n\u22120.09\n4.59+0.35\n\u22120.30\n43.5+3.3\n\u22122.9\n[144]\nWoolley et al. (1970) 743\u00b17 1.346\u00b10.013 4.39\u00b10.04 41.5\u00b10.4 [145]\nGliese & Jahrei\u00df (1991) 749.0\u00b14.7 1.335\u00b10.008 4.355\u00b10.027 41.20\u00b10.26 [146]\nvan Altena et al. (1995) 749.9\u00b15.4 1.334\u00b10.010 4.349+0.032\n\u22120.031\n41.15+0.30\n\u22120.29\n[147]\nPerryman et al. (1997) (A and B) 742.12\u00b11.40 1.3475\u00b10.0025 4.395\u00b10.008 41.58\u00b10.08 [148]\nS\u00f6derhjelm (1999) 747.1\u00b11.2 1.3385+0.0022\n\u22120.0021\n4.366\u00b10.007 41.30\u00b10.07 [152]\nvan Leeuwen (2007) (A) 754.81\u00b14.11 1.325\u00b10.007 4.321+0.024\n\u22120.023\n40.88\u00b10.22 [153]\nvan Leeuwen (2007) (B) 796.92\u00b125.90 1.25\u00b10.04 4.09+0.14\n\u22120.13\n38.7+1.3\n\u22121.2\n[154]\nRECONS TOP100 (2012) 747.23\u00b11.17[note 3] 1.3383\u00b10.0021 4.365\u00b10.007 41.29\u00b10.06 [65]\n\nNotes\n\n1. ^ The coordinates of the Sun would be diametrically opposite Alpha Centauri AB, at \u03b1=02h\u00a039m\u00a036.4951s, \u03b4=+60\u00b0\u00a050\u2032\u00a002.308\u2033\n2. ^ Spellings include Rigjl Kentaurus, Hyde T., \"Ulugh Beighi Tabulae Stellarum Fixarum\", Tabulae Long. ac Lat. Stellarum Fixarum ex Observatione Ulugh Beighi, Oxford, 1665, p. 142., Hyde T., \"In Ulugh Beighi Tabulae Stellarum Fixarum Commentarii\", op. cit., p. 67., Portuguese Riguel Kentaurus da Silva Oliveira, R., \"Crux Australis: o Cruzeiro do Sul\", Artigos: Planetario Movel Inflavel AsterDomus.\n3. ^ Weighted parallax based on parallaxes from van Altena et al. (1995) and S\u00f6derhjelm (1999).\n\nReferences\n\n1. Van Leeuwen, F. (2007). \"Validation of the new Hipparcos reduction\". Astronomy and Astrophysics. 474 (2): 653. arXiv:. Bibcode:2007A&A...474..653V. doi:10.1051\/0004-6361:20078357.\n2. Ducati, J. R. (2002). \"VizieR Online Data Catalog: Catalogue of Stellar Photometry in Johnson's 11-color system\". CDS\/ADC Collection of Electronic Catalogues. 2237: 0. Bibcode:2002yCat.2237....0D.\n3. ^ a b Torres, C. A. O.; Quast, G. R.; da Silva, L .; de la Reza, R.; Melo, C. H. F.; Sterzik, M. (2006). \"Search for associations containing young stars (SACY)\". 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\section{Introduction}
Over the years, drug discovery has predominantly transformed from crude and serendipitous characteristics to a well-structured and rational scientific paradigm. The paradox, however, is that the growth experienced in the domain has not made the identification of drugs any easier as attested to by the high attrition rates and huge budgets typically involved in the process\cite{DiMasi2003}. Traditionally, \emph{in vitro} screening experiments are conducted in order to identify new interactions. However, considering that there are about $10^{60}$ synthetically feasible compounds, \emph{in silico} or virtual screening alternatives are mostly used for this process \cite{Polishchuk2013}.
The two main \emph{in silico} approaches to Drug-Target Interaction (DTI) prediction are docking simulations and machine learning approaches. Docking simulations utilize compound and target conformations to discover binding sites whereas machine learning methods are based on using features of compounds and/or targets, or their similarities.
A central aspect in applying these computational models is the featurization of compounds and biological targets into numerical vectors. This is achieved using molecular descriptors which encode properties such as bonds, valence structures, sequence information, and other related properties \cite{Rifaioglu2018}. Digitally, 2D structures of compounds are represented using line notations such the Simplified Molecular Input Line Entry System (SMILES) \cite{Weininger1988} whereas targets are represented using sequences, and/or their conformations when available. These digital forms are then used by toolkits (e.g. RDKit \cite{Landrum2006}) to derive the molecular descriptors.
However, there exist several different kinds of molecular descriptors in the literature with Extended Connectivity Fingerprints (ECFP) being one of the widely used descriptors. Considering that for a given compound, different descriptors produce different properties which affect model performance, this makes the choice a featurization method in model development a significant one \cite{CERETOMASSAGUE201558,Kogej2006}.
In certain cases, the performance of certain descriptors tend to be task related \cite{DUAN2010157,Rifaioglu2018}. To this end, it is usual in the domain to find different descriptors being combined as input to a model, an approach referred to as Joint Multi-Modal Learning~\cite{Baltrusaitis2019}. Nonetheless, the unimodal features that are used in constructing the joint representations tend to be constructed from pre-determined descriptors.
In this study, we propose an integrated view predictive architecture that is trained adversarially~\cite{Lotter2015} for predicting compound-target binding affinities. The motivation is that, these descriptors tend to complement one another in many cases and that the different modalities could provide an in-depth perspective about a sample~\cite{Rifaioglu2018}. Additionally, the enormity of the chemical space connotes that task-specific representation of compounds is a desideratum of DTI prediction research~\cite{Wu2018}. Therefore, our departure from constructing joint representations exclusively with predefined descriptors to leveraging differential feature learning and such predefined descriptors dovetails into the concept of tailoring DTI tasks to their input space.
The subsequent sections are organized as follows: section \ref{sec:relwrk} highlights related work of our study, section \ref{sec:model} discusses our proposed model, section \ref{sec:exp} presents the experiments design of our study. We also discuss the results of our experiments in section~\ref{sec:res_discu} and draw our conclusions in section~\ref{sec:conc}.
\section{Related Work}\label{sec:relwrk}
The concept of utilizing multiple unimodal descriptors toward predicting bioactivity has been well studied in the literature. Since different descriptors tend to represent different properties of compounds~\cite{CERETOMASSAGUE201558}, integrating these descriptors has been considered in several studies. In \cite{Sawada2014}, 18 different chemical descriptors are benchmarked on DTI prediction tasks and their findings reveal that integrating multiple descriptors typically improves model performance. The works of Soufan et al~\cite{Soufan2016,Soufan2015} also corroborate this observation.
Hence, the combination enables the participating descriptors to create informative feature vectors.
While these studies espouse integrating multiple chemical descriptors, existing studies have mostly employed predefined feature sets, such as structure-based fingerprints and pharmacophore descriptors proposed by experts in the domain, on DTI prediction problems. Recent studies have also proposed end-to-end compound descriptor learning functions toward ensuring a closer relationship between the learning objective and the input space ~\cite{Wu2018, Gomes2017,Kearnes2016}. Although several studies have approached DTI prediction as a binary classification problem~\cite{Lee2019}, the nature of bioactivity is deemed to be continuous~\cite{Pahikkala2015a}. In \cite{Feng2018}, a DL model using ECFP (with diameter 4) is compared to a Molecular Graph Convolution (GraphConv) model on predicting binding affinities. In both cases, target information, in the form of Protein Sequence Composition (PSC), is combined with the descriptor of a compound for predicting the binding strengths. The work in~\cite{Feng2018} also shows that using DL methods for predicting bioactivity generally leads to better performance than kernel- and gradient boosting machines-based methods~\cite{Pahikkala2015a,He2017}.
We propose a predictive generative adversarial network~\cite{Lotter2015} architecture, for leveraging the complementary relationship between the seemingly disparate featurization methods in the domain. We show that our approach generally improves the findings in~\cite{Feng2018}.
\section{Model}\label{sec:model}
\subsection{Problem Formulation}
We consider the problem of predicting a real-valued binding affinity $y_i$ between a given compound $c_i$ and target $p_i$, $i\in\mathbb{R}$. The compound $c_i$ is represented as a SMILES~\cite{Weininger1988} string whereas the target $p_i$ is represented as an amino acid sequence. The target feature vector is constructed using Protein Sequence Composition (PSC), which comprises of the Amino Acid Composition (AAC), Dipeptide Composition (DC), and Tripeptide Composition (TC), using ProPy~\cite{Cao2013}. The SMILES string of $c_i$ is an encoding of a chemical graph structure $d_i=\{V_i,E_i\}$, where $V_i$ is the set of atoms constituting $c_i$ and $E_i$ is a set of undirected chemical bonds between these atoms. While predefined fingerprints are computed by directly examining $d_i$, descriptor learning functions like GraphConv~\cite{Altae-Tran2017} take as input $d_i$ and learn the numerical representation of $c_i$ using backpropagation.
\subsection{Proposed Architecture}
The proposed Integrated Views Predictive Generative Adverserial Network (IVPGAN) for DTI, is shown in figure~\ref{fig:integrated}. Given a predefined descriptor vector $v_i^c$ of $c_i$, chemical graph structure $d_i$, and the PSC vector $v_i^p$ of $p_i$, we optimize the following mean squared error (MSE) loss,
\begin{equation}
\operatorname*{argmin}_{\theta^f,\theta^g} \sum_{i=0}^N (y_i - f([v_i^c,g(d_i;\theta^g),v_i^p];\theta^f))^2
\label{eq:mse}
\end{equation}
where $\theta^f$ and $\theta^g$ are trainable parameters.
Thus, we form a joint representation of the query entities $c_i$ and $p_i$ by concatenating the predefined molecular descriptor, the outputs of the parameterized descriptor learning function $g(\cdot;\theta^g)$, and the PSC feature vector of $p_i$ We refer to this joint representation as the Combined Input Vector (CIV). Since equation~\ref{eq:mse} is able to estimate the bias and variance of an estimator, this makes it a good fit for real-valued models.
However, the squared loss is sensitive to the overall departure of the samples and tends to represent the output distribution by placing masses in parts of the space with low densities. In computer vision problems, this results in a blurring effect. Therefore, we follow Lotter et. al~\cite{Lotter2015} to train our DTI prediction model adversarially by applying Adversarial Loss (AL). Specifically, we view the model accepting CIV input as \emph{generating} a binding strength between a given pair, as against a vanilla prediction model. This perspective enables us to leverage techniques in Generative Adverserial Networks (GANS)~\cite{Goodfellow14generativeadversarial} to mitigate the aforementioned problem of equation~\ref{eq:mse}. Also, models trained adverserially are able to learn the structured patterns in a distribution~\cite{Lotter2015}.
To this end, given a set of generated binding strengths $\mathbf{\hat{y}}=\{\hat{y}_1,\hat{y}_2,...,\hat{y}_N\}$ produced by a generator $G$ and their corresponding ground truths $\mathbf{y}=\{y_1,y_2,...,y_N\}$, we construct two neighborhood alignment datasets for the adversarial training phase.
Let $Y=\{\mathbf{\hat{y}},\mathbf{y}\}$ be the set of predicted and label vectors. We construct the data matrix $M^{(l)}$ from $Y^{(l)}$, $0<l\leq 2$, as:
\begin{equation}
M^{(l)}_{m,k} =
\begin{pmatrix}
a_{1,1} & a_{1,2} & \cdots & a_{1,k} \\
a_{2,1} & a_{2,2} & \cdots & a_{2,k} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m,1} & a_{m,2} & \cdots & a_{m,k}
\end{pmatrix}
\end{equation}
where $M^{(l)}_{i,:k}=\left[|Y^{(l)}_i-Y^{(l)}_1|, |Y^{(l)}_i-Y^{(l)}_2|, \cdots, |Y^{(l)}_i-Y^{(l)}_N|\right]_{:k}$ such that $a_{i,j}\leq a_{i,j+1}$, where $k\leq N$ and $[\cdots]_{:k}$ denotes array slicing up to the $k$th element. Intuitively, each row is a vector whose elements are the magnitudes of the differences a specific datapoint has with its closest-$k$ neighbors in its corresponding distribution.
This information serves as the feature vectors of the datapoints for adversarial training. The learning objective then is: $f(\cdot;\theta^f)$ is to generate binding strengths that are closer to their ground truths and also have a similar neighborhood structure as the labels distribution. The resulting composite objective for the minimization operation then takes the form:
\begin{equation}
L_G = L_G^{MSE} + \lambda L_G^{AL}
\end{equation}
where the adversarial training elements for minimization are:
\begin{align}
\label{eq:d_loss}
L_D^{AL} &= \mathbb{E}_{\mathbf{x}\sim p} \left[-log D(\mathbf{x}) \right] + \mathbb{E}_{\mathbf{x}\sim G}\left[-log(1-D(\mathbf{x}))\right] \\
\label{eq:g_loss}
L_G^{AL} &= \mathbb{E}_{\mathbf{x}\sim G} \left[-log D(\mathbf{x})\right]
\end{align}
The distributions $p$ and $G$ of equations~\ref{eq:d_loss}-\ref{eq:g_loss} are represented by the matrices constructed from the labels and predicted values, respectively. $\lambda$ is a hyperparameter that is used to control the combination of MSE and AL losses of the generator.
In what follows, we demonstrate how this composite loss, together with the integration of the predefined descriptors and end-to-end descriptor learning, improves the model (generator) skill at predicting the binding strengths between a given compound-target pair.
\begin{figure*}
\centering
\fbox{\includegraphics[width=.75\linewidth]{integrated_gan.eps}}
\caption{An integrated architecture of different views for DTI prediction using a Predictive GAN approach.}
\label{fig:integrated}
\end{figure*}
\section{Experiments Protocol}\label{sec:exp}
In this section, we present the design of our experiments and baselines. We also provide our source code and ancillary files at \url{https://github.com/bbrighttaer/ivpgan}.
\subsection{Datasets and Implementations}\label{sec:data_impl}
The benchmark datasets used are the Metz \cite{Metz2011}, KIBA \cite{Tang2014}, and Davis \cite{Davis2011} datasets as provided by the work in \cite{Feng2018}. In their work, they applied a filter threshold to each dataset for which compounds and targets with total number of samples not above the threshold are removed.
The summary of these datasets are presented in table~\ref{tab:datasets}.
\begin{table}[]
\caption{Dataset sizes}
\label{tab:datasets}
\centering
\begin{tabular}{|l|l|l|l|l|}
\hline
\textbf{Dataset} & \textbf{\begin{tabular}[c]{@{}l@{}}Number of \\ compounds\\/drugs\end{tabular}} & \textbf{\begin{tabular}[c]{@{}l@{}}Number \\ of targets\end{tabular}} & \textbf{\begin{tabular}[c]{@{}l@{}}Total number\\ of pair samples\end{tabular}} & \textbf{\begin{tabular}[c]{@{}l@{}}Filter \\ threshold \\ used\end{tabular}} \\ \hline
Davis & 72 & 442 & 31824 & 6 \\ \hline
Metz & 1423 & 170 & 35259 & 1 \\ \hline
KIBA & 3807 & 408 & 160296 & 6 \\ \hline
\end{tabular}
\end{table}
In our experiments, the ECFP8~\cite{Rogers2010} and Molecular Graph Convolution (GraphConv)~\cite{Altae-Tran2017} serve as representatives of predefined molecular descriptors and differentiable molecular descriptors, respectively.
We used the data loading and metrics procedures provided by~\cite{Feng2018} (with modifications where necessary) and implemented all models using the Pytorch framework. All our experiments were spread over the servers described in table~\ref{tab:hdw_specs}.
\begin{table}[]
\caption{Simulation hardware specifications}
\label{tab:hdw_specs}
\begin{tabular}{|l|l|l|l|l|}
\hline
\multicolumn{1}{|c|}{\textbf{Model}} & \multicolumn{1}{c|}{\textbf{\# Cores}} & \multicolumn{1}{c|}{\textbf{\begin{tabular}[c]{@{}c@{}}RAM \\ (GB)\end{tabular}}} & \multicolumn{1}{c|}{\textbf{\begin{tabular}[c]{@{}c@{}}Avail. \\ GPUs\end{tabular}}} & \multicolumn{1}{c|}{\textbf{\begin{tabular}[c]{@{}c@{}}\# GPUs \\ used\end{tabular}}} \\ \hline
\begin{tabular}[c]{@{}l@{}}Intel Xeon \\ CPU E5-2687W\end{tabular} & 48 & 128 & \begin{tabular}[c]{@{}l@{}}1 GeForce\\ GTX 1080\end{tabular} & 1 \\ \hline
\begin{tabular}[c]{@{}l@{}}Intel Xeon \\ CPU E5-2687W\end{tabular} & 24 & 128 & \begin{tabular}[c]{@{}l@{}}4 GeForce \\ GTX 1080Ti\end{tabular} & 2 \\ \hline
\end{tabular}
\end{table}
\subsection{Baselines}
We compare our proposal to the parametric models proposed in~\cite{Feng2018}.
In our implementation of the ECFP-PSC architecture, we used the ECFP8 variant, other than the ECFP4 used in~\cite{Feng2018} and in several previous studies. In our preliminary experiments of comparing ECPF4-PSC and ECFP8-PSC architectures, ECFP8 variant mostly outperformed the ECFP4 model. This finding corroborates the view in~\cite{Rogers2010} that while fewer iterations could lead to good performances in similarity and clustering tasks, activity prediction models tend to perform better with greater structure details.
\subsection{Model Training and Evaluation}\label{sec:train_eval}
In our experiments, we used a 5-fold double Cross Validation (CV) model training approach in which three main splitting schemes were used:
\begin{itemize}
\item \textbf{Warm split}: Every drug or target in the validation set is encountered in the training set.
\item \textbf{Cold-drug split}: Compounds in the validation set are absent from the training set.
\item \textbf{Cold-target split}: Targets in the validation set are absent from the training set.
\end{itemize}
Since \emph{cold-start} predictions are typically found in DTI use cases, the cold splits offer an interesting and more challenging validation schemes for the trained models.
As regards evaluation metrics, we measure the Root Mean Squared Error (RMSE) and Pearson correlation coefficient ($ R^2 $) on the validation sets in each CV-fold. Additionally, we measure the Concordance Index (CI) on the validation set as proposed by \cite{Pahikkala2015a}.
We follow the averaging CV approach where the reported metrics are the averages across the different folds. We also repeat the CV evaluation for different random seeds to minimize randomness. Consequently, all statistics are also averaged across such seeds. Hyperparameters were searched for on the warm split of the davis dataset using the Bayesian optimization API of scikit-optimize.
\section{Results and Discussion}\label{sec:res_discu}
In tables~\ref{tab:rmse_results}-\ref{tab:r2_results}, we present the RMSE, CI, and R2 values as measured on the best trained models on each of the benchmark datasets, respectively. The standard deviation is placed beneath the mean value of each case.
Firstly, model complexity and data sizes were influential in model performances. While the IVPGAN and GraphConv-PSC models took longer training times due to the large number of parameters, ECFP8-PSC took much less time to train. The simplicity of ECFP8-PSC also ensured less overfitting with adequate regularization in the face of fewer samples in a number of cases.
Notwithstanding the foregoing observation, IVPGAN mostly achieved the best results than the baseline models, with the GraphConv-PSC being outperformed by the ECFP8-PSC model. Also, just as there exists a general trend of increasing difficulty of prediction from warm split to cold target split in~\cite{Feng2018}, our implementations experienced this behavior as well albeit, with significant improvements in many cases.
Furthermore, there exist a similar trend across tables~\ref{tab:rmse_results}-\ref{tab:r2_results}. Feng et. al~\cite{Feng2018} observed that, for datasets where there are more samples of compounds than targets, cold drug split performances had the tendency to perform better than cold target splits with the reverse being true. However, in our experiments, we observed that such a relationship may be tenuous, at best, and that model skill seem to depend more on model capacity and hyperparameters used for training. In the case of warm splits results, our experiments align with the observation in~\cite{Feng2018} that they are always better than both cold drug and cold target split performances due to the variation in sample sizes. Indeed, it can be observed that cold target split proved to be the most challenging splitting scheme for all models in our experiments.
Additionally, on the KIBA dataset, although the number of compounds significantly outweighs that of targets, the difference in cold target and cold drug performances, as measured on IVPGAN, is not as pronounced as seen in the baseline models. Thus, with IVPGAN, diversity in compound features seem more necessary for richer representation of compound-target samples.
While IVPGAN mostly outperformed the baseline models, and especially so in the cold split schemes, it was mostly outperformed on the Metz dataset. Aside a possible overfitting due to sample size (also for GraphConv), the hyperparameters used may be less suited for the Metz dataset and its CV split schemes.
\begin{table}[]
\caption{Performance of regression on benchmark datasets measured in RMSE.}
\label{tab:rmse_results}
\begin{tabular}{|l|l|l|l|l|}
\hline
\multicolumn{5}{|c|}{\textbf{RMSE}} \\ \hline
\textbf{Datatset} & \textbf{CV split type} & \textbf{ECFP8} & \textbf{GraphConv} & \textbf{IVPGAN} \\ \hline
\multirow{3}{*}{Davis} & Warm & \begin{tabular}[c]{@{}l@{}}0.2216 \\ $\pm 0.082$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.3537 \\ $\pm 0.053$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.2014} \\ $\pm 0.043$\end{tabular} \\ \cline{2-5}
& Cold drug & \begin{tabular}[c]{@{}l@{}}0.3978 \\ $\pm 0.105$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.4751 \\ $\pm 0.123$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.2895} \\ $\pm 0.163$\end{tabular} \\ \cline{2-5}
& Cold target & \begin{tabular}[c]{@{}l@{}}0.5517 \\ $\pm 0.088$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5752 \\ $\pm 0.101$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.2202} \\ $\pm 0.139$\end{tabular} \\ \hline
\multirow{3}{*}{Metz} & Warm & \begin{tabular}[c]{@{}l@{}}\textbf{0.3321} \\ $\pm 0.057$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5537 \\ $\pm 0.033$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5529 \\ $\pm 0.033$\end{tabular} \\ \cline{2-5}
& Cold drug & \begin{tabular}[c]{@{}l@{}}\textbf{0.3778} \\ $\pm 0.097$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5711 \\ $\pm 0.057$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5477 \\ $\pm 0.064$\end{tabular} \\ \cline{2-5}
& Cold target & \begin{tabular}[c]{@{}l@{}}0.6998 \\ $\pm 0.065$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.7398 \\ $\pm 0.047$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.5745} \\ $\pm 0.054$\end{tabular} \\ \hline
\multirow{3}{*}{KIBA} & Warm & \begin{tabular}[c]{@{}l@{}}0.4350 \\ $\pm 0.086$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5604 \\ $\pm 0.120$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.4003} \\ $\pm 0.082$\end{tabular} \\ \cline{2-5}
& Cold drug & \begin{tabular}[c]{@{}l@{}}\textbf{0.4502} \\ $\pm 0.128$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.552 \\ $\pm 0.156$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.4690 \\ $\pm 0.132$\end{tabular} \\ \cline{2-5}
& Cold target & \begin{tabular}[c]{@{}l@{}}0.6645 \\ $\pm 0.137$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.7555 \\ $\pm 0.153$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.4486} \\ $\pm 0.106$\end{tabular} \\ \hline
\end{tabular}
\end{table}
\begin{table}[]
\caption{Performance of regression on benchmark datasets measured in CI}
\label{tab:ci_results}
\begin{tabular}{|l|l|l|l|l|}
\hline
\multicolumn{5}{|c|}{\textbf{Concordance Index}} \\ \hline
\textbf{Dataset} & \textbf{CV split type} & \textbf{ECFP8} & \textbf{GraphConv} & \textbf{IVPGAN} \\ \hline
\multirow{3}{*}{Davis} & Warm & \begin{tabular}[c]{@{}l@{}}0.9647 \\ $\pm 0.020$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.9335 \\ $\pm 0.011$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.9729} \\ $\pm 0.008$\end{tabular} \\ \cline{2-5}
& Cold drug & \begin{tabular}[c]{@{}l@{}}0.9099\\ $\pm 0.049$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.8784 \\ $\pm 0.052$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.9493} \\ $\pm 0.044$\end{tabular} \\ \cline{2-5}
& Cold target & \begin{tabular}[c]{@{}l@{}}0.8683 \\ $\pm 0.033$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.8480 \\ $\pm 0.038$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.9631} \\ $\pm 0.036$\end{tabular} \\ \hline
\multirow{3}{*}{Metz} & Warm & \begin{tabular}[c]{@{}l@{}}\textbf{0.8923} \\ $\pm 0.025$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.7968 \\ $\pm 0.027$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.7913 \\ $\pm 0.029$\end{tabular} \\ \cline{2-5}
& Cold drug & \begin{tabular}[c]{@{}l@{}}\textbf{0.8730}\\ $\pm 0.044$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.7850 \\ $\pm 0.040$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.7894 \\ $\pm 0.042$\end{tabular} \\ \cline{2-5}
& Cold target & \begin{tabular}[c]{@{}l@{}}0.7304 \\ $\pm 0.039$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.7084 \\ $\pm 0.041$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.7776} \\ $\pm 0.038$\end{tabular} \\ \hline
\multirow{3}{*}{KIBA} & Warm & \begin{tabular}[c]{@{}l@{}}0.8322\\ $\pm 0.024$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.7873 \\ $\pm 0.029$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.8433} \\ $\pm 0.023$\end{tabular} \\ \cline{2-5}
& Cold drug & \begin{tabular}[c]{@{}l@{}}\textbf{0.8132} \\ $\pm 0.047$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.7736 \\ $\pm 0.048$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.8070 \\ $\pm 0.051$\end{tabular} \\ \cline{2-5}
& Cold target & \begin{tabular}[c]{@{}l@{}}0.7185\\ $\pm 0.044$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.6661 \\ $\pm 0.052$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.8234} \\ $\pm 0.044$\end{tabular} \\ \hline
\end{tabular}
\end{table}
\begin{table}[]
\caption{Performance of regression on benchmark datasets measured in $R^2$.}
\label{tab:r2_results}
\begin{tabular}{|l|l|l|l|l|}
\hline
\multicolumn{5}{|c|}{\textbf{R2}} \\ \hline
\textbf{Dataset} & \textbf{CV split type} & \textbf{ECFP8} & \textbf{GraphConv} & \textbf{IVPGAN} \\ \hline
\multirow{3}{*}{Davis} & Warm & \begin{tabular}[c]{@{}l@{}}0.9252 \\ $\pm 0.061$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.8254 \\ $\pm 0.039$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.9449} \\ $\pm 0.021$\end{tabular} \\ \cline{2-5}
& Cold drug & \begin{tabular}[c]{@{}l@{}}0.7573 \\ $\pm 0.171$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.6773 \\ $\pm 0.159$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.8635} \\ $\pm 0.151$\end{tabular} \\ \cline{2-5}
& Cold target & \begin{tabular}[c]{@{}l@{}}0.5916 \\ $\pm 0.120$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5423 \\ $\pm 0.121$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.9059} \\ $\pm 0.121$\end{tabular} \\ \hline
\multirow{3}{*}{Metz} & Warm & \begin{tabular}[c]{@{}l@{}}\textbf{0.8637} \\ $\pm 0.057$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.6279 \\ $\pm 0.075$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.6285 \\ $\pm 0.078$\end{tabular} \\ \cline{2-5}
& Cold drug & \begin{tabular}[c]{@{}l@{}}\textbf{0.8124} \\ $\pm 0.117$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5860 \\ $\pm 0.120$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.6166 \\ $\pm 0.120$\end{tabular} \\ \cline{2-5}
& Cold target & \begin{tabular}[c]{@{}l@{}}0.4259 \\ $\pm 0.121$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.3619 \\ $\pm 0.112$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.5931} \\ $\pm 0.106$\end{tabular} \\ \hline
\multirow{3}{*}{KIBA} & Warm & \begin{tabular}[c]{@{}l@{}}0.7212 \\ $\pm 0.072$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5513 \\ $\pm 0.097$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.7658} \\ $\pm 0.065$\end{tabular} \\ \cline{2-5}
& Cold drug & \begin{tabular}[c]{@{}l@{}}\textbf{0.6677} \\ $\pm 0.137$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.5026 \\ $\pm 0.152$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.6475 \\ $\pm 0.142$\end{tabular} \\ \cline{2-5}
& Cold target & \begin{tabular}[c]{@{}l@{}}0.3648 \\ $\pm 0.128$\end{tabular} & \begin{tabular}[c]{@{}l@{}}0.1910 \\ $\pm 0.088$\end{tabular} & \begin{tabular}[c]{@{}l@{}}\textbf{0.7056} \\ $\pm 0.113$\end{tabular} \\ \hline
\end{tabular}
\end{table}
We also conducted qualitative investigations into the prediction performances of all models trained herein. The resulting scatter and joint plots could be seen at \url{https://github.com/bbrighttaer/ivpgan}.
These plots align with the trends identified in tables~\ref{tab:rmse_results}-\ref{tab:r2_results}. We realized that IVPGAN is able to learn the labels distribution better than the baseline models in most of the cases and more so in the cold target CV schemes when there are significantly fewer targets. The realization that the GraphConv-PSC model is not able to properly model the target distribution for smaller datasets, with the ECFP8-PSC model being mostly less so, highlights the potential of IVPGAN.
The neighborhood alignment dataset in the adversarial training also enables the reduction of residues in most of the scatter plots.
In summary, these results and findings demonstrate the feasibility and effectiveness of our approach to DTI prediction.
\section{Conclusion}\label{sec:conc}
In this study, we have discussed the use of DL models in DTI prediction and emphasized the significance of the choice of featurization schemes in model training. Using the ECFP8-PSC and GraphConv-PSC models as baselines, we have demonstrated that the IVPGAN approach results in improved model skill in most challenging use cases such as cold target splits.
Future studies could examine how coordinated multi-view representation learning mechanisms compare to the joint approach adopted in this study.
In addition, other proposed GAN training techniques could be adopted to address problems associated with GAN training.
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,326 |
Wybory do Parlamentu Europejskiego VIII kadencji w Hiszpanii zostały przeprowadzone 25 maja 2014. Hiszpanie wybrali 54 eurodeputowanych. Frekwencja wyniosła 43,81%. W wyborach wystartowało 39 podmiotów, spośród których 27 uzyskało poparcie poniżej 1%.
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hiszpańscy posłowie do Parlamentu Europejskiego VIII kadencji
Bibliografia
2014 w Hiszpanii
Hiszpania
2014 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,949 |
Guy Pearce
10/5/1967 (53 years old) Ely, Cambridgeshire, England
Filmography Facts Awards
Marvel Studios' Iron Man 3
Lockout (Unrated)
The Time Machine (2002)
At the age of 16, won the Junior Mr. Victoria bodybuilding competition.
Landed a role on the long-running Australian soap Neighbours soon after graduating from Geelong College.
Was nominated for Most Promising Actor at the Chicago Film Critics Awards for his American movie debut, the 1997 crime drama L.A. Confidential.
Won Best Actor at the Las Vegas Film Critics Awards and the San Diego Film Critics Awards for the acclaimed 2001 thriller Memento.
AACTA Awards
Best Lead Actor
Screen Actors Guild Awards
Outstanding Performance by a Cast in a Motion Picture
International Award for Best Actor
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,234 |
Undulatus är en specialform hos moln som visar ett vågformigt mönster. Dessa vågor finns i moln bestående av flak eller skikt. Molnen kan dock antingen vara likformiga eller bestå av åtskilda eller sammansatta element. Ibland förekommer dubbla vågsystem. Beteckningen används för huvudmolnslagen cirrocumulus, cirrostratus, altocumulus, altostratus, stratocumulus och stratus.
Referenser
Noter
Tryckta källor
Specialformer (moln) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,710 |
Q: Flutter 2 upgrade dependencies failed I everyone,
I upgrade to flutter 2 and I got this error:
Because geoflutterfire 2.2.1 depends on rxdart ^0.24.1 and no versions of geoflutterfire match >2.2.1 <3.0.0, geoflutterfire ^2.2.1 requires rxdart ^0.24.1.
So, because sample_app depends on both rxdart ^0.26.0 and geoflutterfire ^2.2.1, version solving failed.
pub get failed (1; So, because sample_app depends on both rxdart ^0.26.0 and geoflutterfire ^2.2.1, version solving failed.)
Flutter doctor:
Doctor summary (to see all details, run flutter doctor -v):
[✓] Flutter (Channel stable, 2.0.0, on macOS 11.1 20C69 darwin-x64, locale en-IL)
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! CocoaPods 1.9.1 out of date (1.10.0 is recommended).
CocoaPods is used to retrieve the iOS and macOS platform side's plugin code that responds to your plugin usage on the Dart side.
Without CocoaPods, plugins will not work on iOS or macOS.
For more info, see https://flutter.dev/platform-plugins
To upgrade see https://guides.cocoapods.org/using/getting-started.html#installation for instructions.
[✓] Chrome - develop for the web
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[✓] Connected device (2 available)
A: SOLVED:
add this lines below dev_dependencies
dependency_overrides:
plugin_platform_interface: '>=2.0.0'
intl: '>=0.17.0'
http: '>=0.13.0'
quiver: '>=2.0.0'
http_parser: '>=4.0.0'
path_provider: '>=2.0.1'
flutter_cache_manager: '>=2.1.1'
rxdart: '>=0.26.0'
**Notice
Don't copy past my override dependencies instead look at which error you got then override it.
Moreover, you need to follow for any updates of these plugins, and if it fixed then remove the override dependencies.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,859 |
Command Sgt. Maj. Ken Killingsworth
Command Sergeant Major, 2nd Security Assistance Force Brigade
Command Sergeant Major Ken Killingsworth hails from Chattanooga, Tennessee. He enlisted in the Army in February, 1992 and attended Basic Training and Advanced Infantry Training at Fort Benning, Georgia.
He currently serves as the 2nd Security Force Assistance Brigade Command Sergeant Major, Fort Bragg, North Carolina and has held positions as a Rifleman, Team Leader, Squad Leader, Section Leader, Company, Battalion & Division Master Gunners, Platoon Sergeant, First Sergeant, Team Sergeant, Battalion, Brigade, and Division Operations Sergeant Major, Battalion Command Sergeant Major and Brigade Command Sergeant Major. His assignments include Korea; Fort Polk, Louisiana; Ray Barracks, Germany; Fort Benning, Georgia; Bad Krueznach, Germany; Fort Bliss, Tx; Fort Riley, Kansas, Fort Stewart, Ga; Fort Campbell, Ky and Fort Shafter, Hawaii. He deployed in support of Operation Joint Guardian Kosovo and has a total of 42 months in Iraq and Afghanistan.
His military and civilian education include all levels of the Noncommissioned Officers Education System, Airborne School, Air Assault School, Bradley Master Gunner School, Battle Staff, Army Instructor Training Course, Mission Command Information System Integrator Course, Combative Level I, the Basic and Advanced Military Transition Team Courses and the Combat Advisor Training Course. He is a graduate of the United States Army Sergeant's Major Academy, class 60 and holds a Bachelor's Degree from Excelsior College.
His awards and decorations include the Legion of Merit, Bronze Star Medal (three Bronze Oak Leaf Clusters), Meritorious Service Medal (four Bronze Oak Leaf Clusters), Army Commendation Medal (one Silver and three Bronze Oak Leaf Clusters), Army Achievement Medal (one Silver and three Bronze Oak Leaf Clusters); Army Good Conduct Medal 8th Award, National Defense Medal with two Bronze stars, Global War on Terrorism Service Medal, Afghanistan Campaign Medal with two Bronze stars, Iraqi Campaign Meal with three Bronze stars, NCO Professional Development Ribbon with numeral 4; Army Service Ribbon; Overseas Service Ribbon, NATO Medal, Army Superior Unit Award, Parachutist Badge, Air Assault Badge, Expert Infantryman's Badge, Combat Infantryman's Badge, the Order of Saint Maurice and a Distinguished Member of the 187th Infantry Regiment.
Page Last Modified: 5/3/19, 7:19 PM | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,793 |
\section{Introduction}
\label{sec:intro}
A better determination of the unitarity triangle angle $\gamma= \arg({-V_{\rm ud}V^*_{\rm ub}/ V_{\rm cd}V_{\rm cb}^*})$ is required for testing the $CP$ violation mechanism within the Standard Model. Sensitivity to $\gamma$
can be obtained by studying $CP$-violating observables in $B^\mp \to D K^\mp$ decays, where $D$ indicates a neutral charm meson reconstructed in a final state common to both $D^0$ and $\bar{D}^0$ mesons, including $CP$-eigenstates~\cite{GLW}. The current world average precision on $\gamma$ is much worse than that of the other angles of the unitarity triangle~\cite{PDG}. Therefore, including additional $D$-meson final states is desirable to reduce the statistical uncertainty on $\gamma$ at current and future facilities.
In the case that the $D$ does not decay to a pure $CP$ eigenstate, information is required on the strong decay dynamics in order to relate the $CP$-violating observables to $\gamma$. This information can be obtained from studies of quantum-correlated $D\bar{D}$ mesons produced in $e^{+}e^{-}$ collisions at an energy corresponding to the mass of the $\psi(3770)$~\cite{GGR,GGSZ,ANTONBONDAR,ATWOODSONI}. The decay $D \to \pi^+\pi^-\pi^0$ is a promising candidate to be added to the modes used in the $\gamma$ measurement.
Its Dalitz plot has been studied by the CLEO and BaBar collaboration using flavour-tagged $D^0$ decays and exhibits a strikingly symmetric distribution that suggests the decay may be dominated by a single $CP$ eigenstate~\cite{CLEOPIPIPI0,BaBarPIPIPI0}. An isospin analysis \cite{BRIAN} of the amplitude model for $D^{0}\to \pi^+\pi^-\pi^0$ presented in Ref.~\cite{BaBarPIPIPI0} concludes that the final state is almost exclusively $I=0$. Therefore, given that the parity and $G$-parity of the three-pion final state is odd and $G=(-1)^{I}C$, the final state is expected to be $C=-1$ and $CP=+1$. As its branching ratio of $1.43 \pm 0.06\%$~\cite{PDG} is significantly larger than those of the pure two-body $CP$-even modes, it has the potential to contribute strongly in any analysis making use of such decays. The channel $D\to K^+ K^- \pi^0$ is a similar, but less abundant, self-conjugate mode that has also attracted interest \cite{CLEOKKPI0,BaBarKKPI0}. These proceedings present the first analysis of these decays using quantum-correlated $D\bar{D}$ decays, and measurements of their $CP$ content, making use of the CLEO-c $\psi(3770)$ data set. These measurements allow the inclusive decays to be included in future $B^\mp \to DK^\mp$ analyses in a straightforward and model-independent manner, thus allowing for an improved determination of the angle $\gamma$. Further it has been shown that improved determinations of CP violating parameters in the charm sector can be made with these measurements \cite{THOMAS}.
These proceedings are based on Refs. \cite{NAYAK} and \cite{4PI} and are structured as follows. Section~\ref{sec:cpcontent} describes how quantum-correlated $D$ decays are used to determine the $CP$ content. The results are presented in Sect.~\ref{sec:results}. In Sect.~\ref{sec:implications} the implications for the measurement of the unitarity triangle angle $\gamma$ are discussed. Section~\ref{sec:conc} gives the conclusions.
\section{Measuring the $CP$ content}\label{sec:cpcontent}
Consider a $\psi(3770) \to D\bar{D}$ analysis in which the signal decay mode is $D \to h^+h^-\pi^0$.
Let $M^+$ designate the number of ``double-tagged'' candidates, after background subtraction, where one $D$ meson is reconstructed in the signal mode of interest, and the other is reconstructed in a $CP$-odd eigenstate. The quantum-numbers of the $\psi(3770)$ resonance then require that the signal mode is in a $CP$-even state, hence the $+$ superscript. The observable $M^-$ is defined in an analogous manner. Let $S^+$ ($S^-$) designate the number of ``single-tagged'' $CP$-odd ($CP$-even) candidates in the data sample, where a $D$ meson is reconstructed decaying to a $CP$ eigenstate, with no requirement on the final state of the other $D$ meson in the event. The small effects of $D^0\bar{D}^0$ mixing are eliminated from the measurement \cite{NAYAK}.
On the assumption that for double-tagged candidates the reconstruction efficiencies of each $D$ meson are independent, then the quantity $N^{+} \equiv M^+ / S^+$ has no dependence on the branching fractions or reconstruction efficiencies of the $CP$-eigenstate modes, and can be directly compared with the analogous quantity $N^-$ to gain insight into the $CP$ content of the signal mode. The $CP$ fraction is defined
\begin{equation}
F_+ \equiv \frac{N^+}{N^+ \, + \, N^-} \; ,
\label{eq:Fplus}
\end{equation}
and is $1$ ($0$) for a signal mode that is fully $CP$-even ($CP$-odd). The notation $F_+ (\pi^+\pi^-\pi^0)$ and $F_+ (K^+K^-\pi^0)$ is used in the discussion when it is necessary to distinguish between the two final states. In addition, tagging the final state with
$K^{0}\pi^{+}\pi^{-}$ and measuring the yield in bins of the $K^{0}\pi^{+}\pi^{-}$ Dalitz of plot for which the strong phase parameters of the decay are known \cite{CLEOKSPIPI} yields further sensitivity to $F_{+}$ \cite{4PI}.
Amplitude models of $D^0 \to \pi^+\pi^-\pi^0$ and $D^0 \to K^+K^-\pi^0$ are available from studies of flavour-tagged $D^0$ decays performed by the BaBar collaboration~\cite{BaBarPIPIPI0,BaBarKKPI0}. These models can be used to calculate predictions for the $CP$ content for each decay. Values of $F_+ ({\pi^+\pi^-\pi^0}) = 0.92$ and $F_+ ({K^+K^-\pi^0}) = 0.64$ are obtained.
\section{Results}\label{sec:results}
The data set analysed consists of $e^+e^-$ collisions produced by the Cornell Electron Storage Ring (CESR) at $\sqrt{s}=3.77$~GeV and collected with the CLEO-c detector. The integrated luminosity of the data set is 818~$\rm pb^{-1}$. The CLEO-c detector is described in detail elsewhere~\cite{CLEOC}. Simulated Monte Carlo (MC) samples of signal decays are used to estimate selection efficiencies. Possible background contributions are determined from a generic MC sample corresponding to
approximately ten times the integrated luminosity of the data set. The EVTGEN generator~\cite{EVTGEN} is used to simulate the decays. The detector response is modelled using the GEANT software package~\cite{GEANT}.
Table~\ref{tab:finalstates} lists the reconstructed $D^{0}$ and
$\bar{D}^{0}$ final states. The unstable final state particles are reconstructed in the following decay modes: $\pi^{0}\to\gamma\gamma$, $K^{0}_{\rm S}\to\pi^{+}\pi^{-}$,
$\omega\to\pi^+\pi^-\pi^0$,
$\eta\to\gamma\gamma$, $\eta\to\pi^+\pi^-\pi^0$ and
$\eta^{\prime}\to\eta(\gamma\gamma)\pi^{+}\pi^{-}$. The $\pi^{0}$, $K^{0}_{\rm S}$, $\omega$, $\eta$ and $\eta^{\prime}$
reconstruction procedure is identical to that used in Ref. \cite{WINGS}.
\begin{table}[th]
\begin{center}
\caption{$D$ final states reconstructed in this analysis.} \vspace*{0.1cm}
\label{tab:finalstates}
\begin{tabular}{cc}\hline\hline
Type & Final states \\ \hline
Signal & $\pi^+\pi^-\pi^0$, $K^+K^-\pi^0$ \\
$CP$-even & $K^{+}K^{-}$, $\pi^{+}\pi^{-}$, $K^{0}_{\rm S}\pi^{0}\pi^{0}$, $K^{0}_{\rm L}\pi^{0}$, $K^{0}_{\rm L}\omega$ \\
$CP$-odd & $K^{0}_{\rm S}\pi^{0}$, $K^{0}_{\rm S}\omega$, $K^{0}_{\rm S}\eta$, $K^{0}_{\rm S}\eta^{\prime}$ \\
Mixed CP & $K^{0}_{\rm S}\pi^{+}\pi^{-}$, $K^{0}_{L}\pi^{+}\pi^{-}$ \\
\hline
\hline
\end{tabular}
\end{center}
\end{table}
Final states that do not contain a $K^{0}_{\rm L}$ are fully reconstructed via two kinematic variables: the
beam-constrained candidate mass, $M_{bc}\equiv\sqrt{s/4c^{4}-\mathbf{p}_{D}^{2}/c^{2}}$, where
$\mathbf{p}_{D}$ is the $D$-candidate momentum, and $\Delta E\equiv E_{D}-\sqrt{s}/2$, where $E_{D}$ is the
$D$-candidate energy. The $M_{bc}$ and $\Delta E$ distributions of correctly reconstructed $D$-meson candidates will peak at the nominal $D^{0}$ mass and zero, respectively. Neither $\Delta E$ nor $M_{bc}$ distributions exhibit any peaking structure for combinatoric background. The double-tagged yield is determined from counting events in signal and
sideband regions of $M_{bc}$ after placing requirements on $\Delta E$. The yield determination procedure is identical to that presented in Refs.~\cite{TQCA1,WINGS}.
The selection procedures are almost identical to those presented in Refs.~\cite{TQCA1,WINGS}; additional details of the selection can be found in Ref.~\cite{NAYAK}. Figure~\ref{fig:hhpi0_signal_mbc} shows the $M_{bc}$ distributions for $CP$-tagged signal candidates, summed over all $CP$-even and $CP$-odd tags, respectively, where the $CP$-tag final state does not contain a $K^{0}_{\rm L}$ meson. No significant signal is seen in any of the modes tagged by a $CP$-even eigenstate, whereas significant signals are seen in most modes tagged by $CP$-odd eigenstates.
Many $K^{0}_{\rm L}$ mesons produced do not deposit any reconstructible signal in the detector. However, double-tag candidates can be fully reconstructed using a missing-mass squared $(M_{\mathrm{miss}}^2)$ technique \cite{K0LPRL} for tags containing a single $K^{0}_{\rm L}$ meson. Yields are extracted from the signal and sideband regions of the
$M_{\mathrm{miss}}^2$ distribution. Figure~\ref{fig:hhpi0_signal_MM2} shows the $M_{\mathrm{miss}}^2$ distributions for candidates tagged with either a $K^0_{\rm L} \pi^0$ or $K^0_{\rm L} \omega$ tag.
\begin{figure}[th]
\begin{center}
\begin{tabular}{cc}
\includegraphics[width=0.45\columnwidth]{pipipi0CPEvenTag.pdf} &
\includegraphics[width=0.45\columnwidth]{pipipi0CPOddTag.pdf}
\end{tabular}
\caption{$M_{bc}$ distributions for $D \to\pi^+\pi^-\pi^0$ candidates tagged by $CP$-even (a) and $CP$-odd (b) eigenstates. Tags involving a $K^0_{\rm L}$ are not included.
The vertical dotted lines indicate the applied signal window.} \label{fig:hhpi0_signal_mbc}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\begin{tabular}{c}
\includegraphics[width=0.45\columnwidth]{pipipi0_KL.pdf}
\end{tabular}
\caption{$M_{\mathrm{miss}}^2$ distributions for $D \to\pi^{+}\pi^{-}\pi^{0}$. The shaded histogram indicates the peaking background. The vertical dotted lines indicate the applied signal window.} \label{fig:hhpi0_signal_MM2}
\end{center}
\end{figure}
It is also necessary to know the single-tag yield for the $CP$-eigenstates to normalise the double-tagged yields appropriately to obtain a value of $F_{+}$. The details of this selection can be found in Ref.~\cite{NAYAK}
The yields of double-tagged and single $CP$-tag candidates are used to determine the quantities $N^+$ and $N^-$, and from these the $CP$ fraction $F_+$. The values for $N^+$ and $N^-$ are calculated from the ensemble of $CP$-odd and $CP$-even tags, respectively, accounting for statistical and systematic uncertainties, and allowing for the correlations that exist between certain systematic components.
The measured values for $N^+$ and $N^-$ for the two signal modes are displayed in Fig.~\ref{fig:results}. It can be seen that there is consistency between the individual $CP$ tags for each measurement. From these results it is determined that
$F_+ ({\pi^+\pi^-\pi^0}) = 0.968 \pm 0.017 \pm 0.006$ and $F_+({K^+K^-\pi^0}) = 0.731 \pm 0.058 \pm 0.021$, where the first uncertainty is statistical and the second is systematic. In addition, the binned yields from the $K^{0}_{L,S}\pi^{+}\pi^{-}$ tagged are used to determine values of $F_+$ which are found to be consistent with those from the $CP$ tags alone \cite{4PI}. The combined values are $0.973 \pm 0.017$ and $0.732 \pm 0.055$ for $\pi^+\pi^-\pi^0$ and $ K^+K^-\pi^0$, respectively \cite{4PI}. These values are slightly higher than, but compatible with, the model predictions reported in Sect.~\ref{sec:cpcontent}.
\begin{figure}[th]
\begin{center}
\begin{tabular}{cc}
\includegraphics[width=0.45\columnwidth]{pipipi0_N+.pdf} &
\includegraphics[width=0.45\columnwidth]{pipipi0_N-.pdf} \\
\end{tabular}
\caption{$D \to \pi^+\pi^-\pi^0$ results for $N^+$ (a) and $N^-$ (b).
In each plot the vertical yellow band indicates the value obtained from the combination of all tags. } \label{fig:results}
\end{center}
\end{figure}
\section{Implications for the measurement of $\boldmath \gamma$}
\label{sec:implications}
Sensitivity to the unitarity triangle angle $\gamma$ is obtained by measuring the relative rates of $B^\mp \to D({h^+h^-\pi^0}) K^\mp$ decays and related observables. These partial widths and those involving flavour-specific $D$ meson decays can be used to construct the partial-widths ratio $R_{F_+}$ and $CP$-asymmetry $A_{F_+}$:
\begin{eqnarray}
R_{F_+} & \equiv &
\frac{ \Gamma(B^-\to D_{F_+} K^- ) \,+\, \Gamma(B^+ \to D_{F_+} K^+ ) }
{ \Gamma(B^-\to D^0 K^- ) \,+ \, \Gamma(B^+ \to \bar{D}^0 K^+ ) }, \\
A_{F_+} & \equiv &
\frac{ \Gamma(B^-\to D_{F_+} K^- ) \,-\, \Gamma(B^+ \to D_{F_+}K^+) }
{ \Gamma(B^-\to D_{F_+} K^- ) \,+ \, \Gamma(B^+ \to D_{F_+ } K^+)} ,
\end{eqnarray}
where $D_{F_+}$ indicates a $D$ meson of $CP$-even content $F_+$, established through its decay into the final state $h^+h^-\pi^0$. These observables are directly analogous to the usual so-called GLW~\cite{GLW} observables $R_{{\rm CP }\pm}$ and $A_{{\rm CP} \pm}$, where the $D$ meson is reconstructed in a pure $CP$ eigenstate.
Then $R_{F_+}$ and $A_{F_+}$ are found \cite{NAYAK} to have the following dependence on the underlying physics parameters:
\begin{eqnarray}
R_{F_+} & = & 1 \, + \, r_B^2 + (2F_+ -1) \cdot 2r_B\cos\delta_B \cos \gamma, \\
A_{F_+} &=& (2F_+ -1 ) \cdot 2r_B \sin\delta_B \sin\gamma / R_{{F_+}},
\end{eqnarray}
which reduces to the equivalent expressions for $R_{{\rm CP }\pm}$ and $A_{{\rm CP} \pm}$ in the case $F_+$ is $1$ or $0$. Therefore inclusive final states such as $h^+h^-\pi^0$ may be cleanly interpreted in terms of $\gamma$ and the other parameters of interest, provided that $F_+$ is known. At leading order the only difference that the $CP$ asymmetry $A_{F_+}$ has with respect to the pure $CP$-eigenstate case is a dilution factor of $(2F_+ -1)$.
\section{Conclusion}\label{sec:conc}
Data corresponding to an integrated luminosity of 818~$\rm pb^{-1}$ collected by the CLEO-c experiment in $e^+e^-$ collisions at the $\psi(3770)$ resonance have been analysed for the decays $D \to \pi^+\pi^-\pi^0$ and $D \to K^+K^-\pi^0$. Measurements of $F_+$, the fractional $CP$-even content of each decay have been performed showing that $D^{0}\to\pi^+\pi^-\pi^0$ is nearly a pure $CP$-even eigenstate.
It has been demonstrated that such self-conjugate inclusive channels can be cleanly included in measurements of the unitarity-triangle angle $\gamma$, using $B^\mp \to D K^\mp$ decays. The high value of $F_+$ obtained for $D \to \pi^+\pi^-\pi^0$ makes this channel, in particular, a valuable addition to the suite of $D$-decay modes used in the measurement of $\gamma$ at LHCb and Belle-II. Improved precision on the $F_+$ parameters can be obtained using the larger $\psi(3770)$ data set available at BESIII, and similar measurements can also be performed for other self-conjugate final states.
\section*{Acknowledgments}
This analysis was performed using CLEO-c data, and as a member of the former CLEO collaboration I thank it for this privilege. I am grateful for support from the UK-India Education and Research Initiative.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,119 |
\section{Introduction}
A fruitful problem in Riemannian geometry is to study the critical points of the volume functional associated to space of smooth Riemannian structures. In the last decades very much attention has been given to study the critical points of the volume functional. Here, we shall study the space of smooth Riemannian structures on compact manifolds with boundary that satisfies a critical point equation associated to a boundary value problem.
Recently, inspired in a result obtained in \cite{fan} as well as in the characterization of the critical points of the scalar curvature functional, Miao and Tam studied variational properties of the volume functional constrained to the space of metrics of constant scalar curvature on a given compact manifold with boundary. For more details, we refer the reader to \cite{miaotam} and \cite{miaotamTAMS}. Afterward, in a celebrated article \cite{CEM} Corvino, Eichmair and Miao studied this problem in a general context. In fact, they studied the modified problem of finding stationary points for the volume functional on the space of metrics whose scalar curvature is equal to a given constant. To do this, they localized a condition satisfied by such stationary points to smooth bounded domains.
We now recall the definition of critical metrics studied by Miao and Tam. Here, for simplicity, these metrics will be called Miao-Tam critical metrics.
\begin{definition}
\label{def1} A Miao-Tam critical metric is a 3-tuple $(M^n,\,g,\,f),$ where $(M^{n},\,g),$ is a compact Riemannian manifold of dimension at least three with a smooth boundary $\partial M$ and $f: M^{n}\to \Bbb{R}$ is a smooth function such that $f^{-1}(0)=\partial M$ satisfying the overdetermined-elliptic system
\begin{equation}
\label{eqMiaoTam} \mathfrak{L}_{g}^{*}(f)=g.
\end{equation} Here, $\mathfrak{L}_{g}^{*}$ is the formal $L^{2}$-adjoint of the linearization of the scalar curvature operator $\mathfrak{L}_{g}$. Such a function $f$ is called a potential function.
\end{definition}
We recall that $\mathfrak{L}_{g}^{*}(f)=-(\Delta f)g+Hess\,f-f Ric;$ see for instance \cite{besse}. Therefore, the fundamental equation of a Miao-Tam critical metric (\ref{eqMiaoTam}) can be written as
\begin{eqnarray}
\label{eqMiaoTam2}
-(\Delta f)g+Hess\,f-f Ric=g.
\end{eqnarray}
We highlight that some explicit examples of Miao-Tam critical metrics are in the form of warped products. Those examples include the spatial Schwarzschild metrics and AdS-Schwarzschild metrics restricted to certain domains containing their horizon and bounded by two spherically symmetric spheres (cf. Corollaries 3.1 and 3.2 in \cite{miaotamTAMS}).
It is not to hard to show that critical metrics have constant scalar curvature \cite{miaotam}. In 2009, Miao and Tam were able to prove that these metrics arise as critical points of the volume functional on $M^n$ when restricted to the class of metrics $g$ with prescribed constant scalar curvature such that $g\mid_{T \partial M}=h$ for a prescribed Riemannian metric $h$ on the boundary.
Here, we call attention to the paragraph where Miao and Tam \cite{miaotamTAMS} wrote:
\begin{flushright}
\begin{minipage}[t]{4.37in}
\emph{``we want to know if there exist non-constant sectional curvature critical metrics on a compact manifold whose boundary is isometric to standard sphere. If yes, what can we say about the structure of such metrics?"}
\end{minipage}
\end{flushright}
Indeed, they studied these critical metrics under Einstein and conformally flat assumptions. In particular, they proved that a connected, compact, Einstein manifold $(M^n ,\,g)$ with smooth boundary that satisfies (\ref{eqMiaoTam2}) must be isometric to a geodesic ball in a simply connected space form $\Bbb{R}^{n},$ $\Bbb{H}^{n}$ or $\Bbb{S}^{n}.$ Moreover, based on the techniques developed in a work of Kobayashi and Obata \cite{obata}, Miao and Tam showed that the result even is true replacing the Einstein condition by the assumption that $(M^n ,\,g)$ is locally conformally flat with boundary isometric to a standard sphere. More precisely, they proved the following result.
\begin{theorem}[Miao-Tam, \cite{miaotamTAMS}]
\label{theoremMT}
Let $(M^n,g,f)$ be a locally conformally flat simply connected, compact Miao-Tam critical metric with boundary isometric to a standard sphere $\Bbb{S}^{n-1}.$ Then $(M^n ,\,g)$ is isometric to a geodesic ball in a simply connected space form $\Bbb{R}^{n},$ $\Bbb{H}^{n}$ or $\Bbb{S}^{n}$.
\end{theorem}
It should be emphasized that the hypothesis that the boundary of $M^n$ is isometric to a standard sphere $\Bbb{S}^{n-1}$ considered by Miao and Tam is not artificial. To clarify this, we consider that the boundary of $M^n$ is totally geodesic and is isometric to a standard sphere $\Bbb{S}^{n-1}.$ Under these conditions, motivated by the positive mass theorem, Min-Oo conjectured that if $M^n$ has scalar curvature at least $n(n-1),$ then $M^n$ must be isometric to the hemisphere $\Bbb{S}^{n}_{+}$ with standard metric (cf. \cite{MinO}). However, an elegant article due to Brendle, Marques and Neves shows counterexamples to Min-Oo's Conjecture in dimensions $n\geq 3.$ For more details see \cite{marques}. We also highlight that $\Bbb{S}^{n}_{+}$ satisfies (\ref{eqMiaoTam2}) for a suitable potential function (cf. \cite{miaotam} p. 153).
We now recall that the Bach tensor on a Riemannian manifold $(M^n,g)$, $n\geq 4,$ which was introduced in the early 1920s to study conformal relativity, see \cite{bach}, is defined in term of the components of the Weyl tensor $W_{ikjl}$ as follows
\begin{equation}
\label{bach} B_{ij}=\frac{1}{n-3}\nabla^{k}\nabla^{l}W_{ikjl}+\frac{1}{n-2}R_{kl}W_{i}\,^{k}\,_{j}\,^{l},
\end{equation}
while for $n=3$ it is given by
\begin{equation}
\label{bach3} B_{ij}=\nabla^kC_{kij}.
\end{equation}
We say that $(M^n,g)$ is Bach-flat when $B_{ij}=0.$ On 4-dimensional compact manifolds, Bach-flat metrics are precisely critical points of the conformally invariant functional $\mathcal{W}(g)$ defined on the space of smooth Riemannian structures as follows
\begin{equation*}
\mathcal{W}(g)=\int_{M}|W_{g}|^2 dM_{g},
\end{equation*}
where $W_{g}$ denotes the Weyl tensor of $g$. It is not difficult to check that locally conformally flat metrics as well as Einstein metrics are Bach-flat. Recently, Cao and Chen have studied Bach-flat gradient Ricci solitons, more precisely, they showed a stronger classification for gradient Ricci solitons under the Bach-flat assumption. For more details, we refer the reader to \cite{CaoChen} and \cite{CaoChenT}.
It is well-known that 4-dimensional compact Riemannian manifolds have special behavior; for more details see for instance \cite{AMS}, \cite{besse} and \cite{scorpan}. Here, we shall investigate Bach-flat critical metrics of the volume functional on 4-dimensional manifolds with boundary. More precisely, we replace the assumption of locally conformally flat in the Miao-Tam result by the Bach-flat condition, which is weaker that the former. We now state our first result.
\begin{theorem}\label{thm1}
Let $(M^4,g,f)$ be a simply connected, compact Miao-Tam critical metric with boundary isometric to a standard sphere $\Bbb{S}^{3}.$ Then $(M^4 ,\,g)$ is isometric to a geodesic ball in a simply connected space form $\Bbb{R}^{4},$ $\Bbb{H}^{4}$ or $\Bbb{S}^{4}$ provided $$\int_M f^2B(\nabla f,\nabla f)dM_{g}\geq 0,$$ where $B$ is the Bach tensor.
\end{theorem}
The proof of Theorem \ref{thm1} was inspired in the trend developed by Cao and Chen in \cite{CaoChen}. In the sequel, as an immediate consequence of Theorem \ref{thm1} we deduce the following corollary.
\begin{corollary}
Let $(M^4,g,f)$ be a Bach-flat simply connected, compact Miao-Tam critical metric with boundary isometric to a standard sphere $\Bbb{S}^{3}.$ Then $(M^4 ,\,g)$ is isometric to a geodesic ball in a simply connected space form $\Bbb{R}^{4},$ $\Bbb{H}^{4}$ or $\Bbb{S}^{4}$.
\end{corollary}
Based in the previous result, it is natural to ask what occurs in lower dimension. To do so, inspired in the ideas developed in \cite{CCCMM} (see also \cite{CaoChenT} and \cite{CaoChen}) we shall prove a rigidity result for a 3-dimensional Miao-Tam critical metric with divergence-free Bach tensor, i.e. $div B= 0,$ and boundary isometric to a standard sphere $\Bbb{S}^2.$ Clearly, the assumption of divergence-free Bach tensor is weaker than the Bach-flat condition considered in Theorem \ref{thm1}. More precisely, we have the following result.
\begin{theorem}\label{thm2}
Let $(M^3,\,g,\,f)$ be a simply connected, compact Miao-Tam critical metric with boundary isometric to a standard sphere $\Bbb{S}^2.$ If $div B(\nabla f)=0$ in $M,$ where $B$ is the Bach tensor, then $(M^3,\,g)$ is isometric to a geodesic ball in a simply connected space form $\Bbb{R}^{3},$ $\Bbb{H}^{3}$ or $\Bbb{S}^3.$
\end{theorem}
Finally, we get the following rigidity result.
\begin{corollary}
\label{cor2}
Let $(M^3,\,g,\,f)$ be a simply connected, compact Miao-Tam critical metric with divergence-free Bach tensor and boundary isometric to a standard sphere $\Bbb{S}^2.$ Then $(M^3,\,g)$ is isometric to a geodesic ball in a simply connected space form $\Bbb{R}^{3},$ $\Bbb{H}^{3}$ or $\Bbb{S}^3.$
\end{corollary}
\section{Preliminaries and Key Lemmas}
In this section we shall present a couple of lemmas that will be useful in the proof of our main results. We begin recalling that $$ \mathfrak{L}_{g}^{*}(f)=-(\Delta f)g+Hess\,f-f Ric.$$ So, as it was previously mentioned the fundamental equation of a Miao-Tam critical metric (\ref{eqMiaoTam}) becomes
\begin{equation}
\label{eqfund1}
-(\Delta f)g+Hess f-fRic=g.
\end{equation}
Tracing (\ref{eqfund1}) we arrive at
\begin{equation}
\label{eqtrace}
(n-1)\Delta f+Rf=-n.
\end{equation}
Moreover, by using (\ref{eqtrace}) it is not difficult to check that
\begin{equation}
\label{IdRicHess} f\mathring{Ric}=\mathring{Hess} f,
\end{equation} where $\mathring{T}$ stands for the traceless of $T.$
For simplicity, we now rewrite equation (\ref{eqfund1}) in the tensorial language as follows
\begin{equation}
\label{fundeqtens} -(\Delta f)g_{ij}+\nabla_{i}\nabla_{j}f -fR_{ij}=g_{ij}.
\end{equation}
Next, since a Miao-Tam critical metric has constant scalar curvature (cf. \cite{miaotam}), we use the last identity in order to obtain the following lemma.
\begin{lemma}
\label{lem1} Let $\big(M^n,\,g,\,f)$ be a Miao-Tam critical metric. Then
\begin{equation*}
f\big(\nabla_{i}R_{jk}-\nabla_{j}R_{ik}\big)=R_{ijks}\nabla^{s}f + \frac{R}{n-1}\big(\nabla_{i}f
g_{jk}-\nabla_{j}f g_{ik}\big)- \big(\nabla_{i}f R_{jk}-\nabla_{j}f R_{ik}\big).
\end{equation*}
\end{lemma}
\begin{proof} Computing $\nabla_{i}(fR_{jk})$ with the aid of (\ref{fundeqtens}) we infer
\begin{equation}
\label{eq1lem1}
(\nabla_{i}f)R_{jk}+f\nabla_{i}R_{jk}=\nabla_{i}\nabla_{j}\nabla_{k}f-(\nabla_{i}\Delta f)g_{jk}.
\end{equation}
Since $R$ is constant (\ref{eqtrace}) yields $\nabla_{i}\Delta f=-\frac{R}{n-1}\nabla_{i}f$. Hence we use this data in (\ref{eq1lem1}) to deduce
\begin{equation}
\label{eq2lem2}
f\nabla_{i}R_{jk}=-(\nabla_{i}f)R_{jk}+\nabla_{i}\nabla_{j}\nabla_{k}f+\frac{R}{n-1}\nabla_{i}fg_{jk}.
\end{equation}
Therefore, it suffices to apply the Ricci identity to finish the proof of the lemma.
\end{proof}
To fix notations we recall three special tensors in the study of curvature for a Riemannian manifold $(M^n,\,g),\,n\ge 3.$ The first one is the Weyl tensor $W$ which is defined by the following decomposition formula
\begin{eqnarray}
\label{weyl}
R_{ijkl}&=&W_{ijkl}+\frac{1}{n-2}\big(R_{ik}g_{jl}+R_{jl}g_{ik}-R_{il}g_{jk}-R_{jk}g_{il}\big) \nonumber\\
&&-\frac{R}{(n-1)(n-2)}\big(g_{jl}g_{ik}-g_{il}g_{jk}\big),
\end{eqnarray}
where $R_{ijkl}$ stands for the Riemann curvature operator, whereas the second one is the Cotton tensor $C$ given by
\begin{equation}
\label{cotton} \displaystyle{C_{ijk}=\nabla_{i}R_{jk}-\nabla_{j}R_{ik}-\frac{1}{2(n-1)}\big(\nabla_{i}R
g_{jk}-\nabla_{j}R g_{ik}).}
\end{equation}
These two tensors are related as follows
\begin{equation}
\label{cottonwyel} \displaystyle{C_{ijk}=-\frac{(n-2)}{(n-3)}\nabla_{l}W_{ijkl},}
\end{equation}provided $n\ge 4.$
Finally, the Schouten tensor $A$ is defined by
\begin{equation}
\label{schouten} A_{ij}=\frac{1}{n-2}\left(R_{ij}-\frac{R}{2(n-1)}g_{ij}\right).
\end{equation}
Combining equations (\ref{weyl}) and (\ref{schouten}) we have the following splitting
\begin{equation}
\label{WS} R_{ijkl}=\frac{1}{n-2}(A\odot g)_{ijkl}+W_{ijkl},
\end{equation}
where $\odot$ is the Kulkarni-Nomizu product. For more details about these tensors, we refer to \cite{besse}.
From now on we introduce the covariant 3-tensor $T_{ijk}$ by
\begin{eqnarray}
\label{T}
T_{ijk}&=&\frac{n-1}{n-2}\left(R_{ik}\nabla_{j}f-R_{jk}\nabla_{i}f\right)
-\frac{R}{n-2}\left(g_{ik}\nabla_{j}f-g_{jk}\nabla_{i}f\right)\nonumber\\
&&+\frac{1}{n-2}\left(g_{ik}R_{js}\nabla^{s}f-g_{jk}R_{is}\nabla^{s}f\right).
\end{eqnarray}
It is important to highlight that $T_{ijk}$ was defined similarly to $D_{ijk}$ in \cite{CaoChen}. Now, we may announce our second lemma.
\begin{lemma}\label{lemTCW} Let $(M^n,g,f)$ be a Miao-Tam critical metric. Then the following identity holds:
\begin{equation*}
fC_{ijk}=T_{ijk}+W_{ijks}\nabla^{s}f.
\end{equation*}
\end{lemma}
\begin{proof} First of all, we compare (\ref{cotton}) with Lemma \ref{lem1} to arrive at
\begin{equation}
\label{eq1pl2} fC_{ijk}=R_{ijks}\nabla^{s}f + \frac{R}{n-1}\big(\nabla_{i}f g_{jk}-\nabla_{j}f g_{ik}\big)-
\big(\nabla_{i}f R_{jk}-\nabla_{j}f R_{ik}\big).
\end{equation}
On the other hand, from (\ref{weyl}) we obtain
\begin{eqnarray*}
R_{ijks}\nabla^{s}f&=&W_{ijks}\nabla^{s}f+\frac{1}{n-2}\big(R_{ik}g_{js}+R_{js}g_{ik}-R_{is}g_{jk}-R_{jk}g_{is}\big)\nabla^{s}f\\&&-\frac{R}{(n-1)(n-2)}\big(g_{js}g_{ik}-g_{is}g_{jk}\big)\nabla^{s}f.
\end{eqnarray*}
From this it follows that
\begin{eqnarray*}
fC_{ijk}&=&W_{ijks}\nabla^{s}f + \frac{(n-1)}{(n-2)}\big(R_{ik}\nabla_{j}f-R_{jk}\nabla_{i}f\big)-\frac{R}{(n-2)}\big(g_{ik}\nabla_{j}f - g_{jk}\nabla_{i}f\big)\\
&&+\frac{1}{n-2}\big(g_{ik}R_{js}\nabla^{s}f-g_{jk}R_{is}\nabla^{s}f\big)\\
&=&T_{ijk}+W_{ijks}\nabla^{s}f,
\end{eqnarray*}which concludes the proof of the lemma.
\end{proof}
To simplify some computations we shall define a function $\rho$ on $M^n$ by
\begin{equation}\label{rho}
\rho=|\nabla f|^2+\frac{2}{n-1}f+\frac{R}{n-1}f^2.
\end{equation} We claim that
\begin{equation}\label{gradrho}
\frac{1}{2}\nabla\rho=fRic(\nabla f).
\end{equation}Indeed, since $R$ is constant we have $
\frac{1}{2}\nabla\rho=Hess f(\nabla f) +\frac{1}{n-1}\nabla f +\frac{R}{n-1}f\nabla f.$ Next, we use (\ref{eqfund1}) and (\ref{eqtrace}) to obtain
$$
\frac{1}{2}\nabla\rho=Hess f(\nabla f) -(\Delta f+1)\nabla f=fRic(\nabla f),
$$
which settles our claim.
Proceeding we recall that, at regular points of a smooth function $f,$ the vector field $\nu=\frac{\nabla f}{\mid \nabla f \mid}$ is normal to $\Sigma_{c}=\{p\in M:f(p)=c\}.$ In particular the second fundamental form of $\Sigma_{c}$ is given by
\begin{equation}
\label{secff}
h_{ij}=-\langle \nabla_{e_{i}}\nu,e_{j}\rangle,
\end{equation}where $\{e_{1},\ldots,e_{n-1}\}$ is an orthonormal frame on $\Sigma_{c}.$ Then the mean curvature computed at these points, denoted by $H$, is given as follows
\begin{equation}
\label{meancurv1}
H=-\frac{1}{\mid \nabla f \mid}\sum_{i=1}^{n-1}Hessf (e_{i},e_{i}).
\end{equation}
We now follow the trend of Cao and Chen (cf. \cite{CaoChen} and \cite{CaoChenT}) to study the level sets of the potential function of Miao-Tam critical metrics. To this end, first, we deduce a similar result concerning to the tensor $T$ defined by (\ref{T}) on the next lemma.
\begin{lemma}\label{propT}
Let $(M^n,g,f)$ be a Miao-Tam critical metric. Let $\Sigma=\{f=f(p)\}$ be a level set of $f$. If $g_{ab}$ denotes the induced metric on $\Sigma,$ then, at any point where $\nabla f\neq0,$ we have
\begin{equation*}
|fT|^2=\frac{2(n-1)^2}{(n-2)^2}|\nabla
f|^4\sum_{a,b=2}^{n}|h_{ab}-\frac{H}{n-1}g_{ab}|^2+\frac{n-1}{2(n-2)}|\nabla^{\Sigma}\rho|^2,
\end{equation*}
where $\rho$ is given by (\ref{rho}), $h_{ab}$ and $H$ are the second fundamental form and the mean curvature of $\Sigma,$ respectively, while $\nabla^{\Sigma}$ is the Riemannian connection of $\Sigma.$
\end{lemma}
\begin{proof}
We consider an orthonormal frame $\{e_{1},e_2,\ldots,e_{n}\}$ with $e_1=\frac{\nabla f}{|\nabla f|}$ and $e_2,\ldots,e_n$ tangent to $\Sigma.$ A straightforward computation allows us to deduce
\begin{eqnarray*}
|T|^2&=&\frac{2(n-1)^2}{(n-2)^2}(|Ric|^2|\nabla f|^2-|Ric(\nabla f)|^2)+\frac{2(n-1)R^2}{(n-2)^2}|\nabla f|^2 \\&&+\frac{2(n-1)}{(n-2)^2}|Ric(\nabla f)|^2-\frac{4(n-1)R}{(n-2)^2}(R|\nabla f|^2-Ric(\nabla f,\nabla f))\\&&+\frac{4(n-1)}{(n-2)^2}(RRic(\nabla f,\nabla f)-|Ric(\nabla f)|^2)-\frac{4(n-1)R}{(n-2)^2}Ric(\nabla f,\nabla f).
\end{eqnarray*}
Proceeding we can use (\ref{gradrho}) to obtain
\begin{eqnarray}
\label{eqfT} |fT|^2&=&\frac{2(n-1)^2}{(n-2)^2}f^2 |\nabla f|^2 |Ric|^2 -\frac{n(n-1)}{2(n-2)^2}|\nabla\rho|^2\nonumber\\&
&-\frac{2(n-1)R^2}{(n-2)^2}f^2 |\nabla f|^2+\frac{2(n-1)R}{(n-2)^2}f\langle\nabla\rho,\nabla f\rangle.
\end{eqnarray}
On the other hand, the second fundamental form $h_{ab}$ of the level set $\Sigma$ as well as its mean curvature $H,$ are given, respectively, by
\begin{equation*}
h_{ab}=-\left\langle\nabla_{e_a}\left(\frac{\nabla f}{|\nabla f|}\right),e_b\right\rangle=-\frac{1}{|\nabla
f|}\nabla_a\nabla_b f=-\frac{1}{|\nabla f|}\left[fR_{ab}-\Big(\frac{1}{n-1}+\frac{fR}{n-1}\Big)g_{ab}\right]\end{equation*}
and
\begin{equation*}
H=-\frac{1}{|\nabla f|}(fR-fR_{11}-fR-1)=\frac{1}{|\nabla f|}(fR_{11}+1).
\end{equation*}
Whence, we deduce
\begin{eqnarray*}
|h|^2 &=&\frac{1}{|\nabla f|^2}\left[f^2|Ric|^2-2f^2\sum_{a=2}^{n}R_{1a}^{2}-f^2R_{11}^{2}-2f(R-R_{11})\Big(\frac{1}{n-1}+\frac{fR}{n-1}\Big)\right]\\&&+\frac{1}{|\nabla f|^2}\frac{(fR+1)^2}{n-1}
\end{eqnarray*}
and
\begin{equation*}
H^2=\frac{1}{|\nabla f|^2}\left(f^2 R_{11}^{2}+2fR_{11}+1\right).
\end{equation*}
After some computations we obtain
\begin{eqnarray}
\label{eq123}
\sum_{a,b=2}^{n}|h_{ab}-\frac{H}{n-1}g_{ab}|^2 &=&\frac{1}{|\nabla f|^2}\left[f^2|Ric|^2-\Big(\frac{nR_{11}^{2}f^2+f^2 R^2-2f^2 RR_{11}}{n-1}\Big)\right]\nonumber\\&&-\frac{2f^2}{|\nabla f|^2}\sum_{a=2}^{n}R_{1a}^{2}.
\end{eqnarray}
On the other hand, by using once more (\ref{gradrho}) we get
$$
fR_{11}=\frac{1}{|\nabla f|^2}fRic(\nabla f,\nabla f)=\frac{1}{2|\nabla f|^2}\langle\nabla\rho,\nabla
f\rangle$$
and
$$fR_{1a}=\frac{1}{|\nabla f|}fRic(\nabla f,e_{a})=\frac{1}{2|\nabla f|}\langle\nabla\rho,e_{a}\rangle=\frac{1}{2|\nabla f|}\nabla_{a}\rho.$$
Substituting the last two identities in (\ref{eq123}) we obtain
\begin{eqnarray*}
\sum_{a,b=2}^{n}|h_{ab}-\frac{H}{n-1}g_{ab}|^2&=&\frac{1}{|\nabla f|^2}\Big(f^2|Ric|^2-\frac{1}{2|\nabla
f|^2}|\nabla^{\Sigma}\rho|^2-\frac{R^2 f^2}{n-1}\\&-&\frac{n}{4(n-1)|\nabla f|^4}\langle\nabla\rho,\nabla f\rangle^2+\frac{R f}{(n-1)|\nabla f|^2}\langle\nabla\rho,\nabla f\rangle\Big),
\end{eqnarray*}
which can be rewritten as
\begin{eqnarray}
\label{eq235}
f^2|Ric|^2&=&|\nabla f|^2\sum_{a,b=2}^{n} |h_{ab}-\frac{H}{n-1}g_{ab}|^2+\frac{n}{4(n-1)|\nabla f|^4}\langle\nabla\rho,\nabla f\rangle^2\nonumber\\
&&+\frac{1}{2|\nabla
f|^2}|\nabla^{\Sigma}\rho|^2+\frac{R^2 f^2}{n-1}-\frac{R f}{(n-1)|\nabla f|^2}\langle\nabla\rho,\nabla f\rangle.
\end{eqnarray}
Finally, comparing (\ref{eqfT}) with (\ref{eq235}), we deduce
\begin{equation*}
|fT|^2=\frac{2(n-1)^2}{(n-2)^2}|\nabla
f|^4 \sum_{a,b=2}^{n}|h_{ab}-\frac{H}{n-1}g_{ab}|^2+\frac{n-1}{2(n-2)}|\nabla^{\Sigma}\rho|^2,
\end{equation*}
which completes the proof of the lemma.
\end{proof}
We point out that some of these calculations above were also done in \cite{br} and \cite{QingYuan} in a different context to study the CPE conjecture (cf. Besse \cite{besse}, page 128).
Next, as a consequence of Lemma \ref{propT} we derive the following properties concerning a level set of the quoted metrics.
\begin{proposition}\label{propvanishT}
Let $(M^n,\,g,\,f)$ be a Miao-Tam critical metric with $T\equiv 0.$ Let $c$ be a regular value of $f$ and
$\Sigma=\{p\in M;\,f(p)=c\}$ be a level set of $f.$ We consider $e_1=\frac{\nabla f}{|\nabla f|}$ and choose
an orthonormal frame $\{e_2,\ldots,e_n\}$ tangent to $\Sigma.$ Under these conditions the following assertions hold.
\begin{enumerate}
\item \label{item1pT} The second fundamental form $h_{ab}$ of $\Sigma$ is $h_{ab}=\frac{H}{n-1}g_{ab}.$
\item \label{item2pT} $|\nabla f|$ is constant on $\Sigma.$
\item \label{item3pT} $R_{1a}=0$ for any $a\geq2$ and $e_1$ is an eigenvector of $Ric.$
\item \label{item4pT} The mean curvature of $\Sigma$ is constant.
\item \label{item5pT} On $\Sigma,$ the Ricci tensor either has a unique eigenvalue or two distinct eigenvalues with
multiplicity $1$ and $n-1,$ respectively. Moreover, the eigenvalue with multiplicity $1$ is in the direction of $\nabla f.$
\item \label{item6pT} $R_{1abc}=0$, for $a,b,c\in\{2,\ldots,n\}.$
\end{enumerate}
\end{proposition}
\begin{proof}
The first two items follow directly from Lemma \ref{propT} jointly with (\ref{rho}). Since $T\equiv0$ we may use (\ref{T}) to deduce
\begin{eqnarray*}
0&=&T(e_i,\nabla f,\nabla f)\\
&=&Ric(e_i,\nabla f)|\nabla f|^2-Ric(\nabla f,\nabla f)\langle \nabla f, e_{i}\rangle,
\end{eqnarray*}
in other words $$Ric(e_i,\nabla f)|\nabla f|^2=Ric(\nabla f,\nabla f)\langle \nabla f, e_{i}\rangle.$$ So, for $i=a\geq2$, we obtain $R_{1a}=0$. Furthermore $Ric(e_1)=g^{ij}R_{1j}e_i=R_{11}e_1.$ Therefore, $e_1=\frac{\nabla f}{|\nabla f|}$ is an eigenvector of $Ric,$ which establishes the third assertion.
Proceeding we consider the Codazzi equation
\begin{equation}
\label{codazzi} R_{1abc}=\nabla^{\Sigma}_{b}h_{ca}-\nabla^{\Sigma}_{c}h_{ba}, \,\,\, a,b,c=2,\ldots,n.
\end{equation}
By contracting (\ref{codazzi}) with respect to indices $a$ and $c,$ and using (\ref{item1pT}), we get
\begin{equation*}
R_{1b}=\nabla^{\Sigma}_{b}H-g^{ac}\nabla^{\Sigma}_{c}h_{ba}=\frac{n-2}{n-1}\nabla^{\Sigma}_{b}H.
\end{equation*}
Now, we use that $R_{1b}=0$ to conclude that $H$ is constant on $\Sigma,$ which gives the fourth item. Next, since $e_1=\frac{\nabla f}{|\nabla f|}$ is an eigenvector of $Ric,$ we may choose the frame $$\{e_{1}=\frac{\nabla f}{|\nabla f|},e_{2},\ldots,e_{n}\}$$ diagonalizing $Ric$ such that $Ric (e_k)=\lambda_ke_k$ for $k=1,2,\ldots,n.$ Using once more that $T\equiv0,$ we have for all $a,b\geq2$
\begin{eqnarray*}
0&=&T_{a1b}=\frac{n-1}{n-2}(R_{ab}\nabla_{1}f-R_{b1}\nabla_{a}f)-\frac{R}{n-2}(g_{ab}\nabla_{1}f-g_{1b}\nabla_{a}f)\\
&&+\frac{1}{n-2}(g_{ab}R_{1s}\nabla^{s}f-g_{1b}R_{as}\nabla^{s}f)\\
&=&\frac{n-1}{n-2}R_{ab}|\nabla f|-\frac{R}{n-2}g_{ab}|\nabla f|+\frac{1}{n-2}g_{ab}\lambda_1|\nabla f|.
\end{eqnarray*}
From here it follows that $R_{ab}=\frac{R-\lambda_1}{n-1}g_{ab}$ and then $\lambda_2=\ldots=\lambda_n=\frac{R-\lambda_1}{n-1},$ which gives the fifth assertion. Finally, we use (\ref{codazzi}) as well as (\ref{item1pT}) and (\ref{item4pT}) of the proposition to obtain the last one. So, we complete the proof of the proposition.
\end{proof}
Proceeding with such a metric with $T\equiv0$ we obtain the following lemma.
\begin{lemma}\label{lemcvanish}
Let $(M^n,\,g,\,f)$ be a Miao-Tam critical metric with $T\equiv0.$ Then $C\equiv 0,$ namely, $(M^n,\,g)$ has harmonic Weyl tensor.
\end{lemma}
\begin{proof}
The first part of the proof is standard and it follows the proof of Lemma 4.2 of \cite{CaoChen}. Here we present its proof for the sake of completeness.
First, since $T\equiv0$ we invoke Lemma \ref{lemTCW} to deduce $fC_{ijk}=W_{ijkl}\nabla^{l}f,$ which implies
\begin{equation}
\label{lemcvanisheq1}fC_{ijk}\nabla^{k}f=0.
\end{equation}
We now consider a regular point $p\in M^n,$ with associated level set $\Sigma.$ We choose any local coordinates $(\theta^{2},\ldots,\theta^{n})$ on $\Sigma$ and split the metric in the local coordinates $(f,\theta^{2},\ldots,\theta^{n})$ as $$g=\frac{1}{|\nabla f|^{2}}df^2+g_{ab}(f,\,\theta) d\theta^{a}d\theta^{b}.$$ Denoting $\partial_{f}=\partial_{1}=\frac{\nabla f}{|\nabla f|^{2}}$ we get
\begin{eqnarray*}
\nabla_{1}f=1 \,\,\,{\rm and}\,\,\,\nabla_{a}f=0,\,\,\,{\rm for}\,\,\,a\geq 2.
\end{eqnarray*}
From (\ref{lemcvanisheq1}) we have $fC_{ij1}=0$ for all $i,j=1,\ldots,n.$ Moreover, for $a,b,c\geq 2,$ by using the Codazzi equation jointly with first and fourth items of Proposition \ref{propvanishT} we have
\begin{equation*}
R_{1abc}=\nabla_{b}^{\Sigma}h_{ac}-\nabla_{c}^{\Sigma}h_{ab}=0.
\end{equation*}
In particular, using $R_{1a}=0$ we get $$W_{1abc}=R_{1abc}=0.$$ Whence, we obtain for $a,b,c\geq 2$ $$fC_{abc}=W_{abcs}\nabla^{s}f=W_{abc1}\nabla^{1}f=0.$$
We now claim that $fC_{1ab}=0$ for all $a,b\geq 2.$ To do this, first, we notice that
\begin{equation*}
fC_{1ab}=W_{1abs}\nabla^{s}f=W_{1abi}g^{is}\nabla_{s} f,=W_{1ab1}|\nabla f|^2=-\frac{1}{|\nabla f|^{2}}W(\nabla f,\partial_a,\nabla f,\partial_b).
\end{equation*}
On the other hand, from (\ref{weyl}) we have
\begin{eqnarray}
\label{lemcvanisheq2}
\frac{1}{|\nabla f|^{2}}W(\nabla f,\partial_a,\nabla f,\partial_b)&=&\frac{1}{|\nabla f|^{2}}R(\nabla f,\partial_a,\nabla f,\partial_b)+\frac{R}{(n-1)(n-2)}g_{ab}\nonumber\\&&-\frac{1}{(n-2)}\left(\frac{1}{|\nabla f|^{2}}Ric(\nabla f,\nabla f)g_{ab}+R_{ab}\right).
\end{eqnarray}
We now analyze the second fundamental form in the local coordinate $(f,\theta^{2},\ldots,\theta^{n}).$ It is easy to see that
\begin{equation*}
h_{ab}=\frac{1}{|\nabla f|}\langle \nabla f,\nabla_{a}\partial_{b}\rangle=\frac{1}{|\nabla f|}\langle \nabla f,\Gamma_{ab}^{1}\partial_{f}\rangle=\frac{\Gamma_{ab}^{1}}{|\nabla f|}.
\end{equation*}
Moreover, a standard computation allows us to obtain
\begin{eqnarray*}
\Gamma_{ab}^{1}&=&\frac{1}{2}g^{1j}\big(\partial_{a}g_{bj}+\partial_{b}g_{ja}-\partial_{j}g_{ab}\big)\\&=&\frac{1}{2}g^{11}\big(\partial_{a}g_{b1}+\partial_{b}g_{1a}-\partial_{f}g_{ab}\big)\\
&=&-\frac{1}{2}\nabla f (g_{ab}).
\end{eqnarray*}
From here it follows that
\begin{equation}
\label{lemcvanisheq3} h_{ab}=-\frac{\nabla f}{2|\nabla f|}(g_{ab}).
\end{equation}
By Proposition \ref{propvanishT}, $|\nabla f|$ is constant on $\Sigma,$ which implies that
\begin{equation}
\label{lemcvanisheq4}[\partial_a,\nabla f]=0.
\end{equation}
Since $\big\langle \frac{\nabla f}{|\nabla f|},\partial_{a}\big\rangle=0,$ we conclude $\nabla_{\frac{\nabla f}{|\nabla f|}}\frac{\nabla f}{|\nabla f|}=0.$ Hence, we can use (\ref{lemcvanisheq4}) to arrive at
\begin{eqnarray*}
\frac{1}{|\nabla f|^2}R(\nabla f,\partial_a,\nabla f,\partial_b)&=&\frac{1}{|\nabla f|}\langle\nabla_{\frac{\nabla f}{|\nabla f|}}\nabla_{a}\partial_{b}-\nabla_{a}\nabla_{\frac{\nabla f}{|\nabla f|}}\partial_b,\nabla f\rangle\nonumber\\
&=&\frac{1}{|\nabla f|^2}\langle\nabla_{\nabla f}\big(\nabla_{a}^{\Sigma}\partial_b+\nabla_{a}^{\perp}\partial_b\big),\nabla f\rangle- \frac{1}{|\nabla f|}\langle\nabla_{a}\nabla_{\frac{\nabla f}{|\nabla f|}}\partial_b,\nabla f\rangle\nonumber\\
&=&\frac{\nabla f}{|\nabla f|}(h_{ab})+h_{ac}h^{c}_{b}\nonumber.
\end{eqnarray*}
From this, we deduce
\begin{equation}
\label{9990}
\frac{1}{|\nabla f|^2}R(\nabla f,\partial_a,\nabla f,\partial_b)=\frac{\nabla f}{(n-1)|\nabla f|}H g_{ab}-\frac{H^2}{(n-1)^2}g_{ab}.
\end{equation}
In particular, taking the trace in (\ref{9990}) with respect to $a$ and $b$ we have $$\frac{1}{|\nabla f|^2}Ric(\nabla f,\nabla f)=\frac{\nabla f}{|\nabla f|}H-\frac{H^2}{(n-1)}$$ and then (\ref{9990}) can be written as
\begin{equation}\label{sol}
R(\nabla f,\partial_a,\nabla f,\partial_b)=\frac{Ric(\nabla f,\nabla f)}{(n-1)}g_{ab}.
\end{equation} By using Proposition \ref{propvanishT} we have $$\frac{1}{|\nabla f|^2}Ric(\nabla f,\nabla f)=\lambda$$ and $$Ric(\partial_a,\partial_b)=\mu g_{ab},$$ for $a,b\geq2$.
Therefore, substituting (\ref{sol}) in (\ref{lemcvanisheq2}) we get
\begin{eqnarray*}
fC_{1ab}&=&-\frac{1}{|\nabla f|^{2}}W(\nabla f,\partial_a,\nabla f,\partial_b)\\
&=&-\frac{1}{|\nabla f|^{2}}\frac{Ric(\nabla f,\nabla f)}{(n-1)}g_{ab}+\frac{1}{|\nabla f|^2}\frac{Ric(\nabla f,\nabla f)}{(n-2)}g_{ab}+\frac{R_{ab}}{(n-2)}-\frac{R}{(n-1)(n-2)}g_{ab}\\
&=&-\frac{\lambda}{(n-1)}g_{ab}+\frac{\lambda}{(n-2)}g_{ab}+\frac{\mu}{(n-2)}g_{ab}-\frac{\lambda+(n-1)\mu}{(n-1)(n-2)}g_{ab}\\
&=&0,
\end{eqnarray*} which completes our claim.
Finally, we have $fC_{ijk}=0$ at a point $p$ where $\nabla f(p)\neq0.$ Therefore, we use Lemma \ref{lemTCW} to conclude that $fC_{ijk}\equiv0$ in $M^n.$ Using this we obtain $C_{ijk}\equiv0$ in $M\backslash{\partial M}$ and then the proof of the lemma follows from the continuity of the Cotton tensor .
\end{proof}
To finish this section, we shall present a fundamental integral formula.
\begin{lemma}\label{propBT}
Let $(M^n,g,f)$ be a Miao-Tam critical metric. Then
\begin{equation*}
\int_{M}f^2B(\nabla f,\nabla f)dM_{g}=-\frac{1}{2(n-1)}\int_{M}f^2|T|^2 dM_{g}.
\end{equation*}
\end{lemma}
\begin{proof}
From (\ref{cottonwyel}) we can write the Bach tensor as
$$B_{ij}=\frac{1}{n-2}\left(\nabla_{k}C_{kij}+R_{kl}W_{ikjl}\right).$$ Under this notation we get
\begin{eqnarray*}
f^2B_{ij}&=&\frac{1}{n-2}\left(f^2\nabla_k C_{kij}+f^2 R_{kl}W_{ikjl}\right)\\
&=&\frac{1}{n-2}\big(\nabla_k\left(f^2C_{kij}\right)-2fC_{kij}\nabla_{k}f+f^2R_{kl}W_{ikjl}\big).
\end{eqnarray*}
We now use Lemma \ref{lemTCW} jointly with (\ref{cottonwyel}) to obtain
\begin{eqnarray*}
f^2B_{ij}&=&\frac{1}{n-2}\left(\nabla_k\left[f(W_{kijl}\nabla_{l}f+T_{kij})\right]-2fC_{kij}\nabla_{k}f+f^2R_{kl}W_{ikjl}\right)\\
&=&\frac{1}{n-2}\big(\nabla_k\left(fT_{kij}\right)+f\nabla_{k}W_{kijl}\nabla_{l}f+fW_{kijl}\nabla_{k}\nabla_{l}f\\
&&+W_{kijl}\nabla_{k}f\nabla_{l}f-2fC_{kij}\nabla_{k}f+f^2R_{kl}W_{ikjl}\big)\\
&=&\frac{1}{n-2}\Big(\nabla_{k}\left(fT_{kij}\right)+\frac{n-3}{n-2}fC_{jki}\nabla_{k}f+f\left(\nabla_{k}\nabla_{l}f-fR_{kl}\right)W_{kijl}\\
&&+W_{kijl}\nabla_{k}f\nabla_{l}f+2f C_{ikj}\nabla_{k}f\Big).
\end{eqnarray*}
We recall that the Weyl tensor is trace-free on any pair of indices. Next, by using (\ref{fundeqtens}) we deduce
\begin{equation*}
f^2B_{ij}=\frac{1}{n-2}\Big[\nabla_{k}(f T_{kij})+\frac{n-3}{n-2}fC_{jki}\nabla_{k}f+2fC_{ikj}\nabla_{k}f+W_{kijl}\nabla_{k}f\nabla_{l}f\Big].
\end{equation*}
Whence, we obtain
\begin{equation}
\label{123456}
f^2B(\nabla f,\nabla f)=\frac{1}{n-2}\nabla_{k}\left(fT_{kij}\right)\nabla_{i}f\nabla_{j}f.
\end{equation} On the other hand, we notice that $$\nabla_{k}\left(fT_{kij}\right)\nabla_{i}f\nabla_{j}f=\nabla_{k}\left(fT_{kij}\nabla_{i}f\nabla_{j}f\right)- fT_{kij}\nabla_{k}\nabla_{i}f\nabla_{j}f-fT_{kij}\nabla_{i}f\nabla_{k}\nabla_{j}f.$$ Now, on integrating (\ref{123456}) over $M$ and using Stokes formula we arrive at
\begin{eqnarray*}
\int_M f^2 B(\nabla f,\nabla f)dM_{g}
&=&-\frac{1}{n-2}\left(\int_M fT_{kij}\nabla_{k}\nabla_{i}f\nabla_{j}f dM_{g}+\int_M fT_{kij}\nabla_{i}f\nabla_{k}\nabla_{j}fdM_{g}\right)\\
&=&-\frac{1}{n-2}\left(\int_M f^2T_{kij}R_{ki}\nabla_{j}f dM_{g}+\int_M f^2T_{kij}R_{kj}\nabla_{i}fdM_{g}\right),
\end{eqnarray*}
in the last equality we have used once more (\ref{fundeqtens}). Finally, we change $k$ by $i$ above and then using the properties of $T$ defined in (\ref{T}) we achieve
\begin{eqnarray*}
\int_M f^2 B(\nabla f,\nabla f)dM_{g}&=&-\frac{1}{2(n-2)}\left(\int_M f^2T_{kij}R_{ki}\nabla_{j}f dM_{g}+\int_M f^2T_{kij}R_{kj}\nabla_{i}fdM_{g}\right)\\
&&-\frac{1}{2(n-2)}\left(\int_M f^2T_{ikj}R_{ik}\nabla_{j}f dM_{g}+\int_M f^2T_{ikj}R_{ij}\nabla_{k}f dM_{g}\right)\\
&=&\frac{1}{2(n-2)}\int_M f^2T_{ikj}\left(R_{kj}\nabla_{i}f-R_{ij}\nabla_{k}f\right)dM_{g}\\
&=&-\frac{1}{2(n-1)}\int_M f^2|T|^2 dM_{g},
\end{eqnarray*}
that was to be proved.
\end{proof}
\section{Proof of the Results}
\subsection{Proof of Theorem \ref{thm1}}
\begin{proof}
First, since $M^4$ satisfies $\int_M f^2B(\nabla f,\nabla f)dM\geq 0$ we invoke Lemma \ref{propBT} to conclude that $T\equiv0.$ Therefore, from Lemma \ref{lemcvanish} we have $C\equiv0.$ Hence, we use Lemma \ref{lemTCW} to obtain
\begin{equation*}
W_{ijkl}\nabla^{l}f=0.
\end{equation*}
We now consider a point $p\in M^4$ such that $\nabla f (p)\neq0.$ Choosing an orthonormal frame $\{ e_1, e_2, e_3, e_4\}$ with $e_1=\frac{\nabla f}{|\nabla f|}$ at the point $p$ we arrive at
\begin{equation}
\label{123er}
W_{ijk1}=0,
\end{equation} for all $1\le i,\,j,\,k\le 4.$
We now claim that $W_{ijkl}=0$ whenever $\nabla f (p)\neq 0.$ Indeed, recalling that the Weyl tensor is trace-free on any pair of indices, we have
\begin{equation*}
W_{2121}+W_{2222}+W_{2323}+W_{2424}=0.
\end{equation*} By using (\ref{123er}) we have $$W_{2323}=-W_{2424}.$$ In a similar way we have $$W_{2424}=-W_{3434}=W_{2323}.$$ From here it follows that $W_{2323}=0.$ Moreover, we also have
\begin{equation*}
W_{1314}+W_{2324}+W_{3334}+W_{4344}=0.
\end{equation*} Therefore, $W_{2324}=0.$ This proves that $W_{abcd}=0$ unless $a,b,c,d$ are all distinct. But, there are only three choices for the indices. This concludes the proof of our claim.
Hereafter, choosing appropriate coordinates (e.g. harmonic coordinates) we conclude that $f$ and $g$ are analytic, see for instance Theorem 2.8 in \cite{Corvino} (or Proposition 2.1 in \cite{CEM}). Whence, we conclude that $f$ can not vanish identically in a non-empty open set. So, the set of regular points is dense in $M^4.$ This allows us to conclude that $M^4$ is locally conformally flat and we are in position to use Theorem \ref{theoremMT} (see also Theorem 1.2 of \cite{miaotamTAMS}) to conclude that $(M^4 ,\,g)$ is isometric to a geodesic ball in a simply connected space form $\Bbb{R}^{4},$ $\Bbb{H}^{4}$ or $\Bbb{S}^{4}.$ This is what we wanted to prove.
\end{proof}
\subsection{Proof of Theorem \ref{thm2}}
\begin{proof}
The first part of the proof will follow \cite{CCCMM}. To begin with, we consider $(M^3,\,g,\,f)$ be a simply connected, compact Miao-Tam critical metric with boundary isometric to a standard sphere $\Bbb{S}^2.$ Next, we recall that the Cotton tensor can be written as $C_{ijk}=\nabla_iA_{jk}-\nabla_{j}A_{ik}.$ From here it follows that
\begin{eqnarray*}
\nabla_iB_{ij}&=&\nabla_i\nabla_k C_{kij}\\
&=& \big(\nabla_i\nabla_k-\nabla_k\nabla_i\big)\nabla_k A_{ij}.
\end{eqnarray*}
Whence, the previous commutator term implies $$\nabla_iB_{ij}=-R_{il}\nabla_{l}A_{ij}+R_{kl}\nabla_{k}A_{lj}+R_{ikjl}\nabla_kA_{il}$$ and then we get
\begin{eqnarray}
\label{n1}
\nabla_iB_{ij}=R_{ikjl}\nabla_kA_{il}.
\end{eqnarray}
We now remember that $W\equiv 0$ in dimension three. So, a straightforward computation involving (\ref{WS}) and (\ref{n1}) gives
\begin{eqnarray}
\label{n2}
\nabla_iB_{ij} \nabla_{j} f &=&A_{ik}C_{kji}\nabla_{j} f+A_{ik}\nabla_jA_{ki}\nabla_{j} f+A_{jl}\nabla_iA_{il}\nabla_{j} f\nonumber\\
&&-A_{il}\nabla_jA_{il}\nabla_{j} f-A_{jk}g_{il}C_{kil}\nabla_{j} f-A_{jk}g_{il}\nabla_iA_{kl}\nabla_{j} f\nonumber\\
&=&-R_{ik}C_{jki}\nabla_{j} f\nonumber\\
&=&-\frac{1}{2}\left(C_{jki}R_{ik}\nabla_jf+C_{kji}R_{ij}\nabla_kf\right),
\end{eqnarray} where we have used that $C$ is skew-symmetric in the first two indices and that $C$ is trace-free in any two indices. Now, we combine (\ref{n2}) with (\ref{T}) to deduce
\begin{eqnarray*}
(div B)(\nabla f)&=&\frac{1}{2}C_{kji}\left(R_{ik}\nabla_jf-R_{ij}\nabla_kf\right)\\
&=&\frac{1}{4}C_{kji}T_{kji}.
\end{eqnarray*} Using once more that $W\equiv 0$ jointly with Lemma \ref{lemTCW} we arrive at $$(div B)(\nabla f)=\frac{f}{4}|C|^2.$$ Therefore, our assumption together with the continuity of the Cotton tensor implies $C\equiv 0$ in $M^3$ and then $(M^3,\,g)$ is locally conformally flat. Finally, it suffices to use Theorem \ref{theoremMT} to get the promised result.
\end{proof}
\begin{acknowledgement}
The authors want to thank the referees for their careful reading and helpful suggestions.
The third author would like to thank Huai-Dong Cao for valuable conversations about Bach-flat metrics. He would like to extend his special thanks to Pengzi Miao for helpful conversations about critical metrics. Moreover, he wish to express his gratitude for the excellent support during his stay at ICTP-Italy, where part of this work was started. Finally, he wishes to thank the Department of Mathematics - Lehigh University for the warm hospitality and for the fruitful research environment.\end{acknowledgement}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,113 |
When a relic from his past is rediscovered, folklore professor Jeremy Bradshaw puts his life on hold to solve the mystery. Along the way, he's helped by people who challenge everything he believes in, and ultimately tries to answer the question: can the past be rewritten? A supernatural thriller for your ears, starring Misha Collins, Melissa Ponzio, and Alan Tudyk. Created by Aaron Mahnke and written by Lauren Shippen.
Introducing Bridgewater
July 29, 2021 • 1 min
When a relic from his past is rediscovered, folklore professor Jeremy Bradshaw puts his life on hold to solve the mystery. Along the way, he's helped by people who challenge everything he believes in, and ultimately tries to answer the question: can the past be rewritten? Starring Misha Collins, Melissa Ponzio, and Nathan Fillion. Created by Aaron Mahnke and written by Lauren Shippen.
Learn more about your ad-choices at https://ww...
Chapter 1: Remnants
August 6, 2021 • 29 min
When a strange new piece of evidence appears in the 40 year old cold case of missing police officer, Thomas Bradshaw, his son Jeremy is pulled back into the mystery of his own past.
Learn more about your ad-choices at https://www.iheartpodcastnetwork.com
Chapter 2: An Untamed Place
Jeremy and Vipin, his TA, investigate the location where Thomas' badge was found but discover something else entirely.
Chapter 3: Stories
August 13, 2021 • 26 min
Following the trail in their own ways, Jeremy and Anne each uncover new information that promises to add new pieces to the larger puzzle.
Chapter 4: Forgotten Words
Jeremy and Vipin recruit an ally with an unusual connection, but new evidence makes it clear that the stakes are higher—and more deadly—than they first believed.
Chapter 5: Messages
Jeremy and Anne find more than they were expecting in the woods, and it sets them on a dangerous quest for answers from the past. The biggest challenge of all, though, will be keeping an open mind.
Chapter 6: A Little Lost
September 3, 2021 • 28 min
Using their connections at the police station, Jeremy and Anne meet a key witness with a frightening claim. The mystery creeps closer, though, when an ally calls for help. But will it be too late?
Chapter 7: The Real Monsters
When faced with strange evidence from Vipin's encounter in the woods, Jeremy and Anne find themselves at odds over its true meaning, and their conflict threatens to bring an end to their work.
Chapter 8: Ee Wah Chu
The search for Ethan sets everyone on edge, and old grievances return to the surface. But will they find the boy, or something more?
Chapter 9: The Unseen Things
Ethan's experience in the forest proves that blood is indeed thicker than water, but to find it, you have to dig deep. Just be careful what you wish for.
Chapter 10: Blood & Water
It will all happen again. Old wrongs will be set right, answers will be found in the most unlikely places, and the past will refuse to let go.
Bridgewater: Season 2 - Official Trailer
January 6, 2023 • 1 min
The smash hit supernatural audio thriller from Aaron Mahnke and Lauren Shippen returns for a blistering second season. Old wounds have been opened, and the future now hangs in the balance. Starting Misha Collins, Melissa Ponzio, Alan Tudyk, Karan Soni, and Tricia Helfer
Chapter 11: The In Between
January 13, 2023 • 28 min
Once one impossible thing has happened, it feels the world could come apart at the seams. Folklore professor Jeremy Bradshaw does his best to hold himself together after getting everything he's always wanted and having his entire worldview shattered in the process.
Chapter 12: Second Chances
Reunions continue, introductions are made, and monsters are confronted. The Bradshaw-Beckers hope they are at the end of their rocky journey, but they may just be at the beginning of something else.
Chapter 13: Bells & Rings
Eviscerations abound, but a new friend is made. Meanwhile, Vipin and Olivia make a connection.
Chapter 14: Borrowing Trouble
Thomas does his best to adapt to the modern world as Anne and Jeremy worry over what comes next. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,516 |
Манино — деревня в Калужской области, находится в северо-западной части Медынского района, на границе с Московской областью. Входит в состав сельского поселения «Село Передел»
История
Согласно Плану генерального межевания Калужской губернии от 1782 года на месте Манина располагалось пустошь Минеево Катерины Ивановны Савеловой, Евдокима Алексеевича Щербинина (деда Дениса Даывдова) и Николая Ивановича Колычёва.
Деревня относилась к приходу соседнего села Дунино.
В «Списке населённых мест Калужской губернии по сведениям 1863 года» указана как владельческая деревня Манина при безымянном ручье по правую сторону тракта из Медыни в Гжатск, в которой насчитывалось 18 дворов и 111 жителей. После земельной реформы вошла в Дунинскую (позже Незамаевскую) волость Медынского уезда. На 1897 год население деревни составляло 131 человек, а на 1914 год — 161 человек.
Примечания
Незамаевская волость | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,877 |
Q: Add horizontal padding to TextEditor but prevent it from shifting scrollbar inside as a result I'm using a TextEditor that I'd like to include horizontal padding for, so that the text doesn't stick to either edge. However, the problem is if I include it, and the text within is scrollable, then the scrollbar is not positioned to the far-right, but has instead been moved inside by the padding amount.
TextEditor(text: $text)
.background(Color.white)
.foregroundColor(Color.black)
.frame(maxWidth: .infinity, maxHeight: .infinity)
.customFont(.body)
.lineSpacing(8)
.padding(.leading)
.padding(.trailing)
A: You added padding to external frame, but need to indent internal text container. The possible solution (as TextEditor is actually UITextView) to use appearance. So the solution would be to add the following in parent view of TextEditor
init() {
UITextView.appearance().textContainerInset =
UIEdgeInsets(top: 0, left: 12, bottom: 0, right: 12) // << !!
}
// ... other code
TextEditor(text: $text)
.background(Color.white)
.foregroundColor(Color.black)
.frame(maxWidth: .infinity, maxHeight: .infinity)
.customFont(.body)
.lineSpacing(8)
Tested with Xcode 12 / iOS 14
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,453 |
Your next new car: cheaper to buy or lease?
Sales of new cars are booming again – but is buying really best? We crunch the numbers.
Much of the demand was from private buyers rather than firms, the Society of Motor Manufacturers & Traders said as it published the data on Friday.
Buying a new car might help the wider economy – one in seven bought here is built here – but from the point of view of your personal finances, it isn't necessarily the best route.
Personal leasing, when you rent the vehicle for two or three years then hand it back, is growing in popularity. In the United States, where it is established, it accounts for one in four vehicles in private use. And there are other ways to finance your wheels, as explained here.
Should I buy a discontinued car?
Prices of new models, even where the spec is identical, differ widely. The What Car? website is an excellent buyers' resource, as it lists "target" prices based on different models' actual sales prices across many outlets. The prices it publishes indicate the upper end of your spend and it says "in most cases you should be able to get an even better deal". It lists prices of virtually all models' versions and so, for instance, currently shows target prices for 40 Ford Fiestas. Ford's brochure prices for these models range from £9,995 to £17,995. By contrast, the target prices listed by What Car? – based on achievable discounts, which you should hope to better – range from £9,501 to £16,819.
The principle with leasing is that your monthly payments cover the cost to the lease operator of the vehicle's fall in value while you rent it, plus their profit. That's why it's surprisingly cheap to lease upmarket makes such as Mercedes-Benz or Volvo or special editions of other marques expected to hold their "residual" value. Other factors affect depreciation, such as fuel efficiency and tax. When tax or fuel goes up, gas guzzlers depreciate faster.
The significance of a vehicle's expected depreciation also explains why the mileage conditions in a lease contract can be punitive. Heavy mileage devalues cars faster, and so lease terms, generally of 24 or 36 months, include mileage limits (typically 10,000 per year) and penalties if these are topped. Leasing is good for those wanting comfortable or eye-catching vehicles – but not if they are going to rack up serious mileage.
Lease deals require a down payment, usually calculated as a multiple of the monthly rent. A bigger initial payment (for instance, equivalent to nine months rather than six) reduces the subsequent monthly payments. There is usually a choice.
Take a current best-buy, 24-month personal-use lease on an automatic, diesel, four-door Mercedes C-Class Sport Saloon. Your initial payment would be £2,293.20, which is nine times the following 23 months' payments of £254.80. An arrangement fee of £230 also applies. You get a limit of 10,000 miles per year. After 24 months, your use of this car – excluding insurance, fuel, and so on – has cost you £8,383.60.
Say you bought it. The brochure price is slightly less than £33,000 and What Car? gives a target price of £28,700. Motoring organisation the AA puts average depreciation across all makes at 20pc per year – although this average figure works best over long periods of ownership because in the first year the vehicle's value can slump by anything between 10pc and 40pc, it says. Assuming a 20pc depreciation from the target price, owning this Merc would have cost you £11,480 after two years. To come out financially better than you would under the lease arrangement, the car would need to lose about 30pc or less of its value in the period.
The lease operator profits from the discount it achieves.
If you don't pay cash or lease, you will have to borrow in some form. Most dealers offer hire-purchase (HP) arrangements in which after an agreed term of monthly payments the vehicle is yours. On a monthly basis, HP works out at roughly two to three times the cost of leasing. With HP, the depreciation and the interest rate are crucial factors.
More complex are personal contract purchase (PCP) schemes, which are a marriage of HP and leasing. You pay a lower deposit and lower monthly outgoings and then, at the term's end, you can own the vehicle by paying a final "balloon" payment, roll on to a better car with the same dealer or finance provider, or simply walk away. It's cheaper than HP but typically dearer than leasing. Dealers encourage the take-up of PCPs as, in practice, drivers stay and upgrade. But from the driver's point of view, the value of PCP is hard to assess because of the number of factors at play.
The price of the car itself and the cost of the financing arrangements used – if any – are not the only considerations. Another is insurance, especially if the drivers are young. Alan West, who has experience of various forms of vehicle ownership through his work as an electrician, has recently helped his daughter Olivia, a student, buy a new Vauxhall Corsa through specialist younger-driver firm Marmalade.
The vehicle cost £10,000 and Mr West put £1,000 down. The arrangement involved cashback of £2,600, paid on the basis that the driver also insured with Marmalade, which uses "black box" satellite technology to track drivers' usage as a means of reducing cost. In the case of Olivia, who is 19, the premium is £1,460 – about half the premiums quoted on the same vehicle when she and her father checked elsewhere.
Olivia pays £210 per month over a four-year term, at the end of which she can opt to pay an outstanding lump sum to own the car – Mr West expects this to be around £4,000 – or upgrade to another vehicle. She could also simply hand the vehicle back and have no further financial obligations. But the reduced insurance premiums were the real draw.
"Insurance savings over the period will probably outweigh other factors," Mr West said. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,578 |
Q: Monitorar arquivo e ou diretório Tenho esse método que efetua a leitura do arquivo
const fs = require('fs');
const path = require('path');
let arquivo = path.join(__dirname, 'arquivo.txt');
fs.readFile(arquivo, { encoding: 'utf-8' }, function(err, data) {
if (!err) {
// Retorna o conteúdo do arquivo.txt
console.log(data);
} else {
// Retorna o erro
console.log(err);
}
});
Tenho a necessidade de monitorar qualquer alteração feita nesse arquivo e ou diretório e retornar a ultima alteração feita, é possível ?
A: Atualização 1
Monitorar aquivos e diretórios utilizando a biblioteca node-watch.
let watch = require('node-watch');
watch(['arquivo.txt', 'teste/', 'teste/arquivo.txt'], console.log);
Veja funcionando em repl.it
Através dos comentários encontrei o pacote Chokidar e obtive o resultado.
const chokidar = require('chokidar');
const fs = require('fs');
let conteudo_anterior = '';
let arquivo = 'arquivo.txt';
// Faz a leitura inicial
fs.readFile(arquivo, { encoding: 'utf-8' }, function(err, data) {
if (!err) {
let linhas = data.trim().split('\n');
// Retorna o conteúdo
linhas.forEach(function(linha) {
console.log(linha);
conteudo_anterior = linha;
});
} else {
// Retorna o erro
console.log(err);
}
});
// Monitora o arquivo
let watcher = chokidar.watch(arquivo, { persistent: true });
watcher.on('change', (path, stats) => {
if (stats) {
fs.readFile(path, { encoding: 'utf-8' }, function(err, data) {
if (!err) {
let linhas = data.trim().split('\n');
// Última linha
let ultima = linhas.slice(-1)[0];
// Verifica se a linhas tem conteúdo.
// Se tiver conteúdo e se o conteúdo é diferente do anterior, caso contrário nada faz.
(ultima.length > 0 && ultima != conteudo_anterior) ? console.log(ultima) : '';
conteudo_anterior = ultima;
} else {
// Retorna o erro
console.log(err);
}
});
}
});
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,816 |
\section{Introduction} \label{sec:intro}
WDs are assigned to several subtypes according to the major components of the surface atmosphere.
If normally broad Balmer lines appear in a spectrum, it is DA WD.
Similarly, He {\small \bf I}, He {\small \bf II}, Ca {\small \bf II} H \& K and C line for DB, DO, DZ, and DQ respectively \citep{2013ApJS..204....5K}.
Approximately 1.3 million targets were selected from {\it Gaia} Early Data Release (EDR) 3 \citep{2021A&A...649A...1G}, considered to be the candidates of WD \citep{2021arXiv210607669G}.
These candidates were derived by several selection criteria in absolute magnitude, color, etc. from {\it Gaia} EDR3 catalog.
The samples of spectroscopically confirmed SDSS WDs were also adopted to calculate probabilities of being a WD ($P_{\rm WD}$).
Up to nearly 7 million objects, LAMOST \citep{2015RAA....15.1095L} released its 7th data product (Data Release 7, DR7) that included more than 10 million low resolution spectral data.
In this research, we aimed to identify WD candidates of {\it Gaia} EDR 3 using spectra from LAMOST DR7.
\section{Data Selection} \label{sec:data}
We performed a cross-match of WD candidates with LAMOST spectral data onto equinox 2000 and epoch 2000 within $3^{\prime\prime}$ utilizing formula \ref{eq:dis}, where $\alpha$ and $\delta$ represent right ascension and declination respectively.
\begin{equation} \label{eq:dis}
d = \arccos[\cos \delta 1 \cos \delta 2 \cos(\alpha 1-\alpha 2)+\sin \delta 1 \sin \delta 2]
\end{equation}
Considering a LAMOST fiber diameter of $3^{\prime\prime}$ \citep{2015RAA....15.1095L}, the cross radius $d$ was also restricted to $3^{\prime\prime}$.
The accuracy of fiber positioning, on the other hand, had been determined to be no more than $1.5^{\prime\prime}$ on average \citep{2014SPIE..9149....1}.
We start the cross-match procedure based on sky coordinates by using both radii.
The conclusions of this research were based on radius $3^{\prime\prime}$, while a specific field presented in our catalog was used to mark the data if it was more than $1.5^{\prime\prime}$ away from any source of {\it Gaia}.
Moreover, these data that had positive values of offset were dismissed as the inconsistent between observation position and the coordinates from the input catalog.
We then derived 18 232 spectra.
Among all the 1.4 million WD candidates from {\it Gaia}, there existed 12 046 that corresponded with LAMOST spectra.
We also inspected 5.8 million spectra of SDSS DR16 \citep{2020ApJS..249....3A} and calculated the distances between them and our data sample.
Half of the objects of LAMOST's sample were not observed by SDSS yet, they needed to be verified even more.
\section{Identification} \label{sec:identity}
We adopted the same procedure described in \cite{2018PASP..130h4203K} to remove those that had little evidence of spectral lines.
9 496 spectra remained after the machine learning process.
Afterwards, we inspected all the results and rejected those that had little evidence to be a WD and maintained 8 465 spectra of 6 190 objects.
The number of targets would reduce to 6 045 if the radius was fixed at $1.5^{\prime\prime}$.
Meanwhile, these small samples of spectra that located between $1.5^{\prime\prime}$ and $3^{\prime\prime}$ exhibited no characteristics distinct from those within the radius of $1.5^{\prime\prime}$.
During the inspection, all the WD spectra were classified into detailed types, including but not limit of DAB and DBZ.
Considering the $P_{\rm WD}$ from \cite{2021arXiv210607669G}, about 75\% of the spectral confirmed WD objects had values greater than 0.9.
As for the other spectra that may not be WDs, the $P_{\rm WD}$ was relatively lower.
Around 68\% of them were less than 0.5, while 23\% larger than 0.9.
This is partly due to poor quality that we were unable to discover any line features in a spectrum and discard it from our sample.
In the other hand, they might be DC WD that could not be verified by spectra alone.
52 objects with 59 spectra were composed of 2 stellar systems, usually a WD plus a late-type star.
We utilized LAMOST 1D Pipeline to recognize the other components by template fitting and found the majority of them WD plus M.
Interestingly, 64 cataclysmic variables (CVs) \citep{1995cvs..book.....W}, with 49 had obvious double peak structure among their emission Balmer or He lines, were intermixed in our sample.
Most of them had traces of helium in their spectra.
\section{Stellar Parameters} \label{sec:param}
Applying spectral templates for DA and DB \citep{2010MmSAI..81..921K}, we calculated atmosphere parameters of the WD spectra.
In the beginning, all spectral samples were moved to rest-frame relying on the redshift derived from LAMOST 1D Pipeline.
Following the determination of best-fit model, LM were adopted to estimate $T_{\rm eff}$, $\log g$ ~and their uncertainty.
The depth of lines of several spectra with relatively low signal-to-noise ratio, though, were almost the same intensity as noise.
The parameters of these data went out of bounds of the template scope and were to reset to -9999 manually.
\section{Summary}
We present a catalog of spectral confirmed WDs from LAMOST DR7 based on the candidates from {\it Gaia} EDR3.
The full {\it Gaia}-LAMOST spectroscopic sample catalog contains the main information (see Table \ref{tab:catalog}) of WDs and can be downloaded following link: \url{http://paperdata.china-vo.org/XiaoKong/LAMOST_DR7_WD.fits}
\begin{deluxetable*}{ll}
\tablenum{1}
\tablecaption{Format of the LAMOST DR7 Catalog of spectral confirmed WDs.\label{tab:catalog}}
\tablewidth{0pt}
\tablehead{
\colhead{Heading} & \colhead{Description}
}
\startdata
O{\scriptsize BSID} & Unique ID of a spectrum \\
S{\scriptsize OURCE\_ID} & Unique ID for this object in {\it Gaia} EDR3 \\
W{\scriptsize D\_NAME} & LAMOSTJ+J2000 ra (hh mm ss:ss)+dec(dd mm ss.s), equinox and epoch 2000 \\
RA & Right ascension [deg] of object \\
DEC & Declination [deg] of object \\
T{\scriptsize YPE} & Detailed classes for WDs from LAMOST \\
SNR & Signal-to-noise ratio of $u$, $g$, $r$, $i$ and $z$ filter \\
RV & Radial velocity [km/s] of object from template fitting \\
$T_{\rm eff}$ & Effective temperature [K] from fitting the parameter model \\
$\log g$ & Surface gravity from fitting the parameter model \\
N\_{\scriptsize BIB} & Number of references that confirmed type (identify for the first time if 0) \\
R{\scriptsize AD} & 1 means distance between this spectrum and {\it Gaia} source smaller than $1.5^{\prime\prime}$ \\
\enddata
\tablecomments{This catalog involves WD and CV information both. -9999 means the value can not be provided.}
\end{deluxetable*}
Starting from cross-matching spectral data of LAMOST with sources of {\it Gaia}, we identified 8 465 WD spectra, involving DA, DB, DO, DZ, etc.
Some other types, binary or CV for instance, were also noted.
These objects corresponded with 6 190 {\it Gaia} targets.
1 496 stars of our samples were spectral confirmed for the first time.
We then found the best model that fits a spectrum and estimated the atmosphere parameter using LM.
\begin{acknowledgments}
We thank J.K. Zhao and D. Koester for providing the parameter templates for DA and DB WD.
These models were made by D. Koester ranging from 5 000 K to 80 000 K and 7.0 to 9.5 for $T_{\text{eff}}$ and $\log g$ respectively.
This work has made use of data from the European Space Agency (ESA) mission
{\it Gaia} (\url{https://www.cosmos.esa.int/gaia}), processed by the {\it Gaia}
Data Processing and Analysis Consortium (DPAC,
\url{https://www.cosmos.esa.int/web/gaia/dpac/consortium}). Funding for the DPAC
has been provided by national institutions, in particular the institutions
participating in the {\it Gaia} Multilateral Agreement.
Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences.
\end{acknowledgments}
\vspace{5mm}
\facilities{{\it Gaia}, LAMOST}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 795 |
Uber and Moderna partner on COVID-19 vaccine access and information
NOVOSIBIRSK, RUSSIA - NOVEMBER 20, 2020: A taxi driver wears a protective mask in a car amid the COVID-19 pandemic. Kirill Kukhmar/TASS (Photo by Kirill KukhmarTASS via Getty Images)
Uber and pharmaceutical company Moderna have announced a partnership around COVID-19 vaccination, which will include a number of different initiatives. To start, its only confirmed component is to provide users with credible, factual information about COVID-19 vaccine safety through Uber's consumer app, but the companies have also discussed additional "options," including building ride scheduling via Uber directly into the immunization appointment booking process.
Still in its early days, the U.S. COVID-19 vaccination program is already beset with challenges, including providing timely access to vaccines to swaths of the population who need it most. The inoculation program also has to contend with significant misinformation proliferating on social media about vaccine safety, and any app with the surface area of something like Uber has a chance to get positive messages and accurate information in front of a lot of people, so that's good news on its own.
Healthvana's digital COVID-19 vaccination records are about communication, not passports for the immune
But one of the very real challenges to an effective vaccination campaign remains logistical, and getting people to make their initial and follow-up appointments for the first round of the Moderna vaccine, and its second shot booster, is a bigger challenge than many might suspect. I spoke to Healthvana CEO Ramin Bastani about their work with LA County on creating an immunization record that integrates with Apple Wallet to provide patients with timely info and reminders about vaccination appointments, but integrating a ride-booking service or appointment reminder directly in the Uber app that most users already have on their phone anyway could be another very effective way to increase success rates for first and follow-up inoculation visits.
FDA authorizes Moderna's COVID-19 vaccine for emergency use
Uber has already offered up free and discounted rides to help lower the friction of actually going out and getting a vaccine, but a product-level integration could do a lot more than that by providing easy, user-friendly access. As noted, this is still just one of the options being discussed, but if Uber and Moderna are willing to commit it to print, that at least means they're serious about trying to find a way. We're holding them to account, too, so rest assured we'll follow up on their progress as this collaboration develops.
KBRA Releases Research – The Price of Uncertainty: Final General QM Rule and Its Potential Credit Implications
Ready-to-use Therapeutic Food Markets: Solid, Semi-Solid Paste and Drinkable Therapeutic Food - Global $622.2 Million Market Trajectory & Analytics to 2027 - ResearchAndMarkets.com
Urban Air Awarded Top Industry Rankings
President Donald Trump commuted the sentence of Billy Walters, a Vegas gambler convicted of insider trading. Walters had ties to Phil Mickelson and the support of others in golf.
The "Ready-to-use Therapeutic Food - Global Market Trajectory & Analytics" report has been added to ResearchAndMarkets.com's offering.
Kroll Bond Rating Agency (KBRA) discusses the changes to the final Qualified Mortgage (QM) Rule issued by the Consumer Financial Protection Bureau (CFPB) in December 2020. We also evaluate the potential effects of the rule on origination, RMBS issuance, and credit risks.
Leading Tech Repair Franchise to Accelerate Store and Mobile Repair Growth in 2021 uBreakiFix by Asurion uBreakiFix Rounds Out 2020 With 611 Locations, Lands #18 Spot on 2021 Franchise 500® List ORLANDO, Fla., Jan. 20, 2021 (GLOBE NEWSWIRE) -- uBreakiFix, a leading franchise in the tech repair industry, announced substantial growth in the fourth quarter of 2020 with 22 new locations, bringing the brand's total footprint to 611 stores across North America. From Jan. 1 to Dec. 31, uBreakiFix opened a total of 67 locations, pointing to notable development in California which now boasts 52 stores, Texas with 56, and Florida—the brand's home state—with 83. uBreakiFix also closed the year with more than 600 mobile repair vehicles on the road, bringing its professional phone repair services straight to customers' doorsteps. This 'We Come to You' service, in addition to curbside and mail-in services, enabled uBreakiFix to continue supporting customers in new, safe, and convenient ways amidst the pandemic. uBreakiFix plans to continue growing its 'We Come to You' footprint in 2021. "Although 2020 brought its own set of unique challenges, I'm proud of our ability to not only remain focused on growth but meet our customers where they are in this season," said uBreakiFix President and Co-Founder Justin Wetherill. "Behind the steady uptick in new stores and 'We Come To You' vehicles, you'll find a committed group of partners, franchisees, and team members whose number one priority is to continually improve the repair experience." In Q2 of 2020, uBreakiFix worked with Samsung and Google to support frontline healthcare and nursing home workers and first responders with free phone repairs, completing nearly 18,000 free Galaxy and Pixel repairs. uBreakiFix and Samsung teamed up again in December 2020 to bring hassle-free tech recycling to all U.S. uBreakiFix stores. Those looking to part ways with their old tech can now bring eligible devices of any brand, make, or model to their local uBreakiFix store for recycling. Looking ahead to 2021, uBreakiFix plans to increase momentum, projecting 45 store openings during the first quarter alone. January is off to a strong start with seven locations already open, plus recognition on Entrepreneur's annual Franchise 500® list. uBreakiFix ranked #18 on the magazine's 2021 list for outstanding performance in areas including unit growth, financial strength and stability, and brand power. "The past year pushed the franchise industry to new levels of creativity and innovation, which makes us even prouder to be ranked among some of the most successful concepts out there," said Wetherill. "We're honored to be recognized on Entrepreneur's annual Franchise 500® list for our impact as we continue to expand franchise growth, increase corporate support, and elevate the customer experience." uBreakiFix is known for its ability to repair anything with a power button. To date, the brand has fixed more than 10 million devices, including phones, tablets, computers, game consoles, and everything in between. An authorized service provider for Samsung and Google, uBreakiFix leads the industry in strategic partnerships, providing Samsung Galaxy and Google Pixel customers with manufacturer-backed, same-day repair service. uBreakiFix was founded in 2009 by Justin Wetherill and David Reiff, who aligned their skill sets with Eddie Trujillo to offer a brick-and-mortar tech repair option that was quick and affordable, with unmatched customer service. By filling a gap in the repair marketplace, the company has grown organically from a single Florida storefront to an international franchise. For more information, visit ubreakifix.com. About uBreakiFixFounded in 2009, uBreakiFix specializes in the repair of small electronics, ranging from smartphones, game consoles, tablets, computers, and everything in between. Cracked screens, software issues, camera issues, and most other problems can be repaired by visiting uBreakiFix stores across the U.S. and Canada. Since 2016, uBreakiFix has served as the exclusive walk-in repair partner for Google Pixel customers. In 2018, uBreakiFix became a Samsung Care authorized service provider offering same-day, in-person support for Samsung Galaxy customers across the U.S. In 2019, uBreakiFix joined the Asurion family and now operates as a subsidiary of the tech care company while still maintaining the uBreakiFix leadership team and franchise model. For more information, visit ubreakifix.com. A photo accompanying this announcement is available at https://www.globenewswire.com/NewsRoom/AttachmentNg/0158888f-d1e8-4e42-9241-11c1838c571b CONTACT: Media Contact: press@ubreakifix.com
Urban Air Adventure Park, the world's preeminent indoor adventure park, today announced it ranked in Entrepreneur magazine's Franchise 500®, the world's first, best and most comprehensive franchise ranking. Placement in the Franchise 500® is a highly sought-after honor in the franchise industry making it one of the company's most competitive rankings ever.
1_21 PR Tauriga Sciences Inc. Exhibitor Booth at 2020 PGA Merchandise Show The Company Will Showcase Its Flagship Brand, Tauri-Gum™, as Well as Its Expanded Product Offerings NEW YORK, NY, Jan. 20, 2021 (GLOBE NEWSWIRE) -- via NewMediaWire -- Tauriga Sciences, Inc. (OTCQB: TAUG) ("Tauriga" or the "Company"), a revenue generating, diversified life sciences company, with a proprietary line of CBD & CBG infused Supplement chewing gums (Flavors: Pomegranate, Blood Orange, Peach-Lemon, Pear Bellini, Mint, Black Currant) as well as an ongoing Pharmaceutical Development initiative, today announced that it will operate a Virtual Exhibitor Booth ("Virtual Booth") at the Professional Golfers' Association ("PGA") Merchandise Show 2021, which takes place on January 26th- 29th, 2021. Last year, the Company operated a successful and highly visited Corporate Exhibitor Booth (#4507) at the PGA Merchandise Show 2020 – which took place in Orlando, Florida (January 21st- 24th, 2020). The Company has established many important relationships, throughout the golf industry, as a result of the positive exposure from last year's Tradeshow. The Company currently sells its Tauri-Gum™ product line to a number of golf pro shops and industry themed stores. Additionally, the Company has received online E-Commerce order(s) from professional golfer(s). Moving forward, the Company plans to further penetrate this large market segment (golf industry), during calendar year 2021 and beyond. In other news, the Company is pleased to confirm that it has received its 5,000thE-Commerce order (on January 19th, 2021). The average order size ($ dollar amount), per individual online E-Commerce transaction, has been steadily increasing over the past months. The Company is confident that its highest margin E-Commerce business segment will continue to experience meaningful levels of growth. Lastly, the Company has officially launched an improved and updated version of its corporate website (www.tauriga.com). This website version also includes the Company's updated power point presentation (please click on the "Who We Are" tab). ABOUT TAURIGA SCIENCES INC. Tauriga Sciences, Inc. (TAUG) is a revenue generating, diversified life sciences company, engaged in several major business activities and initiatives. The company manufactures and distributes several proprietary retail products and product lines, mainly focused on the Cannabidiol ("CBD") and Cannabigerol ("CBG") Edibles market segment. The main product line, branded as Tauri-Gum™, consists of a proprietary supplement chewing gum that is Kosher certified, Halal certified, and Vegan Formulated (CBD Infused Tauri-Gum™ Flavors: Mint, Blood Orange, Pomegranate), (CBG Infused Tauri-Gum™ Flavors: Peach-Lemon, Black Currant) & (Vitamin C + Zinc "Immune Booster" Flavor: Pear Bellini). The Company's commercialization strategy consists of a broad array of retail customers, distributors, and a fast-growing E-Commerce business segment (E-Commerce website: www.taurigum.com). Please visit our corporate website, for additional information, as well as inquiries, at http://www.tauriga.com Complementary to the Company's retail business, is its ongoing Pharmaceutical Development initiative. This relates to the development of a proposed Pharmaceutical grade version of Tauri-Gum™, for nausea regulation (specifically designed for the following indication: Patients Subjected to Ongoing Chemotherapy Treatment). On March 18, 2020, the Company announced that it had filed a provisional U.S. patent application covering its pharmaceutical grade version of Tauri-Gum™. The Patent, filed with the U.S.P.T.O. is Titled "MEDICATED CBD COMPOSITIONS, METHODS OF MANUFACTURING, AND METHODS OF TREATMENT". On December 18, 2020 the Company disclosed that it had entered into a Master Services Agreement with CSTI to lead the Company's clinical development efforts. On October 6, 2020, the Company announced that it has been approved to operate as a U.S. Government Vendor (CAGE CODE # 8QXV4) The Company is headquartered in Wappingers Falls, New York. In addition, the Company operates a full time E-Commerce fulfillment center located in LaGrangeville, New York. DISCLAIMER -- Forward-Looking Statements This press release contains certain "forward-looking statements" as defined by the Private Securities Litigation Reform Act of 1995 which represent management's beliefs and assumptions concerning future events. These forward-looking statements are often indicated by using words such as "may," "will," "expects," "anticipates," believes, "hopes," "believes," or plans, and may include statements regarding corporate objectives as well as the attainment of certain corporate goals and milestones. Forward-looking statements are based on present circumstances and on management's present beliefs with respect to events that have not occurred, that may not occur, or that may occur with different consequences or timing than those now assumed or anticipated. Actual results may differ materially from those expressed in forward looking statements due to known and unknown risks and uncertainties, such as are not guarantees of general economic and business conditions, the ability to successfully develop and market products, consumer and business consumption habits, the ability to consummate successful acquisition and licensing transactions, fluctuations in exchange rates, and other factors over which Tauriga has little or no control. Many of these risks and uncertainties are discussed in greater detail in the "Risk Factors" section of Tauriga's Form 10-K and other filings made from time to time with the Securities and Exchange Commission. Such forward-looking statements are made only as of the date of this release, and Tauriga assumes no obligation to update forward-looking statements to reflect subsequent events or circumstances. You should not place undue reliance on these forward-looking statements. Contact: Tauriga Sciences, Inc. 4 Nancy Court, Suite 4 Wappingers Falls, NY 12590 Chief Executive Officer Mr. Seth M. Shaw Email: sshaw@tauriga.com cell # (917) 796 9926 Company Instagram: @taurigum Personal Instagram: @sethsms47 Twitter: @SethMShaw Corp. Website: www.tauriga.com E-Commerce Website: www.taurigum.com Attachment 1_21 PR
Jurgen Klopp details how Liverpool can solve goal drought
The Reds have been shut out in their last three Premier League games
Wall Street jumps as Biden takes office
US stocks have opened higher as shares in streaming service Netflix surged 14 per cent.
U.S. Stocks Rise on Earnings; Treasuries Drop: Markets Wrap
(Bloomberg) -- Tech shares led U.S. stocks higher after Netflix Inc. reported strong earnings. Treasuries edged lower alongside the dollar.The Nasdaq 100 Index jumped almost 2% and the S&P 500 Index rose to an all-time high. Netflix Inc. surged more than 13% after a jump in subscribers. Chipmaker ASML Holding NV rallied on solid results. Morgan Stanley gained after reporting record full-year results.Investors also kept an eye on Washington, where Joe Biden is set to be sworn in as president. On Tuesday, Janet Yellen promoted a $1.9 trillion Covid-19 relief proposal to lawmakers as she seeks confirmation as Treasury secretary."The market is likely setting its sight more on the prospects of stimulus than anything else, born not just from Biden's priorities but Yellen's remarks on the Hill yesterday," said Chris Larkin, managing director of trading and investing product at E*Trade Financial.In Asia, Chinese firms trading in Hong Kong saw the bulk of gains, and the Hang Seng Index approached the 30,000 level. Alibaba Group Holding Ltd. rallied after billionaire Jack Ma resurfaced from months out of public view amid escalating scrutiny over his internet empire.Investors are counting on more spending to help propel economic growth under Biden, who is planning a flurry of executive orders on his first day. Still, it won't be all smooth sailing, with Yellen encountering early Republican resistance to Biden's relief plan in her confirmation hearing to become Treasury secretary.Yellen -- who could be confirmed as soon as Thursday -- said that help for the unemployed and small businesses would provide the "biggest bang for the buck." She urged lawmakers to act in efforts to rescue an economy battered by the coronavirus. She also said the U.S. is prepared to take on China's "abusive" trade and economic practices, and that the Biden administration won't pursue a weak dollar.On the virus front, Germany suffered record daily deaths and a study on the South African variant raised concern about the efficacy of vaccines.Elsewhere, crude oil edged higher and gold traded touched an almost two-week high. These are some key events coming up:Joe Biden takes office as U.S. president on Wednesday.Policy decisions are due Wednesday from central banks in Brazil and Canada. The Bank of Japan and the ECB deliver decisions Thursday.Here are the main moves in markets: For more articles like this, please visit us at bloomberg.comSubscribe now to stay ahead with the most trusted business news source.©2021 Bloomberg L.P.
Global Digital Twins Market Report 2020: Trajectory & Analytics, 2012-2019 & 2020-2027 - Market to Reach $38.4 Billion - ResearchAndMarkets.com
The "Digital Twins - Global Market Trajectory & Analytics" report has been added to ResearchAndMarkets.com's offering.
Coronavirus (COVID-19) Consumer Behavior Impacts, 2020 Report - Value for Money, Conscious Shopping and Unique Ways to Reach and Engage with Consumers will be Key Strategic Considerations
Dublin, Jan. 20, 2021 (GLOBE NEWSWIRE) -- The "Life in the "New Normal" - Coronavirus (COVID-19) Impact on Consumer Behavior" report has been added to ResearchAndMarkets.com's offering. Global lockdown and social distancing measures, and fears of a looming global financial recession, have drastically altered how consumers shop, as well as the products and services they are engaging with. The COVID-19 recovery survey reveals that value for money, conscious shopping, and unique ways to reach and engage with consumers will be key strategic considerations for brands throughout the remainder of the year.This report explores the consumer behavior that has emerged since the start of COVID-19 that is here to stay and how brands can align products and services for success post-pandemic.Scope Consumers who will continue or start working from home in future are more likely to spend more time grocery shopping online than the average global consumer.Almost 60% of global consumers claim they will cook more meals at home in the "new normal" after the pandemic.Almost a quarter of global consumers seek general entertainment from brands to distract them amid COVID-19. Reasons to Buy Understand the relevant consumer trends and attitudes that can drive and support innovation, brand activity, or emerging services throughout the COVID-19 outbreak.Gain a broader appreciation of the fast-moving consumer goods industry by gaining insights from both within and outside of your sector.Access valuable strategic take-outs to help direct decision-making and inform new product development. Key Topics Covered: 1. Life in the "New Normal" - Weeks 1-8 IntroductionBare necessitiesConscious shoppingNew routes to market360 degree wellnessInsperiencesTake-Outs 2. About the Survey For more information about this report visit https://www.researchandmarkets.com/r/vfqf73 Research and Markets also offers Custom Research services providing focused, comprehensive and tailored research. CONTACT: CONTACT: ResearchAndMarkets.com Laura Wood, Senior Press Manager press@researchandmarkets.com For E.S.T Office Hours Call 1-917-300-0470 For U.S./CAN Toll Free Call 1-800-526-8630 For GMT Office Hours Call +353-1-416-8900
Alphabet Inc's Google has asked a U.S. judge in Texas to transfer an antitrust lawsuit filed by 10 states in December to a court in California, a state that has more relevant witnesses and documents needed by the company, it said. In December, Texas and nine other states sued Google LLC in a U.S. court in Sherman, Texas, accusing the search engine company of working with Facebook Inc in a way that violated antitrust law to boost its already-dominant online advertising business. All were filed in the Northern District of California, "the venue where Google is headquartered and where more relevant witnesses and documents are located than in any other district in the country," Google said in its request to move the case, which was filed late on Tuesday.
Lunavi Distinguished as Certified Microsoft Azure Expert Managed Service Provider for Second Consecutive Year
Lunavi awarded Microsoft's Azure Expert MSP for the second consecutive year. Company is one of about 85 partners worldwide to earn this distinction.
THIS NEWS RELEASE IS INTENDED FOR DISTRIBUTION IN CANADA ONLY AND IS NOT INTENDED FOR DISTRIBUTION TO UNITED STATES NEWSWIRE SERVICES OR DISSEMINATION IN THE UNITED STATES. TORONTO, Jan. 20, 2021 (GLOBE NEWSWIRE) -- Canada Coal Inc. ("Canada Coal" or the "Company") (TSXV: CCK.H) is pleased to announce that Ayurcann Inc. d.b.a XTRX Solutions Inc. ("Ayurcann") has obtained an amendment to its standard processing licence (the "Amended Licence") from Health Canada which allows Ayurcann to sell extracts, edibles, and topical products directly to provincial and territorial retailers across Canada. On November 24, 2020, Ayurcann and the Company entered into a definitive business combination agreement to effect a reverse takeover of the Company, the details of which are disclosed in the Company's press release dated November 25, 2020. The Amended Licence allows Ayurcann to create new direct relationships with the provincial cannabis boards to list new product SKUs, as well as to open additional revenue streams to produce and white label new finished cannabis products for the growing number of licensed producers and popular brands across the country. "Ayurcann's licensing achievement is a significant milestone, and is a testament not only to the talent within the organization, but its laser-focus on customer service and the production of high-quality, consistent cannabinoid extractions for licensed producers and third-party brands in Canada," commented Igal Sudman, Co-founder and Chief Executive Officer of Ayurcann. Description of Ayurcann and its Business Ayurcann is a leading provider of customized post-harvest outsourcing solutions to licensed cannabis producers. Ayurcann concentrates on the post-harvest requirements of licensed cannabis producers and other brands looking to enter the cannabis market. Ayurcann offers end-to-end full outsourcing solutions including extraction, refinement, formulation, packaging, fulfillment and distribution. Cautionary Statements and Forward Looking Information Neither TSXV nor its Regulation Services Provider (as that term is defined in policies of the TSXV) accepts responsibility for the adequacy or accuracy of this release. This news release contains "forward-looking information" within the meaning of applicable securities laws and such statements, including, but not limited to, statements regarding Ayurcann's ability to create new direct relationships with the provincial cannabis boards to list new product SKUs, Ayurcann's ability to open additional revenue streams, and Ayurcann's ability to produce and white label new finished cannabis products for the growing number of licensed producers and popular brands across the country, as well as information relating to Ayurcann. These forward-looking statements are not representative of historical facts or information or current condition, but instead represent only the Company's beliefs regarding future events, plans or objectives, many of which, by their nature, are inherently uncertain and outside of the Company's control. Generally, such forward-looking information can be identified by the use of forward-looking terminology such as "plans", "expects" or "does not expect", "is expected", "budget", "scheduled", "estimates", "forecasts", "intends", "anticipates" or "does not anticipate", or "believes", or variations of such words and phrases or may contain statements that certain actions, events or results "may", "could", "would", "might" or "will be taken", "will continue", "will occur" or "will be achieved." Readers are cautioned to not place undue reliance on forward-looking information. By their nature, forward-looking statements involve known and unknown risks, uncertainties and other factors which may cause actual results, performance or achievements, or other future events, to be materially different from any future results, performance or achievements expressed or implied by such forward-looking statements. The following represents forward-looking information and users are cautioned that actual results may vary. There is a risk that Ayurcann will not have the necessary financial and labour resources to create new direct relationships with provincial cannabis boards, create new SKUs, open additional revenue streams, and white label new finished cannabis products. The information about Ayurcann contained in the press release has not been independently verified by Canada Coal. Although Canada Coal believes in light of the experience of its officers and directors, current conditions and expected future developments and other factors that have been considered appropriate, that the expectations reflected in this forward-looking information are reasonable, undue reliance should not be placed on them because Canada Coal can give no assurance that they will prove to be correct. Canada Coal and Ayurcann caution that the foregoing list of material factors is not exhaustive. The forward-looking statements contained in this press release represent Canada Coal's and Ayurcann's expectations as of the date of this press release and are subject to change after such date. Canada Coal and Ayurcann have no intention, and undertake no obligation to update or revise any forward- looking statements, whether as a result of new information, future events or otherwise, except as required by law. For more information, please contact: CANADA COAL INC.AYURCANN INC.Olga Nikitovic, Interim CEOTelephone: 905-813-8952Igal Sudman, CEOTelephone: 905-492-3322 x 301Email: olga.nikitovic@sympatico.caEmail: igal@xtrx.ca
Global Pruritus Therapeutics Market – Analysis and Demand with Forecast Overview to 2029 - by PMI
Covina CA, Jan. 20, 2021 (GLOBE NEWSWIRE) -- Growing worldwide prevalence of atopic dermatitis, allergic contact dermatitis, and urticaria is expected to drive market growth during the forecast period. The introduction of new products based on scientific mechanistic understanding such as the identification of new T-cell subsets, particularly Th17, and Th22 and the patent expiration of PROTOPIC (tacrolimus) is expected to open up new avenues for manufacturers to capitalize on over the forecast period. The global pruritus therapeutics market accounted for US$ 3.85 billion in 2019 and is anticipated to register a CAGR of 12.5%. The report "Global Pruritus Therapeutics Market, By Disease Type (Internal Diseases, Atopic Dermatitis, Allergic, and Others), By Treatment (Corticosteroids, and Antihistamines), and By Region (North America, Europe, Asia Pacific, Latin America, and the Middle East & Africa) - Trends, Analysis and Forecast till 2029". Request a Free Sample Copy of this Business Intelligence Report @ https://www.prophecymarketinsights.com/market_insight/Insight/request-sample/4567 Key Highlights: In March 2019, Regeneron Pharmaceuticals and Sanofi received the U.S. Food and Drug Administration (FDA) approval for Dupixent® (dupilumab) for adolescent patients 12 to 17 years of age with moderate-to-severe atopic dermatitis. Dupixent can be used with or without topical corticosteroids. In May 2019, Pfizer announced the positive top-line results from a Phase 3 pivotal study (B7451012) evaluating the efficacy and safety of its investigational oral Janus kinase 1 (JAK1) inhibitor, abrocitinib (PF-04965842), in patients aged 12 and older with moderate to severe atopic dermatitis (AD). Analyst View: Increasing research and development of Pharmaceuticals The global pruritus therapeutics market is growing due to several factors such as, increasing incidence of dermatological disorder influencing the occurrence of pruritus and growing demand for proper diagnostics as well as therapeutics to treat such medical condition. The rising inorganic development strategies, and continuously development of new drugs for the treatment and robust pipeline products are also boosting the growth of the pruritus therapeutic market. Identification of novel T-cell subsets such as Th17 & Th22 and patent expiry of numerous pruritus therapeutic medications such as Protopic (tacrolimus) are also driving the growth of the market. The emerging players have a lucrative opportunity to enter the pruritus therapeutics market, owing to availability of research fundings, and favorable regulatory scenario for external medicines.Browse 60 market data tables* and 35 figures* through 140 slides and in-depth TOC on "Global Pruritus Therapeutics Market", By Disease Type (Internal Diseases, Atopic Dermatitis, Allergic, and Others), By Treatment (Corticosteroids, and Antihistamines), and By Region (North America, Europe, Asia Pacific, Latin America, and the Middle East & Africa) - Trends, Analysis and Forecast till 2029 Ask for a Discount on the Current Pricing @ https://www.prophecymarketinsights.com/market_insight/Insight/request-discount/4567 Key Market Insights from the report: The global pruritus therapeutics market accounted for US$ 3.85 billion in 2019 and is anticipated to register a CAGR of 12.5%. The market report has been segmented on the basis of disease type, treatment and region. Depending upon disease type, the atopic dermatitis segment is projected to grow at highest CAGR over the forecast period. Atopic Dermatitis is one of the most commonly occurring chronic skin conditions that often begin in early childhood. By treatment, the corticosteroids product type held maximum share in the global pruritus market. Corticosteroids are used to treat skin conditions as they suppress inflammation by reducing the amount of collagen production in the skin. It can be applied to the skin in the topical form of ointments, creams, lotions, shampoos, mousses, tapes, or gels. A variety of corticosteroids and other anti-inflammatory creams are available in the market that can be applied to the skin for effective treatment of rashes.By region, North America led the growth of the market majorly on account of the presence of a high prevalence of diseases associated with pruritus, the introduction of new products targeting the unmet medical needs, and growing patient awareness levels. The Asia Pacific pruritus therapeutics market is also expected to grow at a high rate in the coming years. The presence of high unmet healthcare needs and increasing prevalence of allergic contact dermatitis and urticaria in this region are some factors attributing to its rapid growth rate. To know the upcoming trends and insights prevalent in this market, click the link below: https://www.prophecymarketinsights.com/market_insight/Global-Pruritus-Therapeutics-Market-4567# Competitive Landscape: The prominent player operating in the global pruritus therapeutics market includes Sanofi, Pfizer, Tai Guk Pharmaceutical Company, Actavis, Trevi Therapeutics, Cara Therapeutics, Ocera Therapeutics Inc. and NeRRe Therapeutics, Cipla, Merck. The market provides detailed information regarding the industrial base, productivity, strengths, manufacturers, and recent trends which will help companies enlarge the businesses and promote financial growth. Furthermore, the report exhibits dynamic factors including segments, sub-segments, regional marketplaces, competition, dominant key players, and market forecasts. In addition, the market includes recent collaborations, mergers, acquisitions, and partnerships along with regulatory frameworks across different regions impacting the market trajectory. Recent technological advances and innovations influencing the global market are included in the report. About Prophecy Market Insights Prophecy Market Insights is specialized market research, analytics, marketing/business strategy, and solutions that offers strategic and tactical support to clients for making well-informed business decisions and to identify and achieve high-value opportunities in the target business area. We also help our clients to address business challenges and provide the best possible solutions to overcome them and transform their business. Some Important Points Answered in this Market Report Are Given Below: Explains an overview of the product portfolio, including product development, planning, and positioning Explains details about key operational strategies with a focus on R&D strategies, corporate structure, localization strategies, production capabilities, and financial performance of various companies.Detailed analysis of the market revenue over the forecasted period.Examining various outlooks of the market with the help of Porter's five forces analysis, PEST & SWOT Analysis.Study on the segments that are anticipated to dominate the market.Study on the regional analysis that is expected to register the highest growth over the forecast period Key Topics Covered Introduction Study DeliverablesStudy AssumptionsScope of the Study Research MethodologyExecutive Summary Opportunity Map AnalysisMarket at GlanceMarket Share (%) and BPS Analysis, by RegionCompetitive LandscapeHeat Map Analysis Market Presence and Specificity Analysis Investment AnalysisCompetitive Analysis CONTACT: To know more Contact Us: Sales Prophecy Market Insights Email- sales@prophecymarketinsights.com
Forget Bitcoin, This Hot Tech Stock Is a Better Buy
Bitcoin prices have enjoyed meteoric growth over the past few months as institutional investors and big firms have poured money into the digital currency, but the volatility of the cryptocurrency market has started rearing its ugly head once again. What's more, some Wall Street firms are concerned about the value of cryptocurrencies going to zero. The answer is yes, and that safer way is through NVIDIA (NASDAQ: NVDA) -- a hot growth stock that has set the market on fire over the past year.
Mineral Fusion Launches Hydro-Shine Lip Glosses, Inspired by Vacation Destinations We Wish We Could Travel To Right Now
The new lip glosses, available in 13 shades, add a rich splash of color and are incredibly hydrating, perfect for showing your lips some love in the dry winter months. Mineral Fusion Mineral Fusion's Hydro-Shine Lip Gloss range, available in 13 shades, is inspired by iconic vacation destinations across the globe. SAN FRANCISCO NORTH BAY, Calif., Jan. 20, 2021 (GLOBE NEWSWIRE) -- Though most vacation plans are suspended for the foreseeable future, clean beauty lovers can now take a trip around the world thanks to Mineral Fusion, the #1 selling EWG VERIFIED™ natural cosmetics line. The Hydro-Shine Lip Gloss range, available in 13 shades, is inspired by iconic vacation destinations across the globe. Dreaming of a dip in the Caribbean? Try Bermuda, a peachy pink. Longing for an aperitif under the Duomo? Swipe on Florence, a bright, bold red. "With the current stay-at-home orders, so many of us find ourselves fantasizing about exotic locations across the world. We surveyed our social media followers about the top destinations they'd like to visit, and came up with these 13 ultra-hydrating, universally wearable shades inspired by their answers," said Senior Brand Manager of Mineral Fusion, Courtney Cuberly. "With mask-wearing being such a big part of our daily lives now and well into the future, we think it's about time we show our lips some love. So we developed the Hydro-Shine range to be nourishing and hydrating, as well as bold and bright enough to make an impact on Zoom meetings and get-togethers." All of Mineral Fusion's Hydro-Shine Lip Glosses are 100% vegan, paraben-free and cruelty free, and have been thoughtfully designed to flatter all skin tones. Infused with Vitamin E, the lightweight, non-sticky glosses hydrate lips while adding a splash of color and healthy-looking shine. The premium high-payoff wand provides the perfect amount of gloss on each application, so all you have to do is swipe on a coat to be transported across the globe. "At Mineral Fusion, we think looking good goes hand in hand with feeling good," continued Cuberly. "We've all heard the stat about how much lipstick a woman eats in her lifetime — and since you are what you eat, it's crucial your lip products are as clean as possible! You can rest easy knowing Mineral Fusion's Hydro-Shine Lip Glosses are made only with vegan, natural, cruelty-free ingredients." Retailing for $14.99, the Hydro-Shine Lip Glosses are available now at mineralfusion.com and Amazon.com and will be sold at Whole Foods Markets and select natural retailers nationwide in February. ABOUT MINERAL FUSION Mineral Fusion began as a mineral cosmetics brand in 2007 focused on developing products that are a fusion of beauty and skin care that focus on correcting flaws, not just covering them up. Since its launch, Mineral Fusion has grown to become the #1 cosmetic brand at natural retailers. The brand is centered around providing clean cosmetics products that don't compromise on the quality, reliability, exceptional wear, and confidence-boosting performance that consumers know and love. The Mineral Fusion portfolio of products are safe and gentle for all skin types, hypoallergenic and free of gluten, parabens, phthalates, synthetic fragrances, talc and are primarily vegan. In addition to having the most EWG VERIFIED™ products of any beauty brand, Mineral Fusion is also Leaping Bunny Certified cruelty free. Mineral Fusion is available nationwide at Target stores and Target.com, Whole Foods Markets and fine natural health and beauty stores. Mineral Fusion was acquired by BWX Limited, a global natural beauty company, in 2017. For more information about Mineral Fusion, visit www.mineralfusion.com,Instagram at https://www.instagram.com/mineralfusion/,Facebook at www.facebook.com/MineralFusion, andTwitter at https://twitter.com/mineralfusion. ABOUT BWX BWX is a global, natural beauty company with a portfolio of leading natural brands in Australia, USA, Canada, UK, China, and select other international markets. Founded and headquartered in Australia, BWX's expertise is in innovation, product development, manufacturing and marketing natural products. BWX's family of natural brands provides consumers with a natural choice for personal care without compromising on performance. BWX inspires the advancement of plant and mineral-based science without causing unnecessary harm to the planet. It also says NO to testing its products on animals and believes in giving. The company is actively involved in giving back to causes relating to the environment, social responsibility and empowering women. Contact: Mineral Fusion PRMolly AntosT: (847) 848-2090mineralfusion-pr@dadascope.com A photo accompanying this announcement is available at https://www.globenewswire.com/NewsRoom/AttachmentNg/bfbd5b0f-8706-49d2-a065-ead582e00634
The Federal Housing Finance Agency (FHFA) has once again extended its foreclosure and eviction moratorium, this time until Feb. 28. If you're a real estate investor, you're probably wondering how the move will impact your business -- not to mention your bottom line. The FHFA's foreclosure moratorium only applies to properties financed with a GSE-owned loan, meaning one purchased by Fannie Mae (OTCMKTS: FNMA) or Freddie Mac (OTCMKTS: FMCC).
AM Best Announces Appointment of Non-Executive Director to the Boards of A.M. Best Europe Rating Services Ltd., and A.M. Best (EU) Rating Services B.V.
AM Best has appointed Steve Wilson as an independent Non-Executive Director to the Boards of its Europe, Middle East and Africa (EMEA) region subsidiary, A.M. Best Europe Rating Services Ltd. (AMBERS), and its EU-based subsidiary, A.M. Best (EU) Rating Services B.V. (AMBEU). His appointment is with effect from 1 January 2021.
Smartronix Launches Cloud Center of Excellence
Delivers market-leading cloud solutions and expertiseHERNDON, Va., Jan. 20, 2021 (GLOBE NEWSWIRE) -- Smartronix, an OceanSound Partners company; Gartner Magic Quadrant recognized leader; and AWS Premier, Azure Expert Managed Service Provider (MSP), and Google Premier Partner announces the creation of the Smartronix Cloud Center of Excellence (CCoE). The Smartronix CCoE was established to ensure the highest level of cloud innovation and expertise for our customers by providing market-leading, multi-cloud capabilities and solutions on the leading cloud platforms, to include Amazon Web Services, Microsoft Azure, and Google Cloud. The CCoE assists public sector and commercial market customers in orchestrating their cloud initiatives and managing the cloud adoption life cycle — from cloud strategy, roadmap, design, migration, and application modernization to cybersecurity, compliance, and next-generation managed services. These capabilities are delivered within the Smartronix Cloud Assured™ framework for the development and optimization of repeatable cloud best practices and tools that can be used to optimize the delivery of cloud solutions. "The formation of the Smartronix CCoE supports our position as a national leader in cloud solutions," says Rick Kelley, CCoE Lead. "Customers look to us as a trusted advisor as they navigate their path through the cloud adoption life cycle and leverage the innovation cloud brings to achieving their mission goals. Smartronix will continue to build and manage solutions that meet enterprise cloud needs now and into the future." Peter LaMontagne, Smartronix CEO, referenced the establishment of the CCoE as "an investment in our future that reflects our commitment to digital transformation and the people, processes, and technologies that make it possible. The CCoE will develop our solutions and expertise in advancing our nationally recognized leadership in cloud solutions." Smartronix deploys cloud solutions at scale and has achieved FedRAMP Authorization for its Cloud Assured Managed Services (CAMS) platform to support state-of-the-art private, public, and hybrid cloud solutions for highly regulated workloads. Smartronix also has been named a Leader for the third time in Gartner's 2020 Magic Quadrant for Public Cloud Infrastructure Professional and Managed Services, Worldwide. Read the complimentary report here: https://gartnermq.smartronix.com. About Smartronix, LLC Smartronix, an OceanSound Partners company, designs, builds, manages, and secures the world's mission-critical cloud solutions. We are the leading provider of next-generation multi-cloud platforms to highly regulated and security-first organizations. Smartronix provides world-class expertise in application migration, digital modernization, and solution automation; and has created an industry-leading FedRAMP-accredited CAMS and Managed Security Services solution. For more information, please visit https://www.smartronix.com/. Gartner Disclaimer Gartner does not endorse any vendor, product, or service depicted in its research publications, and does not advise technology users to select only those vendors with the highest ratings or other designation. Gartner research publications consist of the opinions of Gartner's research organization and should not be construed as statements of fact. Gartner disclaims all warranties, expressed or implied, with respect to this research, including any warranties of merchantability or fitness for a particular purpose. For inquiries about this press release, please contact us at smartronixcommunications@smartronix.com. | {
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package main.java.DAOs;
/**
* Created by Tatka on 07.12.2016.
*/
public class TypeDAO {
private String typeDTO;
private String typeDAO;
public TypeDAO() {
}
public String getTypeDTO() {
return typeDTO;
}
public String getTypeDAO() {
return typeDAO;
}
}
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Q: Excel - Autoshape get it's name from cell (value) I will try to explain this
I have VBA that based on value selected in sheet called TEXT you can select shape (like Circle, triangle, square) and shape number (1.2.3) and when you double click it immediately goes to next sheet called shapes and find that shape based on values you selected
Example: sheet TEXT in Cell K13 in drop-box select circle
in cell L13 in drop-box select number 1.
then double click in J13 and based on K13 and L13 it goes to sheet SHAPES and select shape that has name Circle1
This works fine because each shapes name (like circle1, circle2, triangle1, traingle2, square1, square2) match all combination that you can select from shape list ..
Problem: If I for some reason want to change names in drop-box from circle, triangle, quare to let say home, apartment, shop... then VBA can't find that names and I have to change names for all shapes to match new names....
Solution: What I need is that all shapes automatically change it's name so if Circle is changed to home etc.. all circle will change to home...
actually each shape looking for it's name from specific cells...
example: circle1 uses it's name from B9+C9, circle2 B9+C10, triangle1 B10+C9, triangle2 B10+C10, square1 B11+C9, square2 B11+C10.. so if circle in B9 is changed to home all circle shape names will change to home, like home1, home2.
rows -column B shape - Column C number
row9 - Circle - 1
row10 - Triangle - 2
row11 - Square - 3
VBA
Private Sub Worksheet_BeforeDoubleClick(ByVal Target As Range, Cancel As Boolean)
Dim test As String
If Not Intersect(Target, Range("J13:J16")) Is Nothing Then
test = Target.Offset(, 1).Value & Target.Offset(, 2).Value
Worksheets("Shapes").Shapes(CStr(test)).Select
Worksheets("Shapes").Activate
End If
End Sub
Thank you
A: You could run code like this. My code (xl2010) assumes that you inserted these shape tyoes
*
*Circle from the autoshape "Oval"
*Square from the autoshape "Rectangle"
*Triangle from the autoshape "Isosceles Triangle"
The code looks at a master range in A8:C11 that I expanded by 1 column form your example to provide a
1) Shape type
2) Shape number
3) Numbering system
(see pic below)
The code when run looks at each shape on the sheet, tests if it is a circle, square or rectangle, looks up the name in the second column of the table, then applies the number of the position in the third column (note that you may need to add more numbers and extend this range).
So the code below names up to three circles as
home1
home2
home3
up to three squares as
square1
square2
square3
etc
You could either run this code when you wanted to manually, or run it automatically with events each time a cell in the name ranging table changes, or when you activtated this sheets etc
Sub ReName()
Dim shp As Shape
Dim rng1 As Range
Dim lngCirc As Long
Dim lngSq As Long
Dim lngTri As Long
Set rng1 = Sheets(1).Range("A8:C18")
For Each shp In ActiveSheet.Shapes
Select Case shp.AutoShapeType
Case msoShapeOval
lngCirc = lngCirc + 1
shp.Name = rng1.Cells(2, 2) & rng1.Cells(1, 3).Offset(lngCirc)
Case msoShapeIsoscelesTriangle
lngTri = lngTri + 1
shp.Name = rng1.Cells(3, 2) & rng1.Cells(1, 3).Offset(lngTri)
Case msoShapeRectangle
lngSq = lngSq + 1
shp.Name = rng1.Cells(4, 2) & rng1.Cells(1, 3).Offset(lngSq)
Case Else
Debug.Print "Check shape: " & shp.Name & " of " & shap.AutoShapeType
End Select
Next
End Sub
| {
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} | 582 |
{"url":"https:\/\/solvedlib.com\/list-the-integers-that-can-replace-n-to-make-the,583","text":"# List the integers that can replace n to make the statement -|8| < n < or = to - |-5|\n\n###### Question:\n\nList the integers that can replace n to make the statement -|8| < n < or = to\n- |-5| true.\n\n#### Similar Solved Questions\n\n##### Please explain why this is a 1,4 addition reaction and what the 1,2 addition reaction would...\nPlease explain why this is a 1,4 addition reaction and what the 1,2 addition reaction would look like: Nu nN: +...\n##### \u03bcx= 10,\u00a0\u00a0\u00a0 \u03c3x =5, \u03bcy=8, \u03c3y=4,\u00a0\u00a0\u00a0\u00a0\u00a0 \u03c1=0 X and Y come from normal distributions Calculate the...\n\u03bcx= 10,\u00a0\u00a0\u00a0 \u03c3x =5, \u03bcy=8, \u03c3y=4,\u00a0\u00a0\u00a0\u00a0\u00a0 \u03c1=0 X and Y come from normal distributions Calculate the probability that X > Y. Z = 3X + 10\u00a0\u00a0 Calculate the probability that Z > 45....\n##### Better to use asa 4. If you have the same number of moles of a salt,...\nbetter to use asa 4. If you have the same number of moles of a salt, which one would be roadway de-icer: NaCI or CaCl2? Remember, colligative properties are mole-based calculations. Show calculations to support your answer and assume both salts dissociate completely. (Assume some number of moles of ...\n##### 1. Consider the reaction below. N2(g) + 3 H2(g) \u21cb 2 NH3(g) Which of the following...\n1. Consider the reaction below. N2(g) + 3 H2(g) \u21cb 2 NH3(g) Which of the following changes would cause less NH3 to be produced? decreasing the volume adding N2 increasing the volume adding H2 2. Consider the following reaction. N2(g) + 3 H2(g) \u21cb 2 NH3(g) The forward reaction...\n##### 0 = (0),\/ '0= (0V :=agT + 1'Jamsue inof Kyiiduis 1Ou oa(poyiauu Jayloue JO} Ipan) ON) \"uopenba Jo sapis 41oq JO WJojsueJI axeide7 Buisn uoinjos Jeinjiued puly\n0 = (0),\/ '0= (0V :=agT + 1 'Jamsue inof Kyiiduis 1Ou oa (poyiauu Jayloue JO} Ipan) ON) \"uopenba Jo sapis 41oq JO WJojsueJI axeide7 Buisn uoinjos Jeinjiued puly...\n##### \u0644\u0642\u0644\u0629 \u0648\u0627\u062d\u062f\u0629 The Tolerance for the shaft for D12(H8\/f7) is HOUSING BUSH SHAFT \u00a9 28 H9...\n\u0644\u0642\u0644\u0629 \u0648\u0627\u062d\u062f\u0629 The Tolerance for the shaft for D12(H8\/f7) is HOUSING BUSH SHAFT \u00a9 28 H9 - 9 18 012 H8-17) 9d - LH 26.5 0.025 30 non of them O 0.0270 mm -0.018 mm O 0.018 mm O 0.0330mm O...\n##### 36. Prove that a square matrix A is invertible if and only if ATA is invertible\n36. Prove that a square matrix A is invertible if and only if ATA is invertible...\n##### Here Is a sample data sel357.1 357.5 363.8 366.7 368.7 369.5 371,2 372.5 3733 374.6 3795 380.2 381.4 381.44 381.4 381.9 382.4 383.8 384.3 384.4 385.3 385.6 386.2 386.8 387.3 387,, 387.6 387.6 388.4 388.6 388.6 389.1 393.1 3953 396.8 397.8 401 401.5 404.8 408 4 408.4 408.4 411 413.7 4 4192 422.6 425.8 428.2 431 433.4 437.7 438.7 440.8Ienm (O)Find the first quartile for this data setFind the third quartile for this data set:Find the interquartile range for this data set IQR =Find the lower fence s\nHere Is a sample data sel 357.1 357.5 363.8 366.7 368.7 369.5 371,2 372.5 3733 374.6 3795 380.2 381.4 381.44 381.4 381.9 382.4 383.8 384.3 384.4 385.3 385.6 386.2 386.8 387.3 387,, 387.6 387.6 388.4 388.6 388.6 389.1 393.1 3953 396.8 397.8 401 401.5 404.8 408 4 408.4 408.4 411 413.7 4 4192 422.6 425...\n##### Question 4 (2 points) Two series of five Mn?' standard addilion solutions (U and U,) were prepared in 50.00 mL volumetric flasks Increasing volumes ol Iho Mn?' substock solulion were added to each flask, with the volumes given in the Iable below: The U; series was prepared by dissolving 0.7753 g (U,) of Ihe steel sample in 4.5 M HNOz in a clean breaker; filtering and Ihen transferring Ioja 50.00 mL volumetric Ilask and diluling to the mark with 1% (vlv) HNOz: From Inis Ilask, 400.0 JIL\nQuestion 4 (2 points) Two series of five Mn?' standard addilion solutions (U and U,) were prepared in 50.00 mL volumetric flasks Increasing volumes ol Iho Mn?' substock solulion were added to each flask, with the volumes given in the Iable below: The U; series was prepared by dissolving 0....\n##### Uso tna graph 4ra fundion ahotn In * (gure te nahtto equrnatendicater Jncon valleIc=0 9i =(Typo iniegocucialletor\nUso tna graph 4ra fundion ahotn In * (gure te nahtto equrnate ndicater Jncon valle Ic=0 9i = (Typo iniego cucial letor...\n##### For a uniform probability density function; the average value for the random variable is:(a-by2Exp(x)npnone of the above\nFor a uniform probability density function; the average value for the random variable is: (a-by2 Exp(x) np none of the above...\n##### Uquld hexane (CH,(CH;) CH,) = matts witn Qascous axygcn Qas (01) produce guseous carpan donlde (C01) Adsedus Walar (H,0} 941g0 earbon dioxlde prod iced Atom tne reaction 0l 4JJI 0t nexanc Jnd 24.9 & % Oxyqen Qas calculata the parcent Yicld carban dlaride.Be tUre YoUr ansvics has the Eortcct number ionuncact diqit In I\nUquld hexane (CH,(CH;) CH,) = matts witn Qascous axygcn Qas (01) produce guseous carpan donlde (C01) Adsedus Walar (H,0} 941g0 earbon dioxlde prod iced Atom tne reaction 0l 4JJI 0t nexanc Jnd 24.9 & % Oxyqen Qas calculata the parcent Yicld carban dlaride. Be tUre YoUr ansvics has the Eortcct n...\n##### (4) Tu his Qrob lemn 0{ & *27t an8 0= 6 ~TT _Ta) Give n 7571717627 7oovaintrrs (19, )-(03,7] fs Poiut. Petermime Ye-turg(ar csord;uetes_ (6) Givr s lindviee careiurts (+,3,-43). Dekrmine 'Qhcr izel <eordinates for the Peiut.\n(4) Tu his Qrob lemn 0{ & *27t an8 0= 6 ~TT _ Ta) Give n 7571717627 7oovaintrrs (19, )-(03,7] fs Poiut. Petermime Ye-turg(ar csord;uetes_ (6) Givr s lindviee careiurts (+,3,-43). Dekrmine 'Qhcr izel <eordinates for the Peiut....\n##### Use the method for solving equations with linear coefficients to solve the following differential equation_(2x y) dx+ (4x+y -3) dy=0Ignoring lost solutions, if any, an implicit solution in the form F(x,y) = C is (Type an expression using X and y as the variables.)=C where C is an arbitrary constant:\nUse the method for solving equations with linear coefficients to solve the following differential equation_ (2x y) dx+ (4x+y -3) dy=0 Ignoring lost solutions, if any, an implicit solution in the form F(x,y) = C is (Type an expression using X and y as the variables.) =C where C is an arbitrary consta...\n##### 3. HC9H704 (MW = 180. g\/mol) is prepared by dissolving 3.60 g into a 1.00 L...\n3. HC9H704 (MW = 180. g\/mol) is prepared by dissolving 3.60 g into a 1.00 L solution. The pH of this solution was determined to be 2.60. What is the K?...\n##### Solve the equationX1+2x2 - 2x3 12x4 = 4X1+3x2 -18x4+6x5 = -6X1 - 6x3 -12x5 = 24,And put the solution on the form[variable vector] [vector with numbers] (free variable)[vector with numbers]Test the solution, all parts, and tell how it is done\nSolve the equation X1+2x2 - 2x3 12x4 = 4 X1+3x2 -18x4+6x5 = -6 X1 - 6x3 -12x5 = 24, And put the solution on the form [variable vector] [vector with numbers] (free variable)[vector with numbers] Test the solution, all parts, and tell how it is done...\n##### Find the percentile for the data value 18) Data &4: 125 data value: 131 B)77122;C) 70D) 75Find the indicated meASufC: 19) The test scores of 32 students are listed below . Find Q3.56 5759 63 65 66 68 70 71 74 74 75 77 78 80 52+5} 86 59 92 95 99 AJRO B} 79C) 21D) 79,5MNE Juswerte ~question: Using the following uniform densily77777 6 \/ Z0) What us the probability that the random variable Vue greater than _ A) 0,750 B) 0.,875 0,625 D) 0.700\nFind the percentile for the data value 18) Data &4: 125 data value: 131 B)77 122; C) 70 D) 75 Find the indicated meASufC: 19) The test scores of 32 students are listed below . Find Q3. 56 5759 63 65 66 68 70 71 74 74 75 77 78 80 52+5} 86 59 92 95 99 AJRO B} 79 C) 21 D) 79,5 MNE Juswerte ~quest...\n##### Question 17 (5 points) A cylinder sealed with a moveable piston contains 0.2 mol of an ideal gas at a temperature of 315 K Heat is transferred slowly into the g3s,and it is allowed to expand isothermally from an initial volume of 1.5 x 10 m3 to 3.5x10-3 m How much heat is transferred into the gas during this process?None of the above539.6 J443.8 J157.5 ]269.3 ]\nQuestion 17 (5 points) A cylinder sealed with a moveable piston contains 0.2 mol of an ideal gas at a temperature of 315 K Heat is transferred slowly into the g3s,and it is allowed to expand isothermally from an initial volume of 1.5 x 10 m3 to 3.5x10-3 m How much heat is transferred into the gas d...\n##### What populations are most vulnerable to HIV\/AIDS in the United States? Speak about social determinants that...\nWhat populations are most vulnerable to HIV\/AIDS in the United States? Speak about social determinants that contribute to their diagnoses....\n##### 1) Suppose a researcher is interested in understanding the variation in the price of store brand...\n1) Suppose a researcher is interested in understanding the variation in the price of store brand milk. A random sample of 36 grocery stores selected from a population and the mean price of store brand milk is calculated. The sample mean is $3.13 with a population standard deviation of$0.23. Constru...\n##### Determine whether true or false1. \u00e2\u02c6\u20ac\u00f0\u009d\u2018\u00a5\u00e2\u02c6\u02c6\u00f0\u009d\u2018\u2026\u00e2\u02c6\u0192\u00f0\u009d\u2018\u00a6\u00e2\u02c6\u02c6\u00f0\u009d\u2018\u2026:\u00f0\u009d\u2018\u00a5^2=\u00f0\u009d\u2018\u00a6^32. \u00e2\u02c6\u20ac\u00f0\u009d\u2018\u017d \u00e2\u02c6\u02c6\u00f0\u009d\u2018\u2026 \u00e2\u02c6\u0192\u00f0\u009d\u2018\u00a5\u00e2\u02c6\u02c6 \u00f0\u009d\u2018\u2026:\u00f0\u009d\u2018\u00a5^11+\u00f0\u009d\u2018\u017d\u00e2\u2039\u2026\u00f0\u009d\u2018\u00a5^3\u00e2\u02c6\u20193=03. \u00e2\u02c6\u0192\u00f0\u009d\u2018\u00a5 \u00e2\u02c6\u02c6 \u00f0\u009d\u2018\u2026\u00e2\u02c6\u20ac\u00f0\u009d\u2018\u00a6 \u00e2\u02c6\u02c6 \u00f0\u009d\u2018\u2026:\u00f0\u009d\u2018\u00a5\u00e2\u2039\u2026\u00f0\u009d\u2018\u00a6 \u00e2\u2030\u00a4 04. \u00e2\u02c6\u0192\u00f0\u009d\u2018\u00a5 \u00e2\u02c6\u02c6 \u00f0\u009d\u2018\u201e\u00e2\u02c6\u20ac\u00f0\u009d\u2018\u00a6 \u00e2\u02c6\u02c6 \u00f0\u009d\u2018\u201e: \u00f0\u009d\u2018\u00a5\u00e2\u2039\u2026\u00f0\u009d\u2018\u00a6=1\nDetermine whether true or false 1. \u00e2\u02c6\u20ac\u00f0\u009d\u2018\u00a5\u00e2\u02c6\u02c6\u00f0\u009d\u2018\u2026\u00e2\u02c6\u0192\u00f0\u009d\u2018\u00a6\u00e2\u02c6\u02c6\u00f0\u009d\u2018\u2026:\u00f0\u009d\u2018\u00a5^2=\u00f0\u009d\u2018\u00a6^3 2. \u00e2\u02c6\u20ac\u00f0\u009d\u2018\u017d \u00e2\u02c6\u02c6\u00f0\u009d\u2018\u2026 \u00e2\u02c6\u0192\u00f0\u009d\u2018\u00a5\u00e2\u02c6\u02c6 \u00f0\u009d\u2018\u2026:\u00f0\u009d\u2018\u00a5^11+\u00f0\u009d\u2018\u017d\u00e2\u2039\u2026\u00f0\u009d\u2018\u00a5^3\u00e2\u02c6\u20193=0 3. \u00e2\u02c6\u0192\u00f0\u009d\u2018\u00a5 \u00e2\u02c6\u02c6 \u00f0\u009d\u2018\u2026\u00e2\u02c6\u20ac\u00f0\u009d\u2018\u00a6 \u00e2...\n##### Finance Practice 2 Krist Question 5 of 5 (2 points) | Question Attempt: 1 of 1...\nFinance Practice 2 Krist Question 5 of 5 (2 points) | Question Attempt: 1 of 1 3 A bank offers an investment account with an annual interest rate of 1.45 % compounded daily. Lucy invests \\$3900 into the account for 5 years. Answer the questions below. Do not round any intermediate computations, and r...\n##### Attention: Due to a bug in Google Chrome, this page may not function correc t e...\nAttention: Due to a bug in Google Chrome, this page may not function correc t e o learn more 2. Introduction to variability Aa Aa 2 A researcher is studying psychological factors in artistic achievement among teenage boys. One variable she is particularly interested in is perseverance. What informat...\n##### This in ASL (American Sign Language) What is the name of the play that lampooned the...\nThis in ASL (American Sign Language) What is the name of the play that lampooned the Gallaudet style of signing?...\n##### Question 7 4 pts This embryonic germ layer is only found in Bilateria. O a.) ectoderm...\nQuestion 7 4 pts This embryonic germ layer is only found in Bilateria. O a.) ectoderm O b.) endoderm c.) mesoderm O a and b O a, b, and...\n##### Jomework: Homework ch 11.7 icor: 11.14Usothe grph tha Nol ontammneFaluc oleondcaledSc05cond ctocn buominj nrcotiun Mu In Ihc ntettcorpbolo your colcoImekedurinotniyClckYoJr nnstrtn'Inon Gc Chach A nertneltuiinna3\nJomework: Homework ch 11.7 icor: 11.14 Usothe grph tha Nol ontammne Faluc oleondcaled Sc05 cond ctocn buominj nrcotiun Mu In Ihc ntett corpbolo your colco Imeke durinotniy Clck YoJr nnstrtn' Inon Gc Chach A nertn eltuiinna 3...\n##### A bicyclist in the Tour de France has a speed of 31.0 miles per hour (mi\/h)...\nA bicyclist in the Tour de France has a speed of 31.0 miles per hour (mi\/h) on a flat section of the road. What is this speed in (a) kilometers per hour (km\/h), and (b) meters per second (m\/s)?...\n##### Tiger Furnishings produces two models of cabinets for home theater components, the Basic and the Dominator....\nTiger Furnishings produces two models of cabinets for home theater components, the Basic and the Dominator. Data on operations and costs for March follow: Units produced Machine-hours Direct labor-hours Direct materials costs Direct labor costs Manufacturing overhead costs Total costs Basic 850 4,50...\n##### Sketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral.Sketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral.\nSketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral. Sketch the region whose area is represented by the definite integral. 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You can drag one or both curves to help you answer the following questions, but you will not be graded on where you place the curves. PRICE OF CORN Dollars per bushell Supply Demand QUANTITY OF CORN (Millions of bushels] Adjust the gra...\n##### Which of the following elements has the smallest (least exothermic) electron affinity?Select the correct answer below:0 K0 Na0FEEDBACKMOREaulenattribution\nWhich of the following elements has the smallest (least exothermic) electron affinity? Select the correct answer below: 0 K 0 Na 0 FEEDBACK MORE aulenattribution...\n##### Answer each of the following questions:Q1 4 marks) Draw the structure corresponding to each name:3,3-dichloropentanal0-bromobenzaldehydeWhat carbonyl compound is needed to make each alcohol by a reduction reaction?CH;OHCH:CHZCHZCHZCHZOH\nAnswer each of the following questions: Q1 4 marks) Draw the structure corresponding to each name: 3,3-dichloropentanal 0-bromobenzaldehyde What carbonyl compound is needed to make each alcohol by a reduction reaction? CH;OH CH:CHZCHZCHZCHZOH...\n##### Be sure to show your math for all parts of this If 4% of question pts) population in equilibrium expresses recessive trait:What is the frequency of the recessive allele in the gene pool?What would be the expected frequency of heterozygotes in the population?What is the probability that two mated individuals who show the dominant phenotype, but for whom the genotype is unknown, will produce child having the recessive phenotype?\nBe sure to show your math for all parts of this If 4% of question pts) population in equilibrium expresses recessive trait: What is the frequency of the recessive allele in the gene pool? What would be the expected frequency of heterozygotes in the population? What is the probability that two mated ...\n##### Draw the organic products of these reactions. \u043e\u043d CrO3. H2504(aq) CH3 CH NaBH4 \u043e\u043d \u043e\u043d \u0420\u0421\u0421...\ndraw the organic products of these reactions. \u043e\u043d CrO3. H2504(aq) CH3 CH NaBH4 \u043e\u043d \u043e\u043d \u0420\u0421\u0421 KMnO4(aq), H3O KMnO4(aq), H3O* NH3 H2(g), Ni(s) NH2 NaBH4 1.NH4CI, KCN 2. 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Het vuurwapen abus (Obüs is Turks voor houwitser) is een vroege vorm van artillerie, ontwikkeld in het Ottomaanse Rijk. De abus is relatief klein, maar te zwaar om al dragend af te vuren, daarom heeft het een statief voor gebruik. De abus heeft een kaliber van rond de 230 mm. Abusgeschut werd ondanks dat het een type houwitser is, voornamelijk tegen infanterie gebruikt.
Artillerie
Ottomaanse Rijk | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,225 |
\section{Introduction}
Understanding the nature of the dark universe is one of the fundamental challenges of modern cosmology today. Galaxy clustering - the statistical analysis of the spatial distribution of galaxy number counts - has been identified as one of the most promising probes available to explore this \citep{Peebles:1980,DETF,WGFC}, with spectroscopic surveys being particularly useful in probing both tangential and radial modes in the Universe.
Galaxy number counts have been extensively studied with current and planned future surveys, and the analysis can be performed in various spaces, for example, Fourier space \citep{Seo:2003Eis,Seo:2007Eis}, configuration space \citep{Eisenstein:2005,baoconfig1,baoconfig2}, and spherical harmonic space \citep[e.g.,][]{Dolney:2006,DK:2012}. For future wide-field spectroscopic surveys, the galaxy field will cover large areas on the sky so that an analysis in spherical space provides a natural decomposition for certain physical effects as well as selection effects. For wide-field spectroscopic surveys, the depth of the survey means that a 3D spherical Fourier-Bessel (SFB) analysis is the most natural to perform \citep{Fisher:1995,Heavens:1995,Rassat:2012bao}.
Previous SFB analyses of the local Universe \citep[e.g.,][]{Erdogdu:2006dv,Erdogdu:2005wi} used relatively small data sets, where straightforward summation methods were sufficient to measure the SFB coefficients. Today, novel numerical methods for 3D spherical analysis are available \citep{3DEX,Lanusse:2011} to prepare for future wide-field surveys that will map the large-scale structure of the Universe with a large number of galaxies. The 3D SFB analysis can also be applied to other probes, for instance weak-lensing \citep{Heavens:2003,CHK:2005,Kitching:2008,KHM:2010,Schafer:2014,3dwl:bao,3dwl:2014} and the integrated Sachs–Wolfe effect \citep[e.g.][]{ISW3D}, which will be crucial for high-precision probe combinations.
Even given the existing 3D SFB tools and the theoretical motivation for this approach, most existing forecasts and survey optimisation for future wide-field surveys focus on a tomographic analysis, that is, one where the survey is split into redshift bins, and 2D spherical harmonic auto- and cross-power spectra $C^{ij}(\ell)$ are measured \citep[e.g.,][]{Redbook,DK:2012}. One of the advantages of a tomographic spherical harmonics analysis is that there are several available codes to rapidly calculate the tomographic spectra, either for galaxy correlations or for other complementary probes \cite[e.g.,][]{class:gg,icosmo1}; another advantage is that it is straightforward to convert survey observables ($\theta, \phi, z$) into a power spectrum measurement without any assumption of cosmological parameters, while the 3D SFB analysis requires an assumption about the fiducial cosmology to translate the observables into the 3D SFB spectrum, which has a dependence of wavenumber $k$. However, in the tomographic analysis, some of the radial information may be lost as a result of redshift binning, while the 3D SFB analysis potentially uses the entire 3D information, especially for a spectroscopic survey. With this in mind, a natural hypothesis is that a 3D SFB spectroscopic analysis might extract more information than a tomographic one.
Several studies have already investigated this, for example, \cite{Clzz} and \cite{Asorey:2012} found that a tomographic analysis returned equivalent or better constraints than a 3D Fourier power spectrum analysis. They concluded that the tomographic approach should be preferred as it avoids the need to assume a particular cosmology to convert redshifts into comoving distances and simplifies the combination with other probes such as weak-lensing. Nevertheless, they both acknowledged that for a spectroscopic survey the tomographic analysis would require a large number of redshift bins to recover the full 3D information, which is limited by shot noise problems. For the first time, \cite{Nicola:2014} compared the tomographic analysis to a 3D SFB analysis and found the tomographic constraints to be superior, but they still noted that the 3D SFB approach was stable with regard to the choice of fiducial cosmology for the necessary conversion from redshift to comoving distance. However, their treatment of the non-linear scale cut-off used in the Fisher matrix comparison is not equivalent between the tomographic and the 3D SFB analysis. While the 3D power spectra is cut off at a physical scale ($k$) corresponding to nonlinear effects, the tomographic power spectra are truncated at fixed arbitrary angular scales. This ignores the interplay between the redshift of the tomographic bins and the wavenumber of the SFB spectrum. As a result, the non-linear cut-off in \cite{Nicola:2014} does not allow a fair comparison between 2D and 3D methods, which means understanding the strength of each method is still an open question. We address this question by carefully excluding non-linear scales.
Understanding how best to extract information for a 3D galaxy survey is of utmost importance to address the fundamental questions in modern cosmology today, and also to ensure that future planned surveys are efficiently analysed as well as optimised. To address this pressing question, we propose here a new investigation of the information that can be extracted from a spectroscopic galaxy survey by tomographic vs. 3D SFB analysis. Our approach focuses on the seven common parameters that are currently used in wide-field survey optimisation and planning, that is, on $\vec{\theta}=\{\Omega_m, h, w_0, w_a, \sigma_8, \Omega_b, n_s\}$, while putting forward a coherent approach regarding the exclusion of non-linear scales for both the 2D and 3D methods for the first time. In addition, we investigate for the first time how tomographic and 3D SFB methods are affected by nuisance parameters related to the galaxy bias, which we allow to be both redshift- and scale-dependent. However, we do not include redshift space distortions (RSD) or relativistic effects in our study. Including RSDs, which will be present in the data, provides an additional probe, which improves constraints. Although a prescription for RSDs in SFB space exists \citep{Heavens:1995}, as a first approach, we do not include them here in either the tomographic or the SFB analysis
to ensure that we compare like with like. Their impact should nonetheless be assessed, which we plan to do in a future work.
Finally, in the spirit of reproducible research, we make available all tomographic and 3D SFB codes used for this analysis, along with the scripts to reproduce our results.
Our paper is structured as follows: in Sect. \ref{sec:theory}, we briefly review the theory behind the statistical analysis of galaxy number counts, including the prescription for the tomographic analysis and the 3D SFB. In Sect. \ref{sec:Forecasting}, we provide
an overview of the Fisher matrix forecasting-approach that we used to compare the relative constraining power of each method, and include the description of the future spectroscopic wide-field survey for which we calculate forecasts, of the question of non-linear scale treatment, and galaxy bias nuisance parameters. In Sect. \ref{sec:results}, we present the comparison between the constraining power of the 3D SFB and tomographic methods and investigate how this comparison holds in the presence of galaxy bias nuisance parameters. We also determine how this affects a future wide-field survey optimisation. In Sect. \ref{sec:ccl}, we present our conclusions in the context of high-precision cosmology with future wide-field surveys.
\section{Theory}
\label{sec:theory}
In this first section we describe the formalism behind the analysis of galaxy clustering in the context of a spectroscopic survey. We present the two methodologies compared in this work, one based on a tomographic analysis of angular correlations, the other based on the correlations of the 3D expansion of the galaxy field on a spherical Fourier-Bessel basis.
\subsection{Galaxy and matter fields}
In a galaxy survey, the quantity observed is the galaxy number density $n(\mathbf{r} = (r,\theta,\varphi)),$ which can be defined in terms of the galaxy overdensity $\delta_g$ through
\begin{equation}
n(\mathbf{r}) = \bar{n}(r) ( 1 + \delta_g(\mathbf{r}, z(r))) \;,
\label{eq:density}
\end{equation}
where $\bar{n}(r)$ is the mean number density of observed galaxies at comoving distance $r$. In this expression, the time dependence of the observed overdensity as a function of comoving distance is made explicit through the $z(r)$ relation. The mean number density $\bar{n}(r)$ can be expressed in terms of the survey selection function $\phi(r)$ as
\begin{equation}
\bar{n}(r) = \phi(r) \bar{n} = \frac{N}{V} \phi(r) \;,
\end{equation}
with $\bar{n}$ the mean number density of observed galaxies, $N$ the total number of observed galaxies, and $V$ the volume of the survey that fulfils $V = \int \phi(r) \mathrm{d}\mathbf{r}$. Note that in the general case, the selection function has both an angular and a radial dependence (see Sect.~\ref{sec:fsky}), but in this work, we did not consider the impact of an angular mask and only account for partial coverage of the sky through a multiplicative $f_{sky}$ factor.
In expression \eqref{eq:density}, the time (or redshift) dependence of the galaxy overdensity is due to the growth of structure and the evolution of galaxy bias with respect to the matter density field with time. Following the approach of \citet{Rassat:2012bao}, in the linear regime this dependence on redshift can be separated in the form of growth and bias prefactors,
\begin{equation}
\delta_g(\mathbf{r},z(r)) = b(r, k) D(r) \delta(\mathbf{r}) + \epsilon(\mathbf{r}) \;, \label{eq:galaxy_overdensity_to_matter_overdensity}
\end{equation}
where $b(r, k)$ is a bias with a possible scale dependence, $D(r)$ is the growth factor, $\delta(\mathbf{r}) = \delta(\mathbf{r}, z = 0)$ is the matter overdensity field at present day, and $\epsilon(\mathbf{r})$ is a Poisson noise term arising from the discrete nature of the observed galaxy number density. As in \citet{Rassat:2008bao}, we considered the linear relation \eqref{eq:galaxy_overdensity_to_matter_overdensity} to hold in the standard cosmological model on large scales up to a redshift-dependent $k_{\max}(z)$ with $k_{\max}(z = 0) \simeq 0.12 h$Mpc$^{-1}$ and $k_{\max}(z = 2) \simeq 0.25 h$Mpc$^{-1}$. We then proceeded to define a modified selection function that includes the effects of bias and growth in the linear regime,
\begin{equation}
\phi^{\mathrm{evol}} = b(r, k) D(r) \phi(r) \;.
\label{eq:modified_selection}
\end{equation}
Using this modified selection function, the observed galaxy density can now be expressed directly as a function of the true matter overdensity at present time:
\begin{equation}
\frac{n(\mathbf{r})}{\bar{n}} = \phi(r) + \phi^\mathrm{evol}(r, k)\delta(\mathbf{r}) + \phi(r) \epsilon(\mathbf{r}) \;.
\label{eq:density_to_overdensity}
\end{equation}
\subsection{Tomographic analysis of galaxy clustering}
In the tomographic analysis, the survey is decomposed into spectroscopic redshift bins from which are computed classical angular correlation functions. The angular number density for one spectroscopic bin $(i)$ limited between $z_{\min}^{(i)}$ and $z_{\max}^{(i)}$ is defined as
\begin{equation}
n^{(i)}(\mathbf{\theta}) = \bar{n}^{(i)} \left(1 + \delta^{(i)}(\mathbf{\theta})\right) = \int_{z_{\min}^{(i)}}^{z_{\max}^{(i)}} n(z, \mathbf{\theta}) \mathrm{d} z \;,
\end{equation}
where $\bar{n}^{(i)}$ is the average galaxy number density per steradians in tomographic bin $(i)$ and $\delta^{(i)}(\mathbf{\theta})$ is the angular galaxy overdensity in bin $(i)$. Expanding the angular overdensity in spherical harmonics yields
\begin{equation}
n_{\ell m}^{(i)} = \int n^{(i)}(\mathbf{\theta}) Y_{\ell m}^*(\mathbf{\theta}) \mathrm{d} \mathbf{\theta} \;,
\end{equation}
From this spherical harmonics expansion, the tomographic angular correlation functions between bins $i$ and $j$, noted $\overline{C}^{(i j)}_\ell$, is defined for $\ell \geq 1$ as
\begin{align}
{\overline{C}^{m m^\prime}_{\ell \ell^\prime}}^{(i j)} &\equiv \frac{1}{\bar{n}^{(i) 2}} <n_{\ell m}^{(i)} n_{\ell^\prime m^\prime}^{(j) *} > \;, \\
&= \left( C^{(i j)}_\ell + \frac{\delta^K_{i j}}{ \bar{n}^{(i)}} \right) \delta_{\ell \ell^\prime}^K \delta^K_{m m^\prime} \;,
\label{eq:tomopowspec}
\end{align}
where $\delta^K$ is the Kronecker symbol. In the last equation, the first term $C^{(i j)}_\ell$ is the contribution from galaxy clustering and the second term $\frac{1}{\bar{n}^{(i)}}$ is the contribution from shot noise, which only affects the auto-correlation power spectra. Note that different angular modes are predicted to be uncorrelated in linear theory for a Gaussian random field; these can become correlated as a result of non-linearities or lack of full-sky coverage, effects that we did not consider in this work. Formally, the correlation functions $C_\ell^{(ij)}$ are related to the matter power spectrum $P(k)$ at $z = 0$, in the linear regime, according to
\begin{align}
C^{(i j)}_{\ell} &= \frac{2}{\pi} \int \mathrm{d}k P(k) k^2 \int w^{(i)}_\mathrm{evol}(r,k) j_\ell(k r) \mathrm{d}r \nonumber \\
& \quad \times \int w^{(j)}_\mathrm{evol}(r^\prime,k) j_\ell(k r^\prime) \mathrm{d}r^\prime \;,
\end{align}
where $w_{\mathrm{evol}}^{(i)}$ is a window function for bin $(i),$ which includes the effects of spectroscopic selection, linear growth, and bias:
\begin{equation}
w^{(i)}_{\mathrm{evol}} = \phi^{\mathrm{evol}}(r,k) s^{(i)}(r) \;,
\end{equation}
with $\phi^{\mathrm{evol}}$ is the modifier selection function including growth and bias introduced in Eq. \eqref{eq:modified_selection} and $s^{(i)}$ is the spectroscopic selection function that defines the redshift bin $i$ , that is, $s^{(i)}(z) = 1$ if $z \in [z^{(i)}_{\min}, z^{(i)}_{\max}]$, $s^{(i)}(z) = 0$ otherwise.
This expression is the full general expression of the tomographic angular power spectrum. However, it is common to evaluate the angular power spectrum through the well-known Limber approximation. To the first order \citep{Loverde:2008limber}, the Limber approximation applied to the previous equation yields\begin{multline}
C^{(i j)}_{\ell |_{\mathrm{ Limber}}} = \int \frac{\mathrm{d}r}{r^2} P\left(\frac{\ell + 1/2}{r}\right) w^{(j)}_\mathrm{evol}\left(r,\frac{\ell + 1/2}{r}\right) \\
\times \quad w^{(i)}_\mathrm{evol}\left(r,\frac{\ell + 1/2}{r}\right) \;.
\end{multline}
The Limber approximation holds to very good accuracy for the auto-correlations under the assumption that the bin window functions do not vary too rapidly or that the overlap between bins is not too small.
\subsection{3D spherical Fourier-Bessel analysis of galaxy clustering}
\label{sec:3DSFB}
The spherical Fourier-Bessel transform of the galaxy number density $n(\mathbf{r})$ is defined as\begin{equation}
n_{l m}(k) = \sqrt{\frac{2}{\pi}} \int n(\mathbf{r}) k j_\ell(k r) Y_{l m}^*(\theta,\varphi) \mathrm{d}\mathbf{r} \;,
\label{eq:SFB}
\end{equation}
where $j_\ell$ are spherical Bessel functions, $Y_{\ell m}$ are spherical harmonics, $\ell$ and $m$ are multipole moments, and $k$ is the wavenumber. Note that in this work we follow the orthonormal convention for the SFB, as in \citet{Rassat:2012bao}, \citet{Fisher:1995}, or \citet{Pratten:2013}. From the SFB coefficients $n_{\ell m}(k)$, the number density can be recovered through the inverse SFB transform as
\begin{equation}
n(r, \theta, \varphi) = \sqrt{\frac{2}{\pi}} \sum\limits_{\ell, m} \int n_{\ell m}(k) k j_\ell(k r) \mathrm{d}k Y_{\ell m}(\theta,\varphi) \;.
\label{eq:Inv_SFB}
\end{equation}
Although the SFB expansion is performed in comoving space, in practice, the galaxy number density is only observed in redshift space. This means that a fiducial cosmology has
to be assumed to relate observed redshift and comoving distance of the galaxies in the survey. To distinguish between true comoving distance $r$ and estimated comoving distance, we introduce the notation
\begin{equation}
\tilde{r} \equiv r_{|_\mathrm{fid}}(z) \;.
\end{equation}
When the fiducial cosmology exactly corresponds to the true cosmology, $\tilde{r} = r,$ but in general, this is not the case. The importance of making this distinction has been stressed in \citet{Heavens:2006}, especially when constraining dark energy parameters, which are very sensitive to the $r(z)$ relation.
For multipoles of order $\ell \ge 1$, the 3D SFB spectrum of the observed galaxy density can be expressed in the form
\begin{align}
\overline{C}_{\ell \ell^{\prime}}^{m m^\prime}(k, k^\prime) &\equiv \frac{1}{\bar{n}^2} <n_{\ell m} (k) n_{\ell^\prime m^\prime}^* (k^\prime) > \;, \\
&= \left( C_\ell(k, k^\prime) + N_\ell(k,k^\prime) \right) \delta_{\ell \ell^\prime}\delta_{m m^\prime} \;. \label{eq:SFBpowspec}
\end{align}
This expression can be directly compared to the definition of the tomographic power spectra in Eq. \eqref{eq:tomopowspec}. Just like in the tomographic case, different angular multipoles are not correlated when an angular mask is neglected. In this expression, the signal power spectrum $C_{\ell}(k, k^\prime)$ takes the form (see \cite{Rassat:2012bao} for this exact prescription or \cite{Heavens:1995})
\begin{equation}
C_\ell(k, k^\prime)= \left(\frac{2}{\pi}\right)^2 \int k^{\prime \prime 2} P(k^{\prime \prime}) W_\ell^{\mathrm{evol}}(k,k^{\prime \prime}) W_\ell^{\mathrm{evol}}(k^\prime,k^{\prime \prime}) \mathrm{d}k^{\prime \prime} \;,
\end{equation}
where the following window function includes the effects of linear growth and bias and the fiducial redshift-comoving distance relation:
\begin{equation}
W_\ell^{\mathrm{evol}}(k,k^{\prime \prime}) = k \int \phi^\mathrm{evol}(r, k^{\prime \prime}) j_\ell(k \tilde{r}) j_\ell(k^{\prime \prime} r) r^2 \mathrm{d}r \;.
\end{equation}
The noise covariance matrix can be expressed as
\begin{equation}
N_\ell(k,k^\prime) = \frac{2 k k^\prime}{\bar{n}\pi} \int \phi(r) j_\ell(k \tilde{r}) j_\ell(k^\prime \tilde{r}) r^2 \mathrm{d}r \;.
\end{equation}
This expression is equivalent to that used in \citet{Desjacques:bao}, and a derivation can be found in Appendix~\ref{sec:ShotNoise}.
When considering a realistic galaxy survey with finite depth, the observed galaxy number density vanishes above a given $r_{\max}$ and fulfils
\begin{equation}
\forall (\theta, \phi), \quad n(r_{\max}, \theta, \phi) = 0 \;.
\end{equation}
Under this boundary condition, the spherical Fourier-Bessel transform can be inverted from discretely sampled coefficients $n_{\ell m}(k_{\ell n})$ and \eqref{eq:Inv_SFB} becomes
\begin{equation}
n(r, \theta, \phi) = \sum\limits_{\ell, m, n} \kappa_{\ell n} n_{\ell m}(k_{\ell n}) k_{\ell n} j_\ell(k_{\ell n} r) Y_{\ell m}(\theta,\phi) \;,
\end{equation}
where the discrete wavenumbers $k_{\ell n}$ are defined in terms of the zeros of the spherical Bessel function $q_{\ell n}$ as
\begin{equation}
k_{\ell n} = \frac{q_{\ell n}}{r_{\max}} \;,
\label{eq:scale_sampling}
\end{equation}
and the normalisation factors $\kappa_{\ell n}$ are defined as $\kappa_{\ell n} = \frac{\sqrt{2 \pi} r_{\max}^{-3}}{j_{l+1}^2(q_{l n})}$ \citep{Fisher:1995}.
In the context of Fisher matrix forecasting, the main consequence of this discretisation is that it imposes a discrete sampling of the SFB spectrum that can be represented in matrix form $C_\ell(n, n^\prime) = C_\ell(k_{\ell n}, k_{\ell n^\prime})$ without loss of information.
\subsection{Effect of partial sky coverage}
\label{sec:fsky}
So far, we have assumed complete sky coverage. However, obscuration and confusion due to our own galaxy means that only a portion of the sky is observable in practice. This effect can be modelled in a similar way for both tomographic and SFB derivations by applying an angular weighting function $M(\theta,\phi)$ to the galaxy density field, for instance with $M(\theta,\phi) = 0$ in masked areas and $M(\theta, \phi) = 1$ otherwise. The effect of such a mask on angular power spectra is well known and results in a coupling of angular modes that would otherwise remain uncorrelated. Formally, the signal part of both tomographic and SFB power spectra becomes
\begin{align}
C_{\ell \ell^\prime}^{m m^\prime (i j)} &= \sum\limits_{\ell'' m''} M_{\ell m \ell'' m''} M_{\ell' m' \ell'' m''} C_{\ell''}^{(i j)} \;, \\
C_{\ell \ell'}^{m m'} (k, k') &= \sum_{\ell'' m''} M_{\ell m \ell'' m''} M_{\ell' m' \ell'' m''} \iint K_{\ell \ell''}(k,k_1) K_{\ell' \ell''}(k',k_2) \nonumber \\
&\quad \times \quad C_{\ell''}(k_1, k_2) \quad \mathrm{d}k_1 \mathrm{d}k_2 \;,
\end{align}
where $M_{\ell m \ell'' m''}$ is an angular coupling kernel defined in terms of the angular mask as
\begin{equation}
M_{\ell m \ell' m'} = \int_\Omega Y_{\ell^\prime m^\prime}(\Omega) M(\Omega) Y_{\ell m}^*(\Omega) \;,
\end{equation}
and $K_{\ell \ell'}(k, k')$ is a wavenumber coupling kernel defined as
\begin{equation}
K_{\ell \ell'}(k, k') = \frac{2}{\pi} k^{\prime 2} \int_r j_{\ell}(k r) j_{\ell'}(k' r) r^2 dr \;.
\end{equation}
The noise part of the power spectra that is the result
of shot noise can be approximated as only affected by a simple area scaling \citep{3dwl:2014}. Note that the coupling matrix $K_{\ell \ell'}(k, k')$ reduces to a Dirac delta function when $\ell = \ell'$ thanks to the orthogonality of the spherical Bessel functions. In both cases, the mask will induce a coupling of angular modes. In the SFB case, this also means that the coupling kernels $K_{\ell \ell'}(k, k')$ can no longer be considered as Dirac delta functions and induce an additional coupling between different wavenumbers.
In practice, the impact of the mask can conveniently be taken into account using the pseudo-$C_\ell$ methodology, which is well known for studies of the cosmic microwave background \citep{Hivon:2002}. In the tomographic as well as the SFB analysis, the pseudo-$C_\ell$ estimator can be linked to the theoretical $C_\ell$ power spectrum using either a 2D or 3D mixing matrix:
\begin{align}
<\widetilde{C}_\ell(k_{\ell n}, k_{\ell n'})> &= \sum\limits_{\ell' n_1 n_2} M^{3D}_{\ell \ell' n n_1 n' n_2} C_{\ell'}(k_{\ell' n_1}, k_{\ell' n_2}) \;, \\
<\widetilde{C}_\ell^{(i j)}> &= \sum\limits_{\ell \ell'} M^{2D}_{\ell \ell'} C_{\ell'}^{(i j)} \;.
\end{align}
A derivation of the 2D mixing matrix can be found in \cite{Hivon:2002}, while the 3D matrix for the galaxy clustering SFB power spectrum is derived in \cite{Pratten:2013}.
For the purpose of this paper, it is important to point out that the effect of the mask can be taken into account in a similar way using pseudo-$C_\ell$s for the two methodologies explored here. Consequently, in a likelihood analyses using these expressions for the measured power spectra, the effect of the mask should be equivalent for the tomographic and SFB approaches. Therefore we only took partial sky coverage through the common $f_{sky}$ scaling factor into account here for simplicity. This is standard practice for Fisher matrix analyses.
\section{Forecasting cosmological constraints}
\label{sec:Forecasting}
\subsection{Fisher matrix forecasting}
Expected cosmological constraints using the two different analysis techniques introduced in the previous section can be estimated with the Fisher matrix formalism \citep*{Tegmark:1997th}. The Fisher information matrix provides a lower bound on the expected errors on cosmological parameters under the assumption that the likelihood can be approximated by a Gaussian at its peaks. It is formally defined as the expectation value of the second derivative of the logarithmic likelihood with respect to the parameters $\Theta_\alpha, \Theta_\beta $:
\begin{equation}
F_{\alpha\beta} = - \left\langle \frac{\partial^2 \ln L}{\partial\Theta_\alpha \partial \Theta_\beta} \right\rangle \;.
\end{equation}
From this matrix, the marginal error on parameter $\Theta_\alpha$ in particular can be extracted
as $\sqrt{(F^{-1})_{\alpha \alpha}}$ , and the error on $\Theta_\alpha$, all other parameters being fixed, is bounded by $(F_{\alpha \alpha})^{-1/2}$.
The Fisher matrix may be computed from the covariance matrix of the observable and its derivatives as
\begin{equation}
F_{\alpha \beta} = \frac{1}{2} Tr[C^{-1} C_{,\alpha} C^{-1} C_{,\beta}] \;.
\end{equation}
\subsubsection{Implementing the tomographic Fisher matrix}
For the tomographic spectra $C_\ell^{(i j)}$, we computed the covariances between spectra under the Gaussian approximation following the approach of \citet{Hu:2004} and \citet{Joachimi:2009}. Denoting by $\Delta C_\ell^{(i j)}$ the difference between the ensemble average of the spectrum and its estimator, the tomographic power spectra covariance is defined as
\begin{align}
\mathrm{Cov}^{(ijkl)}_\ell &\equiv \left\langle \Delta C_\ell^{(i j)} \Delta C_\ell^{(k l)}\right\rangle \;, \\
&= \frac{\delta_{\ell \ell^\prime}}{f_{sky} (2 \ell + 1)} \left[ \bar{C}_\ell^{(ik)} \bar{C}_\ell^{(jl)} +\bar{C}_\ell^{(il)}\bar{C}_\ell^{(jk)} \right] \;,
\end{align}
where $f_{sky}$ accounts for partial coverage of the sky and $\bar{C}_\ell^{(ij)}$ is the tomographic power spectrum including shot noise defined in Eq. \eqref{eq:tomopowspec}. The expression of the tomographic Fisher matrix becomes
\begin{equation}
F_{\alpha\beta}^{tomo} = \sum\limits_{(ij), (kl)} \sum\limits_{\ell}^{\ell_{\max}(ijkl)} \frac{\partial C_\ell^{(ij)}}{\partial \Theta_\alpha} {\mathrm{Cov}^{-1}}_\ell^{(ij kl)} \frac{\partial C_\ell^{(kl)}}{\partial \Theta_\beta} \;,
\end{equation}
where the sum over $(ij), (kl)$ indices loops over all $N_{zbins} (N_{zbins} +1)/2$ combinations of bins, and $\ell_{max}$ is a cut in multipole. The aim of this cut is to restrict the Fisher matrix to linear scales. Several strategies are possible to define $\ell_{\max}$; we describe the one adopted in this work in Sect.~\ref{sec:LinearScales}.
For the binning strategy, we chose to use equal galaxy density bins with no overlap. This choice led to bins with irregular widths, but constant shot noise.
\subsubsection{Implementing the SFB Fisher matrix}
The Fisher matrix for the 3D SFB spectra was computed using the non-diagonal covariance matrix obtained by discretising wavenumbers $k$ under the boundary condition $n(r_{\max}) = 0$ as explained in Sect. \ref{sec:3DSFB}. Details of computing the non-diagonal covariance matrix are given in Appendix~\ref{sec:SFBCov}. In the absence of angular mask, Eq.~\ref{eq:SFBpowspec} shows that the SFB coefficients are uncorrelated between different angular multipoles $\ell$. Therefore, the Fisher matrix for the SFB spectra takes the following form:
\begin{equation}
F^{SFB}_{\alpha \beta} = f_{sky} \sum\limits_{\ell} \frac{(2 \ell + 1 )}{2} \mathrm{Tr}\left[\widehat{C}_\ell^{-1} \frac{\partial \widehat{C}_\ell}{\partial \Theta_\alpha} \widehat{C}_\ell^{-1} \frac{\partial \widehat{C}_\ell}{\partial \Theta_\beta} \right] \;,
\end{equation}
where the matrices $\widehat{C}_\ell$ are defined as
\begin{equation}
\widehat{C}_\ell = \left[\begin{matrix} \overline{C}_\ell(0,0) & \overline{C}_\ell(0,1) & \ldots & \overline{C}_\ell(0,n_{\max}^{\ell}) \\
\overline{C}_\ell(1,0) & \overline{C}_\ell(1,1) & \ldots & \overline{C}_\ell(1,n_{\max}^{\ell}) \\
\vdots& \vdots &\ddots &\vdots\\
\overline{C}_\ell(n_{\max}^\ell,0) & \overline{C}_\ell(n_{\max}^\ell,1) & \ldots & \overline{C}_\ell(n_{\max}^{\ell},n_{\max}^{\ell})
\end{matrix}\right] \;,
\end{equation}
with $\overline{C}_\ell(n,p) = C_\ell(k_{\ell n}, k_{\ell p}) + N_\ell(k_{\ell n}, k_{\ell p})$. The size of each of this matrix $\widehat{C}_\ell$ is $n_{\max}^{\ell} \times n_{\max}^{\ell}$ , where $n_{\max}^\ell$ defines the maximum wavenumber included in the Fisher analysis for each multipole $\ell$. This allows us to restrict the analysis to linear scales. Again, different strategies can be adopted to define this cut in wavenumber; they are described in Sect.~\ref{sec:LinearScales}.
\subsubsection{Fisher analysis baseline}
To conduct this study, we adopted as a fiducial model a `Vanilla' concordance flat cosmology with $h = 0.7$, $\Omega_b=0.045$, $\Omega_m = 0.25$, $\Omega_\Lambda = 0.75$, $\Omega_b = 0.045$, $w_0 = -0.95$, $w_a = 0$, $n_s = 1$, $\tau = 0.09$, and $\sigma_8 = 0.8$. We adopted the standard parametrisation for the dark energy equation of state \citep{Chevallier:2001},\begin{equation}
w(a) = w_0 + w_a (1 - a) \;.
\end{equation}
This fiducial cosmology was also used to compute the $\tilde{r} = r_{\mathrm{fid}}(z)$. In this model, we computed the linear matter power spectra, including baryonic oscillations, using the fitting formula of \cite{EisensteinHu:1998}. We performed our Fisher analysis on the following parameters $\Theta = (h, \Omega_m, w_0, w_a, \Omega_b, n_s, \sigma_8)$ under the constraint of a flat cosmology.
For our baseline analysis we considered a spectroscopic survey with a very small redshift uncertainty $\sigma_z = 0.003(1+z)$ and a Smail-type galaxy distribution $p(z)$ \citep{Smail:1994},
\begin{equation}
p(z) \propto z^{2} e^{ - \left( \frac{z}{0.708} \right)^{1.5}} \;,
\end{equation}
which corresponds to a median redshift of $z_{\mathrm{med}} = 1,$ and we used a mean number density of galaxies of $\bar{n} = 0.9$ gal. arcmin$^{-2}$. To account for partial coverage of the sky, we scaled the Fisher information by $f_{sky} = 0.3636,$ which corresponds to a survey size of 15,000 square degrees. This setting was chosen to correspond to the specification of the stage-IV Euclid spectroscopic survey \citep{Redbook}.
Finally, we adopted a redshift dependent fiducial galaxy bias of the form
\begin{equation}
b(z, k) = \sqrt{1 + z} \;,
\label{eq:bias}
\end{equation} as in \cite{Rassat:2008bao}.
In Sect.~\ref{sec:NuisanceParameters} we describe how we accounted for our lack of knowledge on the actual galaxy bias by parametrising this relation through nuisance parameters.
\subsubsection{Restriction to linear scales}
\label{sec:LinearScales}
The constraints we aim to extract from a galaxy survey result from the information contained in the matter power spectrum. However, since the galaxies are only biased tracers of the actual underlying matter density, our knowledge of the matter power spectrum is limited by our understanding of the bias. This bias becomes more uncertain on small non-linear scales. Assuming an optimistic knowledge of the bias could result in overestimated or cosmologically biased constraints. Hence, following previous galaxy clustering studies \citep[e.g.,][]{Rassat:2007KRL,Rassat:2008bao,Joachimi:2009}, we completely discarded the mildly to non-linear scales and express our uncertainty of the bias on large scales by using nuisance parameters in the next section.
As the aim of this work is to compare the constraining power of two different approaches to galaxy clustering analysis, it is important to apply the exclusion of non-linear scales to the two methods in a coherent way to avoid biasing our results towards the method with the less conservative cut. Following the approach taken in \citet{Joachimi:2009}, which was based on results from \citet{Rassat:2008bao}, we aim to only retain linear scales through the following redshift-dependent cut in wavenumber $k_{\mathrm{lin}}^{\max}$:
\begin{equation}
k_{\mathrm{lin}}^{\max}(z) \approx \min[0.132 z, \quad 0.25] \quad h \mathrm{Mpc}^{-1} \;.
\end{equation}
This formula is a linear fit to the non-linearity scale in Fig. 2 of \citet{Rassat:2008bao}, which was computed as a function of redshift by selecting scales that fulfil $\sigma(R) < 0.20$ and $k_{\max} < 0.25 h$Mpc$^{-1}$, where $\sigma(R)$ corresponds to the amplitude of fluctuations at $R ~h$Mpc$^{-1}$. However, it provides a conservative cut at lower redshift (below z=0.5). Since the purpose of this work is to compare two methodologies given the same framework and set of assumptions, we used this model for the sake of simplicity. An accurate computation of the non-linear scale could be used just as well, but this is not expected to change the conclusions of the comparative analysis.
Because we computed the tomographic power spectra within the Limber approximation, we related wavenumbers $k$ to angular modes $\ell$ through $k = \frac{\ell + 1/2}{r}$. As a result, the non-linear scale cut translates into multipoles $\ell$ for redshift bin $(i)$ as
\begin{equation}
\ell_{max}^{(i)} = k_{\mathrm{lin}}^{\max}(z_{\mathrm{med}}^{(i)}) r( z_{\mathrm{min}}^{(i)}) \;.
\end{equation}
This cut allows us to reject all the multipoles for a given bin $(i)$ that is affected by scales above $k_{\mathrm{lin}}^{\max}(z_{\mathrm{med}}^{(i)})$. When computing the correlation function between two different bins $(i), (j)$ we applied the most conservative cut: $\ell_{max}^{(i j)} = \min(\ell_{max}^{(i)}, \ell_{max}^{(j)})$.
In the SFB framework, applying a corresponding wavenumber cut leads to an $\ell$ dependent maximum number of discrete wavenumbers $k_{\ell n}$, noted $n_{\max}^{\ell}$, which can be obtained as the solution of the equation
\begin{equation}
k_{\ell n_{\max}^{\ell}} r \left( \frac{ 0.132}{k_{\ell n_{\max}^{\ell}}} \right) = \ell \;,
\end{equation}
under the constraint $k_{\ell n_{\max}^{\ell}} \leq 0.25 \quad h \mathrm{Mpc}^{-1}$. Both cuts are illustrated in Fig.~\ref{fig:linear}.
\begin{figure}[t]
\includegraphics[width=\columnwidth]{Figures/Fig1}
\caption{Top: Linear-scale limit in $k$ for the SFB power spectra as a function of angular modes. Bottom: Linear-scale limit $\ell_{\max}$ for the tomographic power spectra $C^{(ij)}_\ell$ as a function of the lowest median redshift of the spectroscopic bins $i$ and $j$. The regions above the lines are excluded from the Fisher analysis.}
\label{fig:linear}
\end{figure}
Thanks to this prescription, the same scales are excluded from the tomographic and SFB analysis. This point is the main difference between our work and the analysis performed in \citet{Nicola:2014}, where the exclusion of non-linear scales is not coherent between the two methodologies. In their work, the angular power spectra are truncated at $\ell_{max} = 50$ for all redshifts, whereas as shown in Fig.~\ref{fig:linear}, $\ell_{max}$ should be a function of the median redshifts of the tomographic bins to take into account the time evolution of the non-linear scale as well as the physical size of angular modes as a function of redshift. Similarly, in the SFB analysis performed in their work, a fixed cut at $k_{\max}=0.20 ~ h \mathrm{Mpc}^{-1}$ was applied, which not only ignores the interplay between angular modes and $z$ illustrated by Fig.~\ref{fig:linear}, but is also incoherent with the cut applied in the tomographic analysis.
\subsubsection{Nuisance parameters}
\label{sec:NuisanceParameters}
As mentioned in the previous section, restricting the study to linear scales avoids the high uncertainty on the bias that arises in the non-linear regime. Nevertheless, we also wish to express our uncertainty on the bias even on linear scales. Following the approach of \citet{Bridle:2007}, \citet{Joachimi:2009}, and \citet{DK:2012}, we parametrised the bias in redshift and scale using a grid of nuisance parameters such that the galaxy bias becomes\begin{equation}
b(k, z) = A Q(k, z) b_0(k,z) \;,
\end{equation}
where $b_0$ is our fiducial bias relation \eqref{eq:bias}, $A$ is an overall amplitude and $Q(k, z)$ encodes perturbations around the fiducial bias and is defined in terms of an $N_z \times N_k$ grid of parameters $B_{i j}$:
\begin{multline}
\ln Q(k, z) = K_{i}(k) Z_{j}(z) B_{i j} + [1 - K_{i}(k) ] Z_{j} B_{(i+1) j} \\
+ K_{i} [ 1 - Z_{j}(z)] B_{i (j+1)} + [1 - K_{i}(k) ] [ 1 - Z_{j}(z)] B_{(i+1)(j+1)} \;,
\end{multline}
for $k_i \leq k \leq k_{i+1}$ and $z_j < z \leq z_{j+1}$, where the coefficients $Z_j$ and $K_i$ are expressed as
\begin{align}
K_i(k) =& \frac{\ln(k) - \ln( k_i)}{ \ln(k_{i+1}) - \ln(k_i)} \;, \\
Z_j(k) =& \frac{\ln( 1 + z) - \ln(1 + z_j)}{\ln(1 + z_{j+1}) - \ln(1 + z_j)} \;.
\end{align}
The $k_i$ and $z_j$ fix the nodes of the grid and are spaced logarithmically in the intervals $k \in [10^{-4}, 1.0]$ and $z \in [0, 5]$ such that $k_0 = k_{\min}$, $k_{N_k+1} = k_{\max}$ and $z_0 = z_{\min}$, $z_{N_z + 1} = z_{\max}$. The Fisher matrices are then obtained by marginalising over these $N_k \times N_z +1$ nuisance parameters $\left( A, B_{0 0}, B_{0 1}, B_{1 0}, \ldots , B_{N_k N_z} \right)$.
\subsection{Figures of merit}
\label{sec:FoM}
Throughout the rest of this work we compare the constraining power of the tomographic and SFB methods by evaluating their respective figures of merit (FoM). We consider two FoMs, first the total figure of merit $\mathrm{FoM}_{\mathrm{TOT}}$ defined according to \cite{Joachimi:2009} as
\begin{equation}
\mathrm{FoM}_{\mathrm{TOT}} = \ln\left( \frac{1}{\det(F^{-1}) } \right) \;,
\end{equation}
and second, the dark energy figure of merit recommended by the report of the Dark Energy Task Force \citep{DETF},
\begin{equation}
\mathrm{FoM}_{\mathrm{DETF}} = \frac{1}{\sqrt{\det( F^{-1} )_{w_0 w_a}}} \;.
\end{equation}
The DETF FoM was designed to measure the strength of a given future survey or probe in constraining cosmological parameters related to the nature of dark energy, such that a large FoM$_{\rm DETF}$ value meant a high constraining power on $w_0$ and $w_a$. The total FoM (FoM$_{\rm TOT}$) was designed to encompass the strength of a future survey or probe in constraining several parameters across different sectors of cosmology, such as the nature of dark matter and dark energy and initial conditions. A high value of FoM$_{\rm TOT}$ therefore means a good constraining power across all cosmological sectors. The parameter is taken as an $\ln$ value, since we consider this number for seven cosmological parameters, and the FoM$_{\rm TOT}$ value would grow very quickly otherwise.
\section{Results: SFB vs. tomographic analysis}
\label{sec:results}
\subsection{Comparison of SFB and tomographic analysis in the absence of systematics}
\label{results:3d2d}
Here, we compare the relative constraining power of the tomographic and SFB analysis of galaxy clustering presented in Sect.\ref{sec:theory} using the Fisher matrix formalism and the fiducial cosmology and survey baseline described in Sect.~\ref{sec:Forecasting}. We investigate first the impact of the number of redshift bins and whether the same constraints can be recovered from the two different analysis. Figure~\ref{fig:3dvs2d} shows the FoMs obtained using both methods as a function of number of tomographic spectroscopic bins when assuming perfect knowledge of the bias (in dark blue).
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{Figures/Fig2}
\caption{Comparison of the total ${\rm FoM}_{\mathrm{TOT}}$ (top) and dark energy ${\rm FoM}_{\mathrm{DETF}}$ (bottom) figures of merit for the 3D Fourier-Bessel analysis (horizontal dashed lines) vs. tomographic analysis (solid lines) as a function of number of redshift bins. The upper lines (dashed and triangle) result from assuming a fixed bias, the lower lines (dotted and circle) are obtained when assuming a grid of $5 \times 5$ nuisance parameters in scale and redshift described in Sect.~\ref{sec:NuisanceParameters}.}
\label{fig:3dvs2d}
\end{figure}
As expected, the two figures of merit for the tomographic analysis increase with the number of redshift bins and eventually reach the performance of the SFB analysis for 30 redshift bins. Not only do the two methodologies yield equivalent figures of merit for this number of bins, but the $1\sigma$ contours for all cosmological parameters are extremely similar, both in size of the ellipse and for the direction of the degeneracies. Figure~\ref{fig:constraints} shows the $1\sigma$ contours on all pairs of cosmological parameters considered for the two analysis techniques using 30 tomographic bins with and without nuisance parameters for the bias. For the fixed bias, the contours obtained by the tomographic analysis are plotted in red and are almost indistinguishable from the contours for the SFB analysis, which are depicted in orange.
\begin{figure*}[!ht]
\centering
\includegraphics[width=\textwidth]{Figures/Fig3}
\caption{1$\sigma$ contours for all pairs of cosmological parameters for the SFB analysis and the tomographic analysis for 30 bins with and without nuisance parameters. Inner orange and red contours (almost indistinguishable) result from the SFB and tomographic analysis when assuming a fixed bias. Outer yellow and purple contours are obtained from the SFB and tomographic analysis when using a $5 \times 5$ nuisance parameter grid in scale and redshift for the bias.}
\label{fig:constraints}
\end{figure*}
We conclude that exactly the same information is extracted from the two methodologies for an appropriate number of redshift bins, 30 in our case.
This result disagrees with the conclusions of \citet{Nicola:2014}, who found that the SFB analysis is weaker than a tomographic analysis and not capable of extracting the same radial information. The difference in these conclusions is probably related to the choice of non-linear prescription. In \cite{Nicola:2014}, the tomographic SHT analysis was limited to a fixed $\ell_{\max}$ for all bins, while the SFB analysis was restricted to a fixed $k_{\max}$ for all multipoles. However, we show in Fig.~\ref{fig:linear} that to apply equivalent cuts for the tomographic and SFB analysis, redshift-dependent $\ell_{\max}(z_{med})$ and $\ell$-dependent $k_{\max}(\ell)$ cuts need to be used.
\bigskip
Additionally, Fig.~\ref{fig:3dvs2d} shows that when the number of bins is increased, the tomographic analysis eventually surpasses the SFB analysis. This behaviour is expected, because when the width of the redshift bins reaches the non-linearity scale, the tomographic analysis probes more modes than a 3D analysis \citep{Asorey:2012,Clzz}. Indeed, only non-linear angular scales are excluded from the tomographic analysis, but for very thin redshift bins, small radial scales are being probed that are potentially beyond the non-linear cut-off. \citet{Asorey:2012} found that a tomographic analysis with a bin width of $\Delta r \simeq 0.8 \frac{2 \pi}{k_{\max}}$ was equivalent to a 3D power spectrum analysis including scales up to $k_{\max}$. We found that the tomographic analysis recovers the information from the 3D analysis for about 30 redshift bins. If one expects the two methodologies to give similar results for $\Delta r \simeq \frac{2\pi}{k_{max}}$ , then one would expect a larger number of tomographic bins to be necessary. Here, our 30 bins correspond to a minimum bin width $\Delta r \simeq 0.55 \frac{2\pi}{k_{max}}$ , which is not as close to the non-linearity scale as the results from \citet{Asorey:2012}, but remains of the same order of magnitude.
However, we stress that such a direct comparison is subject to several factors that complicate the interpretation. Firstly, the tomographic spectra are computed within the Limber approximation, which may not be accurate for a large number of thin bins. A recent study of the effect of the Limber approximation for a
spectroscopic survey can be found in \citet{Eriksen:2014}. Because we restricted our analysis to large linear scales, we limited the number of tomographic bins to 30 in the rest of the analysis, which corresponds to redshift widths between $\Delta_z=0.1$ and $\Delta_z=0.05$. In this case, according to \citet{Eriksen:2014}, the error of approximation remains limited (below 15\% for most bins). Therefore, we do not expect the full computation to significantly alter the results of the comparative study lead in this work. Nevertheless, this point should be kept in mind and deserves a thorough analysis, which we will include in future work. We also stress that although care has been taken to apply similar non-linear cuts, they are not strictly equivalent, and different strategies to restrict angular modes in the tomographic analysis would affect the results.
Therefore, we consider that for a fixed bias, both analysis methodologies recover the same information for 30 tomographic bins, which corresponds to a minimum bin width of the order of the non-linearity scale. We also acknowledge that the exact number of bins is likely to change for different binning strategy, computation techniques of angular power spectra, restrictions of non-linear scales and with the inclusion of additional effects such as redshift space distortions or relativistic effects. A thorough study of all these effects will be addressed in a future paper.
\subsection{Impact of systematics due to galaxy bias}\label{sec:nuisance}
After establishing that the same information can be recovered from both methodologies in the absence of systematics on the bias, we now investigate the impact of an unknown bias. As described in Sect.~\ref{sec:NuisanceParameters}, we include in the analysis an uncertainty on the galaxy bias using a grid of nuisance parameters in scale and redshift. Figure~\ref{fig:3dvs2d} demonstrates how the FoMs for both analysis are degraded when using a free bias parametrised in scale and redshift by a $5\times 5$ nuisance parameter grid (in cyan). Whereas the FoMs were equivalent with 30 tomographic bins in the fixed bias case, the tomographic analysis can no longer recover the same information as the SFB analysis in the free bias case, even with 60 redshift bins. The tomographic analysis is much more sensitive to systematics resulting from the unknown bias than the SFB analysis.
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{Figures/Fig4}
\caption{Total FoM$_{\rm TOT}$ (top) and dark energy FoM$_{\rm DETF}$ (bottom) figures of merit as a function of the number of nuisance parameters in redshift (left) and scale (right), for a tomographic with 30 bins (red triangle) and an SFB (blue dot) analysis. When varying the number of nuisance parameters in scale or redshift, the other number of parameters is kept fixed at 5.}
\label{fig:nuisance}
\end{figure}
We investigated the effect of the number of nuisance parameters in scale and redshift $N_k \times N_z$ on the FoMs for the tomographic (red triangle) and SFB (blue dot) analysis in Fig.~\ref{fig:nuisance}. We varied $N_k$ and $N_z$ independently while keeping the other parameter fixed to $5$. When the number of nuisance parameters increases, the constraints from both analyses decreases, although the FoMs from the tomographic analysis degrade faster than for the SFB analysis.
Although the FoMs reach a plateau at about $N_z=12$ and $N_k=6$, these numbers would correspond to a very conservative model of the galaxy bias and therefore are probably unrealistic. Indeed, the evolution of galaxy bias should be smooth on large scales, which prompts us to limit the fiducial parameter grid used in this section to $N_z=5$ and $N_k=5$. Since the trends in FoMs do not change with the number of nuisance parameters, a more complex grid (increasing either $N_z$ or $N_k$) would not change the conclusions on the relative strength of the two methodologies investigated here (the SFB FoM remains higher for any choice of nuisance parameters).
The effect of the free bias on the $1\sigma$ contours on cosmological parameters is shown in Fig.~\ref{fig:constraints}, where the purple and yellow contours are computed from the 30-bin tomographic analysis and the SFB analysis. Interestingly, the constraints on $\sigma_8$ and $n_s$ are affected in the same way for the two methodologies by the inclusion of nuisance parameters; the contours are almost equivalent for $(n_s,\sigma_8)$ with or without nuisance parameters. In contrast, all other parameters are much more degraded by the including nuisance parameters in the case of the tomographic analysis compared to the SFB analysis. This is particularly true for the dark energy parameters $w_0$ and $w_a$.
These results agree with \cite{Asorey:2012}, who noted that the tomographic constraints degrade faster than a 3D power spectrum analysis when a single nuisance parameter on the amplitude of the bias was included. We find a similar behaviour with a more flexible parameterisation of the bias and for the 3D SFB analysis.
Furthermore, these results highlight the well-known sensitivity of galaxy clustering studies to the galaxy bias, which is one of its most important systematics. Although other approaches such as the measurement of the BAO scale are less sensitive to the galaxy bias, this results in the usual trade-off between systematics and statistical constraining power, so that BAO studies alone (i.e. using only BAO scale measurement) only provide conservative constraints without relying on external priors \citep{Rassat:2008bao}.
\subsection{Optimisation of a stage-IV survey}
Since we have shown in Sect. \ref{sec:nuisance} that the 3D SFB and tomographic methods depend differently on nuisance parameters, we are interested in investigating whether there are other differences in using one method or the other to plan for future wide-field surveys.
In this section we investigate the influence of the median redshift on the constraining power of a stage-IV spectroscopic survey using the two techniques. To perform this comparison, we used the same $5 \times 5$ nuisance parameter grid for the bias as in the previous section. We also adapted the number of tomographic bins to the median redshift of the survey to preserve the equivalence between tomographic and SFB constraints in the absence of systematics found in Sect.~\ref{results:3d2d}. The smallest radial scales probed by a tomographic analysis depend on the depth of the survey and on the number of bins. Therefore, to remain coherent for different median redshifts with the SFB analysis, the number of bins needs to be adjusted to the median redshift.
We find that for a median redshift of $z_{med} \simeq 0.4$, the number of bins of the tomographic analysis should be $N=26$ and for $z_{med} \simeq 1.7$ this number increases to $N=42$.
To illustrate this point, we plot in Fig.~\ref{fig:opt} the FoMs
as red triangles as a function of the median redshift using this adapted number of bins. The cyan line shows the evolution of the FoMs when keeping the number of bins fixed at $N=30$. Since this number of 30 tomographic bins was chosen in the previous section based on our fiducial survey with a median redshift of 1, we see that the red and cyan curves cross at $z_{med}=1$. However, using 30 bins below $z_{med}=1$ means probing smaller radial scales, which are beyond the scales probed by the SFB analysis, and this increases the FoMs. In contrast, above $z_{med}=1$, this means using wider tomographic bins and thus probing larger radial scales, which lowers the FoMs compared to when the number of bins is adapted.
We also plot in Fig.~\ref{fig:opt} the 3D SFB FoMs as a function of the median redshift of the survey, using blue circles. This curve should be compared to the red triangles showing the FoMs for the tomographic analysis where we have adapted the number of tomographic bins based on the median redshift, as described above.
The two techniques exhibit a similar scaling with the median redshift of the survey, although the SFB constraints are consistently better than the tomographic constraints. Interestingly, for median redshifts above $z_{med}=1.4$, the SFB dark energy FoM exhibits a better scaling than the tomographic one.
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{Figures/Fig5}
\caption{Total ${\rm FoM}_{\mathrm{TOT}}$ (top) and dark energy ${\rm FoM}_{\mathrm{DETF}}$ (bottom) figures of merit as a function of median redshift of a stage-IV spectroscopic survey using a tomographic analysis (red triangles) and an SFB analysis (blue dots). The cyan line shows the figures of merit for the tomographic analysis when the number of bins is not adapted to the depth of the survey and kept at 30 bins. For the red-dashed lines, the number of bins has been adapted to each median redshift. In all cases, a grid of $5 \times 5$ nuisance parameters in scale and redshift is used to parametrise the galaxy bias.}
\label{fig:opt}
\end{figure}
In conclusion, in the presence of galaxy bias systematics, any desired FOM level can be reached for shallower surveys if a 3D SFB analysis is performed. Furthermore, increasing the depth of the survey is more profitable in terms of FOM$_{\rm DETF}$ for the 3D SFB analysis because the tomographic method reaches
a plateau somewhat after $z=1$, whereas the 3D method continues to increase significantly up to $z=1.8$, potentially pushing the optimisations towards higher median redshifts.
\section{Conclusion}
\label{sec:ccl}
We have compared two different approaches to the three-dimensional analysis of galaxy clustering in the context of wide and deep future spectroscopic galaxy surveys. Based on the Fisher matrix analysis, we have compared the tomographic spherical harmonics and spherical Fourier-Bessel (SFB) methodologies in terms of figures of merit and cosmological parameter constraints.
We focused on the seven common parameters that are currently used in wide-field survey optimisation and planning: $\vec{\theta}=\{\Omega_m, h, w_0, w_a, \sigma_8, \Omega_b, n_s\}$, while putting forward a coherent and realistic approach regarding the exclusion of non-linear scales for both the 2D and 3D methods. In addition, we investigated for the first time how tomographic and 3D SFB methods are affected by nuisance parameters related to the galaxy bias, which we allowed to be both redshift- and scale-dependent.
In the absence of systematics, for an appropriate number of tomographic bins the two methodologies are equivalent and are able to recover the exact same constraints - both in value and in direction of degeneracy between different parameters. Increasing the number of redshift bins further leads to stronger constraints for the tomographic analysis, as seen by \citet{Asorey:2012}, \citet{Clzz}, and \citet{Nicola:2014}. Nevertheless, this effect could result from including radial
scales in the tomographic analysis that are beyond the non-linear cut-off applied to the SFB analysis, and should be investigated further.
On the other hand, when we included unavoidable systematics due to the galaxy bias through a grid of nuisance parameters in scale and redshift, we found that the SFB analysis is more robust than the tomographic analysis, whose constraints suffer more from including nuisance parameters. As a result, we found that when we optimised the median redshift of a stage-IV type spectroscopic galaxy survey, a given level of accuracy can be achieved for shallower surveys if a 3D SFB analysis is performed. Moreover, the scaling of the dark energy figure of merit with median redshift is better for the 3D SFB analysis in the presence of systematics, which means that a given increase of the survey depth yields more information using an SFB analysis than a tomographic analysis.
Our results suggest that an SFB analysis is preferable to a tomographic analysis for realistic future spectroscopic wide-field surveys where the galaxy bias can be both redshift- and scale-dependent, and is unknown. These conclusions should be investigated in more
detail, for example regarding the potential effect of the exact computation of angular power spectra, binning strategy, and including RSD.
In the spirit of reproducible research, the Python package \textbf{CosmicPy} developed to produce all the results presented in this work is freely available at\\ \\
{\centerline{\url{http://cosmicpy.github.io} .}}\\ \\
This package allows for simple and interactive computation of tomographic and 3D SFB power spectra as well as Fisher matrices while relying on a fast C++ implementation of Fourier-Bessel related computations.
\begin{acknowledgements}
The authors thank Chieh-An Lin and Martin Kilbinger for useful comments and discussions. This research is in part supported by the European Research Council grant SparseAstro (ERC-228261) and by the Swiss National Science Foundation (SNSF).
\end{acknowledgements}
\bibliographystyle{aa}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,415 |
package org.dcm4chex.archive.web.maverick.mwl.model;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.Comparator;
import java.util.Date;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Set;
import javax.servlet.http.HttpServletRequest;
import org.dcm4che.data.Dataset;
import org.dcm4che.data.DcmElement;
import org.dcm4che.data.DcmObjectFactory;
import org.dcm4che.dict.Tags;
import org.dcm4chex.archive.web.maverick.BasicFormPagingModel;
import org.dcm4chex.archive.web.maverick.model.PatientModel;
import org.dcm4chex.archive.web.maverick.mwl.MWLConsoleCtrl;
/**
* @author franz.willer
*
* The Model for Media Creation Managment WEB interface.
*/
public class MWLModel extends BasicFormPagingModel {
/** The session attribute name to store the model in http session. */
public static final String MWLMODEL_ATTR_NAME = "mwlModel";
/** Errorcode: unsupported action */
public static final String ERROR_UNSUPPORTED_ACTION = "UNSUPPORTED_ACTION";
private String[] mppsIDs = null;
/** Holds list of MWLEntries */
private Map mwlEntries = new HashMap();
private MWLFilter mwlFilter;
/** True if mwlScpAET is 'local' to allow deletion */
private boolean isLocal = false;
/** Comparator to sort list of SPS datasets. */
private Comparator comparator = new SpsDSComparator();
// hold patient infos for merge (same patients/stickyPatients model structure as FolderForm)
private List patients = new ArrayList();
private final Set stickyPatients = new HashSet();
/** Holds reason of merge. */
private String mergeReason=null;
/** Used to preselect dominant patient in patient_merge view */
private PatientModel dominantPat;
/**
* Creates the model.
* <p>
* Creates the filter instance for this model.
*/
private MWLModel( HttpServletRequest request ) {
super(request);
getFilter();
}
/**
* Get the model for an http request.
* <p>
* Look in the session for an associated model via <code>MWLMODEL_ATTR_NAME</code><br>
* If there is no model stored in session (first request) a new model is created and stored in session.
*
* @param request A http request.
*
* @return The model for given request.
*/
public static final MWLModel getModel( HttpServletRequest request ) {
MWLModel model = (MWLModel) request.getSession().getAttribute(MWLMODEL_ATTR_NAME);
if (model == null) {
model = new MWLModel(request);
request.getSession().setAttribute(MWLMODEL_ATTR_NAME, model);
model.setErrorCode( NO_ERROR ); //reset error code
model.filterWorkList( true );
}
return model;
}
public String getModelName() { return "MWL"; }
/**
* Returns the Filter of this model.
*
* @return MWLFilter instance that hold filter criteria values.
*/
public MWLFilter getFilter() {
if ( mwlFilter == null ) {
mwlFilter = new MWLFilter();
}
return mwlFilter;
}
/**
* Return a list of MWLEntries for display.
*
* @return Returns the mwlEntries.
*/
public Collection getMwlEntries() {
return mwlEntries.values();
}
public MWLEntry getMWLEntry(String spsID) {
return (MWLEntry) mwlEntries.get(spsID);
}
/**
* Returns true if the MwlScpAET is 'local'.
* <p>
* <DL>
* <DT>If it is local:</DT>
* <DD> 1) Entries can be deleted. (shows a button in view)</DD>
* <DD> 2) The query for the working list is done directly without a CFIND.</DD>
* </DL>
* @return Returns the isLocal.
*/
public boolean isLocal() {
return isLocal;
}
/**
* Returns > 0 if MWL console is in 'link' mode.
* <p>
* This mode is set if mwl_console.m is called with action=link.
* <p>
* The value is euivalent to the number of selected MPPS (size of mppsIDs).
*
* @return Returns the linkMode.
*/
public int getLinkMode() {
return mppsIDs == null ? 0 : mppsIDs.length;
}
/**
* @return Returns the mppsIDs.
*/
public String[] getMppsIDs() {
return mppsIDs;
}
/**
* @param mppsIDs The mppsIDs to set.
*/
public void setMppsIDs(String[] mppsIDs) {
this.mppsIDs = mppsIDs;
}
public void setPatMergeAttributes(Map map) {
patients.clear();
stickyPatients.clear();
if ( map != null ) {
dominantPat = new PatientModel( (Dataset) map.get("dominant") );
stickyPatients.add(new Long(dominantPat.getPk()));
patients.add(dominantPat);
Dataset[] dsa = (Dataset[]) map.get("priorPats");
PatientModel pat;
for ( int i = 0 ; i < dsa.length ; i++ ) {
pat = new PatientModel( dsa[i]);
stickyPatients.add(new Long(pat.getPk()));
patients.add(pat);
}
mergeReason="Linking MWL to MPPS requires patient merge!";
} else {
dominantPat = null;
mergeReason = null;
}
}
public final List getPatients() {
return patients;
}
public final Set getStickyPatients() {
return stickyPatients;
}
public String getMergeReason() {
return mergeReason;
}
/**
* @return Returns the dominant patient for necessary merge.
*/
public PatientModel getMergeDominant() {
return dominantPat;
}
/** returns the name of the view used after merge is done. (have to be configured in maverick.xml!) */
public String getMergeViewName() {
return "mpps_link";
}
/**
* Update the list of MWLEntries for the view.
* <p>
* The query use the search criteria values from the filter and use offset and limit for paging.
* <p>
* if <code>newSearch is true</code> will reset paging (set <code>offset</code> to 0!)
* @param newSearch
*/
public void filterWorkList(boolean newSearch) {
if ( newSearch ) setOffset(0);
Dataset searchDS = getSearchDS( mwlFilter );
isLocal = MWLConsoleCtrl.getMwlScuDelegate().isLocal();
List l = MWLConsoleCtrl.getMwlScuDelegate().findMWLEntries( searchDS );
Collections.sort( l, comparator );
int total = l.size();
int offset = getOffset();
int limit = getLimit();
int end;
if ( offset >= total ) {
offset = 0;
end = limit < total ? limit : total;
} else {
end = offset + limit;
if ( end > total ) end = total;
}
Dataset ds;
mwlEntries.clear();
int countNull = 0;
MWLEntry entry;
for ( int i = offset ; i < end ; i++ ){
ds = (Dataset) l.get( i );
if ( ds != null ) {
entry = new MWLEntry( ds );
mwlEntries.put( entry.getSpsID(), entry );
} else {
countNull++;
}
}
setTotal(total - countNull); // the real total (without null entries!)
}
/**
* Returns the query Dataset with search criteria values from filter argument.
* <p>
* The Dataset contains all fields that should be in the result;
* the 'merging' fields will be set to the values from the filter.
*
* @param mwlFilter2 The filter with search criteria values.
*
* @return The Dataset that can be used for query.
*/
private Dataset getSearchDS(MWLFilter filter) {
Dataset ds = DcmObjectFactory.getInstance().newDataset();
//requested procedure
ds.putSH( Tags.RequestedProcedureID );
ds.putUI( Tags.StudyInstanceUID );
//imaging service request
ds.putSH( Tags.AccessionNumber, mwlFilter.getAccessionNumber() );
ds.putLT( Tags.ImagingServiceRequestComments );
ds.putPN( Tags.RequestingPhysician );
ds.putPN( Tags.ReferringPhysicianName );
ds.putLO( Tags.PlacerOrderNumber );
ds.putLO( Tags.FillerOrderNumber );
//Visit Identification
ds.putLO( Tags.AdmissionID );
//Patient Identification
String patientName = mwlFilter.getPatientName();
if ( patientName != null &&
patientName.length() > 0 &&
patientName.indexOf('*') == -1 &&
patientName.indexOf('?') == -1) patientName+="*";
ds.putPN( Tags.PatientName, patientName );
ds.putLO( Tags.PatientID);
//Patient demographic
ds.putDA( Tags.PatientBirthDate );
ds.putCS( Tags.PatientSex );
//Sched. procedure step seq
DcmElement elem = ds.putSQ( Tags.SPSSeq );
Dataset ds1 = elem.addNewItem();
ds1.putAE( Tags.ScheduledStationAET, filter.getStationAET() );
ds1.putSH( Tags.SPSID );
ds1.putCS( Tags.Modality, filter.getModality() );
ds1.putPN( Tags.ScheduledPerformingPhysicianName );
if ( filter.getStartDate() != null || filter.getEndDate() != null ) {
Date startDate = null, endDate = null;
if ( filter.startDateAsLong() != null )
startDate = new Date ( filter.startDateAsLong().longValue() );
if ( filter.endDateAsLong() != null )
endDate = new Date ( filter.endDateAsLong().longValue() );
ds1.putDA( Tags.SPSStartDate, startDate, endDate );
ds1.putTM( Tags.SPSStartTime, startDate, endDate );
} else {
ds1.putDA( Tags.SPSStartDate );
ds1.putTM( Tags.SPSStartTime );
}
ds1.putSH( Tags.ScheduledStationName );
//sched. protocol code seq;
DcmElement spcs = ds1.putSQ( Tags.ScheduledProtocolCodeSeq );
Dataset dsSpcs = spcs.addNewItem();
dsSpcs.putSH( Tags.CodeValue );
dsSpcs.putLO( Tags.CodeMeaning );
dsSpcs.putSH( Tags.CodingSchemeDesignator );
// or
ds1.putLO( Tags.SPSDescription );
//Req. procedure code seq
DcmElement rpcs = ds.putSQ( Tags.RequestedProcedureCodeSeq );
Dataset dsRpcs = rpcs.addNewItem();
dsRpcs.putSH( Tags.CodeValue );
dsRpcs.putLO( Tags.CodeMeaning );
dsRpcs.putSH( Tags.CodingSchemeDesignator );
// or
ds.putLO( Tags.RequestedProcedureDescription );
return ds;
}
/* (non-Javadoc)
* @see org.dcm4chex.archive.web.maverick.BasicFormPagingModel#gotoCurrentPage()
*/
public void gotoCurrentPage() {
filterWorkList( false );
}
/**
* Inner class that compares two datasets for sorting Scheduled Procedure Steps
* according scheduled Procedure step start date.
*
* @author franz.willer
*
* TODO To change the template for this generated type comment go to
* Window - Preferences - Java - Code Style - Code Templates
*/
public class SpsDSComparator implements Comparator {
private final Date DATE_0 = new Date(0l);
public SpsDSComparator() {
}
/**
* Compares the scheduled procedure step start date and time of two Dataset objects.
* <p>
* USe either SPSStartDateAndTime or SPSStartDate and SPSStartTime to get the date.
* <p>
* Use the '0' Date (new Date(0l)) if the date is not in the Dataset.
* <p>
* Compares its two arguments for order. Returns a negative integer, zero, or a positive integer
* as the first argument is less than, equal to, or greater than the second.
* <p>
* Throws an Exception if one of the arguments is null or not a Dataset object.
*
* @param arg0 First argument
* @param arg1 Second argument
*
* @return <0 if arg0<arg1, 0 if equal and >0 if arg0>arg1
*/
public int compare(Object arg0, Object arg1) {
Dataset ds1 = (Dataset) arg0;
Dataset ds2 = (Dataset) arg1;
Date d1 = _getStartDateAsLong( ds1 );
return d1.compareTo( _getStartDateAsLong( ds2 ) );
}
/**
* @param ds1 The dataset
*
* @return the date of this SPS Dataset.
*/
private Date _getStartDateAsLong(Dataset ds) {
if ( ds == null ) return DATE_0;
DcmElement e = ds.get( Tags.SPSSeq );
if ( e == null ) return DATE_0;
Dataset spsItem = e.getItem();//scheduled procedure step sequence item.
Date d = spsItem.getDate( Tags.SPSStartDateAndTime );
if ( d == null ) {
d = spsItem.getDateTime( Tags.SPSStartDate, Tags.SPSStartTime );
}
if ( d == null ) d = DATE_0;
return d;
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,844 |
Ted Sutton is an American actor and voice over artist. He is best known for playing Sergeant Cunningham in M. Night Shyamalan's 2002 film Signs.
Career
Sutton began as a New York actor, but his role in Signs gained him attention, and led to further roles, including guest appearances in 24, Law & Order: SVU, Cold Case, JAG, Charmed, 10-8, and Star Trek: Enterprise. Sutton played a department store regional manager who took a big cash bribe on The Young and the Restless. Sutton says that role was the most fun he has ever had. He is noted for his distinctive speaking voice. He played a doctor in Clint Eastwood's Million Dollar Baby.
Filmography
References
External links
website
Year of birth missing (living people)
Living people
American male film actors
Place of birth missing (living people) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,924 |
{"url":"https:\/\/plainmath.net\/21739\/to-write-the-two-other-true-proportions-for-frac-1-4-equal-frac-5-20","text":"# To write: The two other true proportions for \\frac{1}{4}=\\frac{5}{20}\n\nTo write:\nThe two other true proportions for $\\frac{1}{4}=\\frac{5}{20}$\nYou can still ask an expert for help\n\n\u2022 Questions are typically answered in as fast as 30 minutes\n\nSolve your problem for the price of one coffee\n\n\u2022 Math expert for every subject\n\u2022 Pay only if we can solve it\n\nApproach:\nA proportion is true, if its ratios are equal. As ratios are fractions, one way to determine whether the given proportion is true or false by writting both the ratios in simplest form. Another way is by comparing their cross product.\nIf the cross product are equal, then the proportion is said to be true. If cross product are not equal, then the proportion is false.\nCalculation:\nIf two ratios are equal in a proportion, then it is called a true proportion.\nIf it is a true proportion, their cross product are equal.\n$\\frac{1}{4}=\\frac{5}{20}$\n$1\u00d720=4\u00d75$\nTherefore, the two other true proportions will be\n$\\frac{20}{4}=\\frac{5}{1}$ and $\\frac{4}{20}=\\frac{1}{5}$\nFinal statement:\nThe two other true proportion are $\\frac{20}{4}=\\frac{5}{1}$ and $\\frac{4}{20}=\\frac{1}{5}$\nJeffrey Jordon","date":"2022-05-28 21:03:03","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 32, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8848692178726196, \"perplexity\": 977.9619260240223}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652663019783.90\/warc\/CC-MAIN-20220528185151-20220528215151-00148.warc.gz\"}"} | null | null |
{"url":"https:\/\/mathoverflow.net\/questions\/292818\/why-are-regular-categories-assumed-to-be-finitely-complete","text":"# Why are Regular Categories assumed to be finitely complete?\n\nRegular categories may equivalently defined as those with:\n\n\u2022 finite limits\n\u2022 coequalizers of kernel pairs\n\u2022 pulback stable regular epis\n\nor\n\n\u2022 finite limits\n\u2022 pullback stable regular epi\/mono factorization\n\nWhen carefully proving the equivalence, the only limits required are pullbacks i.e. in a category with pullbacks:\n\ncoequalizers of kernel pairs & stable regular epis $\\iff$ stable regular epi\/mono factorization.\n\nIs there a compelling reason to require all finite limits?\n\n\u2022 Possibly the link to the logic of the internal language suggests one might want a terminal object. Feb 12, 2018 at 20:35\n\u2022 Perhaps one wants equalizers and products (finite ones) and so we might as well require all finite limits, since their existence follows from those ? Feb 12, 2018 at 20:38\n\u2022 David: could you elaborate? Feb 12, 2018 at 20:47\n\u2022 @Tyler Mike said it better in his answer. Feb 13, 2018 at 0:44\n\nThere are many reasons one might give for why the notion of \"regular category\" includes a terminal object (and hence all finite products), but I think one fairly compelling one is that, as David said in a comment, one wants the internal logic of a regular category to be regular logic, and one needs all finite products in order to define a type theory and internal logic: a term $x:A, y:B \\vdash t:C$ is a morphism $A\\times B\\to C$, and a term $\\cdot \\vdash t:C$ is a morphism $1\\to C$. (One can make do with a cartesian multicategory instead, but a locally regular category doesn't have an underlying one of those either.)\n\u2022 Thanks @mike-shulman. I see you had a hand in writing the relevant nlab locally regular category. Is the definition in your answer here equivalent to that given there? Specifically, are there equalizers in a category with stable reg. epi\/mono factorization and pullbacks? Side note: pullbacks + reg. epi\/mono factorization (not necessarily stable) $\\implies$ reg. epi = strong epi = extremal epi. so the extremal epi\/mono factorization will be reg. epi\/mono already. Feb 12, 2018 at 22:48","date":"2023-03-31 21:44:08","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7893868088722229, \"perplexity\": 1452.046495556686}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296949689.58\/warc\/CC-MAIN-20230331210803-20230401000803-00302.warc.gz\"}"} | null | null |
Q: Generating continued fractions for square roots I wrote this code for generating Continued Fraction of a square root N.
But it fails when N = 139.
The output should be {11,1,3,1,3,7,1,1,2,11,2,1,1,7,3,1,3,1,22}
Whilst my code gives me a sequence of 394 terms... of which the first few terms are correct but when it reaches 22 it gives 12!
Can somebody help me with this?
vector <int> f;
int B;double A;
A = sqrt(N*1.0);
B = floor(A);
f.push_back(B);
while (B != 2 * f[0])) {
A = 1.0 / (A - B);
B =floor(A);
f.push_back(B);
}
f.push_back(B);
A: The culprit isn't floor. The culprit is the calculation A= 1.0 / (A - B); Digging deeper, the culprit is the IEEE floating point mechanism your computer uses to represent real numbers. Subtraction and addition lose precision. Repeatedly subtracting as your algorithm is doing repeatedly loses precision.
By the time you have calculated the continued fraction terms {11,1,3,1,3,7,1,1,2,11,2}, your IEEE floating point value of A is good to only six places rather than the fifteen or sixteen one would expect. By the time you get to {11,1,3,1,3,7,1,1,2,11,2,1,1,7,3,1,3,1} your value of A is pure garbage. It has lost all precision.
A: The root problem is that you cannot exactly represent the square root of a non-square as a floating-point number.
If ξ is the exact value and x the approximation (which is supposed to be still quite good, so that in particular floor(ξ) = a = floor(x) still holds), then the difference after the next step of the continued fraction algorithm is
ξ' - x' = 1/(ξ - a) - 1/(x - a) = (x - ξ) / ((ξ - a)*(x - a)) ≈ (x - ξ) / (ξ - a)^2
Thus we see that in each step the absolute value of the difference between the approximation and the real value increases, since 0 < ξ - a < 1. Every time a large partial quotient occurs (ξ - a is close to 0), the difference increases by a large factor. Once (the absolute value of) the difference is 1 or greater, the next computed partial quotient is guaranteed to be wrong, but very probably the first wrong partial quotient occurs earlier.
Charles mentioned the approximation that with an original approximation with n correct digits, you can compute about n partial quotients of the continued fraction. That is a good rule of thumb, but as we saw, any large partial quotients cost more precision and thus reduce the number of obtainable partial quotients, and occasionally you get wrong partial quotients much earlier.
The case of √139 is one with a relatively long period with a couple of large partial quotients, so it's not surprising that the first wrongly computed partial quotient appears before the period is completed (I'm rather surprised that it doesn't occur earlier).
Using floating-point arithmetic, there's no way to prevent that.
But for the case of quadratic surds, we can avoid that problem by using integer arithmetic only. Say you want to compute the continued fraction expansion of
ξ = (√D + P) / Q
where Q divides D - P² and D > 1 is not a perfect square (if the divisibility condition is not satisfied, you can replace D with D*Q², P with P*Q and Q with Q²; your case is P = 0, Q = 1, where it is trivially satisfied). Write the complete quotients as
ξ_k = (√D + P_k) / Q_k (with ξ_0 = ξ, P_0 = P, Q_0 = Q)
and denote the partial quotients a_k. Then
ξ_k - a_k = (√D - (a_k*Q_k - P_k)) / Q_k
and, with P_{k+1} = a_k*Q_k - P_k,
ξ_{k+1} = 1/(ξ_k - a_k) = Q_k / (√D - P_{k+1}) = (√D + P_{k+1}) / [(D - P_{k+1}^2) / Q_k],
so Q_{k+1} = (D - P_{k+1}^2) / Q_k — since P_{k+1}^2 - P_k^2 is a multiple of Q_k, by induction Q_{k+1} is an integer and Q_{k+1} divides D - P_{k+1}^2.
The continued fraction expansion of a real number ξ is periodic if and only if ξ is a quadratic surd, and the period is completed when in the above algorithm, the first pair (P_k, Q_k) repeats. The case of pure square roots is particularly simple, the period is completed when first Q_k = 1 for a k > 0, and P_k, Q_k are always nonnegative.
With R = floor(√D), the partial quotients can be calculated as
a_k = floor((R + P_k) / Q_k)
so the code for the above algorithm becomes
std::vector<unsigned long> sqrtCF(unsigned long D) {
// sqrt(D) may be slightly off for large D.
// If large D are expected, a correction for R is needed.
unsigned long R = floor(sqrt(D));
std::vector<unsigned long> f;
f.push_back(R);
if (R*R == D) {
// Oops, a square
return f;
}
unsigned long a = R, P = 0, Q = 1;
do {
P = a*Q - P;
Q = (D - P*P)/Q;
a = (R + P)/Q;
f.push_back(a);
}while(Q != 1);
return f;
}
which easily calculates the continued fraction of (e.g.) √7981 with a period length of 182.
A: The sqrt function in math is not precise. You can use sympy instead with arbitrarily high precision. Here is a very easy code to calculate continued fractions for any square root or number included in sympy:
from __future__ import division #only needed when working in Python 2.x
import sympy as sp
p=sp.N(sp.sqrt(139), 5000)
n=2000
x=range(n+1)
a=range(n)
x[0]=p
for i in xrange(n):
a[i] = int(x[i])
x[i+1]=1/(x[i]-a[i])
print a[i],
I have set the precision of your number to 5000 and then calculated 2000 continued fraction coefficients in this example code.
A: In case anyone is trying to solve this is in a language without integers, here is the code from the accepted answer adapted for JavaScript.
Note two ~~ (floor operators) have been added.
export const squareRootContinuedFraction = D =>{
let R = ~~Math.sqrt(D);
let f = [];
f.push(R);
if (R*R === D) {
return f;
}
let a = R, P = 0, Q = 1;
do {
P = a*Q - P;
Q = ~~((D - P *P)/Q);
a = ~~((R + P)/Q);
f.push(a);
} while (Q != 1);
return f;
};
A: I used you algo in a spreadsheet and I get 12 as well, I think you must have made a mistake in your algo, I tried for 253 values, and B did not reach the final value of it.
Can you try to explain a bit more what the algo should do and how it would work ?
I think I got your algo and you made a mistake in your question, it should be 12. For future reference, the algo can be found at this page http://en.wikipedia.org/wiki/Continued_fraction and it is very prone to issues with decimal/numerical computational issues if the inverse value is very close to the integer you are trying to round at.
When doing the prototype under Excel, I could not reproduce the example of the wiki page for 3.245, because at some point Floor() floored the number to 3 instead of 4, so some boundary checking to check for accuracy is required ...
In this case you probably want to add a maximum number of iteration, a tolerance for checking the exit condition (the exit condition should be that A is equal to B btw)
A: Your code isn't calculating the square root of n. It attempts to calculate the continued fraction of an already calculated √n. I mean it's OK but, had it been correct, your approach is more suitable for general decimal to rational convertion. However for a sqrt function for the regular (simple) continued fractions (where all numerators are ones) the algorithm is slightly different.
However the problem isn't finished. Yes as a rule, the CF coefficients for √n is in the form of a repeating palindrome which ends with the double of the first nonzero coefficient. Such as √31 =[5;1,1,3,5,3,1,1,10,1,1,3,5,3,1,1,10..]. Now there is no simple way to quess the length of the palindrome for every given n. There are some known patterns however they are far from defining a generalized pattern for all n. So stoping the iteration at the end of the first palindrome is a very undeterministic approach. Imagine
__
√226 =[15;30]
while
____________________________________________________
√244 =[15;1,1,1,1,1,2,1,5,1,1,9,1,6,1,9,1,1,5,1,2,1,1,1,1,1,30]
If you decide to stop the iteration at 2*f[0] most of the time you get either a bad approximation like in √226 or an over-calculated one like in √244 case. Besides, once n grows, chasing the end of the palindrome becomes more meaningless since you will never need such a precision.
___________________________________________________________________________________________________________________________________________________________________________
√7114 = [84;2,1,9,3,1,10,2,23,1,1,1,1,1,2,1,27,2,1,1,3,1,2,1,1,1,16,4,3,1,3,2,1,6,18,1,1,2,6,11,11,6,2,1,1,18,6,1,2,3,1,3,4,16,1,1,1,2,1,3,1,1,2,27,1,2,1,1,1,1,1,23,2,10,1,3,9,1,2,168]
In this case it would be reasonable to stop the iteration once the necessary precision is obtained. As I have mentioned at the beginning, there are two approaches.
*
*The general Decimal to Rational algorithm obtains simple continued fractions from any decimal number. This will give a CF resolving to exactly to that decimal without any floating point errors. For a detailed explanation of this algorithm you may check a previous answer of mine.
*There happens to be a more direct algorithm for √n which is basically the same as 1 but tuned for square roots. In this case you don't provide √n but n.
The idea is as follows. We have to define a general form for the input which involves a square root value at the numerator. Then we try to reach to the same expression in the continued fraction part to be able to iterate.
Let our input be of the form
q + √n
______
p
for simple square root operation we can assume q is 0 and p is 1. If we can establish this form at the next stage then we can easily iterate on.
Starting with the initial stage where q = 0, p = 1, m is the integer part of √n and 1/x is the floating part, our target is to bring x into (q + √n) / p form;
1 1 1 (√n + m) √n + m
√n = m + ___ ⇒ x = _______ ⇒ x = ________ . ________ ⇒ x = ________
x √n - m (√n - m) (√n + m) n - m^2
Now √n is at the numerator and we have the form of;
√n + q
x = ______
p
where q = m and p = n - m^2. Right at this point you can calculate x and the next m by flooring x. The generalized form of the algorithm becomes;
√n + q 1 p p(√n - (q - pm)) p(√n + (pm - q))
x = ______ = m + ___ ⇒ x' = ______________ = _________________ = ________________
p x' √n + (q - pm) n - (q - pm)^2 n - (q - pm)^2
at this point p is divisible by n - (q - pm)^2. This is now stable and we can extend it as long as we want. Let's make new assignments for q and p as;
q' = pm-q;
p' = (n - q'^2)/p;
√n + q'
x' = ______
p'
m' = Math.floor(x')
Note that when p' becomes 1 (n - q'^2 = p) we are at the end of the palindrome. However in order to decide where to stop I am using the same mechanism as described in my toRational algorithm as linked in the alternative 1 above. It basically stops once the JS floating point resolution is reached. The JavaScript code is as follows;
function rationalSqrt(n){
var nr = Math.sqrt(n),
m = Math.floor(nr),
p = n-m**2,
q = m,
cs = [m],
n0 = 1,
d0 = 0,
n1 = m,
d1 = 1,
n2 = 0,
d2 = 1;
if (nr === m) return {n:m,d:1,cs};
while (Math.abs(nr-n2/d2) > Number.EPSILON){
m = Math.floor((nr+q)/p);
q = m*p-q;
p = (n-q**2)/p;
cs.push(m);
n2 = m*n1+n0;
d2 = m*d1+d0;
n0 = n1;
d0 = d1;
n1 = n2;
d1 = d2;
}
return {n:n2,d:d2,cs};
}
These two algorithms differ slightly.
*
*~60% of the time they result same fractions.
*~27% of the time toRational gives smaller numerators and denominators within the JS floating point resolution. However surely it's not a better approximation had we have one more digit in JS.
*~13% of the time rationalSqrt (this one) gives smaller numerators and denominators within the JS floating point resolution.
*rationalSqrt will result exact coefficients as one would expect from a square root but will be truncated once the resolution is enough.
*toRational gives expected coefficients of couse but the last one could be totally unrelated to what you would expect from the square root series.
One such example is;
rationalSqrt(511); //returns
{ n : 882184734
, d : 39025555
, cs: [22,1,1,1,1,6,1,14,4,1,21,1,4,14,1,6,1]
}
while
toRational(Math.sqrt(511));
{ n : 1215746799
, d : 53781472
, cs: [22,1,1,1,1,6,1,14,4,1,21,1,4,14,1,10]
}
Further thoughts:
*
*Consider that we are given the RCF coefficients. Can we reverse the
rationalSqrt alogrithm to obtain it's(q + √n) / p form? This
might come as an interesting task.
*Practiacally limiting the CF with the JS decimal resolution would yield a similar precision in CF arithmetics and you would be wasting your time. In order to achieve higher square root resolution I advise to replace while (Math.abs(nr-n2/d2) > Number.EPSILON) condition with while (cs.length < 30) if 30 CF coefficients of resolution would be sufficient for your application. That figure is up to you.
A: I used a Surd Storage type for infinite precision of the square root of n.
(b * \sqrt(n) + d)/c
=
(b * c * sqrt(n) - c * d + a_i * c^2) / (b^2 * n - d^2 - (a_i * c)^2 + 2* a_i * c * d)
The floor value of the sqrt(n) is only used once. After which the remaining iterations are stored as a surd type. This avoids the rounding errors seen in other algorithms and infinite (memory constrained) resolution can be achieved.
a_0 = floor value of sqrt (n)
a_i = (b_i * a_0 + d_i) / c_i
b_i+1 = b_i * c
c_i+1 = (b_i)^2 * n - (d_i)^2 - (a_i * c_i)^2 + 2 * a_i * c_i * d_i
d_i+1 = a_i * (c_i)^2 - c_i * d_i
g = gcd(b_i+1 , c_i+1 , d_i+1)
b_i+1 = b_i+1 / g
c_i+1 = c_i+1 / g
d_i+1 = d_i+1 / g
a_i+1 = (b_i+1 * x + d_i+1) / c_i+1
Then for i=0 to i=Maximum_terms a continued fraction is produced
beginning with [a_0;a_1,a_2 ... ,2*a_0]
I terminate the fraction when the a_i term equals 2 times the a_0.
This is the point at which the sequence repeats.
The mathematics was done by Electro World and a very nice video on
the mathematics can be found here https://youtu.be/GFJsU9QsytM
The source code written in Java with BigInteger is provided below.
Hope you like it.
A boolean true is returned if a repeat series is found and false if a
repeat sequence is not found for the desired precision.
The precision can be easily modified to suit as per Maximum_terms.
The square root 139
[11;1,3,1,3,7,1,1,2,11,2,1,1,7,3,1,3,1,22] repeat length 18
The square root of 15 [3;1,6] repeat length 2
The square root of 2501 [50;100] repeat length 1
The square root of 10807
[103;1,22,9,2,2,5,4,1,1,1,6,15,1,5,2,1,3,6,34,2,34,6,3,1,2,5,1,15,6,1,1,1,4,5,2,2,9,22,1,206]
repeat length 40
A possible two fold speed up would be to look at the palindromic nature of series.
In this case 34,2,34.
Only half the sequence would need to be determined.
public static Boolean SquareRootConFrac(BigInteger N) {
BigInteger A,B=BigInteger.ONE,C=B,D=BigInteger.ZERO;
BigInteger A0=N.sqrt(),Bi=B,Ci=C,Di=D,G;
BigInteger TwoA0 = BigInteger.TWO.multiply(A0);
int Frac_Length=0, Maximum_terms=10000; //Precision 10000 terms
String str="";
Boolean Repeat=false, Success=false, Initial_BCD=true;
while(!Repeat) {
Frac_Length++; Success=!(Frac_Length==Maximum_terms);
A=((B.multiply(A0)).add(D)).divide(C); Repeat=A.equals(TwoA0)||!Success;
Bi=B.multiply(C);
Ci=(B.multiply(B).multiply(N)).subtract(D.multiply(D)).subtract(A.multiply(A).multiply(C).multiply(C)).add(BigInteger.TWO.multiply(A).multiply(C).multiply(D));
Di=(A.multiply(C).multiply(C)).subtract(C.multiply(D));
G=Bi.gcd(Ci).gcd(Di);
B=Bi.divide(G);C=Ci.divide(G);D=Di.divide(G);
if(Initial_BCD) {str="["+A+";";System.out.print(str);Initial_BCD=false;}
else {str=""+A;System.out.print(str);if(!Repeat){str=",";System.out.print(str);}}
}
str="]";System.out.println(str);
str="repeat length ";System.out.print(str);
if(Success) {str=""+(Frac_Length-1);System.out.println(str);}
else {str="not found";System.out.println(str);}
return Success;
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,623 |
#include "core/editing/VisibleUnits.h"
#include "core/HTMLNames.h"
#include "core/dom/Document.h"
#include "core/dom/Element.h"
#include "core/dom/FirstLetterPseudoElement.h"
#include "core/dom/NodeTraversal.h"
#include "core/dom/Text.h"
#include "core/editing/EditingUtilities.h"
#include "core/editing/FrameSelection.h"
#include "core/editing/Position.h"
#include "core/editing/PositionIterator.h"
#include "core/editing/RenderedPosition.h"
#include "core/editing/TextAffinity.h"
#include "core/editing/VisiblePosition.h"
#include "core/editing/iterators/BackwardsCharacterIterator.h"
#include "core/editing/iterators/BackwardsTextBuffer.h"
#include "core/editing/iterators/CharacterIterator.h"
#include "core/editing/iterators/ForwardsTextBuffer.h"
#include "core/editing/iterators/SimplifiedBackwardsTextIterator.h"
#include "core/editing/iterators/TextIterator.h"
#include "core/frame/LocalFrame.h"
#include "core/frame/Settings.h"
#include "core/html/HTMLBRElement.h"
#include "core/html/TextControlElement.h"
#include "core/layout/HitTestRequest.h"
#include "core/layout/HitTestResult.h"
#include "core/layout/LayoutInline.h"
#include "core/layout/LayoutObject.h"
#include "core/layout/LayoutTextFragment.h"
#include "core/layout/LayoutView.h"
#include "core/layout/api/LayoutItem.h"
#include "core/layout/api/LayoutViewItem.h"
#include "core/layout/api/LineLayoutAPIShim.h"
#include "core/layout/api/LineLayoutItem.h"
#include "core/layout/line/InlineIterator.h"
#include "core/layout/line/InlineTextBox.h"
#include "platform/heap/Handle.h"
#include "platform/text/TextBoundaries.h"
#include "platform/text/TextBreakIterator.h"
namespace blink {
template <typename PositionType>
static PositionType canonicalizeCandidate(const PositionType& candidate) {
if (candidate.isNull())
return PositionType();
DCHECK(isVisuallyEquivalentCandidate(candidate));
PositionType upstream = mostBackwardCaretPosition(candidate);
if (isVisuallyEquivalentCandidate(upstream))
return upstream;
return candidate;
}
template <typename PositionType>
static PositionType canonicalPosition(const PositionType& passedPosition) {
// Sometimes updating selection positions can be extremely expensive and
// occur frequently. Often calling preventDefault on mousedown events can
// avoid doing unnecessary text selection work. http://crbug.com/472258.
TRACE_EVENT0("input", "VisibleUnits::canonicalPosition");
// The updateLayout call below can do so much that even the position passed
// in to us might get changed as a side effect. Specifically, there are code
// paths that pass selection endpoints, and updateLayout can change the
// selection.
PositionType position = passedPosition;
// FIXME (9535): Canonicalizing to the leftmost candidate means that if
// we're at a line wrap, we will ask layoutObjects to paint downstream
// carets for other layoutObjects. To fix this, we need to either a) add
// code to all paintCarets to pass the responsibility off to the appropriate
// layoutObject for VisiblePosition's like these, or b) canonicalize to the
// rightmost candidate unless the affinity is upstream.
if (position.isNull())
return PositionType();
DCHECK(position.document());
DCHECK(!position.document()->needsLayoutTreeUpdate());
Node* node = position.computeContainerNode();
PositionType candidate = mostBackwardCaretPosition(position);
if (isVisuallyEquivalentCandidate(candidate))
return candidate;
candidate = mostForwardCaretPosition(position);
if (isVisuallyEquivalentCandidate(candidate))
return candidate;
// When neither upstream or downstream gets us to a candidate
// (upstream/downstream won't leave blocks or enter new ones), we search
// forward and backward until we find one.
PositionType next = canonicalizeCandidate(nextCandidate(position));
PositionType prev = canonicalizeCandidate(previousCandidate(position));
Node* nextNode = next.anchorNode();
Node* prevNode = prev.anchorNode();
// The new position must be in the same editable element. Enforce that
// first. Unless the descent is from a non-editable html element to an
// editable body.
if (node && node->document().documentElement() == node &&
!hasEditableStyle(*node) && node->document().body() &&
hasEditableStyle(*node->document().body()))
return next.isNotNull() ? next : prev;
Element* editingRoot = rootEditableElementOf(position);
// If the html element is editable, descending into its body will look like
// a descent from non-editable to editable content since
// |rootEditableElementOf()| always stops at the body.
if ((editingRoot &&
editingRoot->document().documentElement() == editingRoot) ||
position.anchorNode()->isDocumentNode())
return next.isNotNull() ? next : prev;
bool prevIsInSameEditableElement =
prevNode && rootEditableElementOf(prev) == editingRoot;
bool nextIsInSameEditableElement =
nextNode && rootEditableElementOf(next) == editingRoot;
if (prevIsInSameEditableElement && !nextIsInSameEditableElement)
return prev;
if (nextIsInSameEditableElement && !prevIsInSameEditableElement)
return next;
if (!nextIsInSameEditableElement && !prevIsInSameEditableElement)
return PositionType();
// The new position should be in the same block flow element. Favor that.
Element* originalBlock = node ? enclosingBlockFlowElement(*node) : 0;
bool nextIsOutsideOriginalBlock =
!nextNode->isDescendantOf(originalBlock) && nextNode != originalBlock;
bool prevIsOutsideOriginalBlock =
!prevNode->isDescendantOf(originalBlock) && prevNode != originalBlock;
if (nextIsOutsideOriginalBlock && !prevIsOutsideOriginalBlock)
return prev;
return next;
}
Position canonicalPositionOf(const Position& position) {
return canonicalPosition(position);
}
PositionInFlatTree canonicalPositionOf(const PositionInFlatTree& position) {
return canonicalPosition(position);
}
template <typename Strategy>
static PositionWithAffinityTemplate<Strategy> honorEditingBoundaryAtOrBefore(
const PositionWithAffinityTemplate<Strategy>& pos,
const PositionTemplate<Strategy>& anchor) {
if (pos.isNull())
return pos;
ContainerNode* highestRoot = highestEditableRoot(anchor);
// Return empty position if |pos| is not somewhere inside the editable
// region containing this position
if (highestRoot && !pos.anchorNode()->isDescendantOf(highestRoot))
return PositionWithAffinityTemplate<Strategy>();
// Return |pos| itself if the two are from the very same editable region, or
// both are non-editable
// TODO(yosin) In the non-editable case, just because the new position is
// non-editable doesn't mean movement to it is allowed.
// |VisibleSelection::adjustForEditableContent()| has this problem too.
if (highestEditableRoot(pos.position()) == highestRoot)
return pos;
// Return empty position if this position is non-editable, but |pos| is
// editable.
// TODO(yosin) Move to the previous non-editable region.
if (!highestRoot)
return PositionWithAffinityTemplate<Strategy>();
// Return the last position before |pos| that is in the same editable region
// as this position
return lastEditablePositionBeforePositionInRoot(pos.position(), *highestRoot);
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> honorEditingBoundaryAtOrBefore(
const VisiblePositionTemplate<Strategy>& pos,
const PositionTemplate<Strategy>& anchor) {
DCHECK(pos.isValid()) << pos;
return createVisiblePosition(
honorEditingBoundaryAtOrBefore(pos.toPositionWithAffinity(), anchor));
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> honorEditingBoundaryAtOrAfter(
const VisiblePositionTemplate<Strategy>& pos,
const PositionTemplate<Strategy>& anchor) {
DCHECK(pos.isValid()) << pos;
if (pos.isNull())
return pos;
ContainerNode* highestRoot = highestEditableRoot(anchor);
// Return empty position if |pos| is not somewhere inside the editable
// region containing this position
if (highestRoot &&
!pos.deepEquivalent().anchorNode()->isDescendantOf(highestRoot))
return VisiblePositionTemplate<Strategy>();
// Return |pos| itself if the two are from the very same editable region, or
// both are non-editable
// TODO(yosin) In the non-editable case, just because the new position is
// non-editable doesn't mean movement to it is allowed.
// |VisibleSelection::adjustForEditableContent()| has this problem too.
if (highestEditableRoot(pos.deepEquivalent()) == highestRoot)
return pos;
// Return empty position if this position is non-editable, but |pos| is
// editable.
// TODO(yosin) Move to the next non-editable region.
if (!highestRoot)
return VisiblePositionTemplate<Strategy>();
// Return the next position after |pos| that is in the same editable region
// as this position
return firstEditableVisiblePositionAfterPositionInRoot(pos.deepEquivalent(),
*highestRoot);
}
static bool hasEditableStyle(const Node& node, EditableType editableType) {
if (editableType == HasEditableAXRole) {
if (AXObjectCache* cache = node.document().existingAXObjectCache()) {
if (cache->rootAXEditableElement(&node))
return true;
}
}
return hasEditableStyle(node);
}
static Element* rootEditableElement(const Node& node,
EditableType editableType) {
if (editableType == HasEditableAXRole) {
if (AXObjectCache* cache = node.document().existingAXObjectCache())
return const_cast<Element*>(cache->rootAXEditableElement(&node));
}
return rootEditableElement(node);
}
static Element* rootAXEditableElementOf(const Position& position) {
Node* node = position.computeContainerNode();
if (!node)
return 0;
if (isDisplayInsideTable(node))
node = node->parentNode();
return rootEditableElement(*node, HasEditableAXRole);
}
static bool hasAXEditableStyle(const Node& node) {
return hasEditableStyle(node, HasEditableAXRole);
}
static ContainerNode* highestEditableRoot(const Position& position,
EditableType editableType) {
if (editableType == HasEditableAXRole)
return highestEditableRoot(position, rootAXEditableElementOf,
hasAXEditableStyle);
return highestEditableRoot(position);
}
static Node* previousLeafWithSameEditability(Node* node,
EditableType editableType) {
bool editable = hasEditableStyle(*node, editableType);
node = previousAtomicLeafNode(*node);
while (node) {
if (editable == hasEditableStyle(*node, editableType))
return node;
node = previousAtomicLeafNode(*node);
}
return 0;
}
static Node* nextLeafWithSameEditability(
Node* node,
EditableType editableType = ContentIsEditable) {
if (!node)
return 0;
bool editable = hasEditableStyle(*node, editableType);
node = nextAtomicLeafNode(*node);
while (node) {
if (editable == hasEditableStyle(*node, editableType))
return node;
node = nextAtomicLeafNode(*node);
}
return 0;
}
// FIXME: consolidate with code in previousLinePosition.
static Position previousRootInlineBoxCandidatePosition(
Node* node,
const VisiblePosition& visiblePosition,
EditableType editableType) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
ContainerNode* highestRoot =
highestEditableRoot(visiblePosition.deepEquivalent(), editableType);
Node* previousNode = previousLeafWithSameEditability(node, editableType);
while (previousNode &&
(!previousNode->layoutObject() ||
inSameLine(
createVisiblePosition(firstPositionInOrBeforeNode(previousNode)),
visiblePosition)))
previousNode = previousLeafWithSameEditability(previousNode, editableType);
while (previousNode && !previousNode->isShadowRoot()) {
if (highestEditableRoot(firstPositionInOrBeforeNode(previousNode),
editableType) != highestRoot)
break;
Position pos = isHTMLBRElement(*previousNode)
? Position::beforeNode(previousNode)
: Position::editingPositionOf(
previousNode, caretMaxOffset(previousNode));
if (isVisuallyEquivalentCandidate(pos))
return pos;
previousNode = previousLeafWithSameEditability(previousNode, editableType);
}
return Position();
}
static Position nextRootInlineBoxCandidatePosition(
Node* node,
const VisiblePosition& visiblePosition,
EditableType editableType) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
ContainerNode* highestRoot =
highestEditableRoot(visiblePosition.deepEquivalent(), editableType);
Node* nextNode = nextLeafWithSameEditability(node, editableType);
while (nextNode && (!nextNode->layoutObject() ||
inSameLine(createVisiblePosition(
firstPositionInOrBeforeNode(nextNode)),
visiblePosition)))
nextNode = nextLeafWithSameEditability(nextNode, ContentIsEditable);
while (nextNode && !nextNode->isShadowRoot()) {
if (highestEditableRoot(firstPositionInOrBeforeNode(nextNode),
editableType) != highestRoot)
break;
Position pos;
pos = Position::editingPositionOf(nextNode, caretMinOffset(nextNode));
if (isVisuallyEquivalentCandidate(pos))
return pos;
nextNode = nextLeafWithSameEditability(nextNode, editableType);
}
return Position();
}
class CachedLogicallyOrderedLeafBoxes {
public:
CachedLogicallyOrderedLeafBoxes();
const InlineTextBox* previousTextBox(const RootInlineBox*,
const InlineTextBox*);
const InlineTextBox* nextTextBox(const RootInlineBox*, const InlineTextBox*);
size_t size() const { return m_leafBoxes.size(); }
const InlineBox* firstBox() const { return m_leafBoxes[0]; }
private:
const Vector<InlineBox*>& collectBoxes(const RootInlineBox*);
int boxIndexInLeaves(const InlineTextBox*) const;
const RootInlineBox* m_rootInlineBox;
Vector<InlineBox*> m_leafBoxes;
};
CachedLogicallyOrderedLeafBoxes::CachedLogicallyOrderedLeafBoxes()
: m_rootInlineBox(0) {}
const InlineTextBox* CachedLogicallyOrderedLeafBoxes::previousTextBox(
const RootInlineBox* root,
const InlineTextBox* box) {
if (!root)
return 0;
collectBoxes(root);
// If box is null, root is box's previous RootInlineBox, and previousBox is
// the last logical box in root.
int boxIndex = m_leafBoxes.size() - 1;
if (box)
boxIndex = boxIndexInLeaves(box) - 1;
for (int i = boxIndex; i >= 0; --i) {
if (m_leafBoxes[i]->isInlineTextBox())
return toInlineTextBox(m_leafBoxes[i]);
}
return 0;
}
const InlineTextBox* CachedLogicallyOrderedLeafBoxes::nextTextBox(
const RootInlineBox* root,
const InlineTextBox* box) {
if (!root)
return 0;
collectBoxes(root);
// If box is null, root is box's next RootInlineBox, and nextBox is the first
// logical box in root. Otherwise, root is box's RootInlineBox, and nextBox is
// the next logical box in the same line.
size_t nextBoxIndex = 0;
if (box)
nextBoxIndex = boxIndexInLeaves(box) + 1;
for (size_t i = nextBoxIndex; i < m_leafBoxes.size(); ++i) {
if (m_leafBoxes[i]->isInlineTextBox())
return toInlineTextBox(m_leafBoxes[i]);
}
return 0;
}
const Vector<InlineBox*>& CachedLogicallyOrderedLeafBoxes::collectBoxes(
const RootInlineBox* root) {
if (m_rootInlineBox != root) {
m_rootInlineBox = root;
m_leafBoxes.clear();
root->collectLeafBoxesInLogicalOrder(m_leafBoxes);
}
return m_leafBoxes;
}
int CachedLogicallyOrderedLeafBoxes::boxIndexInLeaves(
const InlineTextBox* box) const {
for (size_t i = 0; i < m_leafBoxes.size(); ++i) {
if (box == m_leafBoxes[i])
return i;
}
return 0;
}
static const InlineTextBox* logicallyPreviousBox(
const VisiblePosition& visiblePosition,
const InlineTextBox* textBox,
bool& previousBoxInDifferentBlock,
CachedLogicallyOrderedLeafBoxes& leafBoxes) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
const InlineBox* startBox = textBox;
const InlineTextBox* previousBox =
leafBoxes.previousTextBox(&startBox->root(), textBox);
if (previousBox)
return previousBox;
previousBox = leafBoxes.previousTextBox(startBox->root().prevRootBox(), 0);
if (previousBox)
return previousBox;
while (1) {
Node* startNode = startBox->getLineLayoutItem().nonPseudoNode();
if (!startNode)
break;
Position position = previousRootInlineBoxCandidatePosition(
startNode, visiblePosition, ContentIsEditable);
if (position.isNull())
break;
RenderedPosition renderedPosition(position, TextAffinity::Downstream);
RootInlineBox* previousRoot = renderedPosition.rootBox();
if (!previousRoot)
break;
previousBox = leafBoxes.previousTextBox(previousRoot, 0);
if (previousBox) {
previousBoxInDifferentBlock = true;
return previousBox;
}
if (!leafBoxes.size())
break;
startBox = leafBoxes.firstBox();
}
return 0;
}
static const InlineTextBox* logicallyNextBox(
const VisiblePosition& visiblePosition,
const InlineTextBox* textBox,
bool& nextBoxInDifferentBlock,
CachedLogicallyOrderedLeafBoxes& leafBoxes) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
const InlineBox* startBox = textBox;
const InlineTextBox* nextBox =
leafBoxes.nextTextBox(&startBox->root(), textBox);
if (nextBox)
return nextBox;
nextBox = leafBoxes.nextTextBox(startBox->root().nextRootBox(), 0);
if (nextBox)
return nextBox;
while (1) {
Node* startNode = startBox->getLineLayoutItem().nonPseudoNode();
if (!startNode)
break;
Position position = nextRootInlineBoxCandidatePosition(
startNode, visiblePosition, ContentIsEditable);
if (position.isNull())
break;
RenderedPosition renderedPosition(position, TextAffinity::Downstream);
RootInlineBox* nextRoot = renderedPosition.rootBox();
if (!nextRoot)
break;
nextBox = leafBoxes.nextTextBox(nextRoot, 0);
if (nextBox) {
nextBoxInDifferentBlock = true;
return nextBox;
}
if (!leafBoxes.size())
break;
startBox = leafBoxes.firstBox();
}
return 0;
}
static TextBreakIterator* wordBreakIteratorForMinOffsetBoundary(
const VisiblePosition& visiblePosition,
const InlineTextBox* textBox,
int& previousBoxLength,
bool& previousBoxInDifferentBlock,
Vector<UChar, 1024>& string,
CachedLogicallyOrderedLeafBoxes& leafBoxes) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
previousBoxInDifferentBlock = false;
// FIXME: Handle the case when we don't have an inline text box.
const InlineTextBox* previousBox = logicallyPreviousBox(
visiblePosition, textBox, previousBoxInDifferentBlock, leafBoxes);
int len = 0;
string.clear();
if (previousBox) {
previousBoxLength = previousBox->len();
previousBox->getLineLayoutItem().text().appendTo(
string, previousBox->start(), previousBoxLength);
len += previousBoxLength;
}
textBox->getLineLayoutItem().text().appendTo(string, textBox->start(),
textBox->len());
len += textBox->len();
return wordBreakIterator(string.data(), len);
}
static TextBreakIterator* wordBreakIteratorForMaxOffsetBoundary(
const VisiblePosition& visiblePosition,
const InlineTextBox* textBox,
bool& nextBoxInDifferentBlock,
Vector<UChar, 1024>& string,
CachedLogicallyOrderedLeafBoxes& leafBoxes) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
nextBoxInDifferentBlock = false;
// FIXME: Handle the case when we don't have an inline text box.
const InlineTextBox* nextBox = logicallyNextBox(
visiblePosition, textBox, nextBoxInDifferentBlock, leafBoxes);
int len = 0;
string.clear();
textBox->getLineLayoutItem().text().appendTo(string, textBox->start(),
textBox->len());
len += textBox->len();
if (nextBox) {
nextBox->getLineLayoutItem().text().appendTo(string, nextBox->start(),
nextBox->len());
len += nextBox->len();
}
return wordBreakIterator(string.data(), len);
}
static bool isLogicalStartOfWord(TextBreakIterator* iter,
int position,
bool hardLineBreak) {
bool boundary = hardLineBreak ? true : iter->isBoundary(position);
if (!boundary)
return false;
iter->following(position);
// isWordTextBreak returns true after moving across a word and false after
// moving across a punctuation/space.
return isWordTextBreak(iter);
}
static bool islogicalEndOfWord(TextBreakIterator* iter,
int position,
bool hardLineBreak) {
bool boundary = iter->isBoundary(position);
return (hardLineBreak || boundary) && isWordTextBreak(iter);
}
enum CursorMovementDirection { MoveLeft, MoveRight };
static VisiblePosition visualWordPosition(
const VisiblePosition& visiblePosition,
CursorMovementDirection direction,
bool skipsSpaceWhenMovingRight) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
if (visiblePosition.isNull())
return VisiblePosition();
TextDirection blockDirection =
directionOfEnclosingBlock(visiblePosition.deepEquivalent());
InlineBox* previouslyVisitedBox = 0;
VisiblePosition current = visiblePosition;
TextBreakIterator* iter = 0;
CachedLogicallyOrderedLeafBoxes leafBoxes;
Vector<UChar, 1024> string;
while (1) {
VisiblePosition adjacentCharacterPosition = direction == MoveRight
? rightPositionOf(current)
: leftPositionOf(current);
if (adjacentCharacterPosition.deepEquivalent() ==
current.deepEquivalent() ||
adjacentCharacterPosition.isNull())
return VisiblePosition();
InlineBoxPosition boxPosition = computeInlineBoxPosition(
adjacentCharacterPosition.deepEquivalent(), TextAffinity::Upstream);
InlineBox* box = boxPosition.inlineBox;
int offsetInBox = boxPosition.offsetInBox;
if (!box)
break;
if (!box->isInlineTextBox()) {
current = adjacentCharacterPosition;
continue;
}
InlineTextBox* textBox = toInlineTextBox(box);
int previousBoxLength = 0;
bool previousBoxInDifferentBlock = false;
bool nextBoxInDifferentBlock = false;
bool movingIntoNewBox = previouslyVisitedBox != box;
if (offsetInBox == box->caretMinOffset()) {
iter = wordBreakIteratorForMinOffsetBoundary(
visiblePosition, textBox, previousBoxLength,
previousBoxInDifferentBlock, string, leafBoxes);
} else if (offsetInBox == box->caretMaxOffset()) {
iter = wordBreakIteratorForMaxOffsetBoundary(
visiblePosition, textBox, nextBoxInDifferentBlock, string, leafBoxes);
} else if (movingIntoNewBox) {
iter = wordBreakIterator(textBox->getLineLayoutItem().text(),
textBox->start(), textBox->len());
previouslyVisitedBox = box;
}
if (!iter)
break;
iter->first();
int offsetInIterator = offsetInBox - textBox->start() + previousBoxLength;
bool isWordBreak;
bool boxHasSameDirectionalityAsBlock = box->direction() == blockDirection;
bool movingBackward = (direction == MoveLeft && box->direction() == LTR) ||
(direction == MoveRight && box->direction() == RTL);
if ((skipsSpaceWhenMovingRight && boxHasSameDirectionalityAsBlock) ||
(!skipsSpaceWhenMovingRight && movingBackward)) {
bool logicalStartInLayoutObject =
offsetInBox == static_cast<int>(textBox->start()) &&
previousBoxInDifferentBlock;
isWordBreak = isLogicalStartOfWord(iter, offsetInIterator,
logicalStartInLayoutObject);
} else {
bool logicalEndInLayoutObject =
offsetInBox == static_cast<int>(textBox->start() + textBox->len()) &&
nextBoxInDifferentBlock;
isWordBreak =
islogicalEndOfWord(iter, offsetInIterator, logicalEndInLayoutObject);
}
if (isWordBreak)
return adjacentCharacterPosition;
current = adjacentCharacterPosition;
}
return VisiblePosition();
}
VisiblePosition leftWordPosition(const VisiblePosition& visiblePosition,
bool skipsSpaceWhenMovingRight) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
VisiblePosition leftWordBreak =
visualWordPosition(visiblePosition, MoveLeft, skipsSpaceWhenMovingRight);
leftWordBreak = honorEditingBoundaryAtOrBefore(
leftWordBreak, visiblePosition.deepEquivalent());
// FIXME: How should we handle a non-editable position?
if (leftWordBreak.isNull() &&
isEditablePosition(visiblePosition.deepEquivalent())) {
TextDirection blockDirection =
directionOfEnclosingBlock(visiblePosition.deepEquivalent());
leftWordBreak = blockDirection == LTR
? startOfEditableContent(visiblePosition)
: endOfEditableContent(visiblePosition);
}
return leftWordBreak;
}
VisiblePosition rightWordPosition(const VisiblePosition& visiblePosition,
bool skipsSpaceWhenMovingRight) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
VisiblePosition rightWordBreak =
visualWordPosition(visiblePosition, MoveRight, skipsSpaceWhenMovingRight);
rightWordBreak = honorEditingBoundaryAtOrBefore(
rightWordBreak, visiblePosition.deepEquivalent());
// FIXME: How should we handle a non-editable position?
if (rightWordBreak.isNull() &&
isEditablePosition(visiblePosition.deepEquivalent())) {
TextDirection blockDirection =
directionOfEnclosingBlock(visiblePosition.deepEquivalent());
rightWordBreak = blockDirection == LTR
? endOfEditableContent(visiblePosition)
: startOfEditableContent(visiblePosition);
}
return rightWordBreak;
}
template <typename Strategy>
static ContainerNode* nonShadowBoundaryParentNode(Node* node) {
ContainerNode* parent = Strategy::parent(*node);
return parent && !parent->isShadowRoot() ? parent : nullptr;
}
template <typename Strategy>
static Node* parentEditingBoundary(const PositionTemplate<Strategy>& position) {
Node* const anchorNode = position.anchorNode();
if (!anchorNode)
return nullptr;
Node* documentElement = anchorNode->document().documentElement();
if (!documentElement)
return nullptr;
Node* boundary = position.computeContainerNode();
while (boundary != documentElement &&
nonShadowBoundaryParentNode<Strategy>(boundary) &&
hasEditableStyle(*anchorNode) ==
hasEditableStyle(*Strategy::parent(*boundary)))
boundary = nonShadowBoundaryParentNode<Strategy>(boundary);
return boundary;
}
enum BoundarySearchContextAvailability {
DontHaveMoreContext,
MayHaveMoreContext
};
typedef unsigned (*BoundarySearchFunction)(const UChar*,
unsigned length,
unsigned offset,
BoundarySearchContextAvailability,
bool& needMoreContext);
template <typename Strategy>
static VisiblePositionTemplate<Strategy> previousBoundary(
const VisiblePositionTemplate<Strategy>& c,
BoundarySearchFunction searchFunction) {
DCHECK(c.isValid()) << c;
const PositionTemplate<Strategy> pos = c.deepEquivalent();
Node* boundary = parentEditingBoundary(pos);
if (!boundary)
return VisiblePositionTemplate<Strategy>();
const PositionTemplate<Strategy> start =
PositionTemplate<Strategy>::editingPositionOf(boundary, 0)
.parentAnchoredEquivalent();
const PositionTemplate<Strategy> end = pos.parentAnchoredEquivalent();
ForwardsTextBuffer suffixString;
if (requiresContextForWordBoundary(characterBefore(c))) {
TextIteratorAlgorithm<Strategy> forwardsIterator(
end, PositionTemplate<Strategy>::afterNode(boundary));
while (!forwardsIterator.atEnd()) {
forwardsIterator.copyTextTo(&suffixString);
int contextEndIndex = endOfFirstWordBoundaryContext(
suffixString.data() + suffixString.size() - forwardsIterator.length(),
forwardsIterator.length());
if (contextEndIndex < forwardsIterator.length()) {
suffixString.shrink(forwardsIterator.length() - contextEndIndex);
break;
}
forwardsIterator.advance();
}
}
unsigned suffixLength = suffixString.size();
BackwardsTextBuffer string;
string.pushRange(suffixString.data(), suffixString.size());
SimplifiedBackwardsTextIteratorAlgorithm<Strategy> it(start, end);
int remainingLength = 0;
unsigned next = 0;
bool needMoreContext = false;
while (!it.atEnd()) {
bool inTextSecurityMode = it.isInTextSecurityMode();
// iterate to get chunks until the searchFunction returns a non-zero
// value.
if (!inTextSecurityMode) {
int runOffset = 0;
do {
runOffset += it.copyTextTo(&string, runOffset, string.capacity());
// TODO(xiaochengh): The following line takes O(string.size()) time,
// which makes quadratic overall running time in the worst case.
// Should improve it in some way.
next = searchFunction(string.data(), string.size(),
string.size() - suffixLength, MayHaveMoreContext,
needMoreContext);
} while (!next && runOffset < it.length());
if (next) {
remainingLength = it.length() - runOffset;
break;
}
} else {
// Treat bullets used in the text security mode as regular
// characters when looking for boundaries
string.pushCharacters('x', it.length());
next = 0;
}
it.advance();
}
if (needMoreContext) {
// The last search returned the beginning of the buffer and asked for
// more context, but there is no earlier text. Force a search with
// what's available.
// TODO(xiaochengh): Do we have to search the whole string?
next = searchFunction(string.data(), string.size(),
string.size() - suffixLength, DontHaveMoreContext,
needMoreContext);
DCHECK(!needMoreContext);
}
if (!next)
return createVisiblePosition(it.atEnd() ? it.startPosition() : pos);
Node* node = it.startContainer();
int boundaryOffset = remainingLength + next;
if (node->isTextNode() && boundaryOffset <= node->maxCharacterOffset()) {
// The next variable contains a usable index into a text node
return createVisiblePosition(
PositionTemplate<Strategy>(node, boundaryOffset));
}
// Use the character iterator to translate the next value into a DOM
// position.
BackwardsCharacterIteratorAlgorithm<Strategy> charIt(start, end);
charIt.advance(string.size() - suffixLength - next);
// TODO(yosin) charIt can get out of shadow host.
return createVisiblePosition(charIt.endPosition());
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> nextBoundary(
const VisiblePositionTemplate<Strategy>& c,
BoundarySearchFunction searchFunction) {
DCHECK(c.isValid()) << c;
PositionTemplate<Strategy> pos = c.deepEquivalent();
Node* boundary = parentEditingBoundary(pos);
if (!boundary)
return VisiblePositionTemplate<Strategy>();
Document& d = boundary->document();
const PositionTemplate<Strategy> start(pos.parentAnchoredEquivalent());
BackwardsTextBuffer prefixString;
if (requiresContextForWordBoundary(characterAfter(c))) {
SimplifiedBackwardsTextIteratorAlgorithm<Strategy> backwardsIterator(
PositionTemplate<Strategy>::firstPositionInNode(&d), start);
while (!backwardsIterator.atEnd()) {
backwardsIterator.copyTextTo(&prefixString);
int contextStartIndex = startOfLastWordBoundaryContext(
prefixString.data(), backwardsIterator.length());
if (contextStartIndex > 0) {
prefixString.shrink(contextStartIndex);
break;
}
backwardsIterator.advance();
}
}
unsigned prefixLength = prefixString.size();
ForwardsTextBuffer string;
string.pushRange(prefixString.data(), prefixString.size());
const PositionTemplate<Strategy> searchStart =
PositionTemplate<Strategy>::editingPositionOf(
start.anchorNode(), start.offsetInContainerNode());
const PositionTemplate<Strategy> searchEnd =
PositionTemplate<Strategy>::lastPositionInNode(boundary);
TextIteratorAlgorithm<Strategy> it(
searchStart, searchEnd,
TextIteratorEmitsCharactersBetweenAllVisiblePositions);
const unsigned invalidOffset = static_cast<unsigned>(-1);
unsigned next = invalidOffset;
unsigned offset = prefixLength;
bool needMoreContext = false;
while (!it.atEnd()) {
// Keep asking the iterator for chunks until the search function
// returns an end value not equal to the length of the string passed to
// it.
bool inTextSecurityMode = it.isInTextSecurityMode();
if (!inTextSecurityMode) {
int runOffset = 0;
do {
runOffset += it.copyTextTo(&string, runOffset, string.capacity());
next = searchFunction(string.data(), string.size(), offset,
MayHaveMoreContext, needMoreContext);
if (!needMoreContext) {
// When the search does not need more context, skip all examined
// characters except the last one, in case it is a boundary.
offset = string.size();
U16_BACK_1(string.data(), 0, offset);
}
} while (next == string.size() && runOffset < it.length());
if (next != string.size())
break;
} else {
// Treat bullets used in the text security mode as regular
// characters when looking for boundaries
string.pushCharacters('x', it.length());
next = string.size();
}
it.advance();
}
if (needMoreContext) {
// The last search returned the end of the buffer and asked for more
// context, but there is no further text. Force a search with what's
// available.
// TODO(xiaochengh): Do we still have to search the whole string?
next = searchFunction(string.data(), string.size(), prefixLength,
DontHaveMoreContext, needMoreContext);
DCHECK(!needMoreContext);
}
if (it.atEnd() && next == string.size()) {
pos = it.startPositionInCurrentContainer();
} else if (next != invalidOffset && next != prefixLength) {
// Use the character iterator to translate the next value into a DOM
// position.
CharacterIteratorAlgorithm<Strategy> charIt(
searchStart, searchEnd,
TextIteratorEmitsCharactersBetweenAllVisiblePositions);
charIt.advance(next - prefixLength - 1);
pos = charIt.endPosition();
if (charIt.characterAt(0) == '\n') {
// TODO(yosin) workaround for collapsed range (where only start
// position is correct) emitted for some emitted newlines
// (see rdar://5192593)
const VisiblePositionTemplate<Strategy> visPos =
createVisiblePosition(pos);
if (visPos.deepEquivalent() ==
createVisiblePosition(charIt.startPosition()).deepEquivalent()) {
charIt.advance(1);
pos = charIt.startPosition();
}
}
}
// generate VisiblePosition, use TextAffinity::Upstream affinity if possible
return createVisiblePosition(pos, VP_UPSTREAM_IF_POSSIBLE);
}
// ---------
static unsigned startWordBoundary(
const UChar* characters,
unsigned length,
unsigned offset,
BoundarySearchContextAvailability mayHaveMoreContext,
bool& needMoreContext) {
TRACE_EVENT0("blink", "startWordBoundary");
DCHECK(offset);
if (mayHaveMoreContext &&
!startOfLastWordBoundaryContext(characters, offset)) {
needMoreContext = true;
return 0;
}
needMoreContext = false;
int start, end;
U16_BACK_1(characters, 0, offset);
findWordBoundary(characters, length, offset, &start, &end);
return start;
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> startOfWordAlgorithm(
const VisiblePositionTemplate<Strategy>& c,
EWordSide side) {
DCHECK(c.isValid()) << c;
// TODO(yosin) This returns a null VP for c at the start of the document
// and |side| == |LeftWordIfOnBoundary|
VisiblePositionTemplate<Strategy> p = c;
if (side == RightWordIfOnBoundary) {
// at paragraph end, the startofWord is the current position
if (isEndOfParagraph(c))
return c;
p = nextPositionOf(c);
if (p.isNull())
return c;
}
return previousBoundary(p, startWordBoundary);
}
VisiblePosition startOfWord(const VisiblePosition& c, EWordSide side) {
return startOfWordAlgorithm<EditingStrategy>(c, side);
}
VisiblePositionInFlatTree startOfWord(const VisiblePositionInFlatTree& c,
EWordSide side) {
return startOfWordAlgorithm<EditingInFlatTreeStrategy>(c, side);
}
static unsigned endWordBoundary(
const UChar* characters,
unsigned length,
unsigned offset,
BoundarySearchContextAvailability mayHaveMoreContext,
bool& needMoreContext) {
DCHECK_LE(offset, length);
if (mayHaveMoreContext &&
endOfFirstWordBoundaryContext(characters + offset, length - offset) ==
static_cast<int>(length - offset)) {
needMoreContext = true;
return length;
}
needMoreContext = false;
return findWordEndBoundary(characters, length, offset);
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> endOfWordAlgorithm(
const VisiblePositionTemplate<Strategy>& c,
EWordSide side) {
DCHECK(c.isValid()) << c;
VisiblePositionTemplate<Strategy> p = c;
if (side == LeftWordIfOnBoundary) {
if (isStartOfParagraph(c))
return c;
p = previousPositionOf(c);
if (p.isNull())
return c;
} else if (isEndOfParagraph(c)) {
return c;
}
return nextBoundary(p, endWordBoundary);
}
VisiblePosition endOfWord(const VisiblePosition& c, EWordSide side) {
return endOfWordAlgorithm<EditingStrategy>(c, side);
}
VisiblePositionInFlatTree endOfWord(const VisiblePositionInFlatTree& c,
EWordSide side) {
return endOfWordAlgorithm<EditingInFlatTreeStrategy>(c, side);
}
static unsigned previousWordPositionBoundary(
const UChar* characters,
unsigned length,
unsigned offset,
BoundarySearchContextAvailability mayHaveMoreContext,
bool& needMoreContext) {
if (mayHaveMoreContext &&
!startOfLastWordBoundaryContext(characters, offset)) {
needMoreContext = true;
return 0;
}
needMoreContext = false;
return findNextWordFromIndex(characters, length, offset, false);
}
VisiblePosition previousWordPosition(const VisiblePosition& c) {
DCHECK(c.isValid()) << c;
VisiblePosition prev = previousBoundary(c, previousWordPositionBoundary);
return honorEditingBoundaryAtOrBefore(prev, c.deepEquivalent());
}
static unsigned nextWordPositionBoundary(
const UChar* characters,
unsigned length,
unsigned offset,
BoundarySearchContextAvailability mayHaveMoreContext,
bool& needMoreContext) {
if (mayHaveMoreContext &&
endOfFirstWordBoundaryContext(characters + offset, length - offset) ==
static_cast<int>(length - offset)) {
needMoreContext = true;
return length;
}
needMoreContext = false;
return findNextWordFromIndex(characters, length, offset, true);
}
VisiblePosition nextWordPosition(const VisiblePosition& c) {
DCHECK(c.isValid()) << c;
VisiblePosition next = nextBoundary(c, nextWordPositionBoundary);
return honorEditingBoundaryAtOrAfter(next, c.deepEquivalent());
}
// ---------
enum LineEndpointComputationMode { UseLogicalOrdering, UseInlineBoxOrdering };
template <typename Strategy>
static PositionWithAffinityTemplate<Strategy> startPositionForLine(
const PositionWithAffinityTemplate<Strategy>& c,
LineEndpointComputationMode mode) {
if (c.isNull())
return PositionWithAffinityTemplate<Strategy>();
RootInlineBox* rootBox =
RenderedPosition(c.position(), c.affinity()).rootBox();
if (!rootBox) {
// There are VisiblePositions at offset 0 in blocks without
// RootInlineBoxes, like empty editable blocks and bordered blocks.
PositionTemplate<Strategy> p = c.position();
if (p.anchorNode()->layoutObject() &&
p.anchorNode()->layoutObject()->isLayoutBlock() &&
!p.computeEditingOffset())
return c;
return PositionWithAffinityTemplate<Strategy>();
}
Node* startNode;
InlineBox* startBox;
if (mode == UseLogicalOrdering) {
startNode = rootBox->getLogicalStartBoxWithNode(startBox);
if (!startNode)
return PositionWithAffinityTemplate<Strategy>();
} else {
// Generated content (e.g. list markers and CSS :before and :after
// pseudoelements) have no corresponding DOM element, and so cannot be
// represented by a VisiblePosition. Use whatever follows instead.
startBox = rootBox->firstLeafChild();
while (true) {
if (!startBox)
return PositionWithAffinityTemplate<Strategy>();
startNode = startBox->getLineLayoutItem().nonPseudoNode();
if (startNode)
break;
startBox = startBox->nextLeafChild();
}
}
return PositionWithAffinityTemplate<Strategy>(
startNode->isTextNode()
? PositionTemplate<Strategy>(toText(startNode),
toInlineTextBox(startBox)->start())
: PositionTemplate<Strategy>::beforeNode(startNode));
}
template <typename Strategy>
static PositionWithAffinityTemplate<Strategy> startOfLineAlgorithm(
const PositionWithAffinityTemplate<Strategy>& c) {
// TODO: this is the current behavior that might need to be fixed.
// Please refer to https://bugs.webkit.org/show_bug.cgi?id=49107 for detail.
PositionWithAffinityTemplate<Strategy> visPos =
startPositionForLine(c, UseInlineBoxOrdering);
return honorEditingBoundaryAtOrBefore(visPos, c.position());
}
static PositionWithAffinity startOfLine(
const PositionWithAffinity& currentPosition) {
return startOfLineAlgorithm<EditingStrategy>(currentPosition);
}
static PositionInFlatTreeWithAffinity startOfLine(
const PositionInFlatTreeWithAffinity& currentPosition) {
return startOfLineAlgorithm<EditingInFlatTreeStrategy>(currentPosition);
}
// FIXME: Rename this function to reflect the fact it ignores bidi levels.
VisiblePosition startOfLine(const VisiblePosition& currentPosition) {
DCHECK(currentPosition.isValid()) << currentPosition;
return createVisiblePosition(
startOfLine(currentPosition.toPositionWithAffinity()));
}
VisiblePositionInFlatTree startOfLine(
const VisiblePositionInFlatTree& currentPosition) {
DCHECK(currentPosition.isValid()) << currentPosition;
return createVisiblePosition(
startOfLine(currentPosition.toPositionWithAffinity()));
}
template <typename Strategy>
static PositionWithAffinityTemplate<Strategy> logicalStartOfLineAlgorithm(
const PositionWithAffinityTemplate<Strategy>& c) {
// TODO: this is the current behavior that might need to be fixed.
// Please refer to https://bugs.webkit.org/show_bug.cgi?id=49107 for detail.
PositionWithAffinityTemplate<Strategy> visPos =
startPositionForLine(c, UseLogicalOrdering);
if (ContainerNode* editableRoot = highestEditableRoot(c.position())) {
if (!editableRoot->contains(visPos.position().computeContainerNode()))
return PositionWithAffinityTemplate<Strategy>(
PositionTemplate<Strategy>::firstPositionInNode(editableRoot));
}
return honorEditingBoundaryAtOrBefore(visPos, c.position());
}
VisiblePosition logicalStartOfLine(const VisiblePosition& currentPosition) {
DCHECK(currentPosition.isValid()) << currentPosition;
return createVisiblePosition(logicalStartOfLineAlgorithm<EditingStrategy>(
currentPosition.toPositionWithAffinity()));
}
VisiblePositionInFlatTree logicalStartOfLine(
const VisiblePositionInFlatTree& currentPosition) {
DCHECK(currentPosition.isValid()) << currentPosition;
return createVisiblePosition(
logicalStartOfLineAlgorithm<EditingInFlatTreeStrategy>(
currentPosition.toPositionWithAffinity()));
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> endPositionForLine(
const VisiblePositionTemplate<Strategy>& c,
LineEndpointComputationMode mode) {
DCHECK(c.isValid()) << c;
if (c.isNull())
return VisiblePositionTemplate<Strategy>();
RootInlineBox* rootBox = RenderedPosition(c).rootBox();
if (!rootBox) {
// There are VisiblePositions at offset 0 in blocks without
// RootInlineBoxes, like empty editable blocks and bordered blocks.
const PositionTemplate<Strategy> p = c.deepEquivalent();
if (p.anchorNode()->layoutObject() &&
p.anchorNode()->layoutObject()->isLayoutBlock() &&
!p.computeEditingOffset())
return c;
return VisiblePositionTemplate<Strategy>();
}
Node* endNode;
InlineBox* endBox;
if (mode == UseLogicalOrdering) {
endNode = rootBox->getLogicalEndBoxWithNode(endBox);
if (!endNode)
return VisiblePositionTemplate<Strategy>();
} else {
// Generated content (e.g. list markers and CSS :before and :after
// pseudo elements) have no corresponding DOM element, and so cannot be
// represented by a VisiblePosition. Use whatever precedes instead.
endBox = rootBox->lastLeafChild();
while (true) {
if (!endBox)
return VisiblePositionTemplate<Strategy>();
endNode = endBox->getLineLayoutItem().nonPseudoNode();
if (endNode)
break;
endBox = endBox->prevLeafChild();
}
}
PositionTemplate<Strategy> pos;
if (isHTMLBRElement(*endNode)) {
pos = PositionTemplate<Strategy>::beforeNode(endNode);
} else if (endBox->isInlineTextBox() && endNode->isTextNode()) {
InlineTextBox* endTextBox = toInlineTextBox(endBox);
int endOffset = endTextBox->start();
if (!endTextBox->isLineBreak())
endOffset += endTextBox->len();
pos = PositionTemplate<Strategy>(toText(endNode), endOffset);
} else {
pos = PositionTemplate<Strategy>::afterNode(endNode);
}
return createVisiblePosition(pos, VP_UPSTREAM_IF_POSSIBLE);
}
// TODO(yosin) Rename this function to reflect the fact it ignores bidi levels.
template <typename Strategy>
static VisiblePositionTemplate<Strategy> endOfLineAlgorithm(
const VisiblePositionTemplate<Strategy>& currentPosition) {
DCHECK(currentPosition.isValid()) << currentPosition;
// TODO(yosin) this is the current behavior that might need to be fixed.
// Please refer to https://bugs.webkit.org/show_bug.cgi?id=49107 for detail.
VisiblePositionTemplate<Strategy> visPos =
endPositionForLine(currentPosition, UseInlineBoxOrdering);
// Make sure the end of line is at the same line as the given input
// position. Else use the previous position to obtain end of line. This
// condition happens when the input position is before the space character
// at the end of a soft-wrapped non-editable line. In this scenario,
// |endPositionForLine()| would incorrectly hand back a position in the next
// line instead. This fix is to account for the discrepancy between lines
// with "webkit-line-break:after-white-space" style versus lines without
// that style, which would break before a space by default.
if (!inSameLine(currentPosition, visPos)) {
visPos = previousPositionOf(currentPosition);
if (visPos.isNull())
return VisiblePositionTemplate<Strategy>();
visPos = endPositionForLine(visPos, UseInlineBoxOrdering);
}
return honorEditingBoundaryAtOrAfter(visPos,
currentPosition.deepEquivalent());
}
// TODO(yosin) Rename this function to reflect the fact it ignores bidi levels.
VisiblePosition endOfLine(const VisiblePosition& currentPosition) {
return endOfLineAlgorithm<EditingStrategy>(currentPosition);
}
VisiblePositionInFlatTree endOfLine(
const VisiblePositionInFlatTree& currentPosition) {
return endOfLineAlgorithm<EditingInFlatTreeStrategy>(currentPosition);
}
template <typename Strategy>
static bool inSameLogicalLine(const VisiblePositionTemplate<Strategy>& a,
const VisiblePositionTemplate<Strategy>& b) {
DCHECK(a.isValid()) << a;
DCHECK(b.isValid()) << b;
return a.isNotNull() &&
logicalStartOfLine(a).deepEquivalent() ==
logicalStartOfLine(b).deepEquivalent();
}
template <typename Strategy>
VisiblePositionTemplate<Strategy> logicalEndOfLineAlgorithm(
const VisiblePositionTemplate<Strategy>& currentPosition) {
DCHECK(currentPosition.isValid()) << currentPosition;
// TODO(yosin) this is the current behavior that might need to be fixed.
// Please refer to https://bugs.webkit.org/show_bug.cgi?id=49107 for detail.
VisiblePositionTemplate<Strategy> visPos =
endPositionForLine(currentPosition, UseLogicalOrdering);
// Make sure the end of line is at the same line as the given input
// position. For a wrapping line, the logical end position for the
// not-last-2-lines might incorrectly hand back the logical beginning of the
// next line. For example,
// <div contenteditable dir="rtl" style="line-break:before-white-space">xyz
// a xyz xyz xyz xyz xyz xyz xyz xyz xyz xyz </div>
// In this case, use the previous position of the computed logical end
// position.
if (!inSameLogicalLine(currentPosition, visPos))
visPos = previousPositionOf(visPos);
if (ContainerNode* editableRoot =
highestEditableRoot(currentPosition.deepEquivalent())) {
if (!editableRoot->contains(visPos.deepEquivalent().computeContainerNode()))
return createVisiblePosition(
PositionTemplate<Strategy>::lastPositionInNode(editableRoot));
}
return honorEditingBoundaryAtOrAfter(visPos,
currentPosition.deepEquivalent());
}
VisiblePosition logicalEndOfLine(const VisiblePosition& currentPosition) {
return logicalEndOfLineAlgorithm<EditingStrategy>(currentPosition);
}
VisiblePositionInFlatTree logicalEndOfLine(
const VisiblePositionInFlatTree& currentPosition) {
return logicalEndOfLineAlgorithm<EditingInFlatTreeStrategy>(currentPosition);
}
template <typename Strategy>
bool inSameLineAlgorithm(
const PositionWithAffinityTemplate<Strategy>& position1,
const PositionWithAffinityTemplate<Strategy>& position2) {
if (position1.isNull() || position2.isNull())
return false;
DCHECK_EQ(position1.document(), position2.document());
DCHECK(!position1.document()->needsLayoutTreeUpdate());
PositionWithAffinityTemplate<Strategy> startOfLine1 = startOfLine(position1);
PositionWithAffinityTemplate<Strategy> startOfLine2 = startOfLine(position2);
if (startOfLine1 == startOfLine2)
return true;
PositionTemplate<Strategy> canonicalized1 =
canonicalPositionOf(startOfLine1.position());
if (canonicalized1 == startOfLine2.position())
return true;
return canonicalized1 == canonicalPositionOf(startOfLine2.position());
}
bool inSameLine(const PositionWithAffinity& a, const PositionWithAffinity& b) {
return inSameLineAlgorithm<EditingStrategy>(a, b);
}
bool inSameLine(const PositionInFlatTreeWithAffinity& position1,
const PositionInFlatTreeWithAffinity& position2) {
return inSameLineAlgorithm<EditingInFlatTreeStrategy>(position1, position2);
}
bool inSameLine(const VisiblePosition& position1,
const VisiblePosition& position2) {
DCHECK(position1.isValid()) << position1;
DCHECK(position2.isValid()) << position2;
return inSameLine(position1.toPositionWithAffinity(),
position2.toPositionWithAffinity());
}
bool inSameLine(const VisiblePositionInFlatTree& position1,
const VisiblePositionInFlatTree& position2) {
DCHECK(position1.isValid()) << position1;
DCHECK(position2.isValid()) << position2;
return inSameLine(position1.toPositionWithAffinity(),
position2.toPositionWithAffinity());
}
template <typename Strategy>
bool isStartOfLineAlgorithm(const VisiblePositionTemplate<Strategy>& p) {
DCHECK(p.isValid()) << p;
return p.isNotNull() && p.deepEquivalent() == startOfLine(p).deepEquivalent();
}
bool isStartOfLine(const VisiblePosition& p) {
return isStartOfLineAlgorithm<EditingStrategy>(p);
}
bool isStartOfLine(const VisiblePositionInFlatTree& p) {
return isStartOfLineAlgorithm<EditingInFlatTreeStrategy>(p);
}
template <typename Strategy>
bool isEndOfLineAlgorithm(const VisiblePositionTemplate<Strategy>& p) {
DCHECK(p.isValid()) << p;
return p.isNotNull() && p.deepEquivalent() == endOfLine(p).deepEquivalent();
}
bool isEndOfLine(const VisiblePosition& p) {
return isEndOfLineAlgorithm<EditingStrategy>(p);
}
bool isEndOfLine(const VisiblePositionInFlatTree& p) {
return isEndOfLineAlgorithm<EditingInFlatTreeStrategy>(p);
}
template <typename Strategy>
static bool isLogicalEndOfLineAlgorithm(
const VisiblePositionTemplate<Strategy>& p) {
DCHECK(p.isValid()) << p;
return p.isNotNull() &&
p.deepEquivalent() == logicalEndOfLine(p).deepEquivalent();
}
bool isLogicalEndOfLine(const VisiblePosition& p) {
return isLogicalEndOfLineAlgorithm<EditingStrategy>(p);
}
bool isLogicalEndOfLine(const VisiblePositionInFlatTree& p) {
return isLogicalEndOfLineAlgorithm<EditingInFlatTreeStrategy>(p);
}
static inline LayoutPoint absoluteLineDirectionPointToLocalPointInBlock(
RootInlineBox* root,
LayoutUnit lineDirectionPoint) {
DCHECK(root);
LineLayoutBlockFlow containingBlock = root->block();
FloatPoint absoluteBlockPoint = containingBlock.localToAbsolute(FloatPoint());
if (containingBlock.hasOverflowClip())
absoluteBlockPoint -= FloatSize(containingBlock.scrolledContentOffset());
if (root->block().isHorizontalWritingMode())
return LayoutPoint(LayoutUnit(lineDirectionPoint - absoluteBlockPoint.x()),
root->blockDirectionPointInLine());
return LayoutPoint(root->blockDirectionPointInLine(),
LayoutUnit(lineDirectionPoint - absoluteBlockPoint.y()));
}
VisiblePosition previousLinePosition(const VisiblePosition& visiblePosition,
LayoutUnit lineDirectionPoint,
EditableType editableType) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
Position p = visiblePosition.deepEquivalent();
Node* node = p.anchorNode();
if (!node)
return VisiblePosition();
LayoutObject* layoutObject = node->layoutObject();
if (!layoutObject)
return VisiblePosition();
RootInlineBox* root = 0;
InlineBox* box = computeInlineBoxPosition(visiblePosition).inlineBox;
if (box) {
root = box->root().prevRootBox();
// We want to skip zero height boxes.
// This could happen in case it is a TrailingFloatsRootInlineBox.
if (!root || !root->logicalHeight() || !root->firstLeafChild())
root = 0;
}
if (!root) {
Position position = previousRootInlineBoxCandidatePosition(
node, visiblePosition, editableType);
if (position.isNotNull()) {
RenderedPosition renderedPosition((createVisiblePosition(position)));
root = renderedPosition.rootBox();
if (!root)
return createVisiblePosition(position);
}
}
if (root) {
// FIXME: Can be wrong for multi-column layout and with transforms.
LayoutPoint pointInLine =
absoluteLineDirectionPointToLocalPointInBlock(root, lineDirectionPoint);
LineLayoutItem lineLayoutItem =
root->closestLeafChildForPoint(pointInLine, isEditablePosition(p))
->getLineLayoutItem();
Node* node = lineLayoutItem.node();
if (node && editingIgnoresContent(*node))
return VisiblePosition::inParentBeforeNode(*node);
return createVisiblePosition(lineLayoutItem.positionForPoint(pointInLine));
}
// Could not find a previous line. This means we must already be on the first
// line. Move to the start of the content in this block, which effectively
// moves us to the start of the line we're on.
Element* rootElement = hasEditableStyle(*node, editableType)
? rootEditableElement(*node, editableType)
: node->document().documentElement();
if (!rootElement)
return VisiblePosition();
return VisiblePosition::firstPositionInNode(rootElement);
}
VisiblePosition nextLinePosition(const VisiblePosition& visiblePosition,
LayoutUnit lineDirectionPoint,
EditableType editableType) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
Position p = visiblePosition.deepEquivalent();
Node* node = p.anchorNode();
if (!node)
return VisiblePosition();
LayoutObject* layoutObject = node->layoutObject();
if (!layoutObject)
return VisiblePosition();
RootInlineBox* root = 0;
InlineBox* box = computeInlineBoxPosition(visiblePosition).inlineBox;
if (box) {
root = box->root().nextRootBox();
// We want to skip zero height boxes.
// This could happen in case it is a TrailingFloatsRootInlineBox.
if (!root || !root->logicalHeight() || !root->firstLeafChild())
root = 0;
}
if (!root) {
// FIXME: We need do the same in previousLinePosition.
Node* child = NodeTraversal::childAt(*node, p.computeEditingOffset());
node = child ? child : &NodeTraversal::lastWithinOrSelf(*node);
Position position =
nextRootInlineBoxCandidatePosition(node, visiblePosition, editableType);
if (position.isNotNull()) {
RenderedPosition renderedPosition((createVisiblePosition(position)));
root = renderedPosition.rootBox();
if (!root)
return createVisiblePosition(position);
}
}
if (root) {
// FIXME: Can be wrong for multi-column layout and with transforms.
LayoutPoint pointInLine =
absoluteLineDirectionPointToLocalPointInBlock(root, lineDirectionPoint);
LineLayoutItem lineLayoutItem =
root->closestLeafChildForPoint(pointInLine, isEditablePosition(p))
->getLineLayoutItem();
Node* node = lineLayoutItem.node();
if (node && editingIgnoresContent(*node))
return VisiblePosition::inParentBeforeNode(*node);
return createVisiblePosition(lineLayoutItem.positionForPoint(pointInLine));
}
// Could not find a next line. This means we must already be on the last line.
// Move to the end of the content in this block, which effectively moves us
// to the end of the line we're on.
Element* rootElement = hasEditableStyle(*node, editableType)
? rootEditableElement(*node, editableType)
: node->document().documentElement();
if (!rootElement)
return VisiblePosition();
return VisiblePosition::lastPositionInNode(rootElement);
}
// ---------
static unsigned startSentenceBoundary(const UChar* characters,
unsigned length,
unsigned,
BoundarySearchContextAvailability,
bool&) {
TextBreakIterator* iterator = sentenceBreakIterator(characters, length);
// FIXME: The following function can return -1; we don't handle that.
return iterator->preceding(length);
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> startOfSentenceAlgorithm(
const VisiblePositionTemplate<Strategy>& c) {
DCHECK(c.isValid()) << c;
return previousBoundary(c, startSentenceBoundary);
}
VisiblePosition startOfSentence(const VisiblePosition& c) {
return startOfSentenceAlgorithm<EditingStrategy>(c);
}
VisiblePositionInFlatTree startOfSentence(const VisiblePositionInFlatTree& c) {
return startOfSentenceAlgorithm<EditingInFlatTreeStrategy>(c);
}
static unsigned endSentenceBoundary(const UChar* characters,
unsigned length,
unsigned,
BoundarySearchContextAvailability,
bool&) {
TextBreakIterator* iterator = sentenceBreakIterator(characters, length);
return iterator->next();
}
// TODO(yosin) This includes the space after the punctuation that marks the end
// of the sentence.
template <typename Strategy>
static VisiblePositionTemplate<Strategy> endOfSentenceAlgorithm(
const VisiblePositionTemplate<Strategy>& c) {
DCHECK(c.isValid()) << c;
return nextBoundary(c, endSentenceBoundary);
}
VisiblePosition endOfSentence(const VisiblePosition& c) {
return endOfSentenceAlgorithm<EditingStrategy>(c);
}
VisiblePositionInFlatTree endOfSentence(const VisiblePositionInFlatTree& c) {
return endOfSentenceAlgorithm<EditingInFlatTreeStrategy>(c);
}
static unsigned previousSentencePositionBoundary(
const UChar* characters,
unsigned length,
unsigned,
BoundarySearchContextAvailability,
bool&) {
// FIXME: This is identical to startSentenceBoundary. I'm pretty sure that's
// not right.
TextBreakIterator* iterator = sentenceBreakIterator(characters, length);
// FIXME: The following function can return -1; we don't handle that.
return iterator->preceding(length);
}
VisiblePosition previousSentencePosition(const VisiblePosition& c) {
DCHECK(c.isValid()) << c;
VisiblePosition prev = previousBoundary(c, previousSentencePositionBoundary);
return honorEditingBoundaryAtOrBefore(prev, c.deepEquivalent());
}
static unsigned nextSentencePositionBoundary(const UChar* characters,
unsigned length,
unsigned,
BoundarySearchContextAvailability,
bool&) {
// FIXME: This is identical to endSentenceBoundary. This isn't right, it needs
// to move to the equivlant position in the following sentence.
TextBreakIterator* iterator = sentenceBreakIterator(characters, length);
return iterator->following(0);
}
VisiblePosition nextSentencePosition(const VisiblePosition& c) {
DCHECK(c.isValid()) << c;
VisiblePosition next = nextBoundary(c, nextSentencePositionBoundary);
return honorEditingBoundaryAtOrAfter(next, c.deepEquivalent());
}
template <typename Strategy>
PositionTemplate<Strategy> startOfParagraphAlgorithm(
const PositionTemplate<Strategy>& position,
EditingBoundaryCrossingRule boundaryCrossingRule) {
Node* const startNode = position.anchorNode();
if (!startNode)
return PositionTemplate<Strategy>();
if (isRenderedAsNonInlineTableImageOrHR(startNode))
return PositionTemplate<Strategy>::beforeNode(startNode);
Element* const startBlock = enclosingBlock(
PositionTemplate<Strategy>::firstPositionInOrBeforeNode(startNode),
CannotCrossEditingBoundary);
ContainerNode* const highestRoot = highestEditableRoot(position);
const bool startNodeIsEditable = hasEditableStyle(*startNode);
Node* candidateNode = startNode;
PositionAnchorType candidateType = position.anchorType();
int candidateOffset = position.computeEditingOffset();
Node* prevousNodeIterator = startNode;
while (prevousNodeIterator) {
if (boundaryCrossingRule == CannotCrossEditingBoundary &&
!nodeIsUserSelectAll(prevousNodeIterator) &&
hasEditableStyle(*prevousNodeIterator) != startNodeIsEditable)
break;
if (boundaryCrossingRule == CanSkipOverEditingBoundary) {
while (prevousNodeIterator &&
hasEditableStyle(*prevousNodeIterator) != startNodeIsEditable)
prevousNodeIterator =
Strategy::previousPostOrder(*prevousNodeIterator, startBlock);
if (!prevousNodeIterator ||
!prevousNodeIterator->isDescendantOf(highestRoot))
break;
}
const LayoutItem layoutItem =
LayoutItem(prevousNodeIterator->layoutObject());
if (layoutItem.isNull()) {
prevousNodeIterator =
Strategy::previousPostOrder(*prevousNodeIterator, startBlock);
continue;
}
const ComputedStyle& style = layoutItem.styleRef();
if (style.visibility() != EVisibility::Visible) {
prevousNodeIterator =
Strategy::previousPostOrder(*prevousNodeIterator, startBlock);
continue;
}
if (layoutItem.isBR() || isEnclosingBlock(prevousNodeIterator))
break;
if (layoutItem.isText() &&
toLayoutText(prevousNodeIterator->layoutObject())
->resolvedTextLength()) {
SECURITY_DCHECK(prevousNodeIterator->isTextNode());
if (style.preserveNewline()) {
LayoutText* text = toLayoutText(prevousNodeIterator->layoutObject());
int index = text->textLength();
if (prevousNodeIterator == startNode && candidateOffset < index)
index = max(0, candidateOffset);
while (--index >= 0) {
if ((*text)[index] == '\n')
return PositionTemplate<Strategy>(toText(prevousNodeIterator),
index + 1);
}
}
candidateNode = prevousNodeIterator;
candidateType = PositionAnchorType::OffsetInAnchor;
candidateOffset = 0;
prevousNodeIterator =
Strategy::previousPostOrder(*prevousNodeIterator, startBlock);
} else if (editingIgnoresContent(*prevousNodeIterator) ||
isDisplayInsideTable(prevousNodeIterator)) {
candidateNode = prevousNodeIterator;
candidateType = PositionAnchorType::BeforeAnchor;
prevousNodeIterator =
prevousNodeIterator->previousSibling()
? prevousNodeIterator->previousSibling()
: Strategy::previousPostOrder(*prevousNodeIterator, startBlock);
} else {
prevousNodeIterator =
Strategy::previousPostOrder(*prevousNodeIterator, startBlock);
}
}
if (candidateType == PositionAnchorType::OffsetInAnchor)
return PositionTemplate<Strategy>(candidateNode, candidateOffset);
return PositionTemplate<Strategy>(candidateNode, candidateType);
}
template <typename Strategy>
VisiblePositionTemplate<Strategy> startOfParagraphAlgorithm(
const VisiblePositionTemplate<Strategy>& visiblePosition,
EditingBoundaryCrossingRule boundaryCrossingRule) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
return createVisiblePosition(startOfParagraphAlgorithm(
visiblePosition.deepEquivalent(), boundaryCrossingRule));
}
VisiblePosition startOfParagraph(
const VisiblePosition& c,
EditingBoundaryCrossingRule boundaryCrossingRule) {
return startOfParagraphAlgorithm<EditingStrategy>(c, boundaryCrossingRule);
}
VisiblePositionInFlatTree startOfParagraph(
const VisiblePositionInFlatTree& c,
EditingBoundaryCrossingRule boundaryCrossingRule) {
return startOfParagraphAlgorithm<EditingInFlatTreeStrategy>(
c, boundaryCrossingRule);
}
template <typename Strategy>
static PositionTemplate<Strategy> endOfParagraphAlgorithm(
const PositionTemplate<Strategy>& position,
EditingBoundaryCrossingRule boundaryCrossingRule) {
Node* const startNode = position.anchorNode();
if (!startNode)
return PositionTemplate<Strategy>();
if (isRenderedAsNonInlineTableImageOrHR(startNode))
return PositionTemplate<Strategy>::afterNode(startNode);
Element* const startBlock = enclosingBlock(
PositionTemplate<Strategy>::firstPositionInOrBeforeNode(startNode),
CannotCrossEditingBoundary);
ContainerNode* const highestRoot = highestEditableRoot(position);
const bool startNodeIsEditable = hasEditableStyle(*startNode);
Node* candidateNode = startNode;
PositionAnchorType candidateType = position.anchorType();
int candidateOffset = position.computeEditingOffset();
Node* nextNodeItreator = startNode;
while (nextNodeItreator) {
if (boundaryCrossingRule == CannotCrossEditingBoundary &&
!nodeIsUserSelectAll(nextNodeItreator) &&
hasEditableStyle(*nextNodeItreator) != startNodeIsEditable)
break;
if (boundaryCrossingRule == CanSkipOverEditingBoundary) {
while (nextNodeItreator &&
hasEditableStyle(*nextNodeItreator) != startNodeIsEditable)
nextNodeItreator = Strategy::next(*nextNodeItreator, startBlock);
if (!nextNodeItreator || !nextNodeItreator->isDescendantOf(highestRoot))
break;
}
LayoutObject* const layoutObject = nextNodeItreator->layoutObject();
if (!layoutObject) {
nextNodeItreator = Strategy::next(*nextNodeItreator, startBlock);
continue;
}
const ComputedStyle& style = layoutObject->styleRef();
if (style.visibility() != EVisibility::Visible) {
nextNodeItreator = Strategy::next(*nextNodeItreator, startBlock);
continue;
}
if (layoutObject->isBR() || isEnclosingBlock(nextNodeItreator))
break;
// FIXME: We avoid returning a position where the layoutObject can't accept
// the caret.
if (layoutObject->isText() &&
toLayoutText(layoutObject)->resolvedTextLength()) {
SECURITY_DCHECK(nextNodeItreator->isTextNode());
LayoutText* const text = toLayoutText(layoutObject);
if (style.preserveNewline()) {
const int length = toLayoutText(layoutObject)->textLength();
for (int i = (nextNodeItreator == startNode ? candidateOffset : 0);
i < length; ++i) {
if ((*text)[i] == '\n')
return PositionTemplate<Strategy>(toText(nextNodeItreator),
i + text->textStartOffset());
}
}
candidateNode = nextNodeItreator;
candidateType = PositionAnchorType::OffsetInAnchor;
candidateOffset =
layoutObject->caretMaxOffset() + text->textStartOffset();
nextNodeItreator = Strategy::next(*nextNodeItreator, startBlock);
} else if (editingIgnoresContent(*nextNodeItreator) ||
isDisplayInsideTable(nextNodeItreator)) {
candidateNode = nextNodeItreator;
candidateType = PositionAnchorType::AfterAnchor;
nextNodeItreator =
Strategy::nextSkippingChildren(*nextNodeItreator, startBlock);
} else {
nextNodeItreator = Strategy::next(*nextNodeItreator, startBlock);
}
}
if (candidateType == PositionAnchorType::OffsetInAnchor)
return PositionTemplate<Strategy>(candidateNode, candidateOffset);
return PositionTemplate<Strategy>(candidateNode, candidateType);
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> endOfParagraphAlgorithm(
const VisiblePositionTemplate<Strategy>& visiblePosition,
EditingBoundaryCrossingRule boundaryCrossingRule) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
return createVisiblePosition(endOfParagraphAlgorithm(
visiblePosition.deepEquivalent(), boundaryCrossingRule));
}
VisiblePosition endOfParagraph(
const VisiblePosition& c,
EditingBoundaryCrossingRule boundaryCrossingRule) {
return endOfParagraphAlgorithm<EditingStrategy>(c, boundaryCrossingRule);
}
VisiblePositionInFlatTree endOfParagraph(
const VisiblePositionInFlatTree& c,
EditingBoundaryCrossingRule boundaryCrossingRule) {
return endOfParagraphAlgorithm<EditingInFlatTreeStrategy>(
c, boundaryCrossingRule);
}
// FIXME: isStartOfParagraph(startOfNextParagraph(pos)) is not always true
VisiblePosition startOfNextParagraph(const VisiblePosition& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
VisiblePosition paragraphEnd(
endOfParagraph(visiblePosition, CanSkipOverEditingBoundary));
VisiblePosition afterParagraphEnd(
nextPositionOf(paragraphEnd, CannotCrossEditingBoundary));
// The position after the last position in the last cell of a table
// is not the start of the next paragraph.
if (tableElementJustBefore(afterParagraphEnd))
return nextPositionOf(afterParagraphEnd, CannotCrossEditingBoundary);
return afterParagraphEnd;
}
// FIXME: isStartOfParagraph(startOfNextParagraph(pos)) is not always true
bool inSameParagraph(const VisiblePosition& a,
const VisiblePosition& b,
EditingBoundaryCrossingRule boundaryCrossingRule) {
DCHECK(a.isValid()) << a;
DCHECK(b.isValid()) << b;
return a.isNotNull() &&
startOfParagraph(a, boundaryCrossingRule).deepEquivalent() ==
startOfParagraph(b, boundaryCrossingRule).deepEquivalent();
}
template <typename Strategy>
static bool isStartOfParagraphAlgorithm(
const VisiblePositionTemplate<Strategy>& pos,
EditingBoundaryCrossingRule boundaryCrossingRule) {
DCHECK(pos.isValid()) << pos;
return pos.isNotNull() &&
pos.deepEquivalent() ==
startOfParagraph(pos, boundaryCrossingRule).deepEquivalent();
}
bool isStartOfParagraph(const VisiblePosition& pos,
EditingBoundaryCrossingRule boundaryCrossingRule) {
return isStartOfParagraphAlgorithm<EditingStrategy>(pos,
boundaryCrossingRule);
}
bool isStartOfParagraph(const VisiblePositionInFlatTree& pos,
EditingBoundaryCrossingRule boundaryCrossingRule) {
return isStartOfParagraphAlgorithm<EditingInFlatTreeStrategy>(
pos, boundaryCrossingRule);
}
template <typename Strategy>
static bool isEndOfParagraphAlgorithm(
const VisiblePositionTemplate<Strategy>& pos,
EditingBoundaryCrossingRule boundaryCrossingRule) {
DCHECK(pos.isValid()) << pos;
return pos.isNotNull() &&
pos.deepEquivalent() ==
endOfParagraph(pos, boundaryCrossingRule).deepEquivalent();
}
bool isEndOfParagraph(const VisiblePosition& pos,
EditingBoundaryCrossingRule boundaryCrossingRule) {
return isEndOfParagraphAlgorithm<EditingStrategy>(pos, boundaryCrossingRule);
}
bool isEndOfParagraph(const VisiblePositionInFlatTree& pos,
EditingBoundaryCrossingRule boundaryCrossingRule) {
return isEndOfParagraphAlgorithm<EditingInFlatTreeStrategy>(
pos, boundaryCrossingRule);
}
VisiblePosition previousParagraphPosition(const VisiblePosition& p,
LayoutUnit x) {
DCHECK(p.isValid()) << p;
VisiblePosition pos = p;
do {
VisiblePosition n = previousLinePosition(pos, x);
if (n.isNull() || n.deepEquivalent() == pos.deepEquivalent())
break;
pos = n;
} while (inSameParagraph(p, pos));
return pos;
}
VisiblePosition nextParagraphPosition(const VisiblePosition& p, LayoutUnit x) {
DCHECK(p.isValid()) << p;
VisiblePosition pos = p;
do {
VisiblePosition n = nextLinePosition(pos, x);
if (n.isNull() || n.deepEquivalent() == pos.deepEquivalent())
break;
pos = n;
} while (inSameParagraph(p, pos));
return pos;
}
// ---------
VisiblePosition startOfBlock(const VisiblePosition& visiblePosition,
EditingBoundaryCrossingRule rule) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
Position position = visiblePosition.deepEquivalent();
Element* startBlock =
position.computeContainerNode()
? enclosingBlock(position.computeContainerNode(), rule)
: 0;
return startBlock ? VisiblePosition::firstPositionInNode(startBlock)
: VisiblePosition();
}
VisiblePosition endOfBlock(const VisiblePosition& visiblePosition,
EditingBoundaryCrossingRule rule) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
Position position = visiblePosition.deepEquivalent();
Element* endBlock =
position.computeContainerNode()
? enclosingBlock(position.computeContainerNode(), rule)
: 0;
return endBlock ? VisiblePosition::lastPositionInNode(endBlock)
: VisiblePosition();
}
bool inSameBlock(const VisiblePosition& a, const VisiblePosition& b) {
DCHECK(a.isValid()) << a;
DCHECK(b.isValid()) << b;
return !a.isNull() &&
enclosingBlock(a.deepEquivalent().computeContainerNode()) ==
enclosingBlock(b.deepEquivalent().computeContainerNode());
}
bool isStartOfBlock(const VisiblePosition& pos) {
DCHECK(pos.isValid()) << pos;
return pos.isNotNull() &&
pos.deepEquivalent() ==
startOfBlock(pos, CanCrossEditingBoundary).deepEquivalent();
}
bool isEndOfBlock(const VisiblePosition& pos) {
DCHECK(pos.isValid()) << pos;
return pos.isNotNull() &&
pos.deepEquivalent() ==
endOfBlock(pos, CanCrossEditingBoundary).deepEquivalent();
}
// ---------
template <typename Strategy>
static VisiblePositionTemplate<Strategy> startOfDocumentAlgorithm(
const VisiblePositionTemplate<Strategy>& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
Node* node = visiblePosition.deepEquivalent().anchorNode();
if (!node || !node->document().documentElement())
return VisiblePositionTemplate<Strategy>();
return createVisiblePosition(PositionTemplate<Strategy>::firstPositionInNode(
node->document().documentElement()));
}
VisiblePosition startOfDocument(const VisiblePosition& c) {
return startOfDocumentAlgorithm<EditingStrategy>(c);
}
VisiblePositionInFlatTree startOfDocument(const VisiblePositionInFlatTree& c) {
return startOfDocumentAlgorithm<EditingInFlatTreeStrategy>(c);
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> endOfDocumentAlgorithm(
const VisiblePositionTemplate<Strategy>& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
Node* node = visiblePosition.deepEquivalent().anchorNode();
if (!node || !node->document().documentElement())
return VisiblePositionTemplate<Strategy>();
Element* doc = node->document().documentElement();
return createVisiblePosition(
PositionTemplate<Strategy>::lastPositionInNode(doc));
}
VisiblePosition endOfDocument(const VisiblePosition& c) {
return endOfDocumentAlgorithm<EditingStrategy>(c);
}
VisiblePositionInFlatTree endOfDocument(const VisiblePositionInFlatTree& c) {
return endOfDocumentAlgorithm<EditingInFlatTreeStrategy>(c);
}
bool isStartOfDocument(const VisiblePosition& p) {
DCHECK(p.isValid()) << p;
return p.isNotNull() &&
previousPositionOf(p, CanCrossEditingBoundary).isNull();
}
bool isEndOfDocument(const VisiblePosition& p) {
DCHECK(p.isValid()) << p;
return p.isNotNull() && nextPositionOf(p, CanCrossEditingBoundary).isNull();
}
// ---------
VisiblePosition startOfEditableContent(const VisiblePosition& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
ContainerNode* highestRoot =
highestEditableRoot(visiblePosition.deepEquivalent());
if (!highestRoot)
return VisiblePosition();
return VisiblePosition::firstPositionInNode(highestRoot);
}
VisiblePosition endOfEditableContent(const VisiblePosition& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
ContainerNode* highestRoot =
highestEditableRoot(visiblePosition.deepEquivalent());
if (!highestRoot)
return VisiblePosition();
return VisiblePosition::lastPositionInNode(highestRoot);
}
bool isEndOfEditableOrNonEditableContent(const VisiblePosition& position) {
DCHECK(position.isValid()) << position;
return position.isNotNull() && nextPositionOf(position).isNull();
}
// TODO(yosin) We should rename |isEndOfEditableOrNonEditableContent()| what
// this function does, e.g. |isLastVisiblePositionOrEndOfInnerEditor()|.
bool isEndOfEditableOrNonEditableContent(
const VisiblePositionInFlatTree& position) {
DCHECK(position.isValid()) << position;
if (position.isNull())
return false;
const VisiblePositionInFlatTree nextPosition = nextPositionOf(position);
if (nextPosition.isNull())
return true;
// In DOM version, following condition, the last position of inner editor
// of INPUT/TEXTAREA element, by |nextPosition().isNull()|, because of
// an inner editor is an only leaf node.
if (!nextPosition.deepEquivalent().isAfterAnchor())
return false;
return isTextControlElement(nextPosition.deepEquivalent().anchorNode());
}
VisiblePosition leftBoundaryOfLine(const VisiblePosition& c,
TextDirection direction) {
DCHECK(c.isValid()) << c;
return direction == LTR ? logicalStartOfLine(c) : logicalEndOfLine(c);
}
VisiblePosition rightBoundaryOfLine(const VisiblePosition& c,
TextDirection direction) {
DCHECK(c.isValid()) << c;
return direction == LTR ? logicalEndOfLine(c) : logicalStartOfLine(c);
}
static bool isNonTextLeafChild(LayoutObject* object) {
if (object->slowFirstChild())
return false;
if (object->isText())
return false;
return true;
}
static InlineTextBox* searchAheadForBetterMatch(LayoutObject* layoutObject) {
LayoutBlock* container = layoutObject->containingBlock();
for (LayoutObject* next = layoutObject->nextInPreOrder(container); next;
next = next->nextInPreOrder(container)) {
if (next->isLayoutBlock())
return 0;
if (next->isBR())
return 0;
if (isNonTextLeafChild(next))
return 0;
if (next->isText()) {
InlineTextBox* match = 0;
int minOffset = INT_MAX;
for (InlineTextBox* box = toLayoutText(next)->firstTextBox(); box;
box = box->nextTextBox()) {
int caretMinOffset = box->caretMinOffset();
if (caretMinOffset < minOffset) {
match = box;
minOffset = caretMinOffset;
}
}
if (match)
return match;
}
}
return 0;
}
template <typename Strategy>
PositionTemplate<Strategy> downstreamIgnoringEditingBoundaries(
PositionTemplate<Strategy> position) {
PositionTemplate<Strategy> lastPosition;
while (position != lastPosition) {
lastPosition = position;
position = mostForwardCaretPosition(position, CanCrossEditingBoundary);
}
return position;
}
template <typename Strategy>
PositionTemplate<Strategy> upstreamIgnoringEditingBoundaries(
PositionTemplate<Strategy> position) {
PositionTemplate<Strategy> lastPosition;
while (position != lastPosition) {
lastPosition = position;
position = mostBackwardCaretPosition(position, CanCrossEditingBoundary);
}
return position;
}
// Returns true if |inlineBox| starts different direction of embedded text ru.
// See [1] for details.
// [1] UNICODE BIDIRECTIONAL ALGORITHM, http://unicode.org/reports/tr9/
static bool isStartOfDifferentDirection(const InlineBox* inlineBox) {
InlineBox* prevBox = inlineBox->prevLeafChild();
if (!prevBox)
return true;
if (prevBox->direction() == inlineBox->direction())
return true;
DCHECK_NE(prevBox->bidiLevel(), inlineBox->bidiLevel());
return prevBox->bidiLevel() > inlineBox->bidiLevel();
}
template <typename Strategy>
static InlineBoxPosition computeInlineBoxPositionTemplate(
const PositionTemplate<Strategy>& position,
TextAffinity affinity,
TextDirection primaryDirection) {
InlineBox* inlineBox = nullptr;
int caretOffset = position.computeEditingOffset();
Node* const anchorNode = position.anchorNode();
LayoutObject* layoutObject =
anchorNode->isShadowRoot()
? toShadowRoot(anchorNode)->host().layoutObject()
: anchorNode->layoutObject();
DCHECK(layoutObject) << position;
if (!layoutObject->isText()) {
inlineBox = 0;
if (canHaveChildrenForEditing(anchorNode) &&
layoutObject->isLayoutBlockFlow() &&
hasRenderedNonAnonymousDescendantsWithHeight(layoutObject)) {
// Try a visually equivalent position with possibly opposite
// editability. This helps in case |this| is in an editable block
// but surrounded by non-editable positions. It acts to negate the
// logic at the beginning of
// |LayoutObject::createPositionWithAffinity()|.
PositionTemplate<Strategy> equivalent =
downstreamIgnoringEditingBoundaries(position);
if (equivalent == position) {
equivalent = upstreamIgnoringEditingBoundaries(position);
if (equivalent == position ||
downstreamIgnoringEditingBoundaries(equivalent) == position)
return InlineBoxPosition(inlineBox, caretOffset);
}
return computeInlineBoxPosition(equivalent, TextAffinity::Upstream,
primaryDirection);
}
if (layoutObject->isBox()) {
inlineBox = toLayoutBox(layoutObject)->inlineBoxWrapper();
if (!inlineBox || (caretOffset > inlineBox->caretMinOffset() &&
caretOffset < inlineBox->caretMaxOffset()))
return InlineBoxPosition(inlineBox, caretOffset);
}
} else {
LayoutText* textLayoutObject = toLayoutText(layoutObject);
InlineTextBox* box;
InlineTextBox* candidate = 0;
for (box = textLayoutObject->firstTextBox(); box;
box = box->nextTextBox()) {
int caretMinOffset = box->caretMinOffset();
int caretMaxOffset = box->caretMaxOffset();
if (caretOffset < caretMinOffset || caretOffset > caretMaxOffset ||
(caretOffset == caretMaxOffset && box->isLineBreak()))
continue;
if (caretOffset > caretMinOffset && caretOffset < caretMaxOffset)
return InlineBoxPosition(box, caretOffset);
if (((caretOffset == caretMaxOffset) ^
(affinity == TextAffinity::Downstream)) ||
((caretOffset == caretMinOffset) ^
(affinity == TextAffinity::Upstream)) ||
(caretOffset == caretMaxOffset && box->nextLeafChild() &&
box->nextLeafChild()->isLineBreak()))
break;
candidate = box;
}
if (candidate && candidate == textLayoutObject->lastTextBox() &&
affinity == TextAffinity::Downstream) {
box = searchAheadForBetterMatch(textLayoutObject);
if (box)
caretOffset = box->caretMinOffset();
}
inlineBox = box ? box : candidate;
}
if (!inlineBox)
return InlineBoxPosition(inlineBox, caretOffset);
unsigned char level = inlineBox->bidiLevel();
if (inlineBox->direction() == primaryDirection) {
if (caretOffset == inlineBox->caretRightmostOffset()) {
InlineBox* nextBox = inlineBox->nextLeafChild();
if (!nextBox || nextBox->bidiLevel() >= level)
return InlineBoxPosition(inlineBox, caretOffset);
level = nextBox->bidiLevel();
InlineBox* prevBox = inlineBox;
do {
prevBox = prevBox->prevLeafChild();
} while (prevBox && prevBox->bidiLevel() > level);
// For example, abc FED 123 ^ CBA
if (prevBox && prevBox->bidiLevel() == level)
return InlineBoxPosition(inlineBox, caretOffset);
// For example, abc 123 ^ CBA
while (InlineBox* nextBox = inlineBox->nextLeafChild()) {
if (nextBox->bidiLevel() < level)
break;
inlineBox = nextBox;
}
return InlineBoxPosition(inlineBox, inlineBox->caretRightmostOffset());
}
if (isStartOfDifferentDirection(inlineBox))
return InlineBoxPosition(inlineBox, caretOffset);
level = inlineBox->prevLeafChild()->bidiLevel();
InlineBox* nextBox = inlineBox;
do {
nextBox = nextBox->nextLeafChild();
} while (nextBox && nextBox->bidiLevel() > level);
if (nextBox && nextBox->bidiLevel() == level)
return InlineBoxPosition(inlineBox, caretOffset);
while (InlineBox* prevBox = inlineBox->prevLeafChild()) {
if (prevBox->bidiLevel() < level)
break;
inlineBox = prevBox;
}
return InlineBoxPosition(inlineBox, inlineBox->caretLeftmostOffset());
}
if (caretOffset == inlineBox->caretLeftmostOffset()) {
InlineBox* prevBox = inlineBox->prevLeafChildIgnoringLineBreak();
if (!prevBox || prevBox->bidiLevel() < level) {
// Left edge of a secondary run. Set to the right edge of the entire
// run.
while (InlineBox* nextBox = inlineBox->nextLeafChildIgnoringLineBreak()) {
if (nextBox->bidiLevel() < level)
break;
inlineBox = nextBox;
}
return InlineBoxPosition(inlineBox, inlineBox->caretRightmostOffset());
}
if (prevBox->bidiLevel() > level) {
// Right edge of a "tertiary" run. Set to the left edge of that run.
while (InlineBox* tertiaryBox =
inlineBox->prevLeafChildIgnoringLineBreak()) {
if (tertiaryBox->bidiLevel() <= level)
break;
inlineBox = tertiaryBox;
}
return InlineBoxPosition(inlineBox, inlineBox->caretLeftmostOffset());
}
return InlineBoxPosition(inlineBox, caretOffset);
}
if (layoutObject && layoutObject->style()->unicodeBidi() == Plaintext) {
if (inlineBox->bidiLevel() < level)
return InlineBoxPosition(inlineBox, inlineBox->caretLeftmostOffset());
return InlineBoxPosition(inlineBox, inlineBox->caretRightmostOffset());
}
InlineBox* nextBox = inlineBox->nextLeafChildIgnoringLineBreak();
if (!nextBox || nextBox->bidiLevel() < level) {
// Right edge of a secondary run. Set to the left edge of the entire
// run.
while (InlineBox* prevBox = inlineBox->prevLeafChildIgnoringLineBreak()) {
if (prevBox->bidiLevel() < level)
break;
inlineBox = prevBox;
}
return InlineBoxPosition(inlineBox, inlineBox->caretLeftmostOffset());
}
if (nextBox->bidiLevel() <= level)
return InlineBoxPosition(inlineBox, caretOffset);
// Left edge of a "tertiary" run. Set to the right edge of that run.
while (InlineBox* tertiaryBox = inlineBox->nextLeafChildIgnoringLineBreak()) {
if (tertiaryBox->bidiLevel() <= level)
break;
inlineBox = tertiaryBox;
}
return InlineBoxPosition(inlineBox, inlineBox->caretRightmostOffset());
}
template <typename Strategy>
static InlineBoxPosition computeInlineBoxPositionTemplate(
const PositionTemplate<Strategy>& position,
TextAffinity affinity) {
return computeInlineBoxPositionTemplate<Strategy>(
position, affinity, primaryDirectionOf(*position.anchorNode()));
}
InlineBoxPosition computeInlineBoxPosition(const Position& position,
TextAffinity affinity) {
return computeInlineBoxPositionTemplate<EditingStrategy>(position, affinity);
}
InlineBoxPosition computeInlineBoxPosition(const PositionInFlatTree& position,
TextAffinity affinity) {
return computeInlineBoxPositionTemplate<EditingInFlatTreeStrategy>(position,
affinity);
}
InlineBoxPosition computeInlineBoxPosition(const VisiblePosition& position) {
DCHECK(position.isValid()) << position;
return computeInlineBoxPosition(position.deepEquivalent(),
position.affinity());
}
InlineBoxPosition computeInlineBoxPosition(
const VisiblePositionInFlatTree& position) {
DCHECK(position.isValid()) << position;
return computeInlineBoxPosition(position.deepEquivalent(),
position.affinity());
}
InlineBoxPosition computeInlineBoxPosition(const Position& position,
TextAffinity affinity,
TextDirection primaryDirection) {
return computeInlineBoxPositionTemplate<EditingStrategy>(position, affinity,
primaryDirection);
}
InlineBoxPosition computeInlineBoxPosition(const PositionInFlatTree& position,
TextAffinity affinity,
TextDirection primaryDirection) {
return computeInlineBoxPositionTemplate<EditingInFlatTreeStrategy>(
position, affinity, primaryDirection);
}
template <typename Strategy>
LayoutRect localCaretRectOfPositionTemplate(
const PositionWithAffinityTemplate<Strategy>& position,
LayoutObject*& layoutObject) {
if (position.isNull()) {
layoutObject = nullptr;
return LayoutRect();
}
Node* node = position.anchorNode();
layoutObject = node->layoutObject();
if (!layoutObject)
return LayoutRect();
InlineBoxPosition boxPosition =
computeInlineBoxPosition(position.position(), position.affinity());
if (boxPosition.inlineBox)
layoutObject = LineLayoutAPIShim::layoutObjectFrom(
boxPosition.inlineBox->getLineLayoutItem());
return layoutObject->localCaretRect(boxPosition.inlineBox,
boxPosition.offsetInBox);
}
LayoutRect localCaretRectOfPosition(const PositionWithAffinity& position,
LayoutObject*& layoutObject) {
return localCaretRectOfPositionTemplate<EditingStrategy>(position,
layoutObject);
}
LayoutRect localCaretRectOfPosition(
const PositionInFlatTreeWithAffinity& position,
LayoutObject*& layoutObject) {
return localCaretRectOfPositionTemplate<EditingInFlatTreeStrategy>(
position, layoutObject);
}
static LayoutUnit boundingBoxLogicalHeight(LayoutObject* o,
const LayoutRect& rect) {
return o->style()->isHorizontalWritingMode() ? rect.height() : rect.width();
}
bool hasRenderedNonAnonymousDescendantsWithHeight(LayoutObject* layoutObject) {
LayoutObject* stop = layoutObject->nextInPreOrderAfterChildren();
for (LayoutObject* o = layoutObject->slowFirstChild(); o && o != stop;
o = o->nextInPreOrder()) {
if (o->nonPseudoNode()) {
if ((o->isText() &&
boundingBoxLogicalHeight(o, toLayoutText(o)->linesBoundingBox())) ||
(o->isBox() && toLayoutBox(o)->pixelSnappedLogicalHeight()) ||
(o->isLayoutInline() && isEmptyInline(LineLayoutItem(o)) &&
boundingBoxLogicalHeight(o, toLayoutInline(o)->linesBoundingBox())))
return true;
}
}
return false;
}
VisiblePosition visiblePositionForContentsPoint(const IntPoint& contentsPoint,
LocalFrame* frame) {
HitTestRequest request = HitTestRequest::Move | HitTestRequest::ReadOnly |
HitTestRequest::Active |
HitTestRequest::IgnoreClipping;
HitTestResult result(request, contentsPoint);
frame->document()->layoutViewItem().hitTest(result);
if (Node* node = result.innerNode())
return createVisiblePosition(positionRespectingEditingBoundary(
frame->selection().selection().start(), result.localPoint(), node));
return VisiblePosition();
}
// TODO(yosin): We should use |associatedLayoutObjectOf()| in "VisibleUnits.cpp"
// where it takes |LayoutObject| from |Position|.
// Note about ::first-letter pseudo-element:
// When an element has ::first-letter pseudo-element, first letter characters
// are taken from |Text| node and first letter characters are considered
// as content of <pseudo:first-letter>.
// For following HTML,
// <style>div::first-letter {color: red}</style>
// <div>abc</div>
// we have following layout tree:
// LayoutBlockFlow {DIV} at (0,0) size 784x55
// LayoutInline {<pseudo:first-letter>} at (0,0) size 22x53
// LayoutTextFragment (anonymous) at (0,1) size 22x53
// text run at (0,1) width 22: "a"
// LayoutTextFragment {#text} at (21,30) size 16x17
// text run at (21,30) width 16: "bc"
// In this case, |Text::layoutObject()| for "abc" returns |LayoutTextFragment|
// containing "bc", and it is called remaining part.
//
// Even if |Text| node contains only first-letter characters, e.g. just "a",
// remaining part of |LayoutTextFragment|, with |fragmentLength()| == 0, is
// appeared in layout tree.
//
// When |Text| node contains only first-letter characters and whitespaces, e.g.
// "B\n", associated |LayoutTextFragment| is first-letter part instead of
// remaining part.
//
// Punctuation characters are considered as first-letter. For "(1)ab",
// "(1)" are first-letter part and "ab" are remaining part.
LayoutObject* associatedLayoutObjectOf(const Node& node, int offsetInNode) {
DCHECK_GE(offsetInNode, 0);
LayoutObject* layoutObject = node.layoutObject();
if (!node.isTextNode() || !layoutObject ||
!toLayoutText(layoutObject)->isTextFragment())
return layoutObject;
LayoutTextFragment* layoutTextFragment = toLayoutTextFragment(layoutObject);
if (!layoutTextFragment->isRemainingTextLayoutObject()) {
DCHECK_LE(
static_cast<unsigned>(offsetInNode),
layoutTextFragment->start() + layoutTextFragment->fragmentLength());
return layoutTextFragment;
}
if (layoutTextFragment->fragmentLength() &&
static_cast<unsigned>(offsetInNode) >= layoutTextFragment->start())
return layoutObject;
LayoutObject* firstLetterLayoutObject =
layoutTextFragment->firstLetterPseudoElement()->layoutObject();
// TODO(yosin): We're not sure when |firstLetterLayoutObject| has
// multiple child layout object.
DCHECK_EQ(firstLetterLayoutObject->slowFirstChild(),
firstLetterLayoutObject->slowLastChild());
return firstLetterLayoutObject->slowFirstChild();
}
int caretMinOffset(const Node* node) {
LayoutObject* layoutObject = associatedLayoutObjectOf(*node, 0);
return layoutObject ? layoutObject->caretMinOffset() : 0;
}
int caretMaxOffset(const Node* n) {
return EditingStrategy::caretMaxOffset(*n);
}
template <typename Strategy>
static bool inRenderedText(const PositionTemplate<Strategy>& position) {
Node* const anchorNode = position.anchorNode();
if (!anchorNode || !anchorNode->isTextNode())
return false;
const int offsetInNode = position.computeEditingOffset();
LayoutObject* layoutObject =
associatedLayoutObjectOf(*anchorNode, offsetInNode);
if (!layoutObject)
return false;
LayoutText* textLayoutObject = toLayoutText(layoutObject);
const int textOffset = offsetInNode - textLayoutObject->textStartOffset();
for (InlineTextBox* box = textLayoutObject->firstTextBox(); box;
box = box->nextTextBox()) {
if (textOffset < static_cast<int>(box->start()) &&
!textLayoutObject->containsReversedText()) {
// The offset we're looking for is before this node
// this means the offset must be in content that is
// not laid out. Return false.
return false;
}
if (box->containsCaretOffset(textOffset)) {
// Return false for offsets inside composed characters.
return textOffset == 0 ||
textOffset == nextGraphemeBoundaryOf(anchorNode,
previousGraphemeBoundaryOf(
anchorNode, textOffset));
}
}
return false;
}
bool rendersInDifferentPosition(const Position& position1,
const Position& position2) {
if (position1.isNull() || position2.isNull())
return false;
LayoutObject* layoutObject1;
const LayoutRect& rect1 =
localCaretRectOfPosition(PositionWithAffinity(position1), layoutObject1);
LayoutObject* layoutObject2;
const LayoutRect& rect2 =
localCaretRectOfPosition(PositionWithAffinity(position2), layoutObject2);
if (!layoutObject1 || !layoutObject2)
return layoutObject1 != layoutObject2;
return layoutObject1->localToAbsoluteQuad(FloatRect(rect1)) !=
layoutObject2->localToAbsoluteQuad(FloatRect(rect2));
}
static bool isVisuallyEmpty(const LayoutObject* layout) {
for (LayoutObject* child = layout->slowFirstChild(); child;
child = child->nextSibling()) {
// TODO(xiaochengh): Replace type-based conditioning by virtual function.
if (child->isBox()) {
if (!toLayoutBox(child)->size().isEmpty())
return false;
} else if (child->isLayoutInline()) {
if (toLayoutInline(child)->firstLineBoxIncludingCulling())
return false;
} else if (child->isText()) {
if (toLayoutText(child)->hasTextBoxes())
return false;
} else {
return false;
}
}
return true;
}
// FIXME: Share code with isCandidate, if possible.
bool endsOfNodeAreVisuallyDistinctPositions(const Node* node) {
if (!node || !node->layoutObject())
return false;
if (!node->layoutObject()->isInline())
return true;
// Don't include inline tables.
if (isHTMLTableElement(*node))
return false;
// A Marquee elements are moving so we should assume their ends are always
// visibily distinct.
if (isHTMLMarqueeElement(*node))
return true;
// There is a VisiblePosition inside an empty inline-block container.
return node->layoutObject()->isAtomicInlineLevel() &&
canHaveChildrenForEditing(node) &&
!toLayoutBox(node->layoutObject())->size().isEmpty() &&
isVisuallyEmpty(node->layoutObject());
}
template <typename Strategy>
static Node* enclosingVisualBoundary(Node* node) {
while (node && !endsOfNodeAreVisuallyDistinctPositions(node))
node = Strategy::parent(*node);
return node;
}
// upstream() and downstream() want to return positions that are either in a
// text node or at just before a non-text node. This method checks for that.
template <typename Strategy>
static bool isStreamer(const PositionIteratorAlgorithm<Strategy>& pos) {
if (!pos.node())
return true;
if (isAtomicNode(pos.node()))
return true;
return pos.atStartOfNode();
}
template <typename Strategy>
static PositionTemplate<Strategy> mostBackwardCaretPosition(
const PositionTemplate<Strategy>& position,
EditingBoundaryCrossingRule rule) {
TRACE_EVENT0("input", "VisibleUnits::mostBackwardCaretPosition");
Node* startNode = position.anchorNode();
if (!startNode)
return PositionTemplate<Strategy>();
// iterate backward from there, looking for a qualified position
Node* boundary = enclosingVisualBoundary<Strategy>(startNode);
// FIXME: PositionIterator should respect Before and After positions.
PositionIteratorAlgorithm<Strategy> lastVisible(
position.isAfterAnchor()
? PositionTemplate<Strategy>::editingPositionOf(
position.anchorNode(),
Strategy::caretMaxOffset(*position.anchorNode()))
: position);
PositionIteratorAlgorithm<Strategy> currentPos = lastVisible;
bool startEditable = hasEditableStyle(*startNode);
Node* lastNode = startNode;
bool boundaryCrossed = false;
for (; !currentPos.atStart(); currentPos.decrement()) {
Node* currentNode = currentPos.node();
// Don't check for an editability change if we haven't moved to a different
// node, to avoid the expense of computing hasEditableStyle().
if (currentNode != lastNode) {
// Don't change editability.
bool currentEditable = hasEditableStyle(*currentNode);
if (startEditable != currentEditable) {
if (rule == CannotCrossEditingBoundary)
break;
boundaryCrossed = true;
}
lastNode = currentNode;
}
// If we've moved to a position that is visually distinct, return the last
// saved position. There is code below that terminates early if we're
// *about* to move to a visually distinct position.
if (endsOfNodeAreVisuallyDistinctPositions(currentNode) &&
currentNode != boundary)
return lastVisible.deprecatedComputePosition();
// skip position in non-laid out or invisible node
LayoutObject* layoutObject =
associatedLayoutObjectOf(*currentNode, currentPos.offsetInLeafNode());
if (!layoutObject ||
layoutObject->style()->visibility() != EVisibility::Visible)
continue;
if (rule == CanCrossEditingBoundary && boundaryCrossed) {
lastVisible = currentPos;
break;
}
// track last visible streamer position
if (isStreamer<Strategy>(currentPos))
lastVisible = currentPos;
// Don't move past a position that is visually distinct. We could rely on
// code above to terminate and return lastVisible on the next iteration, but
// we terminate early to avoid doing a nodeIndex() call.
if (endsOfNodeAreVisuallyDistinctPositions(currentNode) &&
currentPos.atStartOfNode())
return lastVisible.deprecatedComputePosition();
// Return position after tables and nodes which have content that can be
// ignored.
if (editingIgnoresContent(*currentNode) ||
isDisplayInsideTable(currentNode)) {
if (currentPos.atEndOfNode())
return PositionTemplate<Strategy>::afterNode(currentNode);
continue;
}
// return current position if it is in laid out text
if (layoutObject->isText() && toLayoutText(layoutObject)->firstTextBox()) {
LayoutText* const textLayoutObject = toLayoutText(layoutObject);
const unsigned textStartOffset = textLayoutObject->textStartOffset();
if (currentNode != startNode) {
// This assertion fires in layout tests in the case-transform.html test
// because of a mix-up between offsets in the text in the DOM tree with
// text in the layout tree which can have a different length due to case
// transformation.
// Until we resolve that, disable this so we can run the layout tests!
// DCHECK_GE(currentOffset, layoutObject->caretMaxOffset());
return PositionTemplate<Strategy>(
currentNode, layoutObject->caretMaxOffset() + textStartOffset);
}
// Map offset in DOM node to offset in InlineBox.
DCHECK_GE(currentPos.offsetInLeafNode(),
static_cast<int>(textStartOffset));
const unsigned textOffset =
currentPos.offsetInLeafNode() - textStartOffset;
InlineTextBox* lastTextBox = textLayoutObject->lastTextBox();
for (InlineTextBox* box = textLayoutObject->firstTextBox(); box;
box = box->nextTextBox()) {
if (textOffset == box->start()) {
if (textLayoutObject->isTextFragment() &&
toLayoutTextFragment(layoutObject)
->isRemainingTextLayoutObject()) {
// |currentPos| is at start of remaining text of
// |Text| node with :first-letter.
DCHECK_GE(currentPos.offsetInLeafNode(), 1);
LayoutObject* firstLetterLayoutObject =
toLayoutTextFragment(layoutObject)
->firstLetterPseudoElement()
->layoutObject();
if (firstLetterLayoutObject &&
firstLetterLayoutObject->style()->visibility() ==
EVisibility::Visible)
return currentPos.computePosition();
}
continue;
}
if (textOffset <= box->start() + box->len()) {
if (textOffset > box->start())
return currentPos.computePosition();
continue;
}
if (box == lastTextBox || textOffset != box->start() + box->len() + 1)
continue;
// The text continues on the next line only if the last text box is not
// on this line and none of the boxes on this line have a larger start
// offset.
bool continuesOnNextLine = true;
InlineBox* otherBox = box;
while (continuesOnNextLine) {
otherBox = otherBox->nextLeafChild();
if (!otherBox)
break;
if (otherBox == lastTextBox ||
(LineLayoutAPIShim::layoutObjectFrom(
otherBox->getLineLayoutItem()) == textLayoutObject &&
toInlineTextBox(otherBox)->start() > textOffset))
continuesOnNextLine = false;
}
otherBox = box;
while (continuesOnNextLine) {
otherBox = otherBox->prevLeafChild();
if (!otherBox)
break;
if (otherBox == lastTextBox ||
(LineLayoutAPIShim::layoutObjectFrom(
otherBox->getLineLayoutItem()) == textLayoutObject &&
toInlineTextBox(otherBox)->start() > textOffset))
continuesOnNextLine = false;
}
if (continuesOnNextLine)
return currentPos.computePosition();
}
}
}
return lastVisible.deprecatedComputePosition();
}
Position mostBackwardCaretPosition(const Position& position,
EditingBoundaryCrossingRule rule) {
return mostBackwardCaretPosition<EditingStrategy>(position, rule);
}
PositionInFlatTree mostBackwardCaretPosition(const PositionInFlatTree& position,
EditingBoundaryCrossingRule rule) {
return mostBackwardCaretPosition<EditingInFlatTreeStrategy>(position, rule);
}
template <typename Strategy>
PositionTemplate<Strategy> mostForwardCaretPosition(
const PositionTemplate<Strategy>& position,
EditingBoundaryCrossingRule rule) {
TRACE_EVENT0("input", "VisibleUnits::mostForwardCaretPosition");
Node* startNode = position.anchorNode();
if (!startNode)
return PositionTemplate<Strategy>();
// iterate forward from there, looking for a qualified position
Node* boundary = enclosingVisualBoundary<Strategy>(startNode);
// FIXME: PositionIterator should respect Before and After positions.
PositionIteratorAlgorithm<Strategy> lastVisible(
position.isAfterAnchor()
? PositionTemplate<Strategy>::editingPositionOf(
position.anchorNode(),
Strategy::caretMaxOffset(*position.anchorNode()))
: position);
PositionIteratorAlgorithm<Strategy> currentPos = lastVisible;
bool startEditable = hasEditableStyle(*startNode);
Node* lastNode = startNode;
bool boundaryCrossed = false;
for (; !currentPos.atEnd(); currentPos.increment()) {
Node* currentNode = currentPos.node();
// Don't check for an editability change if we haven't moved to a different
// node, to avoid the expense of computing hasEditableStyle().
if (currentNode != lastNode) {
// Don't change editability.
bool currentEditable = hasEditableStyle(*currentNode);
if (startEditable != currentEditable) {
if (rule == CannotCrossEditingBoundary)
break;
boundaryCrossed = true;
}
lastNode = currentNode;
}
// stop before going above the body, up into the head
// return the last visible streamer position
if (isHTMLBodyElement(*currentNode) && currentPos.atEndOfNode())
break;
// Do not move to a visually distinct position.
if (endsOfNodeAreVisuallyDistinctPositions(currentNode) &&
currentNode != boundary)
return lastVisible.deprecatedComputePosition();
// Do not move past a visually disinct position.
// Note: The first position after the last in a node whose ends are visually
// distinct positions will be [boundary->parentNode(),
// originalBlock->nodeIndex() + 1].
if (boundary && Strategy::parent(*boundary) == currentNode)
return lastVisible.deprecatedComputePosition();
// skip position in non-laid out or invisible node
LayoutObject* layoutObject =
associatedLayoutObjectOf(*currentNode, currentPos.offsetInLeafNode());
if (!layoutObject ||
layoutObject->style()->visibility() != EVisibility::Visible)
continue;
if (rule == CanCrossEditingBoundary && boundaryCrossed) {
lastVisible = currentPos;
break;
}
// track last visible streamer position
if (isStreamer<Strategy>(currentPos))
lastVisible = currentPos;
// Return position before tables and nodes which have content that can be
// ignored.
if (editingIgnoresContent(*currentNode) ||
isDisplayInsideTable(currentNode)) {
if (currentPos.offsetInLeafNode() <= layoutObject->caretMinOffset())
return PositionTemplate<Strategy>::editingPositionOf(
currentNode, layoutObject->caretMinOffset());
continue;
}
// return current position if it is in laid out text
if (layoutObject->isText() && toLayoutText(layoutObject)->firstTextBox()) {
LayoutText* const textLayoutObject = toLayoutText(layoutObject);
const unsigned textStartOffset = textLayoutObject->textStartOffset();
if (currentNode != startNode) {
DCHECK(currentPos.atStartOfNode());
return PositionTemplate<Strategy>(
currentNode, layoutObject->caretMinOffset() + textStartOffset);
}
// Map offset in DOM node to offset in InlineBox.
DCHECK_GE(currentPos.offsetInLeafNode(),
static_cast<int>(textStartOffset));
const unsigned textOffset =
currentPos.offsetInLeafNode() - textStartOffset;
InlineTextBox* lastTextBox = textLayoutObject->lastTextBox();
for (InlineTextBox* box = textLayoutObject->firstTextBox(); box;
box = box->nextTextBox()) {
if (textOffset <= box->end()) {
if (textOffset >= box->start())
return currentPos.computePosition();
continue;
}
if (box == lastTextBox || textOffset != box->start() + box->len())
continue;
// The text continues on the next line only if the last text box is not
// on this line and none of the boxes on this line have a larger start
// offset.
bool continuesOnNextLine = true;
InlineBox* otherBox = box;
while (continuesOnNextLine) {
otherBox = otherBox->nextLeafChild();
if (!otherBox)
break;
if (otherBox == lastTextBox ||
(LineLayoutAPIShim::layoutObjectFrom(
otherBox->getLineLayoutItem()) == textLayoutObject &&
toInlineTextBox(otherBox)->start() >= textOffset))
continuesOnNextLine = false;
}
otherBox = box;
while (continuesOnNextLine) {
otherBox = otherBox->prevLeafChild();
if (!otherBox)
break;
if (otherBox == lastTextBox ||
(LineLayoutAPIShim::layoutObjectFrom(
otherBox->getLineLayoutItem()) == textLayoutObject &&
toInlineTextBox(otherBox)->start() >= textOffset))
continuesOnNextLine = false;
}
if (continuesOnNextLine)
return currentPos.computePosition();
}
}
}
return lastVisible.deprecatedComputePosition();
}
Position mostForwardCaretPosition(const Position& position,
EditingBoundaryCrossingRule rule) {
return mostForwardCaretPosition<EditingStrategy>(position, rule);
}
PositionInFlatTree mostForwardCaretPosition(const PositionInFlatTree& position,
EditingBoundaryCrossingRule rule) {
return mostForwardCaretPosition<EditingInFlatTreeStrategy>(position, rule);
}
// Returns true if the visually equivalent positions around have different
// editability. A position is considered at editing boundary if one of the
// following is true:
// 1. It is the first position in the node and the next visually equivalent
// position is non editable.
// 2. It is the last position in the node and the previous visually equivalent
// position is non editable.
// 3. It is an editable position and both the next and previous visually
// equivalent positions are both non editable.
template <typename Strategy>
static bool atEditingBoundary(const PositionTemplate<Strategy> positions) {
PositionTemplate<Strategy> nextPosition =
mostForwardCaretPosition(positions, CanCrossEditingBoundary);
if (positions.atFirstEditingPositionForNode() && nextPosition.isNotNull() &&
!hasEditableStyle(*nextPosition.anchorNode()))
return true;
PositionTemplate<Strategy> prevPosition =
mostBackwardCaretPosition(positions, CanCrossEditingBoundary);
if (positions.atLastEditingPositionForNode() && prevPosition.isNotNull() &&
!hasEditableStyle(*prevPosition.anchorNode()))
return true;
return nextPosition.isNotNull() &&
!hasEditableStyle(*nextPosition.anchorNode()) &&
prevPosition.isNotNull() &&
!hasEditableStyle(*prevPosition.anchorNode());
}
template <typename Strategy>
static bool isVisuallyEquivalentCandidateAlgorithm(
const PositionTemplate<Strategy>& position) {
Node* const anchorNode = position.anchorNode();
if (!anchorNode)
return false;
LayoutObject* layoutObject = anchorNode->layoutObject();
if (!layoutObject)
return false;
if (layoutObject->style()->visibility() != EVisibility::Visible)
return false;
if (layoutObject->isBR()) {
// TODO(leviw) The condition should be
// m_anchorType == PositionAnchorType::BeforeAnchor, but for now we
// still need to support legacy positions.
if (position.isAfterAnchor())
return false;
if (position.computeEditingOffset())
return false;
const Node* parent = Strategy::parent(*anchorNode);
return parent->layoutObject() && parent->layoutObject()->isSelectable();
}
if (layoutObject->isText())
return layoutObject->isSelectable() && inRenderedText(position);
if (layoutObject->isSVG()) {
// We don't consider SVG elements are contenteditable except for
// associated |layoutObject| returns |isText()| true,
// e.g. |LayoutSVGInlineText|.
return false;
}
if (isDisplayInsideTable(anchorNode) || editingIgnoresContent(*anchorNode)) {
if (!position.atFirstEditingPositionForNode() &&
!position.atLastEditingPositionForNode())
return false;
const Node* parent = Strategy::parent(*anchorNode);
return parent->layoutObject() && parent->layoutObject()->isSelectable();
}
if (anchorNode->document().documentElement() == anchorNode ||
anchorNode->isDocumentNode())
return false;
if (!layoutObject->isSelectable())
return false;
if (layoutObject->isLayoutBlockFlow() || layoutObject->isFlexibleBox() ||
layoutObject->isLayoutGrid()) {
if (toLayoutBlock(layoutObject)->logicalHeight() ||
isHTMLBodyElement(*anchorNode)) {
if (!hasRenderedNonAnonymousDescendantsWithHeight(layoutObject))
return position.atFirstEditingPositionForNode();
return hasEditableStyle(*anchorNode) && atEditingBoundary(position);
}
} else {
return hasEditableStyle(*anchorNode) && atEditingBoundary(position);
}
return false;
}
bool isVisuallyEquivalentCandidate(const Position& position) {
return isVisuallyEquivalentCandidateAlgorithm<EditingStrategy>(position);
}
bool isVisuallyEquivalentCandidate(const PositionInFlatTree& position) {
return isVisuallyEquivalentCandidateAlgorithm<EditingInFlatTreeStrategy>(
position);
}
template <typename Strategy>
static IntRect absoluteCaretBoundsOfAlgorithm(
const VisiblePositionTemplate<Strategy>& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
LayoutObject* layoutObject;
LayoutRect localRect = localCaretRectOfPosition(
visiblePosition.toPositionWithAffinity(), layoutObject);
if (localRect.isEmpty() || !layoutObject)
return IntRect();
return layoutObject->localToAbsoluteQuad(FloatRect(localRect))
.enclosingBoundingBox();
}
IntRect absoluteCaretBoundsOf(const VisiblePosition& visiblePosition) {
return absoluteCaretBoundsOfAlgorithm<EditingStrategy>(visiblePosition);
}
IntRect absoluteCaretBoundsOf(
const VisiblePositionInFlatTree& visiblePosition) {
return absoluteCaretBoundsOfAlgorithm<EditingInFlatTreeStrategy>(
visiblePosition);
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> skipToEndOfEditingBoundary(
const VisiblePositionTemplate<Strategy>& pos,
const PositionTemplate<Strategy>& anchor) {
DCHECK(pos.isValid()) << pos;
if (pos.isNull())
return pos;
ContainerNode* highestRoot = highestEditableRoot(anchor);
ContainerNode* highestRootOfPos = highestEditableRoot(pos.deepEquivalent());
// Return |pos| itself if the two are from the very same editable region,
// or both are non-editable.
if (highestRootOfPos == highestRoot)
return pos;
// If this is not editable but |pos| has an editable root, skip to the end
if (!highestRoot && highestRootOfPos)
return createVisiblePosition(
PositionTemplate<Strategy>(highestRootOfPos,
PositionAnchorType::AfterAnchor)
.parentAnchoredEquivalent());
// That must mean that |pos| is not editable. Return the next position after
// |pos| that is in the same editable region as this position
DCHECK(highestRoot);
return firstEditableVisiblePositionAfterPositionInRoot(pos.deepEquivalent(),
*highestRoot);
}
template <typename Strategy>
static UChar32 characterAfterAlgorithm(
const VisiblePositionTemplate<Strategy>& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
// We canonicalize to the first of two equivalent candidates, but the second
// of the two candidates is the one that will be inside the text node
// containing the character after this visible position.
const PositionTemplate<Strategy> pos =
mostForwardCaretPosition(visiblePosition.deepEquivalent());
if (!pos.isOffsetInAnchor())
return 0;
Node* containerNode = pos.computeContainerNode();
if (!containerNode || !containerNode->isTextNode())
return 0;
unsigned offset = static_cast<unsigned>(pos.offsetInContainerNode());
Text* textNode = toText(containerNode);
unsigned length = textNode->length();
if (offset >= length)
return 0;
return textNode->data().characterStartingAt(offset);
}
UChar32 characterAfter(const VisiblePosition& visiblePosition) {
return characterAfterAlgorithm<EditingStrategy>(visiblePosition);
}
UChar32 characterAfter(const VisiblePositionInFlatTree& visiblePosition) {
return characterAfterAlgorithm<EditingInFlatTreeStrategy>(visiblePosition);
}
template <typename Strategy>
static UChar32 characterBeforeAlgorithm(
const VisiblePositionTemplate<Strategy>& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
return characterAfter(previousPositionOf(visiblePosition));
}
UChar32 characterBefore(const VisiblePosition& visiblePosition) {
return characterBeforeAlgorithm<EditingStrategy>(visiblePosition);
}
UChar32 characterBefore(const VisiblePositionInFlatTree& visiblePosition) {
return characterBeforeAlgorithm<EditingInFlatTreeStrategy>(visiblePosition);
}
template <typename Strategy>
static PositionTemplate<Strategy> leftVisuallyDistinctCandidate(
const VisiblePositionTemplate<Strategy>& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
const PositionTemplate<Strategy> deepPosition =
visiblePosition.deepEquivalent();
PositionTemplate<Strategy> p = deepPosition;
if (p.isNull())
return PositionTemplate<Strategy>();
const PositionTemplate<Strategy> downstreamStart =
mostForwardCaretPosition(p);
TextDirection primaryDirection = primaryDirectionOf(*p.anchorNode());
const TextAffinity affinity = visiblePosition.affinity();
while (true) {
InlineBoxPosition boxPosition =
computeInlineBoxPosition(p, affinity, primaryDirection);
InlineBox* box = boxPosition.inlineBox;
int offset = boxPosition.offsetInBox;
if (!box)
return primaryDirection == LTR
? previousVisuallyDistinctCandidate(deepPosition)
: nextVisuallyDistinctCandidate(deepPosition);
LineLayoutItem lineLayoutItem = box->getLineLayoutItem();
while (true) {
if ((lineLayoutItem.isAtomicInlineLevel() || lineLayoutItem.isBR()) &&
offset == box->caretRightmostOffset())
return box->isLeftToRightDirection()
? previousVisuallyDistinctCandidate(deepPosition)
: nextVisuallyDistinctCandidate(deepPosition);
if (!lineLayoutItem.node()) {
box = box->prevLeafChild();
if (!box)
return primaryDirection == LTR
? previousVisuallyDistinctCandidate(deepPosition)
: nextVisuallyDistinctCandidate(deepPosition);
lineLayoutItem = box->getLineLayoutItem();
offset = box->caretRightmostOffset();
continue;
}
offset = box->isLeftToRightDirection()
? previousGraphemeBoundaryOf(lineLayoutItem.node(), offset)
: nextGraphemeBoundaryOf(lineLayoutItem.node(), offset);
int caretMinOffset = box->caretMinOffset();
int caretMaxOffset = box->caretMaxOffset();
if (offset > caretMinOffset && offset < caretMaxOffset)
break;
if (box->isLeftToRightDirection() ? offset < caretMinOffset
: offset > caretMaxOffset) {
// Overshot to the left.
InlineBox* prevBox = box->prevLeafChildIgnoringLineBreak();
if (!prevBox) {
PositionTemplate<Strategy> positionOnLeft =
primaryDirection == LTR ? previousVisuallyDistinctCandidate(
visiblePosition.deepEquivalent())
: nextVisuallyDistinctCandidate(
visiblePosition.deepEquivalent());
if (positionOnLeft.isNull())
return PositionTemplate<Strategy>();
InlineBox* boxOnLeft = computeInlineBoxPosition(
positionOnLeft, affinity, primaryDirection)
.inlineBox;
if (boxOnLeft && boxOnLeft->root() == box->root())
return PositionTemplate<Strategy>();
return positionOnLeft;
}
// Reposition at the other logical position corresponding to our
// edge's visual position and go for another round.
box = prevBox;
lineLayoutItem = box->getLineLayoutItem();
offset = prevBox->caretRightmostOffset();
continue;
}
DCHECK_EQ(offset, box->caretLeftmostOffset());
unsigned char level = box->bidiLevel();
InlineBox* prevBox = box->prevLeafChild();
if (box->direction() == primaryDirection) {
if (!prevBox) {
InlineBox* logicalStart = 0;
if (primaryDirection == LTR
? box->root().getLogicalStartBoxWithNode(logicalStart)
: box->root().getLogicalEndBoxWithNode(logicalStart)) {
box = logicalStart;
lineLayoutItem = box->getLineLayoutItem();
offset = primaryDirection == LTR ? box->caretMinOffset()
: box->caretMaxOffset();
}
break;
}
if (prevBox->bidiLevel() >= level)
break;
level = prevBox->bidiLevel();
InlineBox* nextBox = box;
do {
nextBox = nextBox->nextLeafChild();
} while (nextBox && nextBox->bidiLevel() > level);
if (nextBox && nextBox->bidiLevel() == level)
break;
box = prevBox;
lineLayoutItem = box->getLineLayoutItem();
offset = box->caretRightmostOffset();
if (box->direction() == primaryDirection)
break;
continue;
}
while (prevBox && !prevBox->getLineLayoutItem().node())
prevBox = prevBox->prevLeafChild();
if (prevBox) {
box = prevBox;
lineLayoutItem = box->getLineLayoutItem();
offset = box->caretRightmostOffset();
if (box->bidiLevel() > level) {
do {
prevBox = prevBox->prevLeafChild();
} while (prevBox && prevBox->bidiLevel() > level);
if (!prevBox || prevBox->bidiLevel() < level)
continue;
}
} else {
// Trailing edge of a secondary run. Set to the leading edge of
// the entire run.
while (true) {
while (InlineBox* nextBox = box->nextLeafChild()) {
if (nextBox->bidiLevel() < level)
break;
box = nextBox;
}
if (box->bidiLevel() == level)
break;
level = box->bidiLevel();
while (InlineBox* prevBox = box->prevLeafChild()) {
if (prevBox->bidiLevel() < level)
break;
box = prevBox;
}
if (box->bidiLevel() == level)
break;
level = box->bidiLevel();
}
lineLayoutItem = box->getLineLayoutItem();
offset = primaryDirection == LTR ? box->caretMinOffset()
: box->caretMaxOffset();
}
break;
}
p = PositionTemplate<Strategy>::editingPositionOf(lineLayoutItem.node(),
offset);
if ((isVisuallyEquivalentCandidate(p) &&
mostForwardCaretPosition(p) != downstreamStart) ||
p.atStartOfTree() || p.atEndOfTree())
return p;
DCHECK_NE(p, deepPosition);
}
}
template <typename Strategy>
VisiblePositionTemplate<Strategy> leftPositionOfAlgorithm(
const VisiblePositionTemplate<Strategy>& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
const PositionTemplate<Strategy> pos =
leftVisuallyDistinctCandidate(visiblePosition);
// TODO(yosin) Why can't we move left from the last position in a tree?
if (pos.atStartOfTree() || pos.atEndOfTree())
return VisiblePositionTemplate<Strategy>();
const VisiblePositionTemplate<Strategy> left = createVisiblePosition(pos);
DCHECK_NE(left.deepEquivalent(), visiblePosition.deepEquivalent());
return directionOfEnclosingBlock(left.deepEquivalent()) == LTR
? honorEditingBoundaryAtOrBefore(left,
visiblePosition.deepEquivalent())
: honorEditingBoundaryAtOrAfter(left,
visiblePosition.deepEquivalent());
}
VisiblePosition leftPositionOf(const VisiblePosition& visiblePosition) {
return leftPositionOfAlgorithm<EditingStrategy>(visiblePosition);
}
VisiblePositionInFlatTree leftPositionOf(
const VisiblePositionInFlatTree& visiblePosition) {
return leftPositionOfAlgorithm<EditingInFlatTreeStrategy>(visiblePosition);
}
template <typename Strategy>
static PositionTemplate<Strategy> rightVisuallyDistinctCandidate(
const VisiblePositionTemplate<Strategy>& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
const PositionTemplate<Strategy> deepPosition =
visiblePosition.deepEquivalent();
PositionTemplate<Strategy> p = deepPosition;
if (p.isNull())
return PositionTemplate<Strategy>();
const PositionTemplate<Strategy> downstreamStart =
mostForwardCaretPosition(p);
TextDirection primaryDirection = primaryDirectionOf(*p.anchorNode());
const TextAffinity affinity = visiblePosition.affinity();
while (true) {
InlineBoxPosition boxPosition =
computeInlineBoxPosition(p, affinity, primaryDirection);
InlineBox* box = boxPosition.inlineBox;
int offset = boxPosition.offsetInBox;
if (!box)
return primaryDirection == LTR
? nextVisuallyDistinctCandidate(deepPosition)
: previousVisuallyDistinctCandidate(deepPosition);
LayoutObject* layoutObject =
LineLayoutAPIShim::layoutObjectFrom(box->getLineLayoutItem());
while (true) {
if ((layoutObject->isAtomicInlineLevel() || layoutObject->isBR()) &&
offset == box->caretLeftmostOffset())
return box->isLeftToRightDirection()
? nextVisuallyDistinctCandidate(deepPosition)
: previousVisuallyDistinctCandidate(deepPosition);
if (!layoutObject->node()) {
box = box->nextLeafChild();
if (!box)
return primaryDirection == LTR
? nextVisuallyDistinctCandidate(deepPosition)
: previousVisuallyDistinctCandidate(deepPosition);
layoutObject =
LineLayoutAPIShim::layoutObjectFrom(box->getLineLayoutItem());
offset = box->caretLeftmostOffset();
continue;
}
offset = box->isLeftToRightDirection()
? nextGraphemeBoundaryOf(layoutObject->node(), offset)
: previousGraphemeBoundaryOf(layoutObject->node(), offset);
int caretMinOffset = box->caretMinOffset();
int caretMaxOffset = box->caretMaxOffset();
if (offset > caretMinOffset && offset < caretMaxOffset)
break;
if (box->isLeftToRightDirection() ? offset > caretMaxOffset
: offset < caretMinOffset) {
// Overshot to the right.
InlineBox* nextBox = box->nextLeafChildIgnoringLineBreak();
if (!nextBox) {
PositionTemplate<Strategy> positionOnRight =
primaryDirection == LTR
? nextVisuallyDistinctCandidate(deepPosition)
: previousVisuallyDistinctCandidate(deepPosition);
if (positionOnRight.isNull())
return PositionTemplate<Strategy>();
InlineBox* boxOnRight =
computeInlineBoxPosition(positionOnRight, affinity,
primaryDirection)
.inlineBox;
if (boxOnRight && boxOnRight->root() == box->root())
return PositionTemplate<Strategy>();
return positionOnRight;
}
// Reposition at the other logical position corresponding to our
// edge's visual position and go for another round.
box = nextBox;
layoutObject =
LineLayoutAPIShim::layoutObjectFrom(box->getLineLayoutItem());
offset = nextBox->caretLeftmostOffset();
continue;
}
DCHECK_EQ(offset, box->caretRightmostOffset());
unsigned char level = box->bidiLevel();
InlineBox* nextBox = box->nextLeafChild();
if (box->direction() == primaryDirection) {
if (!nextBox) {
InlineBox* logicalEnd = 0;
if (primaryDirection == LTR
? box->root().getLogicalEndBoxWithNode(logicalEnd)
: box->root().getLogicalStartBoxWithNode(logicalEnd)) {
box = logicalEnd;
layoutObject =
LineLayoutAPIShim::layoutObjectFrom(box->getLineLayoutItem());
offset = primaryDirection == LTR ? box->caretMaxOffset()
: box->caretMinOffset();
}
break;
}
if (nextBox->bidiLevel() >= level)
break;
level = nextBox->bidiLevel();
InlineBox* prevBox = box;
do {
prevBox = prevBox->prevLeafChild();
} while (prevBox && prevBox->bidiLevel() > level);
// For example, abc FED 123 ^ CBA
if (prevBox && prevBox->bidiLevel() == level)
break;
// For example, abc 123 ^ CBA or 123 ^ CBA abc
box = nextBox;
layoutObject =
LineLayoutAPIShim::layoutObjectFrom(box->getLineLayoutItem());
offset = box->caretLeftmostOffset();
if (box->direction() == primaryDirection)
break;
continue;
}
while (nextBox && !nextBox->getLineLayoutItem().node())
nextBox = nextBox->nextLeafChild();
if (nextBox) {
box = nextBox;
layoutObject =
LineLayoutAPIShim::layoutObjectFrom(box->getLineLayoutItem());
offset = box->caretLeftmostOffset();
if (box->bidiLevel() > level) {
do {
nextBox = nextBox->nextLeafChild();
} while (nextBox && nextBox->bidiLevel() > level);
if (!nextBox || nextBox->bidiLevel() < level)
continue;
}
} else {
// Trailing edge of a secondary run. Set to the leading edge of the
// entire run.
while (true) {
while (InlineBox* prevBox = box->prevLeafChild()) {
if (prevBox->bidiLevel() < level)
break;
box = prevBox;
}
if (box->bidiLevel() == level)
break;
level = box->bidiLevel();
while (InlineBox* nextBox = box->nextLeafChild()) {
if (nextBox->bidiLevel() < level)
break;
box = nextBox;
}
if (box->bidiLevel() == level)
break;
level = box->bidiLevel();
}
layoutObject =
LineLayoutAPIShim::layoutObjectFrom(box->getLineLayoutItem());
offset = primaryDirection == LTR ? box->caretMaxOffset()
: box->caretMinOffset();
}
break;
}
p = PositionTemplate<Strategy>::editingPositionOf(layoutObject->node(),
offset);
if ((isVisuallyEquivalentCandidate(p) &&
mostForwardCaretPosition(p) != downstreamStart) ||
p.atStartOfTree() || p.atEndOfTree())
return p;
DCHECK_NE(p, deepPosition);
}
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> rightPositionOfAlgorithm(
const VisiblePositionTemplate<Strategy>& visiblePosition) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
const PositionTemplate<Strategy> pos =
rightVisuallyDistinctCandidate(visiblePosition);
// FIXME: Why can't we move left from the last position in a tree?
if (pos.atStartOfTree() || pos.atEndOfTree())
return VisiblePositionTemplate<Strategy>();
const VisiblePositionTemplate<Strategy> right = createVisiblePosition(pos);
DCHECK_NE(right.deepEquivalent(), visiblePosition.deepEquivalent());
return directionOfEnclosingBlock(right.deepEquivalent()) == LTR
? honorEditingBoundaryAtOrAfter(right,
visiblePosition.deepEquivalent())
: honorEditingBoundaryAtOrBefore(right,
visiblePosition.deepEquivalent());
}
VisiblePosition rightPositionOf(const VisiblePosition& visiblePosition) {
return rightPositionOfAlgorithm<EditingStrategy>(visiblePosition);
}
VisiblePositionInFlatTree rightPositionOf(
const VisiblePositionInFlatTree& visiblePosition) {
return rightPositionOfAlgorithm<EditingInFlatTreeStrategy>(visiblePosition);
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> nextPositionOfAlgorithm(
const PositionWithAffinityTemplate<Strategy>& position,
EditingBoundaryCrossingRule rule) {
const VisiblePositionTemplate<Strategy> next = createVisiblePosition(
nextVisuallyDistinctCandidate(position.position()), position.affinity());
switch (rule) {
case CanCrossEditingBoundary:
return next;
case CannotCrossEditingBoundary:
return honorEditingBoundaryAtOrAfter(next, position.position());
case CanSkipOverEditingBoundary:
return skipToEndOfEditingBoundary(next, position.position());
}
NOTREACHED();
return honorEditingBoundaryAtOrAfter(next, position.position());
}
VisiblePosition nextPositionOf(const VisiblePosition& visiblePosition,
EditingBoundaryCrossingRule rule) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
return nextPositionOfAlgorithm<EditingStrategy>(
visiblePosition.toPositionWithAffinity(), rule);
}
VisiblePositionInFlatTree nextPositionOf(
const VisiblePositionInFlatTree& visiblePosition,
EditingBoundaryCrossingRule rule) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
return nextPositionOfAlgorithm<EditingInFlatTreeStrategy>(
visiblePosition.toPositionWithAffinity(), rule);
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> skipToStartOfEditingBoundary(
const VisiblePositionTemplate<Strategy>& pos,
const PositionTemplate<Strategy>& anchor) {
DCHECK(pos.isValid()) << pos;
if (pos.isNull())
return pos;
ContainerNode* highestRoot = highestEditableRoot(anchor);
ContainerNode* highestRootOfPos = highestEditableRoot(pos.deepEquivalent());
// Return |pos| itself if the two are from the very same editable region, or
// both are non-editable.
if (highestRootOfPos == highestRoot)
return pos;
// If this is not editable but |pos| has an editable root, skip to the start
if (!highestRoot && highestRootOfPos)
return createVisiblePosition(previousVisuallyDistinctCandidate(
PositionTemplate<Strategy>(highestRootOfPos,
PositionAnchorType::BeforeAnchor)
.parentAnchoredEquivalent()));
// That must mean that |pos| is not editable. Return the last position
// before |pos| that is in the same editable region as this position
DCHECK(highestRoot);
return lastEditableVisiblePositionBeforePositionInRoot(pos.deepEquivalent(),
*highestRoot);
}
template <typename Strategy>
static VisiblePositionTemplate<Strategy> previousPositionOfAlgorithm(
const PositionTemplate<Strategy>& position,
EditingBoundaryCrossingRule rule) {
const PositionTemplate<Strategy> prevPosition =
previousVisuallyDistinctCandidate(position);
// return null visible position if there is no previous visible position
if (prevPosition.atStartOfTree())
return VisiblePositionTemplate<Strategy>();
// we should always be able to make the affinity |TextAffinity::Downstream|,
// because going previous from an |TextAffinity::Upstream| position can
// never yield another |TextAffinity::Upstream position| (unless line wrap
// length is 0!).
const VisiblePositionTemplate<Strategy> prev =
createVisiblePosition(prevPosition);
if (prev.deepEquivalent() == position)
return VisiblePositionTemplate<Strategy>();
switch (rule) {
case CanCrossEditingBoundary:
return prev;
case CannotCrossEditingBoundary:
return honorEditingBoundaryAtOrBefore(prev, position);
case CanSkipOverEditingBoundary:
return skipToStartOfEditingBoundary(prev, position);
}
NOTREACHED();
return honorEditingBoundaryAtOrBefore(prev, position);
}
VisiblePosition previousPositionOf(const VisiblePosition& visiblePosition,
EditingBoundaryCrossingRule rule) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
return previousPositionOfAlgorithm<EditingStrategy>(
visiblePosition.deepEquivalent(), rule);
}
VisiblePositionInFlatTree previousPositionOf(
const VisiblePositionInFlatTree& visiblePosition,
EditingBoundaryCrossingRule rule) {
DCHECK(visiblePosition.isValid()) << visiblePosition;
return previousPositionOfAlgorithm<EditingInFlatTreeStrategy>(
visiblePosition.deepEquivalent(), rule);
}
} // namespace blink
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,219 |
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